Physics Letters B 731 (2014) 232–235 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Baryon asymmetry, dark matter and local baryon number ∗ Pavel Fileviez Pérez , Hiren H. Patel Particle and Astro-Particle Physics Division, Max-Planck Institute for Nuclear Physics (MPIK), Saupfercheckweg 1, 69117 Heidelberg, Germany article info abstract Article history: We propose a new mechanism to understand the relation between baryon and dark matter asymmetries Received 31 January 2014 in the universe in theories where the baryon number is a local symmetry. In these scenarios the B − L Received in revised form 17 February 2014 asymmetry generated through a mechanism such as leptogenesis is transferred to the dark matter and Accepted 21 February 2014 baryonic sectors through sphalerons processes which conserve total baryon number. We show that it is Availableonline26February2014 possible to have a consistent relation between the dark matter relic density and the baryon asymmetry Editor: M. Cveticˇ in the universe even if the baryon number is broken at the low scale through the Higgs mechanism. We also discuss the case where one uses the Stueckelberg mechanism to understand the conservation of baryon number in nature. © 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP3. 1. Introduction The existence of the baryon asymmetry and cold dark matter density in the universe has motivated many studies in cosmology and particle physics. Recently, there has been focus on investiga- tions of possible mechanisms that relate the baryon asymmetry to dark matter density, i.e. ΩDM ∼ 5ΩB . These mechanisms are based on the idea of asymmetric dark matter (ADM). See Ref. [1] for a recent review of ADM mechanisms and Ref. [2] for a review on baryogenesis at the low scale. Crucial to baryogenesis in any theory is the existence of baryon violating processes to generate the observed baryon asymmetry in the early universe. In theories where the baryon number is a local symmetry and spontaneously broken at low scale, one could have a Fig. 1. Schematic representation of the simultaneous generation of the baryon and mechanism which explains the relation of the baryon asymmetry dark matter asymmetry through the sphalerons. and dark matter. For simple realistic theories where the baryon number is a local symmetry, see Refs. [3–5], and for studies of through the Higgs mechanism consistent with collider bounds. baryogenesis in this context, see e.g. Ref. [6]. This simple theory provides a fermionic dark matter candidate for In this article, we propose a new mechanism to simultaneously which stability is a natural consequence of the spontaneous break- generate the baryon and dark matter asymmetries through the ing of baryon number at the low scale. See Ref. [5] for details. electroweak sphalerons. The basic paradigm is illustrated in Fig. 1. We perform an equilibrium thermodynamic analysis that con- In this model baryon number is a local gauge symmetry which is nects the chemical potentials of the standard model quarks, and spontaneously broken at the low scale. Therefore, the sphalerons of the dark matter candidate. In this way, we find a consistent should conserve total baryon number. In this context, the all bary- connection between baryon asymmetry and dark matter relic den- onic anomalies in the standard model are canceled by adding a sity. For completeness, we perform the study in the three possible simple set of vector-like fermionic fields with different baryon cases. In the first case, baryon number is conserved in nature, and numbers. Furthermore, one can generate masses for all new fields the leptophobic gauge boson acquires its mass through the Stueck- elberg mechanism. In the second and third cases, baryon number is broken through the Higgs mechanism. However, only in the third * Corresponding author. E-mail addresses: fi[email protected] (P. Fileviez Pérez), case can one have a Higgs boson with the properties consistent [email protected] (H.H. Patel). with the recent observations at collider experiments. http://dx.doi.org/10.1016/j.physletb.2014.02.047 0370-2693/© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP3. P. Fileviez Pérez, H.H. Patel / Physics Letters B 731 (2014) 232–235 233 This article is organized as follows. In Section 2 we define the theories defined at the high scale where baryon number is con- theory where baryon number is a local gauge symmetry, and we served. For previous studies where the dark matter candidate has discuss the different mechanisms for generating the leptophobic baryon number see Refs. [12–14]. gauge boson mass. In Section 3 we perform the equilibrium ther- In this article we will investigate scenario 3 in detail since we modynamic analysis and find the connection between the baryon can have a consistent model with cosmology and particle physics. asymmetry and dark matter density. Finally, in Section 4 we dis- We will also present the final result for the first two scenarios. cuss the main results. 2.1. Symmetry breaking and mass generation 2. Local baryon number In order to generate masses in a consistent way we extend the In order to understand the conservation or violation of baryon scalar sector with a new Higgs boson S B to allow for spontaneous number in nature we can study a simple model where baryon breaking of baryon number, number is a local symmetry. The theory is based on the gauge ∼ − group S B (1, 1, 0, 3). (3) Notice that the baryon number of the new scalar field is deter- ⊗ ⊗ ⊗ SU(3)C SU(2)L U(1)Y U(1)B . mined once we impose the condition that we need to generate An anomaly-free theory is defined by including additional fermions vector-like masses for the new fermions. The relevant interactions that account for anomaly cancellation. A simple set of fields is of the new fields are given by −L ⊃ ¯ + ¯ + ¯ ˜ Y1ΨL HηR Y2ΨR HηL Y3ΨL HχR 1 1 + Y Ψ¯ H˜ + λ Ψ¯ Ψ S + λ ¯ S ΨL ∼ 1, 2, − , B1 ,ΨR ∼ 1, 2, − , B2 , 4 R χL 1 L R B 2ηR ηL B 2 2 + λ3χ¯ R χL S B + h.c. (4) ηR ∼ (1, 1, −1, B1), ηL ∼ (1, 1, −1, B2), For the special case B1 =−B2, terms such as a1χL χL S B and χR ∼ (1, 1, 0, B1), and χL ∼ (1, 1, 0, B2), (1) † a2χR χR S B are allowed. However, we will focus on the more where we use the convention that Q = T3 + Y to define the nor- generic case where B1 = −B2 and where the dark matter anni- malization of hypercharge. Requirement of anomaly cancellation hilation through Z B is not velocity suppressed [14]. implies the relation Once the new Higgs S B acquires a vacuum expectation value spontaneously breaking local U(1)B , no operator mediating proton B1 − B2 =−3, (2) decay is generated, and the scale for baryon number violation can be very low. For the bounds on the mass of a leptophobic neutral on the assignment of baryon number to the new fermions. gauge boson see Refs. [15,16]. Notice that the baryon numbers of the vector-like fields must The model enjoys three anomaly-free symmetries: be different. Since the local baryon number is an abelian symme- try we can generate mass for the new gauge boson Z associated B • B − L in the Standard Model sector is conserved in the usual with U(1) with or without the Higgs mechanism. We therefore B way. We will refer to this symmetry as (B − L) . consider here three different cases: SM • The accidental η global symmetry in the new sector. Under this symmetry the new fields transform in the following way: • Scenario 1: The Stueckelberg mechanism generates mass for the leptophobic gauge boson Z , and the new fermions ac- iη B ΨL,R → e ΨL,R , quire mass only from the SM Higgs boson. See for example iη Ref. [7] for the application of the Stueckelberg mechanism in ηL,R → e ηL,R , this context. Unfortunately, because of its sizable couplings to iη χL,R → e χL,R . the new fermions, this scenario predicts a reduced branching fraction of the Higgs decay to two photons that is at vari- This conserved charge will determine the dark matter asym- ance with collider experiments. Of course, one can add a set metry as pointed out in models with vector-like fermions in of scalar fields with negative couplings to offset the diphoton Ref. [17]. Notice that this symmetry guarantees the stability of branching fraction. But we do not see this possibility as very the lightest field in the new sector. Therefore, when this new appealing. See Ref. [8] for the study of the Higgs decays in field is electrically neutral, one can have a candidate for cold theories with extra chiral fermions. dark matter in the universe. • • Scenario 2: Using the Higgs mechanism with a new scalar Above the symmetry breaking scale, total baryon number B T carried by particles in both, the standard model and the new field S B with baryon number assignment different from ±3 sector is also conserved. Here we will assume that the sym- we can generate mass only for the gauge boson Z B .Asinthe first scenario one will run into problems with the predictions metry breaking scale for baryon number is low, close to the of the SM Higgs decays.