13,486 research outputs found
Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
We compute the leading-color (planar) three-loop four-point amplitude of N=4
supersymmetric Yang-Mills theory in 4 - 2 epsilon dimensions, as a Laurent
expansion about epsilon = 0 including the finite terms. The amplitude was
constructed previously via the unitarity method, in terms of two Feynman loop
integrals, one of which has been evaluated already. Here we use the
Mellin-Barnes integration technique to evaluate the Laurent expansion of the
second integral. Strikingly, the amplitude is expressible, through the finite
terms, in terms of the corresponding one- and two-loop amplitudes, which
provides strong evidence for a previous conjecture that higher-loop planar N =
4 amplitudes have an iterative structure. The infrared singularities of the
amplitude agree with the predictions of Sterman and Tejeda-Yeomans based on
resummation. Based on the four-point result and the exponentiation of infrared
singularities, we give an exponentiated ansatz for the maximally
helicity-violating n-point amplitudes to all loop orders. The 1/epsilon^2 pole
in the four-point amplitude determines the soft, or cusp, anomalous dimension
at three loops in N = 4 supersymmetric Yang-Mills theory. The result confirms a
prediction by Kotikov, Lipatov, Onishchenko and Velizhanin, which utilizes the
leading-twist anomalous dimensions in QCD computed by Moch, Vermaseren and
Vogt. Following similar logic, we are able to predict a term in the three-loop
quark and gluon form factors in QCD.Comment: 54 pages, 7 figures. v2: Added references, a few additional words
about large spin limit of anomalous dimensions. v3: Expanded Sect. IV.A on
multiloop ansatz; remark that form-factor prediction is now confirmed by
other work; minor typos correcte
Annihilation poles of a Smirnov-type integral formula for solutions to quantum Knizhnik--Zamolodchikov equation
We consider the recently obtained integral representation of quantum
Knizhnik-Zamolodchikov equation of level 0. We obtain the condition for the
integral kernel such that these solutions satisfy three axioms for form factor
\'{a} la Smirnov. We discuss the relation between this integral representation
and the form factor of XXZ spin chain.Comment: 14 pages, latex, no figures
Quark lepton complementarity and renormalization group effects
We consider a scenario for the Quark-Lepton Complementarity relations between
mixing angles in which the bi-maximal mixing follows from the neutrino mass
matrix. According to this scenario in the lowest order the angle \theta_{12} is
\sim 1\sigma (1.5 - 2^\circ) above the best fit point coinciding practically
with the tri-bimaximal mixing prediction. Realization of this scenario in the
context of the seesaw type-I mechanism with leptonic Dirac mass matrices
approximately equal to the quark mass matrices is studied. We calculate the
renormalization group corrections to \theta_{12} as well as to \theta_{13} in
the standard model (SM) and minimal supersymmetric standard model (MSSM). We
find that in large part of the parameter space corrections \Delta \theta_{12}
are small or negligible. In the MSSM version of the scenario the correction
\Delta \theta_{12} is in general positive. Small negative corrections appear in
the case of an inverted mass hierarchy and opposite CP parities of \nu_1 and
\nu_2 when leading contributions to \theta_{12} running are strongly
suppressed. The corrections are negative in the SM version in a large part of
the parameter space for values of the relative CP phase of \nu_1 and \nu_2:
\phi > \pi/2.Comment: version as published in PRD, 14 pages, 12 figure
On the Quantum Inverse Problem for the Closed Toda Chain
We reconstruct the canonical operators of the quantum closed Toda
chain in terms of Sklyanin's separated variables.Comment: 16 page
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