CP3-Origins-2014-039 DNRF90, DIAS-2014-39, HIP-2014-28/TH.
Self-Interacting Dark Matter through the Higgs Portal Chris Kouvaris,1, ∗ Ian M. Shoemaker,1, † and Kimmo Tuominen2, ‡ 1 CP3 -Origins & Danish Institute for Advanced Study DIAS, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark 2 Department of Physics and Helsinki Institute of Physics, P.O.Box 64, FI-00014, University of Helsinki, Finland
We study self-interacting dark matter coupled to the Standard Model via the Higgs portal. We consider a scenario where dark matter is a thermal relic with strong enough self interactions that can alleviate the problems of collisionless dark matter. We study constraints from direct detection searches, the LHC, and Big Bang nucleosynthesis. We show that the tension between these constraints and the need for sufficiently strong self-interactions with light mediators can be alleviated by coupling the mediator to either active or sterile neutrinos. Future direct detection data offers great potential and can be used to find evidence of a light mediator and verify that dark matter scatters via long-range self-interactions.
arXiv:1411.3730v1 [hep-ph] 13 Nov 2014
I.
INTRODUCTION
There appears to be tension between the observations and simulations of small-scale structure of Collisionless Cold Dark Matter (CCDM). Observations of dwarf galaxies seem to confirm that the dark matter (DM) density profile is not cuspy as one gets closer to the center of the galaxy as is seen in simulations of CCDM [1], but rather exhibit a flat core [2, 3]. In addition there is the socalled “missing satellite” problem which is the fact that numerical simulations predict many more dwarf galaxies than what is currently observed in the Milky Way [4–6]. Furthermore there is the “too big to fail” problem [7]: it seems that numerical simulations predict dense dwarf galaxies which cannot host the brightest known dwarf galaxies. Although one can claim that the the “missing satellite” problem may be due to the Milky Way being a statistical fluctuation [8–10], the “too big to fail” problem due to unobserved dim dwarf galaxies and the cusp/core problem due to baryonic-DM interactions [11–14], it is possible that the explanation of all the above problems is the existence of sizeable DM-DM interactions. The idea that DM self-interactions may ameliorate the aforementioned problems has been studied extensively and in various contexts [15–34]. In particular, it was pointed out in [20] that DM interacting with a light force carrier φ that satisfies roughly 2 (mX /10 GeV) (mφ /100 MeV) ∼ 1 (where mφ is the mass of the particle φ), can facilitate nicely the flat profile at the core of dwarf galaxies for a range of Yukawa strengths 10−5 < αX < 1, while evading constraints on self-interactions coming from galactic and cluster scales. Although such types of DM self-interactions can resolve some of the problems associated with CCDM, one must ensure that such self-interactions are not strong enough to destroy the ellipticity of spiral galaxies or dissociate
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the subcluster of the bullet cluster [35]. Depending on the scenario there can be additional strict constraints. For example if φ couples to the Standard Model through a Higgs portal [36–43], one should make sure that φ decays before the start of the Big Bang Nucleosynthesis (BBN) (∼ 1 sec) so the decay products will not affect BBN. This constraint sets a minimum interaction coupling between the Standard Model and the dark sector in order to facilitate the fast decay of φ before the BBN era. However as was argued in [28], the requirement for such a minimum coupling might be at odds with invisible Higgs decay constraints imposed at LHC and with constraints from direct search experiments like LUX [44], since this minimum coupling will lead to a minimum DMnucleon cross section in underground detectors. In this paper here we show how these problems can be avoided. We will demonstrate that by coupling φ to neutrinos, we can still have fast decays of φ in the early universe without leading to violation of the experimental constraints from invisible Higgs decays or direct DM searches. We also provide and study a renormalizable theory where such a model can be realized. The paper is organized as follows: In section II we present the Higgs portal and the relevant constraints that can affect the coupling between the dark sector and the Standard Model. In section III we show how the constraints can be evaded if we couple our mediator to light sterile neutrinos, or to active neutrinos. Finally we conclude in section IV.
II.
HIGGS PORTAL PHENOMENOLOGY A.
The Higgs Portal Model
Consider a scenario in which the dark matter X interacts with a light scalar such that the DM self-scattering cross section is large on dwarf scales, yet small on cluster scales. In general, this scalar φ will interact with the SM Higgs through the scalar potential. In the case of a real
2 singlet scalar, we consider the effective Lagrangian: L ⊃ yX φXX + aφ|H|2 + bφ2 |H|2 .
(1)
where X is a Dirac fermion acting as DM, and H is the SM Higgs doublet. While our essential results depend only on the effective interactions in (1), it is useful to have a simple model realization of these couplings. A simple and concrete renormalizable Lagrangian, which leads to the relevant terms of Eq. (1), is L = LSM + LDM ,
Under these assumptions, we expand the potential in terms of the vacuum expectation values of the fields and fluctuations around the global minimum (vEW , w). The states appearing in Eq. (1) are related to the fields in Eq. (3) σ 0 = cos θ h + sin θ φ, s = cos θ φ − sin θ h, and the physical masses are
(2)
where LSM is the Standard Model Lagrangian, LDM is the Lagrangian for a SM singlet real scalar field S and for the dark matter candidate, a SM singlet Dirac fermion, X, and their renormalizable interactions. Explicitly, see e.g. [45], 1 |∂µ S|2 + Xiγ µ ∂µ X + yX SXX − V (S, Σ), 2 1 1 V (S, Σ) = m2 |Σ|2 + m2S S 2 + λ|Σ|4 + λS S 4 2 4 λSΣ 2 2 µ3 3 2 |Σ| S + S + µ1 |Σ| S. + 2 3 (3)
m2φ = λS w2 + wµ3 −
2
EW
and the singlet as S = s + w. Note that we have included the kinetic term of the Higgs field, the usual Higgs potential and the Yukawa interactions with the SM matter fields in LSM . There are some basic constraints that the parameters in the potential have to satisfy. First,the potential has to be positive at large field values, implying that λ > 0 and λS > 0. The √ constraint for λSΣ turns out to be nontrivial, λSΣ > −2 λλS , which implies that the coupling λSΣ can be negative. We are assuming perturbativity in all couplings. Due to the linear interaction ∼ S|Σ|2 it is inevitable that w must be nonzero whenever vEW is. Of course, we are only interested in the case where the global minimum along the neutral Higgs and singlet directions is at (vEW , w), and we assume that the parameters of the potential are such that this is true. It is convenient to use the minimization condition along S and neutral component of the Higgs field to trade the parameters m2 and m2S with the vacuum expectation values vEW and w. Furthermore, we assume that w vEW and that the dimensionful portal coupling µ1 vEW .
µ1 2 v , 2w EW
2 m2h = 2λvEW + λS w 2 2 = 2λvEW + m2φ − wµ3 +
µ1 2 v . 2w EW
(6)
The mixing angle is sin θ '
LDM =
Where we have assumed that the DM mass arises solely from the vacuum expectation value (VEV) of S. There may exist other sources contributing to the mass of X, and these can be taken into account by adding to the fermion Lagrangian in Eq. (3) a bare mass term, ¯ mX,bare XX. The Higgs field Σ is written in terms of the electroweak VEV, vEW , and fluctuations as σ+ Σ = √1 (σ 0 + iη 0 + v ) , (4)
(5)
vEW w vEW µ1 + λSΣ , 2 mh m2h
(7)
Finally, we find for the dimension three and four Higgs portal couplings, i.e. the parameters a and b of Eq. (1), a = µ1 + λSΣ w + (6vEW λ − 2vEW λSΣ ) sin θ.
(8)
and b = λSΣ . Furthermore, due to mixing, the Yukawa coupling between S and the dark matter fermion X now induces a small coupling between the Higgs and the fermion, δX hXX, where δX = −yX sin θ. It is natural for the mass scales in the dark sector to be comparable, µ1 ∼ µ3 ∼ w and much smaller than the EW scale. Adopting this assumption, Eqs. (6) allow us to express the Higgs self coupling in terms of the physical masses: λ =
m2φ m2h µ1 − − 2 2 2vEW 2vEW 4w m2φ µ1 yX + 2 2vEW 4 (mX − mX,bare ) cos θ
= λSM −
! (9)
In the last line we allow for the possibility that the mass of X does not derive entirely from the VEV of φ but may also include a bare mass contribution. Finally imposing vacuum stability, λ > 0, we find that the trilinear coupling µ1 must satisfy µ1
