[en] The polarization of inclusive Υ(nS) at the Fermilab Tevatron is calculated within the nonrelativistic QCD factorization framework. We use a recent determination of the NRQCD matrix elements from fitting the CDF data on bottomonium production from run IB of the Tevatron. The result for the polarization of Υ(1S) integrated over the transverse momentum bin 8< p_T<20 GeV is consistent with a recent measurement by the CDF Collaboration. The transverse polarization of Υ(1S) is predicted to increase steadily for p_T greater than about 10 GeV. The Υ(2S) and Υ(3S) are predicted to have significantly larger transverse polarizations than Υ(1S)

No abstract available

[en] The polarization of prompt J/ψ at the Fermilab Tevatron is calculated within the nonrelativistic QCD factorization framework. The contribution from radiative decays of P-wave charmonium states decreases, but does not eliminate, the transverse polarization at large transverse momentum. The angular distribution parameter α for leptonic decays of the J/ψ is predicted to increase from near 0 at p_T=5GeV to about 0.5 at p_T=20GeV. The prediction is consistent with measurements by the CDF Collaboration at intermediate values of p_T, but disagrees by about 3 standard deviations at the largest values of p_T measured

No abstract available

[en] A calculation is presented of the radiative decay of the Υ(nS) into a bound state of bottom squarks. Predictions are provided of the branching fraction as a function of the masses of the bottom squark and the gluino. Branching fractions as large as several times 10^-4 are obtained for supersymmetric particle masses in the range suggested by the analysis of bottom-quark production cross sections. Data are shown that limit the range of allowed masses. Forthcoming high-statistics data from the CLEO Collaboration offer possibilities of discovery or significant new bounds on the existence and masses of supersymmetric particles

[en] The short-distance coefficients for the color-octet ³S₁ term in the fragmentation function for a gluon to split into heavy quarkonium states is calculated to order α_s² . The gauge-invariant definition of the fragmentation function by Collins and Soper is employed. Ultraviolet divergences are removed using the MS-bar renormalization procedure. The longitudinal term in the fragmentation function agrees with a previous calculation by Beneke and Rothstein. The next-to-leading order correction to the transverse term disagrees with a previous calculation

[en] As a stringent test of the nonrelativistic QCD factorization approach, which has been successful in explaining the larger-than-expected production rates of heavy quarkonia, we discuss the recent measurements of polarization of J^PC=1^-- heavy quarkonia by the CDF Collaboration at the Fermilab Tevatron compared with the predictions based on the nonrelativistic QCD factorization approach

[en] The short-distance coefficients for the color-octet ³S₁ term in the fragmentation function for a gluon to split into polarized heavy quarkonium states are recalculated to order α_s². The light-cone gauge remarkably simplifies the calculation by eliminating many Feynman diagrams at the expense of introducing spurious poles in loop integrals. We do not use any conventional prescriptions for spurious pole. Instead, we only use gauge invariance with the aid of Collins-Soper definition of the fragmentation function. Our result agrees with a previous calculation of Braaten and Lee in the Feynman gauge, but disagrees with another previous calculation

[en] We derive the formulas for the energy and wavefunction of the time-independent Schrödinger equation with perturbation in a compact form. Unlike the conventional approaches based on Rayleigh–Schrödinger or Brillouin–Wigner perturbation theories, we employ a recently developed approach of matrix-valued Lagrange multipliers that regularizes an eigenproblem. The Lagrange-multiplier regularization makes the characteristic matrix for an eigenproblem invertible. After applying the constraint equation to recover the original equation, we find the solutions of the energy and wavefunction consistent with the conventional approaches. This formalism does not rely on an iterative way and the order-by-order corrections are easily obtained by taking the Taylor expansion. The Lagrange-multiplier regularization formalism for perturbation theory presented in this paper is completely new and can be extended to the degenerate perturbation theory in a straightforward manner. We expect that this new formalism is also pedagogically useful to give insights on the perturbation theory in quantum mechanics

[en] We consider the normal mode problem of a vibrating string loaded with n identical beads of equal spacing, which involves an eigenvalue problem. Unlike the conventional approach to solving this problem by considering the difference equation for the components of the eigenvector, we modify the eigenvalue equation by introducing matrix-valued Lagrange undetermined multipliers, which regularize the secular equation and make the eigenvalue equation non-singular. Then, the eigenvector can be obtained from the regularized eigenvalue equation by multiplying the indeterminate eigenvalue equation by the inverse matrix. We find that the inverse matrix is nothing but the adjugate matrix of the original matrix in the secular determinant up to the determinant of the regularized matrix in the limit that the constraint equation vanishes. The components of the adjugate matrix can be represented in simple factorized forms. Finally, one can directly read off the eigenvector from the adjugate matrix. We expect this new method to be applicable to other eigenvalue problems involving more general forms of the tridiagonal matrices that appear in classical mechanics or quantum physics