Geneviève BELANGÉR, Kristjan KANNIKE, Alexander PUKHOV and Martti RAIDAL

Transcription

1 Geneviève BELANGÉR,, Alexander PUKHOV and Martti RAIDAL cuola Normale uperiore di Pisa calar dark matter models invariant under a discrete Z 3 symmetry are studied. Unlike in te usual Z case, teir penomenology can contain semi-anniilations processes in wic two dark sector particles scatter into a dark sector and a M particle. Te simplest suc model as complex scalar singlet DM stabilised by Z 3. Compared to te well-known Z case, te new processes can significantly cange relic abundance and prospects for direct detection. Te requirement tat Z 3 be not broken spontaneously, owever, places a lower bound on te direct detection cross section and will allow te wole parameter space to be tested by XENONT. Addition of new scalars can stabilise te Higgs potential up to te GUT scale. Te European Pysical ociety Conference on Hig Energy Pysics 8-4 July, 3 tockolm, weden peaker. c Copyrigt owned by te autor(s) under te terms of te Creative Commons Attribution-NonCommercial-areAlike Licence. ttp://pos.sissa.it/

2 . Introduction One of te most appealing candidates of dark matter (DM) is a weakly interacting massive particle or WIMP. In tis case, DM is a termal relic wose cosmic density is determined by freeze-out. At ig temperature, DM is at termal equilibrium wit te rest of te universe but as te universe expands and cools it begins to anniilate away, but freezes out wit furter dilution. Wat keeps a massive DM particle from decaying into tandard Model (M) particles? Te simplest possible symmetry tat prevents DM decay is of course a Z parity. However, tere is a priori no reason to believe tat te symmetry must be Z. It can very well be Z 3, Z 4, or someting more complicated. As we sall see, iger Z N symmetries imply important canges to te penomenology. Wit Z N, were N is larger tan two, semi-anniilation processes x i x j x k X, were x i is a dark sector particle and X is a M particle, become possible [,, 3]. Wit Z 4 and iger, one can ave multi-component DM and te so-called DM conversion x i x i x j x j becomes possible [4, 5, 6]. Tis is anniilation, but from one DM component to anoter. If a field ϕ as discrete carge X ϕ, it transforms under Z N as ϕ e i Xϕ N π ϕ. (.) Terefore, addition of carges is modulo N and witout loss of generality one can consider carges from to N. Te Z N symmetry can come from breaking of a U() gauge group tat may be embedded in O(), for example: O() U() X Z N by a GUT Higgs wit X = N. However, from te penomenological point of view, different assignments of discrete carges can give te same low energy potential. For given field content, tere is a limited number of possible terms in te scalar potential due to renormalisability. For iger N, te Z N symmetry approximates te original U(). In te scalar potential, tere is always a U() symmetric part and ten a few extra terms. In tis talk we look at scalar DM tat is made stable by a Z N symmetry. calars are peraps simplest DM, and tey could be seen via teir couplings to te Higgs boson. Also, te stability of te tandard Model vacuum is a borderline case [7]. Te quartic self-coupling may run to negative values around GeV tis is below te unification scale. It could well be metastable. Adding new scalars to te model can improve te vacuum stability of te scalar potential. From te purely penomenological point of view, te simplest model of DM te scalar singlet stabilised by a Z symmetry. Tis model as been studied very torougly (see [8] and refs. terein). Te model is very constrained because te same coupling tat determines te relic density te quartic coupling of te Higgs and DM gives te direct detection cross section, Fig.a,c, proportional to λ H. If te scalar singlet is instead stabilised by Z 3, owever [9, ], tere is a new, cubic term in te scalar potential: V Z3 = µ H H + λ H H 4 + µ + λ 4 + λ H H + µ 3 (3 + 3 ), (.) wic will induce te semianniilation reaction given by te Feynman diagram in Fig.b, proportional to λ H µ 3.

3 V f V f (a) (b) Figure : Feynman diagrams contributing to (a) anniilation and (b) semi-anniilation of DM; and (c) DM cross section wit nucleons. Tere is a bound on te cubic coupling: max µ 3 λ N (c) N δ M, (.3) were δ (absolute stability is given by δ =, wile δ < gives metastability). Namely, if µ 3 is too large, te minimum of te potential were Z 3 is conserved is not global. To compute te relic density we solve te Boltzmann equations wit te micromegas package [,, 3, 4]. Te equations for te number density, n, ave been generalised to include semi-anniilation processes dn dt = vσ XX ( n n ) vσ ( n nn ) 3Hn, (.4) were X is any M particle. Te treatment of te semi-anniilation term is described in [5] and te fraction of semi-anniilation is defined as vσ α = vσ XX + vσ. (.5) Note tat is te only semi-anniilation process in tis model. We vary te pysical parameters in te ranges allowed by perturbativity and vacuum stability, select points in te experimentally allowed range for te DM relic density. In Fig. we sow te dependence of λ H and µ 3 on DM mass. Te colour code sows te fraction of semi-anniilation. Te narrow black area wit µ 3 corresponds to Z DM. Naïvely it would seem tat we could make semi-anniilation arbitrarily large wile making λ H arbitrarily small and get a zero anniilation and direct detection cross section. But as we saw tere is a bound on µ 3 tat depends on DM mass and also on its self-coupling λ, sown ere for various values. Note tat in order to ave large semi-anniilation one as to ave a rater large self-coupling λ and will require TeV scale new pysics to deal wit loss of perturbativity. We ave also cecked tat if we allow metastability, te results practically do not cange. 3

4 GeV. ΛH M GeV M GeV 8 In Fig. 3, left, we sow te direct detection cross section. In te area at ig mass bounded by a wite line, te model is valid up to te Grand Unified Teory scale. Te larger te semianniilation, te smaller te cross section, but due to te upper bound (.3) on µ3, te model can be disproved in XENONT. -4 L H N ENO -44 X LUX -45 XEN M GeV T ON ΣI cm -43 I cm L H XENON LUX XENONT LZD Mx GeV Figure 3: Direct detection in te Z3 models wit a singlet (left) and singlet and doublet (rigt). Wat if you want a quartic coupling tat gives semi-anniilation? A new, inert doublet as to be added to te model [5]. Te scalar potential is VZ3 = µ H + λ H 4 + µ H + λ H 4 + µ + λ 4 + λ H + λ H + λ3 H H + λ4 (H H )(H H ) + + µ 3 ( + 3 ) (.6) λ µh ( H H + H H ) + (H H + H H ), Te singlet and te doublet H mix into x and x wit a very small mixing angle, to avoid large coupling to te Z boson. x decays into x since tey ave te same discrete carge. Now, besides te several oter new couplings, tere is te quartic semi-anniilation coupling λ, giving rise to a new semi-anniilation process x x x. Te Higgs-DM coupling beaves similarly, but now tere is semi-anniilation also at large masses [5, 6], see Fig. 3, rigt. Te direct detection cross section goes even lower, but again one can expect te scalar couplings to go non-perturbative at a not too ig scale in tis case. Te γγ rate in tis model in Fig. 4 is compatible wit te experimental limits [7]. 4 Figure : Couplings λh and µ3 vs. DM mass. Colour code sows fraction of semi-anniilation α

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