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Electroweak Physics
Mark Pitt Virginia Tech
Electroweak physics is a broad subject. I will limit these lectures to:
• Low energies/momentum transfers Q2 < 1 (GeV/c) 2
• Elastic scattering only (mostly e + N reactions but some + N and e + e)
These lectures will cover the majority of the electroweak physicsgoing on at electron accelerators in the nuclear physics category.
16th Summer School in Nuclear Physics
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Lecture 1
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N e
Z
N e
What are we going to cover?
e + N e + N N = nucleonElectromagnetic Form Factors(GE
p , GMp , GE
n , GMn )
• GEp , GM
p ratio• 2 photon physics
• improved knowledge of GEn
e + N e + N N = nucleonParity-violating electron scatteringNeutral Weak Form Factors(GE
Z,p , GMZ,p , GE
Z,n , GMZ,n , GA
e)
• Strange vector form factors• Nucleon's anapole moment
We will also cover the experimental techniques unique to the parity-violating electron scattering types of experiments.
Low energy Standard Model Tests• Weak charge of the electron• Weak charge of the proton• Weak charge of the neutron
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http://lpsc.in2p3.fr/congres/pavi2004/
http://www.krl.caltech.edu/~subZ/meet/index.html
Some Useful Resource Material on this TopicGood recent review articles:
K.S. Kumar and P.A. Souder, Prog. Part. Nucl. Phys. 45, S333 (2000)D.H. Beck and B.R. Holstein, Int. J. Mod. Phys. E10, 1 (2001)D.H. Beck and R.D. McKeown, Ann. Rev. Nucl. Part. Sci. 51, 189 (2001)
And two very recent topical workshops (talks posted online at both sites)
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Outline of Lectures
1. Develop the formalism of parity-violating electron scattering with stops for:
• electromagnetic form factors• QCD and nucleon "strangeness"
2. Experimental aspects unique to all parity-violating electron scattering experiments
3. Review of experiments devoted to strange form factor measurements (including new results just reported last week)
4. Motivation for low energy Standard Model tests
5. Review of experiments devoted to low energy Standard Model tests
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Kinematics of Elastic Electron-Nucleon Scattering
invariant Lorentz sin'4
transfermomentum-4 squared - -
nucleon recoiling to transfer momentum-3 '
nucleon recoiling nsfer toenergy tra E'-E
22
2222
eEEQ
Qqq
ppq
N e qv
,E , p
E' , 'p
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Recall the Dirac Equation and Currents
0)( mi
0
0
10
01, 00
space 3,2,1 time,0
ej
0 j
Dirac equation for free electron:
0
where:
with:
leads to electron four-vector current density:
where the adjoint is:
satisfies the continuity equation:
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Bilinear Covariants and Their Symmetry Properties
11111Tensor
111Vector Axial
111Vector
111arPseudoscal
111Scalar
CTP
5
5
We describe physical processes through interacting currents need to construct most general form of currents consistent with Lorentz invariance
)44( form theof Terms
32105 where i
P: parity operator (spatial inversion)T: time reversalC: charge conjugation
Note: P (V*V) = +1 P (A*A) = + 1 P (A*V) = -1
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Relation Between Cross Sections and Matrix Elements
For a process A + B C + D
the differential cross section is
2
264
1M
p
p
sd
d
i
fcm
The physics is all in the matrix elementM
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Electromagnetic and Weak Interactions : Historical View
eeppeEMpEM
Q
eJ
Q
eJM
2
2, ,
2
2,
n e
pe-
eweakJ ,
NweakJ ,
p e
eEMJ ,
pEMJ ,
eeFnp
eweakF
Nweak GJGJM
, ,,
EM: e + p e + p elastic scattering
Weak: n e- + p + e neutron beta decay
Fermi (1932) : contact interaction, form inspired by EM
V x V
V x V
Parity Violation (1956, Lee, Yang; 1957, Wu): required modification toform of current - need axial vector as well as vector to get a parity-violatinginteraction
eeFnp
eweakF
Nweak GJGJM
55, ,, 11
(V - A) x (V - A)
Note: weak interaction process here is charged current (CC)
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But Zel'Dovich Suggests - What About Neutral Weak Currents ?
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The Neutral Current, Zel'Dovich continued
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Standard Model of Electroweak Interactions (1967)Weinberg-Salam Model (1967): electroweak - unified EM and weak SU(2) x U(1) gauge theory with spontaneous symmetry breaking fermions:Leptons: e-, e
-, - , + anti-particles
Quarks: u , d s , c b , t + anti-particles
gauge bosons:EM: (m = 0)weak: W+,- (mW = 80 GeV/c2) Z0 (mZ = 91 GeV/c2)
f ' f
Z0
f ' f
W+,-
f ' f electromagnetic interaction:charged fermions participate
charged current weak interaction:all fermions participate
neutral current weak :all fermions participate
Neutral weak currents first observed at CERN in 1973in reactions like
ee
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Feynman Rules for Calculating M in the Standard ModelThe fundamental parameter of the Standard Model is the weak mixing
angle - W
Feynman rules:
couplings weak and neticelectromag theare and wheresin geg
eW
W+,-
e
2
1
Q22
1
WMQ
5
22
g
Z022
1
ZMQ
5
cos2
f
Af
VW
ccg
- only couples to electromagnetic vector currentW, Z - couple to both weak vector and axial-vector currents
constant coupling Fermi theis8
2 :Note
~For
2
2
2,
2
2222
2,
2
2
2
2
WF
ZWEM
weakZ
ZWweakEM
M
gG
Me
Qg
M
MMQ
MQ
gM
Q
eM
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Electromagnetic e- p Elastic Scattering
2121 FFGFFG ME
NN
N uM
qiQFQFuNJN
2)()(|| 2
22
1
2
2
4 NM
Q
eepEMeEMpEM
Q
eJJ
Q
eJM
2
2,, ,
2
2,
From the Feynman rules, the matrix element is:
But the proton (unlike the electron) is not a point-like Dirac particle(need to introduce form factors to characterize its structure):
Dira
c
Pauli
e
MME G
GG
d
dM
d
d 2222
Mott
2 tan2
Another way to write the form factors is the Sachs definition:
The cross section for e-p elastic scattering is then given as:(Rosenbluth formula)
N e
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N
n
91.10)(
n
MG
eqG p
E
0)(
N
p
79.20)(
p
MG
Proton and Neutron EM Form Factors: Measurements
All follow (appear) to follow dipole form:
GpE (Q
2)
GpM (Q
2)
GnM (Q
2)
22 GeV 2 0~ Q
In Breit frame
Fourier transform yields spatial distribution
(R) = o exp(-R/Ro) where R o ~ 0.25 fm
E spatial charge distributionM spatial magnetization distribution
2
2
2
2
)GeV/(71.01
1
cQ
QGD
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NM
qiFFJ
221
Nucleon Spacelike (q2 < 0) Electromagnetic Form Factors
• 1960’s – early 1990’s : GpE , G
pM, Gn
E , Gn
M measured using Rosenbluth separation in e + p (elastic) and e + d (quasielastic):
• early 1990’s – present: Polarization observables and ratio techniques used
Sachs:
Dira
c
Pauli
e
MME G
GG
d
d
d
d 2222
Mott
tan2
2121 FFGFFG ME
||
2||
)/(
22 ......)......(
''''
A
MNe
A
MENe
dd
ME GPPGGPPGGd
dNeNeNeNe
unpol
2
2
4 NM
Q
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Nucleon Spacelike EM Form Factors, World Data - 1993
Knowledge of nucleon spacelike EM form factors in 1993:
GpE , G
pM, Gn
M follow dipole form GD = (1 + Q2/0.71)-2 at ~20% level
GnE ~ 0 (from quasielastic e-d data)
GpM/pGD Gn
M/nGD
GpE/GD
Relative error~ 2%
~ 10-20%
~ 5-10%
(GnE)2/G2
D
~ 50-100%
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Proton Electromagnetic Form Factor Ratio: GpE / G
pM
Older data: Rosenbluth separation
JLab 2000: M. K. Jones, et al.
JLab 2002: O. Gayou, et al.
using measurements of recoilproton polarization in Hall A with
e + p e + p
GEp
GMp
Pt
Pl
Ee Ee'
2Mtan
e
2
Difference in the spatial distribution of charge and magnetization currents in the proton
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Proton EM Form Factor Ratio Fp2 / F
p1 : pQCD predictions
pQCD prediction: As Q2
Fp1 1/Q4 Fp
2 1/Q6
Q2 Fp2 /F
p1 constant
not being reached yet
Ralston, et al. suggested different scaling behavior:
Fp2 /F
p1 1/Q
when quark orbital angular momentum included
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Comparison of Polarization Transfer and Rosenbluth Techniques
Recent work on Rosenbluth:
• reanalyis of old SLAC data (Arrington)• reanalysis of old JLAB data (Christy)• new "Super-Rosenbluth" measurement in Hall A (Segel, Arrington)
Conclusion:• No problem with Rosenbluth• No problem with polarization transfer
What about radiative corrections?Have 2-photon graphs been underestimatedin the past?
M. Vanderhaeghen and others say YES.
Using the GEp and GM
p from polarizationtransfer and improved calculation oftwo photon graphs, they can reproducethe Rosenbluth results.
Still an active area, more later if time...
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Neutron Electric Form Factor
GnE (Q
2)
Neutron Electric Charge Distribution
Data from:beam-target asymmetries
recoil polarizationin:
d (e, e’ n)
d (e, e’ n)
3He (e, e’ n)
at:
Mainz MAMIJefferson Lab
NIKHEFMIT-Bates
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ND3 DNP Polarized Target Apparatus of JLAB E93-026
MicrowaveInput
NMRSignal Out
Refrigerator
LiquidHelium
Magnet
Target(inside coil)
1° K
NMR Coil
To Pumps
7656A14-94
LN2LN2
To Pumps
B5T
e–Beam
Frequency
LiquidHelium
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Neutron’s Magnetic Form Factor GnM : Current Status
The most precise recent datacomes from ratio measurements:
(d(e,e’n))(d(e,e’p))
at NIKHEF/Mainz (Anklin, Kubon, et al.)and ELSA at Bonn (Bruins, et al.)
Large (8-10%) systematic discrepancy between the two data sets : likely due to error in neutron detection efficiency
Newest data: JLAB 95-001 (Xu, et al. 2000) 3He(e, e’) in Hall Aagrees with NIKHEF/Mainz data at Q2 = 0.1, 0.2 GeV2
more data exists (Q2 = 0.3 - 0.6 GeV2) but requires improved nuclear corrections (relativistic effects need to be included)
(JLAB 95-001)
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How can we get the nucleon form factors theoretically?
u
ud
u
us
s
valence quarks
“non-strange” sea (u, u, d, d) quarks
“strange” sea (s, s) quarks
proton
gluon
Quantum chromodynamics (QCD): believed to be the correct theory of strong interactions
• quarks (3 colors for each) inteacting via exchange of • gluons (8 types)
Until recently only stable objects were mesons (2 quark) and baryons (3 quark)
So we know the constituents of the proton, we have a quantum fieldtheory for their interaction why can't we solve for its structure?
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Calculation of Electron’s Magnetic Moment in QED
Quantum Electrodynamics (QED): theory of interacting electrons and photons
perturbation expansion in ~ 1/137
((g-2)/2)theory = (115965230 10) x 10-11
((g-2)/2)experiment = (115965219 1) x 10-11
agreement at 1 part in 108 level
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Non-perturbative QCD
Quantum Chromodynamics (QCD): theory of interacting quarks and gluons
For quarks inside the nucleon,typical momenta q ~ 0.3 GeV/c
s ~ 1 cannot solve perturbatively
(unlike QED where ~ 1/137)
Eventually, lattice QCD should providethe solution; In meantime we can measured well-defined nucleon properties that will serve as benchmarks for lattice QCD
s
QCD(running of s)
like the sea of strange quarks, for example!
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Do Strange Quarks Contribute to Nucleon Properties?
Deep inelastic scattering, contributions of constituents (partons) to total momentum of proton:
valence quarks: uV 21% dV 9%
sea quarks: (u+u) : 7% (d+d): 8% (s+s): 5% (c+c): 3% (b+b): 1%
gluons: 46%
gq JLsdu 2
1
2
1
03.01.010.030.0
ssdu
Proton spin:measured in polarized deep inelastic scattering
“Proton spin crisis”
+ s c + X +
+ +
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What role do strange quarks play in nucleon properties?u
ud
u
us
s
valence quarks
“non-strange” sea (u, u, d, d) quarks
“strange” sea (s, s) quarks
Momentum:
Spin:
Mass:
Charge and current:
Main goal of these experiments : To determine the contributions of the strange quark sea (s s) to the electromagnetic properties of the nucleon ("strange form factors").
(DIS) %4 ~ )(1
0
dxssx
proton
gluon
DIS) (polarized %10 ~ | | NssN
term)-( %30 ~ || NNssN
?? | | sM
sE GGNssN
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Deep exclusive scattering (DES):Generalized parton dist. (GPD):
fully-correlated quark distribution in coordinate and momentum space
The complete nucleon landscape - unified description
Elastic scattering:
transverse quark distributionin coordinate space
sME
dME
u
ME
GGG
GG
ME ,,
known yet not is factors form theseof
iondecompositflavor quark BUT
n p,for
measured- wellfactors
form magnetic and Electric
,
Deep inelastic scattering (DIS):
longitudinal quark distributionin momentum space
39% ~
4% ~
20% ~
37% ~
:)GeV 2 (Q
fractions momentum
nucleon Measured
22
glue
ss
dd
uu
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The question to be answered by this research:
How does the sea of strange quarks (ss pairs)
inside the proton (or neutron) contribute to its electromagnetic
properties:Gp
E , GpM, Gn
E , GnM ?
Let's measure the strange form factorsGs
E , GsM
directly and find out.
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JLAB “contracted” to understand nuclei
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• Measured precision of EM form factors in 0.1 - 1 GeV2 Q2 range ~ 2 - 4%• Projected precision of NW form factors in 0.1 - 1 GeV2 Q2 range ~ 10% from the current generation of experiments (for magnetic)
Z
N e
ZM
ZE
Z GGNJN , ||
neutral weak form factors
...|||| |:is vefunctionnucleon wa thewhere
uuudusuudsuudguudN
Nucleon form factors measured in elastic e-N scatteringNucleon form factors
• well defined experimental observables• provide an important benchmark for testing non-perturbative QCD structure of the nucleon
N e
ME GGNJN , ||
electromagnetic form factors
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eh
)scattering (elastic Ne
LR
LRA
2
e e pp
652
F 1010factorsform4
G-
Q
How to Measure the Neutral weak form factors
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Derive the Parity-Violating Asymmetry (hand-waving)
2*22)Re(2
: toalproportionsection Cross
NCNCEMEM
NCEM
MMMMM
MMM
NNCNNCNNCNEMNEM
eNCeA
eNCeVeeeeW
eNCeEMeeee
eEM
AVJVJ
AgVgJVQQJ,,,,,
,,5
2,,,
sin41
NNCeNCeA
NNCeNCeV
NNCeNCeA
NNCeNCeVNC
NEMeEMeEM
AAgAVgVAgVVgG
M
VVQQ
M
,,,,,,,,
,,2
22~
1~
2,,
,,,,,,,,2
2
*
24
...
)Re(2
NEMeEMe
NNCeNCeV
NEMeEMe
NNCeNCeA
NEMeEMeF
EM
PVNCEM
LR
LR
VVQ
AVgVVQVAgVVQQG
M
MMA
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Derive the Parity-Violating Asymmetry (hand-waving), cont.
2,,
,,,,,,,,2
24
NEMeEMe
NNCeNCeV
NEMeEMe
NNCeNCeA
NEMeEMeF
LR
LR
VVQ
AVgVVQVAgVVQQGA
unpol
AMEF
LR
LR AAAQGA
224
2
= Q2/4M2
= [1+2(1+)tan2(/2)]-1
)()()sin41()()()(
)()()(
222
222
22
QGQGAQGQGQA
QGQGA
MeAWA
MZMM
EZEE
Now how do the neutral weak form factors GEZ and GM
Z give usinformation about the strange form factors?
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NN
qqN u
M
qiFFuNqqN
q
2||
:as
currentquark given a with associated factors formnucleon theDefine
21
NN
N uM
qiQFQFuNJN
2)()(||
: throughfactors form Pauli and Diracnucleon thedefined weRecall,
22
21
qqqM
qqqE FFGFFG 2121
: thenare factors form Sachs The
First some notation
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STANDARDMODEL
COUPLINGS
sME
dME
uME
pZME
nME
pME GGGGGG ,,,
,,
,,
,, ,,,,
Invoke proton/neutron charge symmetry 3 equations, 3 unknowns
Neutral weak form factors strange form factors
psMEW
pdMEW
puMEW
pZME
Z
nsME
ndME
nuME
nME
psME
pdME
puME
pME
GGGGpJp
GGGGnJn
GGGGpJp
,,
2,,
2,,
2,,
,,
,,
,,
,,
,,
,,
,,
,,
sin3
41sin
3
41sin
3
81:||
3
1
3
1
3
2:||
3
1
3
1
3
2:||
Flavor decomposition of nucleon
E/M form factors:
ELECTROWEAKCURRENTS
i
iiZi
Z
iiii qqQJqqQJ
q qZ aZ
e 1 1 + 4 sin2W +1
u +2/3 1 8/3 sin2W 1
d 1/3 1 + 4/3 sin2W +1
s 1/3 1 + 4/3 sin2W +1
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Validity of charge symmetry breaking assumption
nsME
psME
nuME
pdME
ndME
puME GGGGGG
du,,
,,
,,
,,
,,
,,
Size of charge symmetry breaking effects in some n,p observables:
• n - p mass difference (mn - mp)/mn ~ 0.14%
• polarized elastic scattering n + p, p+n A = An - Ap = (33 ± 6) x 10-4
Vigdor et al, PRC 46, 410 (1992) • Forward backward asymmetry n + p d + 0 Afb ~ (17 ± 10)x 10-4 Opper et al., nucl-ex 0306027 (2003)
For vector form factors theoretical CSB estimates indicate < 1% violations (unobservable with currently anticipated uncertainties)
(Miller PRC 57, 1492 (1998) Lewis and Mobed, PRD 59, 073002(1999)
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Parity Violating Electron Scattering - Probe of Neutral Weak Form Factors
polarized electrons, unpolarized target
unpol
AMEF
LR
LR AAAQGA
224
2
2
e e pp
)()()sin41()()()(
)()()(
222
222
22
QGQGAQGQGQA
QGQGA
MeAWA
MZMM
EZEE
eA
sM
sE
GGG
At a given Q2 decomposition of GsE, Gs
M, GeA
Requires 3 measurements for full decomposition:
Forward angle e + p (elastic)Backward angle e + p (elastic)Backward angle e + d (quasi-elastic)
Strange electric and magnetic
form factors,+ axial form factor