Decay rates of various bottomonium systems

Using the Bodwin--Braaten--Lepage factorization theorem in heavy quarkonium decay and production processes, we calculated matrix elements associated with S- and P-wave bottomonium decays via lattice QCD simulation methods. In this work, we report preliminary results on the operator matching between the lattice expression and the continuum expression at one loop level. Phenomenological implications are discussed using these preliminary $\overline{MS}$ matrix elements.Comment: 4 pages, postscript file (gzip compressed, uudecoded), contribution to Lat'9

New results on inclusive quarkonium decays

I review some recent progress, leading to a substantial reduction in the number of non-perturbative parameters, in the calculation of inclusive quarkonium decay widths in the framework of non-relativistic effective field theories.Comment: 4 pages, 3 figures, to be published in the proceedings of the XXXVIIth Rencontres de Moriond (QCD and High Energy Hadronic Interactions), 16-23 March 2002, Les Arcs, Franc

Gluon Fragmentation into 3PJ^3P_J Quarkonium

The functions of the gluon fragmentation into $^3P_J$ quarkonium are calculated to order $\alpha_s^2$. With the recent progress in analysing quarkonium systems in QCD we show explicitly how the socalled divergence in the limit of the zero-binding energy, which is related to $P$-wave quarkonia, is treated correctly in the case of fragmentation functions. The obtained fragmentation functions satisfy explicitly at the order of $\alpha_s^2$ the Altarelli-Parisi equation and when $z\rightarrow 0$ they behave as $z^{-1}$ as expected. Some comments on the previous results are made.Comment: Type-errors in the text and equations are eliminated. Several sentences are added in Sect.4. The file is compressed and uuencoded (E-Mail contact [email protected]

Decays rates for S- and P-wave bottomonium

We use the Bodwin-Braaten-Lepage factorization scheme to separate the long- and short-distance factors that contribute to the decay rates of $\Upsilon$, $\eta_b$ (S-wave) and $\chi_b$,$h_b$ (P-wave). The long distance matrix elements are calculated on the lattice in the quenched approximation using a non-relativistic formulation of the $b$ quark dynamics.Comment: 3 pages Latex using espcrc2.sty and epsf.sty + 2 postscript figure

Fragmentation, Factorization and Infrared Poles in Heavy Quarkonium Production

We explore the role of soft gluon exchange in heavy quarkonium production at large transverse momentum. We find uncanceled infrared poles at NNLO that are not matched by conventional NRQCD matrix elements. We show, however, that gauge invariance and factorization require that conventional NRQCD production operators be modified to include nonabelian phases or Wilson lines. With appropriately modified operators, factorization is restored at NNLO. We also argue that, in the absence of special cancellations, infrared poles at yet higher orders may require the inclusion of additional nonlocal operators, not present in the NRQCD expansion in relative veloctiy.Comment: 10 pages latex, 6 eps figure

NRQCD matrix elements for S-wave bottomonia and Gamma[eta_b(nS) -> gamma gamma] with relativistic corrections

We determine the leading-order nonrelativistic quantum chromodynamics (NRQCD) matrix element _Upsilon and the ratio _Upsilon, for Upsilon=Upsilon(nS) with n=1, 2, and 3 by comparing the measured values for Gamma[Upsilon -> e^+ e^-] with the NRQCD factorization formula in which relativistic corrections are resummed to all orders in the heavy-quark velocity v. The values for _Upsilon, which is the ratio of order-v^2 matrix element to _Upsilon, are new. They can be used for NRQCD predictions involving Upsilon(nS) and eta_b(nS) with relativistic corrections. As an application, we predict the two-photon decay rates for the spin-singlet states: Gamma[eta_b(1S) -> gamma gamma] = 0.512^{+0.096}_{-0.094} keV, Gamma[eta_b(2S) -> gamma gamma] = 0.235^{+0.043}_{-0.043} keV, and Gamma[eta_b(3S) -> gamma gamma] = 0.170^{+0.031}_{-0.031} keV.Comment: 11 pages, minor corrections, version published in Phys. Lett.

Heavy quarkonia

Two complementary approaches to the theory of heavy quarkonia are discussed. The nonrelativistic potential models give amazingly accurate predictions, but lack a theoretical justification. The expansion in powers of $v/c$ is theoretically very acceptable, but is not as good in giving numerical predictions. The importance of combining these two approaches is stressed.Comment: Presented at QCD'96 Montpellier 4-12 June 1996 7 pages, no figures, Latex fil

NRQCD: Fundamentals and Applications to Quarkonium Decay and Production

I discuss NRQCD and, in particular, the NRQCD factorization formalism for quarkonium production and decay. I also summarize the current status of the comparison between the predictions of NRQCD factorization and experimental measurements.Comment: 8 pages, 5 eps figures, uses ws-ijmpa.cls, plenary talk presented at the International Conference on QCD and Hadronic Physics, Beijing, China, June, 16--20, 200