Narrowing the uncertainty on the total charm cross section and itseffect on the J/psi cross section Page: 3 of 21
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Narrowing the uncertainty on the total charm cross section and its effect on the J/p
cross section
R. Nelson1'2, R. Vogt1'2 and A. D. Frawley3
'Physics Division, Lawrence Livermore National Laboratory,
Livermore, CA 94551, USA
2Physics Department, University of California at Davis,
Davis, CA 95616, USA
3Physics Department, Florida State University,
Tallahassee, FL 32306, USA
We explore the available parameter space that gives reasonable fits to the total charm cross section
to make a better estimate of its true uncertainty. We study the effect of the parameter choices on
the energy dependence of the J/u cross section.
I. INTRODUCTION
Because the charm quark mass is finite, the total charm production cross section can be calculated in perturbative
QCD. However, the charm quark mass is relatively light so that there are large uncertainties due to the choice of quark
mass, factorization scale and renormalization scale [1]. Typical lower limits of the factorization and renormalization
scales are half the chosen charm quark mass [1, 2]. Here, the parton densities are subject to backward evolution since
the factorization scale is below the minimum scale of the parton densities. In addition, for renormalization scales
below 1 GeV, the strong coupling constant a, becomes large and the perturbative expansion is unlikely to converge.
Thus is it worth evaluating our assumptions concerning these parameters to determine whether we can find a set of
physically defensible mass and scale parameters that reduce the cross section uncertainty.
In the color evaporation model of J/p production, the J/p cross sections are calculated with the same set of mass
and scale parameters as open charm production [3]. As we will show, the parameters used to calculate the uncertainty
on the charm quark cross sections in Refs. [1, 2] do not place stringent bounds on the J/p production cross section.
We therefore seek to place limits on the J/p cross section calculated in the color evaporation model for the first time.
In this paper we will explore the charm quark mass and scale parameter space to reduce the uncertainty on the
charm total cross section. In Sec. II, we use existing data to set limits on the factorization and renormalization scales.
We will then calculate the lepton distributions from heavy flavor decays with our parameter limits and compare to
data from RHIC and the LHC as a reality check. Section III describes how we use our open charm results in color
evaporation model calculations of J/p production to determine the uncertainties on quarkonium production, both as
a function of incident energy and as a function of the kinematic variables. In Sec. IV, we summarize our results.
II. SETTING LIMITS ON THE TOTAL CHARM CROSS SECTION
In our previous efforts to place uncertainties on the total charm cross section using the same fiducial parameter set
as the FONLL calculation, we found a wide uncertainty band that grew larger at high center of mass energies [1, 4].
At high energies, the lower limit was determined by a factorization scale of half the central value of the charm quark
mass, assumed to be 1.5 GeV. In this region, the behavior of the gluon density at low momentum fraction, x, when
the parton densities are backwards evolved caused the cross section to grow unphysically slowly with energy. The
upper limit of the uncertainty is obtained when the renormalization scale is equal to half the charm quark mass. Here
the two-loop evaluation of the strong coupling constant gives a8 > 0.5, too large for convergence of the perturbative
expansion. Here we will use the total charm cross section data to obtain a more physically motivated set of parameters
for charm production.
We calculate the total hadronic charm production cross section in a pp collision directly using the next-to-leading
order (NLO) matrix elements [5] for the total partonic cross section, &,
UAB(\, m2) d1 X2 2f , 1F) ((x2, /F) j (, 2 2 2) (1)
where m is the charm quark mass, F is the factorization scale, PR is the renormalization scale, fi is the partonic
center of mass energy, xl and 2 are the fractions of the parent proton's momenta carried by the colliding partons
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Nelson, R; Vogt, R & Frawley, A D. Narrowing the uncertainty on the total charm cross section and itseffect on the J/psi cross section, article, August 31, 2012; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc832568/m1/3/: accessed June 6, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.