32,962 research outputs found
The Two-mass Contribution to the Three-Loop Gluonic Operator Matrix Element
We calculate the two-mass QCD contributions to the massive operator matrix
element at in analytic form in Mellin
- and -space, maintaining the complete dependence on the heavy quark mass
ratio. These terms are important ingredients for the matching relations of the
variable flavor number scheme in the presence of two heavy quark flavors, such
as charm and bottom. In Mellin -space the result is given in the form of
nested harmonic, generalized harmonic, cyclotomic and binomial sums, with
arguments depending on the mass ratio. The Mellin inversion of these quantities
to -space gives rise to generalized iterated integrals with square root
valued letters in the alphabet, depending on the mass ratio as well. Numerical
results are presented.Comment: 99 pages LATEX, 2 Figure
Use of Harmonic Inversion Techniques in the Periodic Orbit Quantization of Integrable Systems
Harmonic inversion has already been proven to be a powerful tool for the
analysis of quantum spectra and the periodic orbit orbit quantization of
chaotic systems. The harmonic inversion technique circumvents the convergence
problems of the periodic orbit sum and the uncertainty principle of the usual
Fourier analysis, thus yielding results of high resolution and high precision.
Based on the close analogy between periodic orbit trace formulae for regular
and chaotic systems the technique is generalized in this paper for the
semiclassical quantization of integrable systems. Thus, harmonic inversion is
shown to be a universal tool which can be applied to a wide range of physical
systems. The method is further generalized in two directions: Firstly, the
periodic orbit quantization will be extended to include higher order hbar
corrections to the periodic orbit sum. Secondly, the use of cross-correlated
periodic orbit sums allows us to significantly reduce the required number of
orbits for semiclassical quantization, i.e., to improve the efficiency of the
semiclassical method. As a representative of regular systems, we choose the
circle billiard, whose periodic orbits and quantum eigenvalues can easily be
obtained.Comment: 21 pages, 9 figures, submitted to Eur. Phys. J.
3-Loop Heavy Flavor Corrections in Deep-Inelastic Scattering with Two Heavy Quark Lines
We consider gluonic contributions to the heavy flavor Wilson coefficients at
3-loop order in QCD with two heavy quark lines in the asymptotic region . Here we report on the complete result in the case of two equal
masses for the massive operator matrix element ,
which contributes to the corresponding heavy flavor transition matrix element
in the variable flavor number scheme. Nested finite binomial sums and iterated
integrals over square-root valued alphabets emerge in the result for this
quantity in and -space, respectively. We also present results for the
case of two unequal masses for the flavor non-singlet OMEs and on the scalar
integrals ic case of , which were calculated without a further
approximation. The graphs can be expressed by finite nested binomial sums over
generalized harmonic sums, the alphabet of which contains rational letters in
the ratio .Comment: 10 pages LATEX, 1 Figure, Proceedings of Loops and Legs in Quantum
Field Theory, Weimar April 201
The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function and the Anomalous Dimension
The pure singlet asymptotic heavy flavor corrections to 3-loop order for the
deep-inelastic scattering structure function and the corresponding
transition matrix element in the variable flavor number
scheme are computed. In Mellin- space these inclusive quantities depend on
generalized harmonic sums. We also recalculate the complete 3-loop pure singlet
anomalous dimension for the first time. Numerical results for the Wilson
coefficients, the operator matrix element and the contribution to the structure
function are presented.Comment: 85 pages Latex, 14 Figures, 2 style file
Huyghens, Bohr, Riemann and Galois: Phase-Locking
18 pages paper written in relation to the ICSSUR'05 conference held in Besancon, France to be published at a special issue of IJMPBSeveral mathematical views of phase-locking are developed. The classical Huyghens approach is generalized to include all harmonic and subharmonic resonances and is found to be connected to 1/f noise and prime number theory. Two types of quantum phase-locking operators are defined, one acting on the rational numbers, the other on the elements of a Galois field. In both cases we analyse in detail the phase properties and find them related respectively to the Riemann zeta function and to incomplete Gauss sums
Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter
We continue the study of the construction of analytical coefficients of the
epsilon-expansion of hypergeometric functions and their connection with Feynman
diagrams. In this paper, we show the following results:
Theorem A: The multiple (inverse) binomial sums of arbitrary weight and depth
(see Eq. (1.1)) are expressible in terms of Remiddi-Vermaseren functions.
Theorem B: The epsilon expansion of a hypergeometric function with one
half-integer value of parameter (see Eq. (1.2)) is expressible in terms of the
harmonic polylogarithms of Remiddi and Vermaseren with coefficients that are
ratios of polynomials. Some extra materials are available via the www at this
http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htmlComment: 24 pages, latex with amsmath and JHEP3.cls; v2: some typos corrected
and a few references added; v3: few references added
Multiple harmonic sums and Wolstenholme's theorem
We give a family of congruences for the binomial coefficients in terms of multiple harmonic sums, a generalization of the harmonic
numbers. Each congruence in this family (which depends on an additional
parameter ) involves a linear combination of multiple harmonic sums, and
holds . The coefficients in these congruences are integers
depending on and , but independent of . More generally, we construct
a family of congruences for , whose members
contain a variable number of terms, and show that in this family there is a
unique "optimized" congruence involving the fewest terms. The special case
and recovers Wolstenholme's theorem , valid for all primes . We also characterize those triples
for which the optimized congruence holds modulo an extra power of
: they are precisely those with either dividing the numerator of the
Bernoulli number , or .Comment: 22 page
- …