Single-flavor heavy baryons in a strong magnetic field

TL;DR

This work addresses how a strong magnetic field alters the spectra of single-flavor heavy baryons by framing them as quark–diquark two-body systems and solving the corresponding Schrödinger equations in a constant magnetic field. A systematic formalism is developed for two-body dynamics in a magnetic field, including a Schwinger phase, CM–relative separation, and a Landau-basis treatment, with equal-mass simplifications and a cylindrical-coordinate QDI approach to handle the three-body problem. Numerical results for $Ω_{ccc}$ and $Ω_{bbb}$ show that the magnetic field strongly influences $Ω_{ccc}$, reducing the diquark distance and increasing binding, while $Ω_{bbb}$ is less affected; magnetic-spin (Zeeman) effects dominate over orbital magnetic terms, making $Ω_{ccc}$ the more promising probe of magnetic effects in peripheral heavy-ion collisions. The study provides a framework for predicting magnetic-fieldDependence in heavy baryons and highlights potential observables in collider environments where strong EM fields are present.

Abstract

In this work, we study the properties of single-flavor heavy baryons, $Ω_{\rm ccc}$ and $Ω_{\rm bbb}$, in a strong magnetic field. For that sake, we simply treat the baryons as quark-diquark two-body systems, and a systematic formalism is developed to deal with two-body Schr$\ddot{\text o}$dinger equations in a magnetic field. It is found that: 1. The orbital properties of $Ω_{\rm bbb}$ are almost not affected by the magnetic field. 2. $Ω_{\rm ccc}$ is more tightly bound in the presence of a magnetic field. 3. The magnetic-spin effect dominates over the magnetic-orbital effect. Applying to peripheral heavy ion collisions, $Ω_{\rm ccc}$ is much better than $Ω_{\rm bbb}$ to explore the magnetic effect, and the discovery of $Ω_{\rm ccc}$ could be more promising.

Figures (3)

• Figure 1: A few lowest-lying eigenenergies $E_{\rm t}$ of $\Omega_{\rm ccc}$ (red) and $\Omega_{\rm bbb}$ (blue) as functions of the corresponding self-consistent vertex angles $\theta$ in the vacuum.
• Figure 2: The lowest-lying orbital eigenenergies $2E_{\rm r}$ and two-quark average distances $r_{\rm qq}$ of $\Omega_{\rm ccc}$ (red) and $\Omega_{\rm bbb}$ (blue) as functions of the magnetic field $eB$ for $m_{\rm D}=0$ (solid and dotted) and $0.4~{\rm GeV}$ (dashed and dashdotted).
• Figure 3: The total relative energies $E_{\rm t}$ of $\Omega_{\rm ccc}$ (red) and $\Omega_{\rm bbb}$ (blue) as functions of the magnetic field $eB$ in the quark-gluon-plasma phase with spins $S_{\rm z}= {3\over2}$ (solid), ${1\over2}$ (dotted), $-{1\over2}$ (dashed), and $-{3\over2}$ (dashdotted). The orbital eigenenergies correspond to those given in Fig. \ref{['pB']} for $m_{\rm D}=0.4~{\rm GeV}$.