Sebastian M. Schmidt

A Quantum kinetic equation for particle production in the Schwinger mechanism

A quantum kinetic equation has been derived for the description of pair production in a time-dependent homogeneous electric field

Pair production and optical lasers.

E(t)

Pion electromagnetic form factor at spacelike momenta

. As a source term, the Schwinger mechanism for particle creation is incorporated. Possible particle production due to collisions and collisional damping are neglected. The main result is a closed kinetic equation of the non-Markovian type. In the low density approximation, the source term is reduced to the leading part of the well known Schwinger formula for the probability of pair creation. We compare the formula obtained with other approaches and discuss the differences.

Valence-quark distributions in the pion

Electron-positron pair creation in a standing wave is explored using a parameter-free quantum kinetic equation. Field strengths and frequencies corresponding to modern optical lasers induce a material polarization of the QED vacuum, which may be characterized as a plasma of e+e- quasiparticle pairs with a density of approximately 10(20) cm-3. The plasma vanishes almost completely when the laser field is zero, leaving a very small residual pair density n(r) which is the true manifestation of vacuum decay. The average pair density per period is proportional to the laser intensity but independent of the frequency nu. The density of residual pairs also grows with laser intensity but n(r) proportional to nu(2). With optical lasers at the forefront of the current generation, these dynamical QED vacuum effects can plausibly generate 5-10 observable two-photon annihilation events per laser pulse.

Pair creation: Back reactions and damping

A novel method is employed to compute the pion electromagnetic form factor, F(π)(Q²), on the entire domain of spacelike momentum transfer using the Dyson-Schwinger equation (DSE) framework in QCD. The DSE architecture unifies this prediction with that of the pions valence-quark parton distribution amplitude (PDA). Using this PDA, the leading-order, leading-twist perturbative QCD result for Q²F(π)(Q²) underestimates the full computation by just 15% on Q²≳8 GeV², in stark contrast to the result obtained using the asymptotic PDA. The analysis shows that hard contributions to the pion form factor dominate for Q²≳8 GeV², but, even so, the magnitude of Q²F(π)(Q²) reflects the scale of dynamical chiral symmetry breaking, a pivotal emergent phenomenon in the standard model.

A DYNAMICAL, CONFINING MODEL AND HOT QUARK STARS

We calculate the pions valence-quark momentum-fraction probability distribution using a Dyson-Schwinger equation model. Valence quarks with an active mass of 0.30 GeV carry 71% of the pions momentum at a resolving scale q{sub 0}=0.54 GeV=1/(0.37 fm). The shape of the calculated distribution is characteristic of a strongly bound system and, evolved from q{sub 0} to q=2 GeV, it yields first, second, and third moments in agreement with lattice and phenomenological estimates, and valence-quarks carrying 49% of the pions momentum. However, pointwise there is a discrepancy between our calculated distribution and that hitherto inferred from parametrizations of extant pion-nucleon Drell-Yan data.

Non-Markovian effects in strong-field pair creation

We solve the quantum Vlasov equation for fermions and bosons, incorporating spontaneous pair creation in the presence of back reactions and collisions. Pair creation is initiated by an external impulse field and the source term is non-Markovian. A simultaneous solution of Maxwells equation in the presence of feedback yields an internal current and electric field that exhibit plasma oscillations with a period {tau}{sub pl}. Allowing for collisions, these oscillations are damped on a time scale {tau}{sub r} determined by the collision frequency. Plasma oscillations cannot affect the early stages of the formation of a quark-gluon plasma unless {tau}{sub r}>>{tau}{sub pl} and {tau}{sub pl}{approx}1/{lambda}{sub QCD}{approx}1 fm/c. (c) 1999 The American Physical Society.

Deconfinement at finite chemical potential.

Abstract We explore the consequences of an equation of state (EOS) obtained in a confining Dyson–Schwinger equation model of QCD for the structure and stability of nonstrange quark stars at finite- T , and compare the results with those obtained using a bag-model EOS. Both models support a temperature profile that varies over the stars volume and the consequences of this are model independent. However, in our model the analogue of the bag pressure is ( T , μ )-dependent, which is not the case in the bag model. This is a significant qualitative difference and comparing the results effects a primary goal of elucidating the sensitivity of quark star properties to the form of the EOS.

Sketching the pion's valence-quark generalised parton distribution

We analyze a quantum kinetic equation describing both boson and fermion pair production and explore analytically and numerically the solution of the non-Markovian kinetic equation. In the Markovian limit of the kinetic equation we find an analytical solution for the single particle distribution function of bosons and fermions. The numerical investigation for a homogeneous, constant electric field shows an enhancement (bosons) or a suppression (fermions) of the pair creation rate according to the symmetry character of the produced particles. For strong fields non-Markovian effects are important while they disappear for weak fields. Hence it is sufficient to apply the low density limit for weak fields but necessary to take into account memory effects for strong fields.

Practical corollaries of transverse Ward-Green-Takahashi identities

Abstract In a confining, renormalisable, Dyson-Schwinger equation model of two-flavour QCD we explore the chemical-potential dependence of the dressed-quark propagator, which provides a means of determining the behaviour of the chiral and deconfinement order parameters, and low-energy pion observables. We find coincident, first order deconfinement and chiral symmetry restoration transitions at μ c =375 MeV. fπ is insensitive to μ until μ≈μ 0 :=0.7 μ c when it begins to increase rapidly. mπ is weakly dependent on μ, decreasing slowly with μ and reaching a minimum 6% less than its μ=0 value at μ=μ0. In a two-flavour free-quark gas at μ=μc the baryon number density would be approximately 3 ρ 0 , where ρ 0 =0.16 fm −3 ; while in such a gas at μ0 the density is ρ0.