study of exclusive hard processes with hadron beams at j-parc mini workshop on “structure and...
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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
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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
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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/
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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.
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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)
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Drell-Yan process
10
Wigner Distribution
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Wigner Distribution
d3 r
Transverse Momentum Dependent PDF
Generalized Parton Distr.
d 2kt dzF.T.
d2k t
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)
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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
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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)
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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.
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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)
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•Deuteron wave function at short distances (Fermi motion)•Nucleon off-shell effect•Nuclear correction
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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
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
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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
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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.
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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
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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
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
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)
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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
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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