Baryon-Dark Matter Coincidence in Mirrored Unification

About 80\% of the mass of the present Universe is made up of the unknown (dark matter), while the rest is made up of ordinary matter. It is a very intriguing question why the {\it mass} densities of dark matter and ordinary matter (mainly baryons) are close to each other. It may be hinting the identity of dark matter and furthermore structure of a dark sector. A mirrored world provides a natural explanation to this puzzle. On the other hand, if mirror-symmetry breaking scale is low, it tends to cause cosmological problems. In this letter, we propose a mirrored unification framework, which breaks mirror-symmetry at the grand unified scale, but still addresses the puzzle. The dark matter mass is strongly related with the dynamical scale of QCD, which explains the closeness of the dark matter and baryon masses. Intermediate-energy portal interactions share the generated asymmetry between the visible and dark sectors. Furthermore, our framework is safe from cosmological issues by providing low-energy portal interactions to release the superfluous entropy of the dark sector into the visible sector.


INTRODUCTION
Cosmological observations have established that the mass of the present Universe is made up by so-called dark matter (DM) in addition to ordinary matter. The mass density of DM is about five times larger than that of ordinary matter, i.e., standard model (SM) baryons [1]. The observed closeness of the mass densities may be a hint on DM and dark sector physics. If DM (dark sector) has nothing to do with SM baryon (visible sector), it is puzzling why their mass densities are close to each other.
The concept of a mirror world is a natural option to explain this puzzle (see Refs. [2][3][4][5][6][7][8] for earlier works). In recent years, the mirror world scenarios combined with twin Higgs models also attract attention since they ameliorate the naturalness problem [9][10][11][12]. In those scenarios, the dark sector contains mirror partners of the SM particles, and therefore the coincidence is naturally realized. However, if mirror Z 2 symmetry is kept at a lowenergy scale, mirror-world models tend to be inconsistent with cosmology because the dark sector inevitably includes light particles such as the mirror partners of neutrinos and photon.
Instead, in this letter, we pursue a mirrored Grand Unified Theory (GUT) framework, in which Z 2 symmetry is broken at a GUT scale. We consider a GUT model with gauge dynamics of G VGUT × G DGUT (with a gauge group G = G VGUT = G DGUT ) and an exchanging symmetry between G VGUT and G DGUT [13]. It is remarkable that Z 2 -symmetry breaking at a high-energy scale does not lose good features as long as the lightest "dark" baryons are DM  (see Ref. [54] for a review). The baryon-DM coincidence puzzle is divided into two subproblems: the coincidence of masses and that of number densities between baryons and DM. As for the mass coincidence, the key ingredient is the correspondence between dynamical scales of each sector: the baryon and DM masses are determined by them. Such a correspondence can be achieved once the gauge couplings are related with each other at the GUT scale. As we will see, Z 2 -symmetry breaking below the GUT scale does not spoil this correspondence.
After decoupling of the portal interaction, the entropy densities in the two sectors are conserved separately: the excessive entropy in the dark sector gives a significant contribution to the dark radiation [71]. Therefore, two types of portal interactions are needed for viable (composite) ADM scenarios: intermediate-energy portal interactions to share the asymmetry, and low-energy portal interactions to release the superfluous entropy of the dark sector into the visible sector. Our framework indeed provides such portal interactions, and thus explains the baryon-DM coincidence puzzle in a self-contained manner.
Our framework is based on a supersymmetric Grand Unified Theory (SUSY GUT), in which the Z 2 symmetry is manifest above the GUT scale. The gauge structure of each sector at low energy depends on a choice of vacuum at GUT scale. In our framework, the visible sector is reduced to the SM, while the dark sector follows two-step symmetry breaking and then has a dynamics similar to quantum chromodynamics (QCD) and quantum electro- dynamics (QED). The second symmetry breaking in the dark sector provides the intermediate-energy portal interactions and tiny kinetic mixing of visible photon and "dark" photon. SUSY plays a key role to achieve gauge coupling unification in the visible sector. Electroweak symmetry breaking in the visible sector and "dark" QED breaking are triggered by SUSY breaking effects.

MIRRORED UNIFICATION MODEL
We consider a concrete model with G = SU (5) to demonstrate our framework. Z 2 is the symmetry interchanging SU (5) VGUT and SU (5) DGUT . Under the Z 2 symmetry, dimensionless couplings in the two sectors are identified, while the mass parameters softly break the Z 2 symmetry.
We show the particle contents of the model in Table I, which are similar to those of the minimal SUSY SU (5) GUT in each sector. The chiral multiplets, Ψ V and Φ V , contain all the SM fermions. Ψ D and Φ D include the dark-quarks which provide the ingredients of the composite DM. N i and N i are the right-handed neutrinos, which are doublets under the Z 2 symmetry. U (1) X denotes a global B − L symmetry compatible with the unified gauge group. It should be noted that the model have extra Higgs quintuplets, (X S ,X S ), in addition to the usual Higgs quintuplets, (H S ,H S ).
Both sectors are mostly sequestered with each other up to higher-dimensional interactions suppressed by the reduced Planck mass M Pl . The superpotential W S gives the Yukawa couplings, the Higgs masses, and the Higgs couplings to fields with subscripts S = V, D, Here, λ, λ Σ , ξ, and 3 × 3 matrices Y u,d are dimensionless coupling constants, while M S , M S and µ S are dimensionful parameters. We assume λ, λ Σ , and ξ are of O(1) in the following. The Z 2 symmetry equates all the dimensionless couplings except the mass parameters in the two sectors: we assume mass hierarchy We set M VGUT = O(10 16 ) GeV, which is expected from the unification of extrapolated gauge coupling constants in the supersymmetric SM (SSM). The vacuum of dark sector is chosen to be, The non-vanishing VEV of X D X D is due to the forth term of Eq.  [48,81].
It should be emphasized that the difference between M VGUT and M DGUT is advantageous to explain the tiny kinetic mixing between the dark photon and the visible photon [81]. In fact, a higher-dimensional operator, We obtain a tiny kinetic mixing parameter = 10 −7 -10 −10 for M DGUT = 10 10-13 GeV, which satisfies all the constraints including the beam dump experiments [82] and supernova 1987A [83,84] when the dark photon mass is O(10 1-2 ) MeV.

Intermediate-Scale Effective Theory
Below M VGUT , we assume the SSM for the visible sector, where a pair of Higgs doublets from (H V , H V ) remains almost massless by tuning M V in Eq. (1). All the other components of the extra Higgs have masses of O(M VGUT ) in the visible sector.
In the dark sector, SU (5) DGUT is broken down to SU (4) DGUT at √ M DGUT M Pl ∼ 10 14-16 GeV for M DGUT = 10 10-13 GeV. The gauge multiplets and the pseudo-Goldstone components of (X D , X D ) corresponding to SU (5) DGUT /SU (4) DGUT obtain masses of O( √ M DGUT M Pl ) [85]. Below the SU (5) DGUT breaking scale, the matter and the Higgs multiplets are decomposed into the SU (4) DGUT multiplets by Below M DGUT , SU (4) DGUT is broken down to SU (3) D × U (1) D . We assume a pair of U (1) D charged Higgs multiplet remains almost massless while all the other components in Eqs. (7) and (8)  The U (1) D charged Higgs multiplet will break the U (1) D symmetry at the low energy scale. Since (S D , S D ) do not obtain the VEVs, the matter fields in the dark sector do not obtain masses from the Yukawa interactions in Eq. (1). To generate the mass term, we assume interactions to X D 's such as, with tiny coupling constants [86]. In the following, we take the masses of the dark quarks to be free parameters. For a successful model of ADM, the dynamical scale of SU (3) D , Λ QCD , should be of O(1) GeV. At least, one generation of the quarks should be lighter than Λ QCD so that the lightest dark baryon can be the DM [87]. The last term in Eq. (9) split the masses of the dark quarks and leptons in A D , Q D , and Q D . We assume that the lightest dark lepton is heavier than Λ QCD so that the rapid dark matter decay is avoided [81]. The visible and dark sectors are connected through superpotential W N of the right-handed neutrinos.
where y N and Y N are Yukawa coupling constants. The mass terms of the right-handed neutrinos (denoted by M R collectively) softly break U (1) X . Couplings of N to Φ V realize thermal leptogenesis and tiny neutrino masses via the type-I seesaw mechanism [88][89][90][91][92][93], while the couplings of N are irrelevant because we assume that N is much heavier than N . The dark neutrinos (included in Φ D 's) can easily have either Majorana or Dirac mass terms of O(M DGUT ), and thus our framework is consistent with cosmological constraints on light particles. For example, the Majorana mass would be generated from U (1) X breaking higherdimensional operators such as (X D Φ D ) 2 , while the Dirac mass would be generated from the usual Yukawa coupling, X D Φ D N .
As shown in Ref. [81], the B − L portal operators between the two sectors are generated by integrating out the right-handed neutrino and the dark-colored Higgs; Here, U and D denote the dark quark superfields, and abc is the totally antisymmetric tensor of SU (3) D . These portal interactions successfully mediate the B − L asymmetry generated by thermal leptogenesis for It should be noted that the above portal interactions require at least two generations of dark quarks to be nonvanishing. In the following, we leave only the two generations of U and D below the M DGUT scale, for simplicity.
In Fig. 1, we show the one-loop running of the gauge couplings in the two sectors. We take M DGUT = 8 × 10 10 GeV and the corresponding SU (5) DGUT breaking scale at 10 14 GeV as an example. M DGUT of O(10 10 ) GeV or larger is compatible with the composite ADM scenario with M R 10 9 GeV for thermal leptogenesis [81]. In this  [48,95,96]. Therefore, the dark baryons with the mass of O(1) GeV can be naturally realized as a consequence of the Z 2 symmetry at the high-energy scale.

Baryon-DM Coincidence
The dark confinement scale is restricted in our model since the unified couplings in the two sectors are identified at the GUT scale. The analytic solution of renormalization group equations for gauge couplings gives the dark confinement scale where M SUSY is a typical mass scale of (dark) sfermions for two-generation matter in the dark sector below M DGUT . Fig. 2 shows the ratio of the confiment scales in the two sectors. Here we take SU (5) DGUT breaking scale smaller than M VGUT . We assume the gauginos and higgsino to be 1 TeV and the sfermion masses to be M SUSY = 10 2 TeV (10 3 TeV) on the red (orange) line. As a prominent feature of the model, the dark confinement scale is no longer a free parameter in our scenario and is predicted to be in the range of O(1-10 2 )Λ QCD for a wide range of M DGUT /M VGUT . Here we take Λ QCD 0.3 GeV. This shows that the Z 2 symmetry successfully predicts the dynamical scales are close with each other, despite the vacuum structures are completely different between two sectors below the M VGUT scale.
It should be also noted that the kinetic mixing parameter is predicted to be 10 −10 -10 −8 for Λ QCD /Λ QCD 5-50. This feature is another advantage of the present model.

CONCLUDING REMARKS
In this letter, we have proposed the mirrored GUT framework in which the baryon-DM coincidence is naturally explained. The framework relates the masses of baryon and DM (dynamical scales) and also the number (asymmetry) densities.
In contrast to the models keeping mirror symmetry at a low-energy scale, it is interesting that our framework leads to rich phenomenology and testable signatures [48]. DM decays into SM neutrinos through the intermediate-energy portal interactions [96,97]. DM annihilates through a dark neutron-antineutron oscillation [98]. When DM is composed of dark "charged" baryons, DM interacts with the SM fermions through tiny kinetic mixing between photon and dark photon. The monopoles from the SU (4) DGUT → SU (3) D ×U (1) D breaking , which are finally confined by the cosmic string after the U (1) D breaking and annihilate efficiently, are also worthy of investigation.
We regard the specific model in this paper as a proof of concept and have not addressed the origins of several fine-tuned parameters. Fine-tunings of parameters are just technically natural thanks to SUSY and furthermore most of tuned parameters are irrelevant to explain the baryon-DM coincidence puzzle. However, it is to be addressed in future why chiral symmetry breaking in the dark sector is so tiny, although the dark sector is a vectorlike theory below the SU (5) DGUT → SU (4) DGUT breaking. We may consider a variant of the present model to ameliorate the parameter tunings in the superpotentials (for example, introducing chiral symmetry to suppress the Higgs µ-term). Although our present model is not fully satisfactory, it demonstrates a new vast field of the DM-model building to be explored.