89 research outputs found
Solution to Bethe-Salpeter equation via Mellin-Barnes transform
We consider Mellin-Barnes transform of triangle ladder-like scalar diagram in
d=4 dimensions. It is shown how the multi-fold MB transform of the momentum
integral corresponding to an arbitrary number of rungs is reduced to the
two-fold MB transform. For this purpose we use Belokurov-Usyukina reduction
method for four-dimensional scalar integrals in the position space. The result
is represented in terms of Euler psi-function and its derivatives. We derive
new formulas for the MB two-fold integration in complex planes of two complex
variables. We demonstrate that these formulas solve Bethe-Salpeter equation. We
comment on further applications of the solution to the Bethe-Salpeter equation
for the vertices in N=4 supersymmetric Yang-Mills theory. We show that the
recursive property of the MB transforms observed in the present work for that
kind of diagrams has nothing to do with quantum field theory, theory of
integral transforms, or with theory of polylogarithms in general, but has an
origin in a simple recursive property for smooth functions which can be shown
by using basic methods of mathematical analysis.Comment: 33 pages, 9 figures, revised version, all the factors and symbols of
integration are written explcitly, symbols of proportionality are removed,
section 2 is extended, section 6.3 is shortene
The massless supersymmetric ladder with L rungs
We show that in the massless N=1 supersymmetric Wess-Zumino theory it is
possible to devise a computational strategy by which the x-space calculation of
the ladder 4-point correlators can be carried out without introducing any
regularization. As an application we derive a representation valid at all loop
orders in terms of conformal invariant integrals. We obtain an explicit
expression of the 3-loop ladder diagram for collinear external points.Comment: LaTeX, 17 pages, 8 figure
The decay b -> s g at NLL in the Standard Model
I present the Standard Model calculation of the decay rate for b -> s g (g
denotes a gluon) at next-to-leading logarithms (NLL). In order to get a
meaningful physical result, the decay b -> s g g and certain contributions of b
-> s \bar{f} f (where f are the light quark flavours u, d and s) have to be
included as well. Numerically we get BR^(NLL) = (5.0 +/- 1.0) * 10^{-3} which
is more than a factor 2 larger than the leading logarithmic result BR^(LL) =
(2.2 +/- 0.8) * 10^{-3}. Further, I consider the impact of this contribution on
the charmless hadronic branching ratio BRc, which could be used to extract the
CKM-ratio |V_(ub)/V_(cb)| with more accuracy. Finally, I have a short look at
BRc in scenarios where the Wilson coefficient C_8 is enhanced by new physics.Comment: 7 pages including 5 postscript figures; uses epsfi
Three loop QCD MOM beta-functions
We present the full expressions for the QCD beta-function in the MOMggg, MOMq
and MOMh renormalization schemes at three loops for an arbitrary colour group
in the Landau gauge. The results for all three schemes are in very good
agreement with the SU(3) numerical estimates provided by Chetyrkin and
Seidensticker.Comment: 9 latex page
Two loop QCD vertices at the symmetric point
We compute the triple gluon, quark-gluon and ghost-gluon vertices of QCD at
the symmetric subtraction point at two loops in the MSbar scheme. In addition
we renormalize each of the three vertices in their respective momentum
subtraction schemes, MOMggg, MOMq and MOMh. The conversion functions of all the
wave functions, coupling constant and gauge parameter renormalization constants
of each of the schemes relative to MSbar are determined analytically. These are
then used to derive the three loop anomalous dimensions of the gluon, quark,
Faddeev-Popov ghost and gauge parameter as well as the beta-function in an
arbitrary linear covariant gauge for each MOM scheme. There is good agreement
of the latter with earlier Landau gauge numerical estimates of Chetyrkin and
Seidensticker.Comment: 36 latex pages, anc directory contains txt file with anomalous
dimensions, beta-functions, coupling constant mappings, conversion functions
and amplitudes in analytic for
Belokurov-Usyukina loop reduction in non-integer dimension
Belokurov-Usyukina loop reduction method has been proposed in 1983 to reduce
a number of rungs in triangle ladder-like diagram by one. The disadvantage of
the method is that it works in d=4 dimensions only and it cannot be used for
calculation of amplitudes in field theory in which we are required to put all
the incoming and outgoing momenta on shell. We generalize the
Belokurov-Usyukina loop reduction technique to non-integer d=4-2e dimensions.
In this paper we show how a two-loop triangle diagram with particular values of
indices of scalar propagators in the position space can be reduced to a
combination of three one-loop scalar diagrams. It is known that any one-loop
massless momentum integral can be presented in terms of Appell's function F_4.
This means that particular diagram considered in the present paper can be
represented in terms of Appell's function F_4 too. Such a generalization of
Belokurov-Usyukina loop reduction technique allows us to calculate that diagram
by this method exactly without decomposition in terms of the parameter e.Comment: 6 pages, 3 figure
Massive Loop Amplitudes from Unitarity
We show, for previously uncalculated examples containing a uniform mass in
the loop, that it is possible to obtain complete massive one-loop gauge theory
amplitudes solely from unitarity and known ultraviolet or infrared mass
singularities. In particular, we calculate four-gluon scattering via massive
quark loops in QCD. The contribution of a heavy quark to five-gluon scattering
with identical helicities is also presented.Comment: Minor modifications, 27 pages including two figure
Banks-Zaks fixed point analysis in momentum subtraction schemes
We analyse the critical exponents relating to the quark mass anomalous
dimension and beta-function at the Banks-Zaks fixed point in Quantum
Chromodynamics (QCD) in a variety of representations for the quark in the
momentum subtraction (MOM) schemes of Celmaster and Gonsalves. For a specific
range of values of the number of quark flavours, estimates of the exponents
appear to be scheme independent. Using the recent five loop modified minimal
subtraction (MSbar) scheme quark mass anomalous dimension and estimates of the
fixed point location we estimate the associated exponent as 0.263-0.268 for the
SU(3) colour group and 12 flavours when the quarks are in the fundamental
representation.Comment: 33 latex pages, 25 tables, anc directory contains txt file with
electronic version of renormalization group function
Differential equations and high-energy expansion of two--loop diagrams in D dimensions
New method of calculation of master integrals using differential equations
and asymptotical expansion is presented. This method leads to the results exact
in space-time dimension having the form of the convergent power series. As
an application of this method, we calculate the two--loop master integral for
"crossed--triangle" topology which was previously known only up to O(\ep)
order. The case when a topology contains several master integrals is also
considered. We present an algorithm of the term-by-term calculation of the
asymptotical expansion in this case and analyze in detail the "crossed--box"
topology with three master integrals.Comment: 13 pages,8 figures, uses elsart.cls. Misprints correcte
Систематика и принципы терапии депрессивных расстройств при эпилепсии
Relying on a comprehensive investigation, the author proposes the typology of depressive disorders in epilepsy by identifying ictal, preictal, interictal, and postictal conditions. Risk factors for depressive symptoms are considered. Main approaches to therapy for depressions are offered. Particular emphasis is placed on the normothymic activity of a number of anticonvulsants. Valproates, and depakine in particular, as a normothymic agent are shown to be beneficial in treating affective disorders.На основании комплексного исследования предложена типология депрессивных расстройств при эпилепсии с выделением иктальных, преиктальных, интериктальных и постиктальных состояний. Рассмотрены факторы риска возникновения депрессивной симптоматики. Предложены основные подходы к терапии депрессий. Особое внимание уделяется нормотимическим действиям ряда антиконвульсантов. Показано преимущество вальпроатов, и особенно депакина как нормотимика, при лечении аффективных расстройств
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