Axino Mass in Supergravity Models

We analyze the mass of the axino, the fermionic superpartner of the axion, in general supergravity models incorporating a Peccei–Quinn–symmetry and determine the cosmological constraints on this mass. In particular, we derive a simple criterion to identify models with an LSP–axino which has a mass of O(m3/2/fPQ) = O(keV) and can serve as a candidate for (warm) dark matter. We point out that such models have very special properties and in addition, the small axino mass has to be protected against radiative corrections by demanding small couplings in the Peccei–Quinn–sector. Generically, we find an axino mass of order m3/2. Such masses are constrained by the requirement of an axino decay which occurs before the decoupling of the ordinary LSP. Especially, for a large Peccei–Quinn–scale fPQ > 10 11 GeV this constraint might be difficult to fulfill. Email:[email protected] Email:[email protected] The implications of axions have been examined extensively since their existence was suggested by an attractive mechanism for resolving the strong CP problem [1, 2, 3]. Even though axions are very weakly interacting, their astrophysical and cosmological effects are strong enough to narrow down the window of the Peccei–Quinn–scale fPQ to 10 10 GeV < fPQ < 10 GeV [5]. On the same footing the axino as the supersymmetric partner of the axion can play an important role in astrophysics and cosmology [6]. An interesting feature is that axinos may receive a mass of order keV which would render them a good candidate for warm dark matter. If axinos are heavier than a few keV they have to decay fast enough not to upset any standard prediction of big–bang cosmology. Given the weakness of their interactions, a constraint on their lifetime put a rather severe limit on the lower bound of their mass. Therefore it is very important to know the axino mass in discussing the cosmological implications of supersymmetric axion models. In global supersymmetry (SUSY) the calculation of the axino mass was performed in refs. [7, 8]. In this paper, we will provide the computations in models with local supersymmetry (supergravity). Some partial results have been obtained in refs. [9, 10]. In the case of spontaneously–broken global SUSY the axino mass is of the order m3/2/fPQ ∼ keV where m3/2( < ∼ 1TeV) is taken to be the global SUSY–breaking scale [7, 8]. On the contrary, in the context of supergravity, the axino mass can be of order m3/2 as first noticed in ref. [9]. Soon after this it was realized that the axino mass is truly model–dependent and the global SUSY value m3/2/fPQ may be obtained in supergravity models as well [10]. We will extend those results in a generic treatment of supergravity models also including radiative corrections. The prime motivation for supergravity is well–known. Realistic supersymmetric generalizations of the standard model are based on local SUSY spontaneously broken in a so–called hidden sector at a mass scale of order MS ∼ 10GeV [12]. The induced SUSY breaking scale in the observable sector is determined by a value of the order of the gravitino mass m3/2 ∼ M S/MP where MP is the Planck scale. Axionic extensions of the minimal supersymmetric standard model (MSSM) inevitably incorporate an extra sector which provides spontaneous breaking of the Peccei–Quinn U(1)–symmetry at the scale fPQ. This sector (PQ–sector) is considered as a part of the observable sector. In the framework of effective supergravity theories with a Lagrangian composed out of a global SUSY part and soft terms the hidden sector dependences are encoded in the soft terms. We will rely mostly on this effective approach as it makes the calculations tractable. A color anomaly in the PQ–sector can be introduced in two ways. The fields S in this sector can be coupled to the standard Higgs doublets H1, H2 of the MSSM like gSH1H2 (DFSZ–axion) [2, 4] or to new heavy quarks Q1, Q2 like gSQ1Q2 (KSVZ–axion) [1]. Our analysis of axino mass will be concerned with the tree level result in the effective theory which is obtained after breaking the PQ–symmetry and SUSY and should therefore not depend on