Download Experimental Tests of the Standard Model

Experimental Tests of the Standard
Model
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What is the Standard Model ?
How do we test it ?
Why do we think its incomplete ?
What are the next steps ?
The Standard Model
Goal: a theory which describes all of the fundamental constituents of nature and their
interactions with the minimum of assumptions and free parameters. Ultimately describe
all interactions over small distance scales and cosmological observations.
The Standard Model is our best attempt at this - assess how successfult in this lecture.
6 quarks, 6 leptons, 3 exchange bosons
+ antiparticles.
Two independent forces (electroweak and QCD).
19 free parameters: particle masses, mixing angles,
CP-violating term, couplings....
Consistent method of introducing interactions via
so-called gauge invariance and Feynam diagram
formalism.
The Standard Model assumes massless neutrinos
but this is easily fixed.
Barring neutrino oscillations, the Standard Model has never failed a single experimental test.
There is still one test left to pass - finding the Higgs boson.
History of accelerators in particle
physics
Top quark
Now 2010!
Traditionally collide hadron-hadron
(eg pp, pp...) and electron-positron.
+ ep (HERA)
W+-,Z0
3 light ν
gluon jets
Charm (J/ψ)
Colliders are successful tools
for discovering fundamental
particles and measuring their
properties.
Testing the Standard Model
Method
Colliders
Smaller
scale/”Desk-top”
experiments of
particle properties
Cosmological
experiments
High
Low
High
precision energy (< energy
GeV)
(<5
TeV)
Very
high
energy
>> TeV
x
x
x
x
x
Obs!
Very approximate classification.
Global tests combine information from all different methods.
The world’s major colliders
Name
Colliding
Particles
Approximate
beam energies
(GeV)
Location
Status
SLC
e -e +
50+50
Stanford,
USA
Ended
LEP
e -e +
100+100
CERN,
Geneva
Ended
Tevatron
pp
1000+1000
HERA
e -p
27.5 (e-) +
920 (p)
PEP-II
e -e +
9 (e-) +3.1
(e+)
Stanford, Current
USA
KEKB
e -e +
8 (e-) +3.5
(e+)
Tsukuba, Current
Japan
LHC
pp
7000+7000
Fermilab, Current
USA
DESY,
Hambur
g
CERN,
Geneva
Ended
Start
2009
Designing a collider: e++e- or hadron-hadron ?
e++e-
hadron-hadron
Clean – can study annihilation
reactions with no remnants of
colliding particles
Messy – remnants of
interacting hadrons remain
and influence
measurements.
Lower energy (for same radius)
due to synchrotron radiation.
LEP: ECM~200 GeV
Higher energy (for same
radius)
LHC: ECM~14000 GeV
Energy of e+,e- known.
Energy of q,q not known
(only have pdfs)
Fixed energy of e+,e- for a given
set of operator conditions
Variable energy of q,q for a
given set of operatorational
conditions
Best for detailed study
Best for discovery
Synchrotron
Technology used for modern day cyclic accelerators, eg LHC, HERA, Tevatron...
Principles of a synchrotron:
(1) Acceleration performed in RF-cavities
(2) Accelerated by time-varying electric field.
(3) Bending magnetic field increased after particles pass through cavity
Synchronised to keep same radius:
p
(16.02)
p increases and B increases
qB
Out of time particle orbits corrected by form of time-varying E -field.
A
B
∆R = 0
∆Cr > 0
r=
Eg Particle A arrives in time (synchronised).
Particle B arrives behind A and gets smaller momentum kick.
E
Particle C arrives ahead of A and gets bigger momentum kick
All particles move with v ∼ c. After "momentum kick" in rf cavity.
pA
(16.03)
qB
p
p
Particle B radius rB = B < rA (16.04) Similarly, rC = C > rA (16.05)
qB
qB
Particle A radius rA =
C
A
B
Time
at fixed
point in
rf cavity.
Limitations in energy of a synchrotron
p = qBr ⇒ several factors determining maximum momentum/energy.
(1) radius of curvature ; (2) magnetic field ; (3) synchrotron radiation (next slide).
Factor (1) is determined by construction costs and we'd obviously like it
to be big as possible but practically, accelerators have been restricted to
radii of several km. To illustrate the effects of factors (2) and (3) consider
particles accelerated around the LHC ring at CERN: 27km circumference.
Prior to LHC building for p + p (7+7 TeV) ring was used for LEP: e + + e− (45+45 GeV
and later 104+104 GeV)
Limitations
An accelerating charge loses energy by radiation.
Eg a particle with charge q moving around a circle of radius R.
Energy radiated per turn per particle:
4π q 2 β 3γ 4
∆E =
3ε 0 R
⇒γ =
E
m
(16.10)
m=mass, E =energy.
⇒ Relativistic particles ( β ∼ 1) of fixed energy ∆E ∝
1
m4
4
Synchrotron radiation losses for electron at energy E m p
⇒
= 4 ≈ 1013 (16.11)
Synchrotron radiation losses for proton at energy E
me
Large problem for electrons.
LEP at 45 GeV and ∼ 4km radius - 8 bunches of 4 × 1011 particles
⇒ 0.5MW lost via synchrotron radiation.
⇒ Synchrotron radiation limits beam energies for electron synchrotrons.
Magnetic field strength and size limits hadron synchrotrons.
DIS event at H1 detector at HERA ep collider
(4) Muon Tracker
µ−
(3) Had. Calo
e-
(30 GeV)
jet
p (820 GeV)
(1) Tracker
e-
(2) EM Calo
Generic example of a collider detector system.
Four major components:
(1) Inner tracking system (2) electromagnetic calorimeter
(3) Hadronic Calorimeter (4) Muon tracking system.
Collider tests of the SM
• Particle content
– 3 light neutrinos
– 3 quarks in a proton
• Electroweak unification
– the weak force isn’t weak at all
– precision calculations
There are three light neutrino species
e+ + e− → Z 0
Width and peak of Z 0 sensitive to
invisible decays :
Γ ( Z 0 → ν +ν ) = 0.166 GeV (calculated)
⇒ Nν = 3.00 ± 0.05
A stunning result demonstrating
the precision of particle physics
measurements and theory.
⇒ there aren't any heavy charged
leptons with associated light neutrinos.
⇒ from anomaly condition: if neutrinos are
massless there are only 3 generations of leptons
and quarks. We've already found the fundamental
fermions.
This is where we end the story.
Combined data
from LEP
experiments
Deep-inelastic scattering – probing the proton
An electron interacts with a proton and recoils at a
large angle after scattering off substructure within
the proton.
Modern day Rutherford scattering.
A more sophisticated view of proton structure
Traditionally view the proton as comprising:
2 up and 1 down quark. This is naive.
Valence
quarks
The up and down quarks are "valence quarks".
From the uncertainty principle exchanged gluons can fluctuate
into qq pairs of any flavour (sea quarks):
uu , dd , ss , cc , bb , tt
Lifetime τ ∼
1
(11.21) ⇒ heavy quark content: cc , bb , tt negligible!
mq
⇒ Expect that up, down and strange quarks form the structure of
the proton as seen in DIS interactions.
Non-strange
sea quarks
Strange sea
quarks
electron-nucleon cross section
2

dσ
α2
1  2 θ 
2
2 θ  Q
2
=
 cos   F2 ( x, Q ) + sin   2 F1 ( x, Q )  (11.17)
dE ' d Ω 4 E 2 sin 4 θ ν 
2
 2  xm p

2
F1 ( x, Q 2 ) , F2 ( x, Q 2 ) are "structure functions".
F2 ( x ) = ∑ eq2 xq ( x ) + eq2 xq ( x ) (11.18)
q
sum extends over all flavours of quarks in the proton.
Eg q = u, d ..
q ( x ) dx = average number of quarks of type q with
momentum fraction in range x to x + dx
1
1

F2p ( x ) − F2n ( x ) = x  uvp ( x ) − d vp ( x ) 
3
3

Subtract off the messy sea quarks - we should be
left with the momentum distribution of the valence quarks.
They should peak at x ~
1
.
3
When the weak force become stronger
Compare electromagnetic and weak forces for Q 2 >> M W2 .
Consider the following deep-inelastic scattering processes at HERA collider:
(a) e − + p → e − + X and (b) e − + p → ν e + X .
e-
e-
νe
e-
γ,Z0
W-
p
p
(a) proceeds via em and weak (b) proceeds via weak only.
Very rough order of magnitude estimate:
2 2
g
dσ
(a)
2
Amplitude for (a)
Q2
dQ 2
≈
∼
2
dσ
Amplitude for (b)
gW2
(b)
dQ 2
Q 2 + M W2
2
(13.01)
For Q 2 >> M W2 expect the two processes to become comparable in size.
Electromagnetic and weak force
strength
As expected, for Q 2 > M W2 the cross
sections for electromagnetic and weak
processes are of similar strength.
νe
Data from the HERA electron-proton
collider.
Note that the Standard Model calculations
cover several orders of magnitude in energy.
M W2 ∼ 6400 GeV 2
Smaller scale/”desk top”
experiments
• Anomalous magnetic moments
• Electric dipole moments
• Mass measurements
Anomalous magnetic moments
Dirac equation implies that for every spin
(a) a corresponding spin
1
particle there is
2
1
antiparticle
2
(b) two spin states
Spin and antiparticles arises as a consequence of treating quantum mechanics relativistically
e Intrinsic magnetic moment of elementary particle: µ = g
S (1.23)
2mc
Prediction of Dirac equation for electrons: g = 2
Experiment g ≈ 2.002..
g −2
= (1159652180.7 ± 0.3) × 10−12
2
g −2
Dirac prediction + quantum corrections for e − :
= (1159652153.5 ± 28 ) ×10−12
2
Precision experimental result:
Quantum electrodynamics is "the best theory we've got!"
The Muon g – 2 Experiment
q  g −2
ωa = 
B
m 2 
Shoot in polarised muons and measure Larmor rotation of spin
Brookhaven Lab. USA
Results
• The average of the Muon anomaly is
– aμ = 11659208(6) × 10-10
A lot of people are still excited by this.
11659181(8) × 10-10
Symmetries
Fundamental discrete symmetries:
Charge conjugation Cˆ :
Particle ⇔ antiparticle
p +π − → n +π +
≡ p +π + → n +π −
Parity Pˆ :
r → −r
Is the mirror image of a reaction possible/same rate ?
Time invariance Tˆ
t → −t
Could we be able to tell if a reaction was being played "backwards in time"?
C , P, T are violated and we don't know why.
Interesting because they CP-violating processes treat matter and antimatter
differently -> matter/antimatter asymmetry.
CPT is always respected.
CPT symmetry
ˆ ˆ ˆ operator turns a particle into its antiparticle, inverts space and
The CPT
reverses time.
ˆ ˆ ˆ |ψ (r , t ) >=| ψ (− r , −t ) > (8.10) for particle (antiparticle) a (a )
CPT
a
a
ˆ ˆ ˆ is a good symmetry ⇒ CPT
ˆ ˆ ˆ , Hˆ  = 0.
If CPT


Take simple case of a particle at rest.
ˆ ˆ ˆ ˆ | ψ (r , t ) >= m CPT
ˆ ˆ ˆ | ψ (r , t ) >= m | ψ (−r , −t ) > (8.11)
CPTH
a
a
a
a
a
ˆ ˆ ˆ ˆ | ψ (r , t ) >= Hˆ | ψ (−r , −t ) >= m | ψ (−r , −t ) > (8.12)
HCPT
a
⇒ ma = ma
a
a
a
(8.13)
Proof valid for stable particles - similar derivation possible for decaying particles
CPT symmetry implies a particle and an antiparticle have the same mass!
Tests and consequences of CPT invariance
Consistent particle and anti-particle
masses imply CPT symmetry.
mK 0 = K 0 | H | K 0 ,mK 0 = K 0 | H | K 0
| mK 0 − mK 0 |
mK 0 + mK 0
< 10−18
(current experimental limit)
+ CPT invariance implies particles and
anti-particles have the same lifetime.
τ µ −τ µ
(τ
+
−
µ+
+τ µ −
)
< 10-4 (current experimental limit)
+ CPT invariance also implies that if CP
and T are violated then there must be
at least 3 quark generations.
u
d
( )
( ) ( )
c
s
t
b
If CPT is violated ”all hell breaks loose”
P,T-violation from neutron electric dipole moment
If a, eg neutron, possesses
a permanent non-zero electric dipole
moment then this would violate T and P.
Good test of the SM.
CP Lear Experiment
0
0
0
0
Compare rates for the two processes K → K and K → K
CP/T-reversal transformations .
CPLEAR Experiment at CERN (pp interactions)
Consider two strong reactions pp → K0 (S =1)K− (S = −1)π + , pp → K 0 (S = −1)K+ (S =1)π −
Identify if a K 0 or K 0 was produced by looking for the presence of K − or K +
in one of the reactions.
Observe the decay of that particle and see if it ended life as a K 0 or K 0
by looking for an e + or e − in one of the following decays.
π−
d
π+
e+
νe
u
d
u
W+
d
s
K0
eW-
d
s
K0
νe
CP-Lear Experiment
• Measurement made of an asymmetry AT
(Probability of K 0 → K 0 ) − (Probability of K 0 → K 0 )
AT =
(Probability of K 0 → K 0 ) + (Probability of K 0 → K 0 )
= (6.6 ± 1.6) ×10-3 (integrated over time 20τ s )
• K0 K0 and K0 K0 do not occur at the
same rate
• First direct measurement of T-violation.
• Also CP violation
• Result and experiment to be discussed
(8.05)
The Standard Model
• The standard model is fantastically
predictive
• There is no unambiguous evidence that it
fails and overwhelming evidence that it
works.
• It is the most precisely tested theory in the
history of physics.
• But it has problems
The Higgs boson
The missing particle in the Standard Model. Explains mass generation of
the fundamental particles.
The Higgs mechanism is a way of explaining why, in an apparently unified
electroweak theory, the W +− and Z 0 are heavy and the γ is massless.
Some consequences:
A spin-0 massive boson, the Higgs particle H 0 , is required.
A Higgs field pervades space: fermions interacting with the field acquire mass.
A fermion with mass m f can also couple to the Higgs boson with strength g Hff .
 mf 
g Hff = 2 gW 
 (15.01)
m
 W
Couplings to other particles, with strength proportional to particle mass.
How do we look for the Higgs ?
How is it produced and how does it decay ?
At LEP: e + + e − → H 0 + Z 0
208 GeV centre-of-mass energy
Sensitive to Higgs masses up to ∼ 120 GeV.
Production mechanism
ina
m
Do
b
0
H →b+b
bb
ec
nt d
ay
Observation of a Higgs ?
An excess of events was seen at mass ~115 GeV but reanalysis of
data and rigorous statistical calculation of significance means it is
impossible (and stupid) to conclude a Higgs was seen.
Lower mass limit MH > 113.5 GeV (15.02)
Where is the Higgs ?
Excluded by direct search.
Most likely Higgs mass value from fits to
measured electroweak quantities in the
Standard Model.
The Higgs is either just around the corner or
nature is more complicated than we suppose.
Problems of the Standard Model
A subjective selection of three open areas in particle physics about which the Standard Model has nothing to say.
(i) Cosmology: Dark matter.
22% of universe's energy budget in the form of "dark matter".
Current evidence suggests that WIMPs: electrically neutral and weakly interacting
massive particles with masses 1 ↔ 10 TeV may be responsible ( ∼ LHC energies)
(ii) Forces: unification and gravity
Is there hope for a theory which unifies all of the fundamental forces or at least
the strong, em and weak forces ? Why is gravity weak until the Planck mass
(the hierarchy problem) ?
(iii) Properties of particles: electric charge quantisation
Why do we never observe particles with charge, eg, 1.5234e ?
(iv) What is the origin of CP-violation. Does it have anything to do with the
matter-antimatter asymmetry ?
If the ultimate aim is a theory of everything which predicts particles, forces and
cosmological measurements from a single principle/equations then solutions to
one of the above problems should address in some way the other problems.
*There's loads more, eg neutrino masses, dark energy etc.
but we'll take (i), (ii) and (iii) and (iv) as opportunities to show how a problem is
defined and solutions proposed.
Speculation strategy
We have few answers but that doesn't mean we can't ask sensible questions.
(1) At which energies can we expect that the Standard model will not
describe subatomic particle interactions ?
(2) In which areas is the Standard Model incomplete and which
theories have been proposed address these problems ?
How well can we localise a particle ?
To what precision can we know the position of
a particle, eg electron ?
In quantum mechanics the position can be known
to infinite accuracy if we accept we have no knowledge
of its momentum.
Eg from basic quantum mechanics: Heisenberg's microscope.
1
Resolution in position ∆x ∼ λ ∼
(2.36) ; λ = probing photon wavelength.
pγ
pγ =photon momentum ∼ ∆px maximum change in momentum in x-direction of particle.
⇒ ∆x∆px ∼ 1 (2.12)
Above picture assumes reaction: γ + e − → γ + e −
Quantum field theory changes this picture. If pγ > 2me (me =electron particle)
⇒ kinematically feasible reaction: γ + e− → γ + e− + e− + e+
Two identical particles in final state. No longer possible to say anything about electron
position for pγ > 2me .
⇒ Fundamental limitation on knowledge of position: ∆x ≥∼
1
(15.03)
2m
Gravity
From general relativity: any object of mass m contained within its Scharzschild radius leads to a
gravitational singularity (black hole): Scharzschild radius : rs = 2Gm.
G = Gravitational constant.
Quantum description of nature implies that
a particle position be known to accuracy: λC =
2π
.
m
However, for λC < rc the particle is contained within
such a small size that a gravitational singularity
occurs.
The quantum prediction of a particle localised to
a certain distance must be invalid if that localisation
is taking place inside a black hole :).
⇒ (naively) quantum gravity becomes important at: rc = λC ⇒ 2Gm =
2π
π
⇒m=
(15.05)
m
G
1
= 1.2 ×1019 GeV (15.06) (drop the π )
G
The Standard Model must fail for masses and energies > Planck mass and a theory of quantum
gravity is needed.
Formally define the Planck mass ≈
Eg strong force becomes weak at short distances (<1fm)
⇒ asymptotic freedom.
measurements
The coupling constants vary with momentum transfer
(or distance)
1/coupling
Other possible energy scales
E
Electromagnetic
Weak
~GUT scale
Strong
Log(Momentum transfer, Q(GeV) )
 ( 33 − 2 N f )
 Q
α s ( Q ) = α s ( M Z ) 1 +
α s ( M Z ) ln 
6π

 MZ


 
−1
(12.05)
Couplings appear to unify for Q ∼ 1016 GeV.
⇒ Grand unified theories (GUTs) unify em, weak and strong forces
(to come).
Speculation strategy
We have few answers but that doesn't mean we can't ask sensible questions.
(1) At which energies can we expect that the Standard model will not
describe subatomic particle interactions ?
Quantum gravity effects must play a role for masses and energies at and
above the Planck scale ( ∼ 10
19
GeV). The GUT scale ( ∼ 1016 GeV) looks
a promising energy for "new physics" to appear.
(2) In which areas is the Standard Model incomplete and which
theories have been proposed address these problems ?
Supersymmetry
Every Standard Model has a supersymmetry partner.
Symmetry between bosons and fermion
Quarks (fermions) ↔ Squarks (bosons) ; W , Z , γ , g (bosons) ↔ W , Z , γ, g (fermions)
Symmetry is broken otherwise SM and SUSY particles (sparticleS) would have the
same mass.
SM and SUSY particles have different R-parity. Conservation of R-parity stops SUSY
sparticles decaying to SM particles.
R=(-1) (
3 B − L)+2 S
= +1 SM particles
(15.07)
= -1 SUSY partner particles.
B=baryon number, L=lepton number, S =Spin quantum number.
Why look for SUSY ?
Many reasons for looking for SUSY, amongs them...
(1) It predicts a dark matter candidate: i.e. a WIMP with mass ∼ TeV.
Neutralino: χ 0 a mixed state of SUSY partners of the Higgs, Z and γ .
(2) Unification of the couplings is more exact if SUSY sparticles exist.
Can develop SUSY grand unified theories (GUTs) which unify the electromagnetic,
Standard Model
EElectromagnetic
Weak
1/coupling
1/coupling
weak and strong forces.
Standard Model+SUSY
Electromagnetic
Weak
Strong
Strong
Log(Momentum transfer, Q(GeV) )
Log(Momentum transfer, Q(GeV) )
SUSY
Simulation CMS
experiment.
Missing transverse momentum
SM
SUSY
Grand Unified Theories
Incorporate strong, electromagnetic and weak forces into a GUT.
Simplest model: SU(5) (Georgi-Glashow).
Introduce new heavy exchange bosons X and Y : mass ∼ 1016 GeV.
Prediction of proton decay.
Violation of lepton and baryon number.
Eg p → π 0 + e +
Predictions for lifetime τ ∼ 1030 years.
Current limits (SuperK- lecture) τ >∼ 1033 years.
Other GUTS predict τ > 1033 years.
GUTs also predict heavy magnetic monopoles m ∼ 1016 GeV
and explain charge quantisation.
precision experiments: proton decay
Super kamiokande: neutrino oscillation experiment
11,200 PMTs 50,000 tonnes of ultra-pure
water, 1000m underground in the
Kamioka Mine
Super kamiokande: use data to look for proton decay events
Extra spatial dimensions
Original ideas on extra dimensions from T. Kaluza and O. Klein (1921).
Several different models incorporating extra dimensions on the market
today.
Large Extra Dimensions.
Hierarchy problem → gravity is weak since it
propagates in extra dimensions (bulk) and we see
a diluted form of it in our 3+1 dimension world (brane).
Gravitational potential V ( r ) ∼
1
r n +1
n = number of extra dimensions.
(15.08) where r < R
R = distance scale for interactions at which the effects of
extra dimensions are observed. n ≥ 2 ⇒ R <∼ 1 mm (15.09)
In general, many extra dimensions theories often predict "new" heavy
particles with masses ∼ TeV and provide dark matter candidates.
Micro Black Holes at the LHC
In general, when two particles pass
each other with enough energy, a micro
black hole can be formed.
For three spatial dimensions, gravity is
too weak. With extra dimensions gravity
becomes stronger, micro black holes
can be created.
"Normal" black hole: size ∼ km,
mass ∼ msun , temperature ∼ 0.01K, τ ∼ ∞
"Micro" blackhole: size ∼ 10 −18m, mass ∼ 1 TeV,
temperature ∼ 1016K, τ ∼ 10−27 s (evaporate through
Hawking radition.)
The world won't end when we turn on the LHC.
Electric charge quantisation
Maybe its better not to be too ambitious and just focus on one specific problem.
Electric charge quantisation.
Why is electric charge always meaured in integer multiples of the elementary
charge e ?
Why are the electron and proton charges the same (barring a sign) ?
The best limits state:
qelectron + q proton
qelectron
< 10−20 (15.10)
Is there any way to accommodate electric charge quantisation within
quantum mechanics ?
Speculation strategy
We have few answers but that doesn't mean we can't ask sensible questions.
(1) At which energies can we expect that the Standard model will not
describe subatomic particle interactions ?
Quantum gravity effects must play a role for masses and energies at and
above the Planck scale ( ∼ 10
19
GeV). The GUT scale ( ∼ 1016 GeV) looks
a promising energy for "new physics" to appear.
(2) In which areas is the Standard Model incomplete and which
theories have been proposed address these problems ?
Dark matter, hierarchy problem, force unification, charge quantisation
(to name but four)
SUSY, extra dimensions, magnetic monopoles are just some of the things
we've been speculating..But this is a game - we need data!
So how close are we to a unified theory of all the
forces ?
At present string theory offers the best hope. It is the most promising
candidate theory for quantum gravity.
However, its been the most promising theory for over 20 years now...
Hadron masses can be calculated using a picture of hadrons
as excitations of string. This formed part of the early ideas which led to
string theory.
Point-like particles are tiny quantised one-dimensional strings.
Extra dimensions and supersymmetry accommodated within string theory.
Extremely challenging to come up with a quantitative prediction from string
theory which can be tested.
Time will tell.
Summary
• Higgs discovery would be confirmation of
the Standard Model
• Standard Model is incomplete
• A range of proposed solutions exist which
postulate the existence of ”new” particles
which could be ”around the corner” at LHC
energies.