A rigorous QCD analysis of the inclusive annihilation decay rates of heavy quarkonium states is presented. The effective-field-theory framework of nonrelativistic QCD is used to separate the short-distance scale of annihilation, which is set by the heavy quark mass M , from the longer-distance scales asso- * On leave from Dept. of Physics and Astronomy, Northwestern University, Evanston, IL 60208. 1 ciated with quarkonium structure. The annihilation decay rates are expressed in terms of nonperturbative matrix elements of 4-fermion operators in nonrelativistic QCD, with coefficients that can be computed using perturbation theory in the coupling constant α s (M ). The matrix elements are organized into a hierarchy according to their scaling with v, the typical velocity of the heavy quark. An analogous factorization formalism is developed for the production cross sections of heavy quarkonium in processes involving momentum transfers of order M or larger. The factorization formulas are applied to the annihilation decay rates and production cross sections of S-wave states, up to corrections of relative order v 3 , and of P-wave states, up to corrections of relative order v 2 .

A rigorous QCD analysis of the inclusive annihilation decay rates of heavy quarkonium states is presented. The effective-field-theory framework of nonrelativistic QCD is used to separate the short-distance scale of annihilation, which is set by the heavy quark mass M , from the longer-distance scales asso- *

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We develop, through detailed one-and two-loop examples, a procedure for expressing the leading-twist Drell-Yan cross section in terms of the factored form proposed by Collins, Soper, and Sterman. We then show that this factorization program can be implemented to all orders in perturbation theory. The factored cross section takes the form of an on-shell qq annihilation cross section (less certain collinear subtractions) convolved with structure functions for the incoming hadrons. The structure functions contain all the collinear singularities and spectator interactions. They are shown to be simply related to those that occur in deep-inelastic lepton scattering. We also demonstrate that the qq cross section minus the collinear subtractions is free of infrared singularities if one integrates over the transverse momentum of the lepton pair.

We calculate the decay rates of B mesons into P-wave charmonium states using new factorization formulas that are valid to leading order in the relative velocity of the charmed quark and antiquark and to all orders in the running coupling constant of QCD. We express the production rates for all four P states in terms of two nonperturbative parameters, the derivative of the wavefunction at the origin and another parameter related to the probability for a charmed-quark-antiquark pair in a color-octet S-wave state to radiate a soft gluon and form a P-wave bound state. Using existing data on B meson decays into χ c1 to estimate the color-octet parameter, we find that the color-octet mechanism may account for a significant fraction of the χ c1 production rate and that B mesons should decay into χ c2 at a similar rate.

We present two methods for computing dimensionally-regulated NRQCD heavy-quarkonium matrix elements that are related to the second derivative of the heavy-quarkonium wave function at the origin. The first method makes use of a hard-cutoff regulator as an intermediate step and requires knowledge only of the heavy-quarkonium wave function. It involves a significant cancellation that is an obstacle to achieving high numerical accuracy. The second method is more direct and yields a result that is identical to the Gremm-Kapustin relation, but it is limited to use in potential models. It can be generalized to the computation of matrix elements of higher order in the heavy-quark velocity and can be used to resum the contributions to decay and production rates that are associated with those matrix elements. We apply these methods to the Cornell potential model and compute a matrix element for the J/ψ state that appears in the leading relativistic correction to the production and decay of that state through the color-singlet quark-antiquark channel.

We compute leading-power fragmentation corrections to J/ψ production at the Tevatron and the LHC. We find that, when these corrections are combined with perturbative corrections through next-to-leading order in the strong coupling constant αs, we obtain a good fit to high-pT cross section data from the CDF and CMS Collaborations. The fitted long-distance matrix elements lead to predictions of near-zero J/ψ polarization in the helicity frame at large pT .PACS numbers: 12.38. Bx, 12.39.St, 14.40.Pq Much of the current phenomenology of heavyquarkonium production in high-energy collisions is based on the effective field theory nonrelativistic QCD (NRQCD) [1]. Specifically, calculations are based on the NRQCD factorization conjecture [2], which states that the inclusive cross section to produce a quarkonium state H at large momentum transfer in a collision of particles A and B can be expressed asHere, the dσ A+B→QQ(n)+X are perturbatively calculable short-distance coefficients (SDCs), which are, essentially, the partonic cross sections to produce a heavy-quarkantiquark pair QQ(n) in a particular color and angularmomentum state n, convolved with parton distributions.The O H (n) are nonperturbative, long-distance matrix elements (LDMEs) of NRQCD operators and are, essentially, the probabilities for the pair QQ(n) to evolve into a quarkonium state H plus anything. The LDMEs are conjectured to be universal, i.e., process independent. This conjecture implies that information that is gained about the LDMEs by studying one quarkonium production process can be used to make predictions about another.The LDMEs have a well-defined scaling with the relative velocity v of the Q and theQ in the quarkonium center-of-momentum frame. Consequently, the sum over n in Eq. (1) is actually an expansion in powers of v, where v 2 ≈ 0.25 for the J/ψ charm-anticharm (cc) state. In present-day quarkonium-production phenomenology, the sum over n is usually truncated at relative order v 4 . Four QQ states appear in this truncation:1 ), and QQ( 3 P[8]J ), where we use standard spectroscopic notation for the angular momentum, and the superscripts 1 and 8 denote color-singlet and color-octet states, respectively.Three groups have now completed the formidable task of calculating the SDCs that appear in the four-LDME truncation through next-to-leading order (NLO) in the QCD coupling α s [3][4][5][6][7][8][9]. Generally, the NLO calculations, combined with the four-LDME phenomenology, lead to reasonable agreement with a wide range of inclusive J/ψ production measurements that have been made at the Tevatron, the LHC, and the B factories [10,11]. Problematic exceptions to this agreement arise from NLO predictions, which are based on fits to J/ψ cross sections, that the J/ψ polarization in the helicity frame is substantially transverse at large J/ψ transverse momentum p T [9,11,12]. Measurements of the J/ψ polarization at the Tevatron [13,14] and the LHC [15,16] are in contradiction with these predictions [17].In this Letter we make use of the leading...

Rigorous QCD predictions for the decay rates of the P-wave states of heavy quarkonia are presented. They are based on a new factorization theorem which is valid to leading order in the heavy-quark velocity and to all orders in the running coupling constant of QCD. The decay rates for all four P states into light-hadronic or electromagnetic final states are expressed in terms of two phenomenological parameters, whose coefficients are perturbatively calculable. Logarithms of the binding energy encountered in previous perturbative calculations of P-wave decays are factored into a phenomenological parameter that is related to the probability for the heavy-quark-antiquark pair to be in a color-octet S-wave state. Applying these predictions to charmoniurn, we use measured decay rates for the X,I and xcz to predict the decay rates of the xco and h,. PACS number(s): 13.25.+m, 12.38.Bx, 13.40.Hq, 14.40.G~