We assess the theoretical uncertainties on the inclusive J/psi production
cross section in the Color Evaporation Model (CEM) using values for the charm
quark mass, renormalization and factorization scales obtained from a fit to the
charm production data. We use our new results to provide improved baseline
comparison calculations at RHIC and the LHC. We also study cold matter effects
on J/psi production at leading relative to next-to-leading order in the CEM
within this approach.Comment: Proceedings for Hard Probes 2012, Cagliari, Ital

Frawley, A. D.

Nelson, R. E.

Vogt, R.

English

arXiv

Vogt, R

Nelson, R E

Frawley, A D

UNT Digital Library

LLNL-CONF-563732Improving the J/psi ProductionBaseline at RHIC and the LHCR. Vogt, R. E. Nelson, A. D. FrawleyJuly 10, 2012Hard Probes 2012Cagliari, ItalyMay 28, 2012 through June 1, 2012Disclaimer  This document was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor Lawrence Livermore National Security, LLC, nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or Lawrence Livermore National Security, LLC. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or Lawrence Livermore National Security, LLC, and shall not be used for advertising or product endorsement purposes.  Nuclear Physics A 00 (2012) 1–4Nuclear Physics AImproving the J/ψ Production Baseline at RHIC and the LHCR. Vogt1,2, R. E. Nelson1,2 and A. D. Frawley31Lawrence Livermore National Laboratory, Livermore, CA 94550, USA2University of California, Davis, CA 95616, USA3Florida State University, Tallahassee, FL , USAAbstractWe assess the theoretical uncertainties on the inclusive J/ψ production cross section in the Color EvaporationModel using values for the charm quark mass, renormalization and factorization scales obtained from a fit to thecharm production data. We use our new results to provide improved baseline comparison calculations at RHIC andthe LHC. We also study cold matter effects on J/ψ production at leading relative to next-to-leading order in the CEMwithin this approach.Keywords: quarkonium, cold nuclear matterBecause the charm quark mass is finite, the total charm production cross section can be calculated in perturbativeQCD. However, there are large uncertainties due to the choice of quark mass, factorization scale and renormalizationscale [1]. Typical lower limits of the factorization and renormalization scales are half the chosen charm quark mass[1, 2]. In this case, the factorization scale is below the minimum scale of the parton densities. In addition, forrenormalization scales below 1 GeV, the strong coupling constant αs becomes large and the perturbative expansionis unlikely to converge. Thus we seek a set of physically defensible mass and scale parameters that reduce the crosssection uncertainty. Because the J/ψ cross sections are calculated with the same set of mass and scale parameters asopen charm production in the color evaporation model [3], we also place limits on the J/ψ cross section calculated inthe color evaporation model for the first time.The uncertainties from the mass and scale variations were then added in quadrature. The envelope containing theresulting curves,σmax = σcent +√(σµ,max − σcent)2 + (σm,max − σcent)2 , (1)σmin = σcent −√(σµ,min − σcent)2 + (σm,min − σcent)2 , (2)defines the uncertainty on the total cross section as a function of center of mass energy. The charm quark mass weemploy in our calculations is the Particle Data Group (PDG) value based on lattice determinations of the charm quarkmass in the MS scheme at µ = m: m(m) = 1.27 ± 0.09 GeV [4]. We fit the factorization and renormalization scaleparameters to a subset of the fixed target total charm production data with 250 ≤ Ebeam ≤ 920 GeV. The data wereevaluated and adjusted to the values we employ in our fits using the most up-to-date branching ratios for the measureddecay channels in Ref. [5]. We also include data from both PHENIX [6] and STAR [7, 8]. We neglect unknown next-order uncertainties which could be large for charm where the mass is relatively small and O(α4s) corrections could besignificant./ Nuclear Physics A 00 (2012) 1–4 2The best fit, including the STAR data presented at Quark Matter 2011 [7], mc = 1.27 GeV, µF/m = 2.1+2.55−0.85 andµR/m = 1.6+0.11−0.12. We show the χ2/dof fit contours on the left-hand side of Fig. 1 for ∆χ2/dof = 0.3, 1 and 2.3. The onestandard deviation uncertainty in the fitted value of µF/m (µR/m) was taken as the maximum extent of the ∆χ2/dof = 1contour along the µF/m (µR/m) axis. The one standard deviation uncertainty in the total cross section is the range ofcross sections resulting from all combinations of µF/m and µR/m contained within the ∆χ2/dof = 2.3 contour. The∆χ2/dof = 0.3 contour is to guide the eye. Note the narrow range in µR/m relative to the much broader µF/m range.The uncertainty on µF/m is larger and very asymmetric. There is a greater uncertainty on the upper limit than thelower limit because there is a much greater change in xg(x, µ2F) at lower factorization scales than when µF  µ0, theminimum scale of the parton densities./mFµ1 2 3 4 5 6 7 8 9 10/mRµ1.21.31.41.51.61.71.8 = 0.32χ∆ = 1.02χ∆ = 2.32χ∆-0.12+0.11/m = 1.6Rµ-0.85+2.55/m = 2.1Fµc mass = 1.27/NDF = 1.162χbest Figure 1: (First) The χ2/dof contours for a fit to the fixed target data and the PHENIX and STAR 2011 cross sections at√s = 200 GeV. The bestfit values are given for the furthest extent of the ∆χ2 = 1 contours. (Second) The energy dependence of the charm total cross section comparedto data. The best fit values are given for the furthest extent of the ∆χ2 = 1 contours. The central value of the fit is given by the solid red curvewhile the dashed magenta curves and dot-dashed cyan curves show the extent of the corresponding uncertainty bands. The solid blue curves in therange 19.4 ≤√s ≤ 200 GeV represent the uncertainty obtained from the extent of the ∆χ2 = 2.3 contour. (Third) The contributions to the pTdistributions in (a) divided into rapidity bins, from top to bottom: 2.5 < y < 2.8 (solid red); 2.8 < y < 3.1 (solid blue); 3.1 < y < 3.4 (dashed red);3.4 < y < 3.7 (dashed blue); and 3.7 < y < 4 (dot-dashed red). The top curves are shown at their calculated value, the others are scaled downby successive factors of 10 to separate them. (Fourth) The sum of contributions to the rapidity distribution are compared with the FONLL set forcharm (solid red) and that with m = 1.27 GeV (dashed black). Our calculations are compared with the ALICE inclusive single muon data fromheavy flavor decays [10] at√s = 7 TeV.The second panel of Fig. 1 shows the energy dependence of the total charm cross section for the fits with thecorresponding uncertainty based on results using the one standard deviation uncertainties on the quark mass and scaleparameters. If the central, upper and lower limits of µR,F/m are denoted as C, H, and L respectively, then the sevensets corresponding to the scale uncertainty are {(µF/m, µF/m)} = {(C,C), (H,H), (L, L), (C, L), (L,C), (C,H), (H,C)}.The upper and lower limits on the PDG value of the charm quark mass are 1.36 and 1.18 GeV. The uncertainty bandcan be obtained for the best fit sets using Eqs. (1) and (2). The uncertainty bands are shown for two cases: the regularfiducial region and including the most extreme cases (µF/m, µR/m) = (H, L) and (L,H). The difference between theouter magenta curves, which include these extremes, and the cyan curves, which do not, is very small. Therefore, it isreasonable to neglect the extremes. We also show the result for a one standard deviation uncertainty in the total crosssection obtained from the ∆χ2 = 2.3 contour in the blue lines. We have also added the 2.76 and 7 TeV total crosssections obtained by the ALICE collaboration in pp collisions [9], not included in our fits. The calculations are inrather good agreement with the data.We use the FONLL approach [2] to calculate the heavy flavor semileptonic decay kinematic distributions to com-pare to single lepton spectra which include B decays as well as D decays. The B → µ and B → D → µ bandsare calculated with the same fiducial set of parameters as in Ref. [2]. The D → µ band is calculated for our best fit0Using the final STAR data point [8] in the fitting changes the upper and lower limits on µF/m by 8% and 4% respectively, while the limits onµR/m change by less than 1%./ Nuclear Physics A 00 (2012) 1–4 3parameter set. Figure 1 compares our calculations with the ALICE single muon data in the forward rapidity region,2.5 < y < 4 [10]. The data are given for 2 < pT < 12 GeV and separated into five rapidity bins, each 0.3 units wide,as shown in the third panel of Fig. 1. The calculations agree well with the measurements over the entire pT range. Onthe right-hand side of Fig. 1 we present the results as a function of rapidity integrated over the same pT range as thedata, 2 ≤ pT ≤ 10 GeV. The pT -integrated ALICE data agree well with both calculations. The results with the fittedcharm parameter set narrow the uncertainty band without sacrificing consistency with the measured data.We now turn to a treatment of quarkonium production within this same framework. In the CEM, the quarkoniumproduction cross section is some fraction, FC , of all QQ pairs below the HH threshold where H is the lowest massheavy-flavor hadron. Our fit of FC is based on the total cross section data with only p, Be, Li, C, and Si targetsrespectively. In this way, we avoid uncertainties due to ignoring any cold nuclear matter effects which are on the orderof a few percent in light targets. We also restricted ourselves to the forward cross sections only.Figure 2: (First) The uncertainty band on the forward J/ψ cross section calculated based on the cc fit. The dashed magenta curves and dot-dashedcyan curves show the extent of the corresponding uncertainty bands. The dashed curves outline the most extreme limits of the band. (Second)The J/ψ rapidity distributions compared to data from 7 TeV [11] (red points and band) and 2.76 TeV [12] (blue points and band). (Third) Theforward pT distributions (2.5 < y < 4) are also shown. No additional scaling factor has been applied. A 〈k2T 〉 kick of 1.49 GeV2 (7 TeV) and 1.41GeV2 (2.76 TeV) is applied to the pT distributions. (Fourth) The scale variation of RdAu with the central EPS09 set (blue) compared to the EPS09variation for the central parameter set (red).We use the same values of the central charm quark mass and scale parameters as we found for open charm to obtainthe normalization FC for (m, µF/m, µR/m) = (1.27 GeV, 2.1, 1.6)). We determine FC only for the central parameterset and scale all the other calculations by the same value of FC to obtain the extent of the J/ψ uncertainty band. Theresult is shown on the left-hand side of Fig. 2.The ALICE 2.76 and 7 TeV rapidity and forward pT distributions are shown in the second and third plots of Fig. 2.The rapidity distribution at√s = 7 TeV is flat over several units of rapidity. The calculated rapidity distribution at2.76 TeV is not as broad and the agreement with the data is rather good although the midrapidity point remains highrelative to the central value of the calculation. The agreement of the calculated pT distributions with the forwardrapidity data is quite good with the exception of the lowest pT points where the calculated distributions turn over morequickly than the data.Finally, in the right-hand panel of Fig. 2, we show the ratio RdAu for 200 GeV d+Au collisions at RHIC to NLO inthe total cross section with EPS09 NLO shadowing. The blue band shows the variation with respect to the 31 EPS09sets while the red band indicates the mass and scale variation around the central set. We note that, with the best fit set,the scale uncertainty is now less than the uncertainty due to shadowing.We have narrowed the uncertainty band on the open heavy flavor cross section and, in so doing, have also provideda realistic uncertainty band on J/ψ production in the color evaporation model. The central result, m = 1.27 GeV,µF/m = 2.1 and µR/m = 1.6, is quite compatible with previous calculations using a ‘by-eye’ fit to the data withm = 1.2 GeV, µF/m = µR/m = 2 [3, 13].While the fits have been made by comparing the calculated NLO charm production cross section to available data/ Nuclear Physics A 00 (2012) 1–4 4at fixed-target energies and at RHIC, they are in good agreement with the extracted total charm cross sections at theLHC. The same parameter set also provides good agreement with the distributions of single leptons from semileptonicheavy flavor decays at RHIC and the LHC. The limit on the width of the uncertainty band is now set by the uncertaintydue to bottom quark production and decay.We have used the same fit parameters in the calculation of J/ψ production in the color evaporation model andhave thus provided the first uncertainty band on J/ψ production in this approach. The energy dependence of the totalJ/ψ cross section that results is a good match to the data up to collider energies. The pT distributions are also ingood agreement with the data from RHIC and the LHC. In future work, we will use our new parameter set to placelimits on the contriubtion of B meson decays to J/ψ production and will also study cold nuclear matter effects on J/ψproduction.AcknowledgmentsWe thank M. Cheng, L. Linden Levy, P. Petreczky, R. Soltz and P. Vranas for discussions. The work of R. V.and R. E. N. was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore NationalLaboratory under Contract DE-AC52-07NA27344 and was also supported in part by the JET Collaboration.References[1] R. Vogt, Eur. Phys. J. ST 155, 213 (2008) [arXiv:0709.2531 [hep-ph]].[2] M. Cacciari, P. Nason and R. Vogt, Phys. Rev. Lett. 95, 122001 (2005).[3] R. Gavai, D. Kharzeev, H. Satz, G. A. Schuler, K. Sridhar and R. Vogt, Int. J. Mod. Phys. A 10, 3043 (1995).[4] C. McNeile, C. T. H. Davies, E. Follana, K. Hornbostel and G. P. Lepage, Phys. Rev. D 82, 034512 (2010).[5] C. Lourenço and H. K. Wöhri, Phys. Rept. 433, 127 (2006) [hep-ph/0609101].[6] A. Adare et al. [PHENIX Collaboration], Phys. Rev. Lett. 97, 252002 (2006).[7] Y. Zhang et al. [STAR Collaboration], J. Phys. G 38, 124142 (2011).[8] L. Adamczyk et al. [STAR Collaboration], arXiv:1204.4244 [nucl-ex].[9] B. Abelev et al. [ALICE Collaboration], arXiv:1205.4007 [hep-ex].[10] B. Abelev et al. [ALICE Collaboration], arXiv:1201.3791 [hep-ex].[11] K. Aamodt et al. [ALICE Collaboration], Phys. Lett. B 704, 011 (2011).[12] B. Abelev et al. [ALICE Collaboration], arXiv:1203.3641 [hep-ex].[13] P. L. McGaughey, E. Quack, P. V. Ruuskanen, R. Vogt and X.-N. Wang, Int. J. Mod. Phys. A 10, 2999 (1995).

Improving the J/psi Production Baseline at RHIC and the LHC

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Improving the J/psi Production Baseline at RHIC and the LHC

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