16,884 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
Neutrino Physics: Open Theoretical Questions
We know that neutrino mass and mixing provide a window to physics beyond the
Standard Model. Now this window is open, at least partly. And the questions
are: what do we see, which kind of new physics, and how far "beyond"? I
summarize the present knowledge of neutrino mass and mixing, and then formulate
the main open questions. Following the bottom-up approach, properties of the
neutrino mass matrix are considered. Then different possible ways to uncover
the underlying physics are discussed. Some results along the line of: see-saw,
GUT and SUSY GUT are reviewed.Comment: 17 pages, latex, 12 figures. Talk given at the XXI International
Symposium on Lepton and Photon Interactions at High Energies, ``Lepton Photon
2003", August 11-16, 2003 - Fermilab, Batavia, IL US
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
Solar neutrinos and grand unification
We consider the Grand Unification (GU) scenario for neutrino masses which is
based on the see-saw mechanism with the mass of the heaviest right handed (RH)
neutrino at the GU-scale: , and on the quark-lepton
symmetry for fermions from the third generation. The scenario predicts for the
light neutrinos: eV and eV (in the case of a linear mass hierarchy of the RH neutrinos
or/and in presence of the Planck scale suppressed non-renormalizable
operators). It also predicts large mixing: . In this scenario the solar neutrinos
() undergo both the \nue \nutau resonance conversion in the
Sun and substantial \nue \numu vacuum oscillations on the way from the
Sun to the Earth. The interplay of both effects enlarges the range of neutrino
parameters which solve the -problem. In particular, mixing angle can be as small as the corresponding quark mixing:
. The scenario predicts
peculiar (oscillatory) distortion of the boron neutrino energy spectrum and
seasonal variations of signals. Manifestations of these effects in the
Super-Kamiokande and SNO experiments are studied.Comment: 36 pages, LaTeX, includes 14 figures, revised and expande
- …