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[en] The impact of possible sources of lepton-flavor mixing on K → πν(bar ν) decays is analyzed. At the one-loop level lepton-flavor mixing originated from non-diagonal lepton mass matrices cannot generate a CP-conserving KL → π0ν(bar ν) amplitude. The rates of these modes are sensitive to leptonic flavor violation when there are at least two different leptonic mixing matrices. New interactions that violate both quark and lepton universalities could enhance the CP-conserving component of Λ(KL → π0ν(bar ν)) and have a substantial impact. Explicit examples of these effects in the context of supersymmetric models, with and without R-parity conservation, are discussed
[en] In a low energy approximation of the massless Yukawa theory (Nelson model) we derive a Faddeev–Kulish type formula for the scattering matrix of N electrons and reformulate it in LSZ terms. To this end, we perform a decomposition of the infrared finite Dollard modifier into clouds of real and virtual photons, whose infrared divergencies mutually cancel. We point out that in the original work of Faddeev and Kulish the clouds of real photons are omitted, and consequently their wave-operators are ill-defined on the Fock space of free electrons. To support our observations, we compare our final LSZ expression for with a rigorous non-perturbative construction due to Pizzo. While our discussion contains some heuristic steps, they can be formulated as clear-cut mathematical conjectures.
[en] This is a pedagogical digest of results reported in Curtright, Fairlie, ampersand Zachos 1997, and an explicit implementation of Euler's construction for the solution of the Poisson Bracket dual Nahm equation. But it does not cover 9 and 10-dimensional systems, and subsequent progress on them Fairlie 1997. Cubic interactions are considered in 3 and 7 space dimensions, respectively, for bosonic membranes in Poisson Bracket form. Their symmetries and vacuum configurations are explored. Their associated first order equations are transformed to Nahm's equations, and are hence seen to be integrable, for the 3-dimensional case, by virtue of the explicit Lax pair provided. Most constructions introduced also apply to matrix commutator or Moyal Bracket analogs
[en] We calculate the unpolarized twist-2 three-loop splitting functions and and the associated anomalous dimensions using massive three-loop operator matrix elements. While we calculate directly, is computed from 1200 even moments, without any structural prejudice, using a hierarchy of recurrences obtained for the corresponding operator matrix element. The largest recurrence to be solved is of order 12 and degree 191. We confirm results in the foregoing literature.
[en] We study integrable models solvable by the nested algebraic Bethe ansatz and described by or superalgebras. We obtain explicit determinant representations for form factors of the monodromy matrix entries. We show that all form factors are related to each other at special limits of the Bethe parameters. Our results allow one to obtain determinant formulas for form factors of local operators in the supersymmetric model.
[en] With the latest results of a large mixing angle θ13 for neutrinos by the T2K, MINOS and Double Chooz experiments, we find that the self-complementarity (SC) relations agree with the data in some angle-phase parametrizations of the lepton mixing matrix. There are three kinds of self-complementarity relations: (1) θi+θj=θk=45°; (2) θi+θj=θk; (3) θi+θj=45° (where i, j, k denote the mixing angles in the angle-phase parametrizations). We present a detailed study on the self-complementarity relations in nine different angle-phase parametrizations, and also examine the explicit expressions in reparametrization-invariant form, as well as their deviations from global fit. These self-complementarity relations may lead to new perspective on the mixing pattern of neutrinos.
[en] By solving the right reflection equation proposed in the reference (Hofman and Maldacena, 2007 J. High Energy Phys. JHEP11(2007)063 [arXiv:0708.2272]) to describe the Z = 0 giant graviton branes, we obtain a boundary matrix with two free parameters for the AdS/CFT SU(1|1) spin chain