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N. Brambilla

Publications and source records attributed to N. Brambilla.

48 records · Page 3Linked to original sources
arXiv1996

The relativistic and nonrelativistic quark-antiquark bound state problem in a Wilson loop context

Taking advantage of a semirelativistic and a full relativistic representation of the quark propagator in an external field we present an unified derivation of the semirelativistic potential and of a Bethe-Salpeter like equation for the quark-antiquark system. We consider three different models for the evaluation of the Wilson loop: the Modified Area Law model (MAL), the Stochastic Vacuum Model (SVM) and the Dual QCD (DQCD). We compare the corresponding potentials and show that they all agree at the short and the long distances. In the case of the Bethe-Salpeter equation we treat explicitly only the MAL model and give an expression for the kernel. Then we show that an effective mass operator can be obtained which agrees with the MAL potential in the semirelativistic limit. In the light quark mass limit this mass operator produces straight Regge trajectories with Nambu-Goto slope in agreement with the data. Finally we briefly discuss the mass independence of the hyperfine splitting in the heavy-light case.

hep-ph↗
arXiv1996

Nonperturbative evaluation of a field correlator appearing in the heavy quarkonium system

Recently an electric and magnetic field correlator appearing in the description of the heavy quarkonium system was evaluated on the lattice. Here, we give a nonperturbative analytical evaluation of this field correlator using a dual description of long distance Yang--Mills theory and using the stochastic vacuum model. The two predictions are both compatible with lattice data but show a different dependence on the quark separation. We discuss the analytic results in relation to the lattice data.

hep-ph↗
arXiv1996

Confinement: Understanding the Relation Between the Wilson Loop and Dual Theories of Long Distance Yang Mills Theory

In this paper we express the velocity dependent, spin dependent heavy quark potential $V_{q\bar q}$ in QCD in terms of a Wilson Loop $W(Γ)$ determined by pure Yang Mills theory. We use an effective dual theory of long-distance Yang Mills theory to calculate $W(Γ)$ for large loops; i.e. for loops of size $R > R_{FT}$. ($R_{FT}$ is the flux tube radius, fixed by the value of the Higgs (monopole) mass of the dual theory, which is a concrete realization of the Mandelstam 't Hooft dual superconductor mechanism of confinement). We replace $W(Γ)$ by $W_{eff}(Γ)$, given by a functional integral over the dual variables, which for $R > R_{FT}$ can be evaluated by a semiclassical expansion, since the dual theory is weakly coupled at these distances. The classical approximation gives the leading contribution to $W_{eff}(Γ)$ and yields a velocity dependent heavy quark potential which for large $R$ becomes linear in $R$, and which for small $R$ approaches lowest order perturbative QCD. This latter fact means that these results should remain applicable down to distances where radiative corrections giving rise to a running coupling constant become important. The spin dependence of the potential reflects the vector coupling of the quarks at long range as well as at short range. The methods developed here should be applicable to any realization of the dual superconductor mechanism. They give an expression determining $W_{eff}(Γ)$ independent of the classical approximation, but semi classical corrections due to fluctuations of the flux tube are not worked out in this paper. Taking these into account should lead to an effective string theory free from the conformal anomaly.

hep-ph↗
arXiv1995

Quark--Antiquark Bethe--Salpeter Equation in QCD

We review our recent results \cite{bsult} on the derivation of a B-S equation in QCD in a Wilson loop context. We work in a second order formalism, use the Feynman--Schwinger path integral representation for a quark in external field and obtain a similar expression for a quark--antiquark amplitude in which the gauge fields appears only through the Wilson loop integral $W$. A $ q \bar{q}$ B-S equation is obtained starting from this expression under the assumption, already used in the derivation of heavy quark potential, that $i \ln W$ can be expressed as the sum of a perturbative contribution and an area term. The intrinsically nonperturbative derivation method is first discussed on the simpler case of two spinless particles interacting through a scalar field. The $q \bar{q}$ semirelativistic potential is reobtained in the large quark mass limit.

hep-ph↗
arXiv1995

Three-body relativistic flux tube model from QCD Wilson-loop approach

First we review the derivation of the relativistic flux tube model for a quark-antiquark system from Wilson area law as we have given in a preceding paper. Then we extend the method to the three-quark case and obtain a Lagrangian corresponding to a star flux tube configuration. A Hamiltonian can be explicitly constructed as an expansion in $1 / m^2$ or in the string tension $σ$. In the first case it reproduces the Wilson loop three-quark semirelativistic potential; in the second one, very complicated in general, but it reproduces known string models for slowly rotating quarks.

hep-ph↗
arXiv1995

Confining Bethe--Salpeter equation in QCD

We derive a confining $ q \bar{q}$ Bethe--Salpeter equation starting from the same assumptions on the Wilson loop integral already adopted in the derivation of a semirelativistic heavy quark potential. We show that, by standard approximations, an effective meson squared mass operator can be obtained from our BS kernel and that, from this, by ${1\over m^2}$ expansion, the corresponding Wilson loop potential is recovered, spin--dependent and velocity--dependent terms included. We also show, that, on the contrary, neglecting spin--dependent terms, relativistic flux tube model is reproduced.

hep-ph↗
arXiv1995

Bethe--Salpeter equation in QCD

We extend to regular QCD the derivation of a confining $ q \bar{q}$ Bethe--Salpeter equation previously given for the simplest model of scalar QCD in which quarks are treated as spinless particles. We start from the same assumptions on the Wilson loop integral already adopted in the derivation of a semirelativistic heavy quark potential. We show that, by standard approximations, an effective meson squared mass operator can be obtained from our BS kernel and that, from this, by ${1\over m^2}$ expansion the corresponding Wilson loop potential can be reobtained, spin--dependent and velocity--dependent terms included. We also show that, on the contrary, neglecting spin--dependent terms, relativistic flux tube model is reproduced.

hep-ph↗
arXiv1995

Confining Bethe--Salpeter equation from scalar QCD

We give a nonperturbative derivation of the Bethe--Salpeter equation based on the Feynman--Schwinger path integral representation of the one--particle propagator in an external field. We apply the method to the quark--antiquark system in scalar QCD and obtain a confining BS equation assuming the Wilson area law in the straight line approximation. The result is strictly related to the relativistic flux tube model and to the $q \bar{q}$ semirelativistic potential.

hep-ph↗
arXiv1994

Wilson loops, $q \bar{q}$ and $3 q$ potentials, Bethe--Salpeter equation

The derivation of the $ q \bar q $ and the $ 3q $ potential for two dynamical quarks in a Wilson--loop context is reviewed. Some improvements are introduced. Only the usual assumptions in the evaluation of the Wilson loop integrals and expansions in the quark velocities are required for the result. It is shown that under the same assumptions it is possible to obtain the relativistic flux--tube lagrangian and a $ q \bar{q}$ Bethe--Salpeter equation with a confining kernel for spinless quarks. IFUM 482/FT

hep-th↗
arXiv1994

A consistent derivation of the quark--antiquark and three quark potentials in a Wilson loop context

In this paper we give a new derivation of the quark-antiquark potential in the Wilson loop context. This makes more explicit the approximations involved and enables an immediate extension to the three-quark case. In the $q\overline{q}$ case we find the same semirelativistic potential obtained in preceding papers but for a question of ordering. In the $3q$ case we find a spin dependent potential identical to that already derived in the literature from the ad hoc and non correct assumption of scalar confinement. Furthermore we obtain the correct form of the spin independent potential up to the $1/m^2$ order.

hep-th↗