Parity-Violation with Electrons: Theoretical Perspectives

M.J. Ramsey-Musolf

PV: Past, Present, & Future

1970’s SLAC DIS Standard ModelAtomic PV sin2W ~ 10%

1980’s Mainz 8Be PV eq couplingsMIT 12C ~ 10%

Prehistory

PV: Past, Present, & Future

2000’s SLAC Moller Standard Model & beyondJLab QWeak sin2W < 1%APV Anapole moment

JLab GAN

Mainz HWI (S=0): dA

VVCS: An

1990’s MIT GsE,M ~ few %

JLab GA & rad correctionsMainz n(r)APV sin2W ~ 1%

Anapole moment

Modern Era

2010’s JLab DIS-Parity Standard Model & beyondMoller (2) sin2W < 1%

2020’s NLC Moller (3) sin2W < 0.1%

Future

PV: Past, Present, & Future

Quarks, Gluons, & the Light Elements

How does QCD make hadronic matter?

1.0

1.5

2.0

2.5

qq Mesons

L = 01 2 3 4H

ybrids

exoticnonets

PV & strange quarks

Gluonic effects

GPD’s: “Wigner Distributions” (X. Ji)

Pentaquark,

mq-dependence of nuclear properties

Lattice QCD

Strange Quarks in the Nucleon:What have we learned?

Effects in are much less pronounced than in ,

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N s γ μ s N

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N s s N

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N s γ μγ 5s N

Jaffe ‘89

Hammer, Meissner, Drechsel ‘95

• Dispersion Relations• Narrow Resonances• High Q2 ansatz

OZI violation

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gφNN

gωNN

≈1

2

Strange Quarks in the Nucleon:What have we learned?

Effects in are much less pronounced than in ,

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N s γ μ s N

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N s s N

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N s γ μγ 5s N

HAPPEX

SAMPLE

Strange Quarks in the Nucleon: What have we learned?

• Strange quarks don’t appear in Quark Model picture of the nucleon

• Perturbation theory may not apply

QCD / ms ~ 1 No HQET

mK / ~ 1/2 PT ?

• Symmetry is impotent

Js = J

B + 2 JEM, I=0

Unknown constants

Theory: how do we understand dynamics of small ss effects in vector current channel ?

Challenge to understand QCD at deep, detailed level

Q2 -dependenceof Gs

M

G0 projected

Dispersion theory

Chiral perturbation theory “reasonable range” for slope

SAMPLE 2003

Happex projected

Lattice QCD theory

Lattice Computations

Dong, Liu, & Williams (1998) Lewis, Wilcox, Woloshyn (2003)

• Quenched QCD

• Wilson fermions

• 2000 gauge configurations

• 60-noise estimate/config

• Quenched QCD

• Wilson fermions

• 100 gauge configurations

• 300-noise estimate/config

See also Leinweber et al

Lattice Computations

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s = Fμ p

u

μ Σu , μ s

μ dloop( )

Lattice calculation

• Charge symmetry• Measured octet m.m.’s• Chiral symmetry• Unquenching

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s ≈ −0.05 ± 0.02

Leinweber et al

What PT can (cannot) say

Strange magnetism as an illustration

GMs (qs) = μs + 1

6 q2 rs,M2 +L

μs = 2MN Λ χ( ) bs + L

Unknown low-energy constant (incalculable)

Kaon loop contributions (calculable)

Ito, R-M Hemmert, Meissner, Kubis Hammer, Zhu, Puglia, R-M

What PT can (cannot) say

Strange magnetism as an illustration

GMs (qs) = μs + 1

6 q2 rs,M2 +L

rs,M2 =−

6Λχ

2MN

Λχ

⎛

⎝ ⎜

⎞

⎠ ⎟ bs

r

+118

(5D2 −6DF +9F2)πMN

mK

+7lnmK

μ

⎛

⎝ ⎜ ⎞

⎠ ⎟ +L

{}

LO, parameter free NLO, cancellation

NLO, unknown LEC

Dispersion theory

rs,M2 =

6π

dtImGM

s (t)t2

9mπ2

∞

∫

Strong interaction scattering amplitudes

e+ e- K+ K-, etc.

Slope of GMs

Jaffe Hammer, Drechsel, R-M

rs,M2 =

6π

dtImGM

s (t)t2

4mK2

∞

∫

Perturbation theory (1-loop)€

€

K +

Hammer & R-MDispersion theory

All orders

rs,M2 =

6π

dtImGM

s (t)t2

4mK2

∞

∫

s s

resonance

Perturbation theory (1-loop)

Hammer & R-M

All orders

Dispersion theory

• S-quarks are not inert

• Non-perturbative effects dominate (LEC’s)

rs,M2 =

6π

dtImGM

s (t)t2

4mK2

∞

∫

• Are there higher mass excitations of s s pairs?

• Do they enhance or cancel low-lying excitations?

Can’t do the whole integral

?

Dispersion theory

Models & exp’t suggest cancellationsExperiment & lattice will give an answer

CombiningPT, dispersion theory, & lattice QCD

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GM(s)(Q2 = 0.1) = 0.37 ± 0.20 ± 0.26 ± 0.07

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s = GM(s)(Q2 = 0.1) − 0.13bs

r

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=0.37 ± 0.20 ± 0.26 ± 0.15

RA

“Reasonable range”: lattice & disp rel

SAMPLE

Radiative Corrections & the Hadronic Weak Interaction

• GAe

• N !

• PV photo- and electro-production (threshold)

• Vector analyzing power ()

at Q2=0.1 (GeV/c)2

( ) 39.045.022.01

31.029.014.0

±±==

±±=

TG

GeA

sM

R. Hasty et al., Science 290, 2117 (2000).

• s-quarks contribute less than 5% (1) to the proton’s magnetic form factor.

• proton’s axial structure is complicated!

Models for s

Radiative corrections

Axial Radiative Corrections

e

r e p

p

+⋅⋅⋅γ

“Anapole” effects : Hadronic Weak Interaction

γ

ZZ

γ+

Nucleon Green’s Fn : Analogous effects in neutron -decay, PC electron scattering…

“Anapole” Effects

€

€

+

€

p

€

+L

Zhu, Puglia, Holstein, R-M (PT) Maekawa & van Kolck (PT) Riska (Model)

Zhu et al.

Hadronic PV

Can’t account for a large reduction in GeA

Nuclear PV Effects

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PV NN interaction

Carlson, Paris, Schiavilla Liu, Prezeau, Ramsey-Musolf

Suppressed by ~ 1000

at Q2=0.1 (GeV/c)2

125 MeV:no backgroundsimilar sensitivity to GA

e(T=1)

SAMPLE Results R. Hasty et al., Science 290, 2117 (2000).

200 MeV update 2003:Improved EM radiative corr.Improved acceptance modelCorrection for background

• s-quarks contribute less than 5% (1) to the proton’s magnetic moment.

200 MeV dataMar 2003

D2

H2

Zhu

, et

al.

E. Beise, U MarylandRadiative corrections

Transition Axial Form Factor

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GANΔ (0) =

2

3

gπNΔFπ

mN

1− Δπ( )

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GANΔ,e (0) = GA

NΔ (0) 1+ RAΔ

( )

Off Diagonal Goldberger-Treiman Relation Zhu, R-M

O(p2) chiral corrections ~ few %N!N ~ 5%

Rad corrections, “anapole” ~ 25%Study GA

N(Q2)/ GAN(0)

Measuring GAN(Q2)

GAN & “d”””

Axial response , GAN only

ALR ~ Q2 (1-2sin2W) Zhu, Maekawa, Sacco, Holstein, R-M

Nonzero ALR(Q2= 0)

Weak interactions of s-quarks are puzzling

Hyperon weak decays

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Σ+ → nπ + Σ+ → pπ 0 Σ− → nπ −

Λ → pπ − Λ → nπ 0 Ξ− → Λπ 0 Ξ0 → Λπ 0

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MB → ′ B π = U B A + Bγ 5[ ]UB

S-Wave: Parity-violating

P-Wave: Parity-conserving

symmetry not sufficient

Weak interactions of s-quarks are puzzling

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rΣ+ → pγ ,

r Λ → nγ ,K

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MB → ′ B λ = −i

MB + M ′ B

U σ μν A + Bγ 5( )U F μν

M1 (PC)

E1 (PV)

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αB ′ B =2Re A B*

A2

+ B2

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αB ′ B ~ ms Λχ ~ 0.15

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αΣ+ p

~ − 0.76 ± 0.08

αΞ 0Σ0 ~ − 0.63± 0.09

Th’y

Exp’t

Weak interactions of s-quarks are puzzlingResonance saturation

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B

€

′B

€

′′B

€

€

B

€

′B

€

′′B

€

€

+Holstein & Borasoy

S11

Roper

S-Wave

P-Wave

€

12

+ 12

− 12

+

12

+ 12

+ 12

+

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12

+ 12

− 12

+

12

+ 12

+ 12

+

Fit matrix elements

Weak interactions of s-quarks are puzzlingResonance saturation

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B

€

′B

€

′′B

€

€

B

€

′B

€

′′B

€

€

+Holstein & Borasoy

S11

Roper

S-Wave

P-Wave

€

12

+ 12

− 12

+

12

+ 12

+ 12

+

€

12

+ 12

− 12

+

12

+ 12

+ 12

+

Fit matrix elements

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B

€

′B

€

′′B

€

€

B

€

′B

€

′′B

€

€

+

€

B( ) = −π ′ ′ B ( ) = π ′ B ( ) S/P wave fit Close gap with αBB’

Weak interactions of s-quarks are puzzling

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WB ′ ′ B ~ Λχ gπ

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WB ′ ′ B ~ 5 Λχ gπ

Natural

Fit

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~GF Fπ

2

2 2~ 3.8 ×10−8

Is deviation from QCD-based expectations due to presence of s-quarks or more fundamental dynamics?

We have a S=0 probe

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N

€

€

Use PV to filter out EM transition

Zhu, Maekawa, Holstein, MR-M

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L = ie

Λχ

dΔ Δ μ+ γ λ pF μλ + h.c.PV, E1

Amplitude

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Aγ = 0

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Aγ = 2dΔ

C3V

mN

Λχ

+LPV Asymmetry

Large NC , spin-flavor SU(4) Finite NC

Low energy constant

We have a S=0 probe

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N

€

€

€

L = ie

Λχ

dΔ Δ μ+ γ λ pF μλ + h.c.

Naïve dimensional analysis (NDA)

Resonance saturation

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N

€

€

12

−

€

€

N

€

€

32

−

€

€

+

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HWΔS= 0

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Aγ ~ 5 ×10−8

d~ g

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Aγ ~ 1×10−6 d~ 25g

Measuring d

d = 100 genhanced HW

S=0

d = 0 , GAN only

ALR ~ Q2 (1-2sin2W) Zhu, Maekawa, Sacco, Holstein, R-M

N! Transition

Measure Q2-dependence of ALR to learn

• d

• GANQ2)/ GA

N0)

• RA

• MINERVA: GAN(0) ?

Vector Analyzing Power

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An ~r S ⋅

r K × ′

r K

• T-odd, P-even correlation

• Doubly virtual compton scattering (VVCS):new probe of nucleon structure

• Implications for radiative corrections in other processes: GE

p/GMp, -decay…

• SAMPLE, Mainz, JLab experiments

What specifically could we learn?

Vud

Vector Analyzing Power

γ€

V

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V

γ+

V=: VVCS

Re M(M

boxMcross) Rosenbluth

Im MM

box VAP

V=W,Z: Electroweak VVCS

Re MV(MV

boxMVcross) -decay, RA,…

Im MVMV

box -decay T-violation

Direct probe

Vector Analyzing Power

Mott: MN!1

SAMPLE

EFT to O(p2)

Diaconescu, R-M

I=1, r2

O(p0)

O(p4)

1460

Vector Analyzing Power

Constrained by SAMPLE

300

Dynamical ’s?

Radiative Corrections & the Hadronic Weak Interaction

• GAe

• N !

• PV photo- and electro-production (threshold)

• Vector analyzing power ()

Theory for RA good to ~ 25%

Further test of RAd & HW

qq

EFT for low energy good to ~ 25%; more tests!

New window on electroweak VVCS: -decay, sin2W,…

Weak Mixing Angle: Scale Dependence

sin2W

(GeV)

SLAC E158 (ee) JLab Q-Weak (ep)

e+e- LEP, SLD

Atomic PV N deep inelastic

Czarnecki, Marciano Erler, Kurylov, MR-M

Comparing Qwe and QW

p

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture. -> e+e

SUSY dark matter

is Majorana

RPV 95% CL fit to weak decays, MW, etc.

Kurylov, Su, MR-M

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QWe,SUSY QW

e,SM

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QWp,SUSY QW

p,SM

SUSY loops

Comparing Qwe and QW

p

Erler, Kurylov, R-M

QWP = 0.0716 QW

e = 0.0449

Experiment

SUSY Loops

E6 Z/ boson

RPV SUSY

Leptoquarks

SM SM

€

±0.0029

€

±0.0040

sin2W

(GeV)

SLAC E158 (ee) JLab Q-Weak (ep)

e+e- LEP, SLD

Atomic PV N deep inelastic

Additional PV electron scattering ideas

DIS-Parity, JLab

Moller, JLab

DIS-Parity, SLAC

Czarnecki, Marciano Erler et al.

Linear Collider e-e-

Comparing Qwe and QW

p

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

SUSY dark matter

Kurylov, R-M, Su

SUSY loops

RPV 95% CL€

QWp,SUSY QW

p,SM

€

QWe,SUSY QW

e,SM

E158 &Q-Weak

JLab Moller

Linear collider

Comparing AdDIS and Qw

p,e

e

p

RPV

Loops

SUSY effects

Comparing Qwe and QW

p

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

SUSY dark matter

Kurylov, R-M, Su

SUSY loops

RPV 95% CL€

QWp,SUSY QW

p,SM

€

QWe,SUSY QW

e,SM

E158 &Q-Weak

JLab Moller

Linear collider

“DIS Parity”

Higher Twist “Pollution”

E=11 GeV =12.50

Different PDF fits

Sacco, R-M preliminary

~0.4%

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ALR Q2

€

y

Higher Twist “Pollution”

Castorina & Mulders

Sacco & R-M preliminary

Open issues

• QCD evolution

• Double handbag

• Moment inversion

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FLD, HT

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F2D, HT

Tasks for the “modern era” & futureStrange quarks • Finish the experimental program

• Credible, unquenched lattice calculations

Rad corrections • Further tests of electroweak VVCS with N!, VAP

• Theory: quark mass (m) dependence

• Measure d

SM & new physics

• DIS-Parity: Is there significant I-violationas suggested by NuTeV?

• Theory: how big is twist pollution?

• Theory: relating n(r) & APV

Hardronic PV • Lots of new exp’t & theory….