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Contribution of Two-Photon Exchange with Contribution of Two-Photon Exchange with Excitation to ep Scattering Revisited Excitation to ep Scattering Revisited

Shin Nan YangShin Nan YangNational Taiwan UniversityNational Taiwan University

International Conference on the Structure of Baryons (Baryons2013),

Glasgow, Scotland, June 24 – 28, 2013

In collaboration with Haiqing Zhou, Southeast University, Nanjing

(1232)

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Outline

1.Background

2. Improvements over

previous study

3. Results 4. Summary

3

Background• Proton, the only stable hadron and the lightest baryon, is most

amenable to experimental and theoretical studies.

• Experimental measurements of proton EM form factors started in 1950s (Hofstadter, 1961 Nobel prize)

• Unpolarized data before 2000, analyzed via Rosenbluth formular (LT method), can be fitted by

as quoted in the textbooks and often called as

SCALING LAW

2 22 2

2 202 2 2

0

( ) ( )( ) ( ), 0,

( / ) ( / )

1( ) , 0.71 (GeV/c) ,

(1 / )

p np nM ME D E

p N n N

D

G Q G QG Q G Q G

G Q QQ Q

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big surprise!!!

Polarization transfer experiment at Jlab:

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

e p e p BBBBBBBBBBBBB B

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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 (Qattan et al., 2005) → with 4 - 8% precision,

2 22.64 4.10 GeV/ 1 ,p E MG QG

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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)

Pun05

Gay02

JLab/HallA

recoil pol. data

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Ensuing efforts to understand the discrepancy -

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

• Maximon and Tjon: — ε dependence comes only from proton vertex and TPE corrections; proton vertex corr. < 0.5%

Two photon exchange effects ??

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Blunden, Melnitchouk, & Tjon, 2003

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

N

Blunden, Melnitchouk, Tjon, PRL 91 (2003) 142304; with only nucleon in the intermediate states.

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

GPDs

Chen, et al., PRL, 93, (2004) 122301

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

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Kondratyuk, Blunden, Melnitchouk, Tjon, (KBMT) PRL, 95 (2005) 172503.

Δ Contribution to Δ Contribution to TPE:TPE: hadronichadronic

2 2 2 2( ) ( ) (1 )R M E Nd G Q G Q

Δ(1232) contribution to TPE is not negligible !

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Improvements over KBMT’s calculation

1. correct γN → Δ vertex function

2. realistic γNΔ coupling constants, the Coulomb quardruploe one gc in particular

(g1, g2, g3) = (7, 9, 0) ---- KBMT (6.59, 9.08, 7.12) ---- ZY 3. realistic γNΔ form factors

†

0 0

†

0 0

( , ) ( , ) ----- KBMT

( , ) ( , ) ----- ZY,

N N

N N

p q p

p

q

qq p

1. correct γN → Δ vertex function

2. realistic γNΔ coupling constants, the Coulomb quardruploe one gc in particular

(g1, g2, g3) = (7, 9, 0) ---- KBMT (6.59, 9.08, 7.12) ---- ZY 3. realistic γNΔ form factors

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Effects of realistic γNN form factors

Details ofthe three

improvements

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14

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(1) 2

(2) 2

(3) 2

2

5

1

3

( , ) .

/

(

( , ) .

)

( )

( )

N

N

g

p q const

g p q pF q

F

q p q p q

p q g p q

M q p g p q q p p q

p q const

q

q

g

F

g

(1) 2

(2) 2

(3) 23

1

2

2

( )

( )

- /

(

)

g q p p q p q p q

p q g p q

M q p g p q q p p

F

g

q

q

F q

q

g

g F

1

21 : electric quadrupole tra

nsiti

: magnetic dipo

le transit

i

o

n

on

g

gg

3 - g : Coulomb quadrupole transition

KBMT used (+) sign

here

†

0 0

†

0 0

----- KBM( , ) ( , )

( , ) ( , )

T

----- ZY,

N N

N N

p q p

p p qq

q

correct γN → Δ vertex function

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realistic γNΔ form factors

22(1) 2 (2) 2 (3) 2 1

12 21

2 22(1) 2 (2) 2 31

1 32 2 2 21 3

(3)

KBMT :

ZY:

( ) ( ) ( ) , = 0.84 GeV.

( ) ( ) , = 0.84 GeV, = 2 G

eV,

(

F q F q F qq

F q F qq q

F q

2 22 2 22 31 2 4

2 2 2 2 2 2 2 21 3 2 4

2 4

) (1 ) ,

= 2 GeV, = 0.2 GeV, 0.3.

a aq q q q

a

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Realistic coupling constants from experiments

(g1, g2, g3) = (7, 9, 0) ---- KBMT (6.59, 9.08, 7.12) ---- ZY

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Results

Effects of correct vertex function

Effects of realistic γNΔ form factors

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Effects of realistic γNΔ coupling constants with

correct vertex function but KBMT’s f.f.’s

Combined effects of all three improvements

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2 2 2 2( ) ( ) (1 )R M E Nd G Q G Q

Combined effects

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Comparison with preliminaryrad-uncorr. data from CLAS

Comparison with preliminaryrad-corr. data from Novosibirsk

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Summary

1. Three improvements,

correct vertex function, realistic form

factors, and coupling constants for the

γNΔ vertex, have been implemented

2. Each improvement, implemented separately,

all produced substantial effect, especially

the f.f.’s as in the case of TPE/N.

However, the combined effects are modest,

but non-negligible, in many cases.

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3. TPE effects from N and Δ within hadronic

model can provide a fair account for the

unpolarized cross sections and the

discrepancy found for the ratio GE/GM obtained from LT and PT analyses

4. Substantial discrepancy remains between

predictions of hadronic model with Born plus

TPE and other data like R(e+p/e-p) and

PL/PL (Born)

More experimental and theoretical efforts are called for !!

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The End

Thanks you!!

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Backup slides

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