Galilean-Invariant XEFT at Next-to-Leading Order

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. To simplify calculations beyond leading order, we introduce a new formulation of XEFT with a dynamical field for a pair of charm mesons in the resonant channel. We simplify the renormalization of XEFT by introducing a new renormalization scheme that involves the subtraction of amplitudes at the complex $D^{\ast 0}{\bar{D}}^0$ threshold. The new formulation and the new renormalization scheme are illustrated by calculating the complex pole energy of $X$ and the $D^{\ast 0}{\bar{D}}^0$ scattering amplitude to next-to-leading order using Galilean-invariant XEFT.

arXiv comment47 pages, 18 figures

References in corpus (28)

• Observation of a narrow charmonium-like state in exclusive B+ -> K+ pi+pi- J/psi decays
• Observation of a New Narrow Charmonium State in Exclusive B+-->K+ pi+pi- J/psi Decays
• Universality in Few-body Systems with Large Scattering Length
• The $XYZ$ states: experimental and theoretical status and perspectives
• Non-Standard Heavy Mesons and Baryons, an Experimental Review
• Exotics: Heavy Pentaquarks and Tetraquarks
• Determination of the X(3872) meson quantum numbers
• Multiquark States
• Low-energy Universality and the New Charmonium Resonance at 3870 MeV
• Pion Interactions in the X(3872)
• Study of the lineshape of the ${\chi }_{c1}(3872)$ state
• Coulomb Effects in Low Energy Proton-Proton Scattering
• Novel Method for Precisely Measuring the $X(3872)$ Mass
• Scattering of an Ultrasoft Pion and the X(3872)
• Study of the ${\psi }_2(3823)$ and ${\chi }_{c1}(3872)$ states in $B^{+}\to \left(J\psi {\pi }^{+}{\pi }^{-}\right)K^{+}$ decays
• On the scattering of D and D* mesons off the X(3872)
• Galilean-Invariant XEFT
• Light quark mass dependence of the X(3872) in XEFT
• Triangle singularity in the $B^{-}\to K^{-}{\pi }^{0}X(3872)$ reaction and sensitivity to the $X(3872)$ mass
• Charm-meson Triangle Singularity in $e^{+}{e}^{-}$ Annihilation into $D^{\ast 0}{\bar{D}}^0+\gamma$
• Zero-Range Effective Field Theory for Resonant Wino Dark Matter II. Coulomb Resummation
• Triangle Singularity in the Production of $X(3872)$ and a Photon in $e^{+}{e}^{-}$ Annihilation
• Triangle singularity in $B^{-}\to K^{-}X(3872);X\to {\pi }^0{\pi }^{+}{\pi }^{-}$ and the X(3872) mass
• Production of $X(3872)$ Accompanied by a Pion in $B$ Meson Decay
• Revisiting $X(3872)\to D^0{\bar{D}}^0{\pi }^0$ in XEFT
• $e^{+}{e}^{-}\to \gamma X(3872)$ near the $D^{\ast }{\bar{D}}^{\ast }$ threshold
• Production of $X(3872)$ Accompanied by a Soft Pion at Hadron Colliders
• Possible precise measurements of the $X(3872)$ mass with the $e^{+}{e}^{-}\to {\pi }^0\gamma X(3872)$ and $p\bar{p}\to \gamma X(3872)$ reactions

Cited by in corpus (13)

• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• $T_{cc}^{+}$ decays: Differential spectra and two-body final states
• Production of $X(3872)$ at High Multiplicity
• Revisit the isospin violating decays of $X(3872)$
• Strong decays of $T_{cc}^{+}$ at NLO in an effective field theory
• Triangle Singularity in the Production of $T_{cc}^{+}$(3875) and a Soft Pion
• $D^{\pm }{D}^{\ast \mp }$ Hadronic Atom as a Key to Revealing the $X(3872)$ Mystery
• Hadronic decays of the heavy-quark-spin molecular partner of $T_{cc}^{+}$
• The role of the pion in the lineshape of the $X(3872)$
• ${\bar{B}}^0\to {\bar{K}}^{(\ast )0}X$, $B^{-}\to K^{(\ast )-}X$, ${\bar{B}}_s^0\to \eta ({\eta }^{\prime },\varphi )X$ from the $X(3872)$ molecular perspective
• Constraining the $DD{D}^{\ast }$ three-body bound state via the $Z_c(3900)$ pole
• A short review on the compositeness of the $X(3872)$
• The general propagator for S-wave threshold states