Hadronic Loops versus Factorization in EFT calculations of $X(3872)\to {\chi }_{cJ}{\pi }^0$

Abstract

We compare two existing approaches to calculating the decay of molecular quarkonium states to conventional quarkonia in effective field theory, using $X(3872)\to {\chi }_{cJ}{\pi }^0$ as an example. In one approach the decay of the molecular quarkonium proceeds through a triangle diagram with charmed mesons in the loop. We argue this approach predicts excessively large rates for $\Gamma [X(3872)\to {\chi }_{cJ}{\pi }^0]$ unless both charged and neutral mesons are included and a cancellation between these contributions is arranged to suppress the decay rates. This cancellation occurs naturally if the $X(3872)$ is primarily in the $I=0$ $D{\bar{D}}^{\ast }+c.c.$ scattering channel. The factorization approach to molecular decays calculates the rates in terms of tree-level transitions for the $D$ mesons in the $X(3872)$ to the final state, multiplied by unknown matrix elements. We show that this approach is equivalent to hadronic loops approach if the cutoff on the loop integrations is taken to be a few hundred MeV or smaller, as is appropriate when the charged $D$ mesons have been integrated out of XEFT.

21 pages, 2 figures, journal version, fixed typos, minor changes

References in corpus (12)

• Heavy quarkonium: progress, puzzles, and opportunities
• Pion Interactions in the X(3872)
• An overview of $XYZ$ new particles
• Hadronic Decays of the X(3872) to chi_{cJ} in Effective Field Theory
• A New Hadron Spectroscopy
• Two-photon decays of hadronic molecules
• What can radiative decays of the X(3872) teach us about its nature?
• Pionic transitions from X(3872) to chi_{cJ}
• Detecting the long-distance structure of the X(3872)
• On the scattering of D and D* mesons off the X(3872)
• $X(3872)\to D\bar{D}\gamma$ decays and the structure of X(3872)
• Operator Product Expansion in the Production and Decay of the X(3872)

Cited by in corpus (28)

• Hadronic molecules
• The hidden-charm pentaquark and tetraquark states
• The $XYZ$ states: experimental and theoretical status and perspectives
• Multiquark Resonances
• Nuclear effective field theory: status and perspectives
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Heavy hadronic molecules with pion exchange and quark core couplings: a guide for practitioners
• $T_{cc}^{+}$ decays: Differential spectra and two-body final states
• Observation of the decay $X(3872)\to {\pi }^0{\chi }_{c1}(1P)$
• Strong decays of $T_{cc}^{+}$ at NLO in an effective field theory
• Interpretations of the new LHCb $P_c(4337{)}^{+}$ pentaquark state
• Revisiting $X(3872)\to D^0{\bar{D}}^0{\pi }^0$ in XEFT
• Fully charmed tetraquarks from LHC to FCC: Natural stability from fragmentation
• Hadronic decays of the heavy-quark-spin molecular partner of $T_{cc}^{+}$
• Exotic tetraquarks at the HL-LHC with JETHAD: A high-energy viewpoint
• Bottomoniumlike states in proton collisions: Fragmentation and resummation
• Decays of $X(3872)$ to ${\chi }_{cJ}{\pi }^0$ and $J/\psi {\pi }^{+}{\pi }^{-}$
• Production of the $Z_b^{(\prime )}$ states from the ${\rm Y}(5S,6S)$ decays
• Heavy meson thresholds in Born-Oppenheimer Effective field theory
• Radiative and pionic transitions $Z_c(4020{)}^0\to X(3872)\gamma$ and $Z_c(4020{)}^{\pm }\to X(3872){\pi }^{\pm }$
• Can X(3915) be the tensor partner of the X(3872)?
• Fragmentation of fully heavy tetraquarks: The TQ4Q1.1 functions as a case study
• Decay properties of the $X(3872)$ through the Fierz rearrangement
• Hunting for $X_b$ via hidden bottomonium decays $X_b\to \pi \pi {\chi }_{bJ}$
• Tetraquark-Jet Systems at the High-Luminosity LHC
• Constrain the ${\chi }_{cJ}\to D^{(\ast )}{\bar{D}}^{(\ast )}$ effective couplings via the $X(3872)\to {\pi }^0{\chi }_{cJ}$ decays
• The $X(3872)\to J/\psi \pi \gamma$ and $X(3872)\to J/\psi \pi \pi \gamma$ decays
• All-charm tetraquarks at hadron colliders: A high-precision fragmentation perspective