2,378 research outputs found
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
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
Application of the DRA method to the calculation of the four-loop QED-type tadpoles
We apply the DRA method to the calculation of the four-loop `QED-type'
tadpoles. For arbitrary space-time dimensionality D the results have the form
of multiple convergent sums. We use these results to obtain the
epsilon-expansion of the integrals around D=3 and D=4.Comment: References added, some typos corrected. Results unchange
An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
In the planar N=4 supersymmetric Yang-Mills theory, the conformal symmetry
constrains multi-loop n-edged Wilson loops to be basically given in terms of
the one-loop n-edged Wilson loop, augmented, for n greater than 6, by a
function of conformally invariant cross ratios. We identify a class of
kinematics for which the Wilson loop exhibits exact Regge factorisation and
which leave invariant the analytic form of the multi-loop n-edged Wilson loop.
In those kinematics, the analytic result for the Wilson loop is the same as in
general kinematics, although the computation is remarkably simplified with
respect to general kinematics. Using the simplest of those kinematics, we have
performed the first analytic computation of the two-loop six-edged Wilson loop
in general kinematics.Comment: 17 pages. Extended discussion on how the QMRK limit is taken. Version
accepted by JHEP. A text file containing the Mathematica code with the
analytic expression for the 6-point remainder function is include
ABJ(M) Chiral Primary Three-Point Function at Two-loops
This article is distributed under the terms of the Creative Commons
Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.archiveprefix: arXiv primaryclass: hep-th reportnumber: QMUL-PH-14-10 slaccitation: %%CITATION = ARXIV:1404.1117;%%archiveprefix: arXiv primaryclass: hep-th reportnumber: QMUL-PH-14-10 slaccitation: %%CITATION = ARXIV:1404.1117;%%archiveprefix: arXiv primaryclass: hep-th reportnumber: QMUL-PH-14-10 slaccitation: %%CITATION = ARXIV:1404.1117;%%Article funded by SCOAP
Ultrasoft NLL Running of the Nonrelativistic O(v) QCD Quark Potential
Using the nonrelativistic effective field theory vNRQCD, we determine the
contribution to the next-to-leading logarithmic (NLL) running of the effective
quark-antiquark potential at order v (1/mk) from diagrams with one potential
and two ultrasoft loops, v being the velocity of the quarks in the c.m. frame.
The results are numerically important and complete the description of ultrasoft
next-to-next-to-leading logarithmic (NNLL) order effects in heavy quark pair
production and annihilation close to threshold.Comment: 25 pages, 7 figures, 3 tables; minor modifications, typos corrected,
references added, footnote adde
Mellin–Barnes meets Method of Brackets: a novel approach to Mellin–Barnes representations of Feynman integrals
Analytic results for planar three-loop integrals for massive form factors
We use the method of differential equations to analytically evaluate all planar three-loop Feynman integrals relevant for form factor calculations involving massive particles. Our results for ninety master integrals at general q2 are expressed in terms of multiple polylogarithms, and results for fiftyone master integrals at the threshold q2 = 4m2 are expressed in terms of multiple polylogarithms of argument one, with indices equal to zero or to a sixth root of unity
Foundation and generalization of the expansion by regions
The "expansion by regions" is a method of asymptotic expansion developed by
Beneke and Smirnov in 1997. It expands the integrand according to the scaling
prescriptions of a set of regions and integrates all expanded terms over the
whole integration domain. This method has been applied successfully to many
complicated loop integrals, but a general proof for its correctness has still
been missing. This paper shows how the expansion by regions manages to
reproduce the exact result correctly in an expanded form and clarifies the
conditions on the choice and completeness of the considered regions. A
generalized expression for the full result is presented that involves
additional overlap contributions. These extra pieces normally yield scaleless
integrals which are consistently set to zero, but they may be needed depending
on the choice of the regularization scheme. While the main proofs and formulae
are presented in a general and concise form, a large portion of the paper is
filled with simple, pedagogical one-loop examples which illustrate the
peculiarities of the expansion by regions, explain its application and show how
to evaluate contributions within this method.Comment: 84 pages; v2: comment on scaleless integrals added to conclusions,
version published in JHE
Correlation Functions in 2-Dimensional Integrable Quantum Field Theories
In this talk I discuss the form factor approach used to compute correlation
functions of integrable models in two dimensions. The Sinh-Gordon model is our
basic example. Using Watson's and the recursive equations satisfied by matrix
elements of local operators, I present the computation of the form factors of
the elementary field and the stress-energy tensor of
the theory.Comment: 19pp, LATEX version, (talk at Como Conference on ``Integrable Quantum
Field Theories''
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