<p>We investigate a pseudo-Nambu-Goldstone (pNG) dark matter (DM) model based on a gauged <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi>x</mi></mrow></msub></mrow></math> and a global <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>g</mi></msub></math> symmetries. These symmetries are spontaneously broken to a global <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>D</mi></msub></math> symmetry by a vacuum expectation value of an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>x</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>g</mi></msub></math> bifundamental scalar field. The global <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>g</mi></msub></math> symmetry is also softly broken to a global <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>D</mi></msub></math> symmetry. Under the setup, a complex pNG boson arises. It is stabilized by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>D</mi></msub></math> and is a DM candidate. Its scattering cross section off a nucleon is highly suppressed by small momentum transfer and thus evades the stringent constraints from DM direct detection experiments. Assuming all the couplings in the dark sector are real, a discrete symmetry arises. Consequently, in addition to the pNG DM, the lighter one of an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>x</mi></msub></math> gauge boson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>V</mi><mn>0</mn></msup></math> and a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math>-odd scalar boson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub></math> from the bifundamental scalar field can also serve as a DM candidate. Therefore, the model provides two-component DM scenarios. We find that the relic abundance of the DM candidates explains the measured value of the DM energy density. We also find that the pNG DM is the dominant DM component in large regions of the parameter space. In contrast to the pNG DM, both <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>V</mi><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub></math> scatter off a nucleon, and their scattering cross sections are not suppressed. However, their scattering event rates are suppressed by their number densities. Thus, the scattering cross section is effectively reduced. We show that the effective DM-nucleon scattering cross sections in the two-component scenarios are smaller than the current upper bounds and above the neutrino fog.</p>

Japan

Tomohiro Abe

Kota Ichiki

Tiny yet detectable WIMP-nucleon scattering cross sections in a pseudo-Nambu-Goldstone dark matter model

A dark matter model based on QCD-like SU(N  c ) gauge theory with electroweakly interacting dark quarks is discussed. Assuming the dark quark mass m is smaller than the dynamical scale Λ d  ~ 4πf  d , the main component of the dark matter is the lightest G-parity odd dark pion associated with chiral symmetry breaking in the dark sector. We show that nonzero dark quark mass induces the universal mass contribution to both G-parity odd and even pions, and their masses tend to be degenerate. As a result, dark pion annihilation into heavier G-parity even dark pion also affects the dark matter relic abundance. Thus, our setup naturally accommodates forbidden dark matter scenario and realizes heavy dark matter whose mass is   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (1–100) TeV, which is different from conventional electroweakly interacting dark matter such as minimal dark matter. We also discuss CP-violation from the θ-term in the dark gauge sector and find that the predicted size of the electron electric dipole moment can be as large as ∼ 10 −32 e cm.

Ryosuke Sato

Takumu Yamanaka

Composite dark matter with forbidden annihilation

Abstract We discuss gravitational waves (GWs) in an electroweakly interacting vector dark matter (DM) model. In the model, the electroweak gauge symmetry is extended to SU(2)SU(2)SU(2)U(1) and spontaneously broken into SU(2)U(1) at TeV scale. The model has an exchange symmetry between SU(2) and SU(2). This symmetry stabilizes some massive vector bosons associated with the spontaneous symmetry breaking described above, and an electrically neutral one is a DM candidate. In a previous study, it was found that the gauge couplings of SU(2) and SU(2) are relatively large to explain the measured value of the DM energy density via the freeze-out mechanism. With the large gauge couplings, the gauge bosons potentially have a sizable effect on the scalar potential. In this paper, we focus on the phase transition of SU(2)SU(2)SU(2) SU(2). We calculate the effective potential at finite temperature and find that the phase transition is first-order and strong in a wide range of the parameter space. The strong first-order phase transition generates GWs. We calculate the GW spectrum and find that it will be possible to detect the GWs predicted in the model by future space-based GW interferometers. We explore the regions of the parameter space probed by the GW detection. We find that the GW detection can probe the region where the mass of , a CP-even scalar in the model, is a few TeV.

Katsuya Hashino

Gravitational Waves from First-Order Phase Transition in an Electroweakly Interacting Vector Dark Matter Model Prospects for searches for heavy Z′ and W′ bosons in fermionic final states with the ATLAS experiment at the HL-LHC

Pseudo-Nambu-Goldstone (pNG) dark matter (DM) is a promising DM candidate and able to explain the measured DM abundance by the thermal freeze-out mechanism evading the stringent bound from DM direct detection experiments. We propose a new model providing a pNG DM by introducing two Standard-Model-singlet complex scalars with the same charges of a dark U(1) gauge symmetry. They are also charged under a U(1) global symmetry corresponding to their relative phase rotations, which is explicitly broken by a soft-breaking term in the scalar potential. The both U(1) symmetries are spontaneously broken by their vacuum expectation values, giving rise to one real pNG boson. We also introduce a discrete ℤ2 symmetry exchanging the two scalars to stabilize the pNG boson as DM. It is shown that this model reproduces the DM abundance consistently with the current bound from the direct detection experiments. The model has a gauge kinetic mixing between the dark and U(1) Y  gauge fields, which allows the dark gauge boson to decay even with a relatively light mass and prevents it from being an additional DM component. The Landau pole is avoided thanks to the small gauge coupling constant. In addition, a DM pair dominantly annihilates into a pair of the dark gauge bosons if the gauge boson mass is lighter than the DM mass, and thus its cross section has significantly different parameter dependence from other pNG DM models. We also calculate the DM-nucleon scattering cross section at the loop level. It turns out that it is necessary to probe region covered by the neutrino fog in order to test this model.

Germany

Yu Hamada

Koji Tsumura

A model of pseudo-Nambu-Goldstone dark matter with two complex scalars

Abstract A model of the pseudo-Nambu–Goldstone (pNG) dark matter (DM) is proposed. We assume that there is an SU(2)$_{g}$ global symmetry and a U(1)$_{X}$ gauge symmetry in the dark sector, and they are spontaneously broken into a U(1)$_{D}$ global symmetry after a scalar field develops a vacuum expectation value. We add a soft symmetry-breaking term that breaks the SU(2)$_{g}$ global symmetry into the U(1)$_{g}$ global symmetry explicitly. Our model predicts a stable complex pNG particle under the U(1)$_{D}$ global symmetry. One of the virtues of the pNG DM models is that the models can explain the current null results of the direct detection experiments. The small momentum transfer suppresses the scattering amplitudes thanks to the low-energy behavior of the Nambu–Goldstone boson. In our model, the soft symmetry-breaking term is uniquely determined. This is the advantage of our model compared to some earlier works in which some soft symmetry-breaking terms cannot be forbidden but are simply assumed to be absent to avoid the constraints from the direct detection experiments. We calculate the thermal relic abundance of the pNG DM and find that the model can explain the measured value of the DM energy density under some constraints from perturbative unitarity.

A model of pseudo-Nambu–Goldstone dark matter from a softly broken (2) Global Symmetry With a (1) Gauge Symmetry

We study gamma-ray line signatures from electroweakly interacting non-abelian spin-1 dark matter (DM). In this model, Z 2-odd spin-1 particles including a DM candidate have the SU(2) L  triplet-like features, and the Sommerfeld enhancement is relevant in the annihilation processes. We derive the annihilation cross sections contributing to the photon emission and compare with the SU(2) L  triplet fermions, such as Wino DM in the supersymmetric Standard Model. The Sommerfeld enhancement factor is approximately the same in both systems, while our spin-1 DM predicts the larger annihilation cross sections into γγ/Zγ modes than those of the Wino by   <math> <mfrac> <mn>38</mn> <mn>9</mn> </mfrac> </math>  $$ \frac{38}{9} $$ . This is because a spin-1 DM pair forms not only J = 0 but also J = 2 partial wave states where J denotes the total spin angular momentum. Our spin-1 DM also has a new annihilation mode into Z 2-even extra heavy vector and photon, Z′γ. For this mode, the photon energy depends on the masses of DM and the heavy vector, and thus we have a chance to probe the mass spectrum. The latest gamma-ray line search in the Galactic Center region gives a strong constraint on our spin-1 DM. We can probe the DM mass for ≲ 25.3 TeV by the Cherenkov Telescope Array experiment even if we assume a conservative DM density profile.

Motoko Fujiwara

Junji Hisano

Kohei Matsushita

Gamma-ray line from electroweakly interacting non-abelian spin-1 dark matter

We study the early kinetic decoupling effect in a pseudo-Nambu-Goldstone (pNG) dark matter (DM) model. The pNG DM scattering processes with particles in the thermal bath in the early Universe are suppressed by the small momentum transfer. As a result, kinetic equilibrium is not maintained, and the temperature of DM is different from the temperature of the thermal bath at the freeze-out era. This temperature difference affects the thermal relic abundance of DM. We investigate the early kinetic decoupling in the Higgs resonance region, <math><mrow><mn>50</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>≲</mo><msub><mi>m</mi><mi>χ</mi></msub><mo>≲</mo><msub><mi>m</mi><mi>h</mi></msub><mo>/</mo><mn>2</mn></mrow></math>, where <math><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>χ</mi></mrow></msub></mrow></math> is the mass of the DM, and <math><msub><mi>m</mi><mi>h</mi></msub><mo>/</mo><mn>2</mn><mo>≃</mo><mn>62.5</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. We find that the DM-Higgs coupling determined to obtain the measured value of the DM energy density is underestimated in the literature. The enhancement in the coupling leads larger value of the Higgs invisible decay rate. It enlarges the capability to discover the DM signals from the decay of the Higgs bosons at collider experiments.

Early kinetic decoupling and a pseudo-Nambu-Goldstone dark matter model

We reexamine the inverse Primakoff scattering of axions, whose scattering cross section depends on the distribution of electrons in target atoms. We evaluate it using a form factor computed with a relativistic Hartree-Fock wave function and compare it with the previous results obtained with those based on the screened Coulomb potential for the electrostatic field in the atom. We take xenon as an example for the target atom and show that the scattering cross section was overestimated by more than an order of magnitude for axions with <math><mo>≲</mo><mi>O</mi><mo>(</mo><mn>10</mn><mo>)</mo></math> keV energies, like solar axions. It is also found that inelastic scattering processes, in which the final state contains an excited or ionized atom, can be comparable or even be dominant when the size of momentum transfer is ≲1 keV. For more energetic axions, on the other hand, the total scattering cross section is found to be well approximated by a simple expression and has little dependence on the atomic structure. As an application of this result, we consider supernova axions, whose energy is 10–100 MeV, and show that <math><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> inverse Primakoff events are expected for axions from a nearby supernova in the future neutrino experiments, which may warrant a more detailed study on the search strategy of this process.

Koichi Hamaguchi

Natsumi Nagata

Atomic form factors and inverse Primakoff scattering of axion

We propose a theory of chiral fermion dark matter (DM) with an isospin-<math><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></math> fermion of a dark sector <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mi>D</mi></msub></math> gauge symmetry, which is arguably the simplest chiral theory. An isospin-3 scalar breaks <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mi>D</mi></msub></math> down to a discrete non-Abelian group <math><msup><mi>T</mi><mo>′</mo></msup></math> and generates the DM mass. The <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mi>D</mi></msub></math> gauge symmetry protects the DM mass and guarantees its stability. We derive consistency conditions for the theory and study its DM phenomenology. In some regions of parameters of the theory a two-component DM scenario is realized, consisting of a fermion and a boson, with the boson being the lightest <math><msup><mi>T</mi><mo>′</mo></msup></math> nonsinglet field. In the case of single-component fermionic DM, we find that internal consistency of the theory, perturbativity arguments, and the observed relic abundance limit the DM mass to be less than 280 GeV, except when <math><mi>s</mi></math>-channel resonance regions are open for annihilation. For a significant part of the parameter space, the theory can be tested in DM direct-detection signals at the LZ and XENONnT experiments.

United States

K. S. Babu

Simple theory of chiral fermion dark matter

We study the effect of the early kinetic decoupling in a model of fermionic dark matter (DM) that interacts with the standard model particles only by exchanging the Higgs boson. There are two DM-Higgs couplings, namely <math><mi>C</mi><mi>P</mi></math>-conserving and <math><mi>C</mi><mi>P</mi></math>-violating couplings. If the mass of the DM is slightly below half of the Higgs boson mass, then the couplings are suppressed to obtain the measured value of the DM energy density by the freeze-out mechanism. In addition, the scattering processes of DM off particles in the thermal bath are suppressed by the small momentum transfer if the <math><mi>C</mi><mi>P</mi></math>-violating DM-Higgs coupling is larger than the <math><mi>C</mi><mi>P</mi></math>-conserving one. Due to the suppression, the temperature of the DM can differ from the temperature of the thermal bath. By solving coupled equations for the number density and temperature of the DM, we calculate the DM-Higgs couplings that reproduce the right amount of the DM relic abundance. We find that the couplings have to be larger than the one obtained without taking into account the difference in the temperatures. A consequence of the enhancement of the DM-Higgs couplings is the enhancement of the Higgs invisible decay branching ratio. The enhancement is testable at current and future collider experiments.