We investigate the discovery potential at the MATHUSLA experiment of a long-lived particle (LLP), which is the heavier state of inelastic scalar dark matter (DM) in the third-generation-philic <inline-formula><tex-math id='TM0002' notation='LaTeX'>$U(1)$</tex-math></inline-formula> ( <inline-formula><tex-math id='TM0003' notation='LaTeX'>$U(1)_{X_3}$</tex-math></inline-formula>) extension of the Standard Model. Since the heavier state and DM state form a complex scalar charged under the <inline-formula><tex-math id='TM0004' notation='LaTeX'>$U(1)_{X_3}$</tex-math></inline-formula>, it is natural that the heavier state <italic>P</italic> is almost degenerate with the DM state and is hence long-lived. We find that the third-generation-philic right-handed <inline-formula><tex-math id='TM0006' notation='LaTeX'>$U(1)$</tex-math></inline-formula>, <inline-formula><tex-math id='TM0007' notation='LaTeX'>$U(1)_{R_3}$</tex-math></inline-formula>, model is the most interesting, because third-generation-philic models are less constrained by the current experimental results and right-handed <inline-formula><tex-math id='TM0008' notation='LaTeX'>$U(1)$</tex-math></inline-formula> interactions leave visible final decay products without produing neutrinos. For a benchmark of the model parameters consistent with the current phenomenological constraints, we find that the travel distance of the LLP can be <inline-formula><tex-math id='TM0009' notation='LaTeX'>$\mathcal {O}(100)$</tex-math></inline-formula>&#160;m and the LLP production cross section&#160;at the 14 TeV LHC can be <inline-formula><tex-math id='TM0010' notation='LaTeX'>$\mathcal {O}(10)$</tex-math></inline-formula> fb. Thus, we conclude that the LLP can be discovered at MATHUSLA with a sufficiently large number of LLP decay events inside the MATHUSLA detector.

United States

Nobuchika Okada

Japan

Osamu Seto

Discovery Potential of a Long-Lived Partner of Inelastic Dark Matter at MATHUSLA in the <italic>U</italic>(1) <sub><italic>X</italic><sub>3</sub></sub> Extension of the Standard Model

We consider the gauged U(1) model and examine the situation where the sterile neutrino is a dark matter candidate produced by the freeze-in mechanism. In our model, the dark matter $\textit{N}$ is mainly produced by the decay of a U(1) breaking scalar boson $\textit{ϕ}$. We point out that the on-shell production of $\textit{ϕ}$ through annihilation of the U(1) gauge boson $\textit{Z}$ plays an important role. We find that the single production of $\textit{Z}$ from the gluon bath in the early Universe can become the main production modes for $\textit{Z}$ in some parameter regions. To prevent $\textit{N}$ from being overproduced, we show that the U(1) gauge coupling constant $\textit{g}$ must be as small as 10 –10 . We also consider the case where the decay of $\textit{ϕ}$ into $\textit{N}$ is kinematically forbidden. In this case, $\textit{N}$ is generated by the scattering of $\textit{Z}$ and the $\textit{g}$ takes values of 10 –10 , which can be explored in collider experiments like FASER and SHiP.

Takashi Shimomura

China

Yoshiki Uchida

Freeze-in sterile neutrino dark matter in a feebly gauged $\textit{B}$ − $\textit{L}$ model

Motivated by the observation that tiny neutrino mass cannot be explained within the framework of the Standard Model, we consider extra gauge extended scenarios in which tiny neutrino masses are generated through the seesaw mechanism. These scenarios are equipped with a beyond the Standard Model neutral gauge boson called <math><msup><mi>Z</mi><mo>′</mo></msup></math> in the general <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> symmetry, which is a linear combination of <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>Y</mi></msub></math> and <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math>. In this case, left- and right-handed fermions interact differently with the <math><msup><mi>Z</mi><mo>′</mo></msup></math>. The <math><msup><mi>Z</mi><mo>′</mo></msup></math> gives rise to different processes involving neutrino-nucleon, neutrino-electron, electron-nucleus, and electron-muon scattering processes. By comparing with proton and electron beam-dump experiment data, recast data from searches for the long-lived and dark photon at BABAR, LHCb, and CMS experiments, the electron and muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> data, and the data of the dilepton and dijet searches at the LEP experiment, we derive bounds on the gauge coupling and the corresponding gauge boson mass for different <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> charges and evaluate the prospective limits from the future beam-dump scenarios at DUNE, FASER (2), and ILC. We conclude that large parameter regions could be probed by scattering, beam-dump, and collider experiments in the future.

Kento Asai

Arindam Das

Jinmian Li

Takaaki Nomura

Probing for chiral <math><msup><mi>Z</mi><mo>′</mo></msup></math> gauge boson through scattering measurement experiments

We study the flavor dependent <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><msub><mi>B</mi><mi>i</mi></msub><mo>−</mo><msub><mi>L</mi><mi>j</mi></msub></mrow></msub></math> models, where an <math><mi>i</mi></math>th generation of quarks and <math><mi>j</mi><mo>(</mo><mo>≠</mo><mi>i</mi><mo>)</mo></math>th generation of leptons are charged. By solving the anomaly free condition for the matter sector of the SM fermions and three generations of right-handed (RH) neutrinos, we find that the <math><mi>j</mi></math>th generation of RH neutrino is not necessarily charged under the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><msub><mi>B</mi><mi>i</mi></msub><mo>−</mo><msub><mi>L</mi><mi>j</mi></msub></mrow></msub></math> gauge symmetry with the charge <math><mo>−</mo><mn>1</mn></math> and the other (neither <math><mi>i</mi></math>th nor <math><mi>j</mi></math>th) generation of RH neutrino can also be. As a general solution for the anomaly cancellation conditions, the other two RN neutrinos than the charge <math><mo>−</mo><mn>1</mn></math> RH neutrino may have nonvanishing charge and be stable due to the gauge invariance, and hence it is a candidate for dark matter (DM) in our Universe. We apply this result to a <math><msub><mi>B</mi><mn>3</mn></msub><mo>−</mo><msub><mi>L</mi><mn>2</mn></msub></math> model and consider a light thermal DM and a solution to the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> anomaly. We identify the parameter region to have the DM mass range from MeV to sub-GeV and simultaneously solve the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> anomaly. We also derive the constraints on the gauge kinetic mixing parameter by using the latest Borexino phase-II data.

Intergenerational gauged <math><mi>B</mi><mo>−</mo><mi>L</mi></math> model and its implication to the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> anomaly and thermal dark matter

We investigate the mass range and the corresponding free-streaming length scale of dark matter produced non-thermally from decay of heavy objects which can be either dominant or sub-dominant at the moment of decay. We show that the resulting dark matter could be very light well below keV scale with a free-streaming length satisfying the Lyman-α constraints. We demonstrate two explicit examples for such light cold dark matter.

South Korea

Ki-Young Choi

Jinn-Ouk Gong

Junghoon Joh

Spain

Wan-Il Park

Light cold dark matter from non-thermal decay

We show that three open questions in particle physics and cosmology: the origin of neutrino mass, the identity of dark matter, and the origin of the baryon asymmetry of the universe can be explained simultaneously in the three-loop seesaw model proposed by Krauss, Nasri, and Trodden. We discuss the difficulty of successful leptogenesis with three right-handed neutrinos, and we propose a scenario with four right-handed neutrinos that satisfies all observational constraints. This scenario predicts a sleptonlike particle as light as a few hundreds GeV that can be probed by future collider experiments.

Tetsuo Shindou

Takanao Tsuyuki

Low-scale leptogenesis and dark matter in a three-loop radiative seesaw model

The origin of neutrino mass is a big unsolved problem of the Standard Model (SM) that motivate us to consider beyond the SM (BSM) scenarios where SM-singlet right-handed neutrinos (RHNs) are introduced to explain the origin of the light neutrino masses through the seesaw mechanism. There is a variety of ways which could lead us to this goal, and one of them is a general U(1) extension of the SM. In this scenario, three SM-singlet RHNs are introduced to cancel the gauge and mixed gauge gravity anomalies. After anomaly cancellation, we notice that the left- and right-handed charged fermions are differently charged under the general U(1) gauge group evolving a chiral scenario. After the breaking of the general U(1) symmetry, a neutral BSM gauge boson <math><mo>(</mo><msup><mi>Z</mi><mo>′</mo></msup><mo>)</mo></math> acquires mass, and it is a free parameter. Such <math><msup><mi>Z</mi><mo>′</mo></msup></math>, being lighter than 5 GeV, could be probed at the intensity and lifetime frontiers like FASER, FASER2, DUNE, and ILC beam dump experiments. The estimated bounds are needed to be compared with the existing bounds. We find that existing constraints from Orsay, Nomad, PS191, KEK, LSND, CHARM experiments, and cosmological scenario like SN1987A can be compared in our case once estimated for chiral scenarios. Finally, we compare the parameter spaces showing viable ones that could be probed by FASER, FASER2, DUNE, and ILC beam dump experiments and already excluded regions from Orsay, Nomad, PS191, KEK, LSND, CHARM, and SN1987A for a chiral scenario.

Chiral <math><mrow><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math> in FASER, FASER2, DUNE, and ILC beam dump experiments

We reexamine sterile neutrino dark matter in gauged <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math> model. Improvements have been made by tracing and careful evaluation of the evolution of the number densities of sterile neutrinos <math><mi>N</mi></math> and extra neutral gauge bosons <math><msup><mi>Z</mi><mo>′</mo></msup></math>. As a result, the cosmologically-interesting gauge coupling of <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math> for freeze-in sterile neutrinos turns out to be smaller than the values reported in the literature. This avoids the overproduction of <math><msup><mi>Z</mi><mo>′</mo></msup></math> so that it is consistent with the big bang nucleosynthesis and the cosmic microwave background constraints on the effective number of neutrino species. Similarly, the free-streaming length constraints exclude a large parameter space derived in previous studies. In addition to known freeze-in pair production of <math><mi>N</mi></math> from the standard model fermion pairs, we find the case that <math><mi>N</mi></math> is dominantly produced from a pair of <math><msup><mi>Z</mi><mo>′</mo></msup></math> at the temperature characterized by the <math><mi>B</mi><mo>−</mo><mi>L</mi></math> breaking scalar mass. Thus, the naive truncation of the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math> scalar contribution made in the literature is not valid.

Shintaro Eijima

Revisiting sterile neutrino dark matter in gauged <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math> model

We propose an extra <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> model with an alternative charge assignment for right-handed neutrinos. The type-II seesaw mechanism by a triplet Higgs field is promising for neutrino mass generation because of the alternative charge assignment. The small vacuum expectation value (VEV) of an additional Higgs doublet naturally leads to a very small VEV of the triplet Higgs field, and as a result, the smallness of neutrino mass can be understood. With the minimal Higgs field for <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> with the charge 1, right-handed neutrinos are candidates for Dirac dark matter (DM) and dark radiation (DR). We have derived and imposed the LHC bound, the DR constraint, and the bound from DM direct searches in the wide range of parameter space. Among various <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> choices, the DM direct search bound is found to be weakest for <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>R</mi></msub></math> where the constraints from thermal DM and non-negligible DR can be compatible. Such a number of the effective neutrino species would be interesting from the viewpoint of the so-called Hubble tension.

Dirac dark matter, dark radiation, and the type-II seesaw mechanism in alternative <math><mrow><mi>U</mi><mo>(</mo><mn>1</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>X</mi></mrow></msub></mrow></math> standard model

We study the lepton flavor violating decays such as <math><mi>μ</mi><mo>→</mo><mi>e</mi><mi>γ</mi></math>, <math><mi>τ</mi><mo>→</mo><mi>e</mi><mi>γ</mi></math>, <math><mi>τ</mi><mo>→</mo><mi>μ</mi><mi>γ</mi></math> in the three-loop radiative seesaw model proposed by Krauss, Nasri, and Trodden. In this model, the relevant coupling constants are larger for the heavier scalars that run inside loop diagrams to generate the appropriate magnitude of neutrino masses. Imposing a criterion that all the coupling constants must be small enough to be treated perturbatively, we find an upper bound on the mass of one of the scalars. By combining it with neutrino mass parameters, we derive lower bounds on the branching ratios of the lepton flavor violating processes. In a case with the inverted mass ordering and best-fit neutrino oscillation parameters, one of the lower bounds is <math><mi>Br</mi><mo>(</mo><mi>μ</mi><mo>→</mo><mi>e</mi><mi>γ</mi><mo>)</mo><mo>&gt;</mo><mn>1.1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>13</mn></mrow></msup></math>, which is within the reach of the MEG II experiment.