Threshold effects and the line shape of the X(3872) in effective field theory

Abstract

Latest measurements suggest that the X(3872) mass lies less than 200 keV away from the D 0D0 * threshold, reenforcing its interpretation as a loosely-bound mesonic molecule. This observation implies that in processes like D 0D0 π 0 production, threshold effects could disguise the actual pole position of the X(3872). We propose a new effective field theory with D 0 ,D 0 and π 0 degrees of freedom for the X(3872), considering Galilean invariance to be an exact symmetry. The D 0 * enters as a D 0 π 0 p-wave resonance, allowing for a comprehensive study of the influence of pion interactions on the X(3872) width. We calculate relations between the mass of the X(3872), its width, and its line shape in D 0D0 π 0 production up to next-to-leading order. Our results provide a tool for the extraction of the X(3872) pole position from the experimental data near threshold.

Production of X(3872) accompanied by a pion in B meson decay

“…An alternative Galilean-invariant EFT for S-wave charm mesons and pions that may be more predictive has been introduced by Schmidt, Jansen, and Hammer [30]. The only fields in this EFT are those for the spin-0 charm mesons D and the pions π.…”

“…(22) is contracted with the tensors in the numerators of Eqs. (29) and (30), multiplied by its complex conjugate, and then summed over the spin states of X, the results are…”

Effective Field Theory for Shallow P-Wave States

“…(2) or (4) and leading to the appearance of shallow bound, virtual or resonance states. While such resonant systems have already been extensively studied using EFT formulations with auxiliary dimer fields [30,39,[44][45][46][47][48][49], see Ref. [53] for a review article, we have employed here the effective Lagrangian written solely in terms of contact interactions.…”

“…Refs. [44][45][46][47][48][49]. Notice that the UV divergences in the dimeron self-energy at leading order are cancelled by the counterterms generated by the bare particle-dimeron coupling constant g 1 and the residual dimeron mass 1 , see Refs.…”

Tritonlike Molecules of Three Identical Baryons

“…Some other applications via isobar formalism can be found in Refs [65][66][67][68]. The third useful tool to describe a three-body system called dimer formalism was presented in a series of studies, where a composite field is introduced to describe the two-body subsystem when rescattering with a third particle [69][70][71][72][73][74][75]. The Gauss Expansion Method is another effective tool for few-body systems [76], which has been applied to discuss few-nucleon systems [77] and the DDDK system [78].…”