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
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).
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 Pions and Neutral Pions
Beyond form factors and quark distributions
Generalized Parton and Transverse Momentum Distributions
Proton form factors,
transverse charge &
current densities
2000’s
1990’s
Correlated quark momentum
and helicity distributions in
transverse space - GPDs
Structure functions,
quark longitudinal
momentum & helicity
distributions
Extend longitudinal quark momentum & helicity distributions to
transverse momentum distributions - TMDs
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) dsf Dfh(z)
Sivers distribution
The Incomplete Nucleon: Spin Puzzle
1
2
=
1
2
DS + Lq + Jg
• DS ~ 0.25
• DG small
• Lq?
Longitudinal momentum fraction x
and transverse momentum images
(world DIS)
(RHIC+DIS)
Longitudinal momentum fraction x
and transverse spatial images
Up quark Sivers Function
12 GeV projections: valence quarks well mapped
SIDIS – Flavor Decomposition
DIS probes only the sum of quarks and
anti-quarks  requires assumptions on
the role of sea quarks
SIDIS
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’
Mx2 = W’2 ~ M2 + Q2 (1/x – 1)(1 - z)
1 dσ
(ep  hX) 
σ(e,e') dz
2
h
e
f
(x)D
 q q q (z)
z = Eh/n
Measure inclusive (e,e’)
at same time as (e,e’h)
q
2
e
 q(x)fq(x)
f q (x): parton distribution function
• Leading-Order (LO) QCD
• after integration over pT and f
• NLO: gluon radiation mixes
x and z dependences
Dqh (z ): fragmentation function
• Target-Mass corrections at large z
• ln(1-z) corrections at large z
q
E00-108 Experiment in Hall C/JLab
0.2 < x < 0.6, 2 < Q2 < 4, 0.3 < z < 1
x ~ 0.3, Q2 ~ 2.3 (GeV/c)2
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
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
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
E00-108: Onset of the Parton Model
Seq2q(x) Dqp(z)
factorization
p
quark
D
4 R

D 4 * R  1
R
Collinear
Fragmentation
Nπ 
Nπ 
(Deuterium
data)
(Resonances cancel (in SU(6)) in D-/D+ ratio extracted from deuterium data)
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
E00-108: Onset of the Parton Model in SIDIS
Solid (open) symbols are after (before) subtraction of diffractive r events
x = 0.32
N-D region
x = 0.4
Phys. Rev. C85: 015202 (2012)
CTEQ5M
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
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
1st measurement of 3He (neutron) single-spin asymmetries (SSA)
Measurement of Sivers & Collins SSA’s in X. Qian et al., PRL 107, (2011) 072003
J. Huang et al., PRL 108, (2012) 052001
Target:
(transversely)
polarized 3He ~
polarized neutron
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
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.
Pt = pt + z kt +
O(kt2/Q2)
Linked to framework of Transverse Momentum Dependent Parton Distributions
m
p
TMD
x
TMDu(x,kT)
f1,g1,f1T ,g1T
h1, h1T ,h1L ,h1
Transverse momentum dependence of SIDIS
Linked to framework of Transverse Momentum Dependent Parton Distributions
m
N
U
p
X
TMD
TMDq(x,kT)
q
U
f1
L
T
L
g1
f1T
g1T
T
h1
Unpolarized target
h1 L
Longitudinally pol. target
h1 h1T Transversely pol. target
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
s
f
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
SIDIS Formalism
General formalism for (e,e’h) coincidence reaction with polarized beam:
[A. Bacchetta et al., JHEP 0702 (2007) 093]
ds
2
y2   2 
1   FUU ,T  FUU , L 

2
2
dxdydydzdfh dPh,t xyQ 2(1   )  2 x 
{
cosfh
cos(2fh )
sinfh
2 (1   ) cos fh FUU
  cos( 2fh ) FUU
 e 2 (1   ) sin fh FLU
(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.
}
Transverse momentum dependence of SIDIS
General formalism for (e,e’h) coincidence reaction with polarized beam:
[A. Bacchetta et al., JHEP 0702 (2007) 093]
ds
2
y2   2 
1   FUU ,T  FUU , L 

2
2
dxdydydzdfh dPh,t xyQ 2(1   )  2 x 
{
cosfh
cos(2fh )
sinfh
2 (1   ) cos fh FUU
  cos( 2fh ) FUU
 e 2 (1   ) sin fh FLU
}
(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)
Hall C: Transverse momentum dependence
E00108
Pt dependence very similar for proton and deuterium
targets, but deuterium slopes systematically smaller?
targets
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)
1st example: Hall C, Phys. Lett. B665 (2008) 20
(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)
x = 0.32
z = 0.55
<pt2> (favored)
Numbers are close to expectations! But,
simple model only with many assumptions
coverage, uncertainties in exclusive event &
diffractive r contributions.
<kt2> (up)
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/kt
deconvolution.
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
Transverse momentum dependence of SIDIS
Gaussian approach of Schweitzer, Teckentrup and Metz, PRD 81 (2010) 094019
CLAS
x = 0.32
E00
-108
Gauss: <Ph (z)>2 = p/4 <Ph 2(z)>
HERMES
(also consistent with CLAS)
Curves are from the Gauss model with
the Gauss width fixed from CLAS data
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) resummation, etc.
CLAS
Double Spin Asymmetry
Avakian et al., PRL 105 (2010) 262002
COMPASS
Adolph et al., arXiv:1305.7317v1 (2013)
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) resummation, etc.
HERMES
Airapetian et al., PRD 107 (2013) 074029
Hall C
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
(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
GeV must be well validated to substantiate
the SIDIS science output. Many questions
at intermediate-large z (~0.2-1) and lowintermediate Q2 (~2-10 GeV2) remain.
Solid (open) symbols are after (before)
subtraction of exclusive r events
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 r events
JLab Unpolarized SIDIS 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
Parasitic with
E12-13-010
6 GeV
phase
space
E00-108
Charged pions:
E12-06-104
L/T scan in (z,PT)
No scan in Q2 at
fixed x: RDIS(Q2)
known
E12-09-017
Scan in (x,z,PT)
+ 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)
R = sL/sT in SIDIS (ep  e’p+/-X)
RDIS
Only existing data:
Cornell 70’s data
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
E12-09-017 Projected Results - Kaons
III
IV
II
VI
I
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
IV
II
VI
I
V
R = sL/sT in (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
p+
p• Is RSIDIS = RSIDIS ? Is RSIDISH = RSIDISD ?
• Is RSIDIS
K+
p+
= RSIDIS ? Is RSIDIS
K+
K-
= RSIDIS ?
E2-06-104 measure kaons too! (with about 10% of pion statistics)
Seq2q(x) Dqp(z)
p
quark