Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · hep-ph/0105311

Controlled nonperturbative dynamics of quantum fields out of equilibrium

J. Berges
View original source ↗Read source document ↗Export metadata ↓

Abstract

We compute the nonequilibrium real-time evolution of an O(N)-symmetric scalar quantum field theory from a systematic 1/N expansion of the 2PI effective action to next-to-leading order, which includes scattering and memory effects. In contrast to the standard 1/N expansion of the 1PI effective action, the next-to-leading order expansion in presence of a possible expectation value for the composite operator leads to a bounded time evolution where the truncation error may be controlled by higher powers in 1/N. We present a detailed comparison with the leading-order results and determine the range of validity of standard mean field type approximations. We investigate ``quench'' and ``tsunami'' initial conditions frequently used to mimic idealized far-from-equilibrium pion dynamics in the context of heavy-ion collisions. For spatially homogeneous initial conditions we find three generic regimes, characterized by an early-time exponential damping, a parametrically slow (power-law) behavior at intermediate times, and a late-time exponential approach to thermal equilibrium. The different time scales are obtained from a numerical solution of the time-reversal invariant equations in 1+1 dimensions without further approximations. We discuss in detail the out-of-equilibrium behavior of the nontrivial n-point correlation functions as well as the evolution of a particle number distribution and inverse slope parameter.

Explore related subjects

hep-phcond-mathep-lathep-thnucl-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

J. Berges. 2001-09-05. Controlled nonperturbative dynamics of quantum fields out of equilibrium. https://doi.org/10.1016/s0375-9474(01)01295-7

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Extraction of the pion-nucleon coupling constant using the effective-range expansion with the left-hand cut

We apply the generalized effective-range expansion of Phys. Rev. Lett. 135, 011903(2025), which incorporates the left-hand cut from one-pion exchange, to low-energy neutron-proton scattering in the $^1S_0$ and $^3S_1$ channels. The amplitude zero for the center-of-mass momentum near 0.35 GeV in the $^1S_0$ channel is naturally accommodated within this framework. We extract the pole position, scattering length, effective range, and the pseudoscalar pion-nucleon coupling constant $g_{πN}^2/(4π)$ at different expansion orders. The low-energy parameters are stable and consistent with established values, while $g_{πN}^2/(4π)$ exhibits larger uncertainties. The extraction of $g_{πN}^2/(4π)$ is data-driven, relying on the analytic constraints from the left-hand cut and phase-shift data within the one-pion-exchange approximation. Despite larger uncertainties compared to high-precision extractions, the consistency with established values demonstrates that this framework can probe the left-hand-cut singularity.

hep-ph↗
arXiv2026

True Leptonium ($l^+ l^-$) Production in UPC Triphoton Interaction

True leptonium states ($l^+ l^-$) are compact pure QED systems, first theoretically predicted eight decades ago. Although considerable efforts have been devoted to their search, only positronium has been experimentally confirmed shortly after its theoretical prediction. By contrast, dimuonium ($μ^+ μ^-$) and tauonium ($τ^+ τ^-$) remain unobserved to date, partly due to their low production yields. In this work, we investigate ortho-leptonium production through triphoton interactions in ultraperipheral heavy-ion collisions (UPCs). Two photons originate from different ions in one beam, while the third is supplied by an ion in the opposing beam. Within the equivalent photon approximation, we compare continuum dimuon and $J/ψ$ production with UPC measurements and evaluate ortho-leptonium production at the LHC and FCC. The results illustrate the possible role of triphoton fusion in leptonium production and the sensitivity of the calculated rates to the low-energy photon input.

hep-ph↗
arXiv2026

Semi-analytical two-loop QCD corrections to $e^+e^-\to J/ψ+χ_{cJ}$ at B factories

In this work, we compute the next-to-next-to-leading-order (NNLO) QCD corrections to the process $e^+e^-\to J/ψ+χ_{cJ}$ at B factories within the NRQCD factorization framework. The helicity amplitudes are obtained via asymptotic expansions around $r=0$ and $r=1$, with $r=16m_c^2/s$. Our asymptotic expressions reproduce the exact numerical results with high accuracy across the kinematic range $0\le r \le 1$, achieving a relative error below $10^{-5}$, which is sufficient for phenomenological applications. Notably, the large logarithmic terms are obtained analytically, and the explicit expressions established in this work provide a useful basis for further theoretical investigations. We compute the unpolarized cross sections. The $\mathcal{O}(α_s)$ correction is found to be large, while the $\mathcal{O}(α_s^2)$ correction for $χ_{c0}$ production amounts to $33\%$ of the leading-order (LO) cross section, significantly reducing the scale uncertainties. For $χ_{c1}$, the $\mathcal{O}(α_s)$ and $\mathcal{O}(α_s^2)$ corrections correspond to $35\%$ and $-15\%$, respectively. For $χ_{c2}$, the corresponding corrections are $24\%$ and $-38\%$. The large cancellation between the corrections for $χ_{c2}$ brings the NNLO cross section close to the LO prediction. Our prediction for $χ_{c0}$ is consistent with both the {\tt Belle} and {\tt BaBar} data within uncertainties. We also predict the angular distribution parameters $α^J_θ$, which are independent of nonperturbative inputs. A sharp discrepancy between the theory and the {\tt Belle} measurement is observed for $α^0_θ$, calling for further experimental and theoretical investigations. Moreover, future measurements of the angular distribution parameters for $χ_{c1}$ and $χ_{c2}$ will provide important tests of the theoretical framework.

hep-ph↗