Tobias Binder

Bio: Tobias Binder is an academic researcher from Institute for the Physics and Mathematics of the Universe. The author has contributed to research in topics: Dark matter & Bound state. The author has an hindex of 4, co-authored 9 publications receiving 58 citations. Previous affiliations of Tobias Binder include University of Tokyo.

Rapid Bound State Formation of Dark Matter in the Early Universe

Abstract: The formation and decay of dark matter (DM) bound states deplete the thermal relic density during the chemical decoupling process, allowing for larger DM masses. While so far the bound state formation (BSF) has been described via the emission of an on-shell mediator, we point out that this particular process does not have to be the dominant one in general. If the mediator is coupled in a direct way to any relativistic species present in the early Universe, we demonstrate that BSF can much more efficiently occur through particle scattering. Consequently, DM can be heavier than previously expected.

Dark matter bound-state formation at higher order: a non-equilibrium quantum field theory approach

Abstract: The formation of meta-stable dark matter bound states in coannihilating scenarios could efficiently occur through the scattering with a variety of Standard Model bath particles, where light bosons during the electroweak cross over or even massless photons and gluons are exchanged in the t-channel. The amplitudes for those higher-order processes, however, are divergent in the collinear direction of the in- and out-going bath particles if the mediator is massless. To address the issue of collinear divergences, we derive the bound-state formation collision term in the framework of non-equilibrium quantum field theory. The main result is an expression for a more general cross section, which allows to compute higher-order bound-state formation processes inside the primordial plasma background in a comprehensive manner. Based on this result, we show that next-to-leading order contributions, including the bath-particle scattering, are i) collinear finite and ii) generically dominate over the on-shell emission for temperatures larger than the absolute value of the binding energy. Based on a simplified model, we demonstrate that the impact of these new effects on the thermal relic abundance is significant enough to make it worthwhile to study more realistic coannihilation scenarios.

Dark matter relic abundance beyond kinetic equilibrium

Abstract: We introduce DRAKE, a numerical precision tool for predicting the dark matter relic abundance also in situations where the standard assumption of kinetic equilibrium during the freeze-out process may not be satisfied. DRAKE comes with a set of three dedicated Boltzmann equation solvers that implement, respectively, the traditionally adopted equation for the dark matter number density, fluid-like equations that couple the evolution of number density and velocity dispersion, and a full numerical evolution of the phase-space distribution. We review the general motivation for these approaches and, for illustration, highlight three concrete classes of models where kinetic and chemical decoupling are intertwined in a way that quantitatively impacts the relic density: (i) dark matter annihilation via a narrow resonance, (ii) Sommerfeld-enhanced annihilation and (iii) ‘forbidden’ annihilation to final states that are kinematically inaccessible at threshold. We discuss all these cases in some detail, demonstrating that the commonly adopted, traditional treatment can result in an estimate of the relic density that is wrong by up to an order of magnitude. The public release of DRAKE, along with several examples of how to calculate the relic density in concrete models, is provided at drake.hepforge.org

Non-Abelian Electric Field Correlator at NLO for Dark Matter Relic Abundance and Quarkonium Transport

Abstract: We perform a complete next-to-leading order calculation of the non-Abelian electric field correlator in a SU($N_c$) plasma, which encodes properties of the plasma relevant for heavy particle bound state formation and dissociation. The calculation is carried out in the real-time formalism of thermal field theory and includes both vacuum and finite temperature contributions. By working in the $R_\xi$ gauge, we explicitly show the results are gauge independent, infrared and collinear safe. The previous results on the renormalization of the electric field correlator are also confirmed. Our next-to-leading order calculation can be directly applied to any dipole singlet-adjoint transition of heavy particle pairs. For example, it can be used to describe dissociation and (re)generation of heavy quarkonia inside the quark-gluon plasma well below the melting temperature, as well as heavy dark matter pairs (or charged co-annihilating partners) in the early universe.

Saha equilibrium for metastable bound states and dark matter freeze-out.

Abstract: The formation and decay of metastable bound states can significantly decrease the thermal-relic dark matter density, particularly for dark matter masses around and above the TeV scale. Incorporating bound-state effects in the dark matter thermal decoupling requires in principle a set of coupled Boltzmann equations for the bound and unbound species. However, decaying bound states attain and remain in a quasi-steady state. Here we prove in generality that this reduces the coupled system into a single Boltzmann equation of the standard form, with an effective cross-section that describes the interplay among bound-state formation, ionisation, transitions and decays. We derive a closed-form expression for the effective cross-section for an arbitrary number of bound states, and show that bound-to-bound transitions can only increase it. Excited bound levels may thus decrease the dark matter density more significantly than otherwise estimated. Our results generalise the Saha ionisation equilibrium to metastable bound states, potentially with applications beyond the dark matter thermal decoupling.

On the theory of superconductivity

Abstract: IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

Theory of the many-particle systems.

Abstract: This is the first of a series of papers dealing with many-particle systems from a unified, nonperturbative point of view. It contains derivations and discussions of various field-theoretical techniques which will be applied in subsequent papers, In a short introduction the general method of approach is summarized, and its relationship to other field-theoretic problems indicated. In the second section the macroscopic properties of the spectra of many-particle systems are described. Asymptotic evaluations are performed which characterize these macroscopic features in terms of intensive parameters, and the relationship of these parameters to thermodynamics is discussed. The special characteristics of the ground state are shown to follow as a limiting case of the asymptotic evaluations. The third section is devoted to the time-dependent field correlation functions, or Green's functions, which describe the microscopic behavior of a multiparticle system. These functions are defined, and related to intensive macroscopic variables when the energy and number of particles are large. Spectral representations and other properties of various one-particle Green's functions are derived. In the fourth section the treatment of nonequilibrium processes is considered. As a particular example, the electromagnetic properties of a system are expressed in ternis of the special two-particle Green's function which describes current correlation. The discussion yields specifically a Quctuation-dissipation theorem, a sum rule for conductivity, and certain dispersion relations. The fifth section deals with the differential equations which determine the Green's functions. The boundary conditions that characterize the Green's function equations are exhibited without reference to adiabatic decoupling. A niethod for solving the equations approximately, by treating the correlations among successively larger numbers of particles, is considered. The first approximation in this sequence is shown to yield a generalized Hartree-like equation. A related, but rigorous, identity for the single-particle Green s function is then derived. A second approximation, which takes certain two-particle correlations into account, is shown to produce various additional e8ects: The interaction between particles is altered in a manner characterized by the intensive macroscopic parameters, and the modification and spread of the energy-momentum relation come into play. In the final section compact formal expressions for the Green*s functions and other physical quantities are derived. Alternative equations and systematic approximations for the Green's functions are obtained.

Non‐perturbative Effect on Thermal Relic Abundance of Dark Matter

Abstract: We point out that thermal relic abundance of dark matter is strongly altered by a non‐perturbative effect called the Sommerfeld enhancement, when constituent particles of the dark matter are SU(2)L non‐singlet and much heavier than the weak gauge bosons. Typical candidates are the heavy wino and higgsino. We investigate the non‐perturbative effect on the relic abundance of dark matter for the wino as an example. We show that its thermal abundance is reduced by 50% compared to the perturbative result. The wino mass consistent with the observed dark matter abundance turns out to be 2.7 TeV

An alternative view.

Abstract: I disagree with the view Sally Haslett presented (Nursing Standard week ending April 23) of practice nurses in [Illegible word] efforts to promote her app[Illegible word], to save district health authority family planning clinics!

Precise WIMP Dark Matter Abundance and Standard Model Thermodynamics

Abstract: A weakly interacting massive particle (WIMP) is a leading candidate of the dark matter. The WIMP dark matter abundance is determined by the freeze-out mechanism. Once we know the property of the WIMP particle such as the mass and interaction, we can predict the dark matter abundance. There are, however, several uncertainties in the estimation of the WIMP dark matter abundance. In this work, we focus on the effect from Standard Model thermodynamics. We revisit the estimation of the WIMP dark matter abundance and its uncertainty due to the equation of state (EOS) in the Standard Model. We adopt the up-to-date estimate of the EOS of the Standard Model in the early Universe and find nearly 10% difference in the 1–1000 GeV dark matter abundance, compared to the conventional estimate of the EOS.