arXiv subjects

Kalliopi Petraki

Publications and source records attributed to Kalliopi Petraki.

At least 19 recordsLinked to original sources

arXiv2026

Variable-phase methods and data for long-range scattering

Long-range interactions play an important role in dark-matter phenomenology, affecting the relic abundance, indirect-detection signals, and structure formation on galactic scales. Reliable predictions often require nonperturbative solutions of the Schrödinger equation over broad parameter ranges and many partial waves. We present a numerical framework based on the variable-phase method, which recasts the radial Schrödinger equation as a system of first-order equations and allows both regular and irregular solutions to be computed efficiently. The former determine phase shifts and Sommerfeld factors, while the latter provide additional information relevant for the self-consistent unitarization of contact-like inelastic interactions. We discuss the numerical implementation, integration-domain selection, partial-wave convergence, and comparisons with analytic limits. We release the code together with tables for the Yukawa potential containing phase shifts, Sommerfeld factors, elastic and angularly weighted cross sections, and the irregular-solution information relevant for unitarization. These resources facilitate dark-matter studies without requiring repeated computationally intensive scans.

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arXiv2026

Annihilation feedback on elastic scattering in self-interacting dark matter

Sizable dark-matter self-interactions, motivated by observations of galactic structure, often arise from the exchange of light force mediators. Light mediators can render scattering nonperturbative and make inelastic processes important. Unitarity, via the optical theorem, implies that elastic and inelastic interactions cannot be treated independently: inelasticity induces absorptive contributions to the two-particle self-energy kernel that determines the elastic amplitude, while the resulting incoming-state dynamics also modifies the inelastic amplitudes. We study the feedback of dark-matter annihilation on elastic scattering in the presence of a long-range force. Although annihilation is a short-distance process, it can be strongly enhanced by such a force. We find that its feedback becomes significant near Sommerfeld resonances, where it suppresses the low-velocity growth of the baseline elastic cross section. Near baseline elastic-scattering zeros, it may instead generate a nonzero elastic floor required by unitarity. A companion paper studies the feedback of radiative bound-state formation on elastic scattering, which can generate sizable self-interactions.

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arXiv2026

Self-interacting dark matter from radiative bound-state-formation feedback

Observations of galactic structure motivate sizable dark-matter self-interactions at low velocities, naturally realized through light force mediators. Such mediators can also make inelastic processes very efficient. Unitarity then requires their absorptive contributions to the two-particle self-energy kernel to be resummed, which in turn feeds back into both the elastic and inelastic scattering amplitudes. We study the feedback of radiative bound-state formation on elastic scattering and its implications for self-interacting dark matter. We focus on capture processes through emission of a charged scalar; such transitions are particularly efficient because the scattering and bound states are governed by different effective potentials, a feature also shared by radiative capture through emission of a non-Abelian gauge boson. We show that their feedback can generate sizable elastic scattering relevant for halo dynamics, even when the baseline elastic amplitude vanishes. Notably, the generated elastic cross section can grow toward low velocities, resembling long-range scattering. A companion paper examines the feedback from annihilation processes.

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arXiv2026

Unitarity violation and restoration in radiative bound-state formation

State-of-the-art calculations motivated by dark matter exhibit severe violation of partial-wave unitarity in the non-relativistic regime in radiative bound-state-formation processes. It has been recently shown, in a model-independent fashion, that unitarity is restored by the proper resummation of the inelastic contributions to the self-energy of the incoming state. In this work, we first derive Kramers-like formulae for individual partial waves, demonstrating that existing calculations of bound-state formation severely violate unitarity. We then discuss how unitarity is restored through the resummation of the absorptive contributions to the incoming-state self-energy, generated by bound-state formation processes, taking into account their analytic structure in the complex momentum plane. Our results can be generalized to a variety of theories and employed in phenomenological studies, such as dark-matter freeze-out, indirect detection and self-interactions.

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arXiv2026

Unitarizing non-relativistic scattering

Unitarity imposes coupled constraints on elastic and inelastic amplitudes. Satisfying them requires resummation of the self-energy contributions from both elastic and inelastic channels. Inelastic channels generate anti-Hermitian contributions that can be consistently deduced from the unitarity relation underlying the optical theorem, leading to non-local separable potentials and a compact, unique and complete unitarization scheme in the non-relativistic regime. We present two alternative derivations of the anti-Hermitian kernel, from the continuity equation combined with LSZ reduction, and by integrating out inelastic channels. We further extend the unitarization framework to treat non-analytic and non-convergent behavior of inelastic amplitudes in the complex momentum plane and to incorporate bound states. For non-convergent amplitudes, we demonstrate two renormalization procedures in which anti-Hermitian separable potentials necessarily induce Hermitian separable counterterms, yielding finite cross-sections consistent with unitarity. These results provide a general tool for non-relativistic scattering, with clear applications to dark-matter phenomenology.

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arXiv2025

The role of unitarisation on dark-matter freeze-out via metastable bound states

In many Abelian and non-Abelian theories, standard calculations of radiative bound-state formation violate partial-wave unitarity - even at arbitrarily small couplings - when capture into excited states is considered. Recent work demonstrated that unitarity can be restored by the proper resummation of squared inelastic processes in the self-energy of the incoming state. We examine how unitarisation affects dark-matter thermal decoupling, given that the formation and decay of metastable dark-matter bound states are critical in determining the relic abundance, especially for multi-TeV dark matter. We consider an Abelian model featuring bound-state formation via emission of a light scalar that carries a conserved charge, whose dynamics also emulates relevant aspects of non-Abelian theories. Incorporating capture into excited states, we show that, without proper treatment, unitarity violation is so severe as to prevent freeze-out. Resumming the squared bound-state formation processes restores unitarity and ensures freeze-out, while capture into excited levels still significantly depletes dark matter. We further discuss the impact of higher partial waves, both within and beyond the present model. Finally, we point out the intriguing possibility of late dark-matter decoupling that can affect structure formation.

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arXiv2025

Critical and super-critical scatterings in baryogenesis and leptogenesis

In many theories, matter-antimatter asymmetries originate from out-of-equilibrium decays and scatterings of heavy particles. While decays remain efficient, scattering rates typically drop below the Hubble rate as the universe expands. We point out the possibility of scatterings between non-relativistic particles and the relativistic bath whose cross-sections grow with decreasing temperature, leading to scattering rates that track or exceed the Hubble rate at late times. This results in soaring asymmetry generation, even at low scales and with small CP- or baryon/lepton-violating couplings.

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arXiv2024

Unitarity in the non-relativistic regime and implications for dark matter

Unitarity sets upper limits on partial-wave elastic and inelastic cross-sections, which are often violated by perturbative computations. We discuss the dynamics underlying these limits in the non-relativistic regime, namely long-range interactions, and show how the resummation of the 2-particle-irreducible diagrams arising from squaring inelastic processes unitarizes both elastic and inelastic cross-sections. We provide a simple prescription to obtain the unitarized cross-sections from those that do not include resummation of the squared inelastic processes. Our results are model-independent, apply to all partial waves, and affect elastic and inelastic cross-sections, with extensive implications for new physics scenarios, such as dark-matter freeze-out, indirect detection and self-interactions.

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arXiv2024

Radiation back-reaction during dark-matter freeze-out via metastable bound states

The formation and decay of metastable bound states can deplete significantly the density of multi-TeV thermal-relic dark matter. The effect depends on the interplay of bound-state formation, ionisation, transition and decay processes. Existing calculations take into account bound-state ionisation and excitations due to the radiation of the thermal bath. However, the dynamics of Hydrogen recombination suggests that the resonant radiation produced in bound-state formation or de-excitations may backreact, ionising or exciting the bound states thus impeding recombination. In this paper we examine this effect in the context of dark-matter freeze-out. To this end, we employ the generalised Saha equilibrium equation for metastable bound states, and discuss its salient features. We show that, in sharp contrast to Hydrogen recombination, the radiation produced during dark matter freeze-out is more likely to thermalise or redshift, rather than ionise or excite the metastable bound states. This holds not only for the low-energy (resonant) radiation produced in bound-state formation and transition processes, but also for the high-energy radiation produced in dark-matter annihilations and bound-state decays. While our computations are carried out in a minimal dark $U(1)$ model, our conclusions only strengthen in more complex models.

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arXiv2023

Baryogenesis from ultra-slow-roll inflation

The ultra-slow-roll (USR) inflation represents a class of single-field models with sharp deceleration of the rolling dynamics on small scales, leading to a significantly enhanced power spectrum of the curvature perturbations and primordial black hole (PBH) formation. Such a sharp transition of the inflationary background can trigger the coherent motion of scalar condensates with effective potentials governed by the rolling rate of the inflaton field. We show that a scalar condensate carrying (a combination of) baryon or lepton number can achieve successful baryogenesis through the Affleck-Dine mechanism from unconventional initial conditions excited by the USR transition. Viable parameter space for creating the correct baryon asymmetry of the Universe naturally incorporates the specific limit for PBHs to contribute significantly to dark matter, shedding light on the cosmic coincidence problem between the baryon and dark matter densities today.

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arXiv2022

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

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.

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arXiv2021

Bound states of WIMP dark matter in Higgs-portal models. Part I. Cross-sections and transition rates

We investigate the role of the Higgs \emph{doublet} in the thermal decoupling of multi-TeV dark matter coupled to the Weak interactions of the Standard Model and the Higgs. The Higgs doublet can mediate a long-range force that affects the annihilation processes and binds dark matter into bound states. More importantly, the emission of a Higgs doublet by a pair of dark matter particles can give rise to extremely rapid monopole bound-state formation processes and bound-to-bound transitions. We compute these effects in the unbroken electroweak phase. To this end, we consider the simplest renormalisable fermionic model, consisting of a singlet and a doublet under $SU_{L}(2)$ that are stabilised by a $\mathbb{Z}_2$ symmetry, in the regime where the two multiplets coannihilate. In a companion paper, we use the results to show that the formation of metastable bound states via Higgs-doublet emission and their decay decrease the relic density very significantly.

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arXiv2021

Bound states of WIMP dark matter in Higgs-portal models. Part II. Thermal decoupling

The Higgs doublet can mediate a long-range interaction between multi-TeV particles coupled to the Weak interactions of the Standard Model, while its emission can lead to very rapid bound-state formation processes and bound-to-bound transitions. Using the rates calculated in a companion paper, here we compute the thermal decoupling of multi-TeV WIMP dark matter coupled to the Higgs, and show that the formation of metastable dark matter bound states via Higgs-doublet emission and their decay decrease the relic density very significantly. This in turn implies that WIMP dark matter may be much heavier than previously anticipated, or conversely that for a given mass, the dark matter couplings to the Higgs may be much lower than previously predicted, thereby altering the dark matter phenomenology. While we focus on a minimal singlet-doublet model in the coannihilation regime, our calculations can be extended to larger multiplets where the effects under consideration are expected to be even more significant.

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arXiv2021

Stochastic Baryogenesis

Using a multi-field stochastic approach, we investigate the vacuum expectation value (VEV) during inflation of a scalar field charged under a mildly broken global $U(1)$ symmetry that can play the role of baryon or lepton number, or possibly a dark baryon number or a combination of the three. Even for a CP invariant Lagrangian, the stochastic distribution of inflationary VEVs in general breaks CP spontaneously, allowing for successful baryogenesis via the Affleck-Dine mechanism. For the Hubble scale during inflation $H_\ast$ as high as $10^{13}$ GeV, we show that the post-inflationary relaxation of the charged scalar with stochastic initial conditions can explain the observed baryon asymmetry, and that a charged scalar mass at the order of $H_\ast$ is favored by the isocurvature constraints.

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arXiv2020

Indirect searches for dark matter bound state formation and level transitions

Indirect searches for dark matter (DM) have conventionally been applied to the products of DM annihilation or decay. If DM couples to light force carriers, however, it can be captured into bound states via dissipation of energy that may yield detectable signals. We extend the indirect searches to DM bound state formation and transitions between bound levels, and constrain the emission of unstable dark photons. Our results significantly refine the predicted signal flux that could be observed in experiments. As a concrete example, we use Fermi-LAT dwarf spheroidal observations to obtain constraints in terms of the dark photon mass and energy which we use to search for the formation of stable or unstable bound states.

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arXiv2020

Dark matter bound state formation via emission of a charged scalar

The formation of stable or meta-stable bound states can dramatically affect the phenomenology of dark matter (DM). Although the capture into bound states via emission of a vector is known to be significant, the capture via scalar emission suffers from cancellations that render it important only within narrow parameter space. While this is true for neutral scalar mediators, here we show that bound-state formation via emission of a charged scalar can be extremely significant. To this end, we consider DM charged under a dark $U(1)$ force and coupled also to a light complex scalar that is charged under the same gauge symmetry. We compute the cross-sections for bound-state formation via emission of the charged scalar, and show that they can exceed those for capture via vector emission, as well as annihilation, by orders of magnitude. This holds even for very small values of the DM coupling to the charged scalar, and remains true in the limit of global symmetry. We then compute the DM thermal freeze-out, and find that the capture into meta-stable bound states via emission of a charged scalar can cause a late period of significant DM depletion. Our results include analytical expressions in the Coulomb limit, and are readily generalisable to non-Abelian interactions. We expect them to have implications for Higgs-portal scenarios of multi-TeV WIMP DM, as well as scenarios that feature dark Higgses or (darkly-)charged inert scalars, including models of self-interacting DM.

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arXiv2019

Rapid bound-state formation of Dark Matter in the Early Universe

The thermal decoupling description of dark matter (DM) and co-annihilating partners is reconsidered. If DM is realized at around the TeV-mass region or above, even the heaviest electroweak force carriers could act as long-range forces, leading to the existence of meta-stable DM bound states. The formation and subsequent decay of the latter further deplete the relic density during the freeze-out process on top of the Sommerfeld enhancement, allowing for larger DM masses. While so far the bound-state formation was described via the emission of an on-shell mediator ($W^{\pm}$, $Z$, $H$, $g$, photon or exotic), we point out that this particular process does not have to be the dominant scattering-bound state conversion channel in general. If the mediator is coupled in a direct way to any relativistic species present in the Early Universe, the bound-state formation can efficiently occur through particle scattering, where a mediator is exchanged virtually. To demonstrate that such a virtually stimulated conversion process can dominate the on-shell emission even for all temperatures, we analyze a simplified model where DM is coupled to only one relativistic species in the primordial plasma through an electroweak-scale mediator. We find that the bound-state formation cross section via particle scattering can exceed the on-shell emission by up to several orders of magnitude.

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arXiv2019

Higgs-mediated bound states in dark-matter models

It has been recently demonstrated that the 125 GeV Higgs boson can mediate a long-range force between TeV-scale particles, that can impact considerably their annihilation due to the Sommerfeld effect, and hence the density of thermal relic dark matter. In the presence of long-range interactions, the formation and decay of particle-antiparticle bound states can also deplete dark matter significantly. We consider the Higgs boson as mediator in the formation of bound states, and compute the effect on the dark matter abundance. To this end, we consider a simplified model in which dark matter co-annihilates with coloured particles that have a sizeable coupling to the Higgs. The Higgs-mediated force affects the dark matter depletion via bound state formation in several ways. It enhances the capture cross-sections due to the attraction it mediates between the incoming particles, it increases the binding energy of the bound states, hence rendering their ionisation inefficient sooner in the early universe, and for large enough couplings, it can overcome the gluon repulsion of certain colour representations and give rise to additional bound states. Because it alters the momentum exchange in the bound states, the Higgs-mediated force also affects the gluon-mediated potential via the running of the strong coupling. We comment on the experimental implications and conclude that the Higgs-mediated potential must be taken into account when circumscribing the viable parameter space of related models.

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