Study of Exclusive Hard Processes with Hadron Beams at J-PARC Mini Workshop on “Structure and...

1

Study of Exclusive Hard Processes with Hadron

Beams at J-PARC

Mini Workshop on “Structure and Productions of Charmed Baryons II”

August 7-9, 2014, J-PARC, Tokai

Wen-Chen Chang 章文箴Institute of Physics, Academia Sinica 中央研究院 物理研究所

Outline

• Uniqueness of hadron physics studied at HiPBL of J-PARC

• Selected Physics Processes:• Drell-Yan process• Hard exclusive process

• Feasibility study of exclusive Drell-Yan process in P50 spectrometer

• Summary

2

3

High-res., High-momentum Beam Line• High-intensity secondary Pion beam

• High-resolution beam: Dp/p~0.1%

Dispersive Focal Point (DFP)Dp/p~0.1%

Collimator

15kW Loss Target(SM)

Exp. Target (FF)

Pion BeamUp to 20 GeV/c

H. Noumi

4

High-res., High-momentum Beam Line• High-intensity secondary Pion beam

– >1.0 x 107 pions/sec @ 20GeV/c• High-resolution beam: Dp/p~0.1%

* Sanford-Wang:15 kW Loss on Pt, Acceptance :1.5 msr%, 133.2 m

Open a new platform for hadron physics

0 5 10 15 201.0E+03

1.0E+04

1.0E+05

1.0E+06

1.0E+07

1.0E+08

1.0E+09

[GeV/c]

Co

un

ts/s

ec

0 5 10 15 201.0E+03

1.0E+04

1.0E+05

1.0E+06

1.0E+07

1.0E+08

1.0E+09

[GeV/c]

Co

un

ts/s

ec

Prod. Angle = 0 deg. (Neg.)

p-

K-

pbar

p+

K+

Prod. Angle = 3.1 deg (Pos.)

H. Noumi

http://www-conf.kek.jp/hadron1/j-parc-hm-2013/

5

6

http://j-parc-th.kek.jp/workshops/2014/02-10/

Uniqueness of hadron physics studied at HiPBL of J-PARC• The beam energy at J-PARC at 10-20 GeV might be

most ideal for studying the hard exclusive processes and discerning the quark-hadron transition in the strong interaction.

• Valance-like partonic degrees of freedom of hadrons could be discerned, compared to the collisions at low-energy regime.

• Reasonably large cross sections, compared to the collisions at higher energy.

7

Constituent-Counting Rule in Hard Exclusive Process Kawamura et al., PRD 88, 034010 (2013)

8

p n 0Kp

2

1( ) ( ) CMn a b c d

da b n nc d f

dt sn n n

1 3 2 3 7n 2 3 2 3 8n

Selected Physics Processes

• Drell-Yan process• Inclusive pion-induced Drell-Yan• Exclusive pion-induced Drell-Yan

• Hard exclusive production process• Exclusive pion-N Lambda(1405) production (Sekihara’s

talk)

• Charm production process• Inclusive pion-induced J/psi production• Exclusive pion-N J/psi production• Exotic charmed baryons (this workshop)

9

Drell-Yan process

10

Wigner Distribution

11

Wigner Distribution

d3 r

Transverse Momentum Dependent PDF

Generalized Parton Distr.

d 2kt dzF.T.

d2k t

PDF

dx

Form Factors

GPD

Ji, PRL91,062001(2003)

( , , )TW r x k

f( , )Tx k

f( )x

H( , , t)x

1 2( ), ( )F t F t

u valence

sea (x 0.05)

gluon (x 0.05)

d

Unpolarized Parton Distributions (CTEQ6)

12

13

Is in the proton?

Gottfried Sum Rule

1

2 20

1 1

0 0

[( ( ) ( )) / ]

1 2( ( ) ( )) ( ( )

( f ( ) ( )

( ))3 31

3)

p nG

v v

S F x F x x dx

u x d x dx u x d x dx

i u x d x

=

du

14

Experimental Measurement of Gottfried Sum

New Muon Collaboration (NMC), Phys. Rev. D50 (1994) R1

SG = 0.235 ± 0.026

( Significantly lower than 1/3 ! )

S. Kumano, Physics Reports, 303 (1998) 183

15

Light Antiquark Flavor Asymmetry: Drell-Yan Exps Naïve Assumption:

NA51 (Drell-Yan, 1994)

NMC (Gottfried Sum Rule)

NA 51 Drell-Yan confirms

d(x) > u(x)

16

Light Antiquark Flavor Asymmetry: Drell-Yan Exps Naïve Assumption:

NA51 (Drell-Yan, 1994)

E866/NuSea (Drell-Yan, 1998)

NMC (Gottfried Sum Rule)

Origin of u(x)d(x)?

• Pauli blocking of valance quarks

• Meson cloud in the nucleons (Thomas 1983, Kumano 1991): Sullivan process in DIS.

• Chiral quark model (Eichten et al. 1992; Wakamatsu 1992): Goldstone bosons couple to valence quarks.

17

Momentum Dependence of the Flavor Structure of the Nucleon SeaJ.-C. Peng, W.-C. Chang, H.-Y. Cheng, T.-J. Hou, K.-F. Liu, J.-W. Qiu, arXiv:1401.1705

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JR14 NMC

1. Fluctuation of a valence quark into a quark and a highly virtual gluon,

2. A quick splitting of the gluon into a quark and antiquark pair

3. Annihilation or recombination of the quark and the newly produced antiquark into a highly virtual gluon, which is then

4. Absorbed by the quark.19

u d

Momentum Dependence of the Flavor Structure of the Nucleon SeaJ.-C. Peng, W.-C. Chang, H.-Y. Cheng, T.-J. Hou, K.-F. Liu, J.-W. Qiu, arXiv:1401.1705

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Extracting d-bar/-ubar From Drell-Yan ScatteringRatio of Drell-Yan cross sections

(in leading order—E866 data analysis confirmed in NLO)

Global NLO PDF fits which include E866 cross section ratios agree with E866 results

Fermilab E906/Drell-Yan will extend these measurements and reduce statistical uncertainty.

E906 expects systematic uncertainty to remain at approx. 1% in cross section ratio.

“Flavor Structure of the Nucleon Sea”W.-C. Chang and J.-C. Peng, arXiv:1406.1260

A. Accardi et al.Phys. Rev. D 84, 014008 (2011)

21

•Deuteron wave function at short distances (Fermi motion)•Nucleon off-shell effect•Nuclear correction

22

J.C. Peng

Helium/DME at 80/20 ratio

beam

140 µm

Experimental Setup II: BoNuS RTPC

Fit RTPC points to determine helix of proton trajectory.

Momentum determined from track curvature in solenoid field.

dE/dx along track in RTPC also provides momentum information.

SolenoidMagnet

BoNuSRTPC

Moller Catcher

To BoNuS RTPC

to CLAS

p

n

M. Eric Christy23

Neutron F2 Structure Function via Spectator TaggingPRL 108, 142001 (2012)

24

20.65 4.52 GeV

0.2 0.8

Q

x

Pion-Induced DY Without OR With Spectator Tagging

25

1 2 1 2 1 2

1 2 1 2 1 2

( ) ( ) ( ) ( ) ( ) ( )( )

( ) ( ) ( ) ( ) ( ) ( )

pp p

f nn p

u x u x d x d x u x u xpx

n u x u x d x d x u x d x

1 2 2

2 21 2 1 2

( ) ( ) ( )( )

( ) ( )( ) ( ) ( ) ( )

p p

f p pn p

u x u x u xpx

d d x u xu x u x u x u x

1 2 1 2 1 2

1 2 1 2 1 2

( ) ( ) ( ) ( ) ( ) ( )( )

( ) ( ) ( ) ( ) ( ) ( )

pp p

f nn p

d x d x u x u x d x d xpx

n d x d x u x u x d x u x

1 2 2

2 21 2 1 2

( ) ( ) ( )( )

( ) ( )( ) ( ) ( ) ( )

p p

f p pn p

d x d x d xpx

d u x d xd x d x d x d x

1 2 2

21 2

( ) ( ) ( )( )

( )( ) ( )

p p

f pp

u x u x u xpx

p d xd x d x

Wigner Distribution

26

Wigner Distribution

d3 r

Transverse Momentum Dependent PDF

Generalized Parton Distr.

d 2kt dzF.T.

d2k t

PDF

dx

Form Factors

GPD

Ji, PRL91,062001(2003)

( , , )TW r x k

f( , )Tx k

f( )x

H( , , t)x

1 2( ), ( )F t F t

three distribution functions are necessary to describe the quark structure of the nucleon at LO in the collinear case

Transverse momentum dependent (TMD) PDF

taking into account the quark intrinsic transverse momentum kT ,

At leading order 8 PDFs are needed.

U L T

U

L

T

nucleon polarization“TMDs”

1fnumber density

1ghelicity

1htransversity

TΔ q

Δq

q

T1h

1h

L1h

T1f

T1g

qΔT0

Sivers

Boer-Mulders

T-odd

Sivers function correlation between the transverse spin of the nucleon and the transverse momentum of the quark

sensitive to orbital angular momentum

Boer-Mulders function correlation between the transverse spin and thetransverse momentum of the quark in unpol nucleons 28

qu

ark po

larization

1 ( , )T Tf x k

1 ( , )Th x k

pretzelosity

Global Analysis of SIDIS from HERMES and COMPASS

M. Anselmino et al., Eur.Phys.J.A39:89-100,2009

28

HERMES proton target COMPASS deuteron target

33329

Sivers Functions from SIDISM. Anselmino et al., Eur.Phys.J.A39:89-100, 2009

u u

dd

Sign Change of Sivers & Boer-Mulders FunctionsJ.C. Collins, Phys. Lett. B 536 (2002) 43

A.V. Belitsky, X. Ji, F. Yuan, Nucl. Phys. B 656 (2003) 165D. Boer, P.J. Mulders, F. Pijlman, Nucl. Phys. B 667 (2003) 201

Z.B. Kang, J.W. Qiu, Phys. Rev. Lett. 103 (2009) 172001

30

Sivers, BM | *Sivers, BM |1DY SIDIS

Drell-Yan SIDIS

• QCD gluon gauge link (Wilson line) in the initial state (DY) vs. final state interactions (SIDIS).

• Experimental confirmation of the sign change will be a crucial test of perturbative QCD and TMD physics.

31

experiment particles energy x1 or x2 luminosity timeline

COMPASS(CERN) p± + p↑ 160 GeV

s = 17.4 GeV xt = 0.2 – 0.3 2 x 1033 cm-2 s-1 2014, 2018

PAX(GSI) p↑ + pbar

colliders = 14 GeV xb = 0.1 – 0.9 2 x 1030 cm-2 s-1 >2017

PANDA(GSI) pbar + p

↑ 15 GeVs = 5.5 GeV xt = 0.2 – 0.4 2 x 1032 cm-2 s-1 >2016

NICA(JINR) p↑ + p

colliders = 20 GeV xb = 0.1 – 0.8 1 x 1030 cm-2 s-1 >2018

PHENIX(RHIC) p↑ + p

colliders = 500 GeV xb = 0.05 – 0.1 2 x 1032 cm-2 s-1 >2018

RHIC internaltarget phase-1 p↑ + p

250 GeVs = 22 GeV xb = 0.25 – 0.4 2 x 1033 cm-2 s-1 >2018

RHIC internaltarget phase-1 p↑ + p

250 GeVs = 22 GeV xb = 0.25 – 0.4 6 x 1034 cm-2 s-1 >2018

FNAL Pol tgt (E1039) p + p↑ 120 GeV

s = 15 GeV xt = 0.1 – 0.45 3.4 x 1035 cm-2 s-1 2016

FNAL Pol beam (E1027) p↑ + p

120 GeVs = 15 GeV xb = 0.35 – 0.85 2 x 1035 cm-2 s-1 2018

Planned Polarized Drell-Yan Experiments

Wolfgang Lorenzon

Key Elements of Polarized DY Exp.:Transversely Polarized NH3 Target

32

Magnet

33333

24 9 GeV/cM 22 2.5 GeV/cM

Theoretical Predictions vs. COMPASS Expected Precision

Sivers SiversBoer-Mulders Boer-Mulders

BMPretze. BMtransv BMPretze. BMtransv

three distribution functions are necessary to describe the quark structure of the nucleon at LO in the collinear case

Transverse momentum dependent (TMD) PDF

taking into account the quark intrinsic transverse momentum kT ,

At leading order 8 PDFs are needed.

U L T

U

L

T

nucleon polarization“TMDs”

1fnumber density

1ghelicity

1htransversity

TΔ q

Δq

q

T1h

1h

L1h

T1f

T1g

qΔT0

Sivers

Boer-Mulders

T-odd

Sivers function correlation between the transverse spin of the nucleon and the transverse momentum of the quark

sensitive to orbital angular momentum

Boer-Mulders function correlation between the transverse spin and thetransverse momentum of the quark in unpol nucleons 35

qu

ark po

larization

1 ( , )T Tf x k

1 ( , )Th x k

pretzelosity

Angular Distribution of Lepton Pair

2 2

2 2 2

(1 cos sin 2 cos sin cos 2 )2

( (1 cos ) (1 cos ) sin 2 cos sin cos 2 )T LW W W W

d

d

0

annilation parton model:

O( ) =1, = =0; W 0W1,Ts L

qq

Collins-Soper Frame

35

Lam and Tung (PRD 18, 2447, (1978))Lam-Tung Relation

36

2 2 2[ (1 cos ) (1 cos ) sin 2 cos sin cos 2 ]T L

dW W W W

d

2 2(1 cos sin 2 cos sin cos 2 )2

d

d

1 1 2 =pQCD: O( ), ; 02 Ls W W

E615 (PRD 39, 92 (1989)) Violation of LT Relation in -induced Drell-Yan Process

37

D. Boer

38

D. Boer

0

39

Boer (PRD 60, 014012 (1999))Hadronic Effect, Boer-Mulders Functions

1 1

1

1

Boer-Mulders Function : a correlation between quark's and

transverse spin in

can lead to an azimuthal depe

an unpolar

ndence with

iz

ed

( ) (

hadro

2

n

)

T

h

k

h h

h

N

Consistency of factorizati

0

on in term of TMD

for large

s2 Tk

40

E866 (PRL 99 (2007) 082301) Azimuthal cos2Φ Distribution of DY events in pd

ν(π-Wµ+µ-X)~ [valence h1┴(π)] * [valence h1

┴(p)]

ν(pdµ+µ-X) ~ [valence h1┴(p)] * [sea h1

┴(p)]

Sea-quark BM functions are much smaller than valence quarks 41

Boer-Mulders functions from unpolarized pD and pp Drell-Yan

Z. Lu and I. Schmidt,

PRD 81, 034023 (2010)

V. Barone et al.,PRD 82, 114025 (2010)

Sign of BM functions and their flavor dependence? 42

Flavor separation of the Boer–Mulders functionZ. Lu et al. (PLB 639 (2006) 494)

2 22

2

cos 2 ( ) cos 2

4 4T A B T

TA B A B T A B

q d h h llX qW d d q

M M d dx dx d q M M

MIT Bag Model Spectator Model Large Nc limit

Deuterium target 43

Wigner Distribution

44

Wigner Distribution

d3 r

Transverse Momentum Dependent PDF

Generalized Parton Distr.

d 2kt dzF.T.

d2k t

PDF

dx

Form Factors

GPD

Ji, PRL91,062001(2003)

( , , )TW r x k

f( , )Tx k

f( )x

H( , , t)x

1 2( ), ( )F t F t

x+x x-x

t

GPDs

P P’

( ,0,0) ( ) ( )

( ,0,0) ( ) ( )

f f f

f f f

H x q x q x

H x q x q x

1

1

1

1

2

1

1

1

1

1

( , , ) ( )

( , , ) ( )

( , , ) ( )

( , , ) ( )

ff

ff

f Af

f pf

dx H x t F t

dx E x t F t

dx H x t g t

dx E x t g t

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

1

2

1 1

1

xExHxdxLJ ffff

f

),,( txGPD

Ji’s sum rule

Generalized Parton Distribution (GPD)

2)'( PPt

0t

5

( , , ) ( , , )

( , , ) ( , , )

f f

f f

no spin flip H x t H x t

spin flip E x t E x t

0t

45

Spacelike vs. Timelike ProcessesMuller et al., PRD 86 031502(R) (2012)

46

Deeply Virtual Compton Scattering Timelike Compton Scattering

2 0q 2 0q

Spacelike vs. Timelike ProcessesMuller et al., PRD 86 031502(R) (2012)

47

Deeply Virtual Meson Production Exclusive Meson-induced DY

2 0q 2 0q

N+-N(PLB 523 (2001) 265)

𝑡=(𝑝−𝑝 ′ )2

𝑄 ′ 2=𝑞 ′ 2>0

2 2

2

' '

2 N

Q Q

pq s M

( ')

( ')

p p

p p

48

N+-N(PLB 523 (2001) 265)

𝑡=(𝑝−𝑝 ′ )2

𝑄 ′ 2=𝑞 ′ 2>0

2 2

2

' '

2 N

Q Q

pq s M

( ')

( ')

p p

p p

49

50

Pion-pole Dominance

Pion-pole Dominance (PLB 523 (2001) 265)

51

2pion Timelike Form Factor ( ' )F Q

2'Q

t pion pole Form

(

actor

)

F

poleF t

-2

Pion-Photon Transition Form Factor

in process( ' ) e eF Q

N+-N (PLB 523 (2001) 265)

52

𝑸 ′𝟐=𝒒 ′𝟐=𝟓𝑮𝒆𝑽 𝟐

2 2

2

' '0.2

2 N

Q Q

pq s M

=-0.2 GeV2

Cross sections increase toward small s!

J-PARC

|t| (GeV2)

53

N+-N: |t| and Q (M) dependence

|t| (GeV2)

54

Total Cross Sections of Exclusive Drell-Yan as a function of momentum of Beam

M > 1.5 GeV

10 pb

GPD(xB,Q2) in space-like regime

55

GPD(xB,Q2) in both space-like and time-like regime

56

J-PARC’s results in the time-like and large-Q2 region will be complementary to what to be obtained in space-like region from the deeply virtual Compton scattering (DVCS) deeply virtual meson scattering (DVMS) process to be measured in JLab.

Large-Q2 region

Hard exclusive production process

57

Constituent-Counting Rule in Hard Exclusive ProcessKawamura et al., PRD 88, 034010 (2013)

58

p n 0Kp

2

1( ) ( ) CMn a b c d

da b n nc d f

dt sn n n

1 3 2 3 7n 2 3 2 3 8n

Quark Degrees of (1405)Kawamura et al., PRD 88, 034010 (2013)

59

0K (1405)p

1-100 pb

T. Sekihara’s talk

J-PARC

60

Experimental Difficulties0

0

K (1405)

K

(1405)

p

Charmed production process

61

J/ production in 22 GeV πCu collisionsNucl. Phys. B179 (1981) 189

62

(N)(pN): fusion dominates

(N)(pN): gg fusion dominates

J/-N Interaction StrengthWu and Lee, PRC 88, 015205 (2013)

63

J-PARC

J/-N Interaction StrengthWu and Lee, PRC 88, 015205 (2013)

64

/d J p p

Look for production of hidden charm bound state. arXiv:1212.2440

<0.1 pb

65

66

H. Noumi’s talk

Feasibility study of Drell-Yan processes in the conceptual detector system

67

Pion-Induced Exclusive Drell-Yan Process

2small ( )t q q 2large ( )t q q

: pion distritribution amplitude (DA) TDA : -N transistion distritribution amplitude

•DA characterizes the minimal valence Fock state of hadrons.•DA of pion are also explored by pion-photon transition form factor in Belle and Barbar Exps.

•TDA characterizes the next-to-minimal valence Fock state of hadrons.•TDA of pion-nucleon is related to the pion cloud of nucleons.

Bernard Pire , IWHS2011

68

Wen-Chen Chang, Takahiro SawadaInstitute of Physics, Academia Sinica, Taipei 11529, Taiwan

Hiroyuki Kawamura, Shunzo KumanoKEK Theory Center, Institute of Particle and Nuclear Studies,

High Energy Accelerator Research Organization (KEK)

Jen-Chieh PengDepartment of Physics, University of Illinois at

Urbana-Champaign, Urbana, Illinois 61801, USA

Shin’ya SawadaInstitute of Particle and Nuclear Studies,

High Energy Accelerator Research Organization (KEK)

69

70

Experimental Requirements• Beam:

• High momentum: 15-20 GeV beam • High flux: >108/sec• Similar interesting physics to be explored by other secondary beams

like K and pbar.

• Target: • Long liquid hydrogen• Short nuclei target.

• Detector:• Open aperture without hadron absorber before momentum

determination: minimize multiple-scattering of muons• Spectrometer with good momentum resolution and particle ID• Muon ID in the forward direction at the very downstream

J-PARC P50 Spectrometer

71

72

J-PARC P50 Spectrometer

p-

LH2-target

Ring ImageCherenkovCounter

Internal DC

FM magnet

ps-

K+

Fiber tracker

Beam GC

Internal TOF

Internal TOFDC

TOF wall

2m

Decay p(p+)

20 GeV/cBeamp-

Acceptance: ~ 60% for D*, ~80% for decay p+ Resolution: Dp/p~0.2% at ~5 GeV/c 　（ Rigidity ： ~2.1 Tm)

73

20 GeV π-

Exclusive DYx 200 events

Thanks to K. Shirotori for P50 MC framework.

74

J-PARC P50 Spectrometer + MuID

p-

LH2-target

Ring ImageCherenkovCounter

Internal DC

FM magnet

ps-

K+

Fiber tracker

Beam GC

Internal TOF

Internal TOFDC

TOF wall

2m

Decay p(p+)

20 GeV/cBeamp-

Acceptance: ~ 60% for D*, ~80% for decay p+ Resolution: Dp/p~0.2% at ~5 GeV/c 　（ Rigidity ： ~2.1 Tm)

||<60

Scintillator Muon trigger device

Yield Estimation from J-PARC P50

75

76

Total Cross Sections of Exclusive Drell-Yan as a function of P

M > 1.5 GeV

10 pb

Yield Estimation based on J-PARC P50 Parameters• Ibeam=107 π/s, nTGT=4 g/cm2 (57cm LH2),

ΔΩ/Ω~100% , ε(DAQ, Tracking, PID)=0.9*0.7*0.9 1 events/day/pb• Beam time of 200 days

• Inclusive pion-induced Drell-Yan: OK• Exclusive pion-induced Drell-Yan: Marginally OK• Exclusive pion-N Lambda(1405) production: OK (multi-

particle acceptance?)• Inclusive pion-induced J/psi production: OK• Exclusive pion-N J/psi production: NO

77

20-GeV - + proton+-X MX seen In P-50 Spectrometer + MuID

78

Red: Exclusive DY ( 10 pb )Blue: Inclusive DY ( 500 pb )Green: random BG from meson decay

After 200-day data-taking

Assumption: Δp/p = 0.2 %

Missing Mass MX (GeV2)

Nev

ent The signal of exclusive Drell-

Yan processes can be clearly identified in the missing mass spectrum of dimuon pairs.

Summary (I)

• High-energy hadron beam at J-PARC is ideal for studying hard exclusive processes.

• The study of -induced DY/charm production and hard exclusive processes will offer important understanding on

• Nucleon structure: sea quarks PDF; TMD, GPD• pion structure: DA and Timelike FF• Structure of exotic hadrons• J/ production mechanism, exotic charmed baryons

79

80

Summary (II)

• Spectrometer with large acceptance and good mass resolution is required for the measurement and such measurement in P-50 conceptual detectors seems promising.

• Availability of deuterium target together with the detection of recoiled protons will enable the measurement of flavor separation of BM functions and valance-quark distributions at large-x.

81

Backup Slides

R. Muto, KEK

82

R. Muto, KEK

83

R. Muto, KEK

84

85

J-PARC High-momentum Beam Line• High-intensity secondary Pion beam

– >1.0 x 107 pions/sec @ 20GeV/c• High-resolution beam: p/p~0.1%

* Sanford-Wang:15 kW Loss on Pt, Acceptance :1.5 msr%, 133.2 m

0 5 10 15 201.0E+03

1.0E+04

1.0E+05

1.0E+06

1.0E+07

1.0E+08

1.0E+09

[GeV/c]

Co

un

ts/s

ec

0 5 10 15 201.0E+03

1.0E+04

1.0E+05

1.0E+06

1.0E+07

1.0E+08

1.0E+09

[GeV/c]

Co

un

ts/s

ec

Prod. Angle = 0 deg. (Neg.)

p-

K-

pbar

p+

K+

Prod. Angle = 3.1 deg (Pos.)

87

Parton Interpretation of GPDs(Phys. Rept, 388, 41 (2003), hep-ph/0307382; arXiv:1302.2888)

GPD GPD GPD

DGLAP-II: -1<x<-PDFs of antiquarks

ERBL: |x|<DAs of mesons

DGLAP-I: <x<1PDFs of quarks

Cross-section measurementand beam charge asymmetry (ReT)

integrate GPDs over x

Beam or target spin asymmetrycontain only ImT,

therefore GPDs at x = x and - x

(M.

Va

nd

erh

ae

ghe

n)

1

1

1

1

),,(),,(

~),,(

~ tHidxx

txHPdx

ix

txHT DVCS

*g

p p’

, ,...g M

H,E,H,E~ ~x

tx~xB

88

The GPDs enter in the DVCS amplitude as integrals over x

• GPDs appear in the real part through a Principal-value integral over x• GPDs appear in the imaginary part along the line x=+/-x

GPDs in the DVCS amplitude

VGG model

T DVCS dxH(x,, t)

x i

1

1

P dxH(x,, t)

x i

1

1 H(x ,, t)

x- x+

p-D/2 p’(=p+ /D 2)

, ,...g M

H,E(x,x,t)H,E(x,x,t)

~~

x-x

t=D2

-2x

x+x

GPDs

*g

(Ji, Radyushkin, Muller, Collins, Strikman, Frankfurt)

light-cone dominance, nμ (1, 0, 0, -1) / (2 P+)

p-D/2 p’(=p+ /D 2)

, ,...g M

H,E(x,x,t)H,E(x,x,t)

~~

x-x

t=D2

-2x

x+x

GPDs

*g

Vector Ms : H,E

Large Q2, small t

PS Ms : H,E~ ~

(Ji, Radyushkin, Muller, Collins, Strikman, Frankfurt)

g : sT lead. twist

Mesons : sL

light-cone dominance, nμ (1, 0, 0, -1) / (2 P+)

{g-[Hq(x,x,t)N(p’)g+N(p) + Eq(x,x,t)N(p’)is+kDkN(p)]

+g5 g-[Hq(x,x,t)N(p’)g+ g5 N(p) + Eq(x,x,t)N(p’)g5D+N(p)]}2M_ ~~

2M

_

_

_

, ,...g M

H,E(x,x,t)H,E(x,x,t)

~~

x-x

t=D2

-2x

x+x

*g

{g-[Hq(x,x,t)N(p’)g+N(p) + Eq(x,x,t)N(p’)is+kDkN(p)]

+g5 g-[Hq(x,x,t)N(p’)g+ g5 N(p) + Eq(x,x,t)N(p’)g5D+N(p)]}2M_ ~~

2M

_

_

_

Vector Ms : H,E

Large Q2, small t

PS Ms : H,E~ ~

(Ji, Radyushkin, Muller, Collins, Strikman, Frankfurt)

g : sT lead. twist

Mesons : sL p-D/2 p’(=p+ /D 2)

GPDs

light-cone dominance, nμ (1, 0, 0, -1) / (2 P+)

H, H, E, E (x,ξ,t)~ ~

“Ordinary” parton distributions

H(x,0,0) = q(x), H(x,0,0) = Δq(x) ~

x

Elastic form factors

H(x,ξ,t)dx = F(t) ( ξ)

x

Ji’s sum rule

2Jq = x(H+E)(x,ξ,0)dx

gq LGL 21

21

(nu

cleo

n sp

in)

x+ξ x-ξ

tγ, π, ρ, ω…

-2ξ

: do NOT appear in DIS NEW INFORMATION

xξ-ξ +

1-1 0anti-quark distribution

quark distribution

q q distribution amplitude

94