arXiv subjects

V. Mathieu

Publications and source records attributed to V. Mathieu.

71 records · Page 4Linked to original sources

arXiv2015

Dispersive Analysis of $ω/ϕ\rightarrow 3π,\,πγ^*$

The decays $ω/ϕ\rightarrow 3π$ are considered in the dispersive framework that is based on the isobar decomposition and sub-energy unitarity. The inelastic contributions are parametrized by the power series in a suitably chosen conformal variable that properly accounts for the analytic properties of the amplitude. The Dalitz plot distributions and integrated decay widths are presented. Our results indicate that the final state interactions may be sizable. As a further application of the formalism we also compute the electromagnetic transition form factors of $ω/ϕ\rightarrow π^0γ^*$.

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arXiv2015

Analysis Tools for Next-Generation Hadron Spectroscopy Experiments

The series of workshops on New Partial-Wave Analysis Tools for Next-Generation Hadron Spectroscopy Experiments was initiated with the ATHOS 2012 meeting, which took place in Camogli, Italy, June 20-22, 2012. It was followed by ATHOS 2013 in Kloster Seeon near Munich, Germany, May 21-24, 2013. The third, ATHOS3, meeting is planned for April 13-17, 2015 at The George Washington University Virginia Science and Technology Campus, USA. The workshops focus on the development of amplitude analysis tools for meson and baryon spectroscopy, and complement other programs in hadron spectroscopy organized in the recent past including the INT-JLab Workshop on Hadron Spectroscopy in Seattle in 2009, the International Workshop on Amplitude Analysis in Hadron Spectroscopy at the ECT*-Trento in 2011, the School on Amplitude Analysis in Modern Physics in Bad Honnef in 2011, the Jefferson Lab Advanced Study Institute Summer School in 2012, and the School on Concepts of Modern Amplitude Analysis Techniques in Flecken-Zechlin near Berlin in September 2013. The aim of this document is to summarize the discussions that took place at the ATHOS 2012 and ATHOS 2013 meetings. We do not attempt a comprehensive review of the field of amplitude analysis, but offer a collection of thoughts that we hope may lay the ground for such a document.

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arXiv2014

Double-Regge Exchange Limit for the $γp\rightarrow K^+K^-p$ Reaction

We apply the generalized Veneziano model ($B_5$ model) in the double-Regge exchange limit to the $γp \to K^+ K^- p$ reaction. Four different cases defined by the possible combinations of the signature factors of leading Regge exchanges (($K^*,a_2/f_2$), ($K^*,ρ/ω$), ($K_2^*,a_2/f_2$), and ($K_2^*,ρ/ω$)) have been simulated through the Monte Carlo method. Suitable event candidates for the double-Regge exchange high-energy limit were selected employing \textit{Van Hove} plots as a better alternative to kinematical cuts in the $K^+ K^- p$ Dalitz plot. In this way we predict and analyze the double-Regge contribution to the $K^+ K^- p$ Dalitz plot, which constitutes one of the major backgrounds in the search for strangeonia, hybrids and exotics using $γp\rightarrow K^+K^-p$ reaction. We expect that data currently under analysis, and that to come in the future, will allow verification of the double-Regge behavior and a better assessment of this component of the amplitude.

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arXiv2014

The Boltzmann Equation in Classical Yang-Mills Theory

We give a detailed derivation of the Boltzmann equation, and in particular its collision integral, in classical field theory. We first carry this out in a scalar theory with both cubic and quartic interactions and subsequently in a Yang-Mills theory. Our method is not relied on a doubling of the fields, rather it is based on a diagrammatic approach representing the classical solution to the problem.

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arXiv2013

$(2+1)$-$d$ Glueball Spectrum within a Constituent Picture

The quantum numbers and mass hierarchy of the glueballs observed in $(2+1)$-dimensional lattice QCD with gauge group SU($N_c$) are shown to be in agreement with a constituent picture. The agreement is maintained when going from glueballs to gluelumps, and when the gauge group SO($2N_c$) is taken instead of SU($N_c$).

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arXiv2012

Non Perturbative One Gluon Exchange Potential from Dyson-Schwinger Equations

Recent progress in the solution of Dyson-Schwinger equations of QCD allows for a non perturbative evaluation of the One Gluon Exchange (OGE) interaction. We calculate the interquark static potential for heavy mesons by assuming that it is given by this OGE interaction and we apply it to the description of charmonium.

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arXiv2011

Heavy meson interquark potential

The resolution of Dyson-Schwinger equations leads to the freezing of the QCD running coupling (effective charge) in the infrared, which is best understood as a dynamical generation of a gluon mass function, giving rise to a momentum dependence which is free from infrared divergences. We calculate the interquark potential for heavy mesons by assuming that it is given by a massive One Gluon Exchange potential and compare with phenomenologyical fits inspired by lattice QCD. We apply these potential forms to the description of quarkonia and conclude that, even though some aspects of the confinement mechanism are absent in the Dyson Schwinger formalism, the results for the spectrum are surprisingly accurate. We discuss explanations for this outcome.

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arXiv2011

Massless bound-state excitations and the Schwinger mechanism in QCD

The gauge invariant generation of an effective gluon mass proceeds through the well-known Schwinger mechanism, whose key dynamical ingredient is the nonperturbative formation of longitudinally coupled massless bound-state excitations. These excitations introduce poles in the vertices of the theory, in such a way as to maintain the Slavnov-Taylor identities intact in the presence of massive gluon propagators. In the present work we first focus on the modifications induced to the nonperturbative three-gluon vertex by the inclusion of massless two-gluon bound-states into the kernels appearing in its skeleton-expansion. Certain general relations between the basic building blocks of these bound-states and the gluon mass are then obtained from the Slavnov-Taylor identities and the Schwinger-Dyson equation governing the gluon propagator. The homogeneous Bethe-Salpeter equation determining the wave-function of the aforementioned bound state is then derived, under certain simplifying assumptions. It is then shown, through a detailed analytical and numerical study, that this equation admits non-trivial solutions, indicating that the QCD dynamics support indeed the formation of such massless bound states. These solutions are subsequently used, in conjunction with the aforementioned relations, to determine the momentum-dependence of the dynamical gluon mass. Finally, further possibilities and open questions are briefly discussed.

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arXiv2010

Pseudoscalar glueball and $η-η^\prime$ mixing

We have performed a dynamical analysis of the mixing in the pseudoscalar channel with the goal of understanding the existence and behavior of the pseudoscalar glueball. Our philosophy has not been to predict precise values of the glueball mass but to exploit an adequate effective theory to the point of breaking and to analyze which kind of mechanisms restore compatibility with data. Our study has lead to analytical solutions which allow a clear understanding of the phenomena. The outcome of our calculation leads to a large mass glueball $M_Θ>2000$ MeV, to a large glue content of the $η^\prime$ and to mixing angles in agreement with previous numerical studies.

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arXiv2008

The Glueball Spectrum from Constituent Models

We present a model for odd-$C$ (negative charge parity) glueballs with three constituent gluons. The model is an extension of a previous study of two-gluon glueballs. We show that, even if spin-1 gluons seem to reproduce properly the lattice QCD spectrum for $C=+$ states, the extension for $C=-$ cannot match with the lattice results. Resorting to the helicity formalism, we show how transverse gluons fit in better agreement the lattice QCD spectrum.

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arXiv2008

Constituent gluon interpretation of glueballs and gluelumps

Arguments are given that support the interpretation of the lattice QCD glueball and gluelump spectra in terms of bound states of massless constituent gluons with helicity-1. In this scheme, the mass hierarchy of the currently known gluelumps and glueballs is mainly due to the number of constituent gluons and can be understood within a simple flux tube model. It is also argued that the lattice QCD $0^{+-}$ glueball should be seen as a four-gluon bound state. The flux tube model allows for a parameter-free computation of its mass, which is in good agreement with lattice QCD.

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arXiv2008

Gluons in glueballs: Spin or helicity?

In the last decade, lattice QCD has been able to compute the low-lying glueball spectrum with accuracy. Like other effective approaches of QCD, potential models still have difficulties to cope with gluonic hadrons. Assuming that glueballs are bound states of valence gluons with zero current mass, it is readily understood that the use of a potential model, intrinsically non covariant, could be problematic in this case. The main challenge for this kind of model is actually to find a way to introduce properly the more relevant degree of freedom of the gluon: spin or helicity. In this work, we use the so-called helicity formalism of Jacob and Wick to describe two-gluon glueballs. We show in particular that this helicity formalism exactly reproduces the $J^{PC}$ numbers which are observed in lattice QCD when the constituent gluons have a helicity-1, without introducing extra states as it is the case in most of the potential models. These extra states appear when gluons are seen as spin-1 particles. Using a simple spinless Salpeter model with Cornell potential within the helicity formalism, we obtain a glueball mass spectrum which is in good agreement with lattice QCD predictions for helicity-1 gluons provided instanton-induced interactions are taken into account.

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arXiv2008

Semirelativistic potential model for three-gluon glueballs

The three-gluon glueball states are studied with the generalization of a semirelativistic potential model giving good results for two-gluon glueballs. The Hamiltonian depends only on 3 parameters fixed on two-gluon glueball spectra: the strong coupling constant, the string tension, and a gluon size which removes singularities in the potential. The Casimir scaling determines the structure of the confinement. Our results are in good agreement with other approaches and lattice calculation for the odderon trajectory but differ strongly from lattice in the $J^{+-}$ sector. We propose a possible explanation for this problem.

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arXiv2007

Excited flux tube from $q\bar q g$ hybrid mesons

In the framework of quark models, hybrid mesons are either seen as two-body $q\bar q$ systems with an excited flux tube connecting the quark to the antiquark or as three-body $q\bar q g$ systems including a constituent gluon. In this work we show that, starting from the three-body wave function of the $q\bar q g$ hybrid meson in which the gluonic degrees of freedom are averaged, the excited flux tube picture emerges as an equivalent $q\bar q$ potential. This equivalence between the excited flux tube and the constituent gluon approach is confirmed for heavy hybrid mesons but, for the first time, it is shown to hold in the light sector too, provided the contribution of the quark dynamics is correctly taken into account.

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arXiv2007

Modified Newton's law, braneworlds, and the gravitational quantum well

Most of the theories involving extra dimensions assume that only the gravitational interaction can propagate in them. In such approaches, called brane world models, the effective, 4-dimensional, Newton's law is modified at short as well as at large distances. Usually, the deformation of Newton's law at large distances is parametrized by a Yukawa potential, which arises mainly from theories with compactified extra dimensions. In many other models however, the extra dimensions are infinite. These approaches lead to a large distance power-law deformation of the gravitational newtonian potential $V_N(r)$, namely $V(r)=(1+k_b/r^b)V_N(r)$, which is less studied in the literature. We investigate here the dynamics of a particle in a gravitational quantum well with such a power-law deformation. The effects of the deformation on the energy spectrum are discussed. We also compare our modified spectrum to the results obtained with the GRANIT experiment, where the effects of the Earth's gravitational field on quantum states of ultra cold neutrons moving above a mirror are studied. This comparison leads to upper bounds on $b$ and $k_b$.

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arXiv2006

String deformations induced by retardation effects

The rotating string model is an effective model of mesons, in which the quark and the antiquark are linked by a straight string. We previously developed a new framework to include the retardation effects in the rotating string model, but the string was still kept straight. We now go a step further and show that the retardation effects cause a small deviation of the string from the straight line. We first give general arguments constraining the string shape. Then, we find analytical and numerical solutions for the string deformation induced by retardation effects. We finally discuss the influence of the curved string on the energy spectrum of the model.

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arXiv2006

Semirelativistic potential model for low-lying three-gluon glueballs

The three-gluon glueball states are studied with the generalization of a semirelativistic potential model giving good results for two-gluon glueballs. The Hamiltonian depends only on 3 parameters fixed on two-gluon glueball spectra: the strong coupling constant, the string tension, and a gluon size which removes singularities in the potential. The Casimir scaling determines the structure of the confinement. Low-lying $J^{PC}$ states are computed and compared with recent lattice calculations. A good agreement is found for $1^{--}$ and $3^{--}$ states, but our model predicts a $2^{--}$ state much higher in energy than the lattice result. The $0^{-+}$ mass is also computed.

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