[Paper Review] Systematic Study of Hadronic Molecules in the Heavy-Quark Sector

Martin Cleven|arXiv (Cornell University)|May 16, 2014

Quantum Chromodynamics and Particle Interactions4 citations

TL;DR

This dissertation investigates hadronic molecules in the heavy-quark sector, proposing that $D_{s0}^{*}$ and $D_{s1}$ states arise as $DK$ and $D^{*}K$ molecules, while $Z_b(10610)$ and $Z_b(10650)$ are interpreted as $B^{*}\bar{B}+c.c.$ and $B^{*}\bar{B}^{*}$ molecules. Using chiral and heavy quark symmetries, it predicts that hadronic decays of $D_{sJ}$ states are enhanced by an order of magnitude in the molecular picture, offering a key experimental test.

ABSTRACT

In this work we study the properties of hadronic molecules in the heavy-quark sector. These have become increasingly important since from the beginning of this century a large number of states have been measured that for different reasons do not fit the predictions of simple quark models. In particular we discuss two candidates in the open charm sector, $D_{s0}^*(2317)$ and $D_{s1}(2460)$, and two candidates in the bottomonium sector, $Z_b(10610)$ and $Z_b(10650)$. Theorists have proposed different explanations for these states including tetraquarks, hybrids, hadro-quarkonia and, subject of this work, hadronic molecules. The study of these new states promises to provide insights in an important field of modern physics, the formation of matter by the strong force. Hadronic molecules are bound systems of hadrons in the same way two nucleons form the deuteron. For this the molecular states need to be located close to $S$-wave thresholds of their constituents. The dynamics of their constituents will have a significant impact on the molecules which allows us to make predictions that are unique features of the molecular assignment.

Motivation & Objective

• To investigate the molecular nature of newly observed hadronic states in the open charm and bottomonium sectors that do not fit standard quark model predictions.
• To determine whether $D_{s0}^{*}$ and $D_{s1}$ can be explained as bound states of $DK$ and $D^{*}K$ mesons via unitarized chiral perturbation theory.
• To assess the molecular interpretation of $Z_b(10610)$ and $Z_b(10650)$ as $B^{*}\bar{B}+c.c.$ and $B^{*}\bar{B}^{*}$ molecules using nonrelativistic effective field theory.
• To identify experimentally measurable quantities—particularly decay widths—that can distinguish molecular states from compact four-quark states.
• To provide predictive frameworks for invariant mass spectra and decay branching fractions to guide future experiments at PANDA and B-factories.

Proposed method

• Employed unitarized chiral perturbation theory to generate $D_{s0}^{*}$ and $D_{s1}$ as poles in the $DK$ and $D^{*}K$ scattering amplitudes, incorporating chiral symmetry constraints.
• Used heavy quark symmetry to suppress spin-dependent interactions in the $D^{(*)}K$ system, justifying the molecular assignment of $D_{s0}^{*}$ and $D_{s1}$.
• Applied nonrelativistic effective field theory (NREFT) to compute two-body decay amplitudes for $Z_b^{(ackprime)}$ states into $\Upsilon\pi$, $h_b\pi$, and $\chi_b\gamma$ final states.
• Calculated radiative and hadronic decay rates using relativistic and nonrelativistic Lagrangians, with tensor reduction techniques for loop integrals.
• Modeled invariant mass spectra using Flatté parametrization instead of Breit-Wigner to accurately describe near-threshold states.
• Studied the dependence of molecular state poles on light quark masses (up/down and strange quarks), enabling comparison with lattice QCD.

Experimental results

Research questions

• RQ1 Can the $D_{s0}^{*}$ and $D_{s1}$ states be dynamically generated as $DK$ and $D^{*}K$ molecules within chiral perturbation theory?
• RQ2 What are the distinctive decay signatures of molecular $D_{sJ}$ states compared to compact $c\bar{s}$ states, particularly in hadronic and radiative decays?
• RQ3 Is the $Z_b(10610)$ state best described as a $B^{*}\bar{B}+c.c.$ molecule, and does its decay into $\Upsilon\pi$ and $h_b\pi$ support this interpretation?
• RQ4 How do the invariant mass distributions of $Z_b^{(ackprime)}$ states deviate from standard Breit-Wigner parametrization, and what is the optimal description near open thresholds?
• RQ5 What new decay channels, such as $\chi_b\gamma$, are accessible in the molecular picture and could be observed at next-generation $B$-factories?

Key findings

• The hadronic decay widths of $D_{s0}^{*}$ and $D_{s1}$ are predicted to be about one order of magnitude larger in the molecular picture than in the compact four-quark model, providing a key experimental discriminator.
• Radiative decays $D_{s0}^{*}\to D_{s}\gamma$ and $D_{s1}\to D_{s}^{*}\gamma$ are found to have comparable rates in both molecular and compact interpretations, making them less sensitive to the assignment.
• The $Z_b(10610)$ and $Z_b(10650)$ states can reproduce the Belle group's invariant mass spectra when modeled as $B^{*}\bar{B}+c.c.$ and $B^{*}\bar{B}^{*}$ molecules with poles below the respective thresholds.
• The Flatté parametrization is shown to be essential for accurately describing the lineshape of near-threshold $Z_b^{(ackprime)}$ states, unlike the standard Breit-Wigner form.
• The branching fraction for $Z_b^{(\prime)}\to \chi_{bJ}\gamma$ is predicted to be large enough to be detectable at future $B$-factories, offering a critical test of the molecular hypothesis.
• The $D_{sJ}$ state poles are found to shift with changes in the strange and light quark masses, enabling direct comparison with lattice QCD calculations to test the molecular model.