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We discuss the possible connection between the scale for baryon number violation and the cosmological bound on the dark matter relic density. A simple gauge theory for baryon number which predicts the existence of a leptophobic cold dark matter particle candidate is investigated. In this context, the dark matter candidate is a Dirac fermion with mass defined by the new symmetry breaking scale. Using the cosmological bounds on the dark matter relic density we find the upper bound on the symmetry breaking scale around 200 TeV. The properties of the leptophobic dark matter candidate are investigated in great detail and we show the prospects to test this theory at current and future experiments. We discuss the main implications for the mechanisms to explain the matter and antimatter asymmetry in the Universe.

The possible existence of dark matter in the Universe has drawn the attention of the scientific community for a long time. Fortunately, today we have many different types of experiments looking for possible signatures which can help us to reveal the nature of the dark matter

In the Standard Model of particle physics, the so-called baryon number

One can define a simple anomaly free theory based on

One predicts the existence of a cold dark matter candidate, and its mass is defined by the new symmetry scale.

The spontaneous breaking of baryon number at the low scale is possible in agreement with all experimental bounds in particle physics and cosmology.

A possible relation between the baryon asymmetry and dark matter densities is possible, and one can have a simple mechanism for baryogenesis in this context.

In this article, we investigate carefully the properties of the leptophobic dark matter candidate in a simple theory based on local baryon number. In this theory, the dark matter candidate and the new leptophobic gauge boson masses are defined by the baryon number breaking scale. We study all dark matter annihilation channels in great detail and find that, in order to be in agreement with the cosmological bounds on the dark matter relic density, the local baryon symmetry must be broken below the

This article is organized as follows. In Sec.

The theory we investigate in this article predicts a fermionic dark matter candidate. In this case the cold dark matter is a Standard Model singlet

Integrating out heavy fields in simple extensions of the Standard Model we can obtain a simple effective field theory for the leptophobic dark matter. In the theories we are interested in, one can expect the following dimension five and six operators defining the interactions between the Standard Model fields and the dark matter field

Particle content.

The simplest realistic theories for the spontaneous breaking of baryon number have been proposed in Refs.

The Lagrangian of the theory can be written as

The Higgs sector of the theory is composed of the Standard Model Higgs and the new Higgs

In this theory, there are two physical Higgs bosons,

The quartic couplings in the scalar potential can be written as a function of the Higgs masses and the mixing angle:

In Fig.

Parameter space in the

This theory predicts the existence of a leptophobic gauge boson

Experimental bounds for the leptophobic gauge boson

In the theory discussed above, one predicts the existence of new neutral and charged fermions. After symmetry breaking, we can compute the mass matrix of the new neutral fermions in the basis

The mass matrix for the new charged fermions is given by

In this paper, we will investigate the dark matter properties in the limit when

The lightest new fermion in the theory discussed above can be a good candidate for the cold dark matter if it is neutral. In the previous section, we discussed the properties of the new fermions present in the theory. Since the direct detection bounds are very strong for any dark matter field with

In Fig.

Minimal Mixing Scenario

When there is no mixing between the two Higgs bosons present in the theory

In Fig.

In Fig.

Annihilation into two quarks:

In the top left panel of Fig.

Annihilation into two leptophobic gauge bosons:

In the top right panel of Fig.

Annihilation into the leptophobic gauge boson

In this case, we have three contributions to the annihilation into

Annihilation into two new Higgs bosons

One has also three type of contributions for the annihilation into two Higgs bosons; we have the u and t channels, and the s-channel mediated by the Higgs boson:

Now, combining all the above annihilation channels, we can show the full parameter space allowed by cosmology. Furthermore, it is important to use the perturbativity bound on the relevant Yukawa couplings. In this case we can write

Maximal Mixing Scenario

The mixing angle between the two Higgs bosons can be as large as

Dark matter annihilation channels.

Branching ratios for the different dark matter annihilation channels when the mixing angle between the Higgs bosons is

Allowed regions by the cosmological bound on the relic density for each annihilation channel when

Parameter space allowed by the relic density constraint and perturbativity including all annihilation channels when

Branching ratios for the different dark matter annihilation channels when the mixing angle is

Parameter space allowed by the relic density constraint and perturbativity including all annihilation channels when

In the previous study, we have shown that this theory must be realized at the low scale in order for the theory to be in agreement with the cosmological bounds on the relic density. Nevertheless, one has also to take into account an important aspect of any dark matter study: the study of the predictions for the direct dark matter experiments. In this theory, the spin-independent elastic nucleon-dark matter cross section is given by

Feynman diagrams relevant for dark matter direct detection.

Predictions for the spin-independent dark-matter-nucleon scattering cross section in the context of the minimal (left panel) and maximal (right panel) mixing scenarios in agreement with the dark matter relic density constraint. The gray shaded area represents the excluded area by the Xenon1T bounds

In this theory, there are several annihilation channels for the leptophobic dark matter candidate, with the annihilation into two bottom quarks when

Predictions for the thermal dark matter annihilation into two bottom quarks. In purple we show the points saturating the relic density bound, while the gray shaded area shows the parameter space excluded by the Fermi-LAT Collaboration

In Figs.

Upper bound on the symmetry breaking scale imposed by meeting the relic density constraint

In order to investigate the possibility to find the upper bound on the baryon number violation scale, we have investigated the properties of a leptophobic dark matter candidate in a simple theory where the local baryon number is broken at the low scale. We have studied all the annihilation channels in great detail and found the allowed parameter space in agreement with the cosmological bounds on the cold relic density. Using the cosmological bounds on the relic density, we find that the local baryon number symmetry must be broken below the 200 TeV scale. This is a striking result which tells us that this theory could be tested in the near future at collider experiments.

The unitarity constraints are very important in our study. It is well known that the unitarity constraints generically impose an upper bound around 100 TeV for a thermal produced cold dark matter candidate. However, it is not always the case that the bound coming from unitarity constrains the scale of the new theory, i.e., the mass of the new mediator. In general, it will constrain the ratio between the different mass scales in the theory. The theory we investigated in this paper is very unique because both the dark matter and the new gauge boson

The upper bound on the symmetry breaking scale also has profound implications for cosmology, in particular for baryogenesis, since the scale for baryon number violation must be low. We would like to emphasize that this theory does not have the main problem of most of the extensions of the Standard Model, where the new physical scale can be very large and one cannot be sure about the possibility to test these theories.

One of the main implications of having a low scale for the spontaneous breaking of local baryon number is that one needs to take into account the fact that the local baryon number can be broken at the very low scale. The simplest scenario for baryogenesis in this case is to have leptogenesis at the high scale and impose the conditions on the chemical potentials due to the conservation of baryon number. In this case, the lepton asymmetry generated by leptogenesis is converted to a baryon asymmetry by the sphalerons, but the conversion factor is smaller than the conversion factor in the Standard Model; see Refs.

P. F. P. thanks Mark B. Wise for discussions and the Walter Burke Institute for Theoretical Physics at Caltech for hospitality and support. This work has been partially supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. This work made use of the High Performance Computing Resource in the Core Facility for Advanced Research Computing at Case Western Reserve University. The work of C. M. has been supported in part by Grants No. FPA2014-53631-C2-1-P, No. FPA2017-84445-P and No. SEV-2014-0398 (AEI/ERDF, EU), and a “La Caixa-Severo Ochoa” scholarship.

Here we list some Feynman rules relevant for our discussion:

In our discussion, we have assumed that the lightest new neutral field corresponds to the field

We note that our main goal in this Appendix is to show that the

Predictions for the direct detection spin-independent cross section

Here we revisit the bound on the dark matter mass pointed out in Ref.

Since the angular dependence of the cross section arises through the Mandelstam variable

So, this approximation results in the cross section with no angular dependence, which corresponds to the

To implement this constraint, we calculate the total annihilation cross section of the dark matter candidate with the Mandelstam variable