Year: 2015
Type: article
Abstract: XEFT is a low-energy effective field theory for charm mesons and pions that provides a systematically improvable description of the $X(3872)$ resonance. A Galilean-invariant formulation of XEFT is introduced to exploit the fact that mass is very nearly conserved in the transition ${D}^{*0}\ensuremath{\rightarrow}{D}^{0}{\ensuremath{\pi}}^{0}$. The transitions ${D}^{*0}\ensuremath{\rightarrow}{D}^{0}{\ensuremath{\pi}}^{0}$ and $X\ensuremath{\rightarrow}{D}^{0}{\overline{D}}^{0}{\ensuremath{\pi}}^{0}$ are described explicitly in XEFT. The effects of the decay ${D}^{*0}\ensuremath{\rightarrow}{D}^{0}\ensuremath{\gamma}$ and of short-distance decay modes of the $X(3872)$, such as $J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, can be taken into account by using complex on-shell renormalization schemes for the ${D}^{*0}$ propagator and for the ${D}^{*0}{\overline{D}}^{0}$ propagator in which the positions of their complex poles are specified. Galilean-invariant XEFT is used to calculate the ${D}^{*0}{\overline{D}}^{0}$ scattering length to next-to-leading order. Galilean invariance ensures the cancellation of ultraviolet divergences without the need for truncating an expansion in powers of the ratio of the pion and charm meson masses.
Author: Eric Braaten
Institution: The Ohio State University
Language: Latvian
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: U.S. Department of Energy
OpenAlex ID: W2145635879