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### Studies on transverse spin effects at Jlab

Harut Avakian

QCD Structure of the Nucleon June 12-16, 2006, Rome

Physics motivation

kT-effects from unpolarized data

TMD-studies from polarized target data

Summary

Physics Motivation

- Describe the complex nucleon structure in terms of quark and gluon degrees of freedom using polarized SIDIS

Cross section is a function of scale variables x,y,z

n = E-E’

y = n /E

x = Q2 /2Mn

z = Eh /n

- In 1D world (no orbital motion)
- quarks polarized if nucleon is polarized, 3PDFs.
- No azimuthal asymmetries in LO

z

Transverse spin effects are observable as correlations of transverse spin and transverse momentum of quarks.

Transverse momentum of quarks

Mulders & Tangerman

- kT – lead to 3 dimensional description
- kT – required to describe azimuthal distributions of hadrons and in particular SSAs.
- kT - important for cross section description (also for exclusive production)
- PT distributions of hadrons in DIS
- exclusive photon production (DVCS)
- - hard exclusive vector meson x-section

Off diagonal PDFs related to interference between L=0 and L=1 light-cone wave functions.

- Factorization of kT-dependent PDFs proven at low PT of hadrons (Ji et al)
- Universality of kT-dependent distribution and fragmentation functions proven (Collins,Mets…)

kT – crucial for orbital momentum and spin structure studies.

SIDIS (g*p->pX) x-section at leading twist:

TMD PDFs

f1

h┴1

Unpolarized target

Longitudinally pol.

Transversely pol.

g1

T-odd

h┴1L

f┴1T

g1T

h1

h┴1T

kT-even

kT-odd

Studies of PDFs require three experiments

The structure functions depend on Q2, xB, z, PhT

ST

PT

PT

fC

y

fC

sT

sT

PT

fS

sT

fh

fC

fh

fh

fS’

fS’

x

fS=fh

x

┴

AUL∞h1L H1┴

Collins Effect: azimuthal modulation of the fragmentation functionD(z,PT)=D1(z,PT)+H1┴(z,PT)sin(fh- fS’)

unpolarized

longitudinally polarized

transversely polarized

y

fS

Initial quark polarization

AUT∞h1H1┴

Scattered quark polarization

AUU∞h1┴H1┴ sin(fh- fS’)= h1┴H1┴ cos(2fh)

fC

Combination of Collins asymmetry measurements with 3 different targets will provide info to separate the chiral-odd distribution functions and measure the Collins function

sin(2fh)

p┴= PT– zk┴+ O(k┴2/Q2)

Anselmino et al

data fit on Cahn effect→<m02>=0.25GeV2

EMC (1987) and Fermilab (1993) data

Azimuthal Asymmetries in SIDIS

- Intrinsic transverse momentum of partons (Cahn 1978)
- Higher twists (Berger 1980, Brandenburg et al 1995)
- Gluon bremsstrahlung (Georgi & Politzer, Mendez 1978) at z→1

All known contributions to <cosf> and <cos2f> are “flavor blind”

Unpolarized target azimuthal asymmetries

M.Osipenko

CLAS 5.7 GeV

preliminary

- Significant cosf,cos2f observed at large PT at 5.7 GeV
- New proposal in preparation for JLab PAC to study azimuthal moments at 11 GeV (large Q2 and PT)

Tests of partonic picture

CTEQ5M PDFs + Binnewies FF

GRSV2000

X=0.3, Q2=2.5 GeV2, W=2.5 GeV

E00-108 at JLAB

JLab data consistent with partonic description (0.4<z<0.7, MX>1.5)

Missing mass of pions in ep->e’pX

p0

D++

p-

p+

n

D0

Large Delta(1232) contribution makes p- different (Mx>1.5 GeV applied)

ALL : PT-dependence

- Data is needed in small bins in x,Q2,PT,f to measure m0 andmDfor polarized and unpolarized targets andprobe their variations (Kotzinian et al)
- m0uandm0d
- mDfavandmDunfav

- Expected flat in perturbative limit
- Difference between neutral and charged pions

SSA: PT-dependence of sinf moment

ssinfLU(UL) ~FLU(UL)~ 1/Q (Twist-3)

ALUCLAS @4.3 GeV

AUL(CLAS @5.7 GeV)

AUTHERMES @27.5 GeV

PRELIMINARY

TMD

pQCD

Beam and target SSA for p+ are consistent with increase with PT

In the perturbative limit is expected to behave as 1/PT

Higher Twist SSAs

Target sinf SSA (Bacchetta et al. 0405154)

Discussed as main sources of SSA due to the Collins fragmentation

In jet SIDIS only contributions ~ D1 survive

The same unknown fragmentation function

Beam sinf SSA

With H1┴ (p0)≈0(or measured) Target and Beam SSA can be a valuable source of info on HT T-odd distribution functions

Target SSA measurements at CLAS

- Complete azimuthal coverage crucial for separation of sinf, sin2f moments

ep→e’pX

CLAS PRELIMINARY

p1sinf+p2sin2f

W2>4 GeV2

Q2>1.1 GeV2

y<0.85

0.4<z<0.7

MX>1.4 GeV

p1= 0.059±0.010

p2=-0.041±0.010

p1=-0.042±0.015

p2=-0.052±0.016

p1=0.082±0.018

p2=0.012±0.019

PT<1 GeV

0.12<x<0.48

No indication of Collins effect for p0 (x20 more data expected)

60 days of CLAS+IC (L=1.5.1034cm-2s-1)

Kotzinian-Mulders asymmetry: new CLAS proposalcurves, cQSM from Efremov et al

Hunf=-5Hfav

Hunf=-1.2Hfav

Hunf=0

- Provide measurement of SSA for all 3 pions, extract the Mulders TMD and study Collins fragmentation with longitudinally polarized target
- Allows also measurements of 2-pion asymmetries
- Prospects with polarized deuteron.

First glimpse of Twist-2 TMD h1L┴

For Collins fragmentation use fit to HERMES (Efremov et al)

Distribution functions from cQSM from Efremov et al

PRELIMINARY

CLAS-5.7GeV

Systematic error only from unknown ratio of favored and unfavored Collins functions (R= H1d→p+/H1u→p+), band correspond to -2.5<R<0

- More data expected for p- & p0
- Exclusive 2 pion background may be important

p- and p0 SSA will also give access to h1Ld

Summary

- Significant azimuthal moments in pion production in SIDIS were measured at CLAS providing information on transverse momentum distributions of quarks.
- Measurement of Collins asymmetries at JLab with unpolarized and polarized targets will provide access to leading twist chirall-odd distribution functions (Boer,Mulders and transversity distributions)
- SSA measurements in a wide range of Q2, would allow studies of higher twist effects and probe T-odd distributions
- SSA measurements in a wide range of PT will allow to study the transition from non-perturbative to perturbative description.

Flavor decomposition of T-odd f┴ (g┴, f1T┴ )

In jet SIDIS with massless quarks contributions from H1┴ vanish

gauge link contribution

With SSA measurements for p++p-and p0 on neutron and proton (p=p++p-) assuming Hfav=Hu→p+≈ -Hu→p-=-Hunfav

With H1┴ (p0)≈0(or measured) target and beam HT SSAs can be a valuable source of info on HT T-odd distribution functions

CLAS12: kinematic distributions

CLAS12 allow wide kinematical coverage of SIDIS

SSA: PT-dependence of sinf moment

ssinfLU(UL) ~FLU(UL)~ 1/Q (Twist-3)

ALUCLAS @4.3 GeV

AUL(CLAS @5.7 GeV)

AUTHERMES @27.5 GeV

PRELIMINARY

TMD

pQCD

Beam and target SSA for p+ are consistent with increase with PT

In the perturbative limit is expected to behave as 1/PT

Azimuthal Asymmetries in semi-exclusive limit

- Higher twists (Berger 1980, Brandenburg et al 1995) z→1 dominant contribution u+e- →e- p+ d

Dominant contribution to meson wave function is the perturbative one gluon exchange and approach is valid at factor ~3 lower Q2 than in case of hard exclusive scattering (Afanasev & Carlson 1997)

PT-dependence of beam SSA

ssinfLU(UL) ~FLU(UL)~ 1/Q (Twist-3)

In the perturbative limit 1/PT behavior expected

2.0

Perturbative region

Non-perturbative TMD

Asymmetries from kT-odd (g┴,h1┴) and kT-even (g1) distribution functions are expected to have a very different behavior.

Single pion production in hard scatteringPDF

PDF

h

xF<0 (target fragmentation)

xF- momentum in the CM frame

Target fragmentation

Current fragmentation

h

h

h

h

M

GPD

1

-1

0

xF

Fracture Functions

kT-dependent PDFs

Generalized PDFs

Wide kinematic coverage of large acceptance detectors allows studies of hadronization both in the target and current fragmentation regions

SIDIS (g*p→pX) cross section: Unpolarized target

e

Unpolarized target

- cosf (Boer-Mulders function h1┴) and sinf (g┴) azimuthal moments of the x- section as a function of x, Q2, PT, z
- cosf, cos2f azimuthal moments and Cahn and Berger effects
- Transition from non-perturbative to
- perturbative description at large PT
- Target fragmentation (Lambda, azimuthal moments)

at leading twist

Study the transverse polarization of quarks in the unpolarized nucleon.

p

Longitudinally pol. target

SIDIS (g*p→pX) cross section: polarized targetat leading twist

- sinf (Mulders function h1L┴) and sinf (fL┴) azimuthal moments of the x-section as a function of x, Q2, PT, z
- A1 and flavor decomposition (g1),
- PT-dependence of A1
- Target fragmentation (Lambda, azimuthal moments)

Study the transverse polarization of quarks in the longitudinally polarized nucleon.

e

p

SIDIS (g*p→pX) cross section: polarized target- sinf-fS (Sivers, f1T┴), sinf+fS(transversity, h1) and cosfS (g1T) azimuthal moments of the x-section as a function of x,Q2,PT,z
- 2 pion SSA (h1)
- Target fragmentation (Lambda, azimuthal moments)

at leading twist

Study the transverse polarization of quarks in the Transversely polarized nucleon.

cos2f: predictions

V.Barone

- Significant asymmetry predicted for HERMES
- Asymmetry is LT! (not decreasing with 1/Q)

The only mechanism with sign change from p+ to p-

Projections for CLAS12 in progress..

e

p

Longitudinally pol. target

Transversely pol. target

e

p

SIDIS (g*p→pX) cross section at leading twist (Ji et al.)e

Boer-Mulders

1998

Kotzinian-Mulders

1996

Collins-1993

structure functions = pdf × fragm × hard × soft (all universal)

Off diagonal PDFs related to interference between L=0 and L=1 light-cone wave functions.

To observe the transverse polarization of quarks in SIDIS spin dependent fragmentation is required!

ST

PT

fC

sT

fS

fh

fS

fS’ = p-fS

fS’

sin(fh+fS)

spin of quark flips wrt y-axis

x

FUU∞h1 ┴H1┴

┴

sT(p×kT)↔ h1┴

(sTkT)(pSL)↔ h1L

sinfC=sin(fh- fS’)

y

PT

sT

fC

fh

fS=fh

┴

cos(2fh)

FUL∞h1L H1┴

Collins Effect: azimuthal modulation of the fragmentation functionFUT∞h1H1┴

sT(q×PT)↔H1┴

y

fC

PT

fC

sT

D(z,PT)=D1(z,PT)+H1┴(z,PT)sin(fh- fS’)

fh

fS’

x

fC

fS= p/2+fh

x

sin(2fh)

fS’ = p-fS= p-fh

fS’ = p-fS= p/2-fh

sin(2fh)

Higher Twist SSAs

Target sinf SSA (Bacchetta et al. 0405154)

Discussed as main sources of SSA due to the Collins fragmentation

In jet SIDIS only contributions ~ D1 survive

The same unknown fragmentation function

Beam sinf SSA

With H1┴ (p0)≈0(or measured) Target and Beam SSA can be a valuable source of info on HT T-odd distribution functions

CLAS12: kinematic distributions

Large Q2 accessible with CLAS12 are important for cos2f studies

KM

Collins Effect and Kotzinian-Mulders Asymmetrylongitudinally polarized target

Study the Collins fragmentation with longitudinally polarized target.

Measure the twist-2 Mulders TMD (real part of interference of L=0 and L=1 wave functions)

Non-zero asymmetry measured at 5.7 GeV, new proposal will improve erors by a factor ~3

Measurement at 11 GeV will allow extend the Q2 and x range and perform a flavor decomposition of u/d contributions.

KM

CLAS12 : Mulders TMD projectionsSimultaneous measurement of, exclusive r,r+,w with a longitudinally polarized target important to control the background.

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