Double detection
5.3 Dark matter and Dark radiation scenario
In this section we discuss the first extension of the minimal decaying DM scenario studied in the previous section. Specifically, in this extension the spectrum of the Beyond Standard Model (BSM) states is augmented with another SM singlet χ and the scalar spectrum is constituted by two fields, a SU(2) doublet and a singlet. The photon line is now produced by the decay ψ→χγ, whose Feynman diagram has been drawn in Figure 5.4. Such a decay is described by the following lagrangian:
Leff =λLψq¯ LΣ†q+λRψt¯ RΣ†u
+h.c.
+λ0Lχq¯ LΣ†q+λ0Rχt¯ RΣ†u+h.c.
+µHΣqΣ†u+h.c. . (5.9)
We have assigned to the two scalar fields the quantum numbers of a left-handed and right-handed up-quark in order to enhance the loop function through the top mass and possibly achieve the desired value of the DM lifetime for suppressed couplings, such that the scalar fields are long-lived at the LHC. Given the strong sensitivity of the DM lifetime on the SM fermion
Chapter 3. 3.55 keV X-ray from DM decay at LHC 127
Figure 5.4: Diagrams contributing at one-loop to the DM 2-body decay intoγ and χinduced by scalar-mixing.
masses, we have assumed for simplicity that the two SM singletsχandψ are coupled only with the third generation quarks. The couplings of the scalar field with only SM fermions, which we have omitted for simplicity, are not relevant for the DM decay and they can be set to be of comparable value to the couplings governing the decay of the scalar field into DM.
In this case after the electroweak symmetry breaking the fields Σq,Σu mix with each other, thus giving the physical fields Σ1, Σ2, which are the eigenstates of the mass matrix:
M= m2Σu µv µv m2Σ
q
!
, (5.10)
where v is the v.e.v. of the Higgs field. The eigenvalues of the matrix Mare instead given by the expression:
and they can be obtained by diagonalizingMthrough the generic matrix:
η = cosθ sinθ
−sinθ cosθ
!
(5.12) where the mixing angle is given by:
tan 2θ= 2µv
m2Σq −m2Σu . (5.13)
In the above expressions mΣq and mΣu represent the mass terms of the SU(2) doublet and sin-glets. These are assumed to be originated by conventional mass terms of the formm2Σq,uΣ†q,uΣq,u. As already mentioned, additional mass terms can be originated by terms, allowed by gauge symmetries, of the typeλhhΣΣ|H|2|Σq,u|2 and/or λhhΣΣ(HΣq)†(HΣq) whose contributions are O(100GeV) for couplings of order one. Moreover, we expect them to be subleading compared to that proportional to the dimensionful quantity µ since they do not mix the two states and just change mΣu,d. A theoretical investigation of the scalar sector of the theory is beyond the scope of this work; our results will be thus expressed in terms of the mass eigenstates mΣ1
Chapter 3. 3.55 keV X-ray from DM decay at LHC 128 and mΣ2, assumed to be free parameters, and we will regard (5.10) and (5.12) as a generic parametrization.
The DM decay rate is then given by:
Γ (ψ→χγ) = αm3ψ the DM lifetime is mostly determined by the contribution from the lightest eigenstate in that case.
Neglecting the mass of χ (the reason will be clarified in the following) it can be expressed as: The DM production is as well dominated by Σ1 and λ is again determined by Equation (5.5).
The expected value of λ0 from the combined requirement of reproducing the photon-line and the correct DM relic density is:
λ0 '1.5×10−4 mψ
This value, although sensitively lower than the one obtained in the previous case, is still large enough to make the scalar field decay promptly at the LHC. Note that in the case of nearly degenerate mass eigenstates, a partial cancellation between the two contribution takes place and therefore larger couplings are required to match the same lifetime. Being substantially free parameters, the couplings of the scalar field with only SM fermions can be of comparable order as (5.16) in order to allow for the observation of a double LHC signal. Since we are still dealing with prompt decays, the strong limits from LHC searches must be taken into consideration.
The most stringent ones come from searches of top squarks. In particular, current limits allow 177 . mΣ1 . 200 GeV or mΣ1 > 750 GeV [54–56]. These ranges can be actually relaxed in presence of a branching ratio of decay into missing energy lower than 1.
We have compared, analogously to what done in the previous section, in Figure 5.5 the prospects of LHC detection with the information from DM phenomenology. The scenario de-picted is analogous to the minimal scenario of the previous section with the (standard) cos-mology that strongly prefers prompt decays. Despite the different experimental signature (top plus missing energy) the prospects of hypothetical LHC detection are as well very similar to the previous scenario. On the other hand, within the assumption of no extra symmetries with
Chapter 3. 3.55 keV X-ray from DM decay at LHC 129
Figure 5.5: The same as Figure 5.3 but for the DM+Dark Radiation scenario. We give here as red solid and dashed lines the values of the couplingλ0 corresponding to the right DM lifetime and FIMP production and to the out-of-equilibrium condition respectively. The other lines are as in Fig. 5.3. Notice that the limits and the future sensitivity for prompt decays refer here to
searches for supersymmetric top partners decaying into top quarks and missing energy.
respect to the SM, a coupling between the scalar field and only SM fermions is allowed and can be of the same order as λ0, providing then two types of decays and signatures (low and high amount of missing energy) for the scalar field. As already mentioned in the previous section, this discussion is strictly valid under the assumption that LHC phenomenology is dominated by a single heavy charged state. In case also the heavier mass eigenstate Σ2 is efficiently pro-duced we would have additional signals like the one studied in [229] which could not be directly correlated with DM signals. We remind, on the other hand, that the two scalar fields Σq and Σu are mostly produced at the LHC through gluon fusion and their production cross-section is strongly sensitive to the mass of the pair-produced states. Our scenario requires a sizable value of µv, in order not to suppress the mixing angle, implying a sizable mass splitting between the two mass eigenstates Σ1 and Σ2. The assumption that the dominant LHC signals are mostly related to Σ1 appears thus reasonable.
Notice also that the stateχis cosmologically stable if it is very light and might give a sizable contribution to the overall DM abundance. Indeed, contrary to the case of ψ, the value of the couplingλ0is high enough to create, at early stages of the history of the Universe, a thermal pop-ulation ofχparticles through decays/inverse decays of the scalar fields and the 2→2 scattering processes with top quarks. In that moment the χ particles undergo a relativistic freeze-out at temperatures between 100 GeV and 1 TeV. In order to avoid bounds from overclosure of the Universe and structure formation, we impose a very small mass for this new state,mχ.O(eV).
Such a light state would then remain relativistic for a long time and contribute to the number of effective neutrinos Neff. The deviation from the SM prediction Neff = 3.046 induced by the
Chapter 3. 3.55 keV X-ray from DM decay at LHC 130
W
γ νL
`L νL
`L
ψ
`L
γ νL
νL W W ψ
Figure 5.6: Diagrams contributing at one-loop to the DM 2-body decay into γ and ν induced byW.
χ particles can be expressed as [230,231]:
∆Neff = 23.73
(gs∗(Td))4/3 , (5.17)
where Td represents the decoupling temperature from the primordial thermal bath of the χ particles. Thanks to the rather high decoupling temperature, we have gs∗(Td) ∼ 100 due to Standard Model states and therefore ∆Neff ∼0.05, which is compatible with the current con-straints [232]. Unfortunately such a small contribution to the number of relativistic species is at the boundary of detection even for an ideal CMB experiment including polarization [233].
Before moving onto our last DM decay scenario, it is worth remarking the direct correlation of the X-ray signal with the presence of one of the SM singlets in our scenario in thermal equilibrium. Indeed, in order to the ensure the desired lifetime of the DM we needλλ0 ∼10−12. Comparing this value with Equation (5.6) we notice that the two couplings cannot contemporary satisfy the out-of-equilibrium condition.