Light Dark Matter in a Minimal Extension with Two Additional Real Singlets

PHYSICAL REVIEW D 103, 015010 (2021) Light dark matter in a minimal extension with two additional real singlets Markos Maniatis * Centro de Ciencias Exactas and Departamento de Ciencias Básicas, UBB, Avenida Andres Bello 720, 3780000 Chillán, Chile (Received 24 August 2020; accepted 12 December 2020; published 8 January 2021) The direct searches for heavy scalar dark matter with a mass of order 100 GeV are much more sensitive than for light dark matter of order 1 GeV. The question arises whether dark matter could be light and has escaped detection so far. We study a simple extension of the Standard Model with two additional real singlets. We show that this simple extension may provide the observed relic dark matter density, does neither disturb big bang nucleosynthesis nor the cosmic microwave background radiation observations, and fulfills the conditions of clumping behavior for different sizes of Galaxies. The potential of one Standard Model–like Higgs-boson doublet and the two singlets gives rise to a changed Higgs phenomenology, in particular, an enhanced invisible Higgs-boson decay rate is expected, detectable by missing transversal momentum searches at the ATLAS and CMS experiments at CERN. DOI: 10.1103/PhysRevD.103.015010 I. INTRODUCTION collisions. In particular, in this way a DM candidate may enhance the invisible decay rate of a SM-like Higgs boson. Recently it has been reported [1] that the NGC1052–DF2 Note that in the SM the only invisible decay channel of galaxy with a stellar mass of approximately 2 × 108 solar the Higgs boson (h) is via two electroweak Z bosons masses has a rotational movement in accordance with its which subsequently decay into pairs of neutrinos (ν), that observed mass. If this negative indirect search for dark is, h → ZZ → 4ν. matter (DM) is confirmed it challenges any attempt to solve The collider experiments ATLAS [15] and CMS [16] the puzzle of galaxy rotations by modifications of gravity. have measured upper limits on the spin-independent On the other hand we are facing very severe negative DM-nucleon scattering cross section [17,18]. Under the results from direct searches of DM, for instance from assumption that DM couples to the Higgs boson, these the cryogenic experiments SuperCDMS [2], CRESST [3], measurements provide the most stringent bounds available EDELWEISS [4], and the noble liquid experiments on light DM detection, far below the underground DM- ArDM [5], DarkSide [6], DEAP [7],LUX[8], PandaX nucleon direct-detection limits. However, the upper bounds [9], WARP [10], XENON [11], and ZEPLIN [12]. These for light scalar DM are orders of magnitudes less stringent experiments provide very low upper limits for the interaction than the bounds for heavy DM particles with masses cross sections of DM with nucleons. For instance, the of Oð100 GeVÞ. XENON100 [13] direct detection experiment at Gran Let us in this context recall that interactions of DM with Sasso excludes spin-independent elastic nucleon cross sec- SM particles can also not be arbitrarily small: supposing 2 10−45 2 tions down to values as tiny as × cm for DM that DM is produced dynamically in the evolution of the particles with a mass of 55 GeV at 90% confidence level. Universe, for decreasing annihilation cross sections of the In case that the Higgs boson couples to DM also collider DM particles to Standard Model particles, the annihilation experiments may detect DM; for an overview of this subject processes become more and more rare in the evolution of the we refer to [14]. Even that DM is expected not to show Universe and freeze out happens earlier—corresponding to a traces in the detector components, since it is expected to higher DM number density. Eventually this would lead to an couple only very weakly to Standard Model (SM) particles, overclosure of the Universe. it may be discovered as missing transversal momentum in One example of this is the so called Lee-Weinberg bound [19]: in case of leptonic dark matter it has been shown that *[email protected] its mass has to be greater than of the order of 2 GeV in order not to lead to an overclosure of the Universe. However this Published by the American Physical Society under the terms of bound refers to dark matter lepton candidates. If instead the the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to annihilation is not mediated by electroweak gauge bosons the author(s) and the published article’s title, journal citation, this bound does not apply—opening the window for light and DOI. Funded by SCOAP3. dark matter. 2470-0010=2021=103(1)=015010(9) 015010-1 Published by the American Physical Society MARKOS MANIATIS PHYS. REV. D 103, 015010 (2021) Supersymmetric models provide generically new We employ the convention that the upper component of the weakly interacting bosons and fermions, and therefore doublet is charged. The doublet gives as usual masses to the in principle these models can provide light DM particles. fermions and gauge bosons. The potential reads [33,34] However, at least the simplest supersymmetric extension DM μ2φ†φ μ2χ2 μ2η2 λ φ†φ 2 λ χ4 λ η4 of the Standard Model appears to be disfavored, since Vlight ¼ h þ χ þ η þ hð Þ þ χ þ η there is a tension of the predicted Higgs mass spectrum in † 2 † 2 2 2 þ λ χðφ φÞχ þ λ ηðφ φÞη þ λχηχ η ; ð2Þ contrast to observations—in particular the detected Higgs h h boson is too heavy in order to be a supersymmetric where we suppress the argument of the fields from here on particle in the minimal supersymmetric extension (see in most cases. Inspecting this potential we encounter apart for instance the review [20]). 2 1 from the electroweak symmetry SUð ÞL × Uð ÞY the dis- Here we want to study a simple model with two addi- Z 2 0 tional real scalars. One of theses scalars serves as a DM crete symmetries Z2 with χ transforming as χ! − χ and Z2 Z0 candidate (χ) and the other is a scalar mediator (η). Since 2 as η! − η, where we assume that the Higgs doublet as well we expect that the DM particle χ annihilates into a pair η as all Standard Model fields transform trivially. We want of scalar mediators , we are not confronted with the the potential to provide vacuum expectation values for Lee-Weinberg bound and we may have sufficiently large 0 the neutral component of the doublet, φ , as well as for the annihilation cross sections χχ → ηη. On the other hand, field η, that is, besides electroweak symmetry breaking through couplings of the mediator η to neutrinos, similar to SUð2Þ × Uð1Þ → Uð1Þ , the potential should break Z0 the studies [21,22], this annihilation cross section does L Y em 2 spontaneously. Since the symmetry Z2 is not broken, neither disturb big bang nucleosynthesis nor the observed neither explicitly nor spontaneously, we expect a stable cosmic microwave background radiation [23]. Moreover, particle χ providing DM. through the coupling of DM χ to the mediator η we The domain wall problem [36], appearing inevitably for automatically get DM self-interactions [24,25] which do a spontaneously broken discrete symmetry, is expected to not contradict structure formation simulations for different be circumvented in the usual way: we assume that the sizes of galaxies [26]. discrete symmetry Z0 is broken explicitly by an additional The potential of the Higgs boson h andthetworeal 2 cubic mass-parameter term linear in η. This additional term scalars χ, η provides couplings among these elementary however is Planck-mass suppressed and therefore only of particles. These couplings give a changed Higgs phe- relevance at very high energies and therefore negligible in nomenology compared to the SM. For instance, from our analysis here and not further taken into account. the coupling of the Higgs boson h to the DM candidate χ We want the mediator η to decay sufficiently fast in we get an enhanced invisible Higgs-decay rate at order to not disturb big bang nucleosynthesis. This can be colliders, since χ is expected to be stable and escapes achieved by a coupling of η to right-handed neutrinos. We detection. Therefore it is expected to have an enhanced arrange theses couplings by imposing the right-handed invisible decay rate at the large hadron collider at CERN neutrinos to transform under Z0 as at the experiments ATLAS and CMS. The signature 2 comes from missing transversal momentum with 0 0 0 Z2 Z2 Z2 respect to the collision direction in observations at these νR;e→ þ νR;e; νR;μ→ − νR;μ; νR;τ→ − νR;τ; ð3Þ experiments. Scalar DM has been studied, for instance in [27–31] and and add appropriate Majorana kinetic terms and mass terms references therein. In [21,32–34] models are studied with λ the scalar DM candidate accompanied by a mediator, with ij c Lν ¼ iν¯ =∂ν − ην¯ ν þ H:c: ; ð4Þ the DM particle mass of the order of 100 GeV. For a review R R;i R;i 2 R;i R;j of light DM we refer to [35]. Here we focus on the two-real- scalar extension of the SM with one light DM candidate with i; j ∈ fe; μ; τg the indices denoting the three flavors 0 accompanied by a mediator. of the neutrinos. Different choices for the Z2 symmetry behavior of the right-handed neutrinos in (3) could be II. THE MINIMAL EXTENSION WITH TWO chosen, however this assignment keeps the number of λ ADDITIONAL REAL SINGLETS parameters for the matrix ij rather restricted.

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