When a pair of dark matter particles interacts via a long-range force mediated by a light particle, their nonrelativistic annihilation cross section can be significantly enhanced — a phenomenon known as the Sommerfeld enhancement. This enhancement exhibits resonant behavior if the long-range potential supports shallow bound states or narrow resonances, which can lead to violations of the partial-wave unitarity bound. We identify the origin of this pathological behavior as the emergence of secular terms in perturbative expansions associated with low-energy composite states of the long-range potential. To address this issue, we propose a renormalization group improvement of the perturbative series. The resulting improved amplitude provides a unitarity-consistent form of the Sommerfeld enhancement, with its poles acquiring an imaginary part that reflects the decay width of the annihilating bound states. We also briefly discuss the implications of our approach from the perspective of Wilsonian renormalization group, and comment on its potential application to higher-order annihilation processes such as bound-state formation.

Japan

Yuki Watanabe

Unitarization of the Sommerfeld enhancement through the renormalization group

We explore the indirect detection of sterile neutrino dark matter within the gauged U(1) extension of the Standard Model, in which three right-handed neutrinos account for neutrino masses, the baryon asymmetry, and dark matter. Focusing on the MeV mass range, we investigate two decay channels: the radiative decay $\textit{N}$ → $\textit{νγ}$, which produces a monochromatic photon, and the three-body decay $\textit{N}$ → $\textit{e}$ $\textit{e}$ $\textit{ν}$, which leads to a 511 keV photon signal from positronium decay. Taking the upcoming COSI mission as a case study, we show that both signals are experimentally accessible and complementary, with the 511 keV channel extending the sensitivity reach up to $$\mathcal{O}(100)$$ MeV. We propose a novel analysis strategy in Compton data space to isolate the diffuse 511 keV emission. Furthermore, we incorporate, for the first time, the Sommerfeld enhancement in the decay width of $\textit{N}$ → $\textit{e}$ $\textit{e}$ $\textit{ν}$, enabling more accurate predictions of the signal near the kinematic threshold. The combined observation of both channels would provide a distinctive and testable signature of the sterile neutrino dark matter hypothesis.

Subaru Fujisawa

Tatsuya Hayashi

Shigeki Matsumoto

Detecting sterile neutrino dark matter at MeV gamma-ray observatories

The stochastic dynamics of a scalar field in de Sitter space-time can be regarded as a nonperturbative diffusion process, for which exact distribution and correlation functions are constructed by utilizing the correspondence between diffusion and Schrödinger equations. The Krein–Adler transformation of the quantum harmonic oscillator deletes several pairs of the energy levels to define anharmonic oscillators that we dub quantum deficient oscillators, based on which this article constructs a new class of exact solutions in stochastic inflation. In addition to the simplest single-well model, an exactly solvable double-well model is also presented. The results are further extended to exactly solvable models with multiple wells, allowing analytical studies on various cosmological phenomenologies.

Yuta Nasuda

Koki Tokeshi

Scalar Field Stochastic Dynamics in de Sitter Space-time from Exact Solutions of Quantum Deficient Oscillators

Sub-GeV dark matter (DM) has been attracting more attention due to the negative results searching for traditional weakly interacting massive particles (WIMPs). Such particles are expected to produce gamma rays from annihilation in the MeV energy region. Advancements in technology have opened up possibilities to precisely detect MeV gamma rays, leading to the upcoming space-based mission of the Compton Spectrometer and Imager (COSI). We comprehensively and quantitatively study the phenomenology of sub-GeV DM to determine if the COSI observations will probe their viable model parameter regions. We first construct models to describe sub-GeV DM based on the minimality and renormalizability of quantum field theory. Next, we impose various constraints on the models obtained from cosmological observations (CMB, BBN) and DM searches (accelerator, underground, astrophysical experiments, etc.). Finally, we identify viable parameter regions in each model and discuss whether or not COSI will be sensitive to the parameter regions. We find that a velocity-dependent annihilation cross-section is predicted in some regions, enabling COSI to detect the DM signal while avoiding severe constraints from cosmological observations.

Yu Watanabe

United States

Christopher Karwin

Tom Melia

Michela Negro

Germany

Thomas Siegert

Hiroki Yoneda

Tadayuki Takahashi

Sub-GeV dark matter and MeV gamma-ray detection with COSI

<p>The new gauge boson introduced in the minimal extension of the standard model (SM) by gauging the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">B</mi><mo>−</mo><mi mathvariant="normal">L</mi></mrow></msub></mrow></math> symmetry plays the role of dark matter when the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">B</mi><mo>−</mo><mi mathvariant="normal">L</mi></mrow></msub></mrow></math> gauge coupling is highly suppressed. This dark matter, named the Féeton dark matter is known to be efficiently created in the early Universe by inflationary fluctuations with minimal gravity coupling, hence the framework, the gauged <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">B</mi><mo>−</mo><mi mathvariant="normal">L</mi></mrow></msub></mrow></math> extended <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SM</mi><mo>+</mo><mtext>inflation</mtext></mrow></math>, solves the four major problems of the SM; neutrino masses/mixings, dark matter, baryon asymmetry of the Universe, and the initial condition of the Universe (inflation). We comprehensively study the phenomenology of the dark matter when it is heavier than the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup></math> threshold, namely twice the electron mass, considering the threshold effect on the dark matter decay into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup></math>. The viable parameter region is found only in the threshold region, while the branching fraction of the decay into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup></math> (i.e., the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup></math> signal) never vanishes even at the threshold due to the effect. As a result, the pure <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">B</mi><mo>−</mo><mi mathvariant="normal">L</mi></mrow></msub></mrow></math> extension without the kinetic mixing between the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">B</mi><mo>−</mo><mi mathvariant="normal">L</mi></mrow></msub></mrow></math> and hypercharge gauge bosons have already been excluded by the present observation of the 511 keV photon from the galactic center. So, the Féeton dark matter requires a nonzero kinetic mixing to be a viable dark matter candidate and will be efficiently explored by future MeV-gamma ray telescopes thanks to the nonvanishing decay process into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup></math>.</p>

China

Tsutomu T. Yanagida

Gauge <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">B</mi><mo>−</mo><mi mathvariant="normal">L</mi></mrow></msub></mrow></math> dark matter above the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup></math> threshold

The decay of the mediator particle into standard model (SM) particles plays a significant role in exploring the dark sector scenario. We consider such a decay, taking the dark photon mediator as an example that mixes with the SM photon. We find that it requires a careful analysis of the decay rate in the presence of an SM vector boson (e.g., $\textit{Z}$ boson, $\textit{ρ}$ meson, and true muonium, etc.) nearly degenerate with the mediator particle in mass. The decay rate of the mediator particle calculated in the mass eigenstate basis agree with the correct result, given by the imaginary parts of the poles for the vector boson propagators, when the mixing parameter is smaller than a specific value. In such a case, the decay rate calculated by treating the mixing as a perturbative parameter is in agreement with the correct result. We clarify specific values for the mixing parameter quantitatively using several concrete examples of the SM vector bosons degenerate with the dark photon. When the mass mixing between the vector boson and dark photon is smaller (larger) than the decay width of the vector boson, the latter (former) method to calculate the decay rate of the mediator particle gives the correct result.

Poland

Ayuki Kamada

Takumi Kuwahara

Mediator decay through mixing with degenerate spectrum

A light mediator particle is often predicted in the dark sector scenario, which weakly interacts with the standard model (SM) particles. The weakness of the interaction is usually described by a small coupling; however, the small coupling does not always guarantee the weakness of the interaction. When the mass of the mediator particle lies in a threshold region, the so-called threshold singularity may emerge, and then the perturbative calculation fails. This singularity causes several effects, e.g., the mixing between the mediator particle and bound states, the Sommerfeld effect on the final state of the mediator particle decay, etc. Taking the minimal model of the vector mediator particle decaying mainly into the SM particles as an example, we develop a method to describe the singularity quantitatively. We also calculate some physical quantities using this method, such as the lifetime of the mediator particle and find that those could be significantly altered compared with the result of the perturbative calculation.

Graham White

Decay of the mediator particle at threshold

The cosmic history before the BBN is highly determined by the physics that operates beyond the Standard Model (BSM) of particle physics and it is poorly constrained observationally. Ongoing and future precision measurements of the CMB observables can provide us with significant information about the pre-BBN era and hence possibly test the cosmological predictions of different BSM scenarios. Supersymmetry is a particularly motivated BSM theory and it is often the case that different superymmetry breaking schemes require different cosmic histories with specific reheating temperatures or low entropy production in order to be cosmologically viable. In this paper we quantify the effects of the possible alternative cosmic histories on the n s and r CMB observables assuming a generic non-thermal stage after cosmic inflation. We analyze TeV and especially multi-TeV super-symmetry breaking schemes assuming the neutralino and gravitino dark matter scenarios. We complement our analysis considering the Starobinsky R 2 inflation model to exemplify the improved CMB predictions that a unified description of the early universe cosmic evolution yields. Our analysis underlines the importance of the CMB precision measurements that can be viewed, to some extend, as complementary to the laboratory experimental searches for supersymmetry or other BSM theories.

Greece

Ioannis Dalianis

Probing the BSM physics with CMB precision cosmology: an application to supersymmetry

We study reheating processes and its cosmological consequences in the Starobinsky model embedded in the old-minimal supergravity. First, we consider minimal coupling between the gravity and matter sectors in the higher curvature theory, and transform it to the equivalent standard supergravity coupled to additional matter superfields. We then discuss characteristic decay modes of the inflaton and the reheating temperature T R . Considering a simple model of supersymmetry breaking sector, we estimate gravitino abundance from inflaton decay, and obtain limits on the masses of gravitino and supersymmetry breaking field. We find T R ≃ 1.0 × 10 9 GeV and the allowed range of gravitino mass as 10 4 GeV ≲ m 3/2 ≲ 10 5 GeV, assuming anomaly-induced decay into the gauge sector as the dominant decay channel.

Takahiro Terada

Yusuke Yamada

Jun’ichi Yokoyama

Reheating processes after Starobinsky inflation in old-minimal supergravity

In this paper we show that the Germani-Kehagias model of Higgs inflation (or New Higgs Inflation), where the Higgs boson is kinetically non-minimally coupled to the Einstein tensor is in perfect compatibility with the latest Planck and BICEP2 data. Moreover, we show that the tension between the Planck and BICEP2 data can be relieved within the New Higgs inflation scenario by a negative running of the spectral index. Regarding the unitarity of the model, we argue that it is unitary throughout the evolution of the Universe. Weak couplings in the Higgs-Higgs and Higgs-graviton sectors are provided by a large background dependent cut-off scale during inflation. In the same regime, the W and Z gauge bosons acquire a very large mass, thus decouple. On the other hand, if they are also non-minimally coupled to the Higgs boson, their effective masses can be enormously reduced. In this case, the W and Z bosons are no longer decoupled. After inflation, the New Higgs model is well approximated by a quartic Galileon with a renormalizable potential. We argue that this can unitarily create the right conditions for inflation to eventually start.