1

Possible Additional Measurements in E906

• Azimuthal angular distributions of Drell-Yan and J/Ψ

• p+d/p+p ratios for J/Ψ production • Nuclear effects of open-charm production • Recent E866 results E906 prospect

Jen-Chieh Peng

E906 Collaboration Meeting Fermilab, June 20-21, 2008

University of Illinois at Urbana-Champaign

Outline

2

Three parton distributions describing quark’s transverse momentum and/or transverse spin

1) Transversity distribution function

2) Sivers function

3) Boer-Mulders function

Correlation between and q Ns S

Correlation between and q Ns k

Correlation between and q Nk S

3

4

26 4

Q

sxd

),()(])1(1{[ 211

,

22 h

qq

qqq PzDxfey

22 (1) 2

1 12,

22 (1) 2

1 12,

2 21 1

,

cos(2 )

sin(2 )

(1 ) ( ) ( , )4

| |

s

(1 ) ( ) ( , )4

| | (1 ) ( ) (in( )) ,

q qhq h

q qN h

q qhL q L h

q qN h

q

lh

lh

l lh

qhST q h

q qh

Py e h x H z P

z M M

PS y e h x H z P

z M M

PS y e h x H z P

zM

2 2 (1) 21 1

,

32 (2) 2

1 13 2,

2 21 1

,

1| | (1 ) ( ) ( , )

2

| | (1 ) ( ) ( , )6

1| | (1 ) ( ) ( , )

2

1| | (1 )

sin( )

sin(3 )

co ( )2

s

q qhT q T h

q qN

q qhT q T h

q qN h

q qe L q h

q q

he T

N

l lh S

l lh S

l lh S

PS y y e f x D z P

zM

PS y e h x H z P

z M M

S y y e g x D z P

PS y y e

zM

2 (1) 2

1 1,

( ) ( , )}q qq T h

q q

g x D z P

Unpolarized

Polarized target

Polarzied beam and

target

SL and ST: Target Polarizations; λe: Beam Polarization

Sivers

Transversity

Boer-Mulders

TMD and transversity PDFs are probed in Semi-Inclusive DIS

4

TMD and transversity PDFs are also probed in Drell-Yan

1 1

1

- Unpolarized Drell-Yan:

- Single transverse spin asymmetry in polarized Drell

Boer-Mulders

-Yan:

cos

functions:

Sivers functions:

Transversity

(2 )

( ) ( )

distributio

DY

DYN T q q q

d h h

A f x f x

1 1

- Double transverse spin asymmetry in polarized Drell-Yan:

Drell-Yan and SIDIS involve different combinations of TMDs

Drell-Yan does not require

ns:

kno

( ) (

wledge of the fra

)DYTT q qA h x h x

gmentation functions

T-odd TMDs are predicted to change sign from DIS to DY

(Boer-Mulders and Sivers functions)

Remains to be tested experimenta ! lly

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Drell-Yan decay angular distributions

Collins-Soper frame

Θ and Φ are the decay polar and azimuthal angles of the μ+

in the dilepton rest-frame

A general expression for Drell-Yan decay angular distributions:

*"Naive" Drell-Yan (transversely polarized ,

no transverse mo 1, 0, 0mentum)

In general : 1, 0, 0

2 21 31 cos sin 2 cos sin cos 2

4 2

d

d

*1 2

*( )h h x l l q qx

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Decay Angular Distribution of “Naïve” Drell-Yan

Data from Fermilab E772

McGaughey, Moss, JCP ; Annu. Rev. Nucl. Part. Sci. 49 (1999) 217 (hep/ph-9905409)

20Prediction: (1 cos )

d

d

7

Drell-Yan decay angular distributions

Collins-Soper frame

Θ and Φ are the decay polar and azimuthal angles of the μ+

in the dilepton rest-frame

2 21 31 cos sin 2 cos sin cos 2

4 2

d

d

A general expression for Drell-Yan decay angular distributions:

Reflect the spin-1/2 nature of quarks

(analog of the Callan-Gross relation in DI

Ins

Lam-Tung relation:

ensitive to QCD -

S

c

)

orrection

2

s

1

8

Decay angular distributions in pion-induced Drell-Yan

Z. Phys.

37 (1988) 545

T0 and increases with p

Dashed curves are from pQCD

calculations

NA10 π- +W

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Decay angular distributions in pion-induced Drell-Yan

Data from NA10 (Z. Phys. 37 (1988) 545)

Is the Lam-Tung relation violated?

Violation of the Lam-Tung relation suggests

new mechanisms withnon-perturbative origin

140 GeV/c 194 GeV/c 286 GeV/c

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Decay angular distributions in pion-induced Drell-Yan

Phys. Rev. D 39 (1989) 92

1, 0, 0 and they vary with , , andTm p x

E615 Data 252 GeV π- + W

2(GeV/c )m x (GeV/c)Tp

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Boer-Mulders function h1┴

1=0.47, MC=2.3 GeV

221 12 2

( , ) ( )T TkC HTT H

T C

M Mh x k c e f x

k M

1

1

1 represents a correlation between quark's and

transverse spin in an unpolarized hadron (ana

is a time-reversal odd, chiral-o

logous to Coll

dd TMD p

ins fu

arton distributio

nction)

n

T

h

h

h k

1 1

1 1

can lead to an azimuthal dependence with h h

f f

2 2

1 2 2 216

( 4 )T C

T C

Q M

Q M

Boer, PRD 60 (1999) 014012

ν>0 implies valence BM functions for pion and nucleon have same signs

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With Boer-Mulders function h1┴:

ν(π-Wµ+µ-X)~ [valence h1┴(π)] * [valence

h1┴(p)]

ν(pdµ+µ-X)~ [valence h1┴(p)] * [sea h1

┴(p)]

Azimuthal cos2Φ Distribution in p+d Drell-YanLingyan Zhu et al., PRL 99 (2007) 082301

ν>0 suggests same sign for the valence and sea BM functions

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Extraction of Boer-Mulders functions from p+d Drell-Yan

(B. Zhang, Z. Lu, B-Q. Ma and I. Schmidt, arXiv:0803.1692)

, 2 2 21 1

Parametrization of the BM functions:

( , ) (1 ) ( ) exp( / )q c qq BMh x p H x x f x p p

c3.99 3.83 0.91 -0.96 0.16 0.45 0.79

uH 2 / dofdH uH

dH

2BMp

(in agreement with model calculations (bag-model,

quark-diquark, relativistic CQM, Lattic

and ha

e) a

ve the same sign and s

nd the

picture giv

imi

en

lar magni

by M. Bur

tude

khar

and

dt)

u d

u

H H

H

are smaller by factor of 4 and have opposite signd

H

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Extraction of Boer-Mulders functions from p+d Drell-Yan

(B. Zhang, Z. Lu, B-Q. Ma and I. Schmidt, arXiv:0803.1692)

Fit to the p+d Drell-Yan data

Satisfy the positivity bound

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Extraction of Boer-Mulders functions from p+d Drell-Yan

• It seems unlikely that p+d data alone can determine the flavor structure of BM functions!

• Additional Drell-Yan data are needed

(B. Zhang, Z. Lu, B-Q. Ma and I. Schmidt, arXiv:0803.1692)

, 2 2 21 1

Parametrization of the BM functions:

( , ) (1 ) ( ) exp( / )q c qq BMh x p H x x f x p p

c3.99 3.83 0.91 -0.96 0.16 0.45 0.79

uH 2 / dofdH uH

dH

2BMp

Prediction on the p+p Drell-Yan

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Angular Distribution in E866 p+p/p+d Drell-Yan

p+p and p+d Drell-Yan show similar angular distributions. Should be analysed togther for

better constraints on BM.

Preliminary

Prelim

inary

PreliminaryPrelim

inary

PT (GeV/c)

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What more could be done in Fermilab E906?

1) Boer-Mulders functions can be measured at larger x

2) Study Nuclear effects of Boer-Mulders functions

3) Measure azimuthal angular dependence of J/Ψ decay

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Nuclear modification of spin-dependent PDF?

Bentz, Cloet et al., arXiv:0711.0392

EMC effect for g1(x)

Very difficult to measure !

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Nuclear Dependence of the Boer-Mulders function?

NA10 Z. Phys. C37, 545 (1988)Open: DeuteriumSolid: Tungsten

We might have a better measurement of the nuclear effects of the Boer-Mulders function in

E906

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Nuclear effects of J/Ψ and Ψ’ and open-charm

p + A → J/Ψ or Ψ’ at s1/2 = 38.8 GeV

α(xF) is largely the same for J/Ψ and Ψ’

‘Universal’ behavior for α(pT) (similar for J/Ψ, Ψ’)

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Nuclear effects of open-charm productionp + A → D + x at s1/2 = 38.8 GeV

E789 open-aperture, silicon vertex + dihadron detection

h+h- mass spectrum (after vertex cut)

D0 → K- π+

No nuclear effect for D production (at xF ~ 0)

Need to extend the measurements to large xF region

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Targets (Z = -24.0”)0 = Empty1 = 0.502 “ Copper2 = 2.036 “ Beryllium3 = 1.004 “ Copper

High-pT Single Muon Trigger

Single muon measurement in E866 p+A

Thesis of Stephen Klinksiek

High-pT single muon events are dominated by D-meson decays

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Preliminary E866 results on the single-muon (open-charm) nuclear-dependence

Cu / Be Ratios

PT (GeV/C) Rapidity (y)

PT and XF (y) dependences have similar trend as J/Ψ

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A universal xF-dependence in p-A hadron production?

Kopeliovich et al., hep-ph/0501260

Data cover energy range from 70 to 400 GeV

XF-scaling for a broad energy range nuclear shadowing alone can not

explain the data

Do open-charm and quarkonium also follow

the same trend?

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Gluon distributions in proton versus neutron?

E866data: ( ) / 2 ( )p d X p p X

/ 2 [1 ( ) / ( )] / 2:

/ , : / 2 [1 ( ) / ( )] / 2

pd pp

pd ppn p

d x uDrell Y x

g

an

J x g x

Lingyan Zhu et al., PRL, 100 (2008) 062301 (arXiv: 0710.2344)

Gluon distributions in proton and neutron are very similar

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How large is the EMC effect for deuteron?

E906 can measure ( / ) / 2 ( / )

to determine the nuclear effect in deuteron

p d J X p p J X

This can not be extracted from DIS or Drell-Yan using σ(p+d)/2σ(p+p)

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Constraints on the gluon distributions in nuclei from quarkonium A-dependence

p + A → J/Ψ or Ψ’ at s1/2 = 38.8 GeV

α(xF) is practically flat over the region

-0,1 < xF < 0.3

The flat nuclear dependence for gluon distributions over 0.025 < x < 0.12 can put

constraints on some parametrizations

Arleo, arXiv:0804.2802

21 2 1 2; /Fx x x x x M s

Additional constraints could be provided from E906 A-dependence measurement

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Future tasks

• Monte-Carlo simulations for the acceptance and count rates for these measurements (need to have the updated E906 M-C code).

• Triggers required for these measurements.

• Other additional physics in E906.

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Quark-diquark Models for Boer-Mulders Function h1

┴

Initial-state gluon interaction can produce nonzero h1┴ for the

proton in the quark-scalar diquark model. In this model, h1

┴ =f1T┴.

Boer,Brodsky&Hwang, PRD67,054003(2003).Recent diquark-spectator model Gamberg, Goldstein &

Schlegel, arXiv: 0708.0324.

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Pion Boer-Mulders Function

Final-state interaction with one gluon exchange can produce nonzero h1

┴ for the pion in the quark-spectator-antiquark model with constant coupling g.

Lu&Ma, PRD70,094044(2004).The quark-spectator-antiquark model with effective pion-quark-

antiquark coupling as a dipole form factor Lu & Ma, hep-ph/0504184

Pion-cloud model gives proton sea-quark BM

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Comparison of data and simulation

Blue: simulation

Red: data

(dset8)