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In recent decades, heavy-ion collisions have served as one of the essential methods to study quantum chromodynamics (QCD). It is widely accepted that when heavy nuclei collide at high energy, a deconfinement phase transition takes place and a new state of matter is created, called quark–gluon plasma (QGP) [1,2]. The interaction between quarks and gluons is dominated by the strong interaction, therefore by studying the properties of QGP, one could gain crucial knowledge of QCD. Various probes have been proposed for this purpose, including quarkonium. Heavy quarkonia such as charmonia can survive the QGP and have interesting phenomena including dissociation and recombination while moving in the fireball. Therefore, they are proposed as one of the sensitive probes of QGP [3].
Nuclei are positively charged, so non-centered collisions produce extremely strong magnetic fields. At the initial stage of the collision, one would expect a magnetic field at the magnitude of
$ 1\; m_\pi^2 $ at RHIC and$ 15\; m_\pi^2 $ at the LHC [4–9]. Strong magnetic fields will affect the properties of QGP. Various novel phenomena, including the chiral magnetic effect (CME), have been proposed. The quarkonia will also be affected by the magnetic field. Since some of them are created in initial collisions, they can carry the information of the magnetic field when it is strongest [10]. Therefore, it is possible to study the magnetic field using quarkonia if we quantitatively determine how they are affected by both the hot medium and the strong magnetic field.At zero temperature, the interaction between thecand
$ \bar{c} $ quark can be described by the Cornell potential. Due to the mass of the heavy quarks, the relativity correction for quarkonia is small [11], and one can safely use the Schrödinger equation to study them [12]. The Schrödinger equation has been successfully used to study the dissociation of quarkonium in the hot medium using the free energy from lattice simulation [13]. It is also used to study quarkonium properties in strong magnetic fields [10]. Therefore, it is straightforward to consider these two at the same time. -
The Schrödinger equation for a pair of particles in vacuum can be expressed as
$ \left [\frac{{\boldsymbol{p}}_{a}^{2}}{2m_{q}}+\frac{{\boldsymbol{p}}_{b}^{2}}{2m_{q}} +{\boldsymbol{V}} \right ]\Phi \left ( {\boldsymbol{R}},{\boldsymbol{r}} \right )=\left [ E-2m_{q} \right ]\Phi \left ( {\boldsymbol{R}},{\boldsymbol{r}} \right ), $
(1) where the eigenvalue
E means the total energy of the system, including static mass $ m_{m} $ and the kinetic energyE$ _{k} $ . Using minimal coupling to introduce an electromagnetic field, the Schrödinger equation becomes$ \begin{aligned}[b] &\left[ \frac{\left( {\boldsymbol{p}}_{a}-q_{a}{\boldsymbol{A}}_{a}\right) ^{2}}{2m_{q}}+ \frac{\left( {\boldsymbol{p}}_{b}-q_{b}{\boldsymbol{A}}_{b}\right) ^{2}}{2m_{q}}+{\boldsymbol{V}} -{\boldsymbol{\mu}}\cdot {\boldsymbol{B}}\right] \Phi \left( {\boldsymbol{R}}, {\boldsymbol{r}}\right) \\ =&\left[ E-2m_{q}\right] \Phi \left( {\boldsymbol{R}},{\boldsymbol{r}}\right), \end{aligned} $
(2) where
$ {\boldsymbol{\mu}}=\dfrac{q}{m_{q}}\left({\boldsymbol{S}}_{a}-{\boldsymbol{S}}_{b}\right) $ is the spin magnetic moment. As the kinetic momentum${\boldsymbol{P}}_{\rm kin}={\boldsymbol{p}}_a+{\boldsymbol{p}}_b-q_a {\boldsymbol{A}}_a-q_b{\boldsymbol{A}}_b$ is no longer conserved in such a system, we should define the kinetic energy using its expectation value, so the meson mass here should be defin
Dissociation ofJ/ψin hot medium and magnetic field
- Received Date:2022-03-13
- Available Online:2022-09-15
Abstract:Charmonium dissociation is an important probe of the quark–gluon plasma medium in heavy-ion collisions. The magnetic field produced in non-central collisions can affect the charmonia and their dissociation. We study the
