# Presentation: 881549

## Spin Azimuthal Asymmetries inSemi-Inclusive DIS at JLAB

- Nucleon spin & transverse momentum of partons
- Transverse-momentum dependent distributions
- Spin-azimuthal asymmetries
- Experimental status of single-spin asymmetries
- Projections for JLab at 12 GeV
- Summary & Outlook

- H. Avakian,  L. Elouadrhiri

- Jefferson Lab

- PAC meeting, Jan 17, JLab

## Physics Motivation

- Parton Distribution Functions generalized to contain   information  not only on longitudinal, but also on the transverse distribution of partons:

- Generalized Parton Distributions (GPD) H, E ...
- Transverse-momentum dependent (TMD) parton distributions

- TMD distributions contain direct information about the
- quark orbital motion

- Orbital Angular Momentum (OAM) in the focus.

- Transverse momentum of quarks is a key to OAM.

- Complementary sets of non-perturbative functions sensitive to
- different aspects of transverse distributions

## GPDs and TMDs

- In impact parameter space: partons described by their  longitudinal momentum fraction **x**, transverse distance **b** from proton center and transfer of longitudinal momentum ******.
-    (M.Diehl hep-ph/0205208)

**GPD**s: correlate hadronic wave functions with both different momentum fractions and different transverse positions of the partons.

**TMD**s:  correlation in transverse position of a single quark. The struck quark has a different transverse location relative to the spectator partons in the initial and final state

## - Dependent Parton Distributions

| Distribution
functions |            Chirality         even         odd |
| --- | --- |

**f****1**, **g****1** studied for decades:
**h****1**** ** essentially unknown

- FSI from Brodsky et al. used in gauge invariant definition of TMDs by Collins, Ji et al. 2002

| 
Twist-2 | U
L
T |     f1
    g1
f1T┴,g1T | h1┴
h1L┴ 
h1, h1T┴ |
| --- | --- | --- | --- |

**h****1**

-     **f****1**
-     **g****1**

- U
- L
- T

- Twist-2

| 
Twist-3 | U
L
T |    f┴
  gL┴
gT ,gT┴ |  e
hL 
hT,hT┴ |
| --- | --- | --- | --- |

**Classification of PDF  **by Mulders et al.

- Twist-2 PDFs

## Novel Distributions

**Transversity**: probes relativistic nature of quarks, does not mix with gluons. First moment - tensor charge:

**Sivers function**: describes unpolarized quarks in transversely polarized nucleon. A non-zero
- T-odd f**1T**┴,  requires final state interactions + interference between different helicity states
- (Brodsky et al., Collins, Ji et al. 2002)

**Collins function**: describes fragmentation of transversely polarized quarks into unpolarized hadrons. Physics mechanisms to generate non-zero T-odd H**1**┴ by Collins 1993, Bacchetta et al. 2002

- =  0.56+/-0.09 (Q2=2)

##  Semi-Classical Models

- Collins effect:
- asymmetric fragmentation

- Orbital momentum generated in  string breaking and       pair creation produces left-right asymmetry from transversely polarized quark fragmentation (Artru-hep-ph/9310323).

- Sivers effect:
- asymmetric distribution

- In the transversely polarized proton **u** quarks are shifted down and **d** quark up giving rise to SSA (Burkardt-hep-ph/02091179).
- The shift  (~ 0.4 fm) is defined by spin-flip GPD **E** and anomalous magnetic moment of proton.

## Collins Effect:

- Left-right asymmetry in the  fragmentation
- of transversely polarized quarks

## Sivers Effect:

- Left-right asymmetry in the distribution function

## Transverse Momentum of Partons

-  clean test of QCD  (Georgi, Politzer 1978)
-  intrinsic transverse momentum of partons (Cahn 1979)
-  final state interactions  (Berger 1980)

- Azimuthal Asymmetries in electroproduction:

- The DIS data from EMC (1987) and Fermilab (1993)
- are most consistent with intrinsic parton transverse
- momentum squared,      of ~ 0.25 GeV2

- Non-zero transverse momenta of partons are accessible in measurements of azimuthal distributions of final state hadrons.

## Spin-Azimuthal Asymmetries

- Significant progress made recently in studies of  Single-Spin  Azimuthal Asymmetries (SSA)  with longitudinally polarized target (HERMES), transversely polarized target (SMC), and  polarized beam (CLAS).

- SSA are sensitive to the orbital momentum of quarks.
- provide a window to the physics of partonic final and initial state interactions
- model calculations indicate that SSA are not affected significantly by a wide
-    range   of corrections.
- Good agreement in  SSAs measured in a wide energy range in electroproduction
-   and **pp** scattering.

- SSAs:  appropriate observable at  JLAB beam energies  and **Q****2**

- Spin asymmetries + azimuthal dependence              new class of DIS measurements Spin-Azimuthal Asymmetries:

## Polarized Semi-Inclusive DIS

- Cross section defined by scale variables **x,y,z **

- Parton-Hadron transition: by fragmentation function Dπ+ (z): probability for a **u**-quark to produce a **+** with a momentum fraction **z**

- Hadron-Parton transition: by distribution function f1u(x): probability to find a **u**-quark with a momentum fraction **x**

- 1u

## Contributions to σ in ep→e’X

- σ  for longitudinally polarized leptons scattering off unpolarized protons:

- Different structure functions can be extracted as
**azimuthal moments** of the total cross section.

## Contributions to σ in Polarized SIDIS

- λe, SL, ST  electron and proton long. and trans. pol.
-               sum over quarks and anti-quarks.

## Long. Pol Target SSA for +

- Long. Pol Target SSA for +

- AUL are consistent both in magnitude and sign with predictions based on Collins mechanism

- Target SSA: CLAS (4.3 GeV)  is consistent  with
- HERMES (27.5 GeV)
-  Curves for Sivers effect from BHS-2002.

## Beam SSA: sinφ Moment

- Beam SSA: sinφ Moment

- ALU

- Beam SSA  A**LU ** from CLAS at 4.3GeV and
- HERMES (SPIN-2002) at 27.5 GeV

- Beam SSA measurements for
- different beam energies are
- consistent.

## First Extraction of e(x) from CLAS Data

- 2gT-hL

- Efremov et al.

- x-dependence of CLAS beam SSA (ALU)

- +

- z-dependence of HERMES target SSA  (AUL )

- First glimpse of
- Twist-3 e(x)

- SSA analyzed in terms of the fragmentation effect

- Jaffe,Ji 1992

## Long. Pol. Target SSA for +  at 12GeV

- Long. Pol. Target SSA for **+  **at 12GeV

-     The sin 2 asymmetry for 2000 h of  projected CLAS++ data.

- Direct measurement of k**T** dependent leading-twist distribution function

- Efremov et al.

- large x  +  high luminosity

- 6 GeV

## Transverse Target SSA at 12GeV

- Expected precision of  the AUT and extracted  ****u/u  from  transverse spin asymmetry

**CLAS at 12 GeV**

- Hall-A

- 0.5<z<0.8

## Other Flavors

- More hadrons (K+, **** ..) allow studies of:

**x/z **factorization
**u**-quark dominance
-  flavor dependence
- universality property
-    of factorization

- LUND-MC 12 GeV

## Semi-inclusive DIS at JLab

- Key goal: study the transition between the  nonperturbative and
-             perturbative  regimes of QCD utilizing JLab’s advantages:

- High luminosity
- Full coverage in azimuthal angle (separate all contributions)
- Wide kinematic range (test factorization, measure HT)
- Good particle ID  (compare different final state particles)

- X.Ji

## Summary

- Transverse Momentum Dependent distributions of partons contain
-       direct information  about the quark Orbital Angular Momentum.
-      They are  accessible in measurements of spin-azimuthal asymmetries
- Current data are consistent with a partonic picture, and can be described by a variety of theoretical models.
- Significantly higher statistics of JLab data at 12 GeV, in a wide kinematical range will provide a full set of data needed to constrain relevant distribution  (transversity,Sivers,Collins,...) functions.
- Upgraded Jlab will play a leading role in studies of quark orbital motion, providing fundamental insights into important physics quantities like spin, flavor, and multi-parton correlations.

## SIDIS tests at JLAB

- factorization
-  separation of current fragmentation

- Proposed tests to make sure simple parton picture work (SIDIS workshop in April 2002):

-  x and z factorization
-  Ratio of charged pions
-  Ratios of pion yields for proton/neutron
-  Pion production asymmetries

- Open issues

## x,z Factorization

- The** z** distribution for different ranges of Bjorken **x**

- No significant variation observed in **z** dependence for different **x** ranges.

## CLAS data vs LUND-MC

- CLAS data  (4.3GeV) and  LUND-MC comparison

-  0.5<z<0.8

- LUND-MC tuned at higher energies

## Current Fragmentation Region at CLAS

- DIS:
- Q**2**>1
- W**2**>4
- y<0.85

- The separation of CFR with 0.5<z<0.8 is not changing
-  significantly with beam energy.