Semi-Inclusive Charged-Pion Electro-production off Protons and Deuterons: Cross Sections,

Ratios and Transverse Momentum Dependence

Rolf Ent (Jefferson Lab)Baryons 2013Glasgow, UK June 27

Semi-Inclusive Charged-Pion Electro-production off Protons and Deuterons: Cross Sections,

Ratios and Transverse Momentum Dependence

• HERMES data established the potential for semi-inclusive DIS (SIDIS)• JLab/Hall C’s basic SIDIS cross section data at a 6-GeV JLab showed

agreement with partonic expectations and hints at a flavor dependence in transverse momentum dependence, laying the foundation for a vigorous 12-GeV SIDIS program.

T. Navasardyan et al., Phys. Rev. Lett. 98 (2007) 022001;H. Mkrtchyan et al., Phys. Lett. B665 (2008) 20;R. Asaturyan et al., Phys. Rev. C 85 (2012) 015202.

Also M. Osipenko et al. (CLAS), Phys. Rev. D 80 (2009) 032004.• Recently also extensive set of unpolarized SIDIS cross section data

from both HERMES and COMPASS:A. Airapetyan et al., Phys. Rev. D 87 (2013) 074029.C. Adolph et al., arXiv:1305.7317v1 (2013).

Pre-Amble

Outline

• Semi-Inclusive Deep Inelastic Scattering – Introduction

• Towards a Partonic Description

• Semi-Inclusive Deep Inelastic Scattering – Formalism

• Transverse Momentum Dependence – Flavor Dependence

• Unpolarized SIDIS Cross Section Measurements @12 GeV

Charged Pions and Neutral Pions

Semi-Inclusive Charged-Pion Electro-production off Protons and Deuterons: Cross Sections,

Ratios and Transverse Momentum Dependence

Beyond form factors and quark distributions

Generalized Parton and Transverse Momentum Distributions

Proton form factors, transverse charge & current densities

Structure functions,quark longitudinalmomentum & helicity distributions

Correlated quark momentum and helicity distributions in transverse space - GPDs

Extend longitudinal quark momentum & helicity distributions to transverse momentum distributions - TMDs

2000’s

1990’s

The road to orbital motion

The difference between the p+, p–, and K+ asymmetries reveals that quarks and anti-quarks of different flavor are orbiting in different ways within the proton.

Swing to the left, swing to the right: A surprise of transverse-spin experiments

dsh ~ Seq2q(x) dsf Df

h(z)

Sivers distribution

The Incomplete Nucleon: Spin Puzzle

DS Lq Jg++1

2=

1

2

• DS ~ 0.25 (world DIS)• DG small (RHIC+DIS)• Lq?

Longitudinal momentum fraction x and transverse momentum images

Longitudinal momentum fraction x and transverse spatial images

Up quark Sivers Function

12 GeV projections: valence quarks well mapped

Solution: Detect a final state hadron in addition to scattered electron Can ‘tag’ the flavor of the struck quark by measuring the hadrons produced: ‘flavor tagging’

DIS probes only the sum of quarks and anti-quarks requires assumptions on the role of sea quarks

Measure inclusive (e,e’) at same time as (e,e’h)

SIDIS

SIDIS – Flavor Decomposition

• Leading-Order (LO) QCD • after integration over pT and f• NLO: gluon radiation mixes x and z dependences

• Target-Mass corrections at large z

• ln(1-z) corrections at large z

qqq

q

hqqq

(e,e') (x)(x)fe

(z)(x)Dfe

hX)(epdz

dσ

σ 2

2

1

: parton distribution function

: fragmentation function

)(xfq

)(zDhq

Mx2 = W’2 ~ M2 + Q2 (1/x – 1)(1 - z) z = Eh/n

E00-108 Experiment in Hall C/JLab

1) Probe p+ and p- final states2) Use both proton and neutron (deuteron) targets3) Combination of precise cross sections and ratios allows confirmation of interpretation in terms of convolution of quark distribution and fragmentation function4) Combination allows, naively, a separation of quark kt-widths from fragmentation pt-widths(if sea quark contributions small)

Mx2 = W’2 ~ M2 + Q2 (1/x – 1)(1 - z)

z = Eh/nMx2

D region

Convolution of CTEQ5 quark distribution and BKK fragmentation function

x ~ 0.3, Q2 ~ 2.3 (GeV/c)2 0.2 < x < 0.6, 2 < Q2 < 4, 0.3 < z < 1

How Can We Verify Factorization?

Neglect sea quarks and assume no kt dependence to parton distribution functions

Fragmentation function dependence drops out in Leading Order

[sp(p+) + sp(p-)]/[sd(p+) + sd(p-)]

= [4u(x) + d(x)]/[5(u(x) + d(x))]

~ sp/sd independent of z and kt

[sp(p+) - sp(p-)]/[sd(p+) - sd(p-)]

= [4u(x) - d(x)]/[3(u(x) + d(x))]

independent of z and kt,

but more sensitive to assumptions

Closed (open) symbols reflect data after (before) events from coherent r production are subtracted

GRV & CTEQ,@ LO or NLO

(Note: z = 0.65 ~ Mx

2 = 2.5 GeV2)

E00-108: Onset of the Parton Model

Good description for p and d targets for

0.4 < z < 0.65

E00-108: Onset of the Parton Model

1R*4

R4

D

D

π

π

N

NR

(Resonances cancel (in SU(6)) in D-/D+ ratio extracted from deuterium data)

(Deuterium data)

p

quark

Collinear Fragmentation

factorization

Seq2q(x) Dq

p(z)

Destructive interference leads to factorization and duality

F. Close et al : SU(6) Quark ModelHow many resonances does one need to average over to obtain a complete set of states to mimic a parton model? 56 and 70 states o.k. for closure

From deuterium data: D-/D+ = (4 – Np+/Np-)/(4Np+/Np- - 1)

Resonances cancel in D-/D+ ratio extracted from deuterium!

E00-108: Onset of the Parton Model in SIDIS

Curves are parton model calculations using CTEQ5M parton distributions at NLO and BKK fragmentation functions.

Agreement with the parton model expectation is always far better for ratios, also for D/H, Al/D, or for ratios versus z or Q2.

Bodes well for SIDIS at 12 GeV

x = 0.4

x = 0.32 N-D region

Solid (open) symbols are after (before) subtraction of diffractive r events

Phys. Rev. C85: 015202 (2012)

CTEQ5M

dv/uv extracted from differences and ratios of p+ and p- cross sections off H and D targets

New Observable Reveals Interesting Behavior of Quarks

Target:(transversely)

polarized 3He ~ polarized neutron

J. Huang et al., PRL 108, (2012) 052001

1st measurement of ALT beam-target double-spin asymmetry

Indications:• A non-vanishing quark “transversal helicity”

distribution, reveals alignment of quark spin transverse to neutron spin direction

• Quark orbital motions

1st measurement of 3He (neutron) single-spin asymmetries (SSA)Measurement of Sivers & Collins SSA’s in X. Qian et al., PRL 107, (2011) 072003

Pt = pt + z kt + O(kt

2/Q2)

p

m

xTMD

TMDu(x,kT)

f1,g1,f1T ,g1T

h1, h1T ,h1L ,h1

Final transverse momentum of the detected pion Pt arises from convolution of the struck quark transverse momentum kt with the transverse momentum generated during the fragmentation pt.

Linked to framework of Transverse Momentum Dependent Parton Distributions

SIDIS – kT Dependence

TMDq(x,kT)

p

m

XTMD

Transverse momentum dependence of SIDISLinked to framework of Transverse Momentum Dependent Parton Distributions

Unpolarized kT-dependent SIDIS: in framework of Anselmino et al. described in terms of convolution of quark distributions f and (one or more) fragmentation functions D, each with own characteristic (Gaussian) width Emerging new area of study

Unpolarized target

Longitudinally pol. target

Transversely pol. target

N q

U L T

U f1 h1

L g1 h1 L

T f1T g1T h1 h1T

Basic precision cross section measurements:• Crucial information to validate theoretical understanding

- Convolution framework requires validation for most future SIDIS experiments and their interpretation- Can constrain TMD evolution- Questions on target-mass corrections and ln(1-z)

re-summations require precision large-z data

s f

SIDIS FormalismGeneral formalism for (e,e’h) coincidence reaction with polarized beam:

(y = azimuthal angle of e’ around the electron beam axis w.r.t. an arbitrary fixed direction)

[A. Bacchetta et al., JHEP 0702 (2007) 093]

LUUTUU

thh

FFx

y

xyQdPdzddxdyd

d,,

22

2

2

2,

{2

1)1(2

}sin)2cos(cos sin)1(2)2cos(cos)1(2 hhhLUheUUhUUh FFF

Use of polarized beams will provide useful azimuthal beam asymmetry measurements (FLU) at low PT

Unpolarized kT-dependent SIDIS: FUUcos(f) and FUU

cos(2f), in framework of Anselmino et al. described in terms of convolution of quark distributions f and (one or more) fragmentation functions D, each with own characteristic (Gaussian) width.

If beam is unpolarized, and the (e,e’h) measurements are fully integrated over f, only the FUU,T and FUU,L responses, or the usual transverse (sT) and longitudinal (sL) cross section pieces, survive.

Transverse momentum dependence of SIDISGeneral formalism for (e,e’h) coincidence reaction with polarized beam:

(y = azimuthal angle of e’ around the electron beam axis w.r.t. an arbitrary fixed direction)

Azimuthal fh dependence crucial to separate out kinematic effects (Cahn effect) from twist-2 correlations and higher twist effects.

data fit on EMC (1987) and Fermilab (1993) data assuming Cahn effect →

<m02> = 0.25 GeV2

(assuming m0,u =

m0,d)

[A. Bacchetta et al., JHEP 0702 (2007) 093]

LUUTUU

thh

FFx

y

xyQdPdzddxdyd

d,,

22

2

2

2,

{2

1)1(2

}sin)2cos(cos sin)1(2)2cos(cos)1(2 hhhLUheUUhUUh FFF

Hall C: Transverse momentum dependence

Pt dependence very similar for proton and deuterium targets, but deuterium slopes systematically smaller?

E00-108

Pt dependence very similar for proton and deuterium targets

Unpolarized SIDIS – Simple AnalysisConstrain kT dependence of up and down quarks separately

1) Probe p+ and p- final states

2) Use both proton and neutron (d) targets

4) Combination allows, in principle, separation of quark width from fragmentation widths

(if sea quark contributions small)

1st example: Hall C, Phys. Lett. B665 (2008) 20

Numbers are close to expectations! But, simple model only with many assumptions (factorization valid, fragmentation functions do not depend on quark flavor, transverse momentum widths of quark and fragmentation functions are gaussian and can be added in quadrature, sea quarks are negligible, assume Cahn effect, etc.), incomplete cos(f) coverage, uncertainties in exclusive event & diffractive r contributions.

Example

Example

x = 0.32z = 0.55

<p

t2>

(fa

vore

d)

<kt2> (up)

Unpolarized SIDIS – Transverse MomentumWarning: we used here an overly simplistic model analysis in an early effort to show the perspective of Pt-dependent SIDIS experiments.

An alternate analysis was performed in Schweitzer, Teckentrup and Metz, PRD 81 (2010) 094019• Gauss model for Pt distributions

- Do not assume kinematic dominance of Cahn effect• Showing consistency of CLAS, Hall C, HERMES data• Gaussian approach also describes Drell-Yan data,

givingcredence to the factorization approach usedWarning again: a gaussian approach can formally not be correct

For instance, the assumption of Cahn dominance may not be justified. But, the Pt dependence of D seems shallower than H, with an intriguing explanation in terms of flavor/kt deconvolution.

Transverse momentum dependence of SIDIS

CLAS

Gauss: <Ph (z)>2 = p/4 <Ph 2(z)>

HERMES

(also consistent with CLAS)

Gaussian approach of Schweitzer, Teckentrup and Metz, PRD 81 (2010) 094019E00-108

Curves are from the Gauss model with the Gauss width fixed from CLAS data

x = 0.32

Transverse momentum dependence of SIDISIntrinsic value of SIDIS to establish transverse momentum widths of quarks with different flavor and polarization now well established (and they can be different). Steps towards QCD evolution taken. Need precision at large z to validate fragmentation process, verify target-mass correction and ln(1-z) re-summation, etc.

Do

ub

le S

pin

Asy

mm

etry

Avakian et al., PRL 105 (2010) 262002 Adolph et al., arXiv:1305.7317v1 (2013)

CLAS COMPASS

Transverse momentum dependence of SIDISIntrinsic value of SIDIS to establish transverse momentum widths of quarks with different flavor and polarization now well established (and they can be different). Steps towards QCD evolution taken. Need precision at large z to validate fragmentation process, verify target-mass correction and ln(1-z) re-summation, etc.

HERMES Hall CAirapetian et al., PRD 107 (2013) 074029 Asaturyan et al., PRC 105 (2012) 015202

Solid (open) triangles: Cornell data @ x = 0.24 & x = 0,50

Hall C SIDIS Program – basic (e,e’p) cross sections

Why need for (e,e’p0) beyond (e,e’p+/-)?

Low-energy (x,z) factorization, or possible convolution in terms of quark distribution and fragmentation functions, at JLab-12 GeV must be well validated to substantiate the SIDIS science output. Many questions at intermediate-large z (~0.2-1) and low-intermediate Q2 (~2-10 GeV2) remain.

(At a 12-GeV JLab, Hall C’s role will be again to provide basis SIDIS cross sections.)

(e,e’p0): no diffractive r contributions no exclusive pole contributions reduced resonance contributions proportional to average D

Solid (open) symbols are after (before) subtraction of exclusive r events

Ratio of after (before) subtraction of exclusive r events

HERMES PRD87 (2013) 074029

JLab Unpolarized SIDIS Program Kinematics

6 GeV phase space

11 GeV phase space

E00-108

E12-09-017Scan in (x,z,PT)+ scan in Q2

at fixed x

E12-09-002+ scans in z

E12-06-104L/T scan in (z,PT)No scan in Q2 at fixed x: RDIS(Q2) known

E12-13-007Neutral pions:Scan in (x,z,PT)Overlap withE12-09-017 &E12-09-002

Charged pions:

Parasitic with E12-13-010

Accessible Phase Space for SIDIS (and Deep Exclusive Scattering) at 12-GeV JLab

Typical z range: 0.2 to 0.7 (up to 1.0 for smaller Mx2)

RDIS

RDIS (Q2 = 2 GeV2)

Only existing data: Cornell 70’s data

R = sL/sT in SIDIS (ep e’p+/-X)

Conclusion: “data consistent with both R = 0 and R = RDIS”

Some hint of large R at large z in Cornell data?

Example projections given for E12-06-104 assuming RSIDIS = RDIS

E12-09-017 Projected Results - Kaons

III

II

I

IV

VI

V

Semi-Inclusive Charged-Pion Electro-production off Protons and Deuterons: Cross Sections,

Ratios and Transverse Momentum Dependence

• Hall C/E00-108 1,2H(e,e’p+/-) cross section data provided the foundation of the SIDIS framework in terms of convolution at lower energies.

• Agreement with parton model expectations is always far better for ratios.• Transverse momentum dependence of cross section (and asymmetry data)

led to consideration of flavor dependence.• Now the stage of precision data enters, to provide answers to questions

of 1) experimental issues such as r contributions, L/T ratios, etc.2) flavor dependence of transverse momentum widths

(and fragmentation functions)3) QCD evolution and ln(1-z) re-summation

• At a 12-GeV JLab precision unpolarized SIDIS experiments approved for:- Measurement of ratio R = sL/sT in SIDIS (E12-06-104)- Measurement of Transverse Momentum Dependence of

Charged-Pion and Kaon Production (E12-09-017)- Precise Measurement of Charged-Pion Ratios to High Q2 (E12-09-002)- Measurement of Semi-Inclusive Neutral-Pion Production (E12-13-007)

E12-09-017 Projected Results - Pions

III

II

I

IV

VI

V

R = sL/sT in (e,e’p) SIDIS

p

quark

Knowledge on R = sL/sT in SIDIS is essentially non-existing! • If integrated over z (and pT, f, hadrons), RSIDIS = RDIS

• RSIDIS = RDIS test of dominance of quark fragmentation

• RSIDIS may vary with z

• At large z, there are known contributions from exclusive

and diffractive channels: e.g., pions from D and r p+p-

• RSIDIS may vary with transverse momentum pT

• Is RSIDISp+

= RSIDISp-

? Is RSIDISH = RSIDIS

D ?

• Is RSIDISK+

= RSIDISp+

? Is RSIDISK+

= RSIDISK-

? E2-06-

104 measure kaons too! (with about 10% of pion statistics)

Seq2q(x) Dq

p(z)

“A skeleton

in our

closet”