1

The and -Z Exchange Corrections to Parity Violating

Elastic Scattering

周海清 /东南大学物理系 based on PRL99,262001(2007)

in collaboration with C.W.Kao, S.N.Yang 2008/4/27

2

-e p

2

Outline

• Introduction • One boson exchange• Two boson exchange correction• Extraction from experimental data• Conclusion

3

Introduction

Motivation: To extract the strange quark form factors of proton more precisely by parity violating elastic electron-proton scattering, one-loop corrections should be considered more carefully, especially the corrections from box diagrams. The importance of these corrections has been indicated in elastic ep scattering (to extract the electromagnetic form factors of proton).

4

Proton : constructed by u, d, s, c…quarks, one of the most important QCD bound state and component of the world.

Strange quark form factors of proton:

1 2

5 5

( ') | | ( ) ( ')[ ] ( )2

1( ') | | ( ) ( ')[ ] ( )

2

s s

s sA P

iP p s s P p u p F F q u p

M

P p s s P p u p G G q u pM

5

Parity violating elastic electron-proton scattering:

1 2 3 4( , / ) ( ) ( ) ( )e p R L P p e p P p

R LPV

R L

A

6

One boson exchange

, ,1 2( ') | | ( ) ( ')[ ] ( )

2P P iP p J P p u p F F q u p

M

Extract the strange quark form factors from at tree level (one boson exchange)

, ,1 2 5( ') | | ( ) ( ')[ ] ( )

2Z Z P Z P Z

A

iP p J P p u p F F q G u p

M

PVA

7

2 21

2 23

2 22 4 1 2 3 4

( ,0,0, ) ( ,0,0, )

( , sin ,0, cos ) ( , sin ,0, cos )

( ,0,0,0); ;

e

e

p a m a a a

p b m b b b b b

p M p p p p p M

22 1 2 2

3 12(1 2(1 ) tan ) ; ; ( )

2 4 P

QQ q p p

M

x

y

zP e(R /L )

e '

P '

8

21

, 2 , 2[ ( ) ( ) ]4 2

OBE OBE OBEZ F E M A

PV P PE M

G Q A A AA

G G

, ,,

,2 2

,;

(1 4sin ) (1 )(1 )

P PE M

PM

OBE OBZ P Z PE M

ZA

EE M

OBEA W

G G

G

A

A

G

G

A G

( ), ( ), ( ),1 2

( ), ( ), ( ),1 2

Z P Z P Z PE

Z P Z P Z PM

G F F

G F F

(1)

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By assuming charge symmetry:

, , / , , /, ,

u d s p d u s pE M E MG G

And quark content of proton at tree level:

5, ,

; ( )em Z f ff f V A ff f

f u d s f

J Q q q J q g g q

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Results:1

1 2 3

21 2 2

2 2 2

2

, , , ,

, ,

,

3 2

,

,

,

, , 2

,

[(1 4sin ) ]( ) ( )

( ) ( )

'(1 4sin )

( ) ( )

P n P nE E M M

P PE M

P PE M

P PE M

P Z

s

M AP

ZPV

W

W

sM

PE M

E

G G G G

G G

A A A A

A a

A a

A

G G

G G

G Ga

G

G G

G

2 2/ 4 2; ' = (1+ )(1- )Fa G Q

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are obtained by matching with the parity -violating amplitude of

One loop level at zero momentum transfer

Electro-weak radiative corrections( to ) are well defined at quark level and can be parame--terized as the 4-fermion effective Hamiltonion(W.J.Marciano, .Sirlin,PRD27,552(1983), PRD29,75(1984); W.-M.Yao, JPG69,1(2006))

51 2 5, ,

[ ]2

e q FPV q q

q u d s

GH C e eq q C e eq q

1 2 and q qC C

1 2 3 4( ) ( ') ( ) ( ')e p q p e p q p

PVA

12

At zero momentum transfer approximation are not dependent on momentum, and the corrections at quark level can by applied to hadron level directly which results in

1 2 and q qC C

1 2 3

2, , , ,

, ,

, ,

, ,

1 2 2

2 2 2

2, 2

,

,3 2

( , )

[(1 4 sin ) ]( ) ( )

( ) ( )

'(1 4sin )

( ) ( )

P n P nE E M M

P PE M

P PE M

P PE M

P ZM A

P PE M

s

PV

W

sE M

W

A A A A

A a

A a

G G G G

G G

G GG G

G G

G G

GA a

G

2 21 1

1 4 1 2( sin ); ( sin )

2 3 2 3u W d WC C

Usually used to extract the strange quark form factors from experiment data (HAPPEX, A4).

(2)

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Experiment DataSAMPLE Collaboration

PLB583,79(2004)

2 2 o 0

2 2

0.1 , 130 170

6.34 1.45 0.53 ppm

( 0.1 ) 0.34 0.09 0.04 0.05ZM

Q GeV

A

G Q GeV

others form : Science 90,2117(2000)

PRL78,3824(1997)

2

2 ( 1)

2

( 0.1) 5.61 0.67 0.88 ppm

( 0.1) 5.56 3.37 1.54 ppm

( 0.1) 0.37 0.20 0.26 0.07

s e TM A

sM

A Q

A Q G G

G Q

2

fitting method: use

(1 4sin )(1 ) (1 ) + (1)s P P n n ZM W V M V M MG R G R G G

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HAPPEX Collaboration

PLB635,275(2006)

PRL98,032301(2007)

PRC69,065501(2004)2 o0.477, =12.3

15.05 0.98(stat) 0.56(syst)ppm

0.392 0.014 0.020 0.010s sE M

Q

A

G G

by Zhu et.al PRD62,033008(2000)ZAG

2 o0.099, =6.0

1.14 0.24(stat) 0.06(syst)ppm

0.080 0.030 0.025(stat) 0.006(sys) 0012(FF)s sE M

Q

A

G G

2 o0.109, =6.0

1.58 0.12(stat) 0.04(syst)ppm

0.09 0.007 0.011(stat) 0.006(sys)s sE M

Q

A

G G

fitting method: use (2)

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A4 Collaboration

PRL93,022002(2004)

PRL94,152001(2005)

2 o0.23, =30 40

5.44 0.54(stat) 0.26(syst)ppm

0.225 0.039 0.034

o

s sE M

Q

A

G G

2 o0.108, =30 40

1.36 0.29(stat) 0.13(syst)ppm

0.106 0.071 0.036

o

s sE M

Q

A

G G

fitting method: use (2)

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G0 Collaboration

PRL95,092001(2005), Nucl.Phys.Proc.Suppl.159,121(2006)

2 20.12 1 GeV

52 78o o

Q

2 2 oFurther: 0.23,0.63 GeV ; 108Q

fitting method: use (1)and radiative corrections are included as error bar

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Summary

Ex: precision about 0.1 ppm ,

or about 10%, 5%

Theoretic approximation:

Zero momentum transferCharge symmetryDeuteron form factors…..

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Two boson exchange correction

Go beyond zero momentum transfer approximation.

Among the one loop correction, the box diagrams are most important. Hinted by the un-polarized elastic electron-proton scattering.

cross diagrams are implied

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Two model dependent methods are applied to calculated the TPE diagrams’ contribution in unpolarized ep scattering.

A: Hadronic mechanism (hadron level).

Properties: Consistent with effective interaction by zero momentum transfer approximation . The results are model-independent by soft photon approximation.

The correction to unpolarized cross section is calculated. Furthermore, its effects to electromagnetic form factors of proton are analyzed and found to be large.cross diagram is implied

P. G. Blunden et al.PRL91,142304(2003)

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B: General parton distributions (quark level).

The two results are consistent for unpolarized cross section.

Also the correction to unpolarized cross section is calculated and the effects to electromagnetic form factors of proton are analyzed. Corrections to from TPE at high are discussed.

PVA2Q

Y. C. Chen et al. PRL93,122301(2004), A. V. Afanasev et al. PRL94,212301(2005)

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We applied the first method to calculated the exchange contributions to .

2 and -Z PVA

Input parameters: Using elastic intermediate state approximation, take the form factors as the effective vertexes. This results in no new input except the tree level form factors.

PVA

, ,1 2( ') | | ( ) ( ')[ ] ( )

2P P iP p J P p u p F F q u p

M

, ,1 2 5( ') | | ( ) ( ')[ ] ( )

2Z Z P Z P Z

A

iP p J P p u p F F q G u p

M

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A) Monopole form

B) Dipole form

Practical calculation, two forms of the form factors are chose.

, , , , 2 2 21 1

2 2 22 2

/ / / /( )

/ /( )

P P Z P Z PE M p E M

ZA

G G G x G y Q

G z Q

2 2, , , , 11 12

2 2 2 211 12

2 221 22

2 2 2 221 22

/ / /( )( )

/( )( )

P P Z P Z PE M p E M

ZA

G G G x G yQ Q

G zQ Q

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Parameters:

Usual dipole form (Ref HAPPEX, A4)

,2 2 2 2 2

(0)1;

(1 / 0.84 ) (1 )

ZP Z A

E A

GG G

Q Q

1 2 1 2

11 12 21 22

11 12 21 22

1) 0.56, 0.7 2) 0.84, 1.0

3) 0.84, 0.85, 1.00, 1.01

4) 1.00, 1.01, 1.00, 1.01

For comparing choose four case

x, y, z (E. J. Beise etc Prog.Part.Nucl. Phys 54,289(2005))

0.370.36

0.076 0.00264, y=2.08 0.00813 (0)

0.95

sMx G

z s

Then calculating the diagrams…and IR divergence emerges…

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IR divergenceBremsstrahlung contribution should be considered to cancel the IR divergence of the cross sections from box diagrams.

( / ) ' 'e R L p e p

Separate the corrections in the soft photon approximation

( ) ( ') ( ) ( ) ( ') ( )1 1;

2 2c c a d d b

soft MT soft MTM M M M

:MT is factorized correction in soft photon approximation and is model independent and R,L independent.

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; ; ; ;1

1 1 1 1

; ; ; ;

1 1 1 1

1

[1 ]

[1 ]

(1 )(1 )

R LPV

R L

Box f Box f Box f Box fZ R L R L

PV Z Z Z ZR L R L

Bre f Bre f Bre f Bre fR L R L

Z Z Z ZR L R L

ZPV Box Bre

A

A

A

1, , , ,

1 1 1 ; ;, , , , ,

1 ; ;, , ,

(1 )

Z Box BreR L R L R L R L

Z Z Z Box f Bre fR L MT R L Bre R L R L R L

Z Box f Bre fR L MT Bre R L R L

What we calculated.

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Results

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Dotted line: 1 2 ; dashed line: 2

dot-dashed line: sum of 2 , solid line: full results

Z

1

2

monopole form

with parameters:

0.56

0.7

, , centeral values

GeV

GeV

x y z

28

1

2

monopole form

with parameters:

0.84

1.00

, , centeral values

GeV

GeV

x y z

29

11

12

21

22

dipole form

with parameters:

0.84

0.85

1.00

1.01

, , centeral values

GeV

GeV

GeV

GeV

x y z

30

11

12

21

22

dipole form

with parameters:

1.00

1.01

1.00

1.01

, , centeral values

GeV

GeV

GeV

GeV

x y z

31

1

2

monopole form

with parameters:

0.56

0.7

, centeral values

GeV

GeV

x z

32

1

2

monopole form

with parameters:

0.56

0.7

, centeral values

GeV

GeV

x y

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Properties:

1. The total corrections are not sensitive to the input parameters.

2. The dependence of correction is evidently.

3. Not very small: 1-2%.

4. Corrections from respectively are a little sensitive to parameters. (Argument in recent paper J.A.Tjon etc PRL 100, 082003 (2008))

2 and Q

1 2 and 2Z

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Extraction from experimental data

HAPPEX and A4

To avoid double counting of box diagrams, the contributions at zero momentum transfer should be subtracted.

Then

22 3

2

22 2 3

2 2

34(1 4 )[ln( ) ] 3.7 10

2 2

9 3( 4 )(1 4 )[ln( ) ] 5.3 10

2 4 2

Z

Z

ms

M

ms s

s M

( ) (1 2 ) ( ', ')(1 )Exp Z ZPV PV PVA A A

' ; '=

M is strong interactionparameter, chosen as 1GeV.

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Define

Result

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

23

0

23

0 0 0

1 2 3

( ) 4 sin

4 sin ( ) ( ) ( )

ExpPV W

ExpPV

Exp Ex

G

pPV W PV

Exp Exp ExpPV PV PV

A a A

A A

A a A A

A A A A A A

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The values of for HAPPEX and A4 experiments. I,II and III refer to HAPPEX data in 2004, 2006, and 2007(K.A. Aniol et al. PRC 69, 065501(2004), PLB 635, 275 (2006); A. Acha et

al, PRL98, 032301 (2007)), And IV and V correspond to A4 data in 2004 and 2005(F.E. Maas et al ,PRL93, 022002(2004); PRL94, 152

001 (2005)).

1,2,3

37

The corrections to for HAPPEX and A4 experiments.s sG E MG G

large

14.60%, 45.05% 修正为

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SAMPLE:

1: At backward where the correction is larger.

2: is extracted from of deuteron in some case . The box diagrams corrections of latter have not been well estimated theoretically, so the result is not certain.

ZAG PVA

39

weakQ

2 0, 1Q

Now experimentally, 4% uncertainty in , corresponding to 2.2% uncertainty in PVA

the weak charge of proton

2 2

22

2

( 0, 1) ( )(1 4( )sin )(1 )

sin ( 4 )

1 4sin(1 4 sin )W

PV W

W

W

A Q a

a

2 2: 8 , 0.03 , 0.99 0.9%oEx Q GeV

WQ

weakQ

40

2

2

; sin

( 4 )1 4sin

Exp Expold newPV PVW W

W

W

A AQ Q

aa

6.65%1oldW

Q newW

Q

Q

old: 0, 0, 0

new: , , 0

Not small.

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Conclusion

1: exchange corrections to in ep scattering are calculated.

2: The corrections to the current experimental data on strange quark form factor are found to be not small. Even reach to -40% in some case.

3: The corrections to is also analyzed and find to reach about -6.65%.

2 and -Z PVA

weakQ

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1: Correction to the precise measurement of from beta decay of neutron.

Further Work

udV

Thanks!

3: Corrections in e-d scattering.

2: PV in BES and the structure of nucleons.Ⅲ

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APPENDIX

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