944 research outputs found

    Algorithms to Evaluate Multiple Sums for Loop Computations

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    We present algorithms to evaluate two types of multiple sums, which appear in higher-order loop computations. We consider expansions of a generalized hypergeometric-type sums, \sum_{n_1,...,n_N} [Gamma(a1.n+c1) Gamma(a2.n}+c2) ... Gamma(aM.n+cM)] / [Gamma(b1.n+d1) Gamma(b2.n+d2) ... Gamma(bM.n+dM)] x1^n1...xN^nN with ai.n=∑j=1Naijnjai.n=\sum_{j=1}^N a_{ij}nj, etc., in a small parameter epsilon around rational values of ci,di's. Type I sum corresponds to the case where, in the limit epsilon -> 0, the summand reduces to a rational function of nj's times x1^n1...xN^nN; ci,di's can depend on an external integer index. Type II sum is a double sum (N=2), where ci,di's are half-integers or integers as epsilon -> 0 and xi=1; we consider some specific cases where at most six Gamma functions remain in the limit epsilon -> 0. The algorithms enable evaluations of arbitrary expansion coefficients in epsilon in terms of Z-sums and multiple polylogarithms (generalized multiple zeta values). We also present applications of these algorithms. In particular, Type I sums can be used to generate a new class of relations among generalized multiple zeta values. We provide a Mathematica package, in which these algorithms are implemented.Comment: 30 pages, 2 figures; address of Mathematica package in Sec.6; version to appear in J.Math.Phy

    Coding of stereoscopic depth information in visual areas V3 and V3A

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    The process of stereoscopic depth perception is thought to begin with the analysis of absolute binocular disparity, the difference in position of corresponding features in the left and right eye images with respect to the points of fixation. Our sensitivity to depth, however, is greater when depth judgments are based on relative disparity, the difference between two absolute disparities, compared to when they are based on absolute disparity. Therefore, the visual system is thought to compute relative disparities for fine depth discrimination. Functional magnetic resonance imaging studies in humans and monkeys have suggested that visual areas V3 and V3A may be specialized for stereoscopic depth processing based on relative disparities. In this study, we measured absolute and relative disparity tuning of neurons in V3 and V3A of alert fixating monkeys and we compared their basic tuning properties with those published previously for other visual areas. We found that neurons in V3 and V3A predominantly encode absolute, not relative, disparities. We also found that basic parameters of disparity tuning in V3 and V3A are similar to those from other extrastriate visual areas. Finally, by comparing single-unit activity with multi-unit activity measured at the same recording site, we demonstrate that neurons with similar disparity selectivity are clustered in both V3 and V3A. We conclude that areas V3 and V3A are not particularly specialized for processing stereoscopic depth information compared to other early visual areas, at least with respect to the tuning properties that we have examined

    Violation of Casimir Scaling for Static QCD Potential at Three-loop Order

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    We compute the full O(αs4){\cal O}(\alpha_s^4) and O(αs4log⁡αs){\cal O}(\alpha_s^4\log\alpha_s) corrections to the potential VR(r)V_R(r) between the static color sources, where VR(r)V_R(r) is defined from the Wilson loop in a general representation RR of a general gauge group GG. We find a violation of the Casimir scaling of the potential, for the first time, at O(αs4){\cal O}(\alpha_s^4). The effect of the Casimir scaling violation is predicted to reduce the tangent of VR(r)/CRV_R(r)/C_R proportionally to specific color factors dependent on RR. We study the sizes of the Casimir scaling violation for various RR's in the case G=SU(3)G=SU(3). We find that they are well within the present bounds from lattice calculations, in the distance region where both perturbative and lattice computations of VR(r)V_R(r) are valid. We also discuss how to test the Casimir scaling violating effect.Comment: 20 pages, 7 figures, v2: a typo in eq.(13) correcte

    Rotor interaction in the annulus billiard

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    Introducing the rotor interaction in the integrable system of the annulus billiard produces a variety of dynamical phenomena, from integrability to ergodicity

    Exact N3LO results for qq ′ → H + X

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    We compute the contribution to the total cross section for the inclusive production of a Standard Model Higgs boson induced by two quarks with different flavour in the initial state. Our calculation is exact in the Higgs boson mass and the partonic center-of-mass energy. We describe the reduction to master integrals, the construction of a canonical basis, and the solution of the corresponding differential equations. Our analytic result contains both Harmonic Polylogarithms and iterated integrals with additional letters in the alphabet. © 2015, The Author(s)

    Heavy Quarkonium in a weakly-coupled quark-gluon plasma below the melting temperature

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    We calculate the heavy quarkonium energy levels and decay widths in a quark-gluon plasma, whose temperature T and screening mass m_D satisfy the hierarchy m alpha_s >> T >> m alpha_s^2 >> m_D (m being the heavy-quark mass), at order m alpha_s^5. We first sequentially integrate out the scales m, m alpha_s and T, and, next, we carry out the calculations in the resulting effective theory using techniques of integration by regions. A collinear region is identified, which contributes at this order. We also discuss the implications of our results concerning heavy quarkonium suppression in heavy ion collisions.Comment: 25 pages, 2 figure

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

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    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
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