1,857 research outputs found
On the construction of general solution of the generalized sylvester equation
The problem of construction the general solution of the generalized matrix Sylvester equation is considered. Conditions of existence of solution of this equation are obtained and the algorithm for construction of this solution is given. For construction of the algorithm of this solution and the formulation of the condition of existence of this solution, the standard procedures of MATLAB package are used.Publisher's Versio
The Scientific and Social Activity of Professor N. N. Saltykov in Russia in 1894–1919
The scientific and social activity of Professor N. N. Saltykov in Russia in period 1894–1919 is presented
The order and corrections to the decay width of the neutral Higgs boson to the pair
We present the analytical expressions for the contributions of the order
and corrections to the
decay width of the Standard Model Higgs boson into the -pair. The
numerical value of the mixed QED and QCD correction of order
is comparable with the previously calculated
terms in the perturbative series for .Comment: LaTeX 5 pages, accepted for publication in Pisma Zh. Eksp. Teor. Fiz.
v 66, N5 (1997
Relating Physical Observables in QCD without Scale-Scheme Ambiguity
We discuss the St\"uckelberg-Peterman extended renormalization group
equations in perturbative QCD, which express the invariance of physical
observables under renormalization-scale and scheme-parameter transformations.
We introduce a universal coupling function that covers all possible choices of
scale and scheme. Any perturbative series in QCD is shown to be equivalent to a
particular point in this function. This function can be computed from a set of
first-order differential equations involving the extended beta functions. We
propose the use of these evolution equations instead of perturbative series for
numerical evaluation of physical observables. This formalism is free of
scale-scheme ambiguity and allows a reliable error analysis of higher-order
corrections. It also provides a precise definition for as the pole in the associated 't Hooft scheme. A concrete application to
is presented.Comment: Plain TEX, 4 figures (available upon request), 22 pages,
DOE/ER/40322-17
Calculating loops without loop calculations: NLO computation of pentaquark correlators
We compute next-to-leading order (NLO) perturbative QCD corrections to the
correlators of interpolating pentaquark currents. We employ modular techniques
in configuration space which saves us from the onus of having to do loop
calculations. The modular technique is explained in some detail. We present
explicit NLO results for several interpolating pentaquark currents that have
been written down in the literature. Our modular approach is easily adapted to
the case of NLO corrections to multiquark correlators with an arbitrary number
of quarks/antiquarks.Comment: 23 pages, 1 figure, published version. arXiv admin note: text overlap
with arXiv:hep-lat/031001
Recursive Graphical Construction of Feynman Diagrams in phi^4 Theory: Asymmetric Case and Effective Energy
The free energy of a multi-component scalar field theory is considered as a
functional W[G,J] of the free correlation function G and an external current J.
It obeys non-linear functional differential equations which are turned into
recursion relations for the connected Greens functions in a loop expansion.
These relations amount to a simple proof that W[G,J] generates only connected
graphs and can be used to find all such graphs with their combinatoric weights.
A Legendre transformation with respect to the external current converts the
functional differential equations for the free energy into those for the
effective energy Gamma[G,Phi], which is considered as a functional of the free
correlation function G and the field expectation Phi. These equations are
turned into recursion relations for the one-particle irreducible Greens
functions. These relations amount to a simple proof that Gamma[G,J] generates
only one-particle irreducible graphs and can be used to find all such graphs
with their combinatoric weights. The techniques used also allow for a
systematic investigation into resummations of classes of graphs. Examples are
given for resumming one-loop and multi-loop tadpoles, both through all orders
of perturbation theory. Since the functional differential equations derived are
non-perturbative, they constitute also a convenient starting point for other
expansions than those in numbers of loops or powers of coupling constants. We
work with general interactions through four powers in the field.Comment: 34 pages; abstract expanded; section IV.E about absorption of
tadpoles and one related reference added; eqs. (20) and (23) corrected;
further references added; some minor beautifications; to be published by
Phys.Rev.
Next-to-next-to-leading order fits to CCFR'97 data and infrared renormalons
We briefly summarize the outcomes of our recent improved fits to the
experimental data of CCFR collaboration for structure function of deep-inelastic scattering at the next-to-next-to-leading order. Special
attention is paid to the extraction of and the parameter of the
infrared renormalon model for -correction at different orders of
perturbation theory. The results can be of interest for planning similar
studies using possible future data of Neutrino Factories.Comment: 3 pages, presented at WG3 of 4th NuFact'02 Workshop, London 1-6 July,
200
Strong Coupling Constant with Flavour Thresholds at Four Loops in the MS-bar Scheme
We present in analytic form the matching conditions for the strong coupling
constant alpha_s^(n_f)(mu) at the flavour thresholds to three loops in the
modified minimal-subtraction scheme. Taking into account the recently
calculated coefficient beta_3 of the Callan-Symanzik beta function of quantum
chromodynamics, we thus derive a four-loop formula for alpha_s^(n_f)(mu)
together with appropriate relationships between the asymptotic scale parameters
Lambda^(n_f) for different numbers of flavours n_f.Comment: 10 pages (Latex), 3 figures (Postscript
Three loop MSbar renormalization of QED in the 't~Hooft-Veltman gauge
Quantum electrodynamics (QED) fixed in the 't~Hooft-Veltman gauge is
renormalized to three loops in the MSbar scheme. The beta-functions and
anomalous dimensions are computed as functions of the usual QED coupling and
the additional coupling, xi, which is introduced as part of the nonlinear gauge
fixing condition. Similar to the maximal abelian gauge of quantum
chromodynamics, the renormalization of the gauge parameter is singular.Comment: 8 latex page
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