Operator Product Expansion in the Production and Decay of the X(3872)

Abstract

The X(3872) seems to be a weakly-bound hadronic molecule whose constituents are two charm mesons. Its binding energy is much smaller than all the other energy scales in QCD. This separation of scales can be exploited through factorization formulas for production and decay rates of the X. In a low-energy effective field theory for the constituents of the X, the factorization formulas can be derived using the operator product expansion. The derivations are carried out explicitly for the simplest effective theory in which the constituents interact through a contact interaction that produces a large scattering length. The long-distance factors in the operator product expansions for various observables are calculated nonperturbatively in the interaction strength of the contact interaction. After renormalization of the coupling constant, all remaining ultraviolet divergences can be absorbed into the short-distance factors in the operator product expansions.

30 pages, 5 figures

Cited by in corpus (13)

• Heavy quarkonium: progress, puzzles, and opportunities
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Line Shapes of the X(3872)
• X(3872) as a hadronic molecule and its decays to charmonium states and pions
• Hadronic Decays of the X(3872) to chi_{cJ} in Effective Field Theory
• The Effects of Charged Charm Mesons on the Line Shapes of the X(3872)
• On the scattering of D and D* mesons off the X(3872)
• A Phenomenological analysis on isospin-violating decay of $X(3872)$
• Weakly-bound Hadronic Molecule near a 3-body Threshold
• X(3872) and the bound state problem of $D^0{\bar{D}}^{\ast 0}$ (${\bar{D}}^0{D}^{\ast 0}$) in a chiral quark model
• Triangle singularity in the $B^{-}\to K^{-}{\pi }^{0}X(3872)$ reaction and sensitivity to the $X(3872)$ mass
• An Estimate of the Partial Width for X(3872) into p p-bar
• A study of meson-meson potential in the chiral quark model