https://doi.org/10.1140/epjc/s10052-008-0819-8
Regular Article - Theoretical Physics
Schwinger mechanism for gluon-pair production in the presence of arbitrary time-dependent chromo-electric field
C.N. Yang Institute for Theoretical Physics, Stony Brook University, SUNY, Stony Brook, NY, 11794-3840, USA
* e-mail: nayak@max2.physics.sunysb.edu
Received:
17
August
2008
Revised:
10
October
2008
Published online:
5
December
2008
We study the Schwinger mechanism for gluon-pair production in the presence of an arbitrary time-dependent chromo-electric background field E
a
(t) with arbitrary color index a=1,2,…,8 in SU(3) by directly evaluating the path integral. We obtain an exact expression for the probability of non-perturbative gluon-pair production per unit time per unit volume and per unit transverse momentum,
, from arbitrary E
a
(t). We show that the tadpole (or single-gluon) effective action does not contribute to the non-perturbative gluon-pair production rate,
. We find that the exact result for non-perturbative gluon-pair production is independent of all the time derivatives
, where n=1,2,…,∞, and that it has the same functional dependence on the two Casimir invariants, [E
a
(t)E
a
(t)] and [d
abc
E
a
(t)E
b
(t)E
c
(t)]2, as the constant chromo-electric field E
a
result with the replacement: E
a
→E
a
(t). This result relies crucially on the validity of the shift conjecture, which has not yet been established. This result may be relevant to the study of the production of a non-perturbative quark–gluon plasma at RHIC and LHC.
PACS: 11.15.-q – / 11.15.Me – / 12.38.Cy – / 11.15.Tk –
© Springer-Verlag , 2009
