sally dawson, bnl standard model and higgs physics fnal lhc school, 2006
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Sally Dawson, BNL Standard Model and Higgs Physics FNAL LHC School, 2006. Introduction to the Standard Model Review of the SU(2) x U(1) Electroweak theory Experimental status of the EW theory Constraints from Precision Measurements Searching for the Higgs Boson - PowerPoint PPT PresentationTRANSCRIPT
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Sally Dawson, BNLStandard Model and Higgs PhysicsFNAL LHC School, 2006
Introduction to the Standard Model Review of the SU(2) x U(1) Electroweak theory Experimental status of the EW theory Constraints from Precision Measurements
Searching for the Higgs Boson The Importance of the TeV Scale
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Lecture 1
Introduction to the Standard Model Just the SU(2) x U(1) part of it….
Some good references: Chris Quigg, Gauge Theories of the Strong, Weak,
and Electromagnetic Interactions Michael Peskin, An Introduction to Quantum Field
Theory David Rainwater, Sally Dawson, TASI2006,
http://quark.phy.bnl.gov/~dawson/tasi06
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Tevatron LHC LHC Upgrade ILC
2006 2007 2012
Collider Physics Timeline
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What We Know The photon and gluon appear to be
massless The W and Z gauge bosons are heavy
MW=80.404 0.030 GeV MZ =91.1875 0.0021 GeV
There are 6 quarks Mt=172.5 2.3 GeV (171.4 2.1 GeV, ICHEP 2006) Mt >> all the other quark masses
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What We Know There appear to be 3 distinct neutrinos
with small but non-zero masses The pattern of fermions appears to
replicate itself 3 times Why not more?
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Abelian Higgs Model Why are the W and Z boson masses non-zero?
U(1) gauge theory with single spin-1 gauge field, A
U(1) local gauge invariance:
Mass term for A would look like:
Mass term violates local gauge invariance We understand why MA = 0
AAF
FFL
4
1
)()()( xxAxA
AAmFFL 2
2
1
4
1
Gauge invariance is guiding principle
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Abelian Higgs Model, 2 Add complex scalar field, , with charge – e:
Where
L is invariant under local U(1) transformations:
)(4
1 2
VDFFL
2222)(
V
ieAD
)()(
)()()()( xex
xxAxAxie
AAF
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Abelian Higgs Model, 3
Case 1: 2 > 0 QED with MA=0 and m= Unique minimum at =0
)(4
1 2
VDFFL
2222)(
V
ieAD
By convention, > 0
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Abelian Higgs Model, 4 Case 2: 2 < 0
Minimum energy state at:
2222)( V
22
2 v
Vacuum breaks U(1) symmetry
Aside: What fixes sign (2)?
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Abelian Higgs Model, 5 Rewrite
L becomes:
Theory now has: Photon of mass MA=ev Scalar field h with mass-squared –22 > 0 Massless scalar field (Goldstone Boson)
hve vi
2
1
)nsinteractio,(2
1
22
1
24
1 2222
h
hhhAAve
evAFFL
and h are the 2 degrees of freedom of the complex Higgs field
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Abelian Higgs Model, 6 What about mixed -A propagator?
Remove by gauge transformation
field disappears
We say that it has been eaten to give the photon mass field called Goldstone boson This is Abelian Higgs Mechanism This gauge (unitary) contains only physical particles
ev
AA1'
)(2
1
24
1 22
hVhhAAve
FFL
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Higgs Mechanism summarized
Spontaneous breaking of a gauge theoryby a non-zero VEV of a scalar field results in the disappearance of a Goldstone boson and its transformation into the longitudinal component of a massive gauge boson
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R gauges
)1(2222
AA Mk
kkg
Mk
i
22hMk
i
22AMk
i
Mass of Goldstone boson depends on =1: Feynman gauge with massive =0: Landau gauge: Unitarity gauge
Higgs, h
Goldstone Boson, , or Faddeev-Popov ghost
Gauge Boson, A
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Non-Abelian Higgs Mechanism
Vector fields Aa(x) and scalar fields i(x) of
SU(N) group
L is invariant under the non-Abelian symmetry:
a are group generators, a=1…N2-1 for SU(N)
22 )()(
),())((
V
VDDL
jijaa
i i )1(
N
.
.
.1
For SU(2): a=a/2
aa AigD
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Non-Abelian Higgs Mechanism, 2 In exact analogy to the Abelian case
a0 0 Massive vector boson + Goldstone boson
a0=0 Massless vector boson + massive scalar field
...)()(...
...)()(...))((
002
2
0
bai
bi
a
bai
bi
a
AAg
AAgDD
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Non-Abelian Higgs Mechanism, 3 Consider SU(2) example Suppose gets a VEV:
Gauge boson mass term
Using the property of group generators, a,b=ab/2 Mass term for gauge bosons:
a
a
AigD2
v
0
2
1
baba AA
vvgD
0,0
2
1 22
aamass AA
vgL
8
22
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Standard Model Synopsis
Group: SU(3) x SU(2) x U(1)
Gauge bosons: SU(3): G
i, i=1…8 SU(2): W
i, i=1,2,3 U(1): B
Gauge couplings: gs, g, g SU(2) Higgs doublet:
ElectroweakQCD
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SM Higgs Mechanism Standard Model includes complex Higgs SU(2)
doublet
With SU(2) x U(1) invariant scalar potential
If 2 < 0, then spontaneous symmetry breaking Minimum of potential at:
Choice of minimum breaks gauge symmetry Why is 2 < 0?
043
21
2
1
i
i
22 )( V
v
0
2
1
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More on SM Higgs Mechanism Couple to SU(2) x U(1) gauge bosons
(Wi, i=1,2,3; B)
Gauge boson mass terms from:
BYg
iWg
iD
VDDL
ii
S
22
)()()('
...)()()(8
...
...0
))((,08
1...)(
232222122
BggWWgWgv
vBggWBggWvDD bbaa
Justify later: Y=1
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More on SM Higgs Mechanism
With massive gauge bosons:
W = (W
1 W2) /2
Z 0 = (g W3 - g'B )/ (g2+g'2)
Orthogonal combination to Z is massless photon
A 0 = (g' W3+gB )/ (g2+g'2)
MW=gv/2MZ=(g2+g'2)v/2
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More on SM Higgs Mechanism, 2
Weak mixing angle defined
Z = - sin WB + cosWW3
A = cos WB + sinWW3
MW=MZ cos W
2222sincos
gg
g
gg
gWW
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More on SM Higgs Mechanism
Generate mass for W,Z using Higgs mechanism Higgs VEV breaks SU(2) x U(1)U(1)em
Single Higgs doublet is minimal case Just like Abelian Higgs model
Goldstone Bosons Before spontaneous symmetry breaking:
Massless Wi, B, Complex After spontaneous symmetry breaking:
Massive W,Z; massless ; physical Higgs boson h
z,
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Fermi Model Current-current interaction of 4 fermions
Consider just leptonic current
Only left-handed fermions feel charged current weak interactions (maximal P violation)
This induces muon decay
JJGL FFERMI 22
hceJ elept
2
1
2
1 55
e
e GF=1.16637 x 10-5 GeV-2
This structure known since Fermi
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Now include Leptons
Simplest case, include an SU(2) doublet of left-handed leptons
Right-handed electron, eR=(1+5)e/2, is SU(2) singlet No right-handed neutrino
eeL
L
L
)1(2
1
)1(2
1
5
5
*Standard Model has massless neutrinos—discovery of non-zero neutrino mass evidence for physics beyond the SM
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Leptons, 2
Couple gauge fields to leptons
LiiL
RRleptons
Wg
iYBg
ii
eYBg
iieL
22
2
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Leptons, 3
Write in terms of charged and neutral currents
emZleptons JeAJZJWJWgkineticL )(
RWRLWLLLW
Z
LL
emem
eeeeJ
eJ
eeQJ
22 sin2sin21cos2
12
1
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Muon decay
Consider e e
Fermi Theory:
e
e
• EW Theory:
eF uuuugGie
2
1
2
122 55
eW
uuuugMk
ige
2
1
2
11
255
22
2
For k<< MW, 22GF=g2/2MW2
For k>> MW, 1/E2
e
e
W
22
2
2
1
82 vM
gG
W
F
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Parameters of SU(2) x U(1) Sector
g, g',, Trade for: =1/137.03599911(46) from (g-2)e and
quantum Hall effect GF=1.16637(1) x 10-5 GeV-2 from muon lifetime MZ=91.18750.0021 GeV Plus Higgs and fermion masses
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Now Add Quarks to Standard Model Include color triplet quark doublet
Right handed quarks are SU(2) singlets, uR=(1+5)u, dR=(1+5)d
With weak hypercharge YuR=4/3, YdR=-2/3, YQL=1/3
iL
iLL d
uQ
Qem=(I3+Y)/2
i=1,2,3 for color
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Quarks, 2
Couplings of charged current to W and Z’s take the form:
uWddWu
gLWqq )1()1(
2255
qZRLq
gL qq
WZqq )1()1(
cos4 55
Wemq
Wemq
QR
QIL
2
23
sin2
sin2
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What about fermion masses?
Fermion mass term:
Left-handed fermions are SU(2) doublets
Scalar couplings to fermions:
Effective Higgs-fermion coupling
Mass term for down quark:
LRRLmmL
..chdQL RLdd
L
L d
uQ
..0
),(2
1chd
hvduL RLLdd
v
M dd
2
Forbidden by SU(2)xU(1) gauge invariance
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Fermion Masses, 2
Mu from c=i2* (not allowed in SUSY)
For 3 generations, , =1,2,3 (flavor indices)
0
c
hcuQL RcLu v
M uu
2
,
..2
)(chdduu
hvL RLdRLuY
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Fermion masses, 3
Unitary matrices diagonalize mass matrices
Yukawa couplings are diagonal in mass basis Neutral currents remain flavor diagonal Not necessarily true in models with extended Higgs
sectors
mRdR
mRuR
mLdL
mLuL
dVduVu
dUduUu
• Charged current:m
LdumLLL dVUuduJ
)(
2
1
2
1
CKM matrix
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Basics Four free parameters in gauge-Higgs sector
Conventionally chosen to be =1/137.0359895(61) GF =1.16637(1) x 10-5 GeV -2
MZ=91.1875 0.0021 GeV MH
Express everything else in terms of these parameters
22
22
2
1282
WZ
WW
F
MM
MM
gG
Predicts MW
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Inadequacy of Tree Level Calculations Mixing angle is predicted quantity
On-shell definition cos2W=MW2/MZ
2
Predict MW
Plug in numbers: MW predicted =80.939 GeV
MW(exp) =80.404 0.030 GeV
Need to calculate beyond tree level
2
22
ZFWW MG
cs
1
2
2
2
4112
ZFFW
MGGM
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Modification of tree level relations
rMG
WW
F
1
1
sin2 22
W
WtFt mGr
2
2
2
2
sin
cos
28
3
Contributions to r from top quark and Higgs loops
6
5ln
224
112
2
2
2
W
hWFh
M
MMGr
r is a physical quantity which incorporates 1-loop corrections
Extreme sensitivity of precision measurements to mt
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Where are we with Z’s?
At the Z pole: 2 x 107 unpolarized Z’s at LEP 5 x 105 Z’s at SLD with Pe 75%
What did we measure at the Z? Z lineshape , Z, MZ
Z branching ratios Asymmetries
W+W- production at 200 GeV Searches for Zh
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e+e-ff
)1(2
222
zs
QNffee
dz
d fc
zLRLR
zLRLR
MMs
sMGN
ffee
ffee
ZZZ
ZFc
))((2
)1)()((
)(64 2222
22222
2222
42
zLRLRzLRLRMMs
MsMQNffeeffee
ZZZ
ZZfc
2)1(
)(
)( 22222
22
exchange
-Z interference
Changes sign at pole
Z exchangez=cos
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e+e-ff (#2)
Assume energy near the Z-pole, so include only Z exchange
zLRLRzLRLRMMs
sMGNffee
dz
dffeeffee
ZZZ
ZFc ))((2)1)()(()(64
2222222222222
42
Contributes only to asymmetries if acceptance is symmetric
))((24
22222
42
ffeeZ
ZFcpeakZ LRLR
MGNffee
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Z cross section
Number of light neutrinos: N=2.98400.0082
Z
MZ
Requires precise calibration of energy of machine
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TevatronTevatron running pp at s=2 TeV
Scheduled to shut down 2009-2010
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Z’s at the Tevatron
Z-production Amplitude has pole at MZ
Invariant mass distribution of e+e-
eeZqq
222Zeeee Mppm
2)(
1
ee pp
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W’s at the Tevatron
Consider We Invariant mass of the leptonic system
Missing transverse energy of neutrino inferred from observed momenta
Can’t reconstruct invariant mass Define transverse mass observable
2222 )( zezTeTee ppppEEm
)cos1(22
222
TeTTeT
TeTTeTT
EEpp
ppEEm
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Statistics enough to best LEP 2
W Mass Measurement
Location of peak gives MW
Shape of distribution sensitive to W
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World Average for W mass
Direct measurements (Tevatron/LEP2) and indirect measurements (LEP1/SLD) in excellent agreement
Indirect measurements assume a Higgs mass
LEPEWWG home page, 2006
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Data prefer light Higgs
Low Q2 data not included Doesn’t include atomic parity
violation in cesium, parity violation in Moller scattering, & neutrino-nucleon scattering (NuTeV)
Higgs fit not sensitive to low Q2
data Mh< 207 GeV
1-side 95% c.l. upper limit, including direct search limit
(Mh < 166 GeV ICHEP 2006) Direct search limit from e+e-Zh
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Top Quark mass pins down Higgs Mass
Data prefer a light Higgs
2006
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Understanding Higgs Limit
1118.0
)(085.0
1172
525.0102761.0
)(5098.0
100ln008.0
100ln0579.0364.80
2)5(
2
Zs
tZhad
hhW
M
GeV
MM
GeV
M
GeV
MM
MW(experiment)=80.404 0.030
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sin2w depends on scale
Moller scattering, e-e-e-e-
-nucleon scattering Atomic parity violation in
Cesium
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We have a model….And it works to the 1% level
Gives us confidence to predict the future!
Electroweak Theory is Precision Theory
2006