Pion and sigma meson properties in a relativistic quark model

Abstract

A variety of strong and electroweak interaction properties of the pion and the light scalar sigma meson are computed in a relativistic quark model. Under the assumption that the resulting coupling of these mesons to the constituent quarks is identical, the sigma meson mass is determined as M_sigma=385.4 MeV. We discuss in detail the gauging of the non-local meson-quark interaction and calculate the electromagnetic form factor of the pion and the form factors of the pi(0) -> gamma gamma and sigma -> gamma gamma processes. We obtain explicit expressions for the relevant form factors and evaluate the leading and next-to-leading orders for large Euclidean photon virtualities. Turning to the decay properties of the sigma we determine the width of the electromagnetic sigma -> gamma gamma transition and discuss the strong decay sigma -> pi pi. In a final step we compute the nonleptonic decays D -> sigma pi and B -> sigma pi relevant for the possible observation of the sigma meson. All our results are compared to available experimental data and to results of other theoretical studies.Comment: 46 page

Strong and radiative decays of theDs0*(2317)meson in theDK-molecule picture

“…in Ref. [58]. For this purpose in particular we split the contribution of each diagram into a part which is gauge invariant and one which is not: we use the following representation for the four-vectors with open Lorentz indices µ and ν:…”

“…In particular, the compositeness condition excludes the direct interaction of the dressed charged particle (like D * ± s0 mesons) with the electromagnetic field. Taking into account both the tree-level diagram and the diagrams with the self-energy and counter-term insertions into the external legs (that is the tree-level diagram times (Z D * s0 − 1)) one obtains a common factor Z D * s0 which is equal to zero [55,57,58].…”

“…[71] and extensively used in Refs. [57,58]. In particular, to guarantee local invariance of the strong interaction Lagrangian, in L str int each charged constituent meson field (i.e.…”

“…Then it was extensively used in the low-energy hadron phenomenology as the master equation for the treatment of mesons and baryons as bound states of light and heavy constituent quarks (see Refs. [55,57,58,59,60]). In addition this condition was used in Ref.…”

Strange-quark asymmetry in the proton in chiral effective theory

“…Restoration of gauge invariance in the presence of form factors requires the generalization of the chiral Lagrangian to include nonlocal terms [63][64][65]. Following the approach adopted in Ref.…”