We study a three-loop induced neutrino mass scenario from a non-holomorphic modular $\textit{A}$ $_{4}$ flavor symmetry and obtain the minimum scenario leading to predictions of the lepton masses, mixing angles, and Dirac and Majorana phases, which are shown through chi square analyses. In addition, we discuss the lepton flavor violations, muon anomalous magnetic moment, lepton universality, and relic density of the dark matter candidate. Moreover, we show that our model can be extended to satisfy the observed relic density of dark matter within the limit of perturbation by adding one singlet scalar boson without changing predictions in the neutrino sector.

China

Takaaki Nomura

Hiroshi Okada

Neutrino mass model at a three-loop level from a non-holomorphic modular $\textit{A}$ $_{4}$ symmetry * Takaaki Nomura is supported by the Fundamental Research Funds for the Central Universities. Hiroshi Okada is supported by Zhongyuan Talent (Talent Recruitment Series) Foreign Experts Project

Motivated by the recently reported measurement of the W boson mass <math><msub><mrow><mi>M</mi></mrow><mrow><mi>W</mi></mrow></msub><mo>=</mo><mn>80.4335</mn><mo>±</mo><mn>0.0094</mn></math> GeV by the CDF collaboration, we propose a type III seesaw extension of the minimal supersymmetric standard model (MSSM) which also includes an R-parity violating term. Without taking potential SUSY radiative corrections into account, we show that the CDF measurement of <math><msub><mrow><mi>M</mi></mrow><mrow><mi>W</mi></mrow></msub></math> and the LEP measurement of the ρ parameter can be simultaneously accommodated at the 2σ level. A long-lived gravitino in a few GeV mass range is a unique viable dark matter candidate in this framework.

Poland

Anish Ghoshal

United States

Nobuchika Okada

Satomi Okada

Digesh Raut

Qaisar Shafi

Anil Thapa

Type III seesaw with R-parity violation in light of (cdf)

We consider a  $$U(1)_{B-L}$$  <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mrow> <mi>B</mi> <mo>-</mo> <mi>L</mi> </mrow> </msub> </mrow> </math>   model with a  $$Z^\prime $$  <math> <msup> <mi>Z</mi> <mo>′</mo> </msup> </math>   portal Dirac fermion dark matter (DM)  $$\chi $$  <math> <mi>χ</mi> </math>   of low mass which couples very weakly to the  $$B - L$$  <math> <mrow> <mi>B</mi> <mo>-</mo> <mi>L</mi> </mrow> </math>   gauge boson  $$Z^\prime $$  <math> <msup> <mi>Z</mi> <mo>′</mo> </msup> </math>  . An arbitrary  $$B-L$$  <math> <mrow> <mi>B</mi> <mo>-</mo> <mi>L</mi> </mrow> </math>   charge  $$Q\ne \pm 1, \pm 3$$  <math> <mrow> <mi>Q</mi> <mo>≠</mo> <mo>±</mo> <mn>1</mn> <mo>,</mo> <mo>±</mo> <mn>3</mn> </mrow> </math>   of the DM  $$\chi $$  <math> <mi>χ</mi> </math>   ensures its stability. Motivated by the sensitivity reach of forthcoming “Lifetime Frontier” experiments, we focus on the  $$Z^\prime $$  <math> <msup> <mi>Z</mi> <mo>′</mo> </msup> </math>   mass,  $$m_{Z^\prime }$$  <math> <msub> <mi>m</mi> <msup> <mi>Z</mi> <mo>′</mo> </msup> </msub> </math>  , in the sub-GeV to few GeV range. To evaluate the DM relic abundance, we examine both the freeze-out and freeze-in DM scenarios. For the freeze-out scenario, we show that the observed DM abundance is reproduced near the  $$Z^\prime $$  <math> <msup> <mi>Z</mi> <mo>′</mo> </msup> </math>   resonance,  $$m_\chi \simeq m_{Z^\prime }/2$$  <math> <mrow> <msub> <mi>m</mi> <mi>χ</mi> </msub> <mo>≃</mo> <msub> <mi>m</mi> <msup> <mi>Z</mi> <mo>′</mo> </msup> </msub> <mo>/</mo> <mn>2</mn> </mrow> </math>  , where  $$m_\chi $$  <math> <msub> <mi>m</mi> <mi>χ</mi> </msub> </math>   is the DM mass. For the freeze-in scenario, we focus on  $$m_\chi \ll m_{Z^\prime }$$  <math> <mrow> <msub> <mi>m</mi> <mi>χ</mi> </msub> <mo>≪</mo> <msub> <mi>m</mi> <msup> <mi>Z</mi> <mo>′</mo> </msup> </msub> </mrow> </math>  . We show that for a fixed value of  $$m_{Z^\prime }$$  <math> <msub> <mi>m</mi> <msup> <mi>Z</mi> <mo>′</mo> </msup> </msub> </math>  ,  $$g_{BL}$$  <math> <msub> <mi>g</mi> <mrow> <mi>BL</mi> </mrow> </msub> </math>   values roughly scale as 1/Q to reproduce the observed DM abundance. For various Q values in the range between  $$10^{-6}$$  <math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </msup> </math>   and  $$10^2$$  <math> <msup> <mn>10</mn> <mn>2</mn> </msup> </math>  , we show that the gauge coupling values  $$g_{BL}$$  <math> <msub> <mi>g</mi> <mrow> <mi>BL</mi> </mrow> </msub> </math>   needed to reproduce the observed DM abundance lie in the search reach of future planned and/or proposed experiments such as FASER, Belle-II, LDMX, and SHiP. In the freeze-in case, the Q values to realize observable  $$g_{BL}$$  <math> <msub> <mi>g</mi> <mrow> <mi>BL</mi> </mrow> </msub> </math>   values are found to be much smaller than that in the freeze-out case.

Italy

Newton Nath

Light  $$Z^\prime $$  <math> <msup> <mi>Z</mi> <mo>′</mo> </msup> </math>   and Dirac fermion dark matter in the  $$B-L$$  <math> <mrow> <mi>B</mi> <mo>-</mo> <mi>L</mi> </mrow> </math>   model

In the 5-dimensional braneworld cosmology, the Friedmann equation of our 4-dimensional universe on a brane is modified at high temperatures while the standard Big Bang cosmology is reproduced at low temperatures. Based on two well-known scenarios, the Randall–Sundrum and Gauss–Bonnet braneworld cosmologies, we investigate the braneworld cosmological effect on the relic density of a non-thermal dark matter particle whose interactions with the Standard Model particles are so weak that its relic density is determined by the freeze-in mechanism. For dark matter production processes in the early universe, we assume a simple scenario with a light vector-boson mediator for the dark matter particle to communicate with the Standard Model particles. We find that the braneworld cosmological effect can dramatically alters the resultant dark matter relic density from the one in the standard Big Bang cosmology. As an application, we consider a right-handed neutrino dark matter in the minimal  $$B-L$$  <math> <mrow> <mi>B</mi> <mo>-</mo> <mi>L</mi> </mrow> </math>   extended Standard Model with a light  $$B-L$$  <math> <mrow> <mi>B</mi> <mo>-</mo> <mi>L</mi> </mrow> </math>   gauge boson ( $$Z^\prime $$  <math> <msup> <mi>Z</mi> <mo>′</mo> </msup> </math>  ) as a mediator. We find an impact of the braneworld cosmological effect on the search for the long-lived  $$Z^\prime $$  <math> <msup> <mi>Z</mi> <mo>′</mo> </msup> </math>   boson at the planned/proposed Lifetime Frontier experiments.

Victor Baules

Braneworld cosmological effect on freeze-in dark matter density and lifetime frontier

We present a minimal extension of the left-right symmetric model based on the gauge group SU(3) c  × SU(2) L  × SU(2) R  × U(1) B−L  × U(1) X , in which a vector-like fermion pair (ζ  L  and ζ  R ) charged under the U(1) B−L  × U(1)X symmetry is introduced. Associated with the symmetry breaking of the gauge group SU(2) R  × U(1) B−L  × U(1) X  down to the Standard Model (SM) hypercharge U(1) Y , Majorana masses for ζ  L,R  are generated and the lightest mass eigenstate plays a role of the dark matter (DM) in our universe by its communication with the SM particles through a new neutral gauge boson “X”. We consider various phenomenological constraints of this DM scenario, such as the observed DM relic density, the LHC Run-2 constraints from the search for a narrow resonance, and the perturbativity of the gauge couplings below the Planck scale. Combining all constraints, we identify the allowed parameter region which turns out to be very narrow. A significant portion of the currently allowed parameter region will be tested by the High-Luminosity LHC experiments.

Brazil

M. Neves

Majorana fermion dark matter in minimally extended left-right symmetric model

A scalar field having the Coleman-Weinberg type effective potential arises in various contexts of particle physics and serves as a useful framework for discussing cosmic inflation. According to recent studies based on the Markov chain Monte Carlo analysis, the coefficients of such an effective potential are severely constrained by the cosmological data. We investigate the impact of this observation on the physics beyond the Standard Model, focusing on an inflationary model based on the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math>-extended Standard Model as a well-motivated example. We examine the parameter region that is not excluded by the Large Hadron Collider (LHC) run-2 at <math><mrow><mn>139</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>fb</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> integrated luminosity, and show that the model parameters can be further constrained by the high-luminosity LHC experiments in the near future. We also comment on the possible reheating mechanism and the dark matter candidates of this scenario.

South Korea

Shinsuke Kawai

Low-energy implications of cosmological data in <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> Higgs inflation

We consider a U(1)$_{X}$ gauge symmetry extension of the Standard Model (SM) with a <math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math>-portal Majorana fermion dark matter that allows for a relatively light gauge boson <math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math> with mass of 10 MeV− a few GeV and a much heavier dark matter through the freeze-in mechanism. In a second scenario the roles are reversed, and the dark matter mass, in the keV range or so, lies well below the <math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math> mass, say, ∼1 GeV. We outline the parameter space that can be explored for these two scenarios at the future Lifetime Frontier experiments including Belle-II, FASER, LDMX and SHiP.

Light ′ and dark matter from U(1) Gauge Symmetry

A gauged <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>X</mi></mrow></msub></math> symmetry appended to the Standard Model (SM) is particularly well motivated since it can account for the light neutrino masses by the seesaw mechanism, explain the origin of baryon asymmetry of the universe via leptogenesis, and help implement successful cosmological inflation with the <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>X</mi></mrow></msub></math> breaking Higgs field as the inflaton. In this framework, we propose a light dark matter (DM) scenario in which the <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>X</mi></mrow></msub></math> gauge boson <math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math> behaves as a DM particle in the universe. We discuss how this scenario with <math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math> mass of a few keV and a <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>X</mi></mrow></msub></math> gauge coupling <math><msub><mrow><mi>g</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>≃</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>16</mn></mrow></msup></math> can nicely fit the excess in the electronic recoil energy spectrum recently reported by the XENON1T collaboration. In order to reproduce the observed DM relic density in the presence of such a tiny gauge coupling, we propose an extension of the model to a two-component DM scenario. The <math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math> DM density can be comparable to the observed DM density by the freeze-in mechanism through the coupling of <math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math> boson to a partner Higgs-portal scalar DM with a large <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>X</mi></mrow></msub></math> charge.

Dark matter ′ and XENON1T excess from (1) Extended Standard Model

We consider a nonexotic gauged <math><mrow><msub><mrow><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mi>X</mi></msub></mrow></math> extension of the Standard Model (SM), where the <math><mrow><msub><mrow><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mi>X</mi></msub></mrow></math> charge of a SM field is given by a linear combination of its hypercharge and baryon-minus-lepton (<math><mi>B</mi><mo>−</mo><mi>L</mi></math>) number. All the gauge and mixed gauge-gravitational anomalies are canceled in this model with the introduction of three right-handed neutrinos (RHNs). Unlike the conventional minimal <math><mrow><msub><mrow><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mi>X</mi></msub></mrow></math> model, where a universal <math><mrow><msub><mrow><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>X</mi></mrow></msub></mrow></math> charge of <math><mo>−</mo><mn>1</mn></math> is assigned to three RHNs, we consider an alternative charge assignment, namely, two RHNs (<math><msubsup><mi>N</mi><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msubsup></math>) have <math><mrow><msub><mrow><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mi>X</mi></msub></mrow></math> charge <math><mo>−</mo><mn>4</mn></math> while one RHN (<math><msub><mi>N</mi><mi>R</mi></msub></math>) has a <math><mo>+</mo><mn>5</mn></math> charge. With a minimal extension of the Higgs sector, the three RHNs acquire their Majorana masses associated with <math><mrow><msub><mrow><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mi>X</mi></msub></mrow></math> symmetry breaking. While <math><msubsup><mi>N</mi><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msubsup></math> have Yukawa coupling with the SM lepton doublets and play an essential role for the “minimal seesaw” mechanism, <math><msub><mi>N</mi><mi>R</mi></msub></math> is isolated from the SM particles due to its <math><mrow><msub><mrow><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mi>X</mi></msub></mrow></math> charge and hence it is a natural candidate for the dark matter (DM) without invoking additional symmetries. In this model context, we investigate the <math><msup><mi>Z</mi><mo>′</mo></msup></math>-portal RHN DM scenario, where the RHN DM communicates with the SM particles through the <math><mrow><msub><mrow><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mi>X</mi></msub></mrow></math> gauge boson (<math><msup><mi>Z</mi><mo>′</mo></msup></math> boson). We identify a narrow parameter space by combining the constraints from the observed DM relic abundance, the results of the search for a <math><msup><mi>Z</mi><mo>′</mo></msup></math> boson resonance at the Large Hadron Collider Run-2, and the gauge coupling perturbativity up to the Planck/grand unification scale. A special choice of <math><mrow><msub><mrow><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mi>X</mi></msub></mrow></math> charges for the SM fields allows us to extend the model to <math><mrow><mi>SU</mi><mo>(</mo><mn>5</mn><mo>)</mo><mo>×</mo><mi>U</mi><mo>(</mo><mn>1</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>X</mi></mrow></msub></mrow></math> grand unification. In this scenario, the model parameter space is more severely constrained, which will be explored at future high energy collider experiments.

Natural <math><msup><mi>Z</mi><mo>′</mo></msup></math>-portal Majorana dark matter in alternative U(1) extended standard model

We consider a gauged U(1)<math><msub><mrow></mrow><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math> (Baryon-minus-Lepton number) extension of the Standard Model (SM), which is anomaly-free in the presence of three Right-Handed Neutrinos (RHNs). Associated with the U(1)<math><msub><mrow></mrow><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math> symmetry breaking the RHNs acquire their Majorana masses and then play the crucial role to generate the neutrino mass matrix by the seesaw mechanism. Towards the experimental confirmation of the seesaw mechanism, we investigate a RHN pair production through the U(1)<math><msub><mrow></mrow><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math> gauge boson (<math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math>) at the 250 GeV International Linear Collider (ILC). The <math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math> gauge boson has been searched at the Large Hadron Collider (LHC) Run-2 and its production cross section is already severely constrained. The constraint will become more stringent by the future experiments with the High-Luminosity upgrade of the LHC (HL-LHC). We find a possibility that even after a null <math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math> boson search result at the HL-LHC, the 250 GeV ILC can search for the RHN pair production through the final state with same-sign dileptons plus jets, which is a “smoking-gun” signature from the Majorana nature of RHNs. In addition, some of RHNs are long-lived and leave a clean signature with a displaced vertex. Therefore, the 250 GeV ILC can operate as not only a Higgs Factory but also a RHN discovery machine to explore the origin of the Majorana neutrino mass generation, namely the seesaw mechanism.