Decaying Dark Matter Baryons in a Composite Messenger Model

A baryonic bound state with a mass of O(100) TeV, which is composed of strongly interacting messenger quarks in the low scale gauge mediation, can naturally be the cold dark matter. Interestingly, we find that such a baryonic dark matter is generically metastable, and the decay of this dark matter can naturally explain the anomalous positron flux recently observed by the PAMELA collaboration.


Introduction
The origin and nature of the dark matter (DM) are one of the most challenging problems in the particle physics and cosmology. If the DM is in thermal equilibrium in the early universe, the present abundance of the DM is determined by its annihilation cross section σv rel . Here, v rel is the relative velocity of the DM at the freeze out time. The observed DM density requires σv rel ≃ 2×10 −9 GeV −2 . From this result one may derive the upper bound on the mass of the DM as m DM < ∼ 100 TeV [1]. This is because the (s-wave) annihilation cross section never violates the unitarity limit given by The upper-bound value, m DM ≃ 100 TeV, is obtained when the annihilation cross section saturates the unitarity limit and hence the DM is subject to a new strong interaction at the energy scale of 100 TeV. Interestingly, the scale 100 TeV coincides with the supersymmetry (SUSY) breaking scale in the low scale gauge mediation. Therefore, it is intriguing that the DM is one of composite bound states in hidden quarks Q's in the dynamical SUSY-breaking hidden sector [2,3].
In a recent article [4], we proposed DM baryons composed of the messenger quarks P 's, instead of the hidden quarks Q's responsible for the SUSY breaking. Here, the messenger quarks P i α andP α i are assumed to transform as 5 and 5 * under the GUT gauge group, and as anti-fundamental and fundamental representations of a new strongly interacting gauge group SU(N), respectively. Here, the subscript i (α) represents the GUT (SU(N)) index. The DM baryons are expressed as The requirement that these baryons are neutral under the GUT gauge group dictates N = 5.
If the new gauge group is indeed SU(5), the baryon-number violating operators in the superpotential are allowed, W = (1/M 2 P )P 5 + (1/M 2 P )P 5 , and the composite baryons become metastable. Here, M P = 2.4 ×10 18 GeV is the reduced Planck scale. We find that the lifetime of the baryon DM is O(10 24−26 ) sec. It is much longer than the age of the universe and assures the stability of the DM, while it is short enough to leave observable signatures in cosmic rays. Especially, the anomalous positron flux recently observed by the PAMELA collaboration [5] is naturally explained by the decay of the composite DM with the above mass and lifetime.

Strongly interacting messenger model and composite baryons
We consider a SUSY extension of the standard model (SM) in which a SUSY-breaking effect of a hidden sector is communicated to the visible minimal supersymmetric standard model (MSSM) sector by the gauge mediation mechanism [6]. We represent the SUSYbreaking effect of the hidden sector as nonzero vacuum expectation values of scalar and F components of a singlet field Φ S belonging to the hidden sector: We introduce messengers P i α = (L α , D α ) andP α i = (L α ,D α ) which are in the fundamental (5) and anti-fundamental (5 * ) representations of the SM gauge group SU(5) GUT ⊃ SU(3) × SU(2) × U(1). Here, i = 1, · · · , 5 is the index for SU(5) GUT . We assume that the messengers are also in anti-fundamental (5 * ) and fundamental (5) representations of an additional gauge group SU(5) as explained in the Introduction (see also Ref. [4]).
A crucial assumption here is that this additional gauge group is strongly coupled at the messenger mass scale.
The messengers interact with the hidden sector via a Yukawa interaction 1 while they interact with the MSSM sector via the SM gauge interaction. The nonzero scalar and F components of the Φ S yield a mass term for the messengers. This setup is a standard form of the gauge mediation [6].
We now turn to the strongly interacting SU(5) sector. This sector is a SUSY QCD with the number of fundamentals equal to the rank of the gauge group SU(5) (i.e., N f = N = 5). The low energy effective theory of this gauge theory is described by a confined theory with a deformed moduli space [7]. This theory can be described by SU(5) gauge invariant operators made up of messenger quarks. They are mesons and baryons The effective superpotential is given by (with a Lagrange's multiplier field X) [7], where, for simplicity, we consider a supersymmetric mass term for messengers. This term and non-supersymmetric mass terms for messengers are generated by the Yukawa term with the vacuum expectation value of Φ S . This superpotential yields a SUSY invariant vacuum at We can also estimate the masses of the baryons and mesons of the confined theory.
For this purpose, however, we must know the form of the Kähler potential, in particular, the normalization of the kinetic terms. We estimate this by using the Naive Dimensional Analysis (NDA) method [8], which assumes that the confined theory is strongly coupled.
The NDA method gives the above superpotential in terms of canonically normalized fieldŝ B,B,M andX as where g is a constant of order 4π. The corresponding vacuum expectation values are order m.
The baryon and anti-baryon in this theory are neutral under the SM gauge group.
Note also that the baryon number is automatically conserved by the superpotential and where we omit unknown coefficients of order unity. In the confined description, these terms are linear inB andB, and therefore produce a slight shift in the vacuum expectation values of them. We have, instead of Eq. (12), There are interactions between baryons and mesons coming from solving the constraining equation. Upon integratingX and expanding around the vacuum expectation values, There may also be contribution coming from the Kähler potential, e.g., These terms and the above baryon-number violating effects induce the baryons to decay into mesons, which in turn decay into MSSM particles by the gauge interaction or higher dimensional terms in the superpotential (see Ref. [4]). Assuming that the messenger mass m is of the same order as Λ, the lifetime of the baryons are estimated as

Positrons from the DM decays
Before discussing the signals of the DM decays, we give a typical SUSY particle spectrum for concreteness. In our model, it is not easy to calculate the low-energy mass spectrum, since the messenger sector is strongly interacting. We expect that, from the viewpoint of effective theory, the SU (5)  The mass spectrum is shown in Fig. 1, which is calculated by ISAJET 7.72 [9]. It also predicts an ultralight gravitino with mass 0.3 eV. Now let us discuss the signals of the DM decays. For simplicity, we assume that the These decay products emit high energy positrons, and these positron are detected as cosmic rays. Especially, the decays into the gaugino are rich positron source, since almost all of the gauginos decay into the next-to-lightest SUSY particle (NLSP) slepton emitting lepton(s), and subsequently the slepton decays into a gravitino and a lepton. To evaluate the positron spectrum from the decay of the baryon, we have used the program PYTHIA [10]. We estimate the positron fraction following Refs. [11,12,13]. In Fig. 2, we 2 Because of the renormalization effect from SU(5) GUT , the leptonic messenger tends to be light. Therefore, it would be reasonable to assume that the baryon DM dominantly decays to LL mesons because of kinematical reason. Here, for simplicity, we assume that the baryon DM decays into a pair of SU (2)  can naturally explain the anomalous positron flux recently observed by the PAMELA collaboration [5]. We should emphasize that, as shown in Fig. 2, the heavy baryonic DM decay predicts that the positron excess continues up to higher energy, which can be tested by the near future PAMELA data up to about 300 GeV.
In the MSSM LSP DM scenario, the positron flux anomaly stretching up to higher energy indicates the heavier LSP, which may imply the difficulty of the SUSY discovery at the LHC. However, our present model is free from this difficulty.
In addition to the positron signal, this model also predicts high energy cosmic rays such as gamma rays and neutrinos, which are tested by the current of future experiments.
A more detailed study along this line will be given elsewhere.
Note Added: Recently the ATIC collaboration reported an excess in the total e − + e + flux [14], in consistent with the PPB-BETS experiment [15]. This excess may also be explained by the composite DM decay if its mass is O(TeV), which can be realized in our GMSB model by using the SUSY breaking effects to lower the messenger scalar masses [16].