Associated photon and heavy quark production at high energy within k_T-factorization

0.06 MB·English

by  N. P. Zotov

Associated photon and heavy quark production
at high energy within k -factorization
T
A.V. Lipatov, M.A. Malyshev and N.P. Zotov
3 SINP,MoscowStateUniversity,119991Moscow,Russia
1
0
2 Abstract. In the framework of the kT-factorization approach, the production of prompt photons
in association with a heavy (charm or beauty) quarks at high energies is studied. The consider-
n ation is based on the O(aa 2) off-shell amplitudes of gluon-gluon fusion and quark-(anti)quark
a s
interaction subprocesses. The unintegrated parton densities in a proton are determined using the
J
Kimber-Martin-Ryskinprescription.OurnumericalpredictionsarecomparedwiththeD0andCDF
8
experimentaldata.AlsoweextendourresultstoLHCenergies.
2
Keywords: QCD,k -factorization,promptphoton,heavyquark
T
] PACS: 13.85Qk,12.38.Bx
h
p
-
p
INTRODUCTION
e
h
[
Recently the D0 and CDF Collaborations reported data [1, 2, 3] on associated (with

1 a heavy quark jets) prompt photon production at the Tevatron. The D0 Collaboration
v
showed that the measured cross sections are in agreement with the NLO QCD predic-
5 g
1 tions [4] within theoretical and experimental uncertainties in the region up to p 70
5 GeV. However, the substantial disagreement between theory and data for both g T+∼b-jet
6 and g +c-jet production at large pg was observed. The cross section slopes in data sig-
. T
1 nificantly differ from the predicted ones. The results indicate a need for higher order
0 g
perturbativeQCD corrections inthelarge p region.
3 T
1 In the D0 papers [1, 3] it was demonstrated also that the k -factorization predic-
T
:
v tions[5]are inabetteragreement withthedata.
i First application of k -factorization approach to production of photons associated
X T
with the charm or beauty quarks have been performed in our previous paper [6]. The
r
a considerationwasbasedontheO(aa 2)amplitudefortheproductionofasinglephoton
s
associated with a quark pairin the fusion of two off-shell gluons g g g QQ¯. A good
∗ ∗
→
agreement between thenumericalpredictionsand theTevatrondatawas obtainedin the
g
regionofrelativelylow p whereoff-shellgluonfusiondominates.However,thequark-
T
g
induced subprocesses become more important at moderate and large p and therefore
T
should be taken into account. Here we extend a previous predictions [6] by including
into the consideration two additional O(aa 2) subprocesses, namely qq¯ g QQ¯ and
s
q(q¯)Q g q(q¯)Q,where Q is thecharm orbeauty quark[5]. →
→
THEORETICAL FRAMEWORK
According to the k -factorization theorem, the cross section of the prompt photon and
T
associated heavy quark production can be written as a convolution of the relevant off-
shell partonic cross sections and unintegrated parton distribution functions (uPDF) in
theproton f (x,k2,m 2):
i,j T
s =(cid:229) sˆ (x ,x ,k2 ,k2 ) f (x ,k2 ,m 2)f (x ,k2 ,m 2)dx dx dk2 dk2 df 1df 2,
Z ij 1 2 1T 2T i 1 1T j 2 2T 1 2 1T 2T 2p 2p
i,j
where sˆ (x ,x ,k2 ,k2 ),(i, j=q,g) is the relevant partonic cross section. The initial
ij 1 2 1T 2T
off-shell partons have fractions x and x of initial protons longitudinal momenta, non-
1 2
zero transversemomenta k and k and azimuthalanglesf andf .
1T 2T 1 2
InwhatconcernstheuPDF,wetookthemintheKMRform[7].TheKMRformalism
is a prescription for constructing the uPDF from the known standard PDF 1. It gives
k -dependentuPDF forbothgluonand quark.
T
The analytic expressions of the corresponding off-shell matrix elements were listed
in [5]. In the k -factorization approach the gluon polarization density matrix takes so
T
calledBFKLform:(cid:229) e m e n =km kn /k2.Thespindensitymatrixfortheoff-shellspinors
∗ T T T
istakenintheformu(q)u¯(q)=xpˆ,whereqand parethequarkandtheprotonmomenta
inthesmallx and masslessapproximation[5].
In our numerical calculations we took the renormalization and factorization scales
m 2 = m 2 = x 2p2. In order to evaluate theoretical uncertainties, we varied x between
R F T
1/2 and 2 about the default value x = 1. We used the LO formula for the strong
V] 101 D0 V] 101 D0
e g e g
G |y| < 1 G 1.5 < |y| < 2.5
pb/ 100 pb/ 100
[T [T
gp gp
d d
/10-1 /10-1
sd sd
10-2 10-2
10-3 10-3
10-4 10-4
50 100 150 200 250 300 50 100 150 200
g g
p [GeV] p [GeV]
T T
FIGURE1. Differentialcrosssectionds /dpg ofassociatedg +b jetproductionat√s=1960GeV,
T −
yjet <1.5andpjet>15GeV.Thedashed,dottedanddash-dottedcurvescorrespondtothecontributions
|of g|g g QQ¯,qq¯T g QQ¯,q(q¯)Q g q(q¯)Q subprocesses. The solid curve represents their sum. The
→ → →
experimentaldataarefrom [1].
1 Numerically,weusedtheMSTW-2008set[8]intheprotonastheinput.
coupling constant a (m 2) with n = 4 active quark flavours at L = 200 MeV, so
s f QCD
thata (M )=0.1232.Wesetthecharmandbeautyquarkmassesto m =1.5GeVand
S Z c
m =4.75GeV. Weusetheexperimentalisolationcut forproducedphotons[1,2, 3]:
b
Ehad Emax
T
≤
(h had h )2+(j had j )2 R2.
− − ≤
Wetook R=0.4 and Emax =1 GeV as in theTevatron experimentaldata. Theisolation
notonlyreducesthebackgroundfromthesecondaryphotonsproducedbythedecaysof
p 0 andh mesonsbutalsosignificantlyreducesthesocalledfragmentationcomponents,
connectedwithcollinearphotonradiation(10%).
Similarly to the traditional QCD approach the calculated cross section split into two
pieces:
ds =ds (mˆ2)+ds (mˆ2),
direct fragm
where ds (mˆ2) is the perturbative contribution, ds (mˆ2) is the fragmentation
direct fragm
contribution, and mˆ2 is the fragmentation scale. In our calculations mˆ is the invariant
mass of the produced photon and any final quark and we restrict the direct contribution
to mˆ > M = 1 GeV in order to eliminate the collinear divergences in the direct cross
section.Thenthemassoflightquarkcan besafely sent tozero.
NUMERICAL RESULTS
In Figs. 1 – 3 some of the results of our calculation [5] are shown (more details see
in[5]).Wehavefoundthatthefullsetofexperimentaldataisreasonablywelldescribed
bythek -factorizationapproach.Onecanseethatthepropertyoftheuintegratedparton
T
distribution and the non-vanishing transverse momentum of the colliding partons lead
V] 102 CDF V] 101 CDF
e e
G G
pb/ 101 pb/ 100
[T [T
gdp 100 gdp
/ /10-1
sd sd
10-1
10-2
10-2
10-3 10-3
10-4 10-4
50 100 150 200 250 300 50 100 150 200 250 300
g g
p [GeV] p [GeV]
T T
FIGURE2. Differentialcrosssectionds /dpg ofassociatedg +c jet productionat√s=1960GeV,
T −
yg <1, yjet <1.5and pjet >20GeV.NotaionofallcurvesonrightpanelisthesameasinFig.1.The
| | T
dottedhistogramistheNLOpQCDpredictions[4]takenfrom[2].Theexperimentaldataarefrom [2].
V) DØ, L = 8.7 fb-1 data, |yg| < 1.0 V) DØ, L = 8.7 fb-1 data
Ge data, 1.5 < |yg| < 2.5 Ge 10 NLO (Stavreva, Owens)
gs/dpd (pb/T10-11 kNSPTHYL fOTEaHc R(tSIP.A t(Aa,L ,vvi prv6ea1.4vt.o3a2v.,01 ,O Zwoteonvs)) g (pb//dpT 1 kSP|yTHYg f|TEa <HcR t1IP.A .(A0,L ,vi pv6a1.4t.o32v.01, Zotov)
|yjet|<1.5, pjet>15 GeV s d |yjet|<1.5, pjet>15 GeV
T T
10-1
10-2
10-2
10-3
10-3
10-4 (x0.3)
10-4
0 50 100 150 200 250 300 0 50 100 150 200 250 300
pg (GeV) pg (GeV)
T T
FIGURE 3. Differential cross section ds /dpg of associated g +b jet (left panel) and g +c jet
T − −
(rightpanel)productionat√s=1960GeV.Figs.aretakenfrom[1,3].
to a broadering of the photon transverse momentum distributions in comparision with
the collinear pQCD results. As it was noted in [1, 3] our results agree better with the
TevatrondatathantheNLO QCD ones (seeFig. 3)
TheauthorswouldliketothankDESYDirectorateforthesupportintheframeworkof
Moscow — DESY project on MC implementation for HERA — LHC. A.L. and M.M.
were supported in part by the grant of the president of the Russian Federation (MK-
3977.2011.2) and RFBR grant 12-02-31030. This research was supported by the FASI
oftheRussianFederation (grant NS-3920.2012.2),FASI statecontract 02.740.11.0244,
RFBR grant 11-02-01454-a, the RMES (grant the Scientific Research on High Energy
Physics) and the Ministry of education and sciences of Russia (agreement 8412). N.Z.
is very grateful to the Organization Committee, in particular A. Papa and R. Fiore, for
thefinancial support.
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