Axionic Cogenesis of Baryon, Dark Matter and Dark Radiation
Abstract
We argue that coherent oscillations of the axion field excited by the misalignment mechanism and nonthermal leptogenesis by the saxion decay can naturally explain the observed abundance of dark matter and baryon asymmetry, thus providing a solution to the baryondark matter coincidence problem. The successful axionic cogenesis requires a supersymmetry breaking scale of GeV, which is consistent with the recently discovered standardmodel like Higgs boson of mass about GeV. Although the saxion generically decays into a pair of axions, their abundance sensitively depends on the saxion stabilization mechanism as well as couplings with the Higgs field. We discuss various ways to make the saxion dominantly decay into the righthanded neutrinos rather than into axions, and show that the abundance of axion dark radiation can be naturally as small as , which is allowed by the Planck data.
pacs:
I Introduction
There are many coincidences in nature. Some of them may be just a coincidence or may be a consequence of anthropic selection, while others may be due to a novel physical mechanism. We consider the last possibility, since it will provide us with a hint of physics beyond the standard model (SM). In this paper we focus on the baryondark matter coincidence problem, i.e., why the dark matter density is about five times larger than the baryon density, . If these two have a totally different origin, it is a puzzle why they happen to have the density in a similar size.
There have been many works on this longstanding puzzle. Among them, the asymmetric dark matter scenario has recently attracted great attention Kaplan:2009ag . If the dark matter particle has asymmetry which is comparable to the baryon asymmetry, the coincidence problem could be solved for the dark matter mass of order the nucleon mass. Of course this is just a replacement of the problem. The similarity of the baryon and dark matter abundances is replaced with the similarity of the nucleon mass and the dark matter mass. So, if the dark matter mass is independent of the QCD scale, the puzzle remains unsolved. If the coincidence is due to a novel physical mechanism, therefore, the mechanism may be such that the dark matter abundance depends on the QCD scale, which determines the proton mass and thus the baryon density.
The axion is a pseudoNambuGoldstone boson associated with the spontaneous breakdown of the PecceiQuinn (PQ) symmetry, and it elegantly solves the strong CP problem when it couples to the QCD anomaly Peccei:1977hh ; QCDaxion . The invisible axion is one of the plausible candidates for dark matter. Interestingly, its mass and abundance depend on the QCD scale and the PQ breaking scale. To our knowledge, the axion is the only dark matter candidate whose abundance naturally depends on the QCD scale.^{3}^{3}3 Although its dependence on the QCD scale is not exactly same as the baryon density, we will see that it may be related to another interesting coincidence between the QCD scale and the light quark mass (or the weak scale). Therefore, we consider a possibility that the PQ sector is responsible for both the baryon asymmetry and dark matter, i.e., the axionic cogenesis.
One particularly attractive mechanism that offers an explanation for the observed baryon asymmetry is leptogenesis Fukugita:1986hr ; Buchmuller:2005eh . If the righthanded neutrinos are charged under the PQ symmetry, the axion as well as its scalar partner, saxion, are naturally coupled to the righthanded neutrinos.^{4}^{4}4 In this case, the axion becomes a majoron Langacker:1986rj . It is known that the saxion tends to dominate the energy density of the early universe. Then, the saxion decays into righthanded neutrinos, whose CPviolating decays create a lepton asymmetry Lazarides:1991wu ; Asaka:1999yd . As we shall see shortly, the saxion mass should be of GeV, for successful nonthermal leptogenesis.
The saxion generally decays also into a pair of axions. Such nonthermally produced axions remain relativistic until present, giving contributions to the effective number of neutrinos, .^{5}^{5}5 The abundance of relativistic axions produced by flaton decays was studied in Ref. Chun:2000jr . The latetime increase of by decaying particles (e.g. saxion to two axions, and gravitino to axion and axino) was studied in Ref. Ichikawa:2007jv . The string axion production from the modulus decay was considered in Refs. Higaki:2012ba ; Higaki:2012ar ; Cicoli:2012aq . See also Refs. Fischler:2010xz ; Hasenkamp:2011em ; Menestrina:2011mz ; Kobayashi:2011hp ; Hooper:2011aj ; Jeong:2012np ; Choi:2012zna ; Graf:2012hb ; Hasenkamp:2012ii ; Bae:2013qr and many others. The possibility that the particle was in thermal equilibrium was studied in Ref. Nakayama:2010vs . Some of the recent CMB observations gave a slight preference to the excess of , coined dark radiation Hou:2012xq ; Hinshaw:2012fq . On the other hand, the Planck results did not confirm such excess, and place a constraint on Ade:2013lta ,
(1) 
As we shall see shortly, although the axions are generically produced by the saxion decay, its abundance sensitively depends on the saxion stabilization mechanism, and can be naturally as small as , which is still allowed by the Planck data.
Most of our results in this paper can be directly applied to nonsupersymmetric cases, but we use a supersymmetric (SUSY) language for simplicity. We shall return to the nonSUSY case in the last section. In fact, there is an interesting implication in the SUSY framework. In SUSY, the saxion acquires a mass from the SUSY breaking. For a generic Kähler potential, we expect where denotes the gravitino mass. Interestingly, highscale SUSY breaking of GeV is consistent with the recently discovered SMlike Higgs boson of mass about GeV :2012gk ; :2012gu (see Refs. Okada:1990gg ; Giudice:2011cg ). In fact, the observed Higgs boson mass as well as no experimental signatures of SUSY leads to another puzzle: if SUSY is realized in nature, why its breaking scale is much higher than the weak scale, which generically requires severe finetuning for the correct electroweak symmetry breaking. Our framework, the axionic cogenesis, may thus provide explanations for the puzzle, because the nonthermal leptogenesis by the saxion decay would be impossible otherwise.
Ii Setup
The model we shall discuss is a PQ invariant extension of the supersymmetric SM where PQ charged righthanded neutrinos ( with ) are added to implement the seesaw mechanism seesaw . Thus becomes massive after the PQ symmetry breaking, and couples to the saxion with a coupling proportional to its mass. Here and in what follows, we assume that the lepton number is explicitly broken by adding couplings of the PQ scalars with Higgs fields (such as (16) or the second term of (10)) in order to get rid of a massless majoron Langacker:1986rj .
We assume that there are multiple PQ scalar fields, , which acquire a vacuum expectation value (VEV), . The can be expanded around its VEV as
(2) 
where and denote the radial and phase component of , respectively. The axion and saxion are expressed in terms of those components of the PQ breaking fields,
(3)  
(4) 
where is the PQ charge of , and the PQ scale is determined by
(5) 
The interactions relevant to our discussion are written as
(6) 
below the PQ breaking scale . Here the term generates Dirac neutrino masses after electroweak symmetry breaking. The saxion couples to the axions with a coupling Chun:1995hc ,
(7) 
Here one should note that both and depend on the charge normalization, but the combination does not. In the following analysis, we assume a charge normalization such that all are order unity.
The righthanded neutrinos obtain masses from the PQ breaking, which depend on how they couple to the PQ breaking fields. For instance, one can take the PQ charge assignment that allows the superpotential terms
(8) 
where the family indices have been omitted. Then . After integrating out the heavy righthanded neutrinos, light neutrino masses are generated as
(9) 
where is the Higgs vacuum expectation value. We are interested in the case where at least one of the righthanded neutrinos has a mass much smaller than the PQ breaking scale so that it can be produced by saxion decay. As we shall see shortly, the reference values are and the saxion mass . This requires to be smaller than , which can be achieved if are charged under some flavor symmetry. Another way to provide small masses to the righthanded neutrinos is to consider higherdimensional terms,^{6}^{6}6 One may instead consider the Kähler potential term, , for the PQ fields having . Then the righthanded neutrino masses are induced after SUSY breaking via the GiudiceMasiero mechanism Giudice:1988yz , and naturally similar to the saxion mass. In this case, the saxion coupling for is still proportional to with a coefficient of order unity as long as .
(10) 
by assigning appropriate PQ charges to the involved fields. Here can be in general different from , but we assume for simplicity. In this case, the righthanded neutrinos obtain masses about , leading to the light neutrino mass,
(11) 
The value of is determined by , independent of , in contrast to the previous case. The cutoff scale is considered to be around the GUT scale (or the Planck scale if ), for which one can easily obtain the hierarchy as well as small neutrino masses consistent with the observational bounds. Note that the axion coupling with lefthanded leptons at low energy scales is suppressed in this case if , in contrast to the previous case and the original Majoron model.
The saxion coupling to is proportional to , and the numerical coefficient depends on the model. To be concrete, we take the superpotential (10). Then the relation between and is fixed to be,^{7}^{7}7 In the model (8), is two times smaller. Our main results hold also in this case without significant modifications.
(12) 
where denotes the PQ charge of the PQ breaking field that is responsible for the righthanded neutrino mass. From the saxion couplings and , one finds that the branching ratio for is written
(13) 
if the process is kinematically allowed. Here is the saxion mass, and we have defined , which is independent of the charge normalization. denotes the branching ratio for the saxion decay into an axion pair,
(14) 
with being the total saxion decay rate. The above shows that the upper bound on is set by and . If is comparable to or smaller than , is allowed, and the saxion can dominantly decay into righthanded neutrinos. In Sec. IV, we will show that such a value of is obtained naturally in supersymmetric axion models.
Here and in what follows we do not consider the saxion decay into righthanded sneutrinos, assuming that the decay is kinematically forbidden. Since the saxion mass arises from the SUSY breaking, it can be comparable to the righthanded sneutrino mass. Even if the decay mode is allowed, the following argument of nonthermal leptogenesis remains almost intact.^{8}^{8}8 The LSP abundance can be affected. However, they will decay into the SM particles if the Rparity is violated.
Finally we mention the PQ mechanism solving the strong CP problem. In order for this mechanism to work, the PQ symmetry should be anomalous under the QCD so that the axion couples to gluons via
(15) 
where the axion decay constant is given by . The domain wall number is determined by the PQ anomaly coefficient, and it counts the number of discrete degenerate vacua of the axion potential. For the anomalous coupling, we need either to assign PQ charges to the Higgs doublets or introduce additional colored matter fields carrying PQ charges. In the former case, an effective higgsino parameter is generated after the PQ symmetry breaking, for instance, from the superpotential Kim:1983dt
(16) 
It is important to note that the above superpotential induces saxion couplings to higgsinos as well as the SM fermions through mixing with the Higgs, which can significantly suppress depending on the values of and the parameter. This implies that needs not to be equal to one even for the case with of order unity. Alternatively one may include colorcharged matter fields which obtain large masses from the coupling in the superpotential. Unless the coupling is suppressed, the saxion decay into and can be kinematically forbidden so that becomes close to unity.
Iii Cosmology
iii.1 Saxion dynamics
Let us begin by discussing the cosmological role of the saxion. In the SUSY framework, the saxion corresponds to a flat direction in the supersymmetric limit. During inflation the potential receives Hubbleinduced corrections, and therefore the minimum of the potential is generally shifted away from the true vacuum. After inflation the saxion starts to oscillate with a large amplitude when the Hubble parameter becomes comparable to its mass. Furthermore, the saxion dynamics can be significantly affected by thermal effects, and it is possible that the large saxion amplitude is realized by thermal corrections through couplings with the heavy PQ quarks Kawasaki:2011ym . Thus, the saxion tends to dominate the energy density of the universe unless the reheating of the inflaton is extremely low.
In a class of the saxion stabilization models and also in the nonSUSY case, the initial oscillation amplitude of the saxion is considered to be of order the PQ breaking scale . The typical scale of in our scenario is much smaller than the Planck scale, and so, it is nontrivial if the saxion can dominate the universe before the decay. Even in this case, if the saxion sits near the origin after inflation, thermal inflation may take place and the saxiondominant universe is realized. The duration of the thermal inflation does not have to be very long, because we do not aim at solving the moduli problem. Note however that in this case one needs to arrange to avoid the domain wall problem, and that the axion decay constant is constrained to be smaller than about GeV since otherwise the axions produced by unstable stringwall network would overclose the universe Hiramatsu:2010yu ; Hiramatsu:2010yn .
In the following we assume that the coherent oscillations of the saxion dominates the universe. This sets the initial condition for the axionic cogenesis.
iii.2 Dark matter and dark radiation
The axions are produced by the saxion decay and they constitute the dark radiation. The axions thus produced are not thermalized because the decoupling temperature is about Graf:2012hb ; Graf:2010tv , which is many orders of magnitude larger than the saxion decay temperature for the parameter ranges studied here. Thus the axions increase the effective number of neutrino species () by the amount Jeong:2012np ; Choi:1996vz
(17) 
where counts the relativistic degrees of freedom at the saxion decay. In deriving the above expression, we have used the fact that it is the entropy in the comoving volume that is conserved when the light degrees of freedom changes at e.g. the QCD phase transition. Thus, for , , and and , we obtain , , and , respectively. As we shall see shortly, the value of naturally falls in the range of , and therefore the dark radiation with is a robust prediction of this scenario.
Fig. 1 shows how depends on and the mass of the righthanded neutrino. Here we have assumed that the saxion decays dominantly into righthanded neutrinos, axions, and/or gluons, i.e.,
(18) 
The process is mediated by the saxion coupling to gluons, which is analogous to the anomalous axion coupling to gluons (15). Thus is negligibly small compared to as long as . In the yellow shaded region, we have , which is the case when is smaller than about 0.22: the left panel is obtained for quasidegenerate righthanded neutrinos with , while the right panel is for the hierarchical mass spectrum of with . The brown lines are the contours of and , respectively.
On the other hand, the axion obtains a mass through QCD nonperturbative effects, and starts to oscillate coherently when the Hubble parameter becomes comparable to its mass. These coherent axions constitute the cold dark matter of the universe with the relic energy density given by Turner:1985si
(19) 
where is the initial misalignment angle, and denotes the QCD scale. Note that we extracted the dependence of the QCD scale not only from the thermal effects on the axion mass Gross:1980br but also from the zerotemperature axion mass. Thus, the coherent axions produced by an initial misalignment make up the major part of cold dark matter in the universe for the axion decay constant around GeV. For a larger (smaller) value of , we need to finetune the initial position close to the potential minimum (maximum).
iii.3 Nonthermal leptogenesis
A natural way to generate a baryon asymmetry is leptogenesis via the decays of righthanded neutrinos. To produce a sufficient baryon asymmetry in the saxiondominated universe, we consider nonthermal leptogenesis. To proceed, let us estimate the saxion decay temperature. This is determined by the saxion decay rate into particles that thermalize to form a thermal bath:
(20) 
from which it follows,
(21) 
The above relation holds if the decay rate of into leptons and Higgs is much larger than so that the righthanded neutrinos decay almost instantly after production. This is indeed the case when is smaller than , and the branching ratio for is sizable. The decay rate of into leptons is larger than by a factor of approximately , which is about for around 0.2 and eV. Thus in the parameter space with around 0.1 and , which is of our interest, the relation for remains valid.^{9}^{9}9 More precisely, should be replaced by since the axions produced in saxion decays are not thermalized as we will see shortly. However this changes the result only slightly for small .
The righthanded neutrinos are nonthermally produced by saxion decays when is low enough:
(22) 
thereby requiring smaller than . The lepton asymmetry generated by the decays of is partially converted into baryon asymmetry through the sphaleron process according to , where for GeV in the SM.^{10}^{10}10 The saxion mass is considered to be of order the gravitino mass. If all the SUSY particles as well as heavy Higgs bosons have similar masses, there are only SM particles in the plasma at the electroweak phase transition. The present baryon asymmetry is then obtained to be
(23) 
for , where is the entropy density. The condition is necessary to avoid strong washout of the lepton asymmetry produced by decays. The CP asymmetry in the decay receives oneloop vertex and selfenergy contributions Covi:1996wh , and crucially depends on the righthanded neutrino masses and thus on .
Let us estimate the baryon asymmetry generated by nonthermal leptogenesis. There are two cases of interest, depending on the mass spectrum of . First, suppose hierarchical . Then an adequate baryon asymmetry is obtained when has mass not much smaller than while the other two have masses larger than . This is because is proportional to , and less than is needed to avoid strong washout effects. For , the CP asymmetry induced by the decay is given by
(24) 
where is the effective leptogenesis CP phase, and is the heaviest neutrino mass. Taking , the baryon asymmetry reads
(25) 
where an enhancement of a factor 2 can be obtained if the saxion is kinematically allowed to decay into the righthanded sneutrinos. On the other hand, it is also possible to have with masses close to each other. For such quasidegenerate , the induced CP asymmetry is approximately given by
(26) 
where the righthanded neutrinos have masses around with a small splitting . The CP asymmetry is enhanced by a factor , compared to the case with hierarchical . As a result, the baryon asymmetry produced in the decays of three righthanded neutrinos is approximately given by
(27) 
for close to 1, where .
The induced baryon asymmetry depends on , , and , some of which also determine the amounts of axion dark matter and dark radiation. In the next subsection, taking into account such relations, we will explore the region of parameter space where the baryon asymmetry observed in the universe is explained by (25) or (27).
iii.4 Axionic Cogenesis
To get a sufficient baryon asymmetry, the saxion needs to decay mainly into a pair of righthanded neutrinos. The relation (13) tells that this is achieved when is not small, under the natural assumption that is not much smaller than 0.1. This implies that due to axion dark radiation generally lies in the range between about 0.1 and 1 in our scenario, which is consistent with the recent Planck results (1).
Let us move on to the baryon asymmetry and dark matter. It is important to note that an upper bound on comes from the requirement that should be smaller than for given , while a lower bound arises from the requirement of generating adequate baryon asymmetry, provided that the righthanded neutrinos are not extremely degenerate in mass. The coherent axions produced by an initial misalignment make up the major part of cold dark matter in the universe for the axion decay constant around GeV. For the PQ breaking scale in that range, will be low enough to avoid strong washout if the saxion mass is smaller than about GeV. On the other hand, from (25) and (27), we see that is naturally obtained when the righthanded neutrino, whose decay generates the lepton asymmetry, has a mass around or larger than GeV. Therefore the baryon asymmetry and dark matter of the present universe can be achieved simultaneously for
(28) 
thereby providing a natural explanation to the baryondark matter coincidence problem. This also indicates high scale SUSY breaking around GeV because the saxion is massless in the supersymmetric limit. Interestingly, this is the SUSY breaking scale needed to accommodate a 126 GeV Higgs boson within the minimal supersymmetric SM without large stop mixing.
Fig. 2 illustrates how nonthermal leptogenesis works in the saxiondominated universe. Here we have taken the model parameters as follows, for the cases with hierarchical and quasidegenerate righthanded neutrinos:
hierarchical  
quasidegenerate  (29) 
and fixed for both cases, under the assumption that lies in the range between about 0.1 and 0.2. In addition, we have taken for the PQ charge normalization such that the PQ charges of are coprime to each other, for which is given by . For hierarchical (quasidegenerate) with the above properties, is obtained in the upper (lower) orange region. The observed baryon asymmetry can thus be explained within this region by slightly changing the properties of or . In the region above the gray thick line, the saxion decay temperature is higher than the righthanded neutrino mass, and the situation is reduced to the thermal leptogenesis scenario. The successful thermal leptogenesis will require the saxion to have mass of order GeV for GeV. On the other hand, in the yellow region, the coherent axions produced around the QCD phase transition can naturally account for the cold dark matter in the universe. Finally we note that the axion dark radiation is also produced in saxion decays, for instance, for . The amount of baryon asymmetry does not change much for as long as the saxion dominantly decays into righthanded neutrinos. From these we conclude that the axonic cogenesis is realized in the region where the orange and yellow bands meet, that is, for around GeV and in the range GeV.
Before closing this section, let us comment on the lightest supersymmetric particle (LSP) which is stable under the Rparity conservation. In high scale SUSY, the thermal relic abundance of the LSPs may be too large. This can be avoided if is lower than the LSP freezeout temperature. If LSPs are nonthermally produced by saxion decays, its branching fraction must be suppressed. Another way is to consider some mediation mechanism rendering the LSP sufficiently light, or to introduce a very light superparticle in a hidden sector into which the ordinary superparticles decay. Alternatively one can simply assume Rparity violation. We also note that the results on the baryon asymmetry and dark matter in the saxiondominated universe hold even in nonsupersymmetric axion models, if the saxion is stabilized with .
Iv Saxion stabilization
In this section we discuss how to make the saxion dominantly decay into righthanded neutrinos rather than into axions. This requires a small in (13). If PQ symmetry is spontaneously broken by a single field , which is the case for instance in the radiative saxion stabilization, one obtains , implying that is much smaller than . Even in this case, one can avoid an axiondominated universe by introducing the superpotential term, , so that the saxion dominantly decays into SM particles or higgsinos. However small makes it difficult to implement nonthermal leptogenesis successfully. This is resolved when multiple fields are involved in the PQ symmetry breakdown.
Let us consider supergravity models where two PQ fields, and , obtain VEVs around . One simple way to stabilize the saxion is to consider
(30) 
with and , where is a PQ singlet field. In this case, the flat direction is lifted by soft SUSY breaking terms,
(31) 
For and positive similar to or smaller than , the PQ fields are stabilized at
(32) 
with . Thus, if , the PQ fields are fixed with , for which has a tiny value. This implies that can have a small value when and feel SUSY breaking via couplings of similar strength. For having soft scalar masses with , we get . If , which would not require severe finetuning of model parameters, the relation (13) tells . In this case, one can arrange for instance around 0.7 and by taking appropriate righthanded neutrino masses. Note that is not necessarily equal to one in the presence of a superpotential term, .
Another way to stabilize the saxion is through the competition between SUSY breaking effects and a higher dimensional superpotential term:
(33) 
with and . Here we take to forbid a large mass term in the superpotential. It is straightforward to find
(34) 
and , assuming . The value of is fixed to be or , depending on which PQ field is responsible for . Let us suppose that obtain masses from the coupling to one of the PQ fields that gives a smaller value of . Then the saxion stabilization by the higher dimensional operator leads to
(35) 
The first model has and . Thus, to get a sufficient baryon asymmetry, one would need heavy with mass close to GeV if the righthanded neutrino masses are hierarchical. One may instead consider degenerate with GeV and , for which the successful nonthermal leptogenesis is achievable with and . On the other hand, in the second model, we have and . It is thus easy to make the saxion dominantly decay into righthanded neutrinos. We also note that, in both cases, the PQ breaking scale naturally lies in the range GeV for GeV, taking to be the GUT or Planck scale.^{11}^{11}11 The model discussed in Ref. Feldstein:2012bu also realizes an intermediate axion decay constant by relating it to the SUSY breaking scale, . However it is difficult to implement axionic cogenesis in this model because the PQ sector itself participates in SUSY breaking, leading to a too large saxion mass around .
Our discussion so far has assumed that the saxion given by (4) does not mix with other CPeven scalar bosons, and that its decay rate into the PQ sector scalars or fermions is small compared to that into righthanded neutrinos. For the model where and are stabilized by a higher dimensional superpotential term, there appear additional light scalars and singlino. Hence more care should be taken. The saxion indeed corresponds to the eigenstate in the limit of vanishing soft scalar masses, and there is induced small mixing with the other CPeven scalar for . Assuming small soft scalar masses, we find that the additional CP even and odd scalars are both heavier than the saxion in the models (IV). The PQ sector also includes two fermions composed of and . They have masses about and for , while and for the model with . Thus the saxion decay into PQ fermions is kinematically closed in both models.
V Discussion and conclusions
The PQ symmetry may be unbroken during inflation. Then the spontaneous breakdown of the PQ symmetry after inflation leads to the production of topological defects such as axionic strings and domain walls. According to the recent numerical simulations of axion stringwall network Hiramatsu:2010yu ; Hiramatsu:2010yn , the PQ breaking scale should be of order for explaining the dark matter. Based on our above argument, it will be difficult to combine this scenario with nonthermal leptogenesis by the saxion decay. See Fig. 2. However, thermal leptogenesis will be possible, if the reheating temperature is sufficiently high GeV.^{12}^{12}12 The thermal leptogenesis in the axion(=majoron) model was considered in Ref. Langacker:1986rj . See also Ref. Gu:2009hn . The axion will be thermalized, but its contribution to the effective number of neutrinos is suppressed because of large relativistic degrees of freedom at high temperature. Note that the saxion does not have to dominate the universe in this case, and the application to a nonSUSY case is straightforward. It is interesting to note that the baryon and dark matter abundances are determined by a single scale GeV.
If the PQ symmetry is broken during inflation, the axion acquires quantum fluctuations, generating isocurvature perturbations. If the PQ breaking scale does not change during and after inflation, the inflation scale is constrained by the isocurvature constraint as GeV. This bound is relaxed if one of the PQ scalars takes a larger field value during the inflation. Such large deviation will ease the conditions for the saxion domination. The isocurvature perturbations of the axion dark matter may be found or constrained by the future observations of the CMB power spectrum and nonGaussianity Kawasaki:2008sn ; Langlois:2008vk ; Kawakami:2009iu ; Langlois:2011zz ; Langlois:2010fe ; Kobayashi:2013nva .
In this paper we have considered the PQ sector as the origin of baryon asymmetry, dark matter and dark radiation; the axionic cogenesis. We have found that nonthermal leptogenesis by the saxion decay works successfully for the saxion mass of GeV and the PQ breaking scale around . The dark matter can be explained by the axions produced in the misalignment mechanism with an initial deviation of order unity. If the existence of dark radiation is confirmed by future observations such as the Planck satellite, this scenario will be one of the plausible solutions to the cosmological coincidence problems. Intriguingly, in the SUSY framework, the suggested SUSY breaking scale is consistent with the observed SMlike Higgs boson of mass GeV in the minimal supersymmetric SM without large stop mixing. Thus, the axionic cogenesis may give an answer to the question of why the SUSY breaking scale is much higher than the weak scale, which generically requires severe finetuning for the correct electroweak symmetry breaking.
Acknowledgment
We thank Tetsutaro Higaki for pointing out a possibility to generate the righthanded neutrino mass from the GiudiceMasiero mechanism. This work was supported by the GrantinAid for Scientific Research on Innovative Areas (No.24111702, No. 21111006, and No.23104008) [FT], Scientific Research (A) (No. 22244030 and No.21244033) [FT], and JSPS GrantinAid for Young Scientists (B) (No. 24740135) [FT]. This work was also supported by World Premier International Center Initiative (WPI Program), MEXT, Japan [FT], and by GrantsinAid for Scientific Research from the Ministry of Education, Science, Sports, and Culture (MEXT), Japan, No. 23104008 and No. 23540283 [KJS].
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