string theory in the lhc eratheory.uchicago.edu/~marsano/comptonlectures/lecture5/... ·...
TRANSCRIPT
String Theory in the LHC Era
1. Electromagnetism and Special Relativity
2. The Quantum World
3. Why do we need the Higgs?
4. The Standard Model
9. String Theory and Particle Physics
5. Physics Beyond the Standard Model and Supersymmetry
6. Einstein’s Gravity
7. Why is Quantum Gravity so Hard?
8. String Theory and Unification
2
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3
The Standard Model of Particle Physics
Electromagnetism
Strong nuclearforce
Weak nuclearforce
Leptons(electrons and
neutrinos)
Quarks
Tuesday, May 1, 12
4 Hat tip R Lipscombhttp://mblogs.discovermagazine.com/cosmicvariance/2012/04/25/what-particle-are-you/
Tuesday, May 1, 12
5
Quantum Electrodynamics Weak Nuclear Force
Long range force
Weak bosons W±, Z0
Short range force
Range set by
1
Mass of W±, Z0
n
⌫e
e�
p+
W�
Photon � Massless force carrierMassive force carriers
e� e�
�e� e�
Quantum ChromodynamicsGluons g Many massless force carriers
Strongly coupled at long distances q
q
q
q
g
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6
Electromagnetism
Strong nuclearforce
Weak nuclearforce
Leptons(electrons and
neutrinos)
Quarks
The Standard Model of Particle Physics
+ Higgs Boson
All particle masses from coupling to Higgs
Tuesday, May 1, 12
6
Electromagnetism
Strong nuclearforce
Weak nuclearforce
Leptons(electrons and
neutrinos)
Quarks
The Standard Model of Particle Physics
+ Higgs Boson
All particle masses from coupling to Higgs
Photon masslesslong range force
Gluons massless but many of them → confinement
W and Z bosons massiveshort range force
Quark and lepton masses from Higgs
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7
Beyond the Standard Model
Why?
Tuesday, May 1, 12
8
Standard Model doesn’t incorporate gravity
More on this in the remaining lectures.....
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9
Grand Unification
Inverse electromagnetic coupling
Inverse weak interaction coupling
Inverse QCD coupling
F. Wilczek, Nature 433, 239
Grand Unified Theory (GUT) that gives common origin to the three forces of the Standard Model?
Tuesday, May 1, 12
10
Beyond the Standard Model
Why?
We will focus on two additional reasons:
1. Dark Matter
2. Hierarchy Problem
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11
1. Dark Matter
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12
Dark Matter
Stars near the edge of galaxies are rotating faster than they should
Fritz Zwicky
New ‘dark matter’ contributes to the gravitational field that accelerates the stars
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Gravitational Lensing
Can ‘see’ dark matter more directly
Tuesday, May 1, 12
Gravitational Lensing
Can ‘see’ dark matter more directly
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Dark Matter also affects the Cosmic Microwave Background
Key component of standard cosmology
What does this mean for particle physics?
Tuesday, May 1, 12
Standard cosmology: Dark Matter is a WIMP
Weakly Interacting Massive Particle
Couples to the weak interactions
not to electromagnetism or the strong interaction
Tuesday, May 1, 12
Standard cosmology: Dark Matter is a WIMP
Weakly Interacting Massive Particle
Couples to the weak interactions
not to electromagnetism or the strong interaction
Must be stable or have lifetime longer than the age of the universe
(~ 10 billion years)
Tuesday, May 1, 12
Standard cosmology: Dark Matter is a WIMP
Weakly Interacting Massive Particle
Couples to the weak interactions
not to electromagnetism or the strong interaction
Must be stable or have lifetime longer than the age of the universe
(~ 10 billion years)
There is no particle like this in the Standard Model
Tuesday, May 1, 12
There is no particle like this in the Standard Model
...but good reason to see it soon
Early universe Dark matter in ‘thermal equilibrium’
Dark Matter Particles
Standard Model Particles
Dark Matter Particles
Standard Model Particles
Standard Model particles collide to make dark matter
Dark matter particles annihilate back to Standard Model
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There is no particle like this in the Standard Model
...but good reason to see it soon
Dark Matter Particles
Standard Model Particles
Dark Matter Particles
Standard Model Particles
Tuesday, May 1, 12
There is no particle like this in the Standard Model
...but good reason to see it soon
As the universe expands, these reactions stop
Roughly, particles too far apart for them to continue
annihilating
Dark Matter Particles
Standard Model Particles
Dark Matter Particles
Standard Model Particles
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Dark matter density
There is no particle like this in the Standard Model
⌦Dark ⇠ 1h�vi ⇠ m2
Dark
g4
Rate at which dark matter annihilates into Standard Model particles
...but good reason to see it soon
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Dark matter density
There is no particle like this in the Standard Model
⌦Dark ⇠ 1h�vi ⇠ m2
Dark
g4
⇠ 0.1 for WIMP with
mDark ⇠ 100 GeV
Rate at which dark matter annihilates into Standard Model particles
...but good reason to see it soon
Tuesday, May 1, 12
Dark matter density
There is no particle like this in the Standard Model
⌦Dark ⇠ 1h�vi ⇠ m2
Dark
g4
⇠ 0.1 for WIMP with
mDark ⇠ 100 GeV
Observed value
Rate at which dark matter annihilates into Standard Model particles
...but good reason to see it soon
Tuesday, May 1, 12
Dark matter density
There is no particle like this in the Standard Model
⌦Dark ⇠ 1h�vi ⇠ m2
Dark
g4
⇠ 0.1 for WIMP with
mDark ⇠ 100 GeV
Observed value
Mass scales probed at the LHC
Rate at which dark matter annihilates into Standard Model particles
...but good reason to see it soon
Tuesday, May 1, 12
Dark matter density
There is no particle like this in the Standard Model
⌦Dark ⇠ 1h�vi ⇠ m2
Dark
g4
⇠ 0.1 for WIMP with
mDark ⇠ 100 GeV
Observed value
Mass scales probed at the LHC
The ‘WIMP Miracle’
Rate at which dark matter annihilates into Standard Model particles
...but good reason to see it soon
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Get the right (observed) amount of dark matter if we assume it is
A WIMP with mass ~100-1000 GeV
~ Electroweak scale!
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The ‘WIMP Miracle’
Get the right (observed) amount of dark matter if we assume it is
A WIMP with mass ~100-1000 GeV
~ Electroweak scale!
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Dark Matter Searches
Direct Detection Indirect Detection
Look for dark matter colliding with heavy nuclei (Ge, I, Xe, ...)
Look for signs of dark matter annihilation in the sky
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Direct Detection
DAMA and CoGent see something but nobody
else does
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Indirect Detection
Fermi Satellite
Evidence for 130 GeV dark matter annihilation in galactic center?
C Weniger arXiv:1204.2797
waiting for official analysis from Fermi/LAT collaboration
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23
2. Hierarchy Problem
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Hierarchy Problem
Energy Scales
1018 GeV
10�3 GeV
Quantum gravity
Weak scale
Proton mass
Electron mass
16 o
rder
s of
mag
nitu
de
1 GeV
102 GeV
Where did this large scale separation come from?
Higgs boson breaks electroweak symmetryGenerates mass for W and Z bosons
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Hierarchy Problem
Energy Scales
1018 GeV
10�3 GeV
Quantum gravity
Weak scale
Proton mass
Electron mass
16 o
rder
s of
mag
nitu
de
1 GeV
102 GeV
Where did this large scale separation come from?
Higgs boson breaks electroweak symmetryGenerates mass for W and Z bosons
Why do we care?
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Electroweak Hierarchy
Scale of electroweak symmetry breaking determined by Higgs physics
Potential for Higgs field sets the scale of the ‘Higgs bath’
Determined by quantum effects
Higgs boson breaks electroweak symmetry
Generates mass for W and Z bosons
Energy
1018 GeV
10�3 GeV
Quantum gravity
Weak scale
Proton mass
Electron mass
16 o
rder
s of
m
agni
tude
1 GeV
102 GeV
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h h
t
t
Electroweak Hierarchy
Many important contributions, including top loop
Higgs boson breaks electroweak symmetry
Generates mass for W and Z bosons
Energy
1018 GeV
10�3 GeV
Quantum gravity
Weak scale
Proton mass
Electron mass
16 o
rder
s of
m
agni
tude
1 GeV
102 GeV
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h h
t
t
Electroweak Hierarchy
Many important contributions, including top loop
=1 (Infinity)!
Higgs boson breaks electroweak symmetry
Generates mass for W and Z bosons
Energy
1018 GeV
10�3 GeV
Quantum gravity
Weak scale
Proton mass
Electron mass
16 o
rder
s of
m
agni
tude
1 GeV
102 GeV
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h h
t
t
=1 (Infinity)!
Quantum Field Theory generates many infinities
General Rule:
Tuesday, May 1, 12
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h h
t
t
=1 (Infinity)!
Quantum Field Theory generates many infinities
General Rule:
Quantum Field Theory is smarter than we are
If we get an infinite answer then we must have done something wrong
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h h
t
t
Ok so what are we doing wrong?
Quantum Field Theory is smarter than we are
If we get an infinite answer then we must have done something wrong
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h h
t
t
We always ‘sum over histories’
Richard Feynman
...so we allow virtual top quarks to carry arbitrarily high momenta/energies
If we cap this energy at ⇤ then the result is ⇠ ⇤2
The infinity comes precisely from the top quarks with very high energies
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h h
t
t
We always ‘sum over histories’
Richard Feynman
...so we allow virtual top quarks to carry arbitrarily high momenta/energies
If we cap this energy at ⇤ then the result is ⇠ ⇤2
The infinity comes precisely from the top quarks with very high energies
Do we really know what physics looks like at such high energies?
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h h
t
t
We always ‘sum over histories’
Richard Feynman
...so we allow virtual top quarks to carry arbitrarily high momenta/energies
If we cap this energy at ⇤ then the result is ⇠ ⇤2
The infinity comes precisely from the top quarks with very high energies
Do we really know what physics looks like at such high energies?
NO!
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h h
t
t
= 1
We got a nonsense answer because we made an incorrect assumption
Our formalism is not a good description of short distance (high energy) physics
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What can we do? Parametrize our ignorance of short distance physics
h h
t
t
hh
Our old computation
‘New’, unknown short distance physics
+
Controlled by new parameterMust be fixed by measurement
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Infinities everywhere!
Standard Model depends on many details of short distance physics
Miracle of the Standard Model:
Depends on short distance physics only through 19 parameters
(particle masses and couplings)
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If we could describe physics at all distance scales, we could compute all particle masses
and interactions
...but we do not know what is going on at very short distances
The parameters of the Standard Model (masses and couplings) parametrize what we don’t know about this short distance physics
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Standard Model
Measured Parameter Values
Predictions
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Standard Model
Measured Parameter
Values
Predictions
How sensitive are these large mass hierarchies to our parameter values?
Higgs boson breaks electroweak symmetry
Generates mass for W and Z bosons
Energy
1018 GeV
10�3 GeV
Quantum gravity
Weak scale
Proton mass
Electron mass
16 o
rder
s of
m
agni
tude
1 GeV
102 GeV
Question about ‘robustness’ of the Standard Model
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Hierarchy Problem
Energy Scales
1018 GeV
10�3 GeV
Quantum gravity
Weak scale
Proton mass
Electron mass
16 o
rder
s of
mag
nitu
de
1 GeV
102 GeV
This hierarchy is not too sensitive to Standard Model parameters
Happens because the Standard Model effectively captures the physics that sets
the proton mass
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Energy
1018 GeV Quantum gravity
Proton mass
1 GeV
The QCD Hierarchy is dynamically generated
u u
d
p+
++q
q
g
q q
g
QCD is strong at long distances
Strength determines size of proton (and its mass)
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Standard Model
Measured Parameter
Values
Predictions
Hierarchy problem:
The electroweak hierarchy is extremely sensitive to the input parameter values
Our model for physics is ‘not robust’Suggests that essential features are missed
Higgs boson breaks electroweak symmetry
Generates mass for W and Z bosons
Energy
1018 GeV
10�3 GeV
Quantum gravity
Weak scale
Proton mass
Electron mass
16 o
rder
s of
m
agni
tude
1 GeV
102 GeV
→ No explanation for Higgs bath in Standard Model
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Energy
1018 GeV Quantum gravity
Weak scale
16 o
rder
s of
m
agni
tude
102 GeVHiggs boson breaks
electroweak symmetryGenerates mass for W and
Z bosons
Standard Model
Measured Parameter
Values
Predictions
Hierarchy ‘problem’ a matter of taste
Maybe our world is just ‘finely tuned’
...most physicists don’t like this idea
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• Gravity
• Neutrino mass
• Cosmology• Dark matter• Dark energy (related to gravity?)• Matter/antimatter asymmetry
• Hints of Grand Unification
• ‘Hierarchy problem’
Why?
Beyond the Standard Model
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Many ideas for physics beyond the Standard Model
We will focus on one:
Supersymmetry
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Coleman-Mandula Theorem
‘Space-time and internal symmetries cannot be combined in any but a trivial way’
As with most ‘No-Go’ theorems, this one has a loophole Supersymmetry
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Supersymmetry is an extension of space-time symmetry (rotations etc) that mixes
particles of different spin
Electron Selectron
e� e�
� �
e� e�
e�e�
Supersymmetry ⇒ same interaction strength
Spin
1
2
fermion
Spin 0 boson
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Supersymmetry → Each Standard Model particle has a ‘superpartner’
Top quarkStop squark
Gluon Gluino
Electron SelectronTuesday, May 1, 12
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Minimal Supersymmetric Standard Model (MSSM)
Howard GeorgiSavas
Dimopoulos
Don’t see superpartner particles (yet)
→ Supersymmetry not an exact symmetry of nature
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Minimal Supersymmetric Standard Model (MSSM)
Supersymmetry is broken at some energy scale
Superpartner particle masses are around
mSUSY
mSUSY
No fundamental reason to expect mSUSY low enough
to be accessible in near future
If mSUSY ⇠ 100 GeV can address many problems
of Standard Model...
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Hierarchy ProblemEnergy
1018 GeV Quantum gravity
Weak scale
102 GeVHiggs boson breaks
electroweak symmetryGenerates mass for W and
Z bosons
16 o
rder
s of
m
agni
tude h h
t
t
h h
t~
Top loop
Stop loopSuperpartner contributes with opposite sign
Contribution of high energy tops canceled by high energy stops
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h h
t
t
h h
t~
Top loop
Stop loop
General Rule:
Supersymmetry causes ‘infinities’ to ‘cancel’
Reduces sensitivity to ultra-short distance physics
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Hierarchy ProblemEnergy
1018 GeV Quantum gravity
Weak scale
102 GeVHiggs boson breaks
electroweak symmetryGenerates mass for W and
Z bosons
16 o
rder
s of
m
agni
tude
Supersymmetry also gives natural mechanism for generating Higgs potential at the scale mSUSY
can explain electroweak hierarchy if mSUSY ⇠ 100� 1000 GeV
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Dark Matter
Natural symmetry that distinguishes particles and their superpartners
‘R-parity’ + -
conserved in all interactions and decays
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Dark Matter
If we make a superpartner particle in a collision...
+ -...it may decay
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Dark Matter
If we make a superpartner particle in a collision...
+ -...it may decay
t
Standard Model Particles
Superpartner particle
...but there must be at least one superpartner particle in the final state
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Dark Matter
t
Standard Model Particles
Superpartner particle
⇒ the Lightest Superpartner Particle (LSP) is stable!
Dark Matter Candidate!
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Supersymmetry and Grand Unification
Inverse electromagnetic coupling
Inverse weak interaction coupling
Inverse QCD coupling
F. Wilczek, Nature 433, 239
Grand Unification?
e�
e�e�e�
� � �
+
+.......Tuesday, May 1, 12
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Supersymmetry and Grand Unification
Inverse electromagnetic coupling
Inverse weak interaction coupling
Inverse QCD coupling
F. Wilczek, Nature 433, 239
Grand Unification?
e�
e�e�e�
� � �
+
+.......
e�e�
e�
e�+
with supersymmetry
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Supersymmetry and Grand Unification
Inverse electromagnetic coupling
Inverse weak interaction coupling
Inverse QCD coupling
Grand Unification?
F. Wilczek, Nature 433, 239
With supersymmetry at ~100 GeV, unification looks much better
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Supersymmetry is hypothetical but if present at ~100 GeV it can:
• Solve the ‘hierarchy problem’ by generating mass for the W and Z bosons
• Provide a natural dark matter candidate of the right mass
• Improve the picture of Grand Unification
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Searching for Supersymmetry
Minimal Supersymmetric Standard Model (MSSM) has
~125 parameters
Very complicated to do a systematic search of entire parameter space
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Top quarkStop squark
Gluon Gluino
Electron Selectron
Minimal Supersymmetric Standard Model (MSSM)
‘Hidden Sector’
Supersymmetry Broken Here
‘Messenger Sector’
What we see depends mostly on this
Gravity, Charged Messengers, etc
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Top quarkStop squark
Gluon Gluino
Electron Selectron
Minimal Supersymmetric Standard Model (MSSM)
‘Hidden Sector’
Supersymmetry Broken Here
‘Messenger Sector’
What we see depends mostly on this
Gravity, Charged Messengers, etc
Supersymmetry breaking fields
Messengers
Standard Model Particles
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Simplest framework: mSUGRA
Replace125 parameters with 5
1. Gaugino mass2. Scalar mass3. Trilinear ‘A’ coupling4. Tan β5. Sign(µ)
Spin
1
2
partners of force carriers
Scalar partners of quarks, electrons, etc
Interaction between squarks/sleptons and ganginos
Higgs sector parameters
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Experiments must think about many possibilities
Signatures vary widely
Supersymmetry not found yet but too soon to rule out
Mass scale [TeV]-110 1 10
RPV
Long
-live
d pa
rticle
sDG
Third
gen
erat
ion
Inclu
sive
sear
ches
klm ≈ ijmHypercolour scalar gluons : 4 jets, ,missTEMSUGRA/CMSSM - BC1 RPV : 4-lepton + ,missTEBilinear RPV : 1-lep + j's + µRPV : high-mass eτ∼GMSB : stable
SMP : R-hadrons (Pixel det. only)SMP : R-hadronsSMP : R-hadrons
Stable massive particles (SMP) : R-hadrons
±
1χ∼AMSB : long-lived
,missTE) : 3-lep + 01χ∼ 3l → 0
2χ∼±
1χ∼Direct gaugino (
,missTE) : 2-lep SS + 01χ∼ 3l → 0
2χ∼±
1χ∼Direct gaugino (
,missTEll) + b-jet + → (GMSB) : Z(t~t~Direct
,missTE) : 2 b-jets + 01χ∼ b→1b~ (b~b~Direct
,missTE) : multi-j's + 01χ∼tt→g~ (t~Gluino med.
,missTE) : 2-lep (SS) + j's + 01χ∼tt→g~ (t~Gluino med.
,missTE) : 1-lep + b-j's + 01χ∼tt→g~ (t~Gluino med.
,missTE) : 0-lep + b-j's + 01χ∼bb→g~ (b~Gluino med.
,missTE + γγGGM :
,missTE + j's + τGMSB : 2-
,missTE + j's + τGMSB : 1-
,missTE + SFGMSB : 2-lep OS,missTE) : 1-lep + j's + ±χ∼q q→g~ (±χ∼Gluino med. ,missTEPheno model : 0-lep + j's + ,missTEPheno model : 0-lep + j's + ,missTEMSUGRA/CMSSM : multijets + ,missTEMSUGRA/CMSSM : 1-lep + j's + ,missTEMSUGRA/CMSSM : 0-lep + j's +
3 GeV)± 140 ≈ sgm < 100 GeV, sgmsgluon mass (excl: 185 GeV (2010) [1110.2693]-1=34 pbL
massg~1.77 TeV (2011) [ATLAS-CONF-2012-035]-1=2.1 fbL
< 15 mm)LSPτ mass (cg~ = q~760 GeV (2011) [1109.6606]-1=1.0 fbL
=0.05)312λ=0.10, ,311λ mass (τν
∼1.32 TeV (2011) [1109.3089]-1=1.1 fbL
massτ∼136 GeV (2010) [1106.4495]-1=37 pbL
massg~810 GeV (2011) [ATLAS-CONF-2012-022]-1=2.1 fbL
masst~309 GeV (2010) [1103.1984]-1=34 pbL
massb~294 GeV (2010) [1103.1984]-1=34 pbL
massg~562 GeV (2010) [1103.1984]-1=34 pbL
) < 2 ns, 90 GeV limit in [0.2,90] ns)±
1χ∼(τ mass (1 < ±
1χ∼118 GeV
(2011) [CF-2012-034]-1=4.7 fbL
) < 170 GeV, and as above)01χ∼(m mass (±
1χ∼250 GeV (2011) [ATLAS-CONF-2012-023]-1=2.1 fbL
)))02χ∼(m) + 0
1χ∼(m(2
1) = ν∼,l~(m), 02χ∼(m) = ±
1χ∼(m, 0
1χ∼) < 40 GeV, 0
1χ∼(m mass ((±
1χ∼170 GeV (2011) [1110.6189]-1=1.0 fbL
) < 230 GeV)01χ∼(m mass (115 < t~310 GeV (2011) [ATLAS-CONF-2012-036]-1=2.1 fbL
) < 60 GeV)01χ∼(m mass (b~390 GeV (2011) [1112.3832]-1=2.1 fbL
) < 200 GeV)01χ∼(m mass (g~830 GeV (2011) [ATLAS-CONF-2012-037]-1=4.7 fbL
) < 210 GeV)01χ∼(m mass (g~650 GeV (2011) [ATLAS-CONF-2012-004]-1=2.1 fbL
) < 150 GeV)01χ∼(m mass (g~710 GeV (2011) [ATLAS-CONF-2012-003]-1=2.1 fbL
) < 300 GeV)01χ∼(m mass (g~900 GeV (2011) [ATLAS-CONF-2012-003]-1=2.1 fbL
) > 50 GeV)01χ∼(m mass (g~805 GeV (2011) [1111.4116]-1=1.1 fbL
> 20)β mass (tang~990 GeV (2011) [ATLAS-CONF-2012-002]-1=2.1 fbL
> 20)β mass (tang~920 GeV (2011) [ATLAS-CONF-2012-005]-1=2.1 fbL
< 35)β mass (tang~810 GeV (2011) [ATLAS-CONF-2011-156]-1=1.0 fbL
))g~(m)+0χ∼(m(2
1) = ±χ∼(m) < 200 GeV, 0
1χ∼(m mass (g~900 GeV (2011) [ATLAS-CONF-2012-041]-1=4.7 fbL
)01χ∼) < 2 TeV, light q~(m mass (g~940 GeV (2011) [ATLAS-CONF-2012-033]-1=4.7 fbL
)01χ∼) < 2 TeV, light g~(m mass (q~1.38 TeV (2011) [ATLAS-CONF-2012-033]-1=4.7 fbL
)0m mass (large g~850 GeV (2011) [ATLAS-CONF-2012-037]-1=4.7 fbL
massg~ = q~1.20 TeV (2011) [ATLAS-CONF-2012-041]-1=4.7 fbL
massg~ = q~1.40 TeV (2011) [ATLAS-CONF-2012-033]-1=4.7 fbL
Only a selection of the available mass limits on new states or phenomena shown*
-1 = (0.03 - 4.7) fbLdt∫ = 7 TeVs
ATLASPreliminary
ATLAS SUSY Searches* - 95% CL Lower Limits (Status: March 2012)
Tuesday, May 1, 12
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SUMMARY•The Standard Model is very successful but not complete
• No viable dark matter candidate• No explanation of electroweak hierarchy
•Hierarchy problem is a question about ‘robustness’• Calculations in Standard Model get infinities from short distance physics• We don’t know about physics at short distances...introduce ‘model
parameters’ (particle masses and interactions) to parametrize this ignorance• Hierarchy problem: physics we see very sensitive to parameter choices
• Model not robust -- missing essential physics
•Supersymmetry solves many problems of Standard Model• Lightest SuperPartner (LSP) is a dark matter candidate• Cancellation of infinities removes strong dependence on short distance physics• Dynamically generates Higgs bath that gives mass to all particles• Improves Unifcation picture -- very suggestive
•Very challenging to look for supersymmetry at the LHCTuesday, May 1, 12