Fermilab E906/ SeaQuest Experiment: Transverse Momentum Distributions ofDilepton in Hadron-Hadron Collisions.

Ching Him, LEUNGDepartment of Physics, The Chinese University of Hong Kong

Supervisor: Professor Jen-chieh PengDepartment of Physics, University of Illinois at Urbana-Champaign

The theory of strong interaction, QCD, tells us that nucleons are made up of not only valenceup and down quarks, but also gluons which mediate the strong force, as well as the sea-quarksoriginating from the splitting of gluons into quark-anti-quark pairs. The Fermilab E906/SeaQuestexperiment is a fixed target experiment designed to measure the longitudinal momentum distribu-tion of anti-quarks in the proton through Drell-Yan process, in which a pair of energetic µ+ andµ− are produced. In addition, the SeaQuest experiment can provide information on the trans-verse momentum distributions of the quarks and anti-quarks in the nulceon. In this report, dataon the transverse momentum distributions from previous Drell-Yan experiments, preformed bothat fixed-target and collider , have been analyzed and compared with Next-to-Leading-order QCDcalculations.

I. INTRODUCTION

A. Parton Distribution Function

In 1969, Feynman proposed the parton model[1]. Ac-cording to this model, hadrons are composed of point-likeparticles called partons (now identified as quarks and glu-ons). Each nucleon has three valence quarks, for protonsthey are two up and a down quarks, and for neutron theyare two down and a up quarks. However, since the gluonfield density is so high within the hadron, the gluons cansplit into quark and anti-quark pairs, so called sea quarks.These partons can carry a fraction of the hadron’s mo-mentum and Bjorken x is the ratio between the longitu-dinal momentum of the parton and the hadron.

Figure 1. PDF(label as f(x,Q2)) of a proton as a function ofx. Data taken from [2].

The parton distribution function(PDF) is the proba-bility density of a parton carrying a certain x. Figure 1

shows the pdf set CT10 of a proton at Q2 = 100GeV 2.It is assume that quarks and anti-quarks have identicalsea-quark distribution, while the up and down quarksalso contain the additional valance quark contributions.Thus the q(x)− q(x) is the momentum distribution of thevalence quarks.

Form Figure 1, sea quarks dominate in low x regionwhereas in high x region is dominated by valence quarks.

B. Drell-Yan Process

Figure 2. A schematic diagram of the Drell-Yan process takenfrom [3].

The Drall-Yan process is a process where two collidinghadrons react and form a dilepton pair.

As shown in Figure 2, the quark and antiquark fromthe hadrons would annihilate into a virtual photon or a Zboson, which would then decay into a dilepton pair. Thereaction is also shown in Equation 1.

h1 + h2 → l− + l+ + x (1)

2

1. Kinematic Variable

In the following discussion, several kinematic variablesare defined.

τ = x1x2 =M2

sxF = x1 − x2

where: M is the dilepton mass;s is the center-of-mass energy squared;x1 and x2 are the momentum fraction of the quark

from beam and target respectively.

II. METHODOLOGY

In this report, results from previous Drell-Yan ex-periments, namely FNAL E288[4], E605[4], E772[5, 6],E866[7], CDF[8] and ATLAS[9], has been analyzed.

A. Choice of Fitting Functions

In the literature, there are two fitting functions for ana-lyzing differential cross section as a function of transversemomentum, the gaussian form

dσ

dp2T= ae−

p2tb (2)

and the kaplan form

dσ

dp2T= p0

(1 +

p2Tp21

)−6(3)

By definition, the < pT > is given by

< pT >=

∫∞0pT

dσdpT

dpT∫∞0

dσdpT

dpT(4)

and the < p2T > is given by

< p2T >=

∫∞0p2T

dσdpT

dpT∫∞0

dσdpT

dpT(5)

Therefore, < pT > and < p2T > is given by

< pT >=35πp1256

(kaplan form) or

=

√πb

2(gaussian form) (6)

< p2T >=p214

(kaplan form) or =

b (gaussian form) (7)

A study is done to investigate the performance of thetwo functional forms.

(a)

(b)

Figure 3. The result from DYNNLO. 3b shows the result inlog scale.

B. Numerical calculation

To compare the result from experiments to QCD pre-diction, DYNNLO[10][11] and LHAPDF[12] are used togenerate an expected transverse momentum distribution.DYNNLO is a Monte Carlo program that can calculatethe cross section for pp collision up to next-to-next-to-leading order (NNLO) of perturbative QCD (pQCD).

Figure 3 is the result from DYNNLO at√s = 38.7GeV

and 4 ≤ mll ≤ 17 using pdf set MSTW2008. From Figure3, the difference between NLO and NNLO is sufficientlysmall, thus NLO calculation is used throughout this re-port.

It is known that fixed-order pQCD calculation divergesat low pT region. Therefore, a study is done to investigatethe region where the results from DYNNLO exhibit thesame behavior as seen in the experimental results.

3

(a)

(b)

Figure 4. The pT distribution of pp collision from E866 attwo different mass range fitted with Equation 2 and 3

III. RESULT

A. Fitting Function Comparison

From section II A, there are two fitting function andFigure 4 are the plots where data from E866 is fittedwith both functional forms.

In Figure 4, the green line corresponds to the fittedcurve of Equation 2. There is a clear deviation from thedata at high pT , whereas Equation 3 (the blue line) isstill able to describe the pT distribution. Therefore, theEquation 3 is a better functional form and will be usedin this study.

B. Numerical Result

To investigate the validity of the calculation byDYNNLO, the result is compared with E772 and E866 atsmall center-of-mass energy, and CDF and ATLAS dataat high center-of-mass energy.

E772 and E866 is done at√s = 38.76GeV . Figure 5

shows the result from DYNNLO comparing with E772.This agrees with the study by E. Berger, l. Gordon andM. Klasen[13]. Though the overall trend seems to match,at small pT , the calculated cross section diverges. More-over, the calculated cross section is smaller than the mea-sured value by a factor of 4.

As the calculated cross section diverges as small pT ,this region should be excluded while calculating < pT >.Therefore, the result from DYNNLO is fitted with Equa-tion 3 while imposing a lower pT cut. The extracted< pT > and x2red with different pT cut are calculated andshown in Figure 6.

From Figure 6, the extracted < pT > and x2red becomestable when the lower pT cut is larger than 2.5GeV . Thusthe result from DYNNLO can be compared with experi-mental result at region where pT > 2.5GeV .

To investigate the effect of < pT > while imposing aupper pT cut. Figure 7 shows the < pT > as a functionof upper pT cut. From Figure 7, we can conclude thatif the upper pT cut is set at less than 8GeV , the changein < pT > should be negligible. Thus in the followingdiscussion, only result between 2.5GeV and 6GeV is usedin calculating the < pT >.

Figure 8 compares the < pT > of DYNNLO result andE866 at different mass and xF bins. For Figure 8a, thexF is set to be between 0.15 and 0.35; And for Figure 8b,the mass is set to be between 7.2 and 8.7GeV .

The < pT > from DYNNLO and E866 seems to in-crease as the dilepton mass increases and xF decreases.However, the rate of increase for DYNNLO result is sig-nificantly higher than E866. The value of < pT > fromDYNNLO is also larger than that of E866.

At small center-of-mass energy, the divergence at smallpT becomes important, resummation is needed to predictthe pT distribution.

At large center-of-mass energy, the divergence is lessimportant. Figure 9 compare the cross section calculatedby DYNNLO and results from ATLAS and CDF. TheCDF has a center-of-mass energy of 1.96TeV and thecenter-of-mass energy for ATLAS is 7TeV . The resultsagree with each other. The small deviation is expectedto disappear if higher order calculation is used.

C. Empirical formula

1. τ Dependence

In previous study, the transverse momentum was foundto be linearly related to the center-of-mass energy

√s for

a fixed τ .

4

Figure 10 displays the plots of transverse momentumas a function of center-of-mass energy. From Figure 10,there is a clear linear relation between transverse momen-tum and the center-of-mass energy. However, there is aclear deviation from the fitted curve at 38.8GeV . Thesedata points correspond to the result of E866. There sug-gest there is a dependence on other kinematic variable.

IV. CONCLUSIONS

In this report, preliminary study on transverse momen-tum distribution of the dilepton production in hardron-hardron collision has been presented. A fixed-orderpQCD code is used to calculate the transverse momen-tum distribution of the dilepton. At small center-of-massenergy, there is a clear divergence at small pT . Thisdivergence should be removed by resummation of thelogarithmically-enhanced contributions at small trans-

verse momenta. Since the SeaQuest experiment is doneat√s = 15GeV , this divergence is expect to be signif-

icant. A code which combines perturbative QCD andresummation is needed to better predict the pT distribu-tion of a Drell-Yan process. It is hoped that with improvestatistic and better calculation, the intrinsic transversemomentum distribution of partons in hardrons can beextracted from experiment.

ACKNOWLEDGMENTS

The author would like to thank Prof. Jen-chieh Peng,Bryan Kerns, Jason Dove and Shivangi Prasad for valu-able advice on research. Secondly, the author would liketo Prof. M.C. Chu and the Department of Physics ofthe Chinese University of Hong Kong for organizing theSURE program and providing the opportunity to partic-ipating in said program.

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5

(a) (b)

Figure 5. E772 result comparing with theortical calculation. 5a is the reuslt from DYNNLO and 5b is the result from [13]

(a) (b)

Figure 6. The extracted < pT > (6a) and x2red (6b) from DYNNLO result shown in 3 at different lower pT cut.

6

(a) (b)

Figure 7. The extracted < pT > (7a) and x2red (7b) from DYNNLO result at different upper pT cut.

(a) (b)

Figure 8. The < pT > calculated from DYNNLO result and E866 data at different mass and xF bins.

7

(a) (b)

Figure 9. The comparison between the cross section calculated using DYNNLO and the result from ATLAS and CDF.

8

(a) (b)

(c) (d)

(e) (f)

Figure 10. Plots of < pT > as a function of√s