The Higgs-portal scalar dark matter (DM) model is a simple extension of the Standard Model (SM) to incorporate a DM particle to the SM, where a $$Z_2$$ -odd real scalar field is introduced as a DM candidate. We consider this DM model in the context of 5-dimensional brane-world cosmology, where our 3-dimensional space is realized as a hyper-surface embedded in 4-dimensional space. In the setup, all the SM and DM fields reside on the hyper-surface while graviton lives in the bulk. We consider two well-known brane-world cosmologies, namely, the Randall–Sundrum (RS) and the Gauss–Bonnet (GB) brane-world cosmologies, in which the standard Big Bang cosmology is reproduced at low temperatures below the so-called “transition temperature” while at high temperatures the expansion law of the universe is significantly modified. Such a non-standard expansion law directly impacts the prediction for the relic density of the Higgs-portal DM. We investigate the brane-world cosmological effects and identify the allowed model parameter region by combining the constraints from the observed DM relic density, and the direct and indirect DM detection experiments. It is well-known that only DM masses in the vicinity of half the Higgs boson mass are allowed in the Higgs-portal scalar DM model. We find that the allowed parameter region becomes more severely constrained and even disappears in the RS cosmology, while the GB cosmological effect significantly enlarges the allowed region. Upon discovering Higgs-portal DM, we can determine transition temperature in the GB brane-world cosmology.

United States

Taoli Liu

Nobuchika Okada

Digesh Raut

Higgs-portal dark matter in Brane-world cosmology

Abstract In the “Domain-Wall Standard Model,” all the Standard Model (SM) fields are localized in certain domains in a non-compact 5D space-time. While the SM is realized as a 4D effective theory at low energies, the model involves Kaluza–Klein (KK) modes of the SM particles. In this paper we introduce two simple solvable examples which lead to domain-wall configurations for the SM particles and their KK-modes. Based on the examples, we address a variety of phenomenologies of the Domain-Wall SM, such as the KK-mode gauge boson phenomenology at the Large Hadron Collider (LHC), the effect of the KK-mode SM fermions on Higgs boson phenomenology, and the KK-mode fermion search at the LHC with its decay into a corresponding SM fermion and a Nambu–Goldstone boson associated with a spontaneous breaking of the translational invariance in the 5th dimension. We also propose a simple unified picture of localizing all the SM fields.

Desmond Villalba

Aspects of the Domain-Wall Standard Model “Search for a narrow resonance in high-mass dilepton final states in proton-proton collisions using 140fb Of Data at √ = 13 TeV,”

We explore some experimentally testable predictions of an SO(10) axion model which includes two 10-plets of fermions in order to resolve the axion domain wall problem. The axion symmetry can be safely broken after inflation, so that the isocurvature perturbations associated with the axion field are negligibly small. An unbroken gauge  $$Z_2$$  <math> <msub> <mi>Z</mi> <mn>2</mn> </msub> </math>   symmetry in SO(10) ensures the presence of a stable WIMP-like dark matter, a linear combination of the electroweak doublets in the fermion 10-plets and an SO(10) singlet fermion with mass  $$\sim 62.5 \; \textrm{GeV}\; (1 \; \textrm{TeV}) $$  <math> <mrow> <mo>∼</mo> <mn>62.5</mn> <mspace width="0.277778em"></mspace> <mtext>GeV</mtext> <mspace width="0.277778em"></mspace> <mo>(</mo> <mn>1</mn> <mspace width="0.277778em"></mspace> <mtext>TeV</mtext> <mo>)</mo> </mrow> </math>   when it is mostly the singlet (doublet) fermion, that co-exists with axion dark matter. We also discuss gauge coupling unification, proton decay, inflation with non-minimal coupling to gravity and leptogenesis. With the identification of the SM singlet Higgs field in the 126 representation of SO(10) as inflaton, the magnetic monopoles are inflated away, and we find  $$0.963 \lesssim n_s \lesssim 0.965$$  <math> <mrow> <mn>0.963</mn> <mo>≲</mo> <msub> <mi>n</mi> <mi>s</mi> </msub> <mo>≲</mo> <mn>0.965</mn> </mrow> </math>   and  $$0.003 \lesssim r \lesssim 0.036$$  <math> <mrow> <mn>0.003</mn> <mo>≲</mo> <mi>r</mi> <mo>≲</mo> <mn>0.036</mn> </mrow> </math>  , where  $$n_s$$  <math> <msub> <mi>n</mi> <mi>s</mi> </msub> </math>   and r denote the scalar spectral index and tensor-to-scalar ratio, respectively. These predictions can be tested in future experiments such as CMB-S4.

Qaisar Shafi

Axions, WIMPs, proton decay and observable r in SO(10)

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

Satomi Okada

Anil Thapa

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

We investigate a prospect of probing the type-III seesaw neutrino mass generation mechanism at various collider experiments by searching for a disappearing track and a displaced vertex signature originating from the decay of  $$SU(2)_L$$  <math> <mrow> <mi>S</mi> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mi>L</mi> </msub> </mrow> </math>   triplet fermion ( $$\Sigma $$  <math> <mi>Σ</mi> </math>  ). Since  $$\Sigma $$  <math> <mi>Σ</mi> </math>   is primarily produced at colliders through the electroweak gauge interactions, its production rate is uniquely determined by its mass. We find that a  $$\Sigma $$  <math> <mi>Σ</mi> </math>   particle produces a disappearing track signature from the decay of its charged component, which can be searched at the HL-LHC. Furthermore, we show that if the lightest observed neutrino has a mass of around  $$10^{-9}$$  <math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>9</mn> </mrow> </msup> </math>   eV, the neutral component of  $${\Sigma }$$  <math> <mi>Σ</mi> </math>   can be discovered at the proposed MATHUSLA detector. We also show that the charged component of  $${\Sigma }$$  <math> <mi>Σ</mi> </math>   can be potentially be observed at FCC-he as a displaced vertex signature.

Germany

Sudip Jana

Displaced vertex and disappearing track signatures in type-III seesaw

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

We study the low energy implications of a trinification model based on the gauge symmetry  $$G= SU(3)_c \times SU(3)_L \times SU(3)_R$$  <math> <mrow> <mi>G</mi> <mo>=</mo> <mi>S</mi> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> <mi>c</mi> </msub> <mo>×</mo> <mi>S</mi> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> <mi>L</mi> </msub> <mo>×</mo> <mi>S</mi> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> <mi>R</mi> </msub> </mrow> </math>  , without imposing gauge coupling unification. A minimal model requires two Higgs multiplets that reside in the bi-fundamental representation of G, and this is shown to be adequate for accommodating the Standard Model (SM) fermion masses and generate, via loop corrections and seesaw mechanism, suitable masses for the heavy neutral leptons as well as the observed SM neutrinos. We estimate a lower bound of around 15 TeV for the masses of the new down- type quarks that are required by the  $$SU(3)_L \times SU(3)_R$$  <math> <mrow> <mi>S</mi> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> <mi>L</mi> </msub> <mo>×</mo> <mi>S</mi> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> <mi>R</mi> </msub> </mrow> </math>   symmetry. We examine the resonant production at the LHC of the new gauge bosons, which leads to a lower bound of 16 TeV for the symmetry breaking scale of G. We also show how the muon  $$g-2$$  <math> <mrow> <mi>g</mi> <mo>-</mo> <mn>2</mn> </mrow> </math>   anomaly can be resolved in the presence of these new gauge bosons and the heavy charged leptons present in the model. Finally, the model predicts the presence of a topologically stable monopole carrying three quanta  $$(6 \pi /e)$$  <math> <mrow> <mo>(</mo> <mn>6</mn> <mi>π</mi> <mo>/</mo> <mi>e</mi> <mo>)</mo> </mrow> </math>   of Dirac magnetic charge and mass  $$\gtrsim 160$$  <math> <mrow> <mo>≳</mo> <mn>160</mn> </mrow> </math>   TeV. If new matter fields lying in the fundamental representations of G are included, the model predicts the presence of exotic leptons, mesons and baryons carrying fractional electric charges such as  $$\pm e/3$$  <math> <mrow> <mo>±</mo> <mi>e</mi> <mo>/</mo> <mn>3</mn> </mrow> </math>   and  $$\pm 2e/3$$  <math> <mrow> <mo>±</mo> <mn>2</mn> <mi>e</mi> <mo>/</mo> <mn>3</mn> </mrow> </math>  , fully compatible with the Dirac quantization condition.

Monopoles, exotic states and muon  $$g-2$$  <math> <mrow> <mi>g</mi> <mo>-</mo> <mn>2</mn> </mrow> </math>   in TeV scale trinification

We propose a pseudo-Goldstone boson dark matter (pGDM) particle in <math><mrow><mi>S</mi><mi>O</mi><mo>(</mo><mn>10</mn><mo>)</mo></mrow></math> grand unified theory (GUT). Due to its Goldstone nature, this pGDM evades the direct DM detection experiments which, otherwise, severely constrain the parameter space of DM models. In <math><mi>S</mi><mi>O</mi><mo>(</mo><mn>10</mn><mo>)</mo></math>, the pGDM is embedded as a linear combination of the Standard Model (SM) singlet scalars in <math><mrow><msub><mrow><mn>16</mn></mrow><mrow><mi>H</mi></mrow></msub></mrow></math> and <math><mrow><msub><mrow><mover><mrow><mn>126</mn></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>H</mi></mrow></msub></mrow></math> representations. We consider two scenarios for the intermediate route of <math><mi>S</mi><mi>O</mi><mo>(</mo><mn>10</mn><mo>)</mo></math> symmetry breaking (SB) to the SM: <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo><mo>×</mo><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> and Pati-Salam the <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>4</mn><msub><mo>)</mo><mi>c</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mi>L</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mi>R</mi></msub></math> (<math><mrow><mn>4</mn><mtext>−</mtext><mn>2</mn><mtext>−</mtext><mn>2</mn></mrow></math>) gauge groups. The vacuum expectation value of <math><mrow><msub><mrow><mover><mrow><mn>126</mn></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>H</mi></mrow></msub></mrow></math>, which triggers the breaking of <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> and <math><mrow><mn>4</mn><mtext>−</mtext><mn>2</mn><mtext>−</mtext><mn>2</mn></mrow></math> symmetry in the two scenarios, respectively, determines the pGDM lifetime whose astrophysical lower bound provides one of the most stringent constraints. For the <math><mrow><mn>4</mn><mtext>−</mtext><mn>2</mn><mtext>−</mtext><mn>2</mn></mrow></math> route to <math><mi>S</mi><mi>O</mi><mo>(</mo><mn>10</mn><mo>)</mo></math>, the successful SM gauge coupling unification requires the <math><mrow><mn>4</mn><mtext>−</mtext><mn>2</mn><mtext>−</mtext><mn>2</mn></mrow></math> breaking scale to be <math><mi>O</mi><mo>(</mo><msup><mn>10</mn><mn>11</mn></msup><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, and most of the parameter space is excluded. For the <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo><mo>×</mo><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> route, on the other hand, the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> breaking scale can be significantly higher, and a wide range of the parameter space is allowed. Furthermore, the proton lifetime in the <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> case is predicted to be <math><mn>4.53</mn><mo>×</mo><msup><mn>10</mn><mn>34</mn></msup><mtext> </mtext><mtext> </mtext><mi>years</mi></math>, which lies well within the sensitivity reach of the Hyper-Kamiokande experiment. We also examine the constraints on the model parameter space from the Large Hadron Collider and the indirect DM search by Fermi-LAT and MAGIC experiments.

Pseudo-Goldstone dark matter in <math><mi>S</mi><mi>O</mi><mo>(</mo><mn>10</mn><mo>)</mo></math>

We propose a <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo><mo>×</mo><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub><mo>×</mo><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><mi>PQ</mi></mrow></msub></math> model, where <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> is the generalization of the <math><mi>B</mi><mo>−</mo><mi>L</mi></math> (baryon minus lepton number) gauge symmetry and <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><mi>PQ</mi></mrow></msub></math> is the global Peccei-Quinn (PQ) symmetry. There are four fermions families in <math><mover><mn>5</mn><mo>¯</mo></mover><mo>+</mo><mn>10</mn></math> representations of <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math>, a mirror family in <math><mrow><mn>5</mn><mo>+</mo><mover><mrow><mn>10</mn></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> representations, and three <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> singlet Majorana fermions. The <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> related anomalies all cancel in the presence of the Majorana neutrinos. The <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> symmetry is broken at <math><mrow><msub><mrow><mi>M</mi></mrow><mrow><mi>GUT</mi></mrow></msub><mo>≃</mo><mo>(</mo><mn>6</mn><mi>–</mi><mn>9</mn><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>15</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math> and the proton lifetime <math><msub><mi>τ</mi><mi>p</mi></msub></math> is estimated to be well within the expected sensitivity of the future hyper-Kamiokande experiment, <math><msub><mi>τ</mi><mi>p</mi></msub><mo>≲</mo><mn>1.3</mn><mo>×</mo><msup><mn>10</mn><mn>35</mn></msup><mtext> </mtext><mtext> </mtext><mi>years</mi></math>. The <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> breaking also triggers the breaking of the PQ symmetry, resulting in axion dark matter (DM), with the axion decay constant <math><msub><mi>f</mi><mi>a</mi></msub></math> of order <math><msub><mi>M</mi><mrow><mi>GUT</mi></mrow></msub></math> or somewhat larger. The CASPEr experiment can search for such an axion DM candidate. The Hubble parameter during inflation must be low, <math><msub><mi>H</mi><mi>inf</mi></msub><mo>≲</mo><msup><mn>10</mn><mn>9</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, in order to successfully resolve the axion domain wall, axion DM isocurvature and <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> monopole problems. With the identification of the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> breaking Higgs field with the inflaton field, we implement inflection-point inflation, which is capable of realizing the desired value for <math><msub><mi>H</mi><mi>inf</mi></msub></math>. The vectorlike fermions in the model are essential for achieving successful unification of the SM gauge couplings as well as the phenomenological viability of both axion DM and inflation scenario.

<math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo><mo>×</mo><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> axion model with observable proton decay

Gauging the global <math><mi>B</mi><mo>−</mo><mi>L</mi></math> (Baryon number minus Lepton number) symmetry in the standard model (SM) is well motivated since anomaly cancellations require the introduction of three right-handed neutrinos which play an essential role in naturally generating tiny SM neutrino masses through the seesaw mechanism. In the context of the <math><mi>B</mi><mo>−</mo><mi>L</mi></math> extended SM, we propose a pseudo-Goldstone boson dark matter (DM) scenario in which the imaginary component of a complex <math><mi>B</mi><mo>−</mo><mi>L</mi></math> Higgs field serves as the DM in the universe. The DM relic density is determined by the SM Higgs boson mediated process, but its elastic scattering with nucleons through the exchange of Higgs bosons is highly suppressed due to its pseudo-Goldstone boson nature. The model is therefore free from the constraints arising from direct DM detection experiments. We identify regions of the model parameter space for reproducing the observed DM density compatible with the constraints from the Large Hadron Collider and the indirect DM searches by Fermi Large Area Telescope and Major Atmospheric Gamma Imaging Cherenkov.