Nuclear Effects in the Proton-Deuteron Drell-Yan Reaction.

Peter EhlersUniversity of Minnesota, MorrisMentor: Wally Melnitchouk Alberto Accardi

Drell-Yan Process•Two hadrons: proton

(p) and nucleon (N).•Quark () from one

and antiquark () from the other annihilate.

•Virtual photon becomes lepton-antilepton pair (, ).

•Other hadrons (, ) produced are not observed.

N is either another proton (p) or a neutron (n)

Drell-Yan Process•Individual quark flavor distributions can

be probed at high energies.▫Deep inelastic scattering (DIS) measures

sums of quark and antiquark distributions.▫, where and ▫Ratio of pD to pp cross sections

R. S. Towell et al., Phys. Rev. D 64, 052002

Motivation for using Deuterons•Uncover the internal structure of the

neutron.▫Free neutrons are unstable.▫Deuteron is composed of one proton & one

neutron.▫Weak nuclear binding.

•Easy place to start examining nuclear effects.

Goals• Compute the nuclear effects on the

proton-deuteron cross section (▫Earlier analyses use ▫Examined in DIS, very little attention in DY.

•Derive a relation between and that accounts for:▫Nuclear binding▫Fermi motion (internal nucleon motion)▫Nucleon off-shell corrections

Proton-Deuteron DY Process•One scattered

nucleon (N), one spectator nucleon (S).

•p & N are involved in the Drell-Yan process.

•N is now an internal line; not observable.

Energy of the Struck Nucleon•Because N is not observable, it does not

obey the on-mass shell relation .•However, the spectator nucleon S is on-

shell.• in D rest frame.

•A previous analysis1 used time-ordered perturbation theory, where N is on-shell but energy is not conserved.

1H. Kamano and T.-S. H. Lee, Phys. Rev. D 86, 094037

Derivation of the pD Cross Section

Definition of a scattering cross section for the Drell-Yan Process

Deuteron hadron tensor in terms of the nucleon hadron tensor.

• has no transverse momentum or off-shell dependence.• No final state interactions between the spectator nucleon S

and hadronic debris XN.

Results

pD cross section in terms of the light-cone convolution formula.

where is the fraction of nucleon light-cone momentum in the deuteron.

Results

• Steeply peaked near , or

• Quickly approaches zero as y deviates from 1

• DIS smearing function is very similar.▫ Both have factors that

approach in their high energy limits. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

1

2

3

4

5

6

7

8

9

10

Smearing Function

y

f(y)

Results• Ratio is using a

test function for .• Sharp increase

near 1 is because at .

• Only about 1% correction from to

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.95

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

Ratio of pD to pN Cross Sections

x

Rat

io

Results• Ratio is

• CTEQ5m PDFs• Experimental

data use similar parameters.

• Off-shell corrections make a large contribution.0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Ratio of pD to pp Cross Sections

no convconv, no offconv, offData

x_N

Rat

io

R. S. Towell et al., Phys. Rev. D 64, 052002

Results• Ratio is

• CTEQ5m PDFs• Kinematics for the

Fermilab E-906/ SeaQuest experiment.

• Smearing function contributes primarily at large x.

-0.4 0.1 0.60.7

0.8

0.9

1

1.1

1.2

1.3

Ratio of pD to pp Cross Sections

no convconv, no offconv, off

x_N

Rat

io

Conclusion•Nuclear and off-shell corrections will be

integrated into the CJ global PDF analysis.▫http://www.jlab.org/CJ

DIS Comparison• = 20 MeV for

Drell-Yan.

• in DIS, where 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

1

2

3

4

5

6

Smearing Functions

DYDIS

y

f(y)