Daekyoung Kang

Potential-model calculation of an order-v2 nonrelativistic QCD matrix element

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/psi state that appears in the leading relativistic correction to the production and decay of that state through the color-singlet quark-antiquark channel.

Reconciling the light-cone and nonrelativistic QCD approaches to calculating e+ e- → J/ψ + ηc

It has been suggested in Ref. [A. E. Bondar and V. L. Chernyak, Phys. Lett. B 612, 215 (2005)] that the disagreement between theoretical calculations and experimental observations for the rate for the process e+ e- -> J/psi + eta_c at the B factories might be resolved by using the light-cone method to take into account the relative momentum of the heavy-quark and antiquark in the quarkonia. The light-cone result for the production cross section in Ref. [A. E. Bondar and V. L. Chernyak, Phys. Lett. B 612, 215 (2005)] is almost an order of magnitude larger than existing NRQCD factorization results. We investigate this apparent theoretical discrepancy. We compute light-cone distribution functions by making use of quarkonium wave functions from the Cornell potential model. Our light-cone distribution functions are similar in shape to those of Ref. [A. E. Bondar and V. L. Chernyak, Phys. Lett. B 612, 215 (2005)] and yield a similar cross section. However, when we subtract parts of the light-cone distribution functions that correspond to corrections of relative-order alpha_s in the NRQCD approach, we find that the cross section decreases by about a factor of three. When we set certain renormalization factors Z_i in the light-cone calculation equal to unity, we find a further reduction in the cross section of about a factor of two. The resulting light-cone cross section is similar in magnitude to the NRQCD factorization cross sections and shows only a modest enhancement over the light-cone cross section in which the relative momentum of the heavy-quark and antiquark is neglected.

Precise numerical solutions of potential problems using the Crank-Nicolson method

We present a numerically precise treatment of the Crank-Nicolson method with an imaginary time evolution operator in order to solve the Schrodinger equation. The time evolution technique is applied to the inverse-iteration method that provides a systematic way to calculate not only eigenvalues of the ground-state but also of the excited-states. This method systematically produces eigenvalues with the accuracy of eleven digits when the Cornell potential is used. An absolute error estimation technique is implemented based on a power counting rule. This method is examined on exactly solvable problems and produces the numerical accuracy down to 10^-^1^1.

Relativistic corrections to e+e- → J/ψ + ηc in a potential model

We compute relativistic corrections to the process

Inclusive production of four charm hadrons in e+e- annihilation at B factories

e^+e^- to J/psi + eta_c

Inclusive charm production in {chi}{sub b} decays

and find that they resolve the discrepancy between theory and experiment.

Inclusive charm production in chi(b) decays

Measurements by the Belle Collaboration of the exclusive production of two charmonia in e{sup +}e{sup -} annihilation differ substantially from theoretical predictions. Till now, no conclusive explanation for this remarkable discrepancy has been provided. Even the origin of the discrepancy is not identified, yet. We suggest that the measurement of four-charm events in Belle data must provide a strong constraint in identifying the origin of this large discrepancy. Our prediction of the cross section for e{sup +}e{sup -}{yields}cccc, in lowest order in strong coupling constant, at {radical}(s)=10.6 GeV is about 0.1 pb. If measured four-charm cross section is compatible with the prediction based on perturbative QCD, it is very likely that factorization of the hadronization process from perturbative part may be significantly violated or there exists a new production mechanism. If the cross section for the four-charm event is also larger than the prediction like that for the exclusive J/{psi}+{eta}{sub c} production, perturbative QCD expansion itself will be proved to be unreliable and loses predictive power.

Reconciling the light-cone and NRQCD approaches to calculating e{sup +}e{sup -} {yields} J/{psi} + {eta}{sub c}.

We calculate the inclusive decay rate of the spin-triplet bottomonium states

INCLUSIVE PRODUCTION OF FOUR CHARM HADRONS AT B-FACTORIES

{ensuremath{chi}}_{bJ}

A computer simulation of four charm production and fragmentation in e +e - collisions

into charm hadrons, including the leading-order color-singlet and color-octet