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

Latest measurements suggest that the X(3872) mass lies less than 200 keV away from the D⁰D¯ ⁰* threshold, reenforcing its interpretation as a loosely bound mesonic molecule. This observation implies that in processes like D⁰D¯⁰ π⁰ production, threshold effects could disguise the actual pole position of the X(3872). We propose a new effective field theory with D⁰, D¯ ⁰, and π⁰ degrees of freedom for the X(3872), considering Galilean invariance to be an exact symmetry. The D⁰ enters as a D⁰π⁰ p-wave resonance, allowing for a comprehensive study of the influence of pion interactions on the Xð3872Þ width. We calculate relations between the mass of the X(3872), its width, and its line shape in D⁰D¯⁰ π⁰ 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