944 research outputs found

### Algorithms to Evaluate Multiple Sums for Loop Computations

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 $ai.n=\sum_{j=1}^N a_{ij}nj$, 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

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

We compute the full ${\cal O}(\alpha_s^4)$ and ${\cal
O}(\alpha_s^4\log\alpha_s)$ corrections to the potential $V_R(r)$ between the
static color sources, where $V_R(r)$ is defined from the Wilson loop in a
general representation $R$ of a general gauge group $G$. We find a violation of
the Casimir scaling of the potential, for the first time, at ${\cal
O}(\alpha_s^4)$. The effect of the Casimir scaling violation is predicted to
reduce the tangent of $V_R(r)/C_R$ proportionally to specific color factors
dependent on $R$. We study the sizes of the Casimir scaling violation for
various $R$'s in the case $G=SU(3)$. We find that they are well within the
present bounds from lattice calculations, in the distance region where both
perturbative and lattice computations of $V_R(r)$ 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

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

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

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

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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