CC BY
24Complex Systems of Charged Particles and their Interactions with Electromagnetic Radiation 2019
DISSOCIATION OF QUARKONIUM BY A STRONG ELECTRIC FIELD
IN THE QUARK-GLUON PLASMA
A.M. Ishkhanyan1, V.P. Krainov2
institute for Physical Research, National Academy of Sciences of Armenia, Ashtarak, Armenia
e-mail: aishkhanyan@gmail. com Moscow Institute of Physics and Technology, Dolgoprudny, Moscow oblast, Russia
e-mail: vpkrainov@mail. ru
The interest in the properties of bound states of a pair of heavy quarks (quarkonium) has been revived in recent years. These states are generally analogous in properties to the positronium, viz., the neutral bound state of the electron and the positron. Analogous neutral bound states form two systems: charmonium consisting of a charmed quark and antiquark (with charges +2e/3 and -2e/3) and bottomonium, consisting of beautiful quark and antiquark (with charges -e/3 and +e/3). The only difference is that the particles forming positronium are observable, while quarks in free form have never been observed as yet. The exact form of the potential of the interaction between a quark and an antiquark is unknown. There exist different models that describe experimental spectra with the same accuracy. These models include, for example, the Quigg-Rosner potential, the Martin potential, and the so-called Cornell potential proposed by physicists of the Cornell University (Ithaca, New York, USA).
We consider here the decay of charmonium in the Martin model potential of attraction between a heavy quark and an antiquark in their bound state. This potential has the well-known form V(r) = A + Br01. Here A = - 6.0 GeV, B = 6.87 GeV, and the distance r between a heavy quark and
1 3
an antiquark is measured in GeV (approximately 10" Fermi). These constants are determined from the experimental positions of excited s-states of quarkonium. In the quark-gluon plasma containing quarkonium molecules, strong electric fields exist. Such fields are responsible for tunnel ionization of quarkonium leading generally (although with a rather low probability) to a formation of free quarks. The characteristic expression for the electric field strength in the quark-gluon plasma [1] is E = mlc? /he. This ionization is the subject of this communication. We obtained the following simple expression for the tunnel ionization rate [2]:
W = —exp
Tq
r A1'2 /
m
_q
m
V "j
B
v m„c2 ,
V n J
(1)
Here m c2 = 0.135 GeV is the mass of pi-meson, m c2 = 129 GeV is the mass of the charmed
n r 1 q
quark. The characteristic quark time is determined analogously to the atomic time:
T =(m /m )T = 8.6-10-21s. Therefore, the probability of the quarkonium decay into free quarks in a
q \ e q / a
constant electric field in the Martin model is negligibly low: in accordance of relation (1), its decay occurs approximately during 1016 years, which considerably exceeds the lifetime of the Universe.
References
[1] K. Tuchin, 2013 Phys. Rev. C 88 034911.
[2] A. M. Ishkhanyan, V. P. Krainov, 2018 JETP 126 (5) 633.
