Electroweak PhysicsMark 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 ν + 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

Lecture 1

γ

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

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)

Outline of Lectures

1. Develop the formalism of parity-violating electron scatteringwith stops for:• electromagnetic form factors• QCD and nucleon "strangeness"

2. Experimental aspects unique to all parity-violating electron scatteringexperiments

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

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

⎟⎠⎞

⎜⎝⎛

2θ

=

≡=

−==

eEEQ

Qqq

ppq

r

rrr

ν

ν

γ

N e qv r,E , p r

E' , 'p r

Recall the Dirac Equation and Currents

0)( =−∂ ψγ µµ mi

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−

=⎟⎟⎠

⎞⎜⎜⎝

⎛

−==

00

1001, 00

σσ

γγγγγ µr

rr

r

rr

space 3,2,1 time,0 == µµ

ψγψ µµ ej −=

0=∂ µµ j

Dirac equation for free electron:

0γψψ +≡

where:

with:

leads to electron four-vector current density:

where the adjoint is:

satisfies the continuity equation:

Bilinear Covariants and Their Symmetry Properties

( ) ( )( ) ( )

( ) ( ) ( ) ( ) 11111Tensor111Vector Axial111Vector111arPseudoscal111Scalar

CTP

5

5

−−−−−−+−−−−−−+−−+++

νµνµµν

µµµ

µµµ

ψσψψγγψ

ψγψψγψ

ψψ

We describe physical processes through interacting currents→ need to construct most general form of currents consistent with Lorentz invariance

ψψ )44( form theof Terms ×

32105 where γγγγγ i≡

P: parity operator (spatial inversion)T: time reversalC: charge conjugation

Note: P (V*V) = +1 P (A*A) = + 1 P (A*V) = -1

Relation Between Cross Sections and Matrix Elements

For a process A + B → C + D

the differential cross section is

2264

1 Mpp

sdd

i

fcm π

σ=

Ω

The physics is all in the matrix element M

Electromagnetic and Weak Interactions : Historical View

( ) ( )eeppeEMpEM

QeJ

QeJM ψγψψγψ µ

µµ

µ ⎟⎟⎠

⎞⎜⎜⎝

⎛−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−= 2

2, ,

2

2,

nνe

pe-

eweakJ ,µ

NweakJ ,µ

γ

pe

eEMJ ,µ

pEMJ ,µ

( ) ( )eeFnp

eweakF

Nweak GJGJM νµ

µµ

µ ψγψψγψ== , ,,

EM: e + p → e + p elastic scattering

Weak: n → e- + p + νe neutron beta decay

Fermi (1932) : contact interaction, form inspired by EM

V x V

V x VParity 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 νµ

µµ

µ ψγγψψγγψ 55, ,, 11 −−==

(V - A) x (V - A)

Note: weak interaction process here is charged current (CC)

But Zel'Dovich Suggests - What About Neutral Weak Currents ?

The Neutral Current, Zel'Dovich continued

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-, νe µ-, νµ τ- , ντ + anti-particlesQuarks: u , d s , c b , t + anti-particles

gauge bosons:EM: γ (mγ = 0)weak: W+,- (mW = 80 GeV/c2) Z0 (mZ = 91 GeV/c2)

γ

f 'f

Z0

f 'f

W+,-

f 'felectromagnetic 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 µµ νν

Feynman Rules for Calculating M in the Standard ModelThe fundamental parameter of the Standard Model is the weak mixing angle - θW

Feynman rules:

couplings weak and neticelectromag theare and wheresin gege

W =θ

W+,-γ

µγe

2

1Q 22

1

WMQ +

( )5

22γγγ µµ −

g

Z022

1

ZMQ +

( )5

cos2γγγ

θµµ f

Af

VW

ccg−

γ - only couples to electromagnetic vector currentW, Z - couple to both weak vector and axial-vector currents

constant coupling Fermi theis82 :Note

~For

2

2

2,

2

2222

2,

2

2

2

2

WF

ZWEM

weakZ

ZWweakEM

MgG

MeQg

MMMQ

MQgM

QeM

=

<<

+∝∝

Electromagnetic e- p Elastic Scattering

2121 FFGFFG ME +=τ−=

NN

N uM

qiQFQFuNJN ⎟

⎟⎠

⎞⎜⎜⎝

⎛+=

2)()(|| 2

22

1

νµνγ

µγγ

µ

σγ

2

2

4 NMQ

=τ

( ) ( )eepEMeEMpEM

QeJJ

QeJM ψγψ µ

µµ

µ ⎟⎟⎠

⎞⎜⎜⎝

⎛−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−= 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):

↑Dirac

↑Pauli

⎥⎦

⎤⎢⎣

⎡2θ

τ+τ+1

τ+⎟⎠⎞

⎜⎝⎛

Ωσ

=∝Ωσ e

MME GGG

ddM

dd 22

22

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)

γ

N e

N

n91.1

0)(µ−=µ=n

MG

eqG p

E+=

=0)(

N

p

79.20)(

µ=µ=p

MG

Proton and Neutron EM Form Factors: Measurements

All follow (appear) to follow dipole form:

GpE (Q2)

GpM (Q2)

GnM (Q2)

22 GeV 2 0~ −Q

In Breit frame

Fourier transform yields spatial distribution

ρ(R) = ρo 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

NMqi

FFJ221

νµνγ

µγγ

µ

σγ +=

Nucleon Spacelike (q2 < 0) Electromagnetic Form Factors

• 1960’s – early 1990’s : GpE , Gp

M, GnE , Gn

M measured using Rosenbluthseparation in e + p (elastic) and e + d (quasielastic):

• early 1990’s – present: Polarization observables and ratio techniques used

Sachs:

↑Dirac

↑Pauli

⎥⎦

⎤⎢⎣

⎡2θ

τ+τ+1

τ+⎟⎠⎞

⎜⎝⎛

Ωσ

=Ωσ e

MME GGG

dd

dd 22

22

Mott

tan2

2121 FFGFFG ME +=τ−=

4342144344214434421||

2||

)/(

22 ......)......(

''''

A

MNe

A

MENe

dd

ME GPPGGPPGGdd

NeNeNeNe

unpol

+++=Ωσ

+→++→+

⊥

⊥

Ωσ

2

2

4 NMQ

=τ

Nucleon Spacelike EM Form Factors, World Data - 1993

Knowledge of nucleon spacelike EM form factors in 1993:

→ GpE , Gp

M, GnM follow dipole form GD = (1 + Q2/0.71)-2 at ~20% level

→ GnE ~ 0 (from quasielastic e-d data)

GpM/µpGD Gn

M/µnGD

GpE/GD

Relative error~ 2%

~ 10-20%

~ 5-10%

(GnE)2/G2

D~ 50-100%

Proton Electromagnetic Form Factor Ratio: GpE / Gp

M

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

θe

2⎛ ⎝

⎞ ⎠

→ Difference in the spatial distribution of charge and magnetizationcurrents in the proton

Proton EM Form Factor Ratio Fp2 / Fp

1 : pQCD predictions

pQCD prediction: As Q2 → ∞

Fp1 ∝ 1/Q4 Fp

2 ∝ 1/Q6

Q2 Fp2 /Fp

1 → constant

→ not being reached yet

Ralston, et al. suggesteddifferent scaling behavior:

Fp2 /Fp

1 ∝ 1/Q

when quark orbital angular momentum included

Comparison of Polarization Transfer and Rosenbluth TechniquesRecent 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...

Neutron Electric Form Factor

GnE (Q2)

Neutron Electric Charge Distribution

n (u d d)

p (u u d) π (u d) _ _

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

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

LN 2LN 2

To Pumps

B5T

e–Beam

Frequency

LiquidHelium

Neutron’s Magnetic Form Factor GnM : Current Status

The most precise recent datacomes from ratio measurements:

σ(d(e,e’n))σ(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 nuclearcorrections (relativistic effects need to be included)

(JLAB 95-001)

How can we get the nucleon form factors theoretically?

uudu

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?

Calculation of Electron’s Magnetic Moment in QED

Quantum Electrodynamics (QED): theory of interacting electrons and photons

perturbation expansion in α ~ 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

Non-perturbative QCD

Quantum Chromodynamics (QCD): theory of interacting quarks and gluons

For quarks inside the nucleon,typical momenta q ~ 0.3 GeV/c

→ αs ~ 1 cannot solve perturbatively

(unlike QED where α ~ 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

αs

QCD(running of αs)

like the sea of strange quarks, for example!

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 ++∆+∆+∆=21

21

03.01.010.030.0

±−=∆±=∆+∆+∆

ssdu

Proton spin:measured in polarized deep inelastic scattering

→ “Proton spin crisis”

νµ + s → c + X + µ−

µ+ + νµ

What role do strange quarks play in nucleon properties?

uudu

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 ~ | | −>γ< 5 NssN

term)-( %30 ~ || σ π>< NNssN

?? | | sM

sE GGNssN →=>γ< µ

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 distribution

in coordinate space

sME

dME

u

ME

GGG

GG

ME ,, known yet not is factors form theseof

iondecompositflavor quark BUTn p,for

measured- wellfactors form magnetic and Electric

,

Deep inelastic scattering (DIS):longitudinal quark distribution

in momentum space

39% ~ 4% ~ 20% ~ 37% ~

:)GeV 2 (Qfractions momentum

nucleon Measured

22

glue

ss

dd

uu

ε

ε

ε

ε=

+

+

+

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.

JLAB “contracted” to understand nuclei

• 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 , || →>< µ

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 nucleonγ

N e

γγγµ ME GGNJN , || →><

electromagnetic form factors

Z

N e

2 +

γ

N e

γ

N e

2

Z

N e

2

γ

N e

Z

N e

∝σ

= eh+

+

)scattering (elastic Ne +

∝+−

=LR

LRAσσσσ

γ Ζ

γ2

e e pp

( ) 652

F 1010factorsform4G- −− −≈×

⎥⎥⎦

⎤

⎢⎢⎣

⎡

2πα=

Q

How to Measure the Neutral weak form factors

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

µµµµµ

µµµµµµµµ ψγγψψγψθψγψ

+==

+=++−===

[ ]NNCeNCeA

NNCeNCeV

NNCeNCeA

NNCeNCeVNC

NEMeEMeEM

AAgAVgVAgVVgGM

VVQQ

M

,,,,,,,,

,,2

22~

1~

µµµµµµµµ

µµ

+++

⎟⎟⎠

⎞⎜⎜⎝

⎛

( )( )2,,

,,,,,,,,2

2

*

24

...)Re(2

NEMeEMe

NNCeNCeV

NEMeEMe

NNCeNCeA

NEMeEMeF

EM

PVNCEM

LR

LR

VVQ

AVgVVQVAgVVQQG

MMMA

µµ

µµµµµµµµ

πα

σσσσ

+=

+=

+−

=

Derive the Parity-Violating Asymmetry (hand-waving), cont.( )

( )2,,

,,,,,,,,2

24

NEMeEMe

NNCeNCeV

NEMeEMe

NNCeNCeA

NEMeEMeF

LR

LR

VVQ

AVgVVQVAgVVQQGAµµ

µµµµµµµµ

πασσσσ +

=+−

=

unpol

AMEF

LR

LR AAAQGAσπασσ

σσ224

2 ++⎥⎦

⎤⎢⎣

⎡−=

+−

=

τ = Q2/4M2

ε = [1+2(1+τ)tan2(θ /2)]-1

)()()sin41()()()(

)()()(

222

222

22

QGQGAQGQGQA

QGQGA

MeAWA

MZMM

EZEE

γ

γ

γ

εθτ

θε

′−−===

Now how do the neutral weak form factors GEZ and GM

Z give usinformation about the strange form factors?

NN

qqN u

Mqi

FFuNqqN

q

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

2||

:as currentquark given a with associated factors formnucleon theDefine

21

νµν

µµ

σγγ

NN

N uM

qiQFQFuNJN ⎟

⎟⎠

⎞⎜⎜⎝

⎛+=

2)()(||

: throughfactors form Pauli and Diracnucleon thedefined weRecall,

22

21

νµνγ

µγγ

µ

σγ

qqqM

qqqE FFGFFG 2121

: thenare factors form Sachs The+=τ−=

First some notation

STANDARDMODEL

COUPLINGS

( ) ( )sME

dME

uME

pZME

nME

pME GGGGGG ,,,

,,

,,

,, ,,,, ⇔γγ

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,,

,,

,,

,,

,,

,,

,,

,,

,,

sin341sin

341sin

381:||

31

31

32:||

31

31

32:||

⎟⎠⎞

⎜⎝⎛ θ+−+⎟

⎠⎞

⎜⎝⎛ θ+−+⎟

⎠⎞

⎜⎝⎛ θ−=><

−−=><

−−=><

µ

γγµ

γγµFlavor decomposition of nucleon E/M

form factors:

ELECTROWEAKCURRENTS

∑∑ ==i

iiZi

Z

iiii qqQJqqQJ µµµ

γγµ γγ

qγ qZ aZ e −1 −1 + 4 sin2θW +1

u +2/3 1 − 8/3 sin2θW −1 d −1/3 −1 + 4/3 sin2θW +1 s −1/3 −1 + 4/3 sin2θW +1

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 + π0 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)

Parity Violating Electron Scattering -Probe of Neutral Weak Form Factors

polarized electrons, unpolarized target

unpol

AMEF

LR

LR AAAQGAσπασσ

σσ224

2 ++⎥⎦

⎤⎢⎣

⎡−=

+−

=

γ Ζ

γ2

e e pp

)()()sin41()()()(

)()()(

222

222

22

QGQGAQGQGQA

QGQGA

MeAWA

MZMM

EZEE

γ

γ

γ

εθτ

θε

′−−===

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 magneticform factors,

+ axial form factor