Ultrasoft NLL Running of the Nonrelativistic O(v) QCD Quark Potential

Using the nonrelativistic effective field theory vNRQCD, we determine the contribution to the next-to-leading logarithmic (NLL) running of the effective quark-antiquark potential at order v (1/mk) from diagrams with one potential and two ultrasoft loops, v being the velocity of the quarks in the c.m. frame. The results are numerically important and complete the description of ultrasoft next-to-next-to-leading logarithmic (NNLL) order effects in heavy quark pair production and annihilation close to threshold.Comment: 25 pages, 7 figures, 3 tables; minor modifications, typos corrected, references added, footnote adde

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

Electroweak Absorptive Parts in NRQCD Matching Conditions

Electroweak corrections associated with the instability of the top quark to the next-to-next-to-leading logarithmic (NNLL) total top pair threshold cross section in e+e- annihilation are determined. Our method is based on absorptive parts in electroweak matching conditions of the NRQCD operators and the optical theorem. The corrections lead to ultraviolet phase space divergences that have to be renormalized and lead to NLL mixing effects. Numerically, the corrections can amount to several percent and are comparable to the known NNLL QCD corrections.Comment: 17 pages, revtex4, 4 postscript figures included; minor changes in text and references, title modified in printed versio

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

Batch Policy Learning under Constraints

When learning policies for real-world domains, two important questions arise: (i) how to efficiently use pre-collected off-policy, non-optimal behavior data; and (ii) how to mediate among different competing objectives and constraints. We thus study the problem of batch policy learning under multiple constraints, and offer a systematic solution. We first propose a flexible meta-algorithm that admits any batch reinforcement learning and online learning procedure as subroutines. We then present a specific algorithmic instantiation and provide performance guarantees for the main objective and all constraints. To certify constraint satisfaction, we propose a new and simple method for off-policy policy evaluation (OPE) and derive PAC-style bounds. Our algorithm achieves strong empirical results in different domains, including in a challenging problem of simulated car driving subject to multiple constraints such as lane keeping and smooth driving. We also show experimentally that our OPE method outperforms other popular OPE techniques on a standalone basis, especially in a high-dimensional setting

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

Double Bubble Corrections to Heavy Quark Production

Second order ${\cal O}(\alpha_s^2)$ corrections to the heavy quark production cross-section due to massless quarks and coloured scalars are calculated for all energies above threshold. Based on the method introduced in this letter also the gauge non-invariant second order corrections due to the pure gluonic selfenergy insertion and a certain class of ${\cal{O}}(\alpha_s^3)$ and ${\cal{O}}(\alpha_s^4)$ corrections are determined. For the special choice of the gauge parameter, $\xi=4$, the leading threshold and high energy behaviour of the pure second order gluonic corrections to the cross-section are governed by the gluonic self energy insertion.Comment: 9 pages, latex, 17 figures, the complete postscript file of this preprint, including figures, is available via anonymous ftp at ftp://www-ttp.physik.uni-karlsruhe.de/ttp96-04/ttp96-04.ps (129.13.102.139) or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints

Phase Space Matching and Finite Lifetime Effects for Top-Pair Production Close to Threshold

The top-pair $t\bar t$ production cross section close to threshold in $e^+e^-$ collisions is strongly affected by the small lifetime of the top quark. Since the cross section is defined through final states containing the top decay products, a consistent definition of the cross section depends on prescriptions how these final states are accounted for the cross section. Experimentally, these prescriptions are implemented for example through cuts on kinematic quantities such as the reconstructed top quark invariant masses. As long as these cuts do not reject final states that can arise from the decay of a top and an anti-top quark with a small off-shellness compatible with the nonrelativistic power-counting, they can be implemented through imaginary phase space matching conditions in NRQCD. The prescription-dependent cross section can then be determined from the optical theorem using the $e^+e^-$ forward scattering amplitude. We compute the phase space matching conditions associated to cuts on the top and anti-top invariant masses at next-to-next-to-leading logarithmic (NNLL) order and partially at next-to-next-to-next-to-leading logarithmic (N${}^3$LL) order in the nonrelativistic expansion and, together with finite lifetime and electroweak effects known from previous work, analyze their numerical impact on the $t\bar t$ cross section. We show that the phase space matching contributions are essential to make reliable NRQCD predictions, particularly for energies below the peak region, where the cross section is small. We find that irreducible background contributions associated to final states that do not come from top decays are strongly suppressed and can be neglected for the theoretical predictions.Comment: 62 pages, 21 figure