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Kaon oscillations and baryon asymmetry of the universe

Wanpeng Tan

Department of Physics, Institute for Structure and Nuclear Astrophysics (ISNAP), and Joint Institute for Nuclear Astrophysics -

Center for the Evolution of Elements (JINA-CEE),

University of Notre Dame, Notre Dame, Indiana 46556, USA (Dated: September 6, 2020)

Abstract

Baryon asymmetry of the universe (BAU) can likely be explained withK0K00oscillations of a newly developed mirror-matter model and new understanding of quantum chromodynamics (QCD) phase transitions. A consistent picture for the origin of both BAU and dark matter is presented with the aid ofnn0oscillations of the new model. The global symmetry breaking transitions in QCD are proposed to be staged depending on condensation temperatures of strange, charm, bottom, and top quarks in the early universe. The long-standing BAU puzzle could then be understood withK0K00oscillations that occur at the stage of strange quark condensation and baryon number violation via a non-perturbative sphaleron-like (coined \quarkiton") process. Similar processes at charm, bottom, and top quark condensation stages are also discussed including an interesting idea for top quark condensation to break both the QCD globalUt(1)Asymmetry and the electroweak gauge symmetry at the same time. Meanwhile, theU(1)Aor strongCPproblem of particle physics is addressed with a possible explanation under the same framework. wtan@nd.edu

1arXiv:1904.03835v6 [physics.gen-ph] 18 Sep 2019

I. INTRODUCTION

The matter-antimatter imbalance or baryon asymmetry of the universe (BAU) has been a long standing puzzle in the study of cosmology. Such an asymmetry can be quantied in various ways. The cosmic microwave background (CMB) data by Planck set a very precise observed baryon density of the universe at bh2= 0:022420:00014 [1]. This corresponds to today's baryon-to-photon number density ratio ofnB=n = 6:11010. For an adiabatically expanding universe, it would be better to use the baryon-number-to-entropy density ratio ofnB=s= 8:71011to quantify the BAU, which may have to be modied under the new understanding of the neutrino history in the early universe (see Sec. IV). From known physics, it is dicult to explain the observed BAU. For example, for an initially baryon-symmetric universe, the surviving relic baryon density from the annihilation process is about nine orders of magnitude lower than the observed one [2]. Therefore, an asymmetry is needed in the early universe and the BAU has to exist before the temperature of the universe drops belowT= 38 MeV [2] to avoid the annihilation catastrophe between baryons and anti-baryons. Sakharov proposed three criteria to generate the initial BAU: (i) baryon number (B-) violation (ii)CandCPviolation (iii) departure from thermal equilibrium [3]. The Standard Model (SM) is known to violate bothCandCPand it does not conserve baryon number only although it doesBL(dierence of baryon and lepton numbers). Coupled with possible non-equilibrium in the thermal history of the early universe, it seems to be easy to solve the BAU problem. Unfortunately, the violations in SM without new physics are too small to explain the observed fairly large BAU. The only known B-violation processes in SM are non-perturbative, for example, via the so-called sphaleron [4] which involves nine quarks and three leptons from each of the three generations. It was also found out that the sphaleron process can be much faster around or above the temperature of the electroweak symmetry breaking or phase transitionTEW100 GeV [5]. This essentially washes out any BAU generated early or aroundTEWsince the electroweak transition is most likely just a smooth cross-over instead of \desired" strong rst order [6]. It makes the appealing electroweak baryogenesis models [5, 7] ineective and new physics often involving the Higgs have to be added in the models [8{10]. Recently lower energy baryogenesis typically using particle oscillations stimulated some interesting ideas [11, 12]. Other types of models such 2 as leptogenesis [13] are typically less testable or have other diculties. Here we present a simple picture for baryogenesis at energies around quantum chromo- dynamics (QCD) phase transition withK0K00oscillations based on a newly developed mirror matter model [14].K0K00oscillations and the new mirror matter model will be rst introduced to demonstrate how to generate the \potential" amount of BAU as observed. Then the QCD phase transition will be reviewed and the sphaleron-like non-perturbative processes are proposed to provide B-violation and realize the \potential" BAU created by K

0K00oscillations. In the end, the observed BAU is generated right before thenn0

oscillations that determine the nal mirror(dark)-to-normal matter ratio of the universe [14]. Meanwhile, the long-standingU(1)Aand strongCPproblems in particle physics are also naturally resolved under the same framework.

II.K0K00OSCILLATIONS AND THE NEW MODEL

To understand the observed BAU, we need to apply the newly developed particle-mirror particle oscillation model [14]. It is based on the mirror matter theory [15{22], that is, two sectors of particles have identical interactions within their own sector but share the same gravitational force. Such a mirror matter theory has appealing theoretical features. For example, it can be embedded in theE8

E80superstring theory [17, 23, 24] and it can

also be a natural extension of recently developed twin Higgs models [25, 26] that protect the Higgs mass from quadratic divergences and hence solve the hierarchy or ne-tuning problem. The mirror symmetry or twin Higgs mechanism is particularly intriguing as the Large Hadron Collider has found no evidence of supersymmetry so far and we may not need supersymmetry, at least not below energies of 10 TeV. Such a mirror matter theory can explain various observations in the universe including the neutron lifetime puzzle and dark-to-baryon matter ratio [14], evolution and nucleosynthesis in stars [27], ultrahigh energy cosmic rays [28], dark energy [29], and a requirement of strongly self-interacting dark matter to address numerous discrepancies on the galactic scale [30]. In this new mirror matter model [14], no cross-sector interaction is introduced, unlike other particle oscillation type models. The critical assumption of this model is that the mirror symmetry is spontaneously broken by the uneven Higgs vacuum in the two sectors, i.e.,< >6=< 0>, although very slightly (on a relative breaking scale of1015{1014) 3 [14]. When fermion particles obtain their mass from the Yukawa coupling, it automatically leads to the mirror mixing for neutral particles, i.e., the basis of mass eigenstates is not the same as that of mirror eigenstates, similar to the case of ordinary neutrino oscillations due to the family or generation mixing. The Higgs mechanism makes the relative mass splitting scale of1015{1014universal for all the particles that acquired mass from the Higgs vacuum. Further details of the model can be found in Ref. [14]. The immediate result of this model for this study is the probability ofK0K00oscillations in vacuum [14], P

K0K00(t) = sin2(2)sin2(12

K0K00t) (1)

whereis theK0K00mixing angle and sin2(2) denotes the mixing strength of about 10

4,tis the propagation time, K0K00=mK02mK01is the small mass dierence of the

two mass eigenstates of about 10

6eV [14], and natural units (~=c= 1) are used for

simplicity. Note that the equation is valid even for relativistic kaons and in this casetis the proper time in the particle's rest frame. There are actually two weak eigenstates ofK0in each sector, i.e.,K0SandK0Lwith lifetimes of 91011s and 5108s, respectively. Their mass dierence is about 3:5106eV very similar to K0K00, which makes one wonder if the two mass dierences and even theCPviolation may originate from the same source. For kaons that travel in the thermal bath of the early universe, each collision or interaction with another particle will collapse the oscillating wave function into a mirror eigenstate. In other words, during mean free ight timeftheK0K00transition probability isPK0K00(f). The number of such collisions will be 1=fin a unit time. Therefore, the transition rate of K

0K00with interaction is [14],

K0K00=1

fsin2(2)sin2(12

K0K00f):(2)

Note that the Mikheyev-Smirnov-Wolfenstein (MSW) matter eect [31, 32], i.e., coherent forward scattering that could aect the oscillations is negligible as the meson density is very low when kaons start to condensate from the QCD plasma (see more details for in-medium particle oscillations from Ref. [27]), and in particular, the QCD phase transition is most likely a smooth crossover [33, 34]. It is not very well understood how the QCD symmetry breaking or phase transition occur in the early universe, which will be discussed in detail in the next section. Let us suppose that the temperature of QCD phase transitionTcis about 150 MeV and a dierent value 4 (e.g., 200 MeV) here does not aect the following discussions and results. At this time only up, down, and strange quarks are free. It is natural to assume that strange quarks become conned rst during the transition, i.e., forming kaon particles rst instead of pions and nucleons. A better understanding of this process is shown in the next section. As a matter of fact, even if they all form at the same time, the equilibrium makes the ratio of nucleon number to kaon number n Nn

K'(mNm

K)3=2exp((mNmK)=Tc)0:1 (3)

very small due to the fact that kaons are much lighter than nucleons. Once neutral kaons are formed, they start to oscillate by participating in the weak in- teraction with cross section ofEWG2FT2whereGF= 1:17105GeV2is the Fermi coupling constant. Then one can estimateK0's thermally averaged reaction rate over the

Bose-Einstein distribution,

g(2)3Z 1 0 d3pf(p)EWpm g22G 2FT2m Z 1 0 dpp3exp( pp

2+m2=T)1(4)

whereg= 2 for bothK0SandK0L,mis the mass of kaons, andTis the temperature. The expansion rate of the universe at this time can be estimated to beHT2MeVs1whereTMeV is the temperature in unit of MeV. The condition forK0to decouple from the interaction or freeze out is =H <1. It can be easily calculated from Eq. (4) that the freezeout occurs at T fo= 100 MeV. This means that kaon oscillations have to operate betweenTc= 150 MeV andTfo= 100 MeV. And fortunately theK0mesons have long enough lifetime (compared to the weak interaction rate) for such oscillations and BAU to occur during this temperature range. For the standard constraint on the mirror-to-normal matter temperature ratio ofx= T

0=T <1=2 [17, 19] that will be discussed further in Sec. IV, the two oscillation steps of

K

00!K0andK0!K00will be decoupled in a similar way as thenn0oscillations

discussed in Ref. [14]. Using a typical weak interaction rateEW= 1=f=G2FT5T5MeV s

1and the age of the universet= 0:3=T2MeVs during this period of time, one can get the

5 nal-to-initialK0abundance ratio in the ordinary sector for the second step, X fX i= exp(Z P

K0K00(f)EWdt)

= exp(51028sin2(2)(K0K00eV )2Z Tfo T cd(1T

7MeV))

= 10:051(5) and the rst step is negligible due to the much faster expansion rate of the universe [14]. However,K0Shas a lifetime of 91011s that is comparable to the weak interaction rate at such temperatures. Owing to this, only one third ofK0Sparticles participate in the oscillations while the other two thirds decay to pions. In contrast toK0S,K0Lmesons have a much larger lifetime (5108s) and hence almost all of them take part in the oscillations. Considering the above correction, the nal-to-initialK0abundance ratio in the normal world due to oscillations becomes, X fX i= 123 :(6) TheCPviolation amplitude in SM is measured as= 2:228103[35] so that25106 and the oscillation probability ratio can be estimated asPK0K00=PK0K0012. Then the netK0fraction can be obtained as follows,

XK0K0X

K0K0XK0XK0X

K0+XK0=13

2253

108(7)

If the excess ofK0(ds) generated above can survive by some B-violation process, i.e., dumping squarks and leavingdquarks to form nucleons in the end, then assuming that half of strange quarks condensate intoK0L;S(with the other half inK) we will end up with a net baryon density ofnB=s= 5:61010that essentially gives the sum of the observed baryon and dark matter. In the next section, we will demonstrate how such a B-violation process could occur during the QCD phase transition.

In Eq. (5) the mixing strength sin

2(2)104and the mass splitting parameter

K0K00106eV are estimated fromnn0oscillations in Ref. [14] assuming that the single-quark mixing strength is similar and the mass splitting parameter is scaled to the particle's mass. Unfortunately, these estimates are still fairly rough as the neutron lifetime measurements have not yet constrained the oscillation parameters well [14] resulting in a factor of10 uncertainty inof Eq. (5). On the other hand, the observed baryon asym- metry can be used to constrain these parameters under the new mechanism, i.e.,= 0:05 or 6 sin 2(2)2 K

0K00= 1016eV2. Remarkably, such parameters are consistent with the neutron

lifetime experiments and the origin of dark matter under the new model (see more discus- sions in Sec. IV). More detailed studies of the mirror mixing parameters under the context of the CKM matrix and proposed laboratory measurements can be found in a separate paper [36]. III. QCD SYMMTRY BREAKING TRANSITION AND OTHER OSCILLATIONS A massless fermion particle's chirality or helicity has to be preserved, i.e., its left- and right-handed states do not mix [37]. This is essentially also true for extremely relativistic massive particles as required by special relativity. Therefore the globalquotesdbs_dbs25.pdfusesText_31

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