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Benchmark Cross Sections for Bottom Quark Production*

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Benchmark Cross Sections for Bottom Quark Production* Th« «.omitl«d mnxncript h« bttn »ulhivM> bv a contractor of Itw U.S. Gi«™mnl undw conlrKl No. W-3IWENG-3B. Accordiitflv. tl» U. S. Govunim.ii iiarni • noMxcllHWt. roy»HV<"» <«*"•« "> C*!'* or raHoduct th* BuWiVwtf fofm of thit cLXZTor «£T,^ to do «>. .or ANL-HEP-CP-87-121 U. S. GtMrnnwni T . n 1AOO ANL-HEP-CP--87-121 DE88 009981 BENCHMARK CROSS SECTIONS FOR BOTTOM QUARK PRODUCTION* Edmond L. Berger High Energy Physics Division Argonne National Laboratory Argonne, IL 60439 Abstract A summary is presented of theoretical expectations for the total cross sections for bottom quark production, for longitudinal and transverse momentum distributions, and for h,T> momentum correlations at Fermilab fixed target and collider energies. DISCLAIMER This report was prepared as an account or work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsi- bility 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. Refer- ence herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom- mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. 'Work supported by the U.S. Department of Energy, Division of High Energy Physics, Contract W-31-109- ENG-38. To be published in the Proceedings of the Fermilab Workshop on High Sensitivity Beauty Physics, Nov. 11-14, 1987. Total Cross Sections For purposes of planning experiments and comparing various proposals, it is useful to begin with a common set of expected cross sections upon which rate estimates are based. In two recent papers,1-2 predictions were presented of bottom quark cross sections at the energies of the Fermilab pp collider and in the momentum region accessible to the fixed target program at Fermilab. In this note, I begin with a brief discussion and comparison of those predictions. I then extract a set of conservative "benchmark" cross sections which I propose be used as a reference standard. Good theoretical arguments1"4 justify the belief that quantum chromodynamics (QCD) perturbation theory provides reliable predictions for bottom quark cross sections. Principally because the bottom quark mass m» is relatively large, m» =; 5 GeV, non- perturbative, higher-twist, and higher-order perturbative contributions should be substan- tially smaller for bottom quark production than for charm.4 The predictions of Refs. 1 and 2 are based on order a] QCD 2 —*• 2 subprocesses. They should be applicable for total cross sections and for inclusive cross sections differential in rapidity or Feynman Xjr, except for overall multiplicative *K factors" whose size5 for bottom quark production should be modest, in the range K = 2 to 3. Contributions from 3 O (a t) QCD 2 -» 3 subprocesses grow in importance relative to the O (a]) terms when the transverse momentum p? of the bottom quark is large, i.e. pr > m». Thus, for cross sections differential in pr, uK(pr) functions" may become very large for pr "> m». The O (a*) diagrams also provide different event topologies.1 There are prosaic sources of uncertainty in addition to the important role of O (aj) subprocesses. They include choice of the value of m* used in the calculations; of the evolution scale Q* used in evaluating structure functions and a,(Q3); and of structure function parametrizations. These uncertainties have a limited impact on predictions at y/s = 1.8 TeV. However, at fixed target energies, where typical values of the parton fractional momenta are relatively large (x,- ~ 2m»/-v/s), uncertainties associated with m* and Q2 have substantial impact on both the energy dependence of cross sections (e.g. threshold behavior) and the predicted magnitudes. In Figs. 1 and 2 I reproduce two of my figures1 upon which I have superimposed curves from the Ellis-Quigg paper.2 In obtaining my curves, I fixed mj = 5 GeV and varied the evolution scale, whereas Ellis and Quigg fixed the evolution scale and varied mj. Ellis and Quigg used different pion structure functions and a slightly different definition of 2 6 at(Q ). We both used the Duke-Owens set 1 structure functions for the nucleons. In Ref. 1 I discuss the slight differences which arise if different nucleon structure functions are used. Also shown in Fig. 2 is the measurement of the CERN WA78 collaboration,7 in respectable agreement with theoretical expectations. A brief comment is in order concerning expected "nuclear effects" of which there are several.1 The different x dependences of the up quark and down quark densities mean that the cross section of a neutron is different from that of a proton. There are also modifications of structure functions associated with the nuclear bound state,8 the "EMC effect"; shadowing corrections, if x <> 0.1; and, finally, broadening of px spectra. The most easily calculated nuclear effect, and the only one included in Figs. 1 and 2, is that associated with the neutron/proton ratio. For pA scattering, the cross section per nucleon is identical to that for pp —*• QQ X. In other words, for pA scattering there is no nuclear target effect in heavy flavor production associated with the different x dependences of the up and down quark densities in neutrons and protons.1 This conclusion rests on the assumption of SU(2) symmetry of the antiquark densities fCjv(i) = dpi(x)), the usual assumption of isospin symmetry (e.g. up(x) = dn(x)), and the assumption that the gluon densities in protons and neutrons are identical. For pN and x~N collisions there is a difference between the cross sections. The cross sections per nucleon for QQ production from a nucleus are expected to be smaller than the cross sections for production from proton targets.1 For a target N with an equal number of protons and neutrons, the magnitude of the effect in the case of r~N —• QQ X amounts to factors of 0.68,0.80, and 0.87 at laboratory momenta of 200,400, and 600 GeV. For the Ellis-Quigg results in Fig. 2, the target N contains an equal number of neutrons and protons, whereas I computed cross sections per nucleon for ir~U —• bbX. The cross sections per nucleon for ir~U are very slightly smaller than those for w~D, Correspondingly the calculations presented here for ir~U may be used for comparisons with data for all A in the range D < A < U. The sensitivity of predictions to the choices of m» and Q2 was examined in some detail in Refs. 1 and 2. Over the fixed target momentum range shown in Fig. 1, the choice of Q2 = m2 as the evolution scale results in cross sections o(pN —» bbX) larger than for Ql = 4m2 or Q2 = s. The difference between cross sections for Q2 — s and 2 2 Q = rn is a factor of 3.3 at piab = 400 GeV and 3.1 at pi,b = 1000 GeV. Over the range 400 < pub < 1000 GeV, the expected cross section a{pN —» bbX) is decreased by about a factor of two when the b quark mass is increased from m» = 5.0 GeV to m$ = 5.4 GeV, and increased by about a factor of two if the 6 quark mass is decreased from 5.0 GeV to 4.6 GeV. For ir~U —* bbX, shown in Fig. 2, predicted cross sections differ by factors of 2.4, 2.3, and 2.3 at pi,b = 200, 400, and 600 GeV for three choices of the evolution scale Q*. Note the tradeoff between m« and Q2. For example, agreement with the data7 at 2 320 GeV/c in Fig. 2 can be achieved either with (mb =; 5.0 GeV and Q = ml) or with 2 (mt a 4.6 GeV and Q = s). The spread of predicted values shown in Figs. 1 and 2 is perhaps deceptively large. I note in particular that the current quark mass appropriate for perturbative calculations is most likely smaller than one-half the mass of the T. Therefore, m& < 5 GeV is a good bet. I propose that a good set of benchmark cross sections is obtained by selecting values 2 2 intermediate between the curves marked m» = 4.7 and mt = 5.0 GeV for Q = 4m . These are still conservative in the sense that Q2 may be less than 4m\ but is not likely to be greater. Following this procedure, I obtain the values listed in Tables 1 and 2. Table 1: Benchmark Cross Sections for pN —* bbX W.bfGeV/c) *(nb) 400 0.3 if 500 0.8 if 600 1.6 if 700 2.7 K 800 4.0 K Table 2: Benchmark Cross Sections for n N —• bbX Pub(GeV/c) a(nb) 300 1.6 K 400 3.3 K 500 5.6 if 600 8.2 if In these tables I have indicated that all values should be multiplied by a if factor associated with O (aj) contributions. For rate estimates, the conservative choice would be if = 1. However, it is not unrealistic to suppose if = 2 to 3 for pN collisions with a , somewhat smaller value for irN collisions (since the O (a*) gg —* QQsubprocess accounts for less than one-half of the n~N cross section over the momentum range indicated in the table).
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