Download The Standard Model and its Simple Extensions

The Standard Model (and small extensions)
Klaus Mönig
• Introduction
• Strong interactions
• Electroweak interactions
• Mixing in the quark sector
• The neutrino sector
• The Standard Model of cosmology
• Conclusions
CTEQ School 2006
The Standard Model-1
Klaus Mönig
Introduction
• The Standard Model describes the interactions of elementary particles
• Four interactions:
– electroweak (in principle two separate forces)
– strong
– gravitation
however gravitation cannot be included in the model
• The model describes successfully basically all data
• However the model has many problems why we think it cannot be the
final theory
• Every test of the Standard Model should thus be seen as an attempt
to find its limits
CTEQ School 2006
The Standard Model-2
Klaus Mönig
Gauge theories
Elementary particle physics is successfully described by local gauge theories
• Take a gauge group G
• The interactions (gauge bosons) are given by the generators of the group
• The fermions are arranged in multiplets on which the gauge bosons act
• The gauge group of the Standard Model: SU(3) × SU(2) × U(1)
SU(3): strong interactions
SU(2) × U(1): electroweak interaction
Gravity is not included in the Standard Model
• In this scheme all particles have to be massless
• Masses can be generated breaking the symmetry
CTEQ School 2006
The Standard Model-3
Klaus Mönig
Fermions in the Standard Model
• Fermions exist in 3 families
• The families are identical apart from their masses
• Leptons have only electroweak interaction
• Quarks also have strong interactions
Leptons
Flavour
mass
( GeV)
νe
< 1 · 10−8
e
0.000511
νµ
< 0.0002
µ
0.106
ντ
< 0.02
τ
1.78
CTEQ School 2006
Q
0
−1
0
−1
0
−1
Quarks
Flavour mass
Q
( GeV)
u
∼ 0.003 2/3
d
∼ 0.006 −1/3
c
1.3
2/3
s
∼ 0.1 −1/3
t
175
2/3
b
4.3 −1/3
The Standard Model-4
Klaus Mönig
Electroweak gauge bosons:
charged current:
W±
mW ∼ 80 GeV
neutral current:
Z
γ
mZ ∼ 90 GeV
mγ = 0
QED
Gauge group: SU (2) × U (1) with couplings g, g 0
Fermions exist as left handed doublets and right handed singlets
 +
W
SU (2)  W 0  couple to left handed doublets only
W−
U (1) B couples to left and right-handed fermions
Up to here all particles are massless!
CTEQ School 2006
The Standard Model-5
Klaus Mönig
The Higgs mechanism
Complex Higgs doublet Φ with potential V (Φ) = λ(Φ∗Φ − v 2/2)2
0
• Minimum at Φ(0) =
v
• v = 246 GeV precisely known from muon decay
Gauge bosons acquire mass through coupling at Φ, absorbing 3 degrees
of freedom in the longitudinal gauge boson components
Higgs mechanism requires one neutral scalar particle H 0,
Fermion masses are generated by ad hoc Yukawa couplings of the fermions
to the Higgs field
The fermion mass term mΨLΨR couples left- and right handed particles
CTEQ School 2006
The Standard Model-6
Klaus Mönig
W 0 and B mix keeping photon massless:
= W 0 cos θW − B sin θW
= W 0 sin θW + B cos θW
with g sin θW = g 0 cos θW = e
Z
γ
Resulting interactions:
W ±: stay purely left handed
γ: left-right symmetric vector coupling (Maxwell equations)
Z: complicated mixture of left- and right-handed coupling to restore the
SU (2) × U (1) prediction
g
gA =
2
g
gV = (1 − 4|q| sin2 θW )
2
(Neutrinos: electrically neutral ➟ Z coupling pure left-handed ➟ right
handed neutrinos would be sterile)
CTEQ School 2006
The Standard Model-7
Klaus Mönig
What do we know about the Higgs?
• In the Standard Model only one free parameter left (m2H = 2λv 2 )
• LEP searches: mH > 114 GeV
• Higgs couples to mass ⇒ partial widths proportional to particle masses
• Coupling to massless particles via loops
CTEQ School 2006
The Standard Model-8
Klaus Mönig
The hierarchy problem
A “final” theory should be valid up to the Planck scale:
p
mPl = h̄c/GN ≈ 1019 GeV
If the parameters (couplings, masses) are defined at the high scale, they
receive radiative corrections running them down to the low scale
Radiative corrections in the SM: ∆mH ∼ mPl
However Higgs mechanism works only if m√H < 1 TeV
(e.g. WW → WW violates unitarity at s = 1.2 TeV without a light
Higgs)
⇒ enormous fine-tuning required!
CTEQ School 2006
The Standard Model-9
Klaus Mönig
Strong interactions
Strong interactions act only on quarks
Gauge group: SU(3)
• Quarks have to come in triplets of 3 “colours”
10
3
10
2
R
J/ψ
ψ(2S)
Z
φ
ω
10
ρ
ρ
1
10
S
-1
GeV
1
10
10
2
• Exchange particles: 8 massless gluons
CTEQ School 2006
The Standard Model-10
Klaus Mönig
Running of coupling constants
Due to vacuum polarisation effects the coupling “constants” depend on
the momentum transfer
Gauge-boson-fermion interaction: screening The coupling constants fall
with falling energy
Gauge-boson self-interactions: enhancement The coupling constants rise
with falling energy
Electroweak interactions: well behaved at Q2 → 0 with O(10%) changes
between 0 and 100 GeV
Strong interactions: coupling diverges for Q2 → 0
• quarks exist only in colour neutral states: quark-antiquark (mesons), 3
(anti)quarks (baryons) (confinement)
• “free” quarks and gluons are visible at high energy (asymptotic freedom)
CTEQ School 2006
The Standard Model-11
Klaus Mönig
Verification of running is a strong test of the gauge structure of QCD
αs(µ)
0.3
0.2
0.1
0
CTEQ School 2006
1
10
µ GeV
The Standard Model-12
10
2
Klaus Mönig
Experimental tests of electroweak interactions
Gauge sector fully determined by three parameters: g, g 0, v
(In practise the three best measured parameters are used: α(0), GF, mZ)
Can test the model if more than three observables are measured
Expect one-loop correction to be of order α ∼ 1%
➟ have to be taken into account of precision better than that
• quantities get sensitive to other parameters (mt, mH...)
• model is tested at the quantum level
• sensitivity to physics at higher scales
CTEQ School 2006
The Standard Model-13
Klaus Mönig
Electroweak observables
• The fermion sector is completely known (neutrino masses are irrelevant
in this context)
• The W-mass is measured at LEP
and the TEVATRON
• Some other observables like
atomic parity violation or low
energy Moller scattering give
additional information
events / GeV
• α and GF are known with very good precision
• Many observables can be measured on the Z resonance
450
400
350
300
250
200
WW → qqlν
OPAL data
WW signal
WW mis-ID
ZZ
Z/γ
150
100
50
0
CTEQ School 2006
The Standard Model-14
60
80
100
(mqq+mlν)/2 (GeV)
Klaus Mönig
Observables on the Z resonance
Cross-section (pb)
The Z-mass is given by the peak of the resonance curve
10 5
Z
10 4
+ −
e e →hadrons
10 3
10 2
CESR
DORIS
+
WW
PEP
PETRA
KEKB
PEP-II
10
0
20
40
TRISTAN
60
SLC
LEP I
80
100
-
LEP II
120
140
160
180
200
220
Centre-of-mass energy (GeV)
CTEQ School 2006
The Standard Model-15
Klaus Mönig
• All other observables (partial, total widths, asymmetries) can be expressed in terms of the vector and axial vector couplings of the Z to
fermions
– axial vector coupling measures the total normalisation of the SU(2)
coupling constant
– vector coupling is mainly sensitive to the Z-γ mixing, i.e. the weak
mixing angle (v/a = 1 − 4Q sin2 θ)
SLD
L polarization
• Asymmetries measure the
interference of vector and
axial vector coupling
➟ ∝ A = v22va
+a2
CTEQ School 2006
tagged events
bb̄ asymmetry at SLD
tagged events
• Z partial widths: for numerical reasons basically
mainly sensitive to normalisation
cos θ thrust
The Standard Model-16
R polarization
cosθ thrust
Klaus Mönig
The structure of radiative corrections
Most Z-observables and mW can be described with three parameters:
• ∆ρ: total normalisation of the Z-fermion coupling
l : effective weak mixing angle
• sin2 θeff
• ∆r: Radiative corrections for mW
• (Only Zbb̄ couplings are slightly special because of the heavy top)
In the SM there are two independent contributions:
• A large term from isospin violation ∝ m2t − m2b
• A much smaller contribution ∝ log mH/mW
Reparameterisation:
• ε1 = ∆ρ (or S): absorbs the isospin violating corrections
• ε3 (or T): only sensitive to the logarithmic corrections
• ε2 (or U): constant in the SM and most extensions (only mW)
CTEQ School 2006
The Standard Model-17
Klaus Mönig
Electroweak fits
Measurement
(5)
∆αhad(mZ)
mZ [GeV]
ΓZ [GeV]
• All data are fitted simultaneously leaving mH (+...)
as free parameter
• The overall fit quality is
good: χ2/ndf = 17.8/13
• All observables agree individually with the SM prediction after the fit
0
σhad
[nb]
Rl
0,l
Fit
0.02758 ± 0.00035 0.02767
91.1875 ± 0.0021
91.1874
2.4952 ± 0.0023
2.4959
41.540 ± 0.037
41.478
20.767 ± 0.025
20.743
Afb
0.01714 ± 0.00095 0.01643
Rb
0.21629 ± 0.00066 0.21581
Al(Pτ)
Rc
0.1465 ± 0.0032
0.1722
0.0992 ± 0.0016
0.1037
0.0707 ± 0.0035
0.0742
0.923 ± 0.020
0.935
0.670 ± 0.027
0.668
Al(SLD)
0.1513 ± 0.0021
0.1480
0.2324 ± 0.0012
0.2314
mW [GeV]
80.404 ± 0.030
80.376
2.115 ± 0.058
2.092
mt [GeV]
172.5 ± 2.3
172.9
Ab
Ac
2 lept
sin θeff (Qfb)
ΓW [GeV]
0
CTEQ School 2006
The Standard Model-18
meas
fit
meas
−O |/σ
1
2
3
1
3
0.1480
0.1721 ± 0.0030
0,b
Afb
0,c
Afb
|O
0
2
Klaus Mönig
6
• (Of course the limit is only
valid within the SM)
0.02758±0.00035
0.02749±0.00012
4
∆χ2
• (This is perfectly consistent with SUSY)
∆α(5)
had =
5
• Within the Standard
Model the Higgs is predicted to be light
• A one sided 90% c.l. is
around 200 GeV
Theory uncertainty
2
incl. low Q data
3
2
1
0
Excluded
30
100
300
mH [GeV]
CTEQ School 2006
The Standard Model-19
Klaus Mönig
• The data can also be fitted 0.008
with ε1,2,3 (STU) as free
parameters
mt= 172.7 ± 2.9 GeV
mH= 114...1000 GeV
• This shows again the
agreement of the data
0.006
with the SM
ε1
mt
• However this allows also
the interpretation of the
beyond beyond the SM
• E.g. QCD-like technicolour
and a large part of the
parameter space for little
Higgs models can be excluded this way
CTEQ School 2006
0.004
mH
0.004
0.006
68 % CL
0.008
ε3
The Standard Model-20
Klaus Mönig
• The gauge boson couplings are uniquely
defined by the structure of the gauge
group
• A measurement of these couplings thus
probes the gauge structure itself
• The WWZ and WWγ are usually described and terms of 5 parameters where
only 3 can be measured independently at
LEP (no Z-γ separation)
• The measurements agree with the SM on
the few % level
• Hadron colliders can separate the Z and
the γ using WZ and Wγ final states, however the precision is at present not competitive
CTEQ School 2006
The Standard Model-21
λγ
0.2
0.15
LEP Preliminary
0.1
0.05
0
−0.05
−0.1
−0.15
−0.2
κγ
Gauge boson self couplings
0.9
1
1.1
g1Z
1.2
1.15
1.1
1.05
1
0.95
95% c.l.
68% c.l.
2d fit result
0.9
0.85
0.8
−0.1
0
0.1
λγ
Klaus Mönig
Unification of Gauge Couplings
Why do we have 3 (+1) forces in nature and not one?
• GUT theories assume one force at high scales which is broken down to
three forces at the GUT scale
• This requires the three coupling constants to meet at some point
• The precision measurements of the couplings show that this is not possible within in the SM
• Only when new
thresholds
are
introduced (Supersymmetry) gauge
coupling unification is possible
CTEQ School 2006
The Standard Model-22
Klaus Mönig
The quark sector
• Quarks “mix”, i.e. the mass eigenstates are not equal to the weak
eigenstates
• Per construction the mixing is only in the down-quark sector
• Mixing matrix:
→0
−
→
−
d = MCKM d
MCKM = Vij i = u, c, t j = d, s, b


2
λ λ3A(ρ − iη)
1 − λ2


2
λ
2
≈

−λ
1− 2
λ A
1
λ3A(1 − ρ − iη) −λ2A
(Wolfenstein parametrisation)
• The matrix contains one non-trivial complex phase
➟ CP violation
CTEQ School 2006
The Standard Model-23
Klaus Mönig
The importance of CP violation
• CP violation is a prerequisite to transform a symmetric universe into a
matter dominated universe (no antimatter!)
• We need at least three families to have CP violation in the SM
• However the CP violation in the SM is not sufficient to create the
observed baryon-antibaryon asymmetry
• CP violation has been discovered in the K 0 system long ago
• In recent years also many CP violating effects in the B system have
been measured
CTEQ School 2006
The Standard Model-24
Klaus Mönig
The matrix has to be unitary
• No FCNC
P
∗ = 0 m 6= n
• 6 unitarity triangles: i VimVin
∗ +V V∗ +V V∗ =0
• Most interesting one: VudVub
cd cb
td tb
(measures ρ, η)
• The area of the triangle defines CP violation
Amplitude
• Many
complementary
measurements:
B decay rates, BBmixing, CP violation in
K-system, several CP
violating observables in
B-system
L = 1.0 fb-1
CDF Run II Preliminary
data ± 1 σ
1.645 σ
2
95% CL limit 16.7 ps-1
-1
sensitivity
25.8 ps
data ± 1.645 σ
data ± 1.645 σ (stat. only)
0
-2
_
0
_
0
_
B0s → l+ Ds X, Bs → Ds π+, Bs → Ds π+ π+ π0
CTEQ School 2006
The Standard Model-25
10
20
30
∆ms [ps ]
-1
Klaus Mönig
1.5
• Each measurement defines
a region in the ρ − η plane
t CL
> 0.
1
∆md
da
sin 2β
95
CTEQ School 2006
lude
γ
• The combination gives an
accurate measurement of
the parameters
∆ms & ∆md
+0.047
ξ = 1.21 – 0.035 (hep-lat/0510113)
0.5
α
α
εK
η
each
• More important:
measurement is individually consistent with the
combination
➟ the CKM description
describes the quark sector
without the need for new
physics contributions
exc
excluded area has CL > 0.95
γ
0
β
|Vub/Vcb|
-0.5
εK
α
sol. w/ cos 2β < 0
(excl. at CL > 0.95)
-1
CKM
γ
fitter
EPS05+CDF
-1.5
-1
-0.5
0
0.5
1
1.5
2
ρ
The Standard Model-26
Klaus Mönig
The neutrino sector
Mass terms in the SM: mΨRΨL
SM: neutrinos are massless ➟ right handed neutrinos do not exist
Neutrino oscillations:
• atmospheric+accelerator neutrinos: νµ − ντ mix
• solar+reactor neutrinos: νe − νµ mix
• mixing frequency and amplitude:
2
∆m
P (ν1 → ν2) = sin2 θ sin2
4E
⇒ if νs oscillate, they have mass
⇒ oscillation experiments only sensitive to mass differences
• neutrinos must have mass!
CTEQ School 2006
The Standard Model-27
Klaus Mönig
φµτ (× 10 6 cm -2 s-1)
Quantitative results:
νe − νµ mixing
NC
φµ τ 68%, 95%, 99% C.L.
5
4
3
• Solar neutrino experiments show
that neutrinos transform away
from νe on their way to the earth
➟ mixing angle
SNO
2
φCC 68% C.L.
1
φES 68% C.L.
SNO
φNC 68% C.L.
SNO
SK
φES 68% C.L.
0
0
0.5
1
1.5
2
2.5
3
6
3.5
φe (× 10 cm s )
80
-2 -1
no−oscillation
accidentals
Events / 0.425 MeV
• Reactor experiment show µe disappearance at shorter distances
➟ mass difference
16
13
60
C(α,n) O
best−fit oscillation + BG
KamLAND data
40
20
0
0
CTEQ School 2006
BS05
φSSM 68% C.L.
6
The Standard Model-28
1
2
3
4
5
Eprompt (MeV)
6
7
8
Klaus Mönig
Combination gives precise measurement of both quantities
1.2×10−4
10−4
10−5
2
∆m2 (eV )
2
∆m2 (eV )
1×10−4
Solar
KamLAND
8×10−5
KamLAND+Solar fluxes
6×10−5
95% C.L.
95% C.L.
99% C.L.
99% C.L.
99% C.L.
99.73% C.L.
99.73% C.L.
99.73% C.L.
solar best fit
KamLAND best fit
10−1
1
10
4×10
−5
0.2
tan2 θ
CTEQ School 2006
95% C.L.
global best fit
0.3
0.4
0.5
0.6
0.7
0.8
tan2 θ
The Standard Model-29
Klaus Mönig
• Confirmed by accelerator experiment
1.2
1
0.8
0.6
0.4
0.2
0
1
10
10
10
2
L/E (km/GeV)
-2
10
3
10
4
2
– mixing angle maximal
– mass difference2 factor 100
larger than νe − νµ
1.4
2
• Precise measurements from atmospheric neutrinos (up/down νµ/νe
ratio
1.6
∆m (eV )
νµ − ντ mixing
Data/Prediction (null osc.)
1.8
99% C.L.
90% C.L.
68% C.L.
10
CTEQ School 2006
The Standard Model-30
-3
0.7
0.75
0.8
0.85
2
sin 2θ
0.9
0.95
1
Klaus Mönig
• Mixing matrix pretty different from quark sector
• Still two possibilities for the hierarchy
• ν2 > ν1 known from matter effects in the sun
CTEQ School 2006
The Standard Model-31
Klaus Mönig
The nature of neutrinos
• In principle neutrinos can be normal Dirac particles in the SM
• Tritium endpoints measurements: mν < 2 eV
• Difficult to explain the large mass difference in the SM (but we don’t
understand masses anyway)
• Alternative: neutrinos are Majorana particles
small masses follow naturally from the seesaw mechanism
The seesaw mechanism
• Neutrinos are mixture of a Dirac particle with mass mD = O(v) and
a Majorana particle with mass M = O(mGUT)
• Mass matrix
M=
0 mD
mD M
Smaller eigenvalue: mν ≈ m2D /M : right size
CTEQ School 2006
The Standard Model-32
Klaus Mönig
How can the Majorana nature be proven?
Neutrinoless double β decay:
n
p
W
ν
n
W
e
e
p
• Lepton number violation requires Majorana nature
• Helicity flip requires neutrino mass
• Current limits from 76Ge →76 Se ee: mν < 0.36 eV if Majorana particle
CTEQ School 2006
The Standard Model-33
Klaus Mönig
The SM of cosmology or why the SM cannot be all
• The universe originates from an initial singularity ≈ 15 billion years
ago
• Since then it cools and expands
• Many features like light element production are described very well by
this model
• However there are some
features that don’t fit together in the SM
– from the anisotropy of
the cosmic microwave
background it follows
that the geometry is flat
CTEQ School 2006
The Standard Model-34
Klaus Mönig
- The matter needed for this
cannot be all baryonic (dark
matter)
- There are many more pieces
of evidence for dark matter:
rotation curves around galaxies, patterns of galaxy clusters,
further features of cosmic microwave spectrum
- From far supernova explosions
one sees that the expansion of
the universe is accelerating
- This requires that there exists
a dark energy or cosmological
constant
CTEQ School 2006
The Standard Model-35
Klaus Mönig
Supernova C os m ology P rojec t
3
Composition of the universe:
K nop et al. (2 0 0 3 )
Spergel et al. (2 0 0 3 )
A llen et al. (2 0 0 2 )
No Big Bang
2
Supernovae
1
ΩΛ
C M B
expands forever
ll y
a
u
t
n
e
v
e
s
e
s
p
la
l
o
ec
r
0
C lus ters
t
fla
en
op
-1
clo
se
d
0
1
2
3
ΩM
CTEQ School 2006
The Standard Model-36
Klaus Mönig
What do we know about dark matter?
• Weakly interacting particles of mass m = O(100 GeV)
• Dark matter cannot be accommodated in the Standard Model
• However several extensions contain a credible dark matter candidate
(Supersymmetry, universal extra dimensions, little Higgs)
What do we know about dark energy?
• No way to put dark energy into the SM
• Agreement at the loop level shows that the SM is more than an effective
theory
• Factor 1062 smaller than naive calculations (Higgs)
• No idea how to put dark energy into any future theory
CTEQ School 2006
The Standard Model-37
Klaus Mönig
Conclusions
• The Standard Model describes a vast amount of data with very good
precision
• (The neutrino masses may be the first experimental hint beyond the
SM)
• However the SM is unnatural (hierarchy problem)
• Dark matter definitely requires extensions of the SM
• Any new theory has to contain the SM as a low energy approximation
• Dark energy gives a hint that something is fundamentally ununderstood
in our description of subatomic physics
CTEQ School 2006
The Standard Model-38
Klaus Mönig