Improved Perturbative QCD Approach to the Bottomonium Spectrum

Recently it has been shown that the gross structure of the bottomonium spectrum is reproduced reasonably well within the non-relativistic boundstate theory based on perturbative QCD. In that calculation, however, the fine splittings and the S-P level splittings are predicted to be considerably narrower than the corresponding experimental values. We investigate the bottomonium spectrum within a specific framework based on perturbative QCD, which incorporates all the corrections up to O(alpha_S^5 m_b) and O(alpha_S^4 m_b), respectively, in the computations of the fine splittings and the S-P splittings. We find that the agreement with the experimental data for the fine splittings improves drastically due to an enhancement of the wave functions close to the origin as compared to the Coulomb wave functions. The agreement of the S-P splittings with the experimental data also becomes better. We find that natural scales of the fine splittings and the S-P splittings are larger than those of the boundstates themselves. On the other hand, the predictions of the level spacings between consecutive principal quantum numbers depend rather strongly on the scale mu of the operator \propto C_A/(m_b r^2). The agreement of the whole spectrum with the experimental data is much better than the previous predictions when mu \simeq 3-4 GeV for alpha_S(M_Z)=0.1181. There seems to be a phenomenological preference for some suppression mechanism for the above operator.Comment: 26 pages, 16 figures. Minor changes, to be published in PR

Running of the heavy quark production current and 1/k potential in QCD

The 1/k contribution to the heavy quark potential is first generated at one loop order in QCD. We compute the two loop anomalous dimension for this potential, and find that the renormalization group running is significant. The next-to-leading-log coefficient for the heavy quark production current near threshold is determined. The velocity renormalization group result includes the alpha_s^3 ln^2(alpha_s) ``non-renormalization group logarithms'' of Kniehl and Penin.Comment: 30 pages, journal versio

1S and MSbar Bottom Quark Masses from Upsilon Sum Rules

The bottom quark 1S mass, $M_b^{1S}$, is determined using sum rules which relate the masses and the electronic decay widths of the $\Upsilon$ mesons to moments of the vacuum polarization function. The 1S mass is defined as half the perturbative mass of a fictitious ${}^3S_1$ bottom-antibottom quark bound state, and is free of the ambiguity of order $\Lambda_{QCD}$ which plagues the pole mass definition. Compared to an earlier analysis by the same author, which had been carried out in the pole mass scheme, the 1S mass scheme leads to a much better behaved perturbative series of the moments, smaller uncertainties in the mass extraction and to a reduced correlation of the mass and the strong coupling. We arrive at $M_b^{1S}=4.71\pm 0.03$ GeV taking $\alpha_s(M_Z)=0.118\pm 0.004$ as an input. From that we determine the $\bar{MS}$ mass as $\bar m_b(\bar m_b) = 4.20 \pm 0.06$ GeV. The error in $\bar m_b(\bar m_b)$ can be reduced if the three-loop corrections to the relation of pole and $\bar{MS}$ mass are known and if the error in the strong coupling is decreased.Comment: 20 pages, latex; numbers in Tabs. 2,3,4 corrected, a reference and a comment on the fitting procedure added, typos in Eqs. 2 and 23 eliminate

Applications of QCD

Talk given at XIXth International Symposium on Lepton and Photon Interactions at High Energies (LP 99), Stanford, California, 9-14 August 1999.Comment: latex, 26 page

Gauge dependence and matching procedure of a nonrelativistic QED/QCD boundstate formalism

A nonrelativistic boundstate formalism used in contemporary calculations is investigated. It is known that the effective Hamiltonian of the boundstate system depends on the choice of gauge. We obtain the transformation charge Q of the Hamiltonian for an arbitrary infinitesimal change of gauge, by which gauge independence of the mass spectrum and gauge dependences of the boundstate wave functions are dictated. We give formal arguments based on the BRST symmetry supplemented by power countings of Coulomb singularities of diagrams. For illustration: (1)we calculate Q up to O(1/c), (2)we examine gauge dependences of diagrams for a decay of a qqbar boundstate up to O(1/c) and show that cumbersome gauge cancellations can be circumvented by directly calculating Q. As an application we point out that the present calculations of top quark momentum distribution in the ttbar threshold region are gauge dependent. We also show possibilities for incorrect calculations of physical quantities of boundstates when the on-shell matching procedure is employed. We give a proof of a justification for the use of the equation of motion to simplify the form of a local NRQCD Lagrangian. The formalism developed in this work will provide useful cross checks in computations involving NRQED/NRQCD boundstates.Comment: 30 pages, 15 figures (ver1); Presentations of Introduction and Conclusion were modified substantially, although none of our findings have been changed; Side remarks have been added in various parts of the paper. (ver2); Supplementary remarks and minor corrections (ver3

Reducing theoretical uncertainties in mb and lambda1

We calculate general moments of the lepton energy spectrum in inclusive semileptonic B -> X_c l \nu decay. Moments which allow the determination of mb^{1S} and lambda1 with theoretical uncertainties Delta(mb^{1S}) ~ 0.04 GeV and Delta(lambda1) ~ 0.05 GeV^2 are presented. The short distance 1S mass is used to extract a mass parameter free of renormalon ambiguities. Moments which are insensitive to mb and lambda1 and therefore test the size of the 1/mb^3 matrix elements and the validity of the OPE are also presented. Finally, we give an expression for the total branching ratio with a lower cut on the lepton energy, which allows one to eliminate a source of model dependence in current determinations of |Vcb| from B -> X_c l \nu decay.Comment: 8 pages, one figur

Virtual and Soft Pair Corrections to Polarized Muon Decay Spectrum

Radiative corrections to the muon decay spectrum due to soft and virtual electron--positron pairs are calculated.Comment: 10pp, 2 PS figs, details of calculations are adde

Further Improvements in Decoding Performance for 5G LDPC Codes Based on Modified Check-Node Unit

One of the most important units of Low-Density Parity-Check (LDPC) decoders is the Check-Node Unit. Its main task is to find the first two minimum values among incoming variable-to-check messages and return check-to-variable messages. This block significantly affects the decoding performance, as well as the hardware implementation complexity. In this paper, we first propose a modification to the check-node update rule by introducing two optimal offset factors applied to the check-to-variable messages. Then, we present the Check-Node Unit hardware architecture which performs the proposed algorithm. The main objective of this work aims to improve further the decoding performance for 5th Generation (5G) LDPC codes. The simulation results show that the proposed algorithm achieves essential improvements in terms of error correction performance. More precisely, the error-floor does not appear within Bit-Error-Rate (BER) of 10^(-8), while the decoding gain increases up to 0.21 dB compared to the baseline Normalized Min-Sum, as well as several state-of-the-art LDPC-based Min-Sum decoders

On the form of growing strings

Patterns and forms adopted by Nature, such as the shape of living cells, the geometry of shells and the branched structure of plants, are often the result of simple dynamical paradigms. Here we show that a growing self-interacting string attached to a tracking origin, modeled to resemble nascent polypeptides in vivo, develops helical structures which are more pronounced at the growing end. We also show that the dynamic growth ensemble shares several features of an equilibrium ensemble in which the growing end of the polymer is under an effective stretching force. A statistical analysis of native states of proteins shows that the signature of this non-equilibrium phenomenon has been fixed by evolution at the C-terminus, the growing end of a nascent protein. These findings suggest that a generic non-equilibrium growth process might have provided an additional evolutionary advantage for nascent proteins by favoring the preferential selection of helical structures.Comment: 4 pages, 3 figures. Accepted for publication in Phys. Rev. Let