Magnetic field induced hair structure in the charmonium gluon dissociation

We study the electromagnetic field effect on charmonium gluon dissociation in quark-gluon plasma. With the effective Hamiltonian derived from QCD multipole expansion under an external electromagnetic field, we first solve the two-body Schrödinger equation for a pair of charm quarks with mean field potentials for color and electromagnetic interactions and obtain the charmonium binding energies and wave functions, and then calculate the gluon dissociation cross section and decay width by taking the color electric and magnetic dipole interactions as perturbations above the mean field and employing Fermi’s golden rule. Considering the charmonium deformation in a magnetic field, the discrete Landau energy levels make the dissociation cross section grow hair, and the electric dipole channel is significantly changed, especially for the $P$-wave states ${\chi }_{c0}$ and ${\chi }_{c\pm }$. From our numerical calculation, the magnetic field strength $eB=5m_{\pi }^2$ already changes the gluon dissociation strongly, which may indicate measurable effects in high-energy nuclear collisions.

Figure 1

The charmonium mass $M_{\mathrm{\Psi }}$ as a function of magnetic field $eB$ at vanishing temperature and pseudomomentum $T=0$ and ${\mathit{P}}_{\mathrm{ps}}=0$.

Figure 2

The charmonium binding energy $\epsilon$ and longitudinal and transverse mean square radii $⟨z^2⟩$ and $⟨{\rho }^2⟩$ as functions of temperature $T$ at vanishing pseudomomentum ${\mathit{P}}_{\mathrm{ps}}=0$. The temperature and radii are scaled by their values at the deconfinement phase transition temperature $T_c$. The thin and thick solid lines are $\epsilon$ and $⟨z^2⟩$ at $eB=0$ and $5m_{\pi }^2$, and the dashed line is $⟨{\rho }^2⟩$ at $eB=5m_{\pi }^2$.

Figure 3

The charmonium gluon-dissociation cross sections in channels $E1$ and $M1$ at vanishing temperature and conserved momentum $T=0$ and ${\mathit{P}}_{\mathrm{ps}}=0$. The bottom label $E_g-E_B$ is the energy difference between the initial gluon and charmonium, and the top label is $2n+|m|$, characterizing the Landau energy level. The solid and dashed lines are the calculations with and without a magnetic field.

Figure 4

The charmonium decay width through gluon dissociation in channels $E1$ and $M1$ as functions of scaled temperature $T/T_c$ at vanishing pseudomomentum ${\mathit{P}}_{\mathrm{ps}}=0$. Solid and dashed lines are the calculations with and without magnetic field.