gpdsgpds 3d structure functions at and -...

Workshop on hadron tomography at J-PARC and KEKB, January 6, 2017 @ KEK

3D structure functions

at and

Yoshiyuki Miyachi, Yamagata University

GPDsGPDs

Lepton-Nucleon scattering

experiments

Lepton-Nucleon scattering

experiments

2017/01/06@KEK Hadron Tomography at J-PARC and KEKB 2

Contents

● 3D Structure of the Nucleon● Generalized Parton Distributions

● GPDs in lepton-nucleon scattering● Deeply Virtual Compton Scattering

● Experiments: HERMES & COMPASS● DVCS results from COMPASS & HERMES● Summary


3D functions: Generalized Parton Distributions

Nucleon

Parton Parton

(x+ξ) P̄ (x−ξ) P̄

F (x , ξ ,t ,μ2)P P 't=(P'−P)

2


GPDs in lepton-nucleon scattering

l

l '

γ∗

N N '

A

l+N→ l '+N '+A

GPSs are studied with “Hard Exclusive Production” of A


Hard Exclusive Production and GPDs

q q'

P P’

t

Deeply Virtual Compton Scattering (DVCS):

Deeply Virtual Meson Production (DVMP):

q q'

P P’

t

e+N →e ' +N ' +γ

e+N →e ' +N ' +{ρ , π , ...}

Involved GPDs: clean reaction

vs Bethe-Heitler process

H , E , H , E

vector meson:pseudo-scalar meson:Meson amplitude involved

H , EH , E

⇔Exclusive DY: π−+ p→ n+ l−+l+


Experimental requirements

l

l '

γ∗

N N '

A

Q2>1GeV2

Hard scatteringHard scattering

Exclusive

Production

Exclusive

Production

・　recoil detection

・　missing mass


Experiments: HERMES and COMPASS

Beam

Target

Unpol. H/D

w/ recoil

detector

2006, 20072006, 2007

Unpol. H

w/ recoil

detector

2012,2016, 2017

2012,2016, 2017

w/ ECAL upgrade

L-pol. H/D

T-pol. H

w/o recoil

detector

2002~20052002~2005

1996~20001996~2000

Pol. NH3,

Pol. 6LiD

w/o recoil

detector

2002~20112002~2011

Pol. e+/e- in HERA e-ring

E = 27.6 GeV

e−/← , e−/→ ,e+ /← , e+ /→

Pol. μ+/μ-

E = 160~200 GeV

μ+ /← ,μ−/→@ 160 GeV

@DESY @CERN


Exclusive γ production at

e

e+ N → e '+ N + γe+ N → e '+ N + γ

Missing-mass spectrum

1996 ~ 2005: w/ Polarized H/D target

No detector for the recoil protonCut on missing-mass spectrum

Exc

lusi

ve


● Sub-detectors in 1 T Solenoid

● Photon Detector (PD)

– 3 Tungsten/Scintillator layers, π0, π/p

● Scintillation Fiber Tracker (SFT)

– 2 x (2 Parallel and 2 Stereo layers), momentum reconstruction and π/p

● Silicon Strip Detector (SSD)

– 2 layers of 16 double sided sensor, momentum reconstruction and π/p

● Unpol. H&D targets: (2006, 2007)

HERMES Recoil Detector ( 2006 ~ 2007)


+ kinematic constraint

e

Forward + recoil

Missing mass spectrum


COMPASS without a recoil detector

“Exclusive meson production”“Exclusive meson production”


COMPASS with a recoil detector (2012 Pilot Run, 2016 ~ 2017)


Exclusivity Check: Forward spectrometer vs CAMERA


Cross section of exclusive γ production

Bethe-Heitler (BH)

σDVCS≪σBH@HERMES

DVCS


Expected azimuthal distribution @ COMPASS


Exclusive photon azimuthal distribution(COMPASS 2012 Pilot Run) ~ 4 weeks

0.005< x<0.01 0.01<x<0.03

x>0.03● BH Monte Carlo normalization

based on integrated luminosity

● BH process dominant at small x

● π0 background contributing at large x


DVCS cross section t-slope(COMPASS 2012 Pilot Run)

x>0.03

● Subtract BH contribution● Subtract π0 background● Acceptance correction & Luminosity normalization

d σ (μ+←

)+d σ (μ−→

)∝

d σBH

+d σDVCS

+K s1Isin ϕ

d σDVCS

d|t|∼exp(−B|t|)

d σDVCS

d|t|∼exp(−B|t|)

Integrate over ϕ


Comparison with HERA results

⟨r⊥2 ⟩∼2B( xB)


0.01<x<0.03

σDVCS≪σBH@HERMES


Differential cross section

d σ∝

Unpol. target

Beam helicityBeam helicityBeam ChargeBeam Charge


Cross section asymmetries and GPDs

ALU

PRL 87 (2001) 182001PRL 87 (2001) 182001

AC


@HERMES, COMPASS@HERMES, COMPASS

Negligible

Sum of quark flavors

Compton form factorsCompton form factors NPB629 (2002) 323-392


with a transversely polarized target


DVCS with a transversely polarized target

UT →　GPD EUT →　GPD E


Experimental requirements

l

l '

γ∗

N N '

A

Q2>1GeV2Hard scatteringHard scattering Exclusive

Production

Exclusive

Production

・　recoil detection

・　missing energy

Polarized beam

Anti-lepton beam

Polarized beam

Anti-lepton beam

Transverse pol. for ETransverse pol. for ENot available yet


Extracted overall asymmetries @ HERMES

Beam Charge Asymmetries

Beam Spin Asymmetries

Target Spin Asymmetries

Double Spin Asymmetries



T-p

ol.

targ

etL-

pol.

targ

et

H

GPD

E

~H

PRL 87 (2001) 182001PRD 75 (2007) 011103JHEP 11 (2009) 083JHEP 07 (2012)032JHEP 10 (2012) 042NPB 829 (2010) 1


JHEP 06 (2008) 066PLB 704 (2011) 15JHEP 06 (2008) 066PLB 704 (2011) 15

JHEP 06 (2010) 019NPB 842 (2011) 265JHEP 06 (2010) 019NPB 842 (2011) 265


Beam charge asymmetry


Beam spin asymmetry


Beam Spin Asymmetry with Recoil Detector at HERMES

JHEP 10 (2012) 042JHEP 10 (2012) 042


DVCS with T-pol. H target HERMES,

JHEP06 (2008) 066

ACcos

∝ℜ[ F H ]

AUT , DVCSsin− S

∝ℑ[H E ∗−E H ∗

E H ∗− H E ∗

]

AUT , Isin− S

∝−AUT ,Isin −Scos

∝ℑ[ F1E −F2H ]


Extracted overall asymmetries @ HERMES

Beam Charge Asymmetries

Beam Spin Asymmetries





T-p

ol.

targ

etL-

pol.

targ

et

H

GPD

E

~H



JHEP 06 (2008) 066PLB 704 (2011) 15JHEP 06 (2008) 066PLB 704 (2011) 15

JHEP 06 (2010) 019NPB 842 (2011) 265JHEP 06 (2010) 019NPB 842 (2011) 265


COMPASS 2016 ~ 2017(2 × 6 months)

0.01<x<0.03


Expected beam charge spin asymmetries


Summary

● “Hard Exclusive Production in lepton-nucleon scattering” is a tool to study GPDs.

● Deeply Virtual Compton Scattering● Hard exclusive meson production Exclusive DY⇔

● DVCS @ HERMES● 27.6 GeV polarized e-/e+

– Combine analysis of “Charge” & “Spin”● L-Pol. H/D targets, T-Pol. H target (w/o the recoil detector)

● Unpol. H/D targets (w/ the recoil detector)● Various azimuthal amplitudes were extracted


Summary

● DVCS @ COMPASS● 160 GeV μ-/μ+● Unpol. H target with the recoil detector

● 2012 Pilot Run

● t-slope of σDVCS

extracted

● 2016 Run successfully finished + 2017 Run (2 × 6 months)● GPD H via Interference term

● >2018: DVCS with transv. pol. target and recoil detector● GPD E● Future addendum to COMPASS-II proposal

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