311 research outputs found
Resummation of Threshold, Low- and High-Energy Expansions for Heavy-Quark Correlators
With the help of the Mellin-Barnes transform, we show how to simultaneously
resum the expansion of a heavy-quark correlator around q^2=0 (low-energy), q^2=
4 m^2 (threshold, where m is the quark mass) and q^2=-\infty (high-energy) in a
systematic way. We exemplify the method for the perturbative vector correlator
at O(alpha_s^2) and O(alpha_s^3). We show that the coefficients, Omega(n), of
the Taylor expansion of the vacuum polarization function in terms of the
conformal variable \omega admit, for large n, an expansion in powers of 1/n (up
to logarithms of n) that we can calculate exactly. This large-n expansion has a
sign-alternating component given by the logarithms of the OPE, and a fixed-sign
component given by the logarithms of the threshold expansion in the external
momentum q^2.Comment: 27 pages, 8 figures. We fix typos in Eqs. (18), (27), (55) and (56).
Results unchange
Re-Scaling of Energy in the Stringy Charged Black Hole Solutions using Approximate Symmetries
This paper is devoted to study the energy problem in general relativity using
approximate Lie symmetry methods for differential equations. We evaluate
second-order approximate symmetries of the geodesic equations for the stringy
charged black hole solutions. It is concluded that energy must be re-scaled by
some factor in the second-order approximation.Comment: 18 pages, accepted for publication in Canadian J. Physic
УВЛЕЧЕНИЕ ВЯЗКОПЛАСТИЧЕСКОЙ ЖИДКОСТИ ДВИЖУЩЕЙСЯ ВЕРТИКАЛЬНО ПЛАСТИНОЙ
The liquid capture by a moving surface is the most widespread process in chemical engineering along with calendaring, extrusion moulding, pouring, and pressure moulding. The theoretical analysis of the medium capture by a moving surface, which allows revealing the fundamental physical principles and mechanisms of the process over the entire withdrawal speed range realized in practice, was performed for Newtonian, non-Newtonian, and viscoplastic liquids. However, such an analysis of the withdrawal of viscoplastic liquids with a finite yield was not made because of the features of these liquids. Shear flow of viscoplastic liquid is possible only after the stress exceeds its yield. This fact causes serious mathematical difficulties in stating and solving the problem. In the proposed work, such a theory is being developed for viscoplastic liquids.Захват жидкости движущейся поверхностью является наиболее распространённым процессом в химической технологии наряду с каландрованием, экструзионным формованием, заливкой, формованием под давлением. Теоретический анализ увлечения среды движущейся поверхностью, позволяющей вскрыть основные физические принципы и механизмы процесса во всем диапазоне скоростей извлечения, реализуемом на практике, был проведен для ньютоновских, нелинейновязких, вязкопластичных жидкостей. Однако такой анализ по увлечению вязкопластичных жидкостей, обладающих конечным пределом текучести, проведен не был в силу специфических особенностей этих жидкостей. Для вязкопластичной жидкости сдвиговое течение возможно лишь после того как напряжение превысит предел текучести. Данное обстоятельство вносит серьезные математические трудности при постановке и решении задачи. В предлагаемой работе такая теория развивается для вязкопластичных жидкостей
The Dimensional Recurrence and Analyticity Method for Multicomponent Master Integrals: Using Unitarity Cuts to Construct Homogeneous Solutions
We consider the application of the DRA method to the case of several master
integrals in a given sector. We establish a connection between the homogeneous
part of dimensional recurrence and maximal unitarity cuts of the corresponding
integrals: a maximally cut master integral appears to be a solution of the
homogeneous part of the dimensional recurrence relation. This observation
allows us to make a necessary step of the DRA method, the construction of the
general solution of the homogeneous equation, which, in this case, is a coupled
system of difference equations.Comment: 17 pages, 2 figure
The analytical singlet QCD contributions into the -annihilation Adler function and the generalized Crewther relations
The generalized Crewther relations in the channels of the non-singlet and
vector quark currents are considered. They follow from the double application
of the operator product expansion approach to the same axial
vector-vector-vector triangle amplitude in two regions, adjoining to the angle
sides (or ). We assume that the generalized Crewther relations
in these two kinematic regimes result in the existence of the same perturbation
expression for two products of the coefficient functions of annihilation and
deep-inelastic scattering processes in the non-singlet and vector channels.
Taking into account the 4-th order result for and the perturbative
effects of the violation of the conformal symmetry in the generalized Crewther
relation, we obtain the analytical contribution to the singlet
correction to the -function. Its a-posteriori comparison with the
recent result of direct diagram-by-diagram evaluation of the singlet 4-th order
corrections to - function demonstrates the coincidence of the
predicted and obtained -contributions to the singlet term. They can
be obtained in the conformal invariant limit from the original Crewther
relation. On the contrary to previous belief, the appearance of -terms
in perturbative series in gauge models does not contradict to the property of
conformal symmetry and can be considered as ragular feature. The Banks-Zaks
motivated relation between our predicted and obtained 4-th order corrections is
mentioned. This confirms Baikov-Chetyrkin-Kuhn expectation that the generalized
Crewther relation in the channel of vector currents receives additional singlet
contribution, which in this order of perturbation theory is proportional to the
first coefficient of the QCD -function.Comment: Concrete new foundations explained, abstract updated, presentation
improved, 2 references added, extra acknowledgements added. This work is
dedicated to K. G. Chetyrkin on the occasion of his 60th anniversary, to be
published in Jetp. Lett supposedly in vol.94, issue 1
Properties of equations of the continuous Toda type
We study a modified version of an equation of the continuous Toda type in 1+1
dimensions. This equation contains a friction-like term which can be switched
off by annihilating a free parameter \ep. We apply the prolongation method,
the symmetry and the approximate symmetry approach. This strategy allows us to
get insight into both the equations for \ep =0 and \ep \ne 0, whose
properties arising in the above frameworks are mutually compared. For \ep =0,
the related prolongation equations are solved by means of certain series
expansions which lead to an infinite- dimensional Lie algebra. Furthermore,
using a realization of the Lie algebra of the Euclidean group , a
connection is shown between the continuous Toda equation and a linear wave
equation which resembles a special case of a three-dimensional wave equation
that occurs in a generalized Gibbons-Hawking ansatz \cite{lebrun}. Nontrivial
solutions to the wave equation expressed in terms of Bessel functions are
determined.
For \ep\,\ne\,0, we obtain a finite-dimensional Lie algebra with four
elements. A matrix representation of this algebra yields solutions of the
modified continuous Toda equation associated with a reduced form of a
perturbative Liouville equation. This result coincides with that achieved in
the context of the approximate symmetry approach. Example of exact solutions
are also provided. In particular, the inverse of the exponential-integral
function turns out to be defined by the reduced differential equation coming
from a linear combination of the time and space translations. Finally, a Lie
algebra characterizing the approximate symmetries is discussed.Comment: LaTex file, 27 page
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