11

Professor John Alexander Tjon (張尊儒 ) in Tarogo Gorge, Taiwan (April, 2006)

John has great devotion to science, not for fame/PR, but only for science.Einstein on Madame Curie: “She was probably the only person who was not corrupted by the fame she had won”

22

Two-boson exchange physicsTwo-boson exchange physicsShin Nan YangShin Nan Yang

National Taiwan UniversityNational Taiwan University

The 5th Asian-Pacific Conference on Few-Body Problems in Physics,Seoul, Korea, August 21-26, 2011

In memory of Professor John Alexander Tjon

Collaborators NTU: Yu-Chun Chen, Haiqing Zhou CYCU: Chung-Wen Kao, Keitaro Nagata

33

Outline1. Two-photon exchange in ep elastic scattering

• nucleon e.m. form factors,

• discrepancy btw GE/GM’s extracted from Rosenbluth and polarization

experiments,• radiative corrections to ep elastic scattering and TPE• current developments and future prospect

2. Two-boson exchange correction to parity-violating

ep elastic scattering• strangeness content of the proton• parity-violating ep scattering in one-boson exchange approximation

• extraction of strange form factors from parity-violating asymmetry APV

and weak radiative corrections• two-boson exchange effects on strange form factors• γZ corrections to the proton weak charge

3. Summary

44

Nucleon e.m. form factors

2

1

2 21 2

1 22

2 2

2

2

( ) ( )

' : Dirac and Pauli from

Sachs form factors

fact

( ) | (0) | ( ) ( )[ ] ( ),2

( ) .

(0) 1,

ors.

: , .4

i

EM

E

M

p

E

QG

qN p J N p u p i u p

M

Q q p p

F F G F

F

G

s

M

Q

F

Q F

F

spatial distributi, of charge and

(0) 2.793.

: Fo magnetizatiurier transforms of the

of the nucleon

on

in Breit fr

o

a

n

me.E

pM p

MG G

G

How to measure form factors?

5

2 2R M EG G

Elastic electron-proton scattering

In one-photon exchange approximation,

Note θ→ 0, ε→1 (forward); θ→ π, ε→ 0 (backward)

Method: fix Q2, vary angle (vary ε), adjusting incoming electron energy as needed and plot reduced cross section

vs. ε

(Rosenbluth separation method)

2 2 2 2 2

22

(1 )( , ) ,

1, 1 2(1 ) tan .

4 2

R M Elab Mott

N

dQ G Q G Q

d

Q

m

Rosenbluth

formular

66

Polarized scattering

In one-photon exchange approximation,

Pt and Pl : polarization components of the recoiling proton perpendicular and parallel to its momentum in the scattering plane

'tan ,

2 2

ptE

pM l N

PG E E

G P m

The one-photon-exchange diagram for the polarized electron-nucleon scattering

Longitudinally polarized electron-proton elastic scattering with one-photon exchange. Polarization of the recoiled proton is measured.

e p e p DDDDDDDDDDDDD D

77

2 2 202 2 2

2 22

4

0

2

1( ) ,

( ) ( )( ) ( ),

0,

/ 1 and both 1

0.71(GeV/c) ,(1 / )

.

wher ,

.

e

/ .

,

p np M ME D

p n

nE

Qp pp E M p

DG Q QQ Q

R

G Q G QG Q G Q

G

G G

i e

Q

Up until the end of last century, experimental results, mostlyfrom Rosenbluth separation method, give

88

big surprise!!!

M.K. Jones et al., Phys. Rev. Letts. 84, 1398 (2000).

exp. in Hall A, Jlab with Elab = 0.934 - 4.090 GeV

• GE falls faster than GM

• GM/μpGD is approximately constant

99

Ensuing efforts to verify the discrepancy -

experimental New global analysis of the world’s

cross section data (Arrington 2003) → still inconsistent with the polarization measurements

High-precision Super-Rosenbluth experiment → with 4 - 8% precision,

2 22.64 4.10 GeV/ 1 ,p E MG QG

1010

proton proton e.m. form factor : statuse.m. form factor : status proton proton e.m. form factor : statuse.m. form factor : status

green : Rosenbluth data (SLAC, JLab)

Pun05Gay02

JLab/HallA

recoil pol. data

new JLab/HallC recoil pol. exp. (spring 2008) : extension up to Q2 ≈ 8.5 GeV2 new MAMI/A1 data up to Q2 ≈ 0.7

GeV2

11

Ensuing efforts to understand the discrepancy -

theoretical• Re-examination of the radiative corrections O (α2)

Feynman diagrams for elastic amplitudes

Feynman diagrams for inelastic amplitudes

1212

• Mo and Tsai, RMP 41, 205 (1969).

basically in soft-photon approximation

2

2 21

0 ( , )

(GeV) (GeV )

For electron-proton scattering

4.4 6.0

:

(1 ).

- 0.2908

d

Q

d Q

1% accuracy in cross section measurements requires knowingradiative corrections to 3% (3% x 0.2908 ~ 1%)

13

Maximon & Tjon, PR C62, 054320 (2000).

• Improve Mo and Tsai’s treatment– mathematical, e.g., the soft bremstralung cross

section is evaluated without approximation, and box diagrams are calculated with less drastic approximation

– physical, namely, q2-dependence in the proton form factor is kept.

– εdependence comes only from proton vertex and TPE corrections

– δ(proton vertex corr.) < 0.5%

2 2

1(GeV) (GeV ) (proton ver. corr.)

Mo-Tsai 4.4 6.0 0.2908

Maximon-Tjon

4.4

6.0

Q

0.2930 0.0068= 0.2862

How about TPE?

14

Rigorous treatment of TPE diagrams Blunden, Melnitchouk & Tjon, PRL 19,

142304 (2003)

N N

Difficulty in the integration on the left lies mostly with power in k. Feyncalc & Formcalc can handle power of k up to 4.

LT separation:

data - open squares

dashed line – global fit

Solid line – with TPE corr.

PT data: open circles

15

N, Δ

Blunden, Melnitchouk, & Tjon, 2005

from Arrington, Blunden, Melnitchouk, arXiv:1105:0951

Two-photon exchange calculation : Two-photon exchange calculation : hadronichadronic

N, Δ

16

Two-photon exchange : Two-photon exchange : partonic calculationpartonic calculation

GPDs

Chen, Afanasev, Brodsky, Carlson,

Vdh (2004)

TPE can account for at least 50% of the discrepancy in the value of μpGE/GM extracted from LT and PT methods !!

17

Recent developmentsRecent developmentsHow to quantify TPE contributions ?

• theoretical: inclusion of higher resonances, dispersion relation, model independent parametrization, pQCD………….

• experimental: more precision measurements, high Q2, e+p/e-

p, beam and target single spin asymmetries……

How to extract GM and GE in the presence of two-photon exchange ?

TPE in other processes, electron-nuclei scattering, hydrogen hyperfine splitting, precise description of simple atoms and positronium, REM of Δ electro- excitation……..

18

Model independent parametrization of TPE

In general,

charge conjugation and crossing symmetry

2 2

2

2 2 2 2 (

effect of the 1 2 i

, )

( , ) :

( , ) (

nterferenc

, ) ( ) ,

e.

R M E F Q

F Q

Q G Q G Q

2 2( , ) ( , ),

w

h

.1

it

1

F Q y F y

y

Q

19

If F(Q2, ε) is required to be smooth and

finite within 0 y 1, and≦ ≦ F →0, y = 0 (ε=1 ), F≠0, y = 1 (ε= 0). choice A,

choice B,

2

2

2 2 2 2 2ˆ ˆ( ) 1 ( ) ( ) (ln ) ,

with ' and ' ( ).

R M

D

G Q R A

A s B

Q y B Q y y

s G Q

2 2 2 2 2( ) 1 ( ) ( )R MG Q R A Q y B Q y

20

fit II: choice Afit III:choice B

21

e+p/e-p probes the real part of TPE

(2 1

) ( )21

( )1 Re( / )

( ),

eT T T

pR T T

e p

data from Nikolenko et al., Phys. Atom. Nucl. 73, 1322 (2010).

Q2 = 1.6 GeV2, ε= 0.4, R = 1.056 ± 0.011

22

Single spin asymmetries (SSA)-probe imaginary part of TPE-

1 2

beam normal spin asymm

interference btw & I

m

try e

.eN

N

mB T

B

TM

Expt. E(GeV) Q2 GeV2 Bn(ppm)

SAMPLE 0.192 0.10 -16.4±5.9

A4 0.570 0.11 -8.59±0.89

A4 0.855 0.23 -8.52±2.31

HAPPEX 3.0 0.11 -6.7 ± 1.5

G0 3.0 0.15 -4.06 ± 1.62

G0 3.0 0.25 -4.82 ± 2.85

E-158(ep)

46.0 0.06 -3.5 -> -2.5

23

Beam Beam normal spin normal spin asymmetryasymmetry

EEee = 0.300 GeV = 0.300 GeV

ΘΘe e = 145 deg= 145 deg

EEee = 0.570 GeV = 0.570 GeV

ΘΘe e = 35 deg= 35 deg

EEee = 0.855 GeV = 0.855 GeV

ΘΘe e = 35 deg= 35 degPasquini &

Vanderhaeghen

Phys.Rev. C70 (2004) 045206 .

MAMI data

A4 experiment

24

1. • σ term in N scattering → an admixture of 20-25% strange quarks

2.

• p deep inelastic scattering with longitudinally polarized ’s and p’s (EMC) → ΔS=-0.12 (EMC94)

• low energy elastic p cross section (BNL 1987) → ΔS=-0.19±0.09

3. • parity-violating electron-proton scattering SAMPLE, HAPPEX, A4, G0

4. from K+ production in DIS (HERMES) →

5. double polarizations in photo- and electroproduction of meson – planned for 2012 at SPring8

Possible experimental indications for“ strangeness in the nucleon ”

( ) | | ( )N p ss N p ( ) | | ( )N p ss N p

5( ) | | ( )N p s s N p 5( ) | | ( )N p s s N p

( ') | | ( )N p s s N p ( ') | | ( )N p s s N p

( ) ( )s x s x 2.5%s s

P

25

Parity-violating ep scattering inone-boson exchange

approximation

weak form factors :

, 2 2 , ,1,2 1,2 1,2 1,2( ) (1 4sin ) ,Z p p n s

WF Q F F F

,1,2Z pF

: proton axial form factorZAG

26

one-boson exchange approximation

Via quark flavor decomposition for and assumption of charge symmetry →

/ , /,Z p n

E MG

2Born 1 2 3

2

, , , ,2

1 2

, ,

2 2

,2

3 2

2

,( , )4 2

1 4sin ,( , )

with ,

,( , )

(1 4sin ) ,( , )

/ 4 2 (1

s s

R L FPV

R L Rem

p n p nE E M M

WR

p pE M

R

p ZM A

WR

F e

E M

m

A A AG QA

Q

G G G GA a

Q

G GA a

G G

Q

G GA a

Q

a G Q

2)(1 )

Strange form factors

27

Radiative correctionsMarciano and Sirlin

(1983,1984)

28

1 2 3

, , , ,2

1 2

2

, ,

2 2

,2

3

2

2

wi

( , ) ,

1 4 sin ,( , )

,( , )

(1 4sin ) ,( , )

t / 4 2 (1h , )(1 )

PV

p n p nE E M M

WR

p pE M

F

R

p ZM

s sE M

AW

em

R

A A A A

G G G GA a

Q

G GA a

Q

G

G G

a

G

Q

G

A

Q

a

Radiative corrections are parametrized via ρ≠1 and κ≠1

PDG values: ρ= 0.9876 and κ=1.0026

Marciano and Sirlin evaluated γZ exchange in Q2 = 0 approximation →

3 3( ) 3.7 10 , ( ) 5.3 10Z Z

Strange form factors

29

Quantification of TBE effects• first define δ by

• set the experimental parity asymmetry

• use to extract the strange form factors

• introduce

(1 2 ) (1 )(1 )PV PVA Z Z A Z

exp (1 2 )

( , )(1 ), ( , ) determinedPV PV

PV PV

A A Z Z

A A

( )(1 )s s s sE M E M GG G G G

( , )A

30

Two-boson exchange effectshadronic model

N, Δ N, Δ

Zhou, Kao, Yang, Nagata,

2007, 2009, 2010;

Tjon et al. 2008, 2009.

31

Two-boson exchange effectspartonic calculation

Afanasev and Carlson, PRL 94, 212301 (2005).

32

Zhou, Kao, Yang, Nagata, PR C81, 035208 (2010).

＊

＊

33

NRQM cal., Kiswandhi, Lee, Yang, arXiv:1107.3072 ; talk by Kiswandhi on Mon.Solid and dashed lines correspond to 0.06% and 2.4% of strangeness content.

34

QWEAK expeiment at Hall C/JlabEe = 1.165 GeV, Q2 = GeV2, θ= 80, 85% polarization

2

Born 2 2

2

0

( ) ,4 2

where,

(1 4sin ) 0.0721,

in tree level in standard model at pole.

WR L F

PVR L em

WW

GQ

Q

QA Q B Q

Z

In the above kinematics, APV ～ -0.30 ppm,

Objective, 0.3% determination of sin2θW → requires 2% precision in APV

=

35

Standard Model running of sin2θW

Erler, Kurylov, Ramsey-Musolf, PR D68, 016006 (2003).

Deviations → a signal of new physics

Agreement → place new and strict constraints on possible SM extensions

36

At low Q2, one has,

exp

2

2

exp

2

or,

( ) 1

(1 ), if is small. ( )

14

1

,2

PVW

RC

PV

FPV w RC Z

em

CZ Z

R

Z

AQ

C

Q

A

A

C

G

Q

Q

Q

Erler, Kurylov, Ramsey-Musolf: 2%,

Zhiu, Kao, Yang: ( ) 0.6%, ( ) 0.1%,

Grorchstein, Horowitz: (R+Regge) 6%, (Dispersion relation, PRL 2009),

Grorchstein, Horowitz, Ramsey-Musolf:

Z

Z Z

Z

N

(R+Regge) 6%, 2.8%. (2011)Z Z

=

37

SummaryTPE effects on proton e.m. form

factors• TPE can account for at least 50% of discrepancy in in the

value of GE/GM from LT and PT methods.• e+p/e-p and beam/target normal spin asymmetry, probe

the real and imaginery parts of TPE amplitudes, respectively, and would be very useful to constrain TPE models.

• much theoretical and experimental works remain to be done.

TBE effects in parity-violating ep scattering

• Nucleon contribution is larger than Δ contribution but are of opposite sign and cancel to give small effects except in a few kinematics cases.

• contribution of γZ box diagrams to the proton weak chargecurrently under intensive study.

N

38

Recent developmentsRecent developmentsHow to quantify TPE contributions ?

• theoretical: inclusion of higher resonances, dispersion relation, model independent parametrization, pQCD………….

• experimental: more precision measurements, high Q2, e+p/e-

p, beam and target single spin asymmetries……

How to extract GM and GE in the presence of two-photon exchange ?

TPE in other processes, electron-nuclei scattering, hydrogen hyperfine splitting, precise description of simple atoms and positronium, REM of Δ electro- excitation……..

39

For much more details, seethe following reviews:

Carlson and Vanderhaeghen Ann. Rev. Nucl. Part. Sci. 57, 171-204 (2007). Arrington, Blunden, and Melnitchouk,

arXiv:1105.0951, Prog. Part. Nucl. Phys., in press

40

The End

Thanks you!!