Three-Loop Anomalous Dimension of the Heavy Quark Pair Production Current in Non-Relativistic QCD

The three-loop non-mixing contributions to the anomalous dimension of the leading order quark pair production current in non-relativistic QCD are computed. It is demonstrated that the renormalization procedure can only be carried out consistently if the dynamics of both soft and the ultrasoft degrees of freedom is present for all scales below the heavy quark mass, and if the soft and ultrasoft renormalization scales are always correlated.Comment: 19 pages, revtex, 5 postscript figures include

Origin of the structural phase transition in Li7La3Zr2O12

Garnet-type Li7La3Zr2O12 (LLZO) is a solid electrolyte material with a low-conductivity tetragonal and a high-conductivity cubic phase. Using density-functional theory and variable cell shape molecular dynamics simulations, we show that the tetragonal phase stability is dependent on a simultaneous ordering of the Li ions on the Li sublattice and a volume-preserving tetragonal distortion that relieves internal structural strain. Supervalent doping introduces vacancies into the Li sublattice, increasing the overall entropy and reducing the free energy gain from ordering, eventually stabilizing the cubic phase. We show that the critical temperature for cubic phase stability is lowered as Li vacancy concentration (dopant level) is raised and that an activated hop of Li ions from one crystallographic site to another always accompanies the transition. By identifying the relevant mechanism and critical concentrations for achieving the high conductivity phase, this work shows how targeted synthesis could be used to improve electrolytic performance

Electroweak non-resonant NLO corrections to e+ e- -> W+ W- b bbar in the t tbar resonance region

We analyse subleading electroweak effects in the top anti-top resonance production region in e+ e- collisions which arise due to the decay of the top and anti-top quarks into the W+ W- b bbar final state. These are NLO corrections adopting the non-relativistic power counting v ~ alpha_s ~ sqrt(alpha_EW). In contrast to the QCD corrections which have been calculated (almost) up to NNNLO, the parametrically larger NLO electroweak contributions have not been completely known so far, but are mandatory for the required accuracy at a future linear collider. The missing parts of these NLO contributions arise from matching coefficients of non-resonant production-decay operators in unstable-particle effective theory which correspond to off-shell top production and decay and other non-resonant irreducible background processes to t tbar production. We consider the total cross section of the e+ e- -> W+ W- b bbar process and additionally implement cuts on the invariant masses of the W+ b and W- bbar pairs.Comment: LaTeX, 33 pages, 6 figure

Ultrasoft Renormalization in Non-Relativistic QCD

For Non-Relativistic QCD the velocity renormalization group correlates the renormalization scales for ultrasoft, potential and soft degrees of freedom. Here we discuss the renormalization of operators by ultrasoft gluons. We show that renormalization of soft vertices can induce new operators, and also present a procedure for correctly subtracting divergences in mixed potential-ultrasoft graphs. Our results affect the running of the spin-independent potentials in QCD. The change for the NNLL t-tbar cross section near threshold is very small, being at the 1% level and essentially independent of the energy. We also discuss implications for analyzing situations where mv^2 ~ Lambda_QCD.Comment: 31 pages, 11 fig

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

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