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Semi-Inclusive Charged-Pion Electro-production off Protons and Deuterons: Cross Sections, Ratios and Transverse Momentum Dependence. Rolf Ent (Jefferson Lab) Baryons 2013 Glasgow, UK June 27. Pre-Amble.

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slide1

Semi-Inclusive Charged-Pion Electro-production off Protons and Deuterons: Cross Sections, Ratios and Transverse Momentum Dependence

Rolf Ent (Jefferson Lab)

Baryons 2013

Glasgow, UK June 27

slide2

Pre-Amble

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 partonicexpectations 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).
slide3

Outline

Semi-Inclusive Charged-Pion Electro-production off Protons and Deuterons: Cross Sections, Ratios and Transverse Momentum Dependence

  • 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 Pionsand Neutral Pions
slide4

Structure functions,

quark longitudinal

momentum & helicity

distributions

Proton form factors, transversecharge & current densities

Beyond form factors and quark distributions

Generalized Parton and Transverse Momentum Distributions

1990’s

Correlated quark momentum

and helicity distributions in

transverse space - GPDs

2000’s

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

the road to orbital motion
The road to orbital motion

Swing to the left, swing to the right:

A surprise of transverse-spin experiments

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.

dsh ~ Seq2q(x) dsfDfh(z)

Sivers distribution

slide6

1

DS

+

Lq

+

Jg

2

1

2

The Incomplete Nucleon: Spin Puzzle

=

  • 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

sidis flavor decomposition
SIDIS – Flavor Decomposition

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

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’

SIDIS

z= Eh/n

Mx2 = W’2 ~ M2 + Q2 (1/x – 1)(1 - z)

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

  • Leading-Order (LO) QCD
  • after integration over pT andf
  • NLO: gluon radiation mixes
  • x and z dependences
  • Target-Mass corrections at large z
  • ln(1-z) corrections at large z

: parton distribution function

: fragmentation function

slide8

E00-108 Experiment in Hall C/JLab

x ~ 0.3, Q2 ~ 2.3 (GeV/c)2

0.2 < x < 0.6, 2 < Q2 < 4, 0.3 < z < 1

1) Probe p+ and p- final states

2) Use both proton and neutron

(deuteron) targets

3) Combination of precise cross

sections and ratios allows

confirmation of interpretation

in terms of convolution of quark

distribution and fragmentation

function

4) Combination allows, naively, a

separation of quark kt-widths

from fragmentation pt-widths

(if sea quark contributions small)

D region

Mx2 = W’2 ~ M2 + Q2 (1/x – 1)(1 - z)

Convolution of CTEQ5 quark distribution and BKK fragmentation function

Mx2

z = Eh/n

slide9

How Can We Verify Factorization?

  • Neglect sea quarks and assume no ktdependence 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/sdindependent 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

slide10

E00-108: Onset of the Parton Model

GRV & CTEQ,

@ LO or NLO

Good description for p and d targets for 0.4 < z < 0.65

(Note: z = 0.65 ~

Mx2 = 2.5 GeV2)

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

slide11

p

quark

E00-108: Onset of the Parton Model

Collinear Fragmentation

Seq2q(x) Dqp(z)

(Deuterium data)

factorization

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

slide12

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

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

F. Close et al : SU(6) Quark Model

How 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

Destructive interference leads to factorization and duality

slide13

E00-108: Onset of the Parton Model in SIDIS

Solid (open) symbols are after (before) subtraction of diffractive revents

x = 0.32

N-D region

CTEQ5M

x = 0.4

Phys. Rev. C85: 015202 (2012)

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

Agreement with the partonmodel 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

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

slide14

New Observable Reveals Interesting Behavior of Quarks

1stmeasurement of 3He (neutron) single-spin asymmetries (SSA)

Measurement of Sivers & Collins SSA’s in X. Qianet al., PRL 107, (2011) 072003

1st measurement of ALT

beam-target double-spin asymmetry

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

Target:

(transversely)

polarized 3He ~ polarized neutron

  • Indications:
  • A non-vanishing quark “transversal helicity” distribution, revealsalignment of quark spin transverse to neutron spin direction
  • Quark orbital motions
slide15

m

p

x

TMD

SIDIS – kT Dependence

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.

TMDu(x,kT)

f1,g1,f1T ,g1T

h1, h1T ,h1L ,h1

Pt= pt +zkt+ O(kt2/Q2)

Linked to framework of Transverse Momentum Dependent Parton Distributions

slide16

m

p

X

TMD

Transverse momentum dependence of SIDIS

Linked to framework of Transverse Momentum Dependent Parton Distributions

s

Unpolarized target

Longitudinally pol. target

TMDq(x,kT)

Transversely pol. target

UnpolarizedkT-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

  • 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

f

slide17

SIDIS Formalism

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

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

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

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

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.

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

slide18

Transverse momentum dependence of SIDIS

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

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

(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)

slide19

Hall C: Transverse momentum dependence

E00-108

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

Pt dependence very similar for proton and deuterium targets

slide20

Unpolarized SIDIS – Simple Analysis

Constrain 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)

Example

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.

x = 0.32

z = 0.55

Example

<pt2> (favored)

<kt2> (up)

slide21

Unpolarized SIDIS – Transverse Momentum

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

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/ktdeconvolution.

  • 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, giving
  • credence to the factorization approach used

Warning again: a gaussian approach can formally not be correct

slide22

Transverse momentum dependence of SIDIS

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

E00-108

CLAS

x = 0.32

Gauss: <Ph (z)>2 = p/4 <Ph2(z)>

HERMES

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

(also consistent with CLAS)

slide23

Transverse momentum dependence of SIDIS

Intrinsic 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.

CLAS

COMPASS

Avakian et al., PRL 105 (2010) 262002

Adolph et al., arXiv:1305.7317v1 (2013)

Double Spin Asymmetry

slide24

Transverse momentum dependence of SIDIS

Intrinsic 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 C

Airapetian et al., PRD 107 (2013) 074029

Asaturyan et al., PRC 105 (2012) 015202

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

slide25

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

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

HERMES PRD87 (2013) 074029

Low-energy (x,z) factorization, or possible convolution in terms of quark distribution and fragmentation functions, at JLab-12 GeVmust 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.

Solid (open) symbols are after (before) subtraction of exclusive revents

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

(e,e’p0):

 no diffractive r contributions

 no exclusive pole contributions

 reduced resonance contributions

 proportional to average D

Ratio of after (before) subtraction of exclusive revents

slide26

JLabUnpolarizedSIDIS Program Kinematics

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

11 GeV phase space

E12-13-007

Neutral pions:

Scan in (x,z,PT)

Overlap with

E12-09-017 &

E12-09-002

Charged pions:

6 GeV phase space

E12-06-104

L/T scan in (z,PT)

No scan in Q2 at fixed x: RDIS(Q2) known

Parasitic with E12-13-010

E12-09-017

Scan in (x,z,PT)

E00-108

+ scan in Q2

at fixed x

E12-09-002

+ scans in z

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

slide27

R = sL/sT in SIDIS (ep e’p+/-X)

Only existing data: Cornell 70’s data

RDIS

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

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

RDIS (Q2 = 2 GeV2)

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

slide29

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)
slide32

p

quark

R = sL/sTin (e,e’p) SIDIS

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 = RSIDISD ?
  • Is RSIDISK+ = RSIDISp+ ? Is RSIDISK+ = RSIDISK- ? E2-06-104 measure kaons too! (with about 10% of pion statistics)

“A skeleton in our closet”

Seq2q(x) Dqp(z)