63 research outputs found
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 R*-operation for Feynman graphs with generic numerators
Abstract The R *-operation by Chetyrkin, Tkachov, and Smirnov is a generalisation of the BPHZ R-operation, which subtracts both ultraviolet and infrared divergences of euclidean Feynman graphs with non-exceptional external momenta. It can be used to compute the divergent parts of such Feynman graphs from products of simpler Feynman graphs of lower loops. In this paper we extend the R *-operation to Feynman graphs with arbitrary numerators, including tensors. We also provide a novel way of defining infrared counterterms which closely resembles the definition of its ultraviolet counterpart. We further express both infrared and ultraviolet counterterms in terms of scaleless vacuum graphs with a logarithmic degree of divergence. By exploiting symmetries, integrand and integral relations, which the counterterms of scaleless vacuum graphs satisfy, we can vastly reduce their number and complexity. A FORM implementation of this method was used to compute the five loop beta function in QCD for a general gauge group. To illustrate the procedure, we compute the poles in the dimensional regulator of all top-level propagator graphs at five loops in four dimensional Ï• 3 theory
An Extremal Chiral Primary Three-Point Function at Two-loops in ABJ(M)
archiveprefix: arXiv primaryclass: hep-th reportnumber: QMUL-PH-14-23 slaccitation: %%CITATION = ARXIV:1411.0626;%%archiveprefix: arXiv primaryclass: hep-th reportnumber: QMUL-PH-14-23 slaccitation: %%CITATION = ARXIV:1411.0626;%%archiveprefix: arXiv primaryclass: hep-th reportnumber: QMUL-PH-14-23 slaccitation: %%CITATION = ARXIV:1411.0626;%
Analytic Results for Massless Three-Loop Form Factors
We evaluate, exactly in d, the master integrals contributing to massless
three-loop QCD form factors. The calculation is based on a combination of a
method recently suggested by one of the authors (R.L.) with other techniques:
sector decomposition implemented in FIESTA, the method of Mellin--Barnes
representation, and the PSLQ algorithm. Using our results for the master
integrals we obtain analytical expressions for two missing constants in the
ep-expansion of the two most complicated master integrals and present the form
factors in a completely analytic form.Comment: minor revisions, to appear in JHE
On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes
We propose a first implementation of the integrand-reduction method for
two-loop scattering amplitudes. We show that the residues of the amplitudes on
multi-particle cuts are polynomials in the irreducible scalar products
involving the loop momenta, and that the reduction of the amplitudes in terms
of master integrals can be realized through polynomial fitting of the
integrand, without any apriori knowledge of the integral basis. We discuss how
the polynomial shapes of the residues determine the basis of master integrals
appearing in the final result. We present a four-dimensional constructive
algorithm that we apply to planar and non-planar contributions to the 4- and
5-point MHV amplitudes in N=4 SYM. The technique hereby discussed extends the
well-established analogous method holding for one-loop amplitudes, and can be
considered a preliminary study towards the systematic reduction at the
integrand-level of two-loop amplitudes in any gauge theory, suitable for their
automated semianalytic evaluation.Comment: 26 pages, 11 figure
Russian Artistic Gymnastics as a Sports Tourism Product: Some Observations and a Research Agenda
Tourism and its importance to the Russian Federation are very much in the headlines at present. Considering the huge investment made in facilities for the Winter Olympics, the building of new sports facilities for such mega events as the Football World Cup, and the status of St Petersburg as a candidate city for the 2028 Olympics, it is clear that Russia has long term plans to attract visitors to their sporting events. The purpose of this paper is to develop a research agenda to explore the potential of artistic gymnastics, a sport in which the Russian Federation has excelled for many years, as an agent of tourism development.
The paper will take a case study approach, considering the nature of fandom and identifying features of artistic gymnastics as cultural heritage and sports tourism product. The national and international environment within which it is set are examined, prior to the development of a research agenda. A detailed review of literature on the historic, current and emerging trends in Russian artistic gymnastics; the place of artistic gymnastics in tourism development and sports tourism in Russia will be carried out.
The paper’s findings will include considerations of:
• The nature of gymnastics fandom, both in Russia and internationally
• The nature of sports tourism development in the Russian Federation
• The nature of gymnastics as a sport and its competition cycle
• Artistic gymnastics as cultural heritage, and its potential as an autonomous means of promoting Russian national identity
• The relationship between Russia’s sometimes fading gymnastics competition results, and its potential to leverage the sport for tourism interest
• The potential for tourism product development linked to artistic gymnastics in the Russian Federation.
The paper contributes to the literature on the nature of sports tourism as it relates to artistic gymnastics in the Russian Federation in particular
Simultaneous decoupling of bottom and charm quarks
We compute the decoupling relations for the strong coupling, the light quark
masses, the gauge-fixing parameter, and the light fields in QCD with heavy
charm and bottom quarks to three-loop accuracy taking into account the exact
dependence on . The application of a low-energy theorem allows the
extraction of the three-loop effective Higgs-gluon coupling valid for
extensions of the Standard Model with additional heavy quarks from the
decoupling constant of .Comment: 30 page
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