Does a given vector-matrix pair correspond to a PH distribution?

The analysis of practical queueing problems benefits if realistic distributions can be used as parameters. Phase type (PH) distributions can approximate many distributions arising in practice, but their practical applicability has always been limited when they are described by a non-Markovian vector–matrix pair. In this case it is hard to check whether the non-Markovian vector–matrix pair defines a non-negative matrix-exponential function or not. In this paper we propose a numerical procedure for checking if the matrix-exponential function defined by a non-Markovian vector–matrix pair can be represented by a Markovian vector–matrix pair with potentially larger size. If so, then the matrix-exponential function is non-negative. The proposed procedure is based on O’Cinneide’s characterization result, which says that a non-Markovian vector–matrix pair with strictly positive density on and with a real dominant eigenvalue has a Markovian representation. Our method checks the existence of a potential Markovian representation in a computationally efficient way utilizing the structural properties of the applied representation transformation procedure

LUSIFER: a LUcid approach to SIx-FERmion production

LUSIFER is a Monte Carlo event generator for all processes e+e-->6fermions, which is based on the multi-channel Monte Carlo integration technique and employs the full set of tree-level diagrams. External fermions are taken to be massless, but can be arbitrarily polarized. The calculation of the helicity amplitudes and of the squared matrix elements is presented in a compact way. Initial-state radiation is included at the leading logarithmic level using the structure-function approach. The discussion of numerical results contains a comprehensive list of cross sections relevant for a 500GeV collider, including a tuned comparison to results obtained with the combination of the WHIZARD and MADGRAPH packages as far as possible. Moreover, for off-shell top-quark pair production and the production of a Higgs boson in the intermediate mass range we additionally discuss some phenomenologically interesting distributions. Finally, we numerically analyze the effects of gauge-invariance violation by comparing various ways of introducing decay widths of intermediate top quarks, gauge and Higgs bosons.Comment: 39 pages, latex, 14 postscript files, some minor misprints corrected, version to appear in Nucl.Phys.

Discrete phase space based on finite fields

The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being defined on a 2N x 2N discrete phase space for a system with N orthogonal states. Here we investigate an alternative class of discrete Wigner functions, in which the field of real numbers that labels the axes of continuous phase space is replaced by a finite field having N elements. There exists such a field if and only if N is a power of a prime; so our formulation can be applied directly only to systems for which the state-space dimension takes such a value. Though this condition may seem limiting, we note that any quantum computer based on qubits meets the condition and can thus be accommodated within our scheme. The geometry of our N x N phase space also leads naturally to a method of constructing a complete set of N+1 mutually unbiased bases for the state space.Comment: 60 pages; minor corrections and additional references in v2 and v3; improved historical introduction in v4; references to quantum error correction in v5; v6 corrects the value quoted for the number of similarity classes for N=

The Leptoquark Hunter's Guide: Pair Production

Leptoquarks occur in many new physics scenarios and could be the next big discovery at the LHC. The purpose of this paper is to point out that a model-independent search strategy covering all possible leptoquarks is possible and has not yet been fully exploited. To be systematic we organize the possible leptoquark final states according to a leptoquark matrix with entries corresponding to nine experimentally distinguishable leptoquark decays: any of {light-jet, b-jet, top} with any of {neutrino, $e/\mu$, $\tau$}. The 9 possibilities can be explored in a largely model-independent fashion with pair-production of leptoquarks at the LHC. We review the status of experimental searches for the 9 components of the leptoquark matrix, pointing out which 3 have not been adequately covered. We plead that experimenters publish bounds on leptoquark cross sections as functions of mass for as wide a range of leptoquark masses as possible. Such bounds are essential for reliable recasts to general leptoquark models. To demonstrate the utility of the leptoquark matrix approach we collect and summarize searches with the same final states as leptoquark pair production and use them to derive bounds on a complete set of Minimal Leptoquark models which span all possible flavor and gauge representations for scalar and vector leptoquarks.Comment: 19 pages + references and appendices, 18 figures, 15 tables. Added references, fixed typo

Geometric Quantum Mechanics

The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given quantum system can be represented by specific geometrical features that are selected and preferentially identified in this complex manifold. Here we construct a number of examples of such geometrical features as they arise in the state spaces for spin-1/2, spin-1, and spin-3/2 systems, and for pairs of spin-1/2 systems. A study is undertaken on the geometry of entangled states, and a natural measure is assigned to the degree of entanglement of a given state for a general multi-particle system. The properties of this measure are analysed for the entangled states of a pair of spin-1/2 particles. With the specification of a quantum Hamiltonian, the resulting Schrodinger trajectory induces a Killing field, which is quasiergodic on a toroidal subspace of the energy surface. When the dynamical trajectory is lifted orthogonally to Hilbert space, it induces a geometric phase shift on the wave function. The uncertainty of an observable in a given state is the length of the gradient vector of the level surface of the expectation of the observable in that state, a fact that allows us to calculate higher order corrections to the Heisenberg relations. A general mixed state is determined by a probability density function on the state space, for which the associated first moment is the density matrix. The advantage of a general state is in its applicability in various attempts to go beyond the standard quantum theory.Comment: 27 pages. Extended with additional materia

On the angular distribution of Λb→Λ(→Nπ)τ+τ−\Lambda_b\to\Lambda(\to N\pi)\tau^+\tau^- decay

We present a full angular distribution of the four body $\Lambda_b\to\Lambda(\to N\pi)\ell^+\ell^-$ decay where the leptons are massive and the $\Lambda_b$ is unpolarized, in an operator basis which includes the Standard Model operators, new vector and axial-vector operators, and scalar and pseudo-scalar operators. The angular coefficients are expressed in terms of transversity amplitudes. We study several $\Lambda_b\to\Lambda(\to p\pi)\tau^+\tau^-$ observables in the Standard Model and in the presence of the new operators. For our numerical analysis, we use the form factors from lattice QCD calculations.Comment: accepted by JHEP (charmonium and duality contributions included in this final version

Heavy Vector-like Top Partners at the LHC and flavour constraints

We consider the phenomenology at the Large Hadron Collider of new heavy vector-like quarks which couple mainly to the third generation quarks via Yukawa interactions, with special emphasis on non-standard doublet representations which are less constrained from present data. We also discuss in detail the flavour limits at tree level and loop level and implications of a generalised CKM mixing matrix to these cases.Comment: 45 pages, 20 figures, 8 tables. Updated limits in the B-physics part, typos corrected, minor modifications in the LHC par