The relativistic degrees of freedom (<math><msub><mi>N</mi><mi>eff</mi></msub></math>) is one of the crucial cosmological parameters. The precise measurement of <math><msub><mi>N</mi><mi>eff</mi></msub></math> at the time of cosmic microwave background formation, by Planck 2018 can be used to understand the new fundamental interactions, in particular involving light mediators. Presence of any new particle with sufficient energy density and sizeable interactions with Standard Model particles at the temperature around <math><mo>∼</mo><mi>MeV</mi></math> can significantly alter the neutrino decoupling and hence <math><msub><mi>N</mi><mi>eff</mi></msub></math>. Thus the bound on <math><msub><mi>N</mi><mi>eff</mi></msub></math> can place stringent constraints on various beyond Standard Model paradigms involving light particles. <math><mrow><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></mrow></math> models are among such scenarios and are widely studied in several aspects. In this work, we consider several popular <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> models with light <math><msup><mi>Z</mi><mo>′</mo></msup></math> boson like <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math>, <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><mi>B</mi><mo>−</mo><mn>3</mn><msub><mi>L</mi><mi>i</mi></msub></mrow></msub></math>, <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><msub><mi>B</mi><mi>i</mi></msub><mo>−</mo><mn>3</mn><msub><mi>L</mi><mi>j</mi></msub></mrow></msub></math>, <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><msub><mi>L</mi><mi>i</mi></msub><mo>−</mo><msub><mi>L</mi><mi>j</mi></msub></mrow></msub></math>; <math><mrow><mrow><mi>i</mi></mrow><mo>,</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></math> being the flavor indices and study their impact on <math><msub><mi>N</mi><mi>eff</mi></msub></math>. We also examine the constraints from ground based experiments like Xenon1T, Borexino, trident, etc. Our analysis shows that for light mass <math><msub><mi>M</mi><msup><mi>Z</mi><mo>′</mo></msup></msub><mo>≲</mo><mi>O</mi><mo>(</mo><mi>MeV</mi><mo>)</mo></math> the <math><msub><mi>N</mi><mi>eff</mi></msub></math> provides the most stringent constraints on the <math><msup><mi>Z</mi><mo>′</mo></msup></math> mass and coupling, far exceeding the existing constraints from other experiments.

India

Dilip Kumar Ghosh

Purusottam Ghosh

Sk Jeesun

Rahul Srivastava

<math><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>eff</mi></mrow></msub></mrow></math> at CMB challenges <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> light gauge boson scenarios

The current upper limit on  $$N_\textrm{eff}$$  <math> <msub> <mi>N</mi> <mtext>eff</mtext> </msub> </math>   at the time of CMB by Planck 2018 can place stringent constraints in the parameter space of BSM paradigms where their additional interactions may affect neutrino decoupling. Motivated by this fact in this paper we explore the consequences of light gauge boson ( $$Z'$$  <math> <msup> <mi>Z</mi> <mo>′</mo> </msup> </math>  ) emerging from local  $$U(1)_X$$  <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>X</mi> </msub> </mrow> </math>   symmetry in  $$N_\textrm{eff}$$  <math> <msub> <mi>N</mi> <mtext>eff</mtext> </msub> </math>   at the time of CMB. First, we analyze the generic  $$U(1)_X$$  <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>X</mi> </msub> </mrow> </math>   models with arbitrary charge assignments for the SM fermions and show that, in the context of  $$N_\textrm{eff}$$  <math> <msub> <mi>N</mi> <mtext>eff</mtext> </msub> </math>   the generic  $$U(1)_X$$  <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>X</mi> </msub> </mrow> </math>   gauged models can be broadly classified into two categories, depending on the charge assignments of first generation leptons. We then perform a detailed analysis with two specific  $$U(1)_X$$  <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>X</mi> </msub> </mrow> </math>   models:  $$U(1)_{B_3-3L_e}$$  <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mrow> <msub> <mi>B</mi> <mn>3</mn> </msub> <mo>-</mo> <mn>3</mn> <msub> <mi>L</mi> <mi>e</mi> </msub> </mrow> </msub> </mrow> </math>   and  $$U(1)_{B_3-3L_\mu }$$  <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mrow> <msub> <mi>B</mi> <mn>3</mn> </msub> <mo>-</mo> <mn>3</mn> <msub> <mi>L</mi> <mi>μ</mi> </msub> </mrow> </msub> </mrow> </math>   and explore the contribution in  $$N_\textrm{eff}$$  <math> <msub> <mi>N</mi> <mtext>eff</mtext> </msub> </math>   due to the presence of  $$Z'$$  <math> <msup> <mi>Z</mi> <mo>′</mo> </msup> </math>   realized in those models. For comparison, we also showcase the constraints from low energy experiments like: Borexino, Xenon 1T, neutrino trident, etc. We show that in a specific parameter space, particularly in the low mass region of  $$Z'$$  <math> <msup> <mi>Z</mi> <mo>′</mo> </msup> </math>  , the bound from  $$N_\textrm{eff}$$  <math> <msub> <mi>N</mi> <mtext>eff</mtext> </msub> </math>   (Planck 2018) is more stringent than the experimental constraints. Additionally, a part of the regions of the same parameter space may also relax the  $$H_0$$  <math> <msub> <mi>H</mi> <mn>0</mn> </msub> </math>   tension.

Dilip Ghosh

Hubble tension and cosmological imprints of  $$U(1)_X$$  <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>X</mi> </msub> </mrow> </math>   gauge symmetry:  $$U(1)_{B_3-3 L_i}$$  <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mrow> <msub> <mi>B</mi> <mn>3</mn> </msub> <mo>-</mo> <mn>3</mn> <msub> <mi>L</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </math>   as a case study

The identification and isolation of two weakly interacting massive particles (WIMP) dark matter (DM) components at colliders is of wide interest on the one hand but extremely challenging on the other, especially when the dominant signal of both DM components is of the mono-<math><mi>X</mi></math> type (<math><mi>X</mi><mo>=</mo><mi>γ</mi></math>, <math><mrow><mi>Z</mi></mrow></math>, <math><mrow><mi>H</mi></mrow></math>). After emphasizing that an <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> collider is more suitable for this goal, we first identify the theoretical principles that govern the occurrence of two peaks in missing energy (<math><mi>E</mi></math>) distribution, in a double-DM scenario. We then identify a variable that rather spectacularly elicits the double-peaking behavior, namely, the plot of bin-wise statistical significance (<math><mi>S</mi><mo>/</mo><msqrt><mi>B</mi></msqrt></math>) against <math><mi>E</mi></math>. Using Gaussian fits of the histograms, we apply a set of criteria developed by us, to illustrate the above points numerically for suitable benchmarks.

Subhaditya Bhattacharya

Germany

Jayita Lahiri

Biswarup Mukhopadhyaya

Mono-<math><mi>X</mi></math> signal and two component dark matter: New distinction criteria

We study the prospect of simultaneous explanation of tiny neutrino masses, dark matter (DM), and the observed baryon asymmetry of the Universe in a Z 3-symmetric complex singlet scalar extended type-II seesaw model. The complex singlet scalar plays the role of DM. Analyzing the thermal history of the model, we identify the region of the parameter space that can generate a first-order electroweak phase transition (FOEWPT) in the early Universe, and the resulting stochastic gravitational waves (GW) can be detected at future space/ground-based GW experiments. First, we find that light triplet scalars do favor an FOEWPT. In our study, we choose the type-II seesaw part of the parameter space in such a way that light triplet scalars, especially the doubly charged ones, evade the strong bounds from their canonical searches at the Large Hadron Collider (LHC). However, the relevant part of the parameter space, where FOEWPT can happen only due to strong SM doublet-triplet interactions, is in tension with the SM-like Higgs decay to a pair of photons, which has already excluded the bulk of this parameter space. On the other hand, the latest spin-independent DM direct detection constraints from XENON-1T and PANDA-4T eliminate a significant amount of parameter space relevant for the dark sector assisted FOEWPT scenarios, and it is only possible when the complex scalar DM is significantly underabundant. In short, we conclude from our analysis that the absence of new physics at the HL-LHC and/or various DM experiments in the near future will severely limit the prospects of detecting a stochastic GW at future GW experiments and will exclude the possibility of electroweak baryogenesis within this model.

Tathagata Ghosh

Subhojit Roy

Interplay among gravitational waves, dark matter and collider signals in the singlet scalar extended type-II seesaw model

In this work we study the hybrid kind of dark matter (DM) production mechanism where both thermal and non-thermal contribution at two different epochs set the DM relic abundance. This hybrid set up in turn shifts the parameter space of DM in contrast to pure thermal DM scenario. We review such production mechanism in the context of the  $$SU(2)_L$$  <math> <mrow> <mi>S</mi> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mi>L</mi> </msub> </mrow> </math>   lepton doublet dark matter  $$(\Psi )$$  <math> <mrow> <mo>(</mo> <mi>Ψ</mi> <mo>)</mo> </mrow> </math>   augmented with an additional singlet dark scalar (S). The neutral component of the dark doublet can serve as a stable DM candidate and in pure thermal scenario, it is under-abundant as well as excluded from direct detection constraints due to its strong gauge interactions in the sub-TeV mass regime. However, in addition to the thermal contribution, the late time non-thermal DM production from the decay of the long-lived dark scalar S helps to fulfill the deficit in DM abundance. On the other hand, the strong gauge mediated direct detection constraint can be evaded with the help of a  $$SU(2)_L$$  <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 scalar(with  $$Y=2),$$  <math> <mrow> <mi>Y</mi> <mo>=</mo> <mn>2</mn> <mo>)</mo> <mo>,</mo> </mrow> </math>   resulting a pseudo-Dirac DM. To realize our proposed scenario we impose a discrete  $${\mathcal {Z}}_2$$  <math> <msub> <mi>Z</mi> <mn>2</mn> </msub> </math>   symmetry under which both  $$\Psi $$  <math> <mi>Ψ</mi> </math>   and S are odd while rest of the fields are even. We find the lepton doublet pseudo-Dirac DM with mass  $$\sim 450{-}1200$$  <math> <mrow> <mo>∼</mo> <mn>450</mn> <mo>-</mo> <mn>1200</mn> </mrow> </math>   GeV, compatible with the observed relic density, direct, indirect, and existing collider search constraints.

Reviving sub-TeV  $$SU(2)_L$$  <math> <mrow> <mi>S</mi> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mi>L</mi> </msub> </mrow> </math>   lepton doublet dark matter

We investigate the phenomenology of a non-thermal dark matter (DM) candidate in the context of flavor models that explain the hierarchy in the masses and mixings of quarks and leptons via the Froggatt-Nielsen (FN) mechanism. A flavor-dependent U(1)FN symmetry explains the fermion mass and mixing hierarchy, and also provides a mechanism for suppressed interactions of the DM, assumed to be a Majorana fermion, with the Standard Model (SM) particles, resulting in its FIMP (feebly interacting massive particle) character. Such feeble interactions are mediated by a flavon field through higher dimensional operators governed by the U(1)FN charges. We point out a natural stabilizing mechanism for the DM within this framework with the choice of half-integer U(1)FN charge n for the DM fermion, along with integer charges for the SM fermions and the flavon field. In this flavon portal scenario, the DM is non-thermally produced from the decay of the flavon in the early universe which becomes a relic through the freeze-in mechanism. We explore the allowed parameter space for this DM candidate from relic abundance by solving the relevant Boltzmann equations. We find that reproducing the correct relic density requires the DM mass to be in the range (100 − 300) keV for n = 7.5 and (3 − 10) MeV for n = 8.5 where n is the U(1)FN charge of the DM fermion.

United States

K. Babu

Shreyashi Chakdar

Nandini Das

FIMP dark matter from flavon portals

We investigate ways of identifying two kinds of dark matter (DM) component particles at high-energy colliders. The strategy is to notice and distinguish double-peaks(humps) in the missing energy/transverse energy distribution. The relative advantage of looking for missing energy is pointed out, in view of the fact that the longitudinal component of the momentum imbalance becomes an added input. It thus turns out that an electron-positron collider is better suited for discovering a two-component DM scenario, so long as both of the components are kinematically accessible. This and a number of associated conclusions are established, using for illustration a scenario including a scalar and a spin-1/2 particle. We also formulate a set of measurable quantities which quantify the distinguishability of the two humps, defined in terms of double-Gaussian fits to the missing energy distribution. The efficacy of these variables in various regions of the parameter space is discussed, using the aforesaid model as illustration.

Distinguishing two dark matter component particles at e + e  −  colliders

We consider a fermionic dark matter (DM) in the left–right symmetric framework by introducing a pair of vector-like (VL) doublets in the particle spectrum. The stability of the DM is ensured through an unbroken  $$\mathcal {Z}_2$$  <math> <msub> <mi>Z</mi> <mn>2</mn> </msub> </math>   symmetry. We explore the parameter space of the model compatible with the observed relic density and direct and indirect detection cross sections. The presence of charged dark fermions opens up an interesting possibility for the doubly charged Higgs signal at LHC and ILC. The signal for the doubly charged scalar decaying into the dark sector is analyzed in multilepton final states for a few representative parameter choices consistent with DM observations.

Shyamashish Dey

Santosh Rai

Confronting dark fermion with a doubly charged Higgs in the left–right symmetric model

In an endeavor to explain the light neutrino masses and dark matter (DM) simultaneously, we study a 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> extension of the standard model (SM). The neutrino masses are generated through a variant of type-II seesaw mechanism in which one of the scalar triplets has a mass in a scale that is accessible at the present generation colliders. Three SM singlet right chiral fermions <math><msub><mi>χ</mi><mrow><mi>i</mi><mi>R</mi></mrow></msub></math> (<math><mi>i</mi><mo>=</mo><mi>e</mi></math>, <math><mrow><mi>μ</mi></mrow></math>, <math><mrow><mi>τ</mi></mrow></math>) with <math><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></math> charges <math><mrow><mo>−</mo><mn>4</mn></mrow></math>, <math><mrow><mo>−</mo><mn>4</mn></mrow></math>, <math><mrow><mo>+</mo><mn>5</mn></mrow></math> are invoked to cancel the <math><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></math> gauge anomalies and the lightest one among these three fermions becomes a viable DM candidate as their stability is guaranteed by a remnant <math><msub><mi>Z</mi><mn>2</mn></msub></math> symmetry to which <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math> gauge symmetry gets spontaneously broken. Interestingly in this scenario, the neutrino mass and the coannihilation of DM are interlinked through the breaking 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> symmetry. Apart from giving rise to the observed neutrino mass and dark matter abundance, the model also predicts exciting signals at the colliders. Especially we see a significant enhancement in the production cross section of the TeV scale doubly charged scalar in presence of the <math><msub><mi>Z</mi><mrow><mi>BL</mi></mrow></msub></math> gauge boson. We discuss all the relevant constraints on model parameters from observed DM abundance and null detection of DM at direct and indirect search experiments as well as the constraints on the <math><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></math> gauge boson from recent colliders.

Satyabrata Mahapatra

Nimmala Narendra

Narendra Sahu

TeV scale modified type-II seesaw mechanism and dark matter in a 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> symmetric model

We examine the impact of a faster expanding Universe on the phenomenology of scalar dark matter (DM) associated with <math><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>L</mi></mrow></msub></mrow></math> multiplets. Earlier works with a radiation dominated Universe have reported the presence of desert region for both inert <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mi>L</mi></msub></math> doublet and triplet DM candidates where the DM is underabundant. We find that the existence of a faster expanding component before big bang nucleosynthesis can revive a substantial part of the desert parameter space consistent with relic density requirements and other direct and indirect search bounds. We also review the possible collider search prospects of the newly obtained parameter space and predict that such region might be probed at the future colliders with improved sensitivity via a disappearing/stable charged track.