Determination of the bb-quark mass mbm_b from the angular screening effects in the ATLAS bb-jet shape data

The dependence of jet shapes in $t\bar{t}$ events on the $b$-quark mass and the strong coupling is investigated. To this end, the Pythia Monte Carlo generator is used to produce samples of $t\bar{t}$ events in $pp$ collisions at $\sqrt{s} = 7 \ \mathrm{TeV}$, performing a scan over the values for the shower QCD scale $\Lambda_s$ and the $b$-quark mass $m_b$. The obtained jet shapes are compared with recently published data from the ATLAS collaboration. From fits to the light-jet data, the Monte Carlo shower scale is determined, while the $b$-quark mass is extracted using the $b$-jet shapes. The result for the mass of the $b$-quark is $m_b = 4.86 ^{+0.49}_{-0.42}\ \mathrm{GeV}$.Comment: 16 pages, 10 figures. Version matching the published versio

Influence of the geometry on a field-road model : the case of a conical field

Field-road models are reaction-diffusion systems which have been recently introduced to account for the effect of a road on propagation phenomena arising in epidemiology and ecology. Such systems consist in coupling a classical Fisher-KPP equation to a line with fast diffusion accounting for a road. A series of works investigate the spreading properties of such systems when the road is a straight line and the field a half-plane. Here, we take interest in the case where the field is a cone. Our main result is that the spreading speed is not influenced by the angle of the cone

Minimal representations of unitary operators and orthogonal polynomials on the unit circle

In this paper we prove that the simplest band representations of unitary operators on a Hilbert space are five-diagonal. Orthogonal polynomials on the unit circle play an essential role in the development of this result, and also provide a parametrization of such five-diagonal representations which shows specially simple and interesting decomposition and factorization properties. As an application we get the reduction of the spectral problem of any unitary Hessenberg matrix to the spectral problem of a five-diagonal one. Two applications of these results to the study of orthogonal polynomials on the unit circle are presented: the first one concerns Krein's Theorem; the second one deals with the movement of mass points of the orthogonality measure under monoparametric perturbations of the Schur parameters.Comment: 31 page

Matrix orthogonal polynomials whose derivatives are also orthogonal

In this paper we prove some characterizations of the matrix orthogonal polynomials whose derivatives are also orthogonal, which generalize other known ones in the scalar case. In particular, we prove that the corresponding orthogonality matrix functional is characterized by a Pearson-type equation with two matrix polynomials of degree not greater than 2 and 1. The proofs are given for a general sequence of matrix orthogonal polynomials, not necessarily associated with an hermitian functional. However, we give several examples of non-diagonalizable positive definite weight matrices satisfying a Pearson-type equation, which show that the previous results are non-trivial even in the positive definite case. A detailed analysis is made for the class of matrix functionals which satisfy a Pearson-type equation whose polynomial of degree not greater than 2 is scalar. We characterize the Pearson-type equations of this kind that yield a sequence of matrix orthogonal polynomials, and we prove that these matrix orthogonal polynomials satisfy a second order differential equation even in the non-hermitian case. Finally, we prove and improve a conjecture of Duran and Grunbaum concerning the triviality of this class in the positive definite case, while some examples show the non-triviality for hermitian functionals which are not positive definite.Comment: 49 page