Quarks

Quarks

•  Quarks are s = ½ fermions, subject to all kind of interactions. •  They have fractional electric charges

•  Quarks and their bound states are the only particles which interact strongly •  Like leptons, quarks occur in 3 generations: •  Corresponding antiquarks are:

⎟⎠

⎞⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛bt

sc

du

⎟⎠

⎞⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛

tb

cs

ud

Brief history of hadron discoveries

•  First known hadrons were proton and neutron

•  The lightest are pions π. There are charged pions π+, π-, with mass of 0.140 GeV/c2, and neutral ones π0, with mass of 0.135 GeV/c2

•  Pions and nucleons are the lightest particles containing u- and d-quarks: were discovered in 1947 in cosmic rays, using photoemulsion to detect particles •  Some reactions induced by cosmic rays:

•  Same reactions can be reproduced in accelerators, with higher rates (but cosmics may provide higher energies)

p+ p→ p+ n+π +

→ p+ p+π 0

→ p+ p+π + +π +

The Neutral Pion

The Neutral Pion

The Neutral Pion 20 /0.135)( cMeVm =π

−+→ eeγγγπ ,0Decay mode Electromagnetic

Decay lifetime s161084.0 −×=τ

BR =98.8% BR =1.2%

Experimental evidence. Cosmic ray studies of «star-like» events in high resolution nuclear emulsions (1950, Carlson, Hooper, King). High energy experiments at the Berkeley Cyclotron. +e

+e

−e

−e

γ

γ

The detachment from the “primary vertex” of the interaction is caused by the neutral pion lifetime

p

“Primary” vertex

Charged pions decay mainly to the muon-neutrino pair (BR ~99.99%) having lifetimes of 2.6x10-8 s. In quark terms:

Neutral pions decay mostly by the electro- magnetic interaction, having shorter lifetime of 0.8x10-16 s At the beginning discovered pions were believed to be responsible for the nuclear forces However, at ranges comparable with the size of nucleons this description fails.

( ) µνµ +→ +du

γγπ +→0

8

Particles with Strangeness Presence of unknown particles in experiments with cloud chambers or emulsions on atmospheric balloons (1947, Rochester and Butler). They turned out to be secondary particles with a characteristic “V” shape decay

−+−− →Λ→ ππππ pKpThese particles were produced in pairs and characterised by: •  Strong Interaction production (cross section) •  Weak Interaction decays (lifetimes)

π

•p

Interazione forte

Interazione debole π

pπ

πmb≈σ s1010−≈τ

Particles with Strangeness π–p→ΛK˚ a ≈ 1 GeV/c nella camera a bolle a H2 liquido da 180 cm di Alvarez. Metà anni ‘50

Solution given by Gell-Mann (1953-56) and independently by Nisishima (1955): a new quantum number, additive, the strangeness S S of the “old” particles = 0 S of strange mesons = +1 And of their anti-particles = –1 S of hyperons = – 1 And of anti-hyperons = +1

π − p→ K 0Λ0 permesso

π − p→ K 0n vietato

π − p→ K −Σ+ vietatonn→ΛΛ vietato

Λ→ pπ − permessoΣ− → nπ − permessoΣ0 →Λγ permesso

Strong interactions save S Weak interactions violate S

Strange particles: kaon discovery

Particles with Strangeness s a new quark (different from u,d) !

)106.2(, 100 snp −− ×=→Λ τππ

2/6.1115)( cMeVm =Λ

)10895.0(, 10000 sKs−−+ ×=→ τππππ

2/6.139)( cMeVm =−π

BR = 64.1%

BR = 35.7%

BR = 30.7%

BR = 69.2%

The long lifetime was explained by the disappearance of a «strange» quark

),,( sdu=Λ

K particles (Kaons), similar to Pions but with the s Quark

20 /0.135)( cMeVm =π

2/495)( cMeVKm ≅

Photon

12

),,( duup=),,( ddun=

+− ee ,+− µµ ,

),(,),( uddu == −+ ππ

γ

ν

Leptons (heavier copies of the electron)

The neutrino, postulated to explain beta decay and observed in inverse beta decay, is always associated to a charged lepton.

The hadrons, particles made up of quarks and obeying mainly to strong nuclear interaction

),,( sdu=Λ

Proton-like particles (baryons)

K,0π Mesons

Particle Classification

Strange mesons

Q S m(MeV) τ(ns) Decadimenti comuni

K+ (us) +1 +1 494 12 µ+νµ, π+ π+ π–, π+ π0

K0(ds) 0 +1 (498) n.a. n.a.

K–(db) –1 –1 494 12 µ-νµ, π+ π– π–, π–π0

K0 (us) 0 –1 (498) n.a. n.a

K˚ and K˚ are electrically neutral, but different since they have opposite strangeness.

K mesons are the only strange mesons which decay weakly, the others decay strongly in very short time.

The strange Hyperons

Q S m(MeV) τ(ps) dec. princ. Λ (uds) 0 –1 1116 263 pπ–/nπ ̊

Q S m(MeV) τ(ps) dec. princ Σ+(uus) +1 –1 1189 80 pπ0/nπ+

Σ0(uds) 0 –1 1193 7.4 ×10–8 Λ γ

Σ–(dds) –1 –1 1197 148 nπ–

Q S m(MeV) τ(ps) dec. princ. Ξ0(uss) 0 –2 1315 290 Λ π0

Ξ–(dss) –1 –2 1321 164 Λ π–

Masses increase with the increase of the s-quark number Σ– is not the antiparticle of Σ+ No strange hyperon, except Σ0 can decay without changing its strangeness, then through weak interaction

The lightest ones are:

More strange particles: S=2

Heavy quarks: the Charm 1974: the October revolution. J/ψ discovery in 2 experiments.

ψ/Jee →−+

XJBep +→+ ψ/1) Brookhaven experiment: 28 GeV protons on a fixed target

−+ee

2) SLAC experiment: electron-positron collider

adroniee ,, −+−+ µµ

Invariant mass distribution for the final states

m2 e+e−( ) = 2me2 + 2E1E2 + 2p1p2 cos θ1 +θ2( )

The charm quark

J/Ψ

20

Width dominated by experimental resolution

Real width from knowledge of cross section and BRs

Width Γ= 0.093 MeV

Lifetime 10-20 s

21

A problem with the J/ψ: Usually the hadron resonances have large widths since they decay via strong interactions and have a very short lifetime.

MeVs 2001010/10 2322 −=Γ⇒Γ

≅=−− τ keVJ 93)/( =Γ ψ

As comparison:

MeVMeVMeV 3.4)(5.8)(150)( =Γ=Γ=Γ φωρ

How can a resonance have a width100/1000 times smaller thn usual but still being a strong interacting particle?

To answer to this question we have to know other particles containing the c-quark.

22

Studying better the production region of a J/Ψ , one could notice also states of the J/ψ type much larger, over a certain threshold.

23

smccJ 2010,3097,/ −=== τψ

J /ψ→DD impossibile

c

c

c

c

u

u

One would expect than that the J/ψ decays as:

J/ψ contains a new quark, the charm.

0/ == CccJ ψ Hidden charm

Particles with “visible” charm were discovered at SLAC in the following years

ucDsmucDdcDsmdcD

=×===

====−

−−+

0130

12

104,1865,10,1870,

τ

τ

But this is not possible, since:

MeVDmJm 3730)(23097)/( =<=ψ

Excited states have high enough mass to decay in charmed mesons

)(2 Dmm <

For all the J/ψ states such that:

For all the J/ψ states such that:

)(2 DmM >

3 gluons exchange

Suppressed by Zweig rule

Other Ψ tests

ψ '→ψ +π + +π − ψ → e+ + e−

26

Charmed mesons The Mark I detector started the search of the charmed pseudoscalar mesons at √s=4.02 GeV in 1976 (having improved its K to π discrimination ability) in:

e+ + e– → D0 +D0 + X e+ + e– → D+ +D_ + XMesons appear as resonances in the final state. Neutral D were observed decaying in the final states D0 → K −π +D0 → K +π−

Charged D-mesons observed in: No resonance in: Mass =1869 MeV

D+ → K –π +π +

D− → K +π −π −

D+ → K +π +π −

D− → K −π +π −

Charmed mesons

ucDsmucDdcDsmdcD

=×===

====−

−−+

0130

12

104,1865,10,1870,

τ

τ Lightest mesons with charm

Main decay modes: type c à s, via weak interactions. For example:

%14,%6, 000 =→=→ +−++++ BRKDBRKD πππππ

Mesons with charm and strange quarks:

)1,1(,)1,1(,105,1969, 13 −=−==+=+=×=== −−+ SCscDSCsmscD Ss τ

Typical decay, with c à s: %5, =→ +−++ BRKKDs π

Barions with charm: ducsmcud cc =Λ×===Λ −−+ 13102,2285, τ

Typical decay, with c à s: %5, =→Λ +−+ BRKpc π

Even heavier charmed mesons were found which contained strange quark as well: Lifetimes of the lightest charmed particles are of ~10-13 s, well in the expected range of weak decays •  Discovery of “charmed” particles was a triumph for electroweak theory, which demanded number of quarks and leptons to be equal

csDscD

s

s

=

=−

+

)1969(

,)1969(

First sign of the 3rd family: the beauty quark

Third family ⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎦

⎤⎢⎣

⎡

−=⎟⎟

⎠

⎞⎜⎜⎝

⎛

sd

sd

CC

CC

C

C

θθ

θθ

cossinsincos

Two families were known in 1977. In the weak interactions, the two families appear rotated (Cabibbo angle)

The mixing in fact, involves all three families (CKM matrix)

Lederman et al. Experiment at Fermilab in 1977. Final state with two muons in proton (400 GeV) collision on a fixed target.

The particle discovered was

keVmbb 54,9460, =Γ==Υ

In complete analogy with the J/ψ case

These particles are composed by an even heavier quark: the b-quark.

b-quark discovery

31

The two arms muon spectrometer Fermilab 1977

1,1,105.1,5366,1,105.1,5279,1,106.1,5279,

120

0120

12

−=+=×===

=+=×===

=+=×===

−

−

−−+

SBsmbsBbdBBsmbdBbuBBsmbuB

S τ

τ

τ

Again, in analogy with the J/ψ

States which decays hadronically in 3 gluons

Y(4s) state, the first one which has enough mass to decay in a B and anti-B

BBS →Υ )4(

Y has a hidden beauty, while mesons with “visibile” beauty are:

The lightest barion with beauty is:

smbudb120 104.1,5620, −×===Λ τ

33

Sα

α

Onia systems J/ψ as quarkonium: non-relativistic combination determined by a basic Coulomb potential

Vs (r) = −43αsr+kr

Decays of particles with beauty, with prevalence of b à c The decays happen in particles with charm

−→ Wcb

Examples of invariant mass reconstruction of particles with beauty

Top quark discovery The sixth quark was found in 1994 at Fermilab. The first evidence came from the CDF experiment in proton/antiproton collisions at the energy of 1.8 TeV. Typical Feynman diagrams for production

Topology of a top event

Gluon-gluon fusion

Quark annihilation

Top quark discovery •  Searched at hadrons colliders for more than a decennium (difficult due to its

very large mass mt=173 GeV). Need CoM energy > 400 GeV •  In a pp collision at √s = 2 TeV a ttbar pair is produced every 1010 collisions.

p+ p→ t + t + X; t→W + + b; t →W − + b

W → eνe o → µνµ

t→W + + b→W + + jet(b); t →W − + b →W − + jet(b )W → eνe o → µνµ e W → qq '→ jet + jet

•  Look in the “clean” channels

•  W decays most often in quark antiquark, but background is huge due to strong interactions

•  Good tag: detect a b in the hadronic jet

Top quark discovery

Important detector elements •  Si microstrip high spatial resolution vertex detector •  Tracking detectors •  Hermetic calorimetry (in the transversal plane) ⇒ missing momenum, neutrinos

38

Top at LHC 32 R. CHIERICI

(TeV)s1 2 3 4 5 6 7 8

) (p

b)

t(t!

10

210

(TeV)s1 2 3 4 5 6 7 8

) (p

b)

t(t!

10

210

CMS di-leptons (L=2.3/fb)ATLAS di-leptons (L=0.7/fb)CDFD0

NLO QCD (pp)

Approx. NNLO QCD (pp)Scale uncertainty

PDF uncertainty"Scale

)pApprox. NNLO QCD (pScale uncertainty

PDF uncertainty"Scale Langenfeld, Moch, Uwer, Phys. Rev. D80 (2009) 054009MSTW 2008 (N)NLO PDF, 90% C.L. uncertainty

Fig. 11. – The most precise ATLAS and CMS top quark pair cross sections are compared tothe predicted cross section evolution with the centre-of-mass energy. Lower energy results fromTevatron are also shown.

ultimately measure directly the top quark Yukawa coupling at the tree level.The signature looked for by ATLAS and CMS consists of one or more extra lep-

tons together with a top quark pair topology. More specifically, CMS has looked foreither three-isolated-lepton final states, two of which of the same flavour and resonantto the Z pole, or two same-sign isolated leptons, in association with at least three jetsin the event [196]. The selections are sensitive to both t̄tW and tt̄Z production. Therequirement of multi leptons drastically reduce any background component coming frommulti-jet or W+jets. The main background in the resulting acceptance are di-bosonwith extra jets, Drell-Yan with other misidentified leptons, or leptons from b-decays, andsingle top. They are determined with MC and data-driven techniques.

The trilepton analysis observes nine events in the whole CMS data sample at�

s =7 TeV, compared to a background expectation of 3.2 ± 0.8 events, whereas the same-sign analysis sees, in the same data-set, a total of 16 events, compared to an expectedbackground contribution of 9.2± 2.6 events. Figure 12, left, shows the event yield afterselection for the three-lepton analysis. Both analysis establish therefore a signal with asignificance of 3 standard deviations or more. The cross section are extracted througha simultaneous measurement performed in the various decay channels, and yield, forthe trilepton channel, a direct measurement of �tt̄Z = 0.28+0.14

�0.11(stat) +0.06�0.03(syst) pb

while in the di-lepton channel a measurement of the t̄tV (V=W,Z) process yields �tt̄V =0.43+0.17

�0.15(stat) +0.09�0.07(syst) pb. Both cross section measurements are compatible with the

NLO predictions [198, 197], as shown in Figure 12, right.

4.3. Single top production cross sections. – Studying single top is particularly impor-tant because single top production is mediated by electroweak vertexes, hence provides adirect probe of the Wtb coupling and is sensitive to several models of new physics [199].Moreover, the single top cross section also allows to constrain the proton b-PDF. As

30 R. CHIERICI

)2 (GeV/ctopm100 150 200 250 300 350 400 450 500 550

)2

Even

ts /

( 1

0 G

eV

/c

0

50

100

150

200

250

300

350

0.025± = 0.351 sigf

CMS data: 3136 events

componenttt

multijet QCD background

and QCDtcombined t

= 7 TeVs at -1

CMS, 3.54 fb

Fig. 9. – Left: three-jets invariant mass in candidate �+jets events in CMS. Right: result ofthe fit on data of top quark pair signal and QCD multi-jet background to the reconstructedtop quark mass in CMS; the uncertainty in the signal fraction, indicated in the figure, is juststatistical.

tion (CMS [193]). In this last example, the consistency of the signal region with topquark pair production can be tested by cutting on the MVA discriminant and looking,for instance, at the three-jets invariant mass in the event. This distribution is shown inFigure 9, and clearly demonstrates the consistency of data with the hypothesis of a topquark.

The entirely hadronic final state is investigated by CMS [194]. To resolve the pairingambiguity and to reduce part of the QCD background, a kinematic fit to the hypothesisof two equal masses decaying into a W boson and a b quark is used. The information ofthe jet b-tagging is also included in the fit on this purpose. The cross section is extractedvia an unbinned maximum likelihood fit to the reconstructed top quark invariant mass,as shown in Figure 9, with the QCD shape determined by using a data-driven method.This method use an appropriate reweighing of the large statistics multi-jet backgroundthat is obtained without imposing any b-tag conditions.

In Figure 10 a summary of the published cross section at 7 TeV by ATLAS and CMSis reported, and is compared to the predictions, at the same centre-of-mass energy, fromNLO, approximate NNLO and full NNLO+NNLL computations. The agreement acrossdi�erent channels, between ATLAS and CMS, and between theory and experiments, isremarkable. The dominating systematic uncertainties come from the knowledge of thejet energy scale, the uncertainty in the description of the radiation in top pair events,and the luminosity. The di�erence in size between the errors of ATLAS and CMS ispartly due to the di�erent statistics of the data-sets used, and in part to the di�erentdefinition of the systematic sources from theory and to the di�erent size of the experi-mental systematic sources, especially on the knowledge of the jet energy scale. The lowererror due to luminosity in CMS comes from a new method for determining it by usingthe pixel detector [195]. A detailed comparison of the error breakdown is currently underdiscussion, in view of a combination of the ATLAS and CMS cross sections.

In Figure 11, the two most precise measurement by ATLAS and CMS are super-imposed to the approximate NNLO theory predictions. The same figure also show theTevatron data with the analogous prediction for pp̄ collisions, as a comparison. With a

Top production cross section copared to QCD calculations

Invariant mass of the jets selected as compatible with all hadronic decay of top

Top quark properities The top quark mass, of about 175 GeV, makes it different from the b- and c-quark. Almost always it decays in :

+→ WbtCan we observe a toponium state, as mesons and barions composed by a quark top? NO. The hadronization time is of order:

scfmcRt 2410/1/ −≅=≅

We can think it as the time a gluon needs to cross a nucleon.

The decay rate of a quark top is proportional to its mass and we have:

τ ≈Γ−1≅5×10−25 s

The top quark decay in a b-quark before hadronizing.

The quark model: Baryons and antibaryons are bound states of 3 quarks Mesons are bound states of a quark and an anti-quark Barions and Mesons are: Hadrons

Hadrons

Quantum Numbers and flavours

Theory postulated in 1964 (Gell-Mann)

e

p

e’ In the 70’s, deep inelastic scattering of electrons on p and bound n show evidence for the quark model

•  Strange, charmed, bottom and top quarks each have an additional quantum number: strageness S, charm C, beauty B and truth T respectively.

•  In strong interactions the flavour quantum number is conserved

•  Quarks can change flavours in weak interactions (DS =±1, DC =±1)

Particles and Interactions

Quarks Charged leptons

Neutrini

Strong

EM

Weak

Hadrons and lifetime

•  Majority of hadrons are unstable and tend to decay by the strong interaction to the state with the lowest possible mass (t ~ 10-23 s) •  Hadrons with the lowest possible mass for each quark number (S, C, etc.) may live much more before decaying weekly (t ~ 10-7- 10-13 s) or electromagnetically (mesons, t~10-16- 10-21 s) Such hadrons are called stable particles

Strangeness is such that S=-1 for s-quark and S =1 for the anti s-quark. Further, C=1 for c-quark, B=-1 for b-quark and T=1 for t-quark Since t-quark is a very short living one, there are no hadrons containg top, i,e, T=0 for all Quark numbers for up and down quarks have no name, but just like any other flavour, they are conserved in strong and em interactions Baryons are assigned own quantum number B: B=1 for baryons, B=-1 for antibaryons, B=0 for mesons