PHYSICAL REVIEW D 100, 063537 (2019) 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 (Received 28 April 2019; revised manuscript received 3 August 2019; published 25 September 2019) 0 Baryon asymmetry of the universe (BAU) can likely be explained with K0 − K0 oscillations 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 of n − n0 oscillations 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 0 universe. The long-standing BAU puzzle could then be understood with K0 − K0 oscillations that occur at the stage of strange quark condensation and baryon number violation via a nonperturbative sphaleronlike (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 global ð1Þ ð1Þ Ut A symmetry and the electroweak gauge symmetry at the same time. Meanwhile, the U A or strong CP problem of particle physics is addressed with a possible explanation under the same framework. DOI: 10.1103/PhysRevD.100.063537 I. INTRODUCTION drops below T ¼ 38 MeV [2] to avoid the annihilation catastrophe between baryons and antibaryons. The matter-antimatter imbalance or baryon asymmetry Sakharov proposed three criteria to generate the initial of the universe (BAU) has been a long standing puzzle BAU: (i) baryon number (B-) violation (ii) C and CP in the study of cosmology. Such an asymmetry can be violation (iii) departure from thermal equilibrium [3]. The quantified in various ways. The cosmic microwave back- Standard Model (SM) is known to violate both C and CP ground (CMB) data by Planck set a very precise observed 2 and it does not conserve baryon number only although it baryon density of the universe at Ω h ¼ 0.02242 Æ b does B − L (difference of baryon and lepton numbers). 0.00014 [1]. This corresponds to today’s baryon-to-photon −10 Coupled with possible nonequilibrium in the thermal number density ratio of n =nγ ¼ 6.1 × 10 . For an B history of the early universe, it seems to be easy to solve adiabatically expanding universe, it would be better to ¼ the BAU problem. Unfortunately, the violations in SM use the baryon-number-to-entropy density ratio of nB=s without new physics are too small to explain the observed 8 7 10−11 . × to quantify the BAU, which may have to be fairly large BAU. The only known B-violation processes in modified under the new understanding of the neutrino SM are nonperturbative, for example, via the so-called history in the early universe (see Sec. IV). sphaleron [4] which involves nine quarks and three leptons From known physics, it is difficult to explain the from each of the three generations. It was also found out observed BAU. For example, for an initially baryon- that the sphaleron process can be much faster around symmetric universe, the surviving relic baryon density or above the temperature of the electroweak symmetry from the annihilation process is about nine orders of ∼ 100 breaking or phase transition TEW GeV [5]. This magnitude lower than the observed one [2]. Therefore, essentially washes out any BAU generated early or around an asymmetry is needed in the early universe and the TEW since the electroweak transition is most likely just a BAU has to exist before the temperature of the universe smooth cross-over instead of “desired” strong first order [6]. It makes the appealing electroweak baryogenesis *[email protected] models [5,7] ineffective and new physics often involving the Higgs have to be added in the models [8–10]. Recently Published by the American Physical Society under the terms of lower energy baryogenesis typically using particle oscil- the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to lations stimulated some interesting ideas [11,12]. Other the author(s) and the published article’s title, journal citation, types of models such as leptogenesis [13] are typically less and DOI. Funded by SCOAP3. testable or have other difficulties. 2470-0010=2019=100(6)=063537(10) 063537-1 Published by the American Physical Society WANPENG TAN PHYS. REV. D 100, 063537 (2019) −15 −14 Here we present a simple picture for baryogenesis ∼10 –10 universal for all the particles that acquired at energies around quantum chromodynamics (QCD) mass from the Higgs vacuum. Further details of the model 0 phase transition with K0 − K0 oscillations based on a can be found in Ref. [14]. 0 K0 − K0 The immediate result of this model for this study is the newly developed mirror matter model [14]. 0 00 oscillations and the new mirror matter model will be first probability of K − K oscillations in vacuum [14], introduced to demonstrate how to generate the “potential” 1 amount of BAU as observed. Then the QCD phase 2 2 P 0 00 ðtÞ¼sin ð2θÞsin Δ 0 00 t ð1Þ transition will be reviewed and the sphaleronlike non- K K 2 K K perturbative processes are proposed to provide B-violation 0 0 0 0 2 and realize the “potential” BAU created by K0 − K0 where θ is the K − K mixing angle and sin ð2θÞ denotes −4 oscillations. In the end, the observed BAU is generated the mixing strength of about 10 , t is the propagation time, 0 − Δ 0 00 ¼ m 0 − m 0 is the small mass difference of the right before the n n oscillations that determine the final K K K2 K1 mirror(dark)-to-normal matter ratio of the universe [14]. two mass eigenstates of about 10−6 eV [14], and natural ð1Þ Meanwhile, the longstanding U A and strong CP prob- units (ℏ ¼ c ¼ 1) are used for simplicity. Note that the lems in particle physics are also naturally resolved under equation is valid even for relativistic kaons and in this case t the same framework. is the proper time in the particle’s rest frame. There are 0 0 actually two weak eigenstates of K in each sector, i.e., KS 0 00 0 9 10−11 5 10−8 II. K − K OSCILLATIONS AND THE and KL with lifetimes of × sand × s, NEW MODEL respectively. Their mass difference is about 3.5 × 10−6 eV very similar to Δ 0 00 , which makes one wonder if the two To understand the observed BAU, we need to apply the K K newly developed particle-mirror particle oscillation model mass differences and even the CP violation may originate [14]. It is based on the mirror matter theory [15–22], that from the same source. is, two sectors of particles have identical interactions For kaons that travel in the thermal bath of the early within their own sector but share the same gravitational universe, each collision or interaction with another particle will collapse the oscillating wave function into a mirror force. Such a mirror matter theory has appealing theoretical τ ⊗ 0 eigenstate. In other words, during mean free flight time f features. For example, it can be embedded in the E8 E8 0 00 − 0 ðτ Þ superstring theory [17,23,24] and it can also be a natural the K K transition probability is PK0K0 f .Thenum- 1 τ extension of recently developed twin Higgs models [25,26] ber of such collisions will be = f in a unit time. Therefore, 0 that protect the Higgs mass from quadratic divergences the transition rate of K0 − K0 with interaction is [14], and hence solve the hierarchy or fine-tuning problem. The mirror symmetry or twin Higgs mechanism is particularly 1 2 2 1 λ 0 ¼ ð2θÞ Δ 0 τ ð Þ K0K0 sin sin K0K0 f : 2 intriguing as the Large Hadron Collider has found no τf 2 evidence of supersymmetry so far and we may not need supersymmetry, at least not below energies of 10 TeV. Such Note that the Mikheyev-Smirnov-Wolfenstein (MSW) a mirror matter theory can explain various observations in matter effect [31,32], i.e., coherent forward scattering that the universe including the neutron lifetime puzzle and dark- could affect the oscillations is negligible as the meson to-baryon matter ratio [14], evolution and nucleosynthesis density is very low when kaons start to condensate from in stars [27], ultrahigh energy cosmic rays [28], dark energy the QCD plasma (see more details for in-medium particle [29], and a requirement of strongly self-interacting dark oscillations from Ref. [27]), and in particular, the QCD matter to address numerous discrepancies on the galactic phase transition is most likely a smooth crossover [33,34]. scale [30]. It is not very well understood how the QCD symmetry In this new mirror matter model [14], no cross-sector breaking or phase transition occur in the early universe, interaction is introduced, unlike other particle oscillation which will be discussed in detail in the next section. type models. The critical assumption of this model is Let us suppose that the temperature of QCD phase that the mirror symmetry is spontaneously broken by the transition Tc is about 150 MeV and a different value uneven Higgs vacuum in the two sectors, i.e., hϕi ≠ hϕ0i, (e.g., 200 MeV) here does not affect the following although very slightly (on a relative breaking scale of discussions and results.