The quantum N-body problem with a minimal length

The quantum $N$-body problem is studied in the context of nonrelativistic quantum mechanics with a one-dimensional deformed Heisenberg algebra of the form $[\hat x,\hat p]=i(1+\beta \hat p^2)$, leading to the existence of a minimal observable length $\sqrt\beta$. For a generic pairwise interaction potential, analytical formulas are obtained that allow to estimate the ground-state energy of the $N$-body system by finding the ground-state energy of a corresponding two-body problem. It is first shown that, in the harmonic oscillator case, the $\beta$-dependent term grows faster with $N$ than the $\beta$-independent one. Then, it is argued that such a behavior should be observed also with generic potentials and for $D$-dimensional systems. In consequence, quantum $N$-body bound states might be interesting places to look at nontrivial manifestations of a minimal length since, the more particles are present, the more the system deviates from standard quantum mechanical predictions.Comment: To appear in PR

Bound cyclic systems with the envelope theory

Approximate but reliable solutions of a quantum system with $N$ identical particles can be easily computed with the envelope theory, also known as the auxiliary field method. This technique has been developed for Hamiltonians with arbitrary kinematics and one- or two-body potentials. It is adapted here for cyclic systems with $N$ identical particles, that is to say systems in which a particle $i$ has only an interaction with particles $i-1$ and $i+1$ (with $N+1\equiv 1$)

Mass formula for strange baryons in large NcN_c QCD versus quark model

A previous work establishing a connection between a quark model, with relativistic kinematics and a $Y$-confinement plus one gluon exchange, and the $1/N_c$ expansion mass formula is extended to strange baryons. Both methods predict values for the SU(3)-breaking mass terms which are in good agreement with each other. Strange and nonstrange baryons are shown to exhibit Regge trajectories with an equal slope, but with an intercept depending on the strangeness. Both approaches agree on the value of the slope and of the intercept and on the existence of a single good quantum number labeling the baryons within a given Regge trajectory.Comment: 2 figure

Towers of hybrid mesons

A hybrid meson is a quark-antiquark pair in which, contrary to ordinary mesons, the gluon field is in an excited state. In the framework of constituent models, the interaction potential is assumed to be the energy of an excited string. An approximate, but accurate, analytical solution of the Schr\"{o}dinger equation with such a potential is presented. When applied to hybrid charmonia and bottomonia, towers of states are predicted in which the masses are a linear function of a harmonic oscillator band number for the quark-antiquark pair. Such a formula could be a reliable guide for the experimental detection of heavy hybrid mesons.Comment: 3 figure

Glueballs and the Yang-Mills plasma in a TT-matrix approach

The strongly coupled phase of Yang-Mills plasma with arbitrary gauge group is studied in a $T$-matrix approach. The existence of lowest-lying glueballs, interpreted as bound states of two transverse gluons (quasi-particles in a many-body set up), is analyzed in a non-perturbative scattering formalism with the input of lattice-QCD static potentials. Glueballs are actually found to be bound up to 1.3 $T_c$. Starting from the $T$-matrix, the plasma equation of state is computed by resorting to Dashen, Ma and Bernstein's formulation of statistical mechanics and favorably compared to quenched lattice data. Special emphasis is put on SU($N$) gauge groups, for which analytical results can be obtained in the large-$N$ limit, and predictions for a $G_2$ gauge group are also given within this work.Comment: Fig. 4 corrected and references adde

The SUSY Yang-Mills plasma in a TT-matrix approach

The thermodynamic properties of ${\cal N}=1$ supersymmetric Yang-Mills theory with an arbitrary gauge group are investigated. In the confined range, we show that identifying the bound state spectrum with a Hagedorn one coming from non-critical closed superstring theory leads to a prediction for the value of the deconfining temperature $T_c$ that agrees with recent lattice data. The deconfined phase is studied by resorting to a $T$-matrix formulation of statistical mechanics in which the medium under study is seen as a gas of quasigluons and quasigluinos interacting nonperturbatively. Emphasis is put on the temperature range (1-5)~$T_c$, where the interaction are expected to be strong enough to generate bound states. Binary bound states of gluons and gluinos are indeed found to be bound up to 1.4 $T_c$ for any gauge group. The equation of state is then computed numerically for SU($N$) and $G_2$, and discussed in the case of an arbitrary gauge group. It is found to be nearly independent of the gauge group and very close to that of non-supersymmetric Yang-Mills when normalized to the Stefan-Boltzmann pressure and expressed as a function of $T/T_c$.Comment: The main conclusions of our previous versions are unchanged. This version is improved and is a fusion of our papers arXiv:1408.0958v2 and arXiv:1408.497

(2+1)(2+1)-dd 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($N_c$)

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.Comment: 3 figure