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New Journal of Physics The open–access journal for physics Axinos as dark matter particles Laura Covi1,3 and Jihn E Kim2,3 1 Deutsches Elektronen SYnchrotron DESY, Notkestrasse 85, D-22603 Hamburg, Germany 2 Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea E-mail: [email protected] and [email protected] New Journal of Physics 11 (2009) 105003 (15pp) Received 5 February 2009 Published 16 October 2009 Online at http://www.njp.org/ doi:10.1088/1367-2630/11/10/105003 Abstract. The identification of dark matter in our particle physics model is still an open question. Here, we argue that axinos can be successful dark matter candidates in models with supersymmetry and the axion solution of the strong CP problem. Axinos can be the lightest supersymmetric particle (LSP) or can be heavier than the LSP. Axinos can be produced at the right abundance by thermal scattering and, if they are the LSP, also by out of equilibrium decays of the lightest superpartner of SM fields (LSPSMs). On the other hand, heavier (not LSP) axinos can generate a part of the neutralino LSP dark matter. Depending on the nature of the supersymmetric spectrum, and if R-parity is strictly conserved or slightly broken, very different signals of the LSP axino scenario can arise in colliders and in astrophysics. 3 Authors to whom any correspondence should be addressed. New Journal of Physics 11 (2009) 105003 1367-2630/09/105003+15$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft 2 Contents 1. Introduction 2 2. Axino models and axino mass 3 2.1. Axion models ................................... 4 2.2. Axino, SUSY breaking and axino mass ..................... 5 3. Axino cosmology with ma˜ < Mχ 6 3.1. Producing axinos in the early universe . ..................... 6 4. Axino cosmology with ma˜ > Mχ 8 5. Axino DM and R-parity breaking 10 6. The LSPSM and colliders 12 6.1. How to distinguish the LSP from LSPSM decay? . 12 7. Conclusions 13 Acknowledgments 13 References 13 1. Introduction The nature of dark matter (DM) as a particle is still unknown today, since its main evidence relies only on the gravitational interaction and is universal. On the other hand, from some of the present data and numerical simulations of structure formation, we do know that it must be a neutral, cold, probably collisionless (i.e. quite weakly interacting) and very long- lived particle [1]. Unfortunately, a particle with these characteristics is not contained in the standard model (SM) of particle physics: the only neutral stable and massive candidates, the electroweakly active neutrinos, are so light that they are, at most, hot DM and therefore only a subdominant component. DM has therefore to be part of a larger picture and of any physics beyond the SM. Probably the best motivated models of this kind rely on supersymmetry (SUSY), which is a unique extension of the Poincaré algebra and calls for a doubling of all degrees of freedom with 1 spin difference 1s 2 [2]. In this context, it is then clear that more particles can be suitable DM candidates, if they= ± are the lightest ones and sufficiently long-lived, in particular the very well studied cases of the neutralino or the gravitino. But if we invoke the Peccei–Quinn (PQ) solution to the strong CP problem in supersymmetric models, a new multiplet has to be introduced, namely the axion multiplet [3, 4]. Such a multiplet must by its very nature interact with the SM particles, but the scale of its interaction is suppressed by the scale at which the PQ symmetry is broken, Fa. Therefore, the fermionic component of the multiplet is naturally a very weakly interacting particle and can easily be the lightest state of the spectrum, but it can also be heavy. We will present in this paper a summary of the axino cold DM (CDM) scenario [5]–[11] and explore the implications of axino DM for the phenomenology of supersymmetric models and for future indirect detection of DM. New Journal of Physics 11 (2009) 105003 (http://www.njp.org/) 3 2. Axino models and axino mass In discussing axino models, one should refer to the corresponding axion models. So, let us start with the axion shift symmetry and the reparametrization invariance as discussed in [12]. The PQ solution of the strong CP problem [13] requires the introduction of the axion a, which renders the θ parameter4 dynamical and allows it to relax to zero after the QCD phase transition. An axion a is a pseudoscalar boson coupling to the gluon anomaly as αsa µν Lθ Gµν G , (1) = 8π Fa ˜ µν where the dual field strength is G 1 µνρσ G , without any other interaction term in the ˜ 2 ρσ potential V . Below the QCD chiral symmetry= breaking scale, an axion potential is developed, which arises purely from integrating out the strongly interacting fields with that anomaly term. If the original potential contains other axion-dependent terms, they should be extremely small and not affect the position of the minimum, such that the axion vaccuum expectation value 11 (VEV), θ a /Fa, should be extremely small, <10− . Let| us| ∼ now h i focus on the QCD interactions containing the axionic degree of freedom. The axion effective Lagrangian below the chiral symmetry breaking scale reads 1 1 L f 2∂µθ∂ θ Ga Gaµν + (q iD/q + q iD/q ) + c (∂ θ)qγ µγ q θ,eff S µ 2 µν L L R R 1 µ 5 = 2 − 4gs ¯ ¯ ¯ θ aµν ic2θ a qL mqR e + h.c. + c G G (or L ) − ¯ 3 32π 2 µν ˜ det θ iµν + c F i F + L (c`, c`), (2) θγ γ 32π 2 em,µν ˜ em leptons,θ 1 2 where θ a/fS with the axion decay constant fS defined up to the domain wall number = ( fS N Fa) and q are the SU(3)c charge-carrying quark fields. The c term is the derivative = DW 1 coupling with quarks respecting the PQ shift symmetry, the c2 term is related to the phase in the quark mass matrix, and the c3 term is the anomalous coupling or the determinental interaction Ldet. The Lagrangian term Lleptons,θ is the axion interaction with leptons, which in principle can ` ` contain other constants c1, c2. The coupling constants c1, c2 and c3 are obtained below the axion scale fS after integrating out the heavy degrees of freedom responsible for the PQ symmetry breaking. The mass parameter m is defined to be real and positive below the electroweak (EW) scale. The Lagrangian (2) has a shift symmetry a a+ (constant), which reparametrizes the → iαa(x) couplings c1, c2 and c3. Explicitly, changing the phases of the quark fields qL e qL iαa(x) → and qR e− qR, we obtain the following reparametrization, where the effective one point irreducible→ action 0 [a(x), Aa (x) c , c , c , m, 3 ] changes to 1PI µ ; 1 2 3 QCD 0 [a(x), Aa (x) c α, c 2α, c + 2α, m, 3 ]. (3) 1PI µ ; 1 − 2 − 3 QCD So we see immediately, from this transformation for a single quark, that if it is massless, the corresponding c1, c2 parameters disappear and we can shift away the anomaly term completely with no physical effect. This is in fact one alternative solution to the strong CP problem; see [12] for a detailed discussion. For determining the axion mass, all c1, c2 and c3 terms may be relevant, but only the combination c2 + c3 actually appears [12]. Usually, in the field theoretic axion models, we start 4 Below, θ denotes the conventional θ θ0 + Arg Det mq . ¯ = New Journal of Physics 11 (2009) 105003 (http://www.njp.org/) 4 with c1 0. In any case, note that the c1 term can be reabsorbed in the c2 term using integration by parts= and the quark equations of motion. So, in the next sections we just start with the couplings c2 and c3. Usually, F is defined by transferring all couplings of the axion to the coefficient of GG and a ˜ rescaling c3 to one. On the other hand, fS is defined to be the VEV of the singlet field σ breaking the PQ symmetry. It turns out that c2 + c3 is an integer, not necessarily one in the pseudoscalar field space, and it determines the number of minima in the axion periodic potential.