Elucidating the nature of axial-vector charm-antibottom tetraquark states

TL;DR

This work computes the magnetic moments of axial-vector open-flavor tetraquarks $Z_{ar{b}c}$ with $I(J^{P})=1(1^{+})$ using QCD light-cone sum rules in a diquark–antidiquark framework. By matching hadronic and QCD representations of a photon-extended correlator and applying double Borel transforms with continuum subtraction, the authors extract the magnetic form factor at $Q^2=0$ and the corresponding magnetic moments, finding values around $\mu_{Z_{ar{b}c}}\approx -2\,\mu_N$ (with small variations across interpolating currents) and nonzero quadrupole moments $\mathcal{D}\sim(1.3$–$1.9)\times10^{-2}\ \mathrm{fm}^2$. The analysis reveals that short-distance photon couplings to quarks dominate the magnetic moments (approximately 85%), with light-quark contributions (notably from $u$ and $d$) playing a decisive role and heavy-quark parts (from $c$ and $b$) remaining negative and smaller in magnitude. These predictions provide concrete benchmarks for future experimental tests and for cross-checks against alternative phenomenological pictures of open-flavor tetraquarks.

Abstract

Investigating the electromagnetic characteristics of unconventional states may offer new insights into their internal structures. In particular, the magnetic moment attributes may serve as a crucial physical observable for differentiating exotic states with disparate configurations or spin-parity quantum numbers. As a promising avenue for research, encompassing both opportunities and challenges, an in-depth examination of the electromagnetic properties of exotic states is crucial for advancing our understanding of unconventional states. Motivated by this, in this study, the magnetic moments of $ \rm{I(J^{P})} = 1(1^{+})$ $Z_{\bar b c}$ tetraquark states are analyzed in the framework of QCD light-cone sum rules by considering the diquark-antidiquark approximation, designated as type $3_c \otimes \bar 3_c$. Although the tetraquark states examined in this study have nearly identical masses, their magnetic moment results exhibit noticeable discrepancies. This may facilitate the differentiation between quantum numbers associated with states with identical quark content. The results show that heavy quarks overcoming light quarks can determine both the sign and the magnitude of the magnetic moments of these tetraquark states. The numerical results obtained in this study suggest that the magnetic moments of $Z_{\bar b c}$ tetraquark states may reveal aspects of their underlying structure, which could distinguish between their spin-parity quantum numbers and their internal structure. The results obtained regarding the magnetic moments of the $Z_{\bar b c}$ tetraquark states may be checked within the context of different phenomenological approaches.

Figures (2)

• Figure 1: Variation of magnetic moments $Z_{\bar{b} c}$ tetraquarks as a function of the $\rm{M^2}$ at different values of $\rm{s_0}$.
• Figure 2: The magnetic $(\mu)$ and quadrupole ($\mathcal{D}$) moments of $Z_{\bar{b} c}$ tetraquark states: (a) and (c) for central values, and (b) and (d) for combined with errors, respectively.