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Particle Colliders

An introductory course for Master 2 students

Theoretical Physics

Dr. Yazid Delenda

Département de Physique, Faculté des Sciences de la Matière

Université Batna 1

[email protected]

1 79 7Université Hadj Lakdh a

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B A T N AEl

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https://theorique05.wordpress.com/collisionneurs-des-particules/

Typeset with LATEX

Lecture notes based on Frontiers of Particle Physics course at Manchester university by various lecturers.

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https://theorique05.wordpress.com/collisionneurs-des-particules/

Contents

1 Modern accelerators and colliders 31.1 classification of particle physics experiments . . . . . . . . . . . . . . . . . . . . 3

2 Introduction to collider physics 62.1 Classification of colliders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 LEP collider 113.1 LEP(1982 - 2000) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Discovery of Z0 boson at LEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.3 Mass and decay width of Z± boson at LEP . . . . . . . . . . . . . . . . . . . . . 243.4 SPS collider and Z0 boson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4 LHC collider: discovery of the Higgs boson 344.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.2 ATLAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.3 CMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.4 Higgs searches at the LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.5 Di-photon higgs decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.6 ATLAS/CMS plots of the Higgs to diphoton . . . . . . . . . . . . . . . . . . . . 464.7 Higgs decay to Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.8 ATLAS’s 2 TeV diboson excess . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5 Tevatron and discovery of top quark 525.1 Tevatron collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.2 CDF and DØ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.3 Discovery of the top quark at Tevatron . . . . . . . . . . . . . . . . . . . . . . . 555.4 Results from CDF and DØ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635.5 Search for Higgs boson at Tevatron . . . . . . . . . . . . . . . . . . . . . . . . . 63

6 HERA 646.1 DIS process and parton model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.2 PDFs and DGLAP evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.3 The HERA collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.4 H1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.5 ZEUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

7 CP violation and BABAR experiment 64

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1 Modern accelerators and colliders

1.1 classification of particle physics experiments

Particle physics experiments may be classified into two types, accelerators and colliders, asdepicted in figure 1:

Target

Detector

Detector

Beam Beam Beam

Fixed-target accelerator Collider

Figure 1: Fixed-target accelerators (left) and colliders (right).

Fixed-target accelerators: accelerated beams of charged particles such as protons p, or elec-trons e−, are fired on a fixed target, which could be a solid (e.g. lead), a liquid (H2) or agas, and the resulting particles are detected by a detector. By conservation of momentum,this leads to a “waste” of input energy.

Colliders: two beams collide head-on in opposite directions. Usually the total linear momen-tum of the initial- (as well as final-) state particles equals zero. For such colliders bothbeams have equal energy if the initial particles have identical mass (e.g. LEP and LHC).This results in a lot more energy going into interesting (new) physics. For instance ifwe have two beams of energy E = 80GeV, then the centre-of-mass energy would equalECM = 160GeV, it would thus be possible to “discover” a particle of a mass up tom = E/c2 = 160GeV/c2.

A key property of colliders is the type of particles to be accelerated for collision. Theaccelerated particles must be charged in order to be able to accelerate them with electricfields and in order to be able to steer and focus them for collision points using magneticfields. They must also be long lived so that they survive long enough to be acceleratedand collided. This in fact limits us to just electrons and protons and their anti-particles.Other particles are either neutral (e.g. the neutron) or short lived (e.g. pions, and muons).

Advantages of colliders include:

• Much higher energies, i.e. achieve maximum invariant mass:

W 2c4 =

(

∑

i

Ei

)2

−(

∑

i

~pic

)2

. (1.1)

For symmetric colliders, such as LEP and LHC, the centre of mass energy is:

ECM = 2Ebeam =√s = W. (1.2)

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• For symmetric colliders, such as LEP, the laboratory frame is the centre-of-mass frame.Outgoing particles are produced uniformly in space with total momentum equal to zero.

However non-symmetric colliders (see figure 2), such as HERA, the total momentum isnot zero, and the lab frame is not the centre of mass frame.

Figure 2: Non-symmetric colliders.

• For e+e− colliders such as LEP, the centre-of-mass energy is pre-set, i.e. exactly known.Particularly if the collider is symmetric then the centre-of-mass energy is just equal totwice the beam energy:

ECM = 2Ebeam . (1.3)

Thus all energy of the beams is useful and goes into creating new particles. This alsomeans that one can scan and/or tune the centre of mass energy easily. For instance atthe LEP collider, the maximum energies of the electron and positron are both about 100GeV, which means a maximum centre of mass energy of 200 GeV, and the energies of thebeams can be scanned so as to match, for instance, the mass of the Z boson, 91GeV.

For hadron colliders, such as the LHC, the elementary quarks which undergo the inter-action carry a fraction x of the momentum of the beam particles, e.g. proton, and thisfraction (0 < x < 1) is not exactly determined meaning that the quarks have a distribu-tion in this momentum fraction. Therefore the centre-of-mass energy (which is relevantfor the actual scattering event) is not pre-set, i.e. is not exactly known, and is subject toa distribution. This is schematically shown in figure 3.

P P

x1P x2P

Figure 3: A symmetric collider but non-symmetric collision for a hadron collider.

In fact most pp̄ (or pp) collision events are “soft”, i.e. due to large-distance collisionsbetween the two incoming protons. For such events the momentum transfer betweenparticles is small, and most of the final-state particles have very low transverse momentumpt and their transverse momentum is dominantly longitudinal (p‖), i.e. parallel to the beamdirection. Such events are called “minimum-bias events” and they are not interesting.The interesting events are those which are due to “hard” scattering of partons (recallthat partons are the constituents of protons: quarks and gluons), i.e. small-distance

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interactions of the incoming partons. For these events the momentum transfer is largeand so massive particles, such as the Higgs, can be produced, and the resulting final-stateparticles have large transverse momentum as well. These events are however very rarecompared to minimum-bias events.

In figure 4, we show a typical LEP event from DELPHI detector compared to a typicalLHC event from ATLAS experiment. In e+e− collisions, i.e. at LEP, the incoming leptonscompletely annihilate to produce new particles, thus e+e− events are very “clean”, andfinal-state particles are all interesting. However at the LHC, as shown in figure 4, most ofthe tracks in the detector are due to minimum bias.

Figure 4: Typical LEP event from Delphi (left) compared with a typical LHC event from ATLAS(right).

In pp or pp̄ hard scattering, partons annihilate (not the whole proton) so the effectivecentre-of-mass energy is smaller than the actual centre-of-mass energy of the machine:

√ŝ =

√xaxbs

where xa and xb are the momentum fractions of the proton carried by the struck partonfor the two incoming beams, as shown in figure 5.

xa

xb

fa/A

fb/B

A

B

a

b

Parton Distributions measured in DIS

Beam fragments of spectator jets

Beam fragments of spectator jets

Hard scattering parton sub-process

σ(a+ b → X)

Figure 5: Interaction of two hadrons (protons).

The colliding protons constitute many partons. The proton is made of three valancequarks (uud) as well as a sea of colourless collection of quarks, anti-quarks and gluons. At

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low momentum transfer (Q2) the sea partons carry very little momentum of the protonand valance quarks equally share most of the momentum of the proton. This means thatthe momentum fraction distributions peak at about xi ∼ 1/3 for the three valance quarkswith small standard deviation (meaning that most likely the valance quarks have 1/3 ofthe momentum of the proton).

At higher values of momentum transfer, though, the sea of partons starts to carry somesignificant fraction of the momentum of the proton. The distributions of the valancequarks in xi slightly shift down and still peak at xi ∼ 1/3, but with a larger standarddeviation.

A collision between two high-energy beams can achieve higher Q2 value than a collisionbetween two low-energy beams.

Advantages of fixed-target accelerators include:

• Higher event rate due to the fact that targets are dense.

• Produced particles in fixed-target accelerators are boosted, i.e. they have large forwardmomentum. Therefore they can produce collimated beams of secondary particles. This isuseful for neutrino beams which are aimed at targets long distances away.

In this course we will mainly be interested in colliders.

2 Introduction to collider physics

2.1 Classification of colliders

Collider experiments in particle physics may be classified into three types: synchrotron colliders,linear accelerators (LINAC) and linear colliders, as shown in figure 6.

Synchrotron colliders: are circular colliders. Examples include:

• LEP e+e− collider at CERN - Geneva (decommissioned)• Tevatron pp̄ collider at FermiLab - Chicago (decommissioned)• LHC pp collider at CERN - Geneva (running)• HERA e±p collider at DESY - Hamburg (decommissioned)

The overall design of a synchrotron collider is shown schematically in figure 7. Notice that,for synchrotron colliders, and in the case of the collider of a particle and anti-particle suchas LEP and Tevatron, the same accelerator can be used to accelerate the particles andanti-particles along the same beam pipe. However in the case of identical particles ortotally different particles, such as LHC and HERA, two different accelerators (thus beampipes) are required.

The main advantage of synchrotron colliders is the multi-chances of collisions since theparticles go around the collider millions of times, leading to higher event rate of colli-sions. The main disadvantage, however, is that the charged particles are in orbit aroundcircular paths due to the bending by the magnets. This means that the particles un-dergo centrifugal accelerations, which by the laws of electrodynamics leads to soft photonbremsstrahlung (synchrotron radiation), as depicted in figure 8. Therefore a lot of en-ergy is lost by synchrotron radiation. As charged particles orbit around the beam pipes

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Synchrotron collider (LHC) Linear accelerator (SLAC) Linear collider (ILC)

b

b b

Figure 6: Different types of colliders.

more and more input energy is required in order to keep them circulating along the samecircular path.

In fact the energy loss per revolution may be expressed as follows:

∆E = q2β3γ41

3ǫ0R, (2.1)

where q is the electric charge of the accelerated particle, β = v/c ≈ 1 for ultra-relativisticparticles, γ is the Lorentz factor, γ = E/(mc2) with E the energy of the particle andm its mass, and R is the radius of curvature of the circular path. Therefore for a givenenergy and radius of curvature, it turns out that the synchrotron radiation that is lost isproportional to m−4. The smaller the mass the more energy is lost. This is particularlylarge for electrons which gives more preference for proton colliders (LHC) than for electroncolliders (LEP). Electrons lose energy 1013 times faster than protons. For LEP and theLHC the energy loss may be expressed as:

ElossLEP ∼10−4

RE4beam MeV/turn ,

ElossLHC ∼10−5

RE4beam MeV/turn ,

where R is the circumference of the collider in kilometers, and Ebeam is the energy of thecolliding particle in GeV for LEP (electron collider), and in TeV for LHC (proton collider).

Substituting the actual circumference of the CERN tunnel (R = 27 km), and the maximumbeam energies of LEP (Ebeam = 100 GeV) and LHC (Ebeam = 7 TeV), we obtain themaximum energy loss per turn for both colliders:

ElossLEP ∼ 2GeV/revolution ,ElossLHC ∼ 5 keV/revolution .

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Magnets that keepcharged particles circling

radio frequency cavities

Detector

Figure 7: Overall design of synchrotron colliders.

Figure 8: A lot of energy is lost in synchrotron colliders by bremsstrahlung of photons.

It is therefore clear that the energy loss due to synchrotron radiation at the LHC is muchless than that at LEP (which — for the latter — leads to warm temperatures) despitethe enormous beam energy at the LHC. Note that the LEP collider was in fact at thepractical energy limit for e+e− collisions. However the energy loss at the LHC (despitebeing physically insignificant) leads to thermal overload on the cryogenics cooling systemof the LHC superconduction bending magnets, which operate at temperatures even lessthan those of outer space!

Note that the energy lost by the particles via bremsstrahlung must continuously be re-placed in order to keep the particles in the same circular path.

Linear accelerators (LINAC): These are commonly used for medical reasons. Examplesinclude the SLAC collider at Stanford university (USA).

Linear colliders: Here two beams collide head on with no circular paths, thus with no syn-chrotron radiation (unless there is a small bending in the path, which should not besignificant). The main disadvantage of linear colliders is that there is only one chance for

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collision. There are currently no linear colliders. There is however a plan to construct the“international linear collider” ILC (construction should start this year or next year), withcollision energy of 500 GeV, with possibility of upgrade to 1 TeV. Host country has notyet been decided, but it may most likely be in Japan, CERN or FermiLab (US).

2.2 Luminosity

In physics the cross-section σ is a measure of the probability of interaction, and may be consid-ered as the effective area available for the reaction by a given target. The cross-section is thenumber of reaction events per unit time per unit flux of incident beam1 per unit particles in thetarget. The cross-section can be specific to a given channel r, σr, or can be a total cross-sectionfor any outcome, σtot =

∑

r σr, where the sum is over all possible channels. The cross-sectionhas units of area, and the barn (1 barn = 10−28m2) is typically used. We may write:

σr =WrJ.N

, (2.2)

where Wr is the number of observed events per unit time, J = n.v is the flux of the incidentbeam (number of incident particles per unit time per unit area), n is the volume density of theincident particles, v is the speed of the incident particles, and N is the number of particles inthe target.

The luminosity L of a machine describes the instantaneous intensity of the beam. The eventrate is then proportional to the luminosity and to the cross-section:

event rate = L × σ . (2.3)

The event rate can also be specific to a given channel or can be a total event rate for anyoutcome. The luminosity is controlled by the machine while the cross-section is purely physics(i.e. Feynman rules etc). From this it is clear that the luminosity of a machine has units ofrate/cross-section, where the rate has units of inverse time. Thus the luminosity is measured bym−2s−1, or inverse-area per unit time. Typically one uses inverse-barn per second. For examplethe design luminosity of the LHC is 1034cm−2s−1.

For two colliding beams, and if n1 and n2 are the number of particles in bunches for eachbeam, and F is the cross-sectional area of the bunches, and f is the collision frequency of thebunches, i.e. the number of times the bunches meet per unit time at a given detector (see figure9), then the luminosity is given by:

L = n1n2F

f . (2.4)

Note that, if there are several bunches in the beams then f = b× ν, where ν is the revolutionfrequency of the bunches and b is the number of bunches in each of the beams, as shown infigure 10. By dimensional analysis we can confirm that the luminosity has units of m−2s−1. Notealso that a commonly used term in describing the amount of data collected is the integratedluminosity, this is the luminosity integrated over some time interval:

Integrated luminosity =

∫ tf

ti

Ldt. (2.5)

The integrated luminosity therefore has dimension of inverse area, which means a typical unitis inverse barn or inverse m2. For example the integrated luminosity for LEP over a single day

1flux of incident beam: is the number of incident particles per unit time per unit area.

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bb

bbb b b

b

b

bbb

bbb

bb

b

bb bb

b

b

bb

b

b

bb

v1

bb

b bbbb

b

b

b bb

bbb

bb

b

bbbb

b

b

bb

b

b

b b

v2

Bunch 1 Bunch 2

n1 particlesn2 particles

F : cross-section area of bunchf : frequency of bunch collision

Figure 9: Collision of two bunches with n1 and n2 particles in each bunch.

e−

e+

Two bunches per beam (b = 2)

e−

e+

e−

e+

One bunch per beam (b = 1)

Detectors

Bunches meet once per revolution Bunches meet twice per revolution

in four detectorsin two detectors

Figure 10: Collision of bunches of particles.

is about 3 pb−1 (inverse pico-barn) in a good day, while for the LHC the average integratedluminosity per day is about 30 pb−1. The integrated luminosity is a measure of the amount ofevents collected over the corresponding period of time.

Below we give the properties of the LHC collider and its luminosity:

• Circumference: R = (26 658 883± 1)mm.

• Volume of bunches of protons: 1mm×3 cm×20µm at the point of interaction, where 3 cmis the length along the beam pipe. Thus the bunch cross-section area is F = 1mm×20µm.

• Number of protons in each bunch n1 = n2 = 1011 proton.

• Maximum energy of each proton 7 TeV.

• Revolution frequency: each bunch circulates at a frequency ν = 11 254 Hz.

• Design luminosity L = 1034cm2s−1.

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• total pp cross-section at 7 TeV is 110 mb, amongst which is 60 mb is inelastic.

• Rate of inelastic collisions 600 × 106 per second (we exclude elastic collisions since theyare not detected by detectors since they outgoing protons do not have sufficient transversemomentum).

• Number of Higgs bosons produced at the LHC ∼ 1 per day!

3 LEP collider

Experiments at colliders (or detectors) usually have a 4π solid angle coverage. For equal energycolliders (such as LHC, LEP) these detectors are designed in a symmetric way, however fornon-symmetric colliders such as HERA, the detectors are usually forward biased. In general,the detectors are designed for general detection ability (general purpose detectors, e.g. ATLAS,CMS), but sometimes they come as specialised in different techniques or physics area (e.g,LHCb). For instance they can have strong detection abilities on hadrons, or charged leptons.Below we discuss some important colliders with their experiments.

The aims of detectors is to identify the particles resulting from hard interactions and measuretheir energies and initial directions as accurately as possible. Stable and long lived particles(photons, electrons, muons, pions, protons and neutrons) in detectors are identified by theirsignature in the detector, while unstable ones are reconstructed from their decay products,e.g. quarks and gluons hadronise to form jets, tau particles too short lived and decay toelectrons/muons with neutrinos or to pions.

A typical detector consists of several layers, each of which identifies and measures (or re-measures) the energy of certain particles. No single detector can detemrmine the identity andmeasure the energy/momentum of all particles.

3.1 LEP(1982 - 2000)

LEP is the “Large Electron Positron” collider at CERN in Geneva. It has circumference of 27km (same tunnel as the LHC) and collides e+ and e−. The maximum beam energy is 106 GeV,and energy variations (error) is about 10 MeV.

The charged particles in colliders are accelerated by the radio frequency (r.f.) cavities —a.k.a., r.f klystrons — They work as a tuning fork for electromagnetic fields and the frequencyof the r.f. cavities is tuned with the period of the circulating e±. They manipulate the chargedparticles passing through them by accelerating/decelerating them.

In order to minimize the energy variation of the accelerated particles, these r.f. cavities havethe property of oscillation (i.e. switch the direction of acceleration). In this way, the particlesin the bunch which arrive at the cavities earlier or later will be accelerated or decelerated sothey will be close to the “ideal” protons in energy, those which arrive to the cavities in exactlythe expected time.

Some of the side effects on the beam energy include:

• Trains passing nearby lead to fluctuations in energy (interesting story which even made itto the press). In fact every few hours there were significant variations in the beam energy,it was later found that the timing of the fluctuations was consistent with the timetable ofthe SNCF Geneva-Paris train time table!

• Heavy rain fall: The gravitational impact of the falling water on the rocks surroundingLEP collider had a small effect on the beam energy

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Figure 11: Radio frequency cavities at the LHC.

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-8

10-7

10

-6

10-5

10

-4

10

-3

10-2

1 10 102

σ[m

b]

ω

ρ

φ

ρ′

J/ψ

ψ(2S)Υ

Z

Figure 12: Cross-section for e+e− → hadrons at LEP 1. Figure from PDG.

• Moon gravitational pull on Switzerland had an impact on the beam energy 4 times per24 hours on regular daily basis.

The LEP collider was run on two phases:

3.1.1 LEP 1: 1989-1995

Maximum beam energy was 50 GeV, with centre of mass energy less than 100 GeV. Note thatin order to achieve the same physics (in other words, the same centre of mass energy) with anaccelerator (i.e. a positron fired on a stationary electron) the beam energy of the acceleratedpositron would have to be about 104 TeV.

The cross-section for e+e− → hadrons is shown in figure 12. From the measured cross-sectionat LEP 1, the confirmation of the existence of the Z0 boson with a mass of about 91.2 GeVwas achieved. When the beam energy is about 45.6 GeV for each of the electron and positron,the Z0 boson is produced as a real particle (on-mass-shell), and the resonance is achieved inthe process e+e− → Z0 → hadrons, as shown in figure 13. It was not possible to produce a Wboson at LEP 1 because by conservation of charge, W bosons can only be produced in pairs,

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e+

e−

γ∗

q̄

q e+

e−

Z0∗

q̄

q

+

Figure 13: The possible diagrams contributing to e+e− → qq̄ contain both intermediate photonsand Z0.

INFN

• LEP and SLC are Z factories providing copious sampl

10

102

103

104

105

0 20 40 60 80 100 120 140 160 180 200 220

Centre-of-mass energy (GeV)

Cro

ss-s

ecti

on

(p

b)

CESRDORIS

PEP

PETRATRISTAN

KEKBPEP-II

SLC

LEP I LEP II

Z

W+W

-

e+e−→hadrons

e

Figure 14: Cross-section for e+e− → hadrons at LEP 2. Figure from CERN webpage.

which required more centre of mass energy. To achieve this a centre of mass energy of about160 GeV was necessary.

3.1.2 LEP 2: 1996 - 2000

The maximum beam energy reached about 100 GeV for each of the beams, with a centre ofmass energy of about 200 GeV. In this run it was possible to produce a pair of W bosons eachwith mass 80.4 GeV. The second run of the LEP collider was characterised by the productionof a pair of W bosons. The cross-section for e+e− → hadrons for LEP 2 is shown in figure 14.

3.1.3 OPAL detector design

The OPAL detector (Omni-Purpose Apparatus for LEP) at LEP was composed of several layers,as shown in figure 15.

The inner part of the detector is called the central tracking detector, and its aim is tomeasure the tracks of charged particles. It consists of four layers:

Micro-vertex detector: is the inner most layer, composed of solid state Silicon strips. Itstask is to detect the paths of charged particles to a precision of 5µm. This allows to

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Figure 15: OPAL detector at LEP. Figure from Cambridge university website.

detect the particles with very short lifetimes such as tau particles and hadrons containingb quarks. For example the B mesons have lifetimes of order of picosecond, and travel adistance of a few millimeters before they decay to other hadrons, as shown in figure 16.

bbbb b

bbb b

Charged particle decaysSilicon strips

Charged particle

5 µm

Figure 16: The micro-vertex is composed of Silicon layers which detected charged particles.

When charged particles pass through the silicon strips pairs of electron/hole are created,and drifted in the strips and thus position of charged particles is measured to a very highaccuracy.

Vertex chamber: is a gas drift chamber, such that when charged particles pass through thechamber the gas within it is ionized and the ions trigger a signal out.

Jet chamber: is the second layer which, as shown in figure 17, measures the positions of thecharged particles by ionizing the gas in the chambers to a precision of about 5 µm. Toavoid left-right ambiguity pixel designs are installed.

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Charged particle

gas ionizedCathode

Signal outMeasure time

vdrift measured to high precision

Figure 17: The jet chamber.

z chambers: their goal is to precisely measure the z component of the charged particles whenthey leave the jet chamber.

The outer layers are composed of:

Solenoid and pressure vessels (Magnetic coils): These coils cause an axial magnetic fieldin the inner layers (tracking system) just like a solenoid, and therefore the tracks ofthe charged particles are bent by this magnetic field. This is useful in determining themomentum of the charged particles. The radius of the bending is related to the momentumof the charged particle. It also helps determine the sign of the charge of the charged particleby determining the direction of bending.

Time of Flight detector: Scintillation detectors are used to measure the time of flight. Ascharged particles excite atoms in the scintillation detectors, they decay by emitting pho-tons. These photons are then picked up by a photomultiplier tube which enhances thesignal. This leads to accurate measurement of the time of flight of the particles to lessthan 500 ps.

The time of flight is crucial for measuring the velocity of the particles. Together with themomentum (which is measured by the radius of bending of the charged particles by themagnetic coils), the mass of the particle is determined, and therefore the particle type isdetermined (particle identification).

Electromagnetic calorimeter: The EM calorimeter is designed to detect photons, e− ande+. It works, as shown in figure 18, by initiating interactions of the particles e± or γ witha medium (usually lead). It leads to an EM shower as shown in figure 19.

The electromagnetic calorimeter has to produce and contain the electromagnetic shower,as well as measure the energy of the particle producing the shower by measuring the totalenergy in the shower. It is made of lead and glass. The lead is used in order to produceand contain the shower, while the glass is used in order to detect photons by Cerenkovradiation. The fact that glass has refractive index n, then the speed of light is v = c/n inthe glass, which gives a photon signal out via a photomultiplier tube (pmt).

The material used in the electromagnetic calorimeter is characterised by a radiation lengthX0, which by definition is the average length in which a particle losses 1/e of its energy bybremsstrahlung, such that the energy of the particle as a function of the distance traversedthrough the material is:

E = E0 exp (X/X0)

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EM calorimeter

e−

γ

Bremsstrahlung

pair creation

Figure 18: EM shower.

Figure 19: Simulated event by an EM shower.

It is thus more convenient to use a material with a small radiation length (which wouldthus be a strong absorber). For lead X0 ∼ 0.6 cm and for Fe X0 = 1.8 cm, thus lead hasmore preference then iron.

Hadron calorimeter: The hadron calorimeter is made of sheets of iron intercepted with activedetectors (drift tube), in order to induce strong interactions of hadrons with atomic nucleiof iron. The hadron calorimeter must have enough interaction length in order to induceand contain a shower of hadrons from the initial hadron

Hadrone.g. π

Figure 20: Hadron calorimeter.

Muon detector: The muon detector detects all charged particles that make it that far tothe outer layers of the detector, which in principle is just the muons µ±. For othercharged leptons do not make it that far: the electrons are absorbed by the electromagneticcalorimeter, and the tauons are too short lived to arrive at this layer, in fact they onlytravel very short distances in the tracking system (micro-vertex) and then decay to muonsor electrons. Hadrons also do not make it to the muon detector because they are absorbedby the hadron calorimeter.

The muons do not get absorbed in the previous layers because the bremsstrahlung crosssection is inversely proportional to the fourth power of the mass, σbrems ∝ m−4, and

16

since the mass of the muon is much larger than that of the electron mµ ∼ 200me, thenthe elections are absorbed 2004 ∼ 109 times more than muons, which effectively meansthat muons do bremsstrahlung and not interact with the electromagnetic calorimeterFurthermore, since muons do not interact strongly they escape the hadron calorimeter.And since muons are relatively long lived they do not decay too quickly and survive longenough to arrive at the outer regions of the detector.

The muon detector is basically made of gas drift chambers which work by ionizing thegas.

Forward detector: The aim of the forward detector is to detect particles with large rapidity.It consists of many parts with different detecting abilities, forward calorimeters, tubechambers, gamma catcher, fine luminosity catcher and the far forward monitor.

3.1.4 OPAL event display

Muon event: In a muon pair event

e+ + e− → µ+µ−

a Z/γ decays into a pair of muons. The outgoing muons penetrate through the hadronand electromagnetic calorimeters and leave clear tracks in the muon calorimeter. Theevent display and Feynman diagrams are shown in figure 21.

e−

e+ µ−

µ+

Run :even t 4093 : 4556 Da te 930527 T ime 22439 Ebeam 45 .658 Ev i s 90 .8 Emi ss 0 .6 Vt x ( -0 .05 , 0 .08 , 0 .36) Bz=4 .350 Thrus t=0 .9999 Ap l an=0 .0000 Ob l a t=0 .0110 Spher=0 .0003

Ct rk (N= 2 Sump= 86 .8) Eca l (N= 5 SumE= 1 .6) Hca l (N= 4 SumE= 4 .0) Muon(N= 2) Sec Vt x (N= 0) Fde t (N= 0 SumE= 0 .0)

Y

XZ

200 . cm.

Cen t re o f sc reen i s ( 0 .0000 , 0 .0000 , 0 .0000)

50 GeV2010 5

Figure 21: γ/Z decay into muons.

Tauon event: In a tauon event

e+ + e− → τ+τ−

a Z/γ decays into a pair of tauons. However the outgoing tau particles are very short lived.Although the tau particles leave visible tracks in the micro-vertex detector, they howeverdo not show tracks in other layers because they decay. The decay products are thendetected whether being leptonic or hadronic. For example, in figure 22, one of the tauonsdecays into a muon and the other decays into an electron, each of which is accompaniedby a couple of neutrino which is totally undetected. In total there are 4 neutrinos in thisevent.

17

e−

e+τ−

τ+

µ+

νµ

ν̄τ

e−

ν̄e

ντ

W+

W−

γ/Z

Y

XZ

200 . cm.


50 GeV2010 5

Run :even t 4177 : 49573 Da te 930611 T ime 203852 Ebeam 45 .661 Ev i s 52 .1 Emi ss 39 .3 Vt x ( -0 .03 , 0 .08 , 0 .45) Bz=4 .350 Thrus t=0 .9975 Ap l an=0 .0000 Ob l a t=0 .0332 Spher=0 .0020


Figure 22: γ/Z decay into tau particles.

Tau decay: As we said before, a tau particle is very short lived and travels very short distancesbefore it decays. However it survives long enough to leave clear tracks in the micro-vertex,as shown in figure 23. The tracks clearly indicate a decay of a muon to three hadrons.Note that the identity of the tau particle is known in the micro-vertex detector by itsmass (which, as we said before, is determined by knowing the momentum and velocity ofthe particles as it passes through the detectors).

Run :even t 4302 : 75672 Da te 930717 T ime 225034 Ebeam 45 .610 Ev i s 121 .9 Emi ss -30 .7 Vt x ( -0 .04 , 0 .04 , 0 .29) Bz=4 .350 Thrus t=0 .9993 Ap l an=0 .0001 Ob l a t=0 .0061 Spher=0 .0006


Y

XZ

2 . cm.


Figure 23: Decay of a tau particle to three hadrons..

Two jet event: In a two-jet event:

e+e− → Z/γ → q + q̄

a pair of quark–anti-quark is produced. The resulting quarks then hadronise to form jetsof hadrons, as shown in figure 24. The hadrons penetrate through the electromagneticcalorimeter and are completely absorbed into the hadron calorimeter with no tracks inthe muon chambers.

18

e−

e+q

q̄

γ/Z

Y

XZ

200 . cm.


50 GeV2010 5

Run :even t 4093 : 1000 Da te 930527 T ime 20716 Ebeam 45 .658 Ev i s 99 .9 Emi ss -8 .6 Vt x ( -0 .07 , 0 .06 , -0 .80) Bz=4 .350 Thrus t=0 .9873 Ap l an=0 .0017 Ob l a t=0 .0248 Spher=0 .0073

Ct rk (N= 39 Sump= 73 .3) Eca l (N= 25 SumE= 32 .6) Hca l (N=22 SumE= 22 .6) Muon(N= 0) Sec Vt x (N= 3) Fde t (N= 0 SumE= 0 .0)

Figure 24: Two jet event.

Three jet event: In a three jet event:

e+e− → Z/γ → q + q̄ + g

a hard gluon emission occurs which then results in a third jet. This is shown in figure 25

e−

e+q

q̄

γ/Z

Y

XZ

200 . cm.


50 GeV2010 5

Run :even t 2542 : 63750 Da te 911014 T ime 35925 Ebeam 45 .609 Ev i s 86 .2 Emi ss 5 .0 Vt x ( -0 .05 , 0 .12 , -0 .90) Bz=4 .350 Thrus t=0 .8223 Ap l an=0 .0120 Ob l a t=0 .3338 Spher=0 .2463


Figure 25: Three jet event.

3.2 Discovery of Z0 boson at LEP

The Z0 boson is neutral, it couples to leptons and quarks, as shown in figure 26. For examplethe electron – proton scattering in QWD (with range ∼ 10−18 m) is depicted in figure 27.

Experimental tests of flavour conservation at the Z0 vertex have been achieved by consideringtwo possible processes changing strangeness, which are shown in figure 28, and which are:

K+ → π0 + µ+ + νµ

andK+ → π+ + νℓ + ν̄ℓ

19

Z0

νℓ

ν̄ℓ

Z0

ℓ+

ℓ−

Z0

q

q̄

Figure 26: Couplings of the Z0 boson to matter sector.

Z0

e− e−

u

du

u

du

Figure 27: Electron – proton elastic scattering mediated by Z0.

The Measured upper limit on the ratio of the decay ratesK+ → π++νℓ+ν̄ℓ toK+ → π0+µ++νµis:

∑

ℓ Γ(K+ → π+ + νℓ + ν̄ℓ)

Γ(K+ → π0 + µ+ + νµ)< 10−7

Thus the Z0 boson does not change (carry) lepton number or quark number (i.e. no FCNC -flavour changing neutral current). Some of these properties are demonstrated by the photon, forexample the electron proton scattering in EM interactions, shown in figure 29. Here the rangeis ∞ (recall that the range can be found using ∆E∆t ∼ ~. For weak interactions ∆E = 100GeV and ∆t = range/c, so range ∼ 10−18m).

Comparing vertices involving γ, W± and Z0, one can conclude that they all are governedby the same coupling constant g ∼ e. Weak interactions only become comparable to EMinteractions if distances are of order 10−18 m, a concept which leads to EW unification.

Consider the e+e− annihilation into µ+µ− process at PETRA (Hamburg), shown in figure 30.In QED the electron and positron collide head-on so the centre of mass frame is the laboratoryframe, as shown in figure 31.

The QED differential cross-section for this process in the high energy limit (ECM ≫ mµ) is:

dσ

dΩ=

α2

4E2CM(1 + cos2 θ)

Thus QED predicts a symmetric angular distribution dσ/dΩ as a function of cos θ, as shown infigure 32. Note that we have not included the production of e+e− because it has more channels(t-channel).

At low energies (13.8 GeV ≪ MZ0 ∼90 GeV) we have the possible processes shown infigure 33, where the Z0 is produced off-shell at such low energies. The interference term in theamplitude-squared between these two processes causes an asymmetry in the differential angulardistribution, as shown in figure 34. The asymmetry is measured by the ratio:

20

W+

νµ

µ+

s̄u

u

ū

K+{

}

π 0

Allowed

Z0

Forbidden

νℓs̄u

u d̄

K+{

}

π +

ν̄ℓ

Figure 28: Decay of K+ via flavour-changing neutral and charged current reactions. Theflavour-changing neutral current processes (right) has not been observed.

γ∗

e− e−

u

du

u

du

Figure 29: Electron-proton scattering e− + p → e− + p via EM interactions.

Aµµ =N(µ back)−N(µ forward)N(µ back) +N(µ forward)

which is known as the backward-forward asymmetry.The measured asymmetry confirms the existence of Z0 and predicts the mass of the Z0

around 93 GeV as this symmetry is restored at 93 GeV where the Z0 is produced on-shell (asa real particle).

In 1983 the first discovery (production) of Z0 boson was achieved in pp̄ collider at CERN, asshown in figure 35. The energy available for the cross-section was small so it took a long time(only few Z0 bosons produced).

In 1989 the LEP collider (CERN) produced the Z0 which decayed into hadrons, as shownin figure 36. The predicted mass and width of the Z0 boson was:

MZ0 = (91.1876± 0.0021)GeVΓZ0 = (2.4952± 0.0023)GeV

which gives a lifetime of about 10−25 s (recall ∆E∆t = ~ ⇒ τ = ~/Γ).Note that having too much or too less energy would produce the Z0 as a virtual particle.

The reason for this is that all the energy and momentum goes into creating the Z0 boson, andby momentum conservation it has zero 3-momentum (i.e. the Z0 is created at rest). So thecentre of mass energy must equal to the mass of the created particle (E2 = ~p 2 + m2) = m2,

21

e+

e−

γ∗

µ+

µ−

Figure 30: Process of e+e− → γ∗ → µ+µ− at PETRA collider in Hamburg.

e+e−

µ+

µ−

θ

Figure 31: The process e+e− → γ∗ → µ+µ− at PETRA collider as seen in a laboratory frame.

so m = E, so the mass of the created particle is less than the actual mass and the particle istherefore not real (off-shell).

3.2.1 Number of neutrino generations

Matter sector consists of three generations of leptons and three generations of quarks. Thelepton generations are:

(

e−

νe

)

,

(

µ−

νµ

)

,

(

τ−

ντ

)

which forms lepton number doublets (i.e. members in the same generation have the same leptonnumber), and the quark generations are:

(

ud

)

,

(

cs

)

,

(

tb

)

which form a lepton number double. There is a weak decay symmetry between the quarkand lepton generations (quark-lepton symmetry), in other words a weak decay e− → νe alsocorresponds to a u → d, both resulting in the emission of a W boson (although quark mixingcomplicates the situation). Are there more generations?

To answer this question we look at the decay of the Z0 boson at LEP. The Z boson decaysto charged leptons, neutral leptons (neutrinos) and pair of quark/anti-quark, as shown in figure26. The decay to neutrinos is not easy to directly detect since the neutrinos do not show in thedetector, and an event with purely neutrinos does not even trigger the detector to record theevent. We must therefore measure the number of neutrino generations indirectly, by lookingeither to the charged-leptonic decay (ℓ± = e±, µ±, τ±), or the decay to jets of hadrons Z0 → qq̄.The latter two are easy to measure at LEP.

22

cos θ

dσ

dΩ

0.5 1.0−1.0 −0.5

1.0

2.0

Figure 32: The differential angular distribution for the process e+e− → γ∗ → µ+µ− is symmet-ric.

e+

e−

γ∗

µ+

µ− e+

e−

Z0∗

µ+

µ−

+

Figure 33: The possible diagrams contributing to e+e− → µ+µ− contain both intermediatephotons and Z0.

The number of neutrinos Nν is measured by considering the total decay width of the Z0

boson, which consists of the decay to all various decay modes. From the Standard model weknow the relative decay widths to neutrinos:

Γ(Z0 → νeν̄e) = Γ(Z0 → νµν̄µ) = Γ(Z0 → ντ ν̄τ )Now the decay width of the Z boson is a sum of the decay widths to neutrinos and to chargedleptons and to quarks. This total decay width may be considered as a sum of a decay to visiblematter (i.e. detectable by the detector) which consists of both charged leptons and quarks Γvisand an invisible decay width representing the decay to the undetected neutrinos:

Γtot = Γinv + Γvis = ΓSM

The invisible decay width is determined by subtracting off the visible decay width from thetotal decay width predicted by the Standard Model. From the experimental observations atLEP experiment the number of neutrino generations was measured to be:

Nν = 2.984± 0.008Another approach that had also been used to measure the number of neutrino generations is

by considering the hadronic decay of the Z0 boson near the on-mass-shell condition. Since thenumber of hadronic events is known experimentally and theoretically, and assuming that thereis a forth neutrino type ν4 to which a Z

0 decays to, then by lepton universality we have:

Γ(Z0 → νeν̄e) = Γ(Z0 → νµν̄µ) = Γ(Z0 → ντ ν̄τ ) = Γ(Z0 → ν4ν̄4)

23

cos θ

0.5 1.0−1.0 −0.5

1.0

2.0

Pure QED

γ-Z0 interference

dσ

dΩ

Figure 34: The interference between the Z0 and γ contributions to the invariant amplitudecauses an asymmetry in the differential angular distribution for the process e+e− → µ+µ−.

Z0

uud

ūūd̄

450 GeV p

{

450 GeV p̄

{

Figure 35: pp̄ collision at SPS collider in CERN to produce Z0 bosons.

This means that more Z0 bosons decay to neutrinos and less to hadrons (since total decaywidth is fixed). Experimental data, shown in figure 37, clearly favour a value of the number ofneutrino generations to be equal to

Nν = 2.994± 0.012

thus excluding a forth neutrino type. Now since this forth neutrino type does not exist then thisimplies that there is no forth charged lepton, and by quark-lepton symmetry no forth generationof quarks, as in the standard model.

3.3 Mass and decay width of W± boson at LEP

The W boson is electrically charged, and couples to quarks and leptons, as shown in figure 38For instance the neutron β decay

n → p+ e− + ν̄eis depicted in figure 39. Recall that the mass in the left hand side of the decay is 939.6 MeV/c2

while that in the right-hand side is 938.8 MeV/c2, hence energetically this decay is allowedwithout input energy. For the β decay process the intermediate W boson is very off-mass-shell,however at high energy scattering at LEP this can be made real. Note that theW boson changesboth lepton type and quark flavour.

At CERN’s SPS collider (pp̄) in 1983, a W boson is produced in the reaction as shown infigure 39 It was sufficient to have an effective centre of mass energy equal to the mass of the W

24

MZ

ΓZ0

σ(e+e− → hadrons)

ECM

e+

e−

Z0

q

q̄

hadrons

hadrons

Figure 36: pp̄ collision at LEP collider in CERN to produce Z0 bosons, which decay to hadrons.

boson, 80 GeV, in order to produce a single W boson as a real particle and have a resonance.

However at LEP collider, since theW boson is charged, a pair ofW bosons must be producedin order to conserve the electric charge, for instance as shown in figure 41. A centre of massenergy which equals the sum of the two W bosons, 160 GeV is therefore necessary to produce acouple of real W bosons, and this was achieved at LEP 2. The cross-section for the productionof a e+e− → W+W−, which subsequently decay to hadrons is shown in figure 14.

The resulting pair of W bosons then decay. The can decay purely leptonically, i.e. bothleptons decay to charged leptons, as shown in figure 42. In this case the detector signatureis two isolated charged leptons (µ± and/or e±) which are easily detected and identifies, and alarge missing energy which indicate the impossible to detect neutrinos.

The W bosons can also purely decay to hadrons with the advantage of no missing energysince no neutrinos are absent, as show in figure ref 43. The detector signature of this decaymode is four jets with no missing energy.

It is also possible to have semi-leptonic decay in which one W boson decays into leptons andthe other into hadrons, as depicted in figure 45. The signature of this decay mode is a chargedlepton with large transverse momentum and a couple of jets.

The LEP 2 collider measured the mass and width of the W boson to be:

MW =(80.419± 0.056)GeVΓW =(2.12± 0.05)GeV

3.3.1 Search for Higgs boson at LEP

In the simplest standard model particle theory, the gauge particles which mediate the weakinteractions W± and Z0 are required to be massless, just like the photon and gluon. Howeverexperimental observations clearly indicate a very heavy weak gauge bosons with masses of nearly100 GeV. How do these particles acquire a mass? and how does that fit within the standardmodel?

Particles in the standard model are assumed to acquire mass via interaction with a field whichis always present even in the absence of any matter or boson. This field therefore populatesempty space and empty space thus has a non-zero vacuum expectation value for this field, asapposed to other fields which have zero vev. Thus field is called the Higgs field named after

25

Figure 37: Cross-section for hadronic decay of a Z0 boson is consistent with a number ofgenerations equal to 3.

W−

ℓ−

ν̄ℓ

d̄, s̄, b̄

u, c, t

W+W+

ℓ+

νℓ ū, c̄, t̄

d, s, b

W−

Figure 38: Couplings of the W± boson to matter sector.

Higgs Peter. As particles pass through this field they interact with it just like a lower massparticle passing through a viscous fluid becoming heavier as it penetrates this field.

In the standard model the Higgs field which is present everywhere in space is assumed tooriginate from a real interaction boson named the Higgs boson (just like electromagnetic field’ssource is a photon). The higgs boson has zero spin (i.e. it is a scalar) and there exists at leastone neutral Higgs boson, the neutral Higgs boson (H0), with a probability of their being othercharged Higgs bosons. It should also be produced as a real particle in particle accelerators.

The Higgs mass is not predicted within the standard model, however some properties of theHiggs are predicted:

• Couples most strongly to most massive particles (mainly top, W/Z)

• Expect Higgs to be decay to most massive particles which are kinematically allowed

• Cross-sections for production processes are predicted within the standard model.

26

W−

e−

ν̄e

ddu

udu

} p

n{

Figure 39: Neutron decay process.

W−

uud

ū

ūd̄

450 GeV p

{

450 GeV p̄

{

Figure 40: pp̄ collision at SPS collider in CERN to produce W± bosons.

The Higgs boson was extensively searched for at LEP, via the production of a Z0 bosonwhich then couples to a Higgs, as shown in figure 44, via the process:

e+ + e− → Z0 → Z0 +H0

The produced Z0 boson then decay either leptonically (Z0 → ℓ+ℓ−. Z0 → νℓ+ν̄ℓ) or hadronicallyZ0 → qq̄, while the higgs decays dominantly to bottom quarks H0 → qq̄ (it cannot decay to apair of W bosons, or to top because this is kinematically disallowed), producing a couple of bjets.

To find the Higgs boson, one plots the cross-section (number of events) which are taggedby the b jets as a function of the invariant mass of the resulting jets. A peak should beobserved which indicates a resonance of a higgs boson. At the early stages of LEP 2 there wasno observation of such a peak implying a Higgs boson with mass mH > 95 GeV at 95% CL(confidence level).

Furthermore, using results from the backward-forward asymmetry and by comparing datato theory from the Minimal Supersymmetric Standard Model (MSSM), an upper limit on themass of the Higgs boson, mH . 125 GeV was also set. The best prediction for the Higgs masswas:

mH = 122+134−77 GeV

This observation was arrived at in January 2000, about 9 months before the LEP was scheduledto permanently shut down to begin LHC construction. We now know that the actual mass of

27

e−

e+

νe

W−

W+

Figure 41: e+e− collision at LEP collider in CERN to produce W± bosons.

ℓ+

W−

W+

νℓ

ℓ−

ν̄ℓ

Figure 42: Purely leptonic decay of a pair of W± bosons at LEP 2.

the Higgs boson is about 126 GeV as measured by ATLAS and CMS at the LHC. Thus it turnsout that kinematically a beam energy of 108.5 GeV for each of the electron and positron atLEP is necessary in order to produce a real Z boson (mass 91 GeV) and a H0 boson (mass 126GeV). The LEP beam energy was just slightly less than this (100 GeV). This is why LEP wasnot able to “detect” a Higgs boson.

However, during the last months of running of the LEP collider, the latter was squeezedto a maximum beam energy in order to achieve higher centre of mass energy, a lower boundon the Higgs mass was set to 115 GeV at 95 % CL with a centre of mass energy 206 GeV.Some Higgs events started to show and for this reason the shut down of the LEP collider wasreported to November 2000. 19 Higgs events were recorded from all 4 experiments at LEP(OPAL, DELPHI, L3 and Aleph). A lower mass of the Higgs boson was then set to 115 GeV,but the statistical significance was quite low (statistical significance was 2.9 σ, in other wordsthere is a chance of 0.4% of not being a Higgs signal, and to announce a discovery of a Higgsboson a statistical significance of 5 σ was necessary). All that was needed is an extra six monthsrunning of LEP to increase the significance to 5σ and announce the discovery of the Higgs, soLEP was at the verge of discovering the Higgs in March 2001. Unfortunately though, the LEPcollider was permanently shut down in December 2000 and the discovery of the Higgs bosonwas “postponed” to July 2012. Note that results from the Tevatron also have set an upper limiton the mass of the Higgs boson of about 130 GeV.

3.4 SPS collider and Z0 boson

The Glashow, Salam Weinberg Model of electroweak interactions is consistent with the observedcharged current reactions mediated by the exchange of W± bosons, such as the neutron β decay(see figure 39). However this model predicted the existence of neutral current interactions

28

qW−

W+

q̄

q

q̄

Figure 43: Purely Hadronic decay of a pair of W± bosons at LEP 2.

W+ℓ−

ν̄ℓ

qW−

q̄

Figure 44: Semi-leptonic decay of a pair of W± bosons at LEP 2.

mediated by neutral γ and Z0, the latter of which had never been observed before.Until 1973 all observed weak interactions were consistent only with charged weak bosons,

however in 1973 at CERN, the first neutral current interaction was observed in the reaction:

νµ + nucleus → νµ + p+ π− + π0

and this suddenly trigged the urge to observe W± and Z0 bosons directly to test the electroweaktheory. For this one must plan a search for these particles by knowing how they are produced(in order to design a collider that can build them) and how they decay (to design a detectorthat could “see” them).

The electroweak theory predicted the masses of the W± and Z0 bosons (theoretically) to be:

mW ≈ 83± 3GeV, mZ ≈ 94± 3GeV

and it predicted that they couple to quarks and leptons, as shown in figures 26 and 38. Thus,in order to be able to produce the W± bosons one needs to build a lepton or hadron collidercapable of creating particles in the mass range of 100 GeV.

At that time there was no machine capable of producing such energy (CERN’s ISR (Inter-secting Storage Rings 1971 to 1984, itself the world’s first proton collider) collider (pp) only had

29

Z0

Z0

H0

e+

e−

ℓ+, q̄, ν̄ℓ

ℓ−, q, νℓ

b

b̄

Figure 45: Production and decay of a pair of Higgs boson at LEP 2.

√s = 61 GeV and LEP was being planned but would not be ready soon). The SPS (super pro-

ton synchrotron) used to be a fixed target accelerator of protons with beam energy Ebeam = 400GeV. However fixed target experiments, as we said before have very low centre of mass energy(√s =

√2mE) and would not produce the required particles. The idea was then to upgrade

the SpS fixed target accelerator to Spp̄S Synchrotron.The Spp̄S had

√s = 540 GeV, and it consisted of 3 bunches of protons and 3 of anti-protons

each containing 1011 protons/anti-protons. It had a luminosity of 5 × 1027 cm−2s−1, and itachieved a first collisions in 1981.

In order to observer the W/Z0 bosons, the most promising decay mode of these particles arethe leptonic decays, as hadronic decay modes suffer from large QCD background, since muchof the high-pt hadronic activity is due to jets from quark and gluon scattering, while the low-ptactivity is due to minimum bias. The detector signatures of the leptonic decay modes are:

• For W+ → ℓ+νℓ: a high-pt lepton (dominantly an electron or a muon) with large missingtransverse energy

• For Z0 → ℓ+ℓ−, a pair of lepton/anti-lepton with high pt.

For this purpose we must build a detector with high capability of detecting the charged leptons(detection, identification, momentum and energy measurements) as well as to be able to measuremissing energy. At the Spp̄S collider, there were six detectors called “Underwound Area” (UA):UA1, UA2, . . . UA6. Amongst these only the UA1 and UA2 were able to detect the W± andZ0 bosons.

3.4.1 UA1 at SPS and observation of W bosons

The UA1 detector at SPS is a general purpose detector, shown schematically in figure 46.It is characterised by its excellent hermiticity (i.e. very few gaps), which is very good formeasurement of missing Et. The tracker and electromagnetic calorimeters are immersed intoa magnetic field, and the magnet return yoke is the hadron calorimeter. It also consists of8 layers of muon detector. However its electromagnetic calorimeter is not so great as it haspoor granularity (divisions), and it has no position detection in the barrel, in addition of beingdifficult to calibrate.

The UA1 search for the W boson through the decay mode W− → e−ν̄e proceeded bycollecting 18 nb−1 of data (about 109 collisions events) from late 1982. For this the signature

30

Figure 46: The UA1 detector at the Spp̄S detector.

is a high-pt electron, which was searched for by looking at events with an electromagneticcalorimeter with Et > 15 GeV, with an isolated high-pt track pointing to cluster, and the energymeasurement of the tracker must match that of the electromagnetic calorimeter. There shouldbe no associated energy deposit in the hadron calorimeter. The UA1 only observed 39 suchevents, amongst which only 5 had no jets, and it was observed that in these 5 events the missingenergy approximately equals the energy of the electron (deposited in the EM calorimeter). Theother 34 events had one or more jets and no missing energy. Similar analysis were performedon end-cap regions and yielded on more event with an electron an no jets. Parallel analysisconcentrating on finding events with missing Et yielded the same 6 events.

A potential issue is the background to these events, as they could be due to some other thingother than the decay of W±. For instance high-pt hadrons or mostly-neutral jets misidentifiedas an electron, or perhaps the decay of neutral hadrons or photons to a pair of electron/positron(π0, η0 γ → e+e−) with one electron missed, or jet with electron (rest undetected) or jet withneutrino (rest undetected)? However with the knowledge of expected theoretical rates of such“background” events and knowledge of the detector response (efficiency of the detector), aswell as explicit search for such background events in the data, it was concluded that all suchbackground events were in fact negligible. One of the 6 W events observed at UA1 is shownin figure 47. The blue line indicates a high pt electron. Other tracks are due to minimum bias(recall pp̄ collisions).

The observation was therefore announced by the UA1 collaboration at the SPS collider, inthe paper: G. Arnison et al. [UA1 Collaboration], Experimental Observation of Isolated LargeTransverse Energy Electrons with Associated Missing Energy at

√s = 540 GeV, Phys. Lett. B

122 (1983) 103. doi:10.1016/0370-2693(83)91177-2

3.4.2 UA2 and observation of W boson

UA2 was principally designed for the observation of W and Z0 bosons decays to high-pt elec-trons. It is schematically shown in figure 48. It is well instrumented in the central region,however its main disadvantage is that the inner tracker had no central magnetic field. As aconsequence vertexing exists only high−pt tracks. On the other hand the calorimeters are finelysegmented, which means that it can achieve good electron identification and energy measure-ment. The electromagnetic calorimeter is good especially in the barrel region, which means agood granularity. The disadvantages is that it had no muon detector and no end-cap calorimetry

31

Figure 47: One of the 6 W events observed at UA1.

Figure 48: The UA2 detector at the Spp̄S detector.

(and no magnetic field in the central region).The UA2 performed similar analysis on the data during the same period of UA1, and found

4 neutrino events W → eν, and they also published their results in the paper: M. Banner et al.[UA2 Collaboration], Observation of Single Isolated Electrons of High Transverse Momentumin Events with Missing Transverse Energy at the CERN pp̄ Collider, Phys. Lett. B 122 (1983)476. doi:10.1016/0370-2693(83)91605-2.

The determination of the masses of the W bosons at UA1 and UA2 proceeds by one of thetwo methods:

Either by measurement of the plot of the distribution of the lepton Et distribution (see figure49, which should peak at mW/2. By comparing to the measured spectrum to the Monte Carlopredictions, the mass of the W boson can be estimated.

Alternatively one can use the transverse mass distribution, as depicted in figure 61. In thisapproach, the transverse mass of the W boson is equal to that of the electron and neutrino,given by:

M2T = (Et + Eν)2 − (~pte + ~ptν)2

where the transverse momenta are measured in the plane transverse to the beam direction. By

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Figure 49: Plot of lepton Et spectrum at UA1.

Figure 50: Determination of the mass of the W boson using the method of transverse mass.

neglecting the masses of the electron and neutrino, we find:

M2T = 2EtEν(1− cosφ)

where φ is the angle between the neutrino and electron in the transverse plane.By comparing to the Monte Carlo predictions the mass of the W boson can be measured.

The advantage of this procedure is that it is independent on the transverse momentum of theW boson, while the Et distribution of the electron can be affected by the transverse momentumof the W boson.

The measured mass of the W boson by UA1 is: mW = 82.1± 1.7 GeV, consistent with theGWS model.

3.4.3 UA1 and UA2 observation of Z0

Furthermore, both UA1 and UA2 collaborations at SPS observed Z0 events which decay tocharged leptons. However because the decay to Z0 to leptons is rare compared to the decay ofW to leptons, there was no observation of Z0 events unil 1983 run. For the decay of Z0 → e+e−

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a pair of high-pt electron/positron are produced. The search strategy is similar to that for Wbosons, but with no missing Et (no neutrinos). UA1 recorded 3 such events and UA2 recorded4 events.

For UA1, and since it did have a muon detector, it could also search for the decay Z0 →µ+µ−. For UA2, there is no muon calorimeter so no such events were possible to detect. ForUA1, two oppositely charged isolated tracks in central tracker with matching tracks in themuon chambers is the signature. Also no missing transverse momentum should be recorded.The search only revealed one such event at UA1.

To determine the mass of the Z0 boson, one uses the method of invariant mass of the leptonssystem which equals the mass of the decaying Z0 boson. The measured mass of the Z0 at SPSboson is:

mZ = 93.0± 1.7GeVFor this both Carlo Rubbia and Simon van won the Nobel price for the “discovery of W and

Z bosons”.

4 LHC collider: discovery of the Higgs boson

4.1 Introduction

The standard model of particle physics describes matter (leptons and quarks) and their funda-mental interactions mediated by the gauge bosons, depicted in figure 51. However the Standard

Figure 51: Particles in the Standard Model.

model does not explain the following:

• Why do particles have mass?

• Why are there three generations of quarks and leptons?

• Are quarks and leptons really fundamental?

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• Why is there a matter—anti-matter asymmetry?

• What is “dark matter” in the universe?

• How does gravity fit in the quantum theory?

In order to answer these questions and many others bigger and higher energy machines areneeded. Specifically the most interesting question that the LHC was set to answer is the originof mass. The Higgs mechanism provides a way to give particles masses which otherwise wouldbreak the gauge symmetry. This mechanism requires the existence of a Higgs boson. The Higgsboson was discovered at the LHC in July 2012 by ATLAS and CMS collaborations.

There are also some extensions to the Standard Model which attempt to answer some of theabove questions, which also predict other new particles at the TeV scale. In fact there is now(as of June 2015) evidence of Beyond standard Model physics.

The aim behind building new and better accelerators is to search for such new physics (aswell as find the Higgs boson) and also to measure the properties of (known of new) particles moreprecisely. This helps boost the understanding of known particles and phenomena and comparethe theoretical findings of the standard model with experimental findings. Discrepancies betweentheory and experiment signal new physics.

Currently the world’s most powerful machine is the LHC (Large Hadron Collider) in CERN(Geneva– Switzerland), as shown in figure 52, a picture of the LHC tunnel is shown in figure

Figure 52: LHC map.

53. The LHC is a p − p collider with a centre of mass energy of 14 TeV, and it also collidesheavy ions (lead), i.e. Pb-Pb collisions for nuclear physics research. It began operation in 2008.It uses the same underground tunnel of the LEP collider which has a circumference of about27 km. It has a design luminosity of 1034 cm2s−1, which is about 100 times bigger than that ofLEP and Tevatron. This collider can search for new particles in the TeV scale.

Beam Energy In order to accelerate protons (or electrons at LEP), one of the following ap-proaches must be followed:

• Pass the particles through very large electric fields. To accelerate a proton to 14TeV a voltage of TV must be applied. This is however impossible with the currenttechnological limitations.

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Figure 53: LHC tunnel.

• Pass the charged particles through many smaller electric fields placed in a line. Thismeans we need many r.f. cavities placed along a line. This is also practically difficultsince it would require a lot of space and will cost a lot of money.

• Pass the charged particles through the same smaller electric fields many times. Toachieve this we require circular paths so that the charged particles get acceleratedthrough the same r.f. cavities many times. For this we require dipole magnets toproduce magnetic fields placed along the circular paths in order to keep the chargedparticles in circular orbits. The momentum (and thus energy of ultra-relativisticparticles) that particles acquire is:

p(TeV) = 0.3×B(Tesla)× R(km) (4.1)

For the last option a delicate balancing act is required in order to keep the acceleratedparticles in the same orbit around the circular collider. Particle energies must constantlybe increased, which gives them larger radius of curvature and thus they would spiral outof the beam pipe. To avoid this the magnetic fields must be increased synchronously withthe electric field to keep the particles in the same circular path.

Radio Frequency Cavities: The radio frequency cavities are responsible for accelerating thecharged particles. They are metal cavities placed along the path of the beam (beam pipes),as shown in figure 11. It contains an oscillating electromagnetic field that is in the stateof a standing wave. As the charged particles circulating the LHC tunnel arrive at the r.f.cavities, they get accelerated/decelerated by the electric field in these cavities. The r.fcavities switch the direction of the electric field in oscillation so that particles which arriveearlier than anticipated (which therefore have greater energy than the ideal protons) getmore acceleration than the “ideal protons”. This results in larger radius of the path, andhence they travel longer distance, and next time they arrive slightly later (and closer tothe “ideal protons”). On the other hand particles which arrive earlier than the “ideal”protons, they get decelerated so that their radius becomes smaller and thus they travel asmaller circumference, and hence they arrive later the next time (and closer to the “ideal”.This procedure leads to minimizing the energy variations of the beam particles.

cross-section: The Standard Model cross-section for the pp or pp̄ collisions is shown in figure54. From this figure it is clear that the cross-section for interesting events is very small,

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0.1 1 1010

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Figure 54: Standard Model cross sections at the Tevatron and LHC colliders.

for instance the cross-section for the production of a higgs boson. Interesting events aretherefore very rare (i.e. have a very low cross-section). One therefore needs as highluminosity as possible in order to maximise the observed number of interesting events.

In addition, the cross-sections for interesting physics (e.g. higgs production) suffers fromlarge QCD background, i.e. those events with jets in the final states which result purelyfrom QCD interactions, and which look like the decay products of interesting new physics.It is therefore difficult to identify interesting particles by their decays to jets. It remainsthus to focus on “clean” decay channels of interesting particles, such as the decay tophotons and leptons. Unfortunately though the branching ratio for the decay of suchparticles to leptons and photons is usually very small. This means that one must have agood lepton/photon identification. For instance, the recent discovery of the Higgs bosonwas mainly extracted from the decay of the higgs boson to di-photons.

why pp and not a pp̄ collider? A pp̄ machine (TEVATRON) is mechanically simpler than app (LHC) machine. For a pp̄, and since beams have equal and opposite charges one canuse the same beam pipes to accelerate the proton and anti-proton including the same rfcavities etc. For pp colliders we need two separate tunnels to accelerate the protons indifferent directions, which includes different rf cavities and beam pipes and even differenttunnels, and at the end the beams need to cross at collision points which is very tricky.However the advantage of pp colliders is that protons are abundant in nature while anti-protons are not, and these need to be produced. This has a direct impact on the luminosity

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of the machine, since the easiest way to maximise luminosity is to increase the number ofparticles per bunch, which is difficult to achive for pp̄ and easy for pp.

Furthermore, recall that at low values of Q2, the valance quarks carry most of the proton’smomentum which means for pp̄, it is more likely to achieve an annihilation of a quark andanti-quark than for a pp. However at high values of Q2, which is dominantly the case athigh energy colliders such as Tevatron and LHC, sea quarks and anti-quarks become morevisible, and here is where pp̄ loses this preference over pp.

The LHC accelerator consists of several stages (chain of accelerators), as shown in figure 55.

Linac2

ALICE

ATLAS

LHCb

CMS

SPS

Booster

LHC

PS

Linac4

LPSPL

PS2p

p

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Proposed injectors with Low Power Superconducting Proton Linac (LPSPL), new PS and new linac

p ��

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Super Proton Synchrotron (SPS)

Present injectors including Proton Synchrotron (PS)

H–

p

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Figure 55: LHC chain of accelerators.

Linear accelerator: Accelerates protons to 50 MeV linearly

Booster arranges bunches of protons and maximises the intensity of the beam

Proton synchrotron (PS) Accelerates protons to 26 GeV

Super Proton synchrotron (SPS) Accelerates protons to 450 GeV. Note that the SPS itselfthe world’s most powerful synchronton, and it discovered W± and Z0 bosons in the 1980’sbefore the LHC.

LHC accelerates protons to a maximum of 7 TeV and brings them to collision.

There are four experiments at the LHC: ATLAS and CMS, both being general purposeexperiments with the aim of searching for new physics and making precision measurements,LHCb with emphasis on b-hadron physics and CP violation, and ALICE which is aimed atstuding heavy-ion collisions.

4.2 ATLAS

The ATLAS (A Toroidal LHC ApparatuS) detector is shown schematically in figure 56.

Inner tracking detector: it measures the parameters of charged particles: sign of charge,momentum, initial direction, point of origin (vertex) with minimum perturbations of the

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Figure 56: ATLAS detector

particles. Therefore the inner tracking system must be made of low mass material to avoidaffecting the energy of the particles passing through.

As charged particles pass through, they deposit energy (usually by ionisation) which canbe detected wither online (record positions in space of the energy deposits in discretedetector elements) or off-line. Recording off line involves determining which points comefrom the same track and fitting a helix. As these tracks are surrounded in a magnetic fieldthe tracks are curved, and the direction of curvature determines the sign of the charge andthe radius of curvature gives the momentum of the particle. It also involves determiningwhere the tracks cross each other in order to determine the points of origin and the initialdirection of the particles.

There are three sub-systems for the inner tracker, as shown in figure 57:

Silicon pixel tracker: Here 3 very precice measurements of the space points are madefor each track. The pixel tracker is the closest to the interaction point, located atR ∼ 5 cm, 9 cm and 12 cm (see figure 57). This results in a very good vertex resolutio

Silicon strip tracker (SCT): this is made of back-to-back modules with relative rota-tion to each other, which helps obtain 3D space points for the particles. It makes 4precise measurements of the positions and it has inner and outer radius 30 cm < R <52 cm (see figure 57).

The Pixel detector and the SCT work in a similar way. For the Pixel detector, ascharged particles pass through they liberate electrons from a crystal lattice of Solidstate Silicon layer which are drifted (via an electric field) to an array of metal spheres(pixels) creating an electric signal. This procedure helps accurately determine theposition of the original particle very quickly (fast and accurate) by knowing whichpixel was hit by the drifting electron. Furthermore, a 3D space point may be obtainedby having two layers with crossed strips. However the disadvantage of this methodis that there is no charge multiplication and therefore a multiplier is necessary, andthe performance of these silicon detectors is vulnerable to radiation damage.

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Figure 57: ATLAS inner tracking system

Transition radiation tacker: The TRT is composed of straw tubes which make up to40 2D measurements per track for 56< R

containing tubes filled with gas, used to detect the passing muon by ionising the gasresulting in electrons which drift to the anode giving a signal out. The position of themuon is measured accurately by these tubes by knowing the drift time to the wire, asshown in figure 58.

Figure 58: Gas chambers at muon detector.

toroidal magnets: create a magnetic field within the muon detector which is roughly orthog-onal to the direction of motion of the muon. This helps measure the momentum of themuon.

forward detector: detects forward-biased particles. The End-caps hadron calorimeter is madeof copper and liquid aragon while the far forward hadron calorimeter is made of tungstenand liquid argon.

Trigger: At the LHC, there are about 109 interactions per second which take place. Howevermost of these interactions are not interesting. One must therefore only keep record of thoseevents which are interesting. The event strorage rate at the ATLAS detector is about 100Hz (100 events per second). This forms a major challenge at the ATLAS detector.

A 3-level trigger system is used in order to record interesting events:

Level 1 Here a fast simple algorithm is the muon detector and the calorimeters searchesfor high-pt leptons and jets, and makes a desicion in about 2 µs. While waiting forthe decision to be made the data in other detectors is temporarily held in pipelines.If the level 1 trigger accepts the event the data is read from the pipeline.

Level 2 If an event from level 1 is filtered, in level 2 the interesting regions of the detectorare examined more carefully. This level is relatively slower than level 1 and takesabout 10 ms to make a decision for each event. If the event is then accepted it ispassed to the event filter (level 3)

Level 3 The data about the full event is collected and some event reconstruction is per-formed. The decision takes a few seconds for each events. Accepted events are finallystored in data bases.

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Note that the ATLAS detector does not detect neutrinos at all. The presence of neutrinosis inferred from missing energy and momentum in the detector. In a real detector, some energyescapes detection especially down the beam pipes (those particles with very low transversemomentum). However transverse energy can easily be measured and any missing transverseenergy is assigned to neutrinos.

4.3 CMS

The CMS (Compact Muon Solenoid) detector is shown schematically in figure 59.

Figure 59: CMS detector

4.4 Higgs searches at the LHC

The Higgs production at pp colliders proceeds dominantly via one of the diagrams shown infigure 60. The Higgs production cross-section is shown in figure 61 From this plot it is clearthat the gluon fusion process dominates for all masses of the higgs. At low masses otherproduction mechanisms contribute but only at the very low level. At very high masses, WWand ZZ fusion becomes important. The number of higgs bosons that can be produced at theLHC per year is in the range 103 to 105 (a typical day will produce 3 Higgses for its currentmass).

The decay rates of the Higgs boson are also shown in figure 62 Also clear from this plot is that,for mH < 130 GeV (which is the actual case), the higgs decay to bottom quarks dominates.However this decay is overwhelmed by QCD background. The Higgs decay to two photonsH → γγ is a very important decay channel because it is very clean (very easy to eliminatebackground), however the disadvantage of this decay channel is the very low branching ratio.

Also note that, when the Higgs mass is in the range 130 GeV< mH < 2mZ , then theH → WW ∗ and H → ZZ∗ become dominant, and for mH > 2mZ the higgs can decay to tworeal W/Z bosons H → ZZ and H → WW (1/3 of the times for each).

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qq → qqH0 qq̄ → H0 +W/Z

Figure 60: Higgs production at p− p colliders.

For all higgs masses, the hadronic final states dominate, however huge QCD backgroundis not easy to eliminate and intrusting Higgs signal events cannot easily be distinguished frombackground. The best search strategy is to look for final states with leptons, missing energyand photons.

For mH < 150 GeV, the branching ratio H → bb̄ ≈ 100%. The QCD background is huge,however, in fact 105 more times than signal (i.e. in every 10 000 event which originates purelyfrom QCD, there is one event which originates from the decay of the Higgs). This decay channelcan still nonetheless be used if there are additional leptons in the event which come from theassociated production (WH , ZH , tt̄H). However the cross-section for the production of suchleptons is very small.

The most promising channel, di-photon decay of the higgs H0 → γγ has a branching rationof about 0.1%. However this is very clean (If about 1000 higgs produced in a year, only 10would decay to two photons!).

Also, intermediate mass regions, 120 GeV< mH < 2mZ , the decay modes:

H0 → WW ∗ → ℓ+1 ν1ℓ−2 ν̄2, H0 → ZZ∗ → ℓ+1 ℓ−1 ℓ−2 ℓ+2 ,are the only two channels which can be extracted from background, while for high mass regions(mH > 2mZ):

H0 → ZZ → ℓ+1 ℓ−1 ℓ−2 ℓ+2 ,forms the “gold-plate channel with no background (almost). Here (in this range) it is alsopossible to have:

H0 → W+W− → ℓ+1 ν1ℓ−2 ν̄2, H0 → ZZ → ℓ+1 ℓ−1 νν̄, or ℓ+ℓ−jet+jet,

4.5 Di-photon higgs decay

Let us concentrate on the higgs decay channel to di-photons H0 → γγ, in the region 80 GeV<mH < 150 GeV. This proceeds via the Feynman diagram depicted in figure 63. For this channel,

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σ(pp→H+X) [pb]√s = 14 TeVMt = 175 GeV

CTEQ4Mgg→H

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Figure 62: Higgs decay rates as a function of the mass of the Higgs boson.

one selects events with two photons with pt ∼ 50 GeV. We need to measure the energies anddirections of the resulting photons. In fact the mass of the decaying higgs boson equals theinvariant mass of the photon pair

MH = mγγ =√

2Eγ1Eγ2 (1− cos θ),

where θ the angle between the photon pair. In order to find the higgs one plots number of eventsas a function of the invariant mass of the photon pair, and a clear peak should be observed atthe mass of the higgs boson. For this a very good electromagnetic calorimeter is needed.

The background to H0 → γγ is mainly from γ-jet production or jet-jet production, wherethe jets fake the photons, as shown in figure 64. This is however quite easy to eliminate if onehas good calorimeters to distinguish isolated photons from jets with photons.

Also another background to this process is the di-photon production shown in figure 65.In fact some final states as signals cannot be entirely eliminated (irreducible background).However if the invariant mass of the resulting γγ pair is measured well enough (which needs

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Figure 63: Higgs decay to di-photon.

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Figure 64: Jet-photon production and jet-jet production as a background to higgs di-photonproduction.

a good electromagnetic calorimeter), then the signal will form a peak above the background.To achieve a better and more accurate measurement of the Higgs mass, a good mass resolutionof the photon pair is required. This results in narrower peak which is easier to see above thebackground.

g

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Figure 65: di-photon QCD production as a background to higgs di-photon production.

The statistical significance of the H → γγ signal is defined by:

significane = Nsignal/√

Nbackground

in the peak region, where Nsignal is the number of signal events and Nbackground is the numberof background events. The significance depends on how good the mass resolution is. If theresolution is poor, then the peak is wide and the number of background events therefore becomeslarge, roughly the same as the number of signal events. The significane also depends on theluminosity. This is because:

Nsignal = L × σsignal, Nbakcground = L × σbackground

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Therefore we deduce that significance ∝√L, the higher the luminosity the better the signifi-

cance. ATLAS needs about 1 year of high luminosity in order to have a 4σ effect.

4.6 ATLAS/CMS plots of the Higgs to diphoton

On july the 4th 2012, both ATLAS and CMS collaborations at CERN announced the discovery ofa new boson of mass around 125 GeV, most likely is the long-waited and celebrated higgs boson.However the confirmation of this discovery is awaited while the properties of this new particleare determined, which incudes spin-parity, couplings etc... Besides searches for additional higgsbosons is continuing in w wide mass range. Hints for beyond standard model are also beingsearched.

An event of a higgs decay to diphotons is shown in figure 71.

Figure 66: Actual CMS event of a Higgs decay to di-photons. The dashed yellow lines (followedby the green line) indicate the photon tracks.

The plot obtained by ATLAS collaboration for the number of events as a function of theinvariant mass of the photon pair is shown in figure 70. The signal+back

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