317 research outputs found
Mellin Amplitudes for Dual Conformal Integrals
Motivated by recent work on the utility of Mellin space for representing
conformal correlators in /CFT, we study its suitability for representing
dual conformal integrals of the type which appear in perturbative scattering
amplitudes in super-Yang-Mills theory. We discuss Feynman-like rules for
writing Mellin amplitudes for a large class of integrals in any dimension, and
find explicit representations for several familiar toy integrals. However we
show that the power of Mellin space is that it provides simple representations
even for fully massive integrals, which except for the single case of the
4-mass box have not yet been computed by any available technology. Mellin space
is also useful for exhibiting differential relations between various multi-loop
integrals, and we show that certain higher-loop integrals may be written as
integral operators acting on the fully massive scalar -gon in
dimensions, whose Mellin amplitude is exactly 1. Our chief example is a very
simple formula expressing the 6-mass double box as a single integral of the
6-mass scalar hexagon in 6 dimensions.Comment: 29+7 page
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
Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
We show how the Hopf algebra structure of multiple polylogarithms can be used
to simplify complicated expressions for multi-loop amplitudes in perturbative
quantum field theory and we argue that, unlike the recently popularized
symbol-based approach, the coproduct incorporates information about the zeta
values. We illustrate our approach by rewriting the two-loop helicity
amplitudes for a Higgs boson plus three gluons in a simplified and compact form
involving only classical polylogarithms.Comment: 46 page
The , , and mesons in a double pole QCD Sum Rule
We use the method of double pole QCD sum rule which is basically a fit with
two exponentials of the correlation function, where we can extract the masses
and decay constants of mesons as a function of the Borel mass. We apply this
method to study the mesons: , , and
. We also present predictions for the toponiuns masses
of m(1S)=357 GeV and m(2S)=374 GeV.Comment: 14 pages, 11 figures in Braz J Phys (2016
Analytic two-loop form factors in N=4 SYM
The original publication is available at www.springerlink.co
Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops
We calculate form factors of half-BPS operators in N=4 super Yang-Mills
theory at tree level and one loop using novel applications of recursion
relations and unitarity. In particular, we determine the expression of the
one-loop form factors with two scalars and an arbitrary number of
positive-helicity gluons. These quantities resemble closely the MHV scattering
amplitudes, including holomorphicity of the tree-level form factor, and the
expansion in terms of two-mass easy box functions of the one-loop result. Next,
we compare our result for these form factors to the calculation of a particular
periodic Wilson loop at one loop, finding agreement. This suggests a novel
duality relating form factors to periodic Wilson loops.Comment: 26 pages, 10 figures. v2: typos fixed, comments adde
Generalised ladders and single-valued polylogarithms
We introduce and solve an infinite class of loop integrals which generalises
the well-known ladder series. The integrals are described in terms of
single-valued polylogarithmic functions which satisfy certain differential
equations. The combination of the differential equations and single-valued
behaviour allow us to explicitly construct the polylogarithms recursively. For
this class of integrals the symbol may be read off from the integrand in a
particularly simple way. We give an explicit formula for the simplest
generalisation of the ladder series. We also relate the generalised ladder
integrals to a class of vacuum diagrams which includes both the wheels and the
zigzags.Comment: 27 pages, 7 figure
From polygons and symbols to polylogarithmic functions
We present a review of the symbol map, a mathematical tool that can be useful
in simplifying expressions among multiple polylogarithms, and recall its main
properties. A recipe is given for how to obtain the symbol of a multiple
polylogarithm in terms of the combinatorial properties of an associated rooted
decorated polygon. We also outline a systematic approach to constructing a
function corresponding to a given symbol, and illustrate it in the particular
case of harmonic polylogarithms up to weight four. Furthermore, part of the
ambiguity of this process is highlighted by exhibiting a family of non-trivial
elements in the kernel of the symbol map for arbitrary weight.Comment: 75 pages. Mathematica files with the expression of all HPLs up to
weight 4 in terms of the spanning set are include
On soft singularities at three loops and beyond
We report on further progress in understanding soft singularities of massless
gauge theory scattering amplitudes. Recently, a set of equations was derived
based on Sudakov factorization, constraining the soft anomalous dimension
matrix of multi-leg scattering amplitudes to any loop order, and relating it to
the cusp anomalous dimension. The minimal solution to these equations was shown
to be a sum over color dipoles. Here we explore potential contributions to the
soft anomalous dimension that go beyond the sum-over-dipoles formula. Such
contributions are constrained by factorization and invariance under rescaling
of parton momenta to be functions of conformally invariant cross ratios.
Therefore, they must correlate the color and kinematic degrees of freedom of at
least four hard partons, corresponding to gluon webs that connect four eikonal
lines, which first appear at three loops. We analyze potential contributions,
combining all available constraints, including Bose symmetry, the expected
degree of transcendentality, and the singularity structure in the limit where
two hard partons become collinear. We find that if the kinematic dependence is
solely through products of logarithms of cross ratios, then at three loops
there is a unique function that is consistent with all available constraints.
If polylogarithms are allowed to appear as well, then at least two additional
structures are consistent with the available constraints.Comment: v2: revised version published in JHEP (minor corrections in Sec. 4;
added discussion in Sec. 5.3; refs. added); v3: minor corrections (eqs. 5.11,
5.12 and 5.29); 38 pages, 3 figure
Large scale analytic calculations in quantum field theories
We present a survey on the mathematical structure of zero- and single scale
quantities and the associated calculation methods and function spaces in higher
order perturbative calculations in relativistic renormalizable quantum field
theories.Comment: 25 pages Latex, 1 style fil
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