Large Representation Recurrences in Large N Random Unitary Matrix Models

In a random unitary matrix model at large N, we study the properties of the expectation value of the character of the unitary matrix in the rank k symmetric tensor representation. We address the problem of whether the standard semiclassical technique for solving the model in the large N limit can be applied when the representation is very large, with k of order N. We find that the eigenvalues do indeed localize on an extremum of the effective potential; however, for finite but sufficiently large k/N, it is not possible to replace the discrete eigenvalue density with a continuous one. Nonetheless, the expectation value of the character has a well-defined large N limit, and when the discreteness of the eigenvalues is properly accounted for, it shows an intriguing approximate periodicity as a function of k/N.Comment: 24 pages, 11 figure

LOOKING FOR SUPERSYMMETRY IN RARE B-MESON DECAYS

We investigate manifestations of SUSY in rare B-meson decays Bd→Kφ0, K+π− which proceed mainly via penguin diagrams. It is shown that there exists a range of masses of SUSY particles where the SUSY contribution to the amplitudes of the processes exceeds the standard one. We obtain constraints on SUSY particle masses which may be competitive with the accelerator ones

SEARCH FOR NEW GAUGE BOSONS IN THE RADIATIVE DECAY Z-]GAMMA-X

We consider the decay Z --> gamma-X where X is a new gauge boson corresponding to an extra U'(1) gauge group factor and find that its partial width can be as large as 5% (the experimental limit for the width of a new decay mode), providing the limit for the X-boson coupling constant: alpha'X less than or similar to 0.1 M(X)/1 GeV)2

SEARCHING FOR NEW Z'-BOSONS AND LEPTOQUARKS AT FUTURE E+E--COLLIDERS

A number of superstring theories predict the existence of an extra new Z′-boson and leptoquarks which may possess massess about 1–10 TeV. We investigate in detail possible manifestations of these particles in polarized e+e− beams on future colliders LEP II and CLIC. We calculate cross-sections and various asymmetries of the processes e+e−→µ+µ−, , ūu taking into account contributions of the Z′-boson and leptoquarks. It is shown that the measurement of the total cross-section σ(e+e−→µ+µ−) is the most sensitive parameter for the existence of Z′-bosons, and the forward-backward asymmetry AFB is that for the existence of leptoquarks

DO KAON DECAYS CONSTRAIN THE 5TH FORCE

It is shown that all the gauge invariant models of the fifth force based on SU(2)×U(1)×U′(1) group are consistent with the experimental data on charged kaon decays