measurement of tmds in semi-inclusive dis rainer joosten university of bonn

R. Joosten, Oct. 7, 2008

Measurement of TMDs in Semi-Inclusive DIS

Rainer JoostenUniversity of Bonn

Charlottesville, VA, October 7, 2008


Content of the talk

• SIDIS Experiments with transversely polarised target HERMES and COMPASS

• Transverse momentum in SIDIS

• Results• Unpolarized cross section

(Cahn effect, Boer-Mulders)• Sivers Distribution Function• Transversity Distribution Function, Collins Function• Other TMD Distribution Functions

• Conclusions


Perspective of the talk

I will focus on SIDIS reactions in one photon exchange

Kinematical Variable:

Q2 = -q2 @ 4 E E' sin2θ/2 resolution n = (El – El') photon energy xBj = Q2/2Mn momentum of the struck quark

z = Eh/n

exclusivity

l N l h X l q l qd DF d FF

(E,k)g* q=(n,q )

nucleon

<


Perspective of the talk

Also I will focus on 1 hadron production up to NLO

using different targets (p, d, n) and identifying the final hadron one can perform flavour separation

unique feature of SIDIS


SIDIS Experimentstransverse spin effects are an important part of the program ofthe experiments

JLAB experimentselectron beam, energy 6 GeV to be upgraded to 12 GeV

HERMES at DESYelectron beam, energy 27.5 GeV

COMPASS at CERN

long pol m beam, energy 160 GeV


results are coming from

Q2 – x range

COMPASS2002-2004

transverse data

CLAS

HERMES

results arecoming from

given the different beam energies, the Q2 – x range is different complementary

information, needed to study energy dependence and to disentangle higher order effects


HERMES

RICH PID: p, K, p ID

27.5 GeV e = 7 GeVs

Pure hydrogen gas target:

flipped at high frequency (60- 90 s)

1H→ <|Pt|> ~ 85 ±3.8 %2H→ <|Pt|> ~ 84 ±3.5 %

1H <|Pt|> ~ 74 ±4.2 %


SM1

SM2

m beam

MuonWall

MuonWall

E/HCAL E/HCAL

RICH

Polarised Target

COMPASS

two stage spectrometer Large Angle Spectrometer (SM1), Small Angle Spectrometer (SM2)

PID RICH in LAS

• high energy beam• large angular acceptance• broad kinematical range

beam:

160 GeV/c longitudinal polarisation -76% intensity 2·108 µ+/spill (4.8s/16.2s)

Polarized Target:

6LiD (PT ≈ 50%) or

NH3 (PT ≈ 85%)solid target cellsPolarization reversal: once a week


running with transversely polarized target2002-2004: 6LiD only

11 days(19)

9 days(14)

14 days(24)

proton only SIDISevents(106)

2007: NH3 target (protons)

Analyzed so far:

10·106 SIDIS events

(~20% of data)

For latest H

ERMES results,

see M. Contalbrig

o talk

in this session

For latest C

OMPASS proton

data, see H. Wollny‘s talk

in this session


How does transverse momentum enter?

- collinear QPM

DTq(x) = qT(x) – qT

(x)

Transversity

Integrated over kT: three quark distribution functions contribute in leading order

Dq(x) = q+(x) – q-(x)

Helicity

q(x) = q+(x) + q-(x)

f1(x)

g1(x)

h1(x)


Transverse momentum in the QPM

- collinear QPM - quark transverse momentum kT

Additional physics!


Transverse momentum

• … can be the transverse momentum kT of the quarks in the struck nucleon. It enters the PDFs (e.g. the Sivers PDF)

• … can be the transverse momentum of the fragmenting quark (and the produced hadron). It enters the PFF (e.g. the Collins FF)

• … can create kinematical effects (Cahn effect)



Full SIDIS cross-section in NLOA B

acchetta, M D

iehl, K G

oeke, A Metz, P

Mulders, M

Schlegel (06)

8 modulations(4 LO)

Sivers

Collins “Pretzelosity”

Cahn and Boer-Mulders

Unpolarized target

longitudinally polarized target

transversely polarized target

Kotzinian, NP B441 (1995) 234

Mulders and Tangermann, NP B461 (1996) 197

Boer and Mulders, PR D57 (1998) 5780

Bacchetta et al., PL B595 (2004) 309

Bacchetta et al., JHEP 0702 (2007) 093

NLO

General expression:

also valid for exclusive reactions and for entire phase space of SIDIS

18 structure functions


Kinematical corrections: Cahn effectl N l h X l q l qd DF d FF

Leading order QED with kT 0

After fragmentation:contributes to cos h and cos 2 h moments

Access to <kT>

R.N. Cahn PL B78 (1978) 269-273 …


SIDIS cross-section: PDFs and PFFsl N l h X l q l qd DF d FF

“Pretzelosity”

11 Hh

Boer Mulders

SiversCollins

1T1 Df 1T1 Hh 11 Hh

1T1 Dg ),( 2

Tkx

),( 2hPz


down

up

Boer Mulders effect

Relation to transverse space

proton

quarks

Side view Front view

A distortion in the distribution of quark spin in transverse space can give rise to a Boer-Mulders function Burkardt, hep-ph/0510408

Quark spin can be unevenly distributed in transverse space

A. Bacchetta

11 , Hh

Convoluted with Collins function

Contributes to cos h and cos 2 h moments

11cos

UUcos

UU , HhFF 2


Unpolarised Target SIDIS Cross-Section

Cahn effect, Boer-Mulders DF and pQCD

Boer- Mulders Collins FF, Cahn effect and pQCD

pQCD and beam polarisation


the azimuthal distributions have to be corrected by the apparatus acceptance

dedicated MC simulations for L and T target polarisation data

acceptance

final azimuthal distribution

the corrected azimuthal distributions are fitted:

Unpolarised Azimuthal Asymmetries

data sample: - part of the 2004 data- L and T target polarisation- each with both target configurations

to cancel possible polarisation effects


Deuteron target

Unpolarised Azimuthal Asymmetries cos modulation (Cahn + Boer-Mulders)

cosΑ

error bars: statistical errors

bands: systematical errors

First determination of charge dependent cos moments


Unpolarised Azimuthal Asymmetries cos modulation

comparison with theory

Effect up to 40%

NOT in agreement with predictions


Unpolarised Azimuthal Asymmetries cos2 modulation (Cahn + Boer-Mulders)

cos2Α



First determination of charge dependent cos2 moments

Deuteron target



cos2 modulation

comparison with theory

• pQCD charge independent

• Cahn charge independent(if kT

u = kTd )

• Boer–Mulders charge dependent

Effect up to 10%

Well in agreement with predictions

Indication for non-vanishing Boer-Mulders function


HERMES results on Cahn and Boer Mulders

Analysis is under way!

See F. Giordano‘s talk later to

day!


LO target transverse spin asymmetries

sin( )1 1

h s q hUT T qA f D sin( )

1 1h s q h

UT qA h H

cos( )1 1

h s q hLT T qA g D sin(3 )

1 1h s q h

UT T qA h H

Sivers Collins

8 Structure Functions for target transverse spin part, 4 LO

Pretzelosity“Boostisity”


Sivers effect

Distortions in transverse space

A distortion in the distribution of quarks in transverse space can give rise to a nonzero Sivers function

The presence of spin can distort the distribution of quarks in transverse space (needs orbital angular momentum of quarks)

down

up

proton

quarks

Side view Front view

A. Bacchetta

1T1 , Df 1T1

)sin(UT

sh DfF

The Sivers asymmetry: ∑∑

q

hq

2q

q

hqT

qT1

2q

Siv )()(

)(),(

zDxfe

zDkxfeA


COMPASS Results: Sivers Effect

only statistical errors shown

Deuteron target

preliminary

preliminary

final results from 2002-2004 data [arXiv:0802.2160]

K0

Data are compatible with 0 !

Strong indication of cancelation of u and d quark Sivers Functions in deuteron target

Constrains d quark contribution in global fit

duT1T1Siv ffA


Sivers asymmetries

p are substantial and positive:

Evidence for a non-zero Sivers function

K: 2.3±0.3 times larger than p

Surprising for u-quark dominance expectations

large sea quark contribution?

)()( 1T1 zDxf

Proton target

p,K are compatible with 0


new results using latest HERMES (p) and COMPASS (d)

pion and kaon data

)()(A 1T1)sin

UTS zDxf qq(

usual unpolarised fragmentation function

extracting the Sivers function


h

h

q q

The Collins FF correlates the

transverse spin of the fragmenting quark and the

transverse momentum Ph of produced hadron h

Collins-effect

:),( Tq

1 pzH

11 Hh 11)sin(

UTsh HhF

The measured asymmetry AColl gives access to the transversity distribution times the Collins fragmentation function:

∑∑

q

hq

q2q

q Tq

1q1

2q

Coll )()(

),()(

zDxfe

pzHxheA


Collins asymmetries

• p asymmetries positive – u-quark dominance

• p large negative asymmetries – suggests

)()( fav,1

disfav,1 zHzH

• K+: consistent with p

• K of opposite sign from p – all-sea object

)()( 11 zHxh

Proton target

• p0 fulfills isospin symmetry


preliminary

COMPASS Results: Collins Effect

only statistical errors shown

Deuteron target

preliminary

final results from 2002-2004 data [arXiv:0802.2160]

K0Asymmetries compatible with 0 !

Again indication of cancelation of u and d Quark contribution for a deuteron target

Access to d quark contribution in global fit

du11Col hhA


)(1 zH

extracting transversity


Xqqee 2jet1jet pp

spin-dependent fragmentation

function

)(1 xh

hep-ex 0805.2975

See A. Vossen‘s talk later today!


Fits to Data

new results using latest HERMES (p)

COMPASS (d)

pion data,

and BELLE

data

A. Prokudin: Transversity 08, Ferrara

See A. Prokudin‘s talk

on Thursday!

fav1

fav1

2DH

unf1

unf1

2DH


……. Sivers

transversity

Transverse target spin asymmetries (4 LO)

by now all measured by COMPASS on deuteron (and proton)

pretzelosity


Target transverse spin results – (LO)

“Pretzelosity”

Avakian, Efremov, Schweitzer, Yuan, hep-ph/0808.3982

Estimate on the basis of the positivity limit


g1T is the only parton DF which ischiral-even, T-even, leading twist function

in addition to the unpolarised DF and to the helicity DF

again cancellation between the u and d quarks in the deuteron ?

Target transverse spin results – (LO)


UUUU)2cos()cos( fixed parameters for:

unbinned Maximum Likelihood fitto the log of the weighted PDF :

definition of angles + asymmetries acc. to “Trento convention”

i

wi

iFL )(

)sin()sin(2)sin()sin(2[ Sh

UTSSh

UTSP

1,,,...,)sin( Sh

UTSi PF

)2sin()2sin(2)3sin()3sin(2 Sh

UTSSh

UTS

])sin()sin(2 Sh

UTS

…takes into account cross contamination of moments

[PRD70(2004),117504]

HERMES results on transverse target spin asymmetries

Accessible in the HERMES data!

Talk by Delia Hasch @ IWHSS 2008


target transverse spin dependent asymmetries (NLO)


CONCLUSIONS • Transversity, Collins Function and Sivers Function

Great progress in determining transversity, Sivers and Collins function based on pion and kaon data by

HERMES, Belle and COMPASS

• Boer Mulders Function and Cahn effect <kT>First COMPASS (d) data on charge dependent cos and cos 2 moments: Indication of non vanishing Boer-Mulders

functionHERMES data and COMPASS proton data underway

• Transverse Target Spin asymmetries (Pretzelosity, g1T)COMPASS transverse target spin asymmetries ondeuteron target available (LO and NLO):

no significant asymmetriesHERMES data on proton (LO) should be available soonCOMPASS proton data (LO and NLO) underway


Outlook

• We have abundant and good data on tape!

• There is more to come from COMPASS and JLAB(SIDIS, Drell-Yan, DVCS)

• Now we have to analyze all data and learn as much as possible from it!

See also A. Bacchetta’s talk on Thursday!

Thank You !!


Backup Slides




2s y)(11y12y

ε


ssin ε/Α

sin modulation

Effect well in agreement with 0 !

Deuteron target


Unpolarised Azimuthal Asymmetries sin modulation

Effect very small !

hep-ex/0612059v1

Proton target


p0 Collins asymmetries

neutral pions:results for the three pion charge

states are consistent with isospin symmetry


SIDIS kinematics


Full cross-section in NLO

NLO


Transversity

Boer-Mulders

Sivers

Pretzelosity

Parton distribution functions with transverse spin

11, Hh

11 , Hh

1T1 , Df

1T1 , Hh


Collins Asymmetry – Proton Datacomparison with M. Anselmino et al. predictions

statistical errors only; systematic errors ~ 0.3 stat


COMPASS proton datacomparison with the most recent predictions from M. Anselmino et al.

statistical errors only; systematic errors ~ 0.5 stat


)(1 zH

extracting transversity


Xqqee 2jet1jet pp

spin-dependent fragmentation

function

)(1 xh

hep-ex 0805.2975

See A. Vossen‘s talk later today!

measurement of tmds in semi-inclusive dis rainer joosten university of bonn

Documents

e e sin22 resolution

ehn exclusivity e

q22mn momentum

sidis reactions

q leptonnucleon

compass transverse momentum

photon energy xbj

struck quark z