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¯0π0 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 X(3872) width. We calculate relations between the mass of the X(3872), its width, and its line shape in D0D¯0π0 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