We study the Schwinger mechanism in QCD 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). We obtain an exact result for the non-perturbative quark (antiquark) pr
oduction from an arbitrary $E^a(t)$ by directly evaluating the path integral. We find that the exact result is independent of all the time derivatives $frac{d^nE^a(t)}{dt^n}$ where $n=1,2,...infty$. This result has the same functional dependence on 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: $E^a rightarrow E^a(t)$. This result relies crucially on the validity of the shift conjecture, which has not yet been established.
We perform path integral for a quark (antiquark) in the presence of an arbitrary space-dependent static color potential A^a_0(x)(=-int dx E^a(x)) with arbitrary color index a=1,2,...8 in SU(3) and obtain an exact non-perturbative expression for the g
enerating functional. We show that such a path integration is possible even if one can not solve the Dirac equation in the presence of arbitrary space-dependent potential. It may be possible to further explore this path integral technique to study non-perturbative bound state formation.
We study Schwinger mechanism for gluon pair production in the presence of 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 $frac{dW}{d^4x d^2p_T}$ 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 $frac{dW}{d^4x d^2p_T}$. We find that the exact result for non-perturbative gluon pair production is independent of all the time derivatives $frac{d^nE^a(t)}{dt^n}$ where $n=1,2,....infty$ and has the same functional dependence on 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: $E^a to E^a(t)$. This result may be relevant to study the production of a non-perturbative quark-gluon plasma at RHIC and LHC.
LHC is expected to be a top quark factory. If the fundamental Planck scale is near a TeV, then we also expect the top quarks to be produced from black holes via Hawking radiation. In this paper we calculate the cross sections for top quark production
from black holes at the LHC and compare it with the direct top quark cross section via parton fusion processes at next-to-next-to-leading order (NNLO). We find that the top quark production from black holes can be larger or smaller than the pQCD predictions at NNLO depending upon the Planck mass and black hole mass. Hence the observation of very high rates for massive particle production (top quarks, higgs or supersymmetry) at the LHC may be an useful signature for black hole production.
