L.X. Gutiérrez Guerrero

ρ-Meson Form Factors From a Contact Interaction

IFM, UMSNHApril 5, 2011

• Hadron form factors are an important source of information onhadronic structure.

Introduction

• We employ a vector-vector contact interaction and aim for adescription of meson and baryon form factors based on a single interaction.

• We follow the methodology of simultaneously solving theSchwinger-Dyson equation for chiral symmetry breaking and the Bethe-Salpeter equation for two quark boundstates: mesons or diquarks.

• We present the calculation of the ρ-meson form factors whichplay a material role in the description of the baryons.

The SDE for the quark propagator in Euclidean space

where

A simple ansatz :

yields NJLmodel gapequation:

with

The Gap Equation in a Contact Interaction

Define

The gap equation gives the solution:

With proper time regularization,

Thus we have a constant constituent mass.

The Gap Equation in a Contact Interaction

The homogenous Bethe-Salpeter equation for a color singletmeson in the rainbow-ladder approximation with the constantglue:

The Bethe-Salpeter Equation

where

is the meson’s Bethe-Salpeter amplitude.

The Bethe-Salpeter Equation

For a contact interaction, in the absence of the dependence therelative momentum, the vector Bethe-Salpeter amplitude takethe form:

where

In the rainbow-ladder approximation:

The Quark Photon Vertex

As the kernel is independent of the exchange kernel, we candecompose the vertex as:

were

The general decomposition put in the IBS-Equation gives:

and

where

with

The Quark Photon Vertex

The dressing function displays a pole at

Rho-meson Elastic Form Factors

• The vector meson form factors are not directly measurable in the experiment.

• However, they are closely related to the axial vector di-quarks which are important in quark-diquark models of nucleon.

• In the impulse approximation:

Rho-meson Elastic Form Factors

Ρ-meson has three elastic form factors. We define them as in:

M.S. Bhagwat and P. Maris, Phys. Rev. C77 025203 (2008)

Rho-meson Elastic Form Factors

The electric, magnetic an quadrupole form factors are constructed as follows

In the limit these form factors define the charge, and magnetic and quadrupole moments of the ρ-meson:

where

S. J. Brodsky and J. R. Hiller, Phys. Rev. D 46, 2141 (1992)

Rho-meson Elastic Form Factors

Leading twist perturbative QCD reveals:

These predictions are satisfied in our computation but only If we carefully remove Λ → ∞, the equations are recovered but at the cost of a logaritmic divergence in the individual form factors.

Rho-meson Elastic Form Factors

Conclusions

Using a vector-vector contact interaction, we calculate the pion and rho as well as scalar and pseudo-vector diquarks.

The simplicity of the contact interaction allows us to calculate the form factors at arbitrarily large space-like momenta.

The diquark form factors are a first step towards calculating Baryon form factors in models where they are considered to be composites of quarks and diquarks.

This is required to be able to make connection with the planned experiments at the 12 GeV upgrade of the Jefferson lab where mesonic as well as baryonic form factors will be probed at higher space-like momenta than before.