

 9 Mar 1995

INCLUSIVE HADRONIC PRODUCTION OF THE Bc MESON

VIA HEAVY QUARK FRAGMENTATION

\Lambda

KINGMAN CHEUNGy Center for Particle Physics, University of Texas at Austin, Austin TX 78712, U.S.A.

E-mail: cheung@utpapa.ph.utexas.edu

ABSTRACT We summarize the studies on the hadronic production of S- and P-wave (_bc) mesons via direct fragmentation of the bottom antiquark as well as the AltarelliParisi induced gluon fragmentation.

The direct production of heavy mesons like J=, \Upsilon , and (_bc) mesons can provide very interesting tests for perturbative QCD. According to the potential model calculation 1, for (_bc) mesons the first two sets (n = 1 and n = 2) of S-wave states, the first (n = 1) and probably the entire second set (n = 2) of P-wave states, and the first set (n = 1) of D-wave states lie below the BD flavor threshold. Since the annihilation channel of excited (_bc) mesons is suppressed relative to the electromagnetic and hadronic transitions, the excited states below the BD threshold will cascade down into the ground state Bc via emission of photons and/or pions. Inclusive production of the Bc meson therefore includes the production of the n = 1 and n = 2 S-wave and P-wave states, and the n = 1 D-wave states. Here we do not include the D-wave contributions since they are expected to be very small.

Intuitively, the dominant production of (_bc) mesons at the large transverse momentum region should come from the direct fragmentation of the heavy _b antiquark 2;3. We calculate the hadronic production of S- and P-wave (_bc) mesons using the fragmentation approach 4;5;6. The fragmentation approach essentially involves the factorization of the whole production process into the production of a high energy parton (a _b antiquark or a gluon) and the fragmentation of this parton into various (_bc) states. The novel feature in our approach 2;3 is that the relevant fragmentation functions at the heavy quark mass scale can be calculated in perturbative QCD. Let H denotes any (_bc) meson states. The differential cross section doe=dpT versus the transverse momentum pT of H is given by

doe dpT (p_p ! H(pT )X) = Xij Z dx1dx2dzfi=p(x1; _)fj=_p(x2; _) "

d^oe dpT (ij ! _b(pT =z)X; _)

\Theta D_b!H(z; _) + d^oedp

T (ij ! g(p

T =z)X; _) Dg!H (z; _)# : (1)

For the production of _b we include the subprocesses gg ! b_b, g_b ! g_b, and q _q ! b_b; while for the gluon g we include the subprocesses gg ! gg, q _q ! gg, and gq(_q) !

\Lambda Talk presented at Beyond the Standard Model IV, Lake Tahoe, California (Dec 1994) yRepresenting also Tzu Chiang Yuan, UC-Davis

Figure 1: The differential cross section doe=pT versus pT of the (_bc) meson (H) in various spin-orbital states with n = 1 at the Tevatron. The acceptance cuts are pT (H) ? 6 GeV and jy(H)j ! 1.

gq(_q). In Eq. (1), a common scale _ is chosen for parton distribution functions, partonparton scattering, and fragmentation functions. We estimate the dependence on _

by varying the scale _ = (0:5 \Gamma 2)_R, where _R = qp2T (parton) + m2b. This choice of scale avoids the large logarithms in the short-distance part ^oe's. However, logarithms of order _R=mb have to be summed in the fragmentation functions, which is implemented by evolving the Altarelli-Parisi (AP) equations for the fragmentation functions 4;5. The initial conditions for the AP equations are the fragmentation functions that we can calculate by perturbative QCD at the initial scale _0, which is of the order of the b-quark mass. At present, all the S-wave 2 and P-wave 3 fragmentation functions for_ b ! (_bc) have been calculated to leading order in ffs. To obtain the fragmentation functions at an arbitrary scale greater than _0, we numerically integrate the AP evolution equations.

Other details in inputs can be found in Ref. 6. We impose pT (H) ? 6 GeV and jy(H)j ! 1 cuts on the (_bc) state H. The pT spectra for the (_bc) state H with various spin-orbital quantum numbers are shown in Fig. 1 and Fig. 2 for n = 1 and n = 2, respectively. Thus, we can also obtain the inclusive production rate of Bc as a function of pminT (Bc) by integrating the pT spectra. Table 1 gives the inclusive cross sections for the Bc meson at the Tevatron as a function of pminT (Bc), including n = 1 and n = 2 S- and P-wave state contributions. The variations versus the scale _ between _R=2 and 2_R are always within a factor of two, and are rather insensitive to changes in scale when pminT (Bc) ?, 10 GeV.

At the end of Run Ib at the Tevatron, the total accumulated luminosities can be up to 100-150 pb

\Gamma 1 or more. With pT ? 6 GeV, there are about 5 \Theta 105 B+c mesons.

Figure 2: Same as Fig.1 for n = 2. In the future, when the Main Injector is installed in the Run II, which can accumulate 1-2 fb

\Gamma 1 luminosity, there will be of order 107 Bc mesons. At the LHC there will be

about 3 \Theta 109 Bc mesons with pT ? 10 GeV at the assumed 100 fb

\Gamma 1 luminosity.

In conclusion, there should be enough signature events to confirm the existence of Bc at the Tevatron, and the LHC will be a copious source of Bc. This work was supported by US DOE-FG03-93ER40757.

1. E. Eichten and C. Quigg, Phys. Rev. D49, 5845 (1994). 2. E. Braaten, K. Cheung, and T. C. Yuan, Phys. Rev. D48, R5049 (1993). 3. T. C. Yuan, Phys. Rev. D50, 5664 (1994). 4. K. Cheung, Phys. Rev. Lett. 71, 3413 (1993). 5. K. Cheung and T. C. Yuan, Phys. Lett. B325, 481 (1994). 6. K. Cheung and T.C. Yuan, preprint UCD-95-4 and CPP-94-37 (Feb 1995).

Table 1: Inclusive production cross sections for the Bc meson at the Tevatron including the contributions from all the S-wave and P-wave states below the BD threshold as a function of pminT (Bc). The acceptance cuts are pT (Bc) ? 6 GeV and jy(Bc)j ! 1.

pminT (GeV) oe (nb)

_ = 12 _R _ = _R _ = 2_R

6 2.81 5.43 6.93 10 0.87 1.16 1.22 15 0.26 0.29 0.26 20 0.098 0.097 0.083 30 0.021 0.018 0.014

