Dynamical renormalization group approach to the Altarelli-Parisi-Lipatov equations

The Altarelli-Parisi-Lipatov equations for the parton distribution functions are rederived using the dynamical renormalization group approach to quantum kinetics. This method systematically treats the ln Q^2 corrections that arises in perturbation theory as a renormalization of the parton distribution function and unambiguously indicates that the strong coupling must be allowed to run with the scale in the evolution kernel. To leading logarithmic accuracy the evolution equation is Markovian and the logarithmic divergences in the perturbative expansion are identified with the secular divergences (terms that grow in time) that emerge in a perturbative treatment of the kinetic equations in nonequilibrium systems. The resummation of the leading logarithms by the Altarelli-Parisi-Lipatov equation is thus similar to the resummation of the leading secular terms by the Boltzmann kinetic equation.Comment: 8 pages, version to appear in Phys. Rev.

Non-Equilibrium Large N Yukawa Dynamics: marching through the Landau pole

The non-equilibrium dynamics of a Yukawa theory with N fermions coupled to a scalar field is studied in the large N limit with the goal of comparing the dynamics predicted from the renormalization group improved effective potential to that obtained including the fermionic backreaction. The effective potential is of the Coleman-Weinberg type. Its renormalization group improvement is unbounded from below and features a Landau pole. When viewed self-consistently, the initial time singularity does not arise. The different regimes of the dynamics of the fully renormalized theory are studied both analytically and numerically. Despite the existence of a Landau pole in the model, the dynamics of the mean field is smooth as it passes the location of the pole. This is a consequence of a remarkable cancellation between the effective potential and the dynamical chiral condensate. The asymptotic evolution is effectively described by a quartic upright effective potential. In all regimes, profuse particle production results in the formation of a dense fermionic plasma with occupation numbers nearly saturated up to a scale of the order of the mean field. This can be interpreted as a chemical potential. We discuss the implications of these results for cosmological preheating.Comment: 36 pages, 14 figures, LaTeX, submitted to Physical Review

Real-time nonequilibrium dynamics in hot QED plasmas: dynamical renormalization group approach

We study the real-time nonequilibrium dynamics in hot QED plasmas implementing a dynamical renormalization group and using the hard thermal loop (HTL) approximation. The focus is on the study of the relaxation of gauge and fermionic mean fields and on the quantum kinetics of the photon and fermion distribution functions. For semihard photons of momentum eT << k << T we find to leading order in the HTL that the gauge mean field relaxes in time with a power law as a result of infrared enhancement of the spectral density near the Landau damping threshold. The dynamical renormalization group reveals the emergence of detailed balance for microscopic time scales larger than 1/k while the rates are still varying with time. The quantum kinetic equation for the photon distribution function allows us to study photon production from a thermalized quark-gluon plasma (QGP) by off-shell effects. We find that for a QGP at temperature T ~ 200 MeV and of lifetime 10 < t < 50 fm/c the hard (k ~ T) photon production from off-shell bremsstrahlung (q -> q \gamma and \bar{q} -> \bar{q}\gamma) at O(\alpha) grows logarithmically in time and is comparable to that produced from on-shell Compton scattering and pair annihilation at O(\alpha \alpha_s). Fermion mean fields relax as e^{-\alpha T t ln(\omega_P t)} with \omega_P=eT/3 the plasma frequency, as a consequence of the emission and absorption of soft magnetic photons. A quantum kinetic equation for hard fermions is obtained directly in real time from a field theoretical approach improved by the dynamical renormalization group. The collision kernel is time-dependent and infrared finite.Comment: RevTeX, 46 pages, including 5 EPS figures, published versio

Large scale magnetogenesis from a non-equilibrium phase transition in the radiation dominated era

We study the generation of large scale primordial magnetic fields by a cosmological phase transition during the radiation dominated era. The setting is a theory of N charged scalar fields coupled to an abelian gauge field, that undergoes a phase transition at a critical temperature much larger than the electroweak scale. The dynamics after the transition features two distinct stages: a spinodal regime dominated by linear long-wavelength instabilities, and a scaling stage in which the non-linearities and backreaction of the scalar fields are dominant. This second stage describes the growth of horizon sized domains. We implement a recently introduced formulation to obtain the spectrum of magnetic fields that includes the dissipative effects of the plasma. We find that large scale magnetogenesis is very efficient during the scaling regime. The ratio between the energy density on scales larger than L and that in the background radiation r(L,T) = rho_B(L,T)/rho_{cmb}(T) is r(L,T) \sim 10^{-34} at the Electroweak scale and r(L,T) \sim 10^{-14} at the QCD scale for L \sim 1 Mpc. The resulting spectrum is insensitive to the magnetic diffusion length. We conjecture that a similar mechanism could be operative after the QCD chiral phase transition.Comment: LaTex, 25 pages, no figures, to appear in Phys. Rev.

Damping Rates and Mean Free Paths of Soft Fermion Collective Excitations in a Hot Fermion-Gauge-Scalar Theory

We study the transport coefficients, damping rates and mean free paths of soft fermion collective excitations in a hot fermion-gauge-scalar plasma with the goal of understanding the main physical mechanisms that determine transport of chirality in scenarios of non-local electroweak baryogenesis. The focus is on identifying the different transport coefficients for the different branches of soft collective excitations of the fermion spectrum. These branches correspond to collective excitations with opposite ratios of chirality to helicity and different dispersion relations. By combining results from the hard thermal loop (HTL) resummation program with a novel mechanism of fermion damping through heavy scalar decay, we obtain a robust description of the different damping rates and mean free paths for the soft collective excitations to leading order in HTL and lowest order in the Yukawa coupling. The space-time evolution of wave packets of collective excitations unambiguously reveals the respective mean free paths. We find that whereas both the gauge and scalar contribution to the damping rates are different for the different branches, the difference of mean free paths for both branches is mainly determined by the decay of the heavy scalar into a hard fermion and a soft collective excitation. We argue that these mechanisms are robust and are therefore relevant for non-local scenarios of baryogenesis either in the Standard Model or extensions thereof.Comment: REVTeX, 19 pages, 4 eps figures, published versio

Fermion Damping in a Fermion-Scalar Plasma

In this article we study the dynamics of fermions in a fermion-scalar plasma. We begin by obtaining the effective in-medium Dirac equation in real time which is fully renormalized and causal and leads to the initial value problem. For a heavy scalar we find the novel result that the decay of the scalar into fermion pairs in the medium leads to damping of the fermionic excitations and their in-medium propagation as quasiparticles. That is, the fermions acquire a width due to the decay of the heavier scalar in the medium. We find the damping rate to lowest order in the Yukawa coupling for arbitrary values of scalar and fermion masses, temperature and fermion momentum. An all-order expression for the damping rate in terms of the exact quasiparticle wave functions is established. A kinetic Boltzmann approach to the relaxation of the fermionic distribution function confirms the damping of fermionic excitations as a consequence of the induced decay of heavy scalars in the medium. A linearization of the Boltzmann equation near equilibrium clearly displays the relationship between the damping rate of fermionic mean fields and the fermion interaction rate to lowest order in the Yukawa coupling directly in real time.Comment: REVTEX, 16 pages, 3 eps figures included, published version. To be published in Phys. Rev.

Advances in perturbative thermal field theory

The progress of the last decade in perturbative quantum field theory at high temperature and density made possible by the use of effective field theories and hard-thermal/dense-loop resummations in ultrarelativistic gauge theories is reviewed. The relevant methods are discussed in field theoretical models from simple scalar theories to non-Abelian gauge theories including gravity. In the simpler models, the aim is to give a pedagogical account of some of the relevant problems and their resolution, while in the more complicated but also more interesting models such as quantum chromodynamics, a summary of the results obtained so far are given together with references to a few most recent developments and open problems.Comment: 84 pages, 18 figues, review article submitted to Reports on Progress in Physics; v2, v3: minor additions and corrections, more reference