Duality in Semi-Inclusive DIS

Duality in Semi-Inclusive DIS

P. Bosted (JLab)

First Workshop on Quark-Hadron Duality and the Transition to pQCD June 6, 2005

Semi-inclusive processes

Factorization as a test of quark-hadron duality

Factorization tests in unpolarized SIDIS

Kinematic dependences of g1/f1

PT dependence of spin and azimuthal asymmetries

Summary & Outlook

P. Bosted, Duality Workshop, June 2005

2

Semi-inclusive DIS

orbital angular momentum of quarksparton distributions at large x

X.Ji Where region I/II boundary?Can useful information come from Region II?

Main focus of SIDIS studies:


3

Semi-Inclusive Deep Inelastic Scattering (SIDIS):

• Probes orbital motion of quarks through quark transverse momentum distribution• Access to new PDFs not accessible in inclusive DIS.

kT-dependent parton distributions

Sivers transversity

Mulders,This talk

Off-diagonal PDFs vanish if quarks only in s-state!

In addition T-odd PDFs require FSI (Brodsky et al., Collins, Ji et al. 2002)

This talk


4

SIDIS kinematic plane and relevant variables

Ey /ν=

)/(sinEEQ ' 24 22 θ=

νMQx 2/2=

'EE −=ν

ν/Ez h=


5

Missing mass of pions in ep->e’X

Duality question: is MX>1.4 GeV (approximately z<0.7 for Q2-2.5 GeV2, W=2.5 GeV) needed for SIDIS factorization to work? Note absence of Delta in 0!

-0

+n

0

++


6

Factorization Test from Unpolarized Multiplicites

Multiplicity (proportional to D+

(z)) is approximately independent of x forW>3 GeV, Q2=2.5 GeV2, x<0.5, and 0.25<z<0.6


7

Du+ KKP (LO)

Factorization Test from Unpolarized Multiplicites

Multiplicity (proportional to D+

(z)) is also approximately independent of x forW>2 GeV, Q2=2 GeV2, 0.1<x<0.6, and 0.45<z<0.7at E=5.5 GeV fromCLAS at JLab


8

Unpolarized SIDIS: new test

Simple picture in valence region:

p(+) = 4u(x)D+(z) + d(x)D-(z)p(-) = 4u(x)D-(z) + d(x)D+(z)d(+) = [u(x)+d(x)] [4D+(z) + D-(z)]d(-) = [u(x)+d(x)] [4D-(z) + D+(z)]

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

= p(x)/d(x)

Rpd should be independent of

z and pt

x-dependence of Rpd should be same asinclusve p(x)/d(x)in valence region


9


Rpd is independent of z for 0.4<z<0.7for W=2.5 GeV,

Q2=2.5 GeV2,x=0.3, low pt

Good agreementGRV (using PEPSI

MC, solid histogram)

10% level deviationsfor z>0.7

(Mx>1.4 GeV)Influence of Delta?


10


Rpd is independent of pt for z=0.55W=2.5 GeV, Q2=2.5 GeV2,

x=0.3

Good agreementGRV (using PEPSI

MC, solid histogram)


11


Rpd follows expectedx-dependence

for z=0.55W=2.5 GeV, Q2=2.5 GeV2,

low pt

Pretty good agreement with

GRV (using PEPSI MC, solid histogram)

12

CLAS Experiment Setup and Kinematics

Scattering of 5.7 GeV polarized electrons off polarized NH3, ND3

~8M + in SIDIS kinematics

x x

13

• Target polarization PT about 0.7 (0.3) for NH3 (ND3)• Beam polarization PB about 0.7• Dilution factor f varies from 0.1 to 0.3: used Lund model for n/p ratio (agrees with Hall C data) and preliminary Hall B data for A-dependence• Depolarization factor DLL(y) evaluated assuming R=L/T same as for inclusive.• Assumed Aperp=0 (not measured)• No radiative corrections applied• “+” and “-” include some K+, K- for P>1.5 GeV • 0 events cleanly identified with two photons

Determination of g1/F1 (approximately A1)

++−+

++−+

+−

≈NN

NN

)y(fDPPA

LLTB

p 11


14

x-depenence of SIDIS proton g1/F1

• Good agreement with HERMES + data at higher W.

• x-dependence follows PEPSI (Lund) Monte Carlo using GRSV polarized PDFs (LO)

• Magnitude also in good agreement with simulation

W>2 GeV, Q2>1.1 GeV2, 0.4<z<0.7


15

Simple picture in valence region:

p(+) = 4u(x)D+(z) + d(x)D-(z)p(-) = 4u(x)D-(z) + d(x)D+(z)p(+) = 4u(x)D+(z) + d(x)D-(z)p(-) = 4u(x)D-(z) + d(x)D+(z)

(g1/F1)+-=[p(+)+p(-)]/[p(+)+p(-)] = [4u(x) + d(x)] / [4u(x) + d(x)]

= (g1/F1)inclusive

Similarly for 0 (g1/F1)0= (g1/F1)inclusive

Polarized SIDIS: factorization tests

(g1/F1)+- and (g1/F1)0

should be independent of

z and pt,and equal to

inclusive (g1/F1)


16

SIDIS: factorization studies

g1/F1 for inclusive, for the sum of , and for are fairly consistent with each other in the range 0.4<z<0.7, as expected in LO if factorization works. Cuts used: Mx>1.4 GeV, Q2>1.1 GeV2, W>2 GeV

GRVS Significant ?


17

z-depenence of SIDIS proton g1/F1

CLAS 5.7 GeV

PRELIMINARY

No significant z-dependence seen for 0 and ++ - for 0.3<z<0.7, as expected if factorization holds

Good agreement with PEPSI predictions including dropoff at high z for -, due to increasing importance of d(x)]


18

pt-depenence of SIDIS proton g1/F1

No pt dependence for 0 (green), as expected if factorization works

+ (red) and - (blue) individually showpt dependence, but the sum of the two (not shown)is almost independent ofpt, as expected if factorization works

Reasonable agreement with PEPSI predictions.

PRELIMINARY

CLAS 5.7 GeV


19

Q2-depenence of SIDIS proton g1/F1

PRELIMINARY

CLAS 5.7 GeV

No Q2 dependence

for Q2>1.1 GeV2. Evidence

of HT for Q2<1.1 GeV2

W>2 GeV 0.4<z<0.7

20

SIDIS g1/F1 for Deuteron

Results don’t agree as well with PEPSI using GRSV, more sensitive to un-favored fragmentation functionand NLO corrections than proton (although errorsare about a factor of two larger)

NLO QCD fits including new SIDIS CLAS data canhelp constrain polarized PDFs in valence region

PRELIMINARYCLAS 5.7 GeV


21

Longitudinally Polarized Target SSA

Clear dependence seen for proton target and +, 0

Fit A*sin() + B*sin(2) for Twist-3 and Twist-2 respectively


22

)()( 12

,

sin zHxxheQ

MS q

Lqqq

LUL⊥

−Σ∝φ

SSA: x-dependence

∑∑ ⊥⊥

=

q

qq

q

qqL

ULTUL zDxf

zHxh

DPA)()(

)()(

11

112sin φ

Twist-2 Higher Twist

T The hL functions depend on both x and pt, so no simple factorization tests aren’t possible. However, cancheck if (x,pt,z) dependence follows model expectations


23

)()( 12

,

sin zHxxheQ

MS q

Lqqq

LUL⊥

−Σ∝φ

SSA: x-dependence

∑∑ ⊥⊥

=

q

qq

q

qqL

ULTUL zDxf

zHxh

DPA)()(

)()(

11

112sin φ

PRELIMINARY 5.7 GeV

Twist-2 Higher Twist

Data in rough agreement with Efremov et al.predictions, exceptfor 0 sin() term(evidence for termsnot involving Collinsfragmentation?)


24

SSA: PT-dependence of sin moment

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

CLAS @4.3 GeV

Beam and target SSA for + (not sensitive to MX-cut) are consistent with increase with PT

CLAS @5.7 GeV


25

Summary•Factorization tests with both unpolarized and polarized data work surprisingly well for W>2 GeV, Q2>1.1 GeV2, 0.3<z<0.7, pt<1 GeV, even for Mx<2 GeV (another evidence of quark-hadron duality)

• Breakdown of factorization at high z: may be due to Delta excitation or diffraction vector meson production (ongoing analysis)

•Target fragmentation may come into play at lower z than naively expected (ongoing analysis)

•Data may be used even with 6 GeV electrons to study PDFs, at least in limited kinematic region

•More data planned all final states at 6 GeV and with 11 GeV at Jlab. High statistical accuracy tests will better quantify the useful kinematic range of SIDIS


26

QUESTIONS

•Factorization W<2 GeV?

• Factorization for kaons at low energy?

•NLO tretment

•TM corrections

•Electroweak current?

•… we’re just in the beginning!


27

support slides…..

For Collins fragmentation function use HERMES data

Systematic error only from unknown ratio of favored and unfavored Collins functions (R= H1

d→/H1u→), band

correspond to -2.5<R<0

CLAS-5.7GeV

First glimpse of Twist-2 TMD h1L┴

PRELIMINARY

•More data required with - & 0 •Exclusive 2 pion background may be important

Distribution functions fromQSM from Efremov et al


29

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

The structure functions depend on Q2, xB, z, PhT 1) Unpolarized target2) Longitudinally pol. target 3) Transversely pol. target

Studies of PDFs require three experiments

f1

h┴1T

g1T

f┴1T

h1

h┴1

g1h┴

1L

kT-even kT-odd

TMD PDFs

T-odd


30

Future: more 0 data in SIDIS

1) SIDIS0 production is not contaminated by diffractive

2) HT effects and exclusive 0 suppressed3) Simple PID by 0-mass (no kaon contamination)4) Provides complementary to +/- information on

PDFs

disadvantages: reconstruction efficiency (requires detection of 2)

advantages:


31

CLAS+Inner Calorimeter (IC)

IC at CLAS opens new avenue for studies of spin and azimuthal

asymmetries of exclusive and semi-inclusive

CLAS

CLAS+IC

CLAS

IC

424 PbWO4 ……..crystals

Reconstruction efficiency of high energy 0 with IC increases ~ 4 times due to small angle coverage

IC E/E=0.0034/E+0.038/√E+0.022

32

UL ~KM

Longitudinally polarized target SSA using CLAS+IC

•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

Hunf=-1.2Hfav

Hunf=-5Hfav

Hunf=0

50 days of CLAS+IC

curves, QSM from Efremov et al


33

SIDIS factorizationStructure functions FUU,FLL… factorize into TMD distribution and fragmentation:

P┴ has contributions from distribution, fragmentation and soft gluon radiation

QCD Factorization (Ji and col.)QCD Factorization (Ji and col.)Naïve Factorization (Mulders and col.)Naïve Factorization (Mulders and col.)

TMD PDF

TMD FF

soft factorsoft factor

hard scatteringhard scattering

SIDIS Factorization proved for low PT !!!


34

ALU x-dependence: CLAS @ 4.3 and 5.7 GeV

0.5<z<0.8

Separation of different HT contribution will require independent measurements of separate contributions

Beam SSA analyzed in terms of the Collins effect by Schweitzer et al. using e(x) from QSM

Photon Sivers Effect Afanasev & Carlson, Metz & Schlegel

Beam SSA analyzed in terms of the Sivers effect by F.Yuan using h1

┴ from MIT bag model


35

double spin asymmetry A1p

1

11

1

F

g

NN

NN

)y(fDPPA

'TB

p ≈+−

= ++−+

++−+

( )( )( ) ,

Ry

y)y(D'

ε

ε

+

−−=

1

21 ,4

2

2222

Q

yxM=


36

NH3 dilution

p

n..f

344974

1+=

Dilution function extracted from PEPSI-MC is consistent with data

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Duality in Semi-Inclusive DIS

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