History of the Mirror Matter Theory

In 1974, Lee connected \(CP\)-violation to spontaneous symmetry breaking [Lee1974], which, as we shall see, can serve similarly as a mechanism for mirror symmetry breaking.

The discovery of \(CP\)-violation also started speculation of possible \(n-\bar{n}\) type oscillations by Kuzmin in 1970 [Kuzmin1970]. In the late 1970s and early 1980s, similar ideas were also pursued by a host of American physicists [Glashow1979,Mohapatra1980,Kuo1980,Chang1980]. However, experimental limit of \(<10^{-23}\) eV on the possible \(n-\bar{n}\) mass splitting [Baldo-Ceolin1994] make such oscillations unlikely.

After a quiet period of time in studies of the mirror matter idea, the topic was revived in the early 1980s, in particular, on possible cosmological and astrophysical manifestations [Blinnikov1982,Blinnikov1983,Kolb1985]. Notably, it was demonstrated [Kolb1985] that mirror matter theory could be consistent with both big bang nucleosynthesis (BBN) and the cold dark matter hypothesis in the standard cosmology model ΛCDM [Peebles1980]. Considering a chaotic inflation model, Hodges presented the feasibility of mirror baryons as dark matter [Hodges1993]. To be compatible with the observed ⁴He abundance produced during BBN, the temperature of the mirror sector has to be less than half of the temperature of the ordinary matter [Kolb1985,Hodges1993].

As it was realized that perfect mirror symmetry is not possible, various types of explicit yet feeble interactions between the two sectors were proposed. For example, the \(U(1)\) photon or so-called kinetic mixing was applied to break the mirror symmetry [Holdom1986]. Foot and his collaborators proposed an extension to the Standard Model (SM) with mirror particles using this scheme [Foot1991]. Based on the kinetic mixing model, they have studied a wide range of problems under the mirror matter theory [Foot2014]. In particular, Foot became one of the most enthusiastic proponents of mirror matter theory and he even published a popular science book (Shadowlands: Quest for Mirror Matter in the Universe, 2002) on this topic besides dozens of academic articles.

Another scheme was studied by introducing the 6-quark interaction term between the two sectors in the work of Ref. [Berezhiani2006]. Its main advocate, Berezhiani, is another major figure with many publications in recent development of mirror matter theory. However, all these early mirror models (see reviews in Refs. [Berezhiani2004,Berezhiani2006,Cui2012,Foot2014]) are not satisfactory due to the introduction of some ad hoc interaction mechanisms between the ordinary and mirror sectors. A historic note on the early development of mirror matter theory can be found in Ref. [Okun2007] by Okun, one of the first three physicists who proposed the mirror matter idea.

Mirror matter as dark matter is probably the most enticing idea and motivating factor in early works on mirror matter theory. Early studies also tried to understand neutrino oscillations with certain models of mirror matter theory [Berezhiani1995,Foot1995]. However, it turned out that the neutrino oscillation puzzle can be explained perfectly by the generation mixing mechanism.

The next advancement on mirror matter theory was to try to use it to explain the neutron lifetime anomaly [Berezhiani2006], leading to an exciting and promising direction for this line of research. Specifically, high-precision neutron lifetime measurements in the past decades since 1980s have demonstrated a puzzling neutron lifetime discrepancy, i.e., the 1% difference between measurements from “Beam” and “Bottle” experiments (see review in [Tan2023a]). However, the understanding of the neutron lifetime issue was probably not correct. The community has shown a strong bias toward the “bottle” approach, believing that the “bottle” lifetime gives the true beta decay lifetime, which, unfortunately, misguided the development of mirror matter models.

Contrary to the common belief, it is most likely the “beam” approach that measures the true \(\beta\)-decay lifetime while the “bottle” method shows the neutron disappearing rate due to ordinary-mirror neutron (\(n-n’\)) oscillations. Based on this new understanding, a new rather exact two-parameter phenomenological \(n-n’\) oscillation model was proposed to explain both the neutron lifetime anomaly and dark matter [Tan2019]. The picture of how the mirror-to-ordinary matter density ratio evolved in the early universe into today’s observed dark-to-baryon matter density ratio (\(\sim 5.4\)) is gracefully demonstrated in that work. The new model was also immediately applied to evolution and nucleosynthesis in stars to provide a better understanding in stellar nuclear processes leading to the formation of progenitor cores of white dwarfs and neutron stars [Tan2019a].

Motivated by an earlier study on ultra-high energy cosmic rays under a different mirror model [Berezhiani2006a], the new model could present an even better understanding of such cosmic rays [Tan2019b]. In particular, it predicts that the 2nd Greisen–Zatsepin–Kuzmin (GZK) cutoff due to mirror Cosmic Microwave Background (CMB) radiation should be much steeper at about \(2\times 10^{20}\) eV. It also provides a probe to determine the third or cosmological parameter of the model — the temperature ratio of mirror-to-ordinary sectors \(T’/T\).

The new model also generalized the \(n-n’\) oscillations into a universal mixing mechanism for neutral hadrons at the quark level but in a topological way. In particular, it predicts an unexpectedly large invisible decay branching fraction of neutral kaons and other relatively long-lived hadrons. A consistent picture for the origin of both baryon asymmetry and dark matter in the early Universe was presented using kaon and neutron oscillations with new insights for the electroweak and QCD phase transitions and B-violation topological processes [Tan2019c].

The new oscillation mechanism also naturally explains the unitarity problem of the CKM matrix. In other words, the conventional CKM matrix is NOT unitary due to the missing strengths from topological transitions or oscillations of neutral hadrons. Most importantly, various feasible experiments (see review in [Tan2023a]) are proposed to test concrete unique predictions of the new theory, including measurement of neutron lifetime anomalies in narrow magnetic traps or under super-strong magnetic fields [Tan2019d], and detection of unexpectedly large branching fractions of invisible decays of long-lived neutral hadrons [Tan2020d].

Based on the new phenomenological mirror matter model, an extension to the Standard Model with mirror matter was proposed to understand the mass hierarchy, nature of neutrinos, and dark energy [Tan2019e]. In particular, a new understanding of mirror symmetry and supersymmetry was presented, and the energy scales of neutrino masses and dark energy were shown to be related to the tiny mass splitting scale between ordinary and mirror sectors due to staged quark condensation and spontaneous mirror symmetry breaking.

Eventually, a new theoretical framework in terms of a series of supersymmetric mirror models under different spacetime dimensions was proposed to potentially explain the arrow of time and the big bang dynamics [Tan2020,Tan2020a]. Under the new framework, gravity is understood as an emergent classical phenomenon from inflated smooth spacetime, and supersymmetric mirror models provide understanding of microphysics of Schwarzschild black holes as 2D boundaries of 4D spacetime [Tan2020b,Tan2021a]. A new set of first principles were then proposed as the foundations of the new framework, i.e., the quantum action principle that provides the formalism, the consistent observation principle that sets physical constraints and symmetries, and the spacetime inflation principle that determines physical contents (particle fields and interactions) [Tan2021]. Under these guiding principles, the supersymmetric mirror models can be naturally constructed to study various phases of the universe at different spacetime dimensions and the dynamics between the phases.

The most recent progress has been on establishing connections between mirror matter theory and string theory [Tan2023b] and a novel superconductivity mechanism for unconventional high-temperature superconducting materials [Tan2023c]. In particular, the concept of mirror symmetry as an orientation symmetry of local spaces was further explored [Tan2023b]. Its connections to T-duality [Giveon1994] and Calabi-Yau mirror symmetry [Strominger1996a] in string theory were established. Many developments in string theory were found to provide a solid foundation for the new framework of mirror matter theory. In particular, supersymmetric mirror models in 4D spacetime can be constructed from the combination of two chiral heterotic strings [Gross1985]. String theory is clearly a very powerful mathematical tool for further developing the new mirror matter theory.

We would like to clarify that other partial or seemingly related proposals in literature are different from the above-discussed mirror matter theory. For example, the twin-Higgs model is just an incomplete mirror model for the Higgs particle only. The brane-world model seems to be an extension to the mirror symmetry but most likely just a mathematical tool lacking physical principles, similar to the relationship between string theory and supersymmetric mirror models. The many world interpretation of quantum mechanics by Everett, the multiverse vision from string theory, and any other parallel world / universe ideas are completely different from the mirror matter theory discussed here.

Major References:

1. T. D. Lee and C. N. Yang, Phys. Rev. 104, 254 (1956).
2. C. S. Wu, E. Ambler, R. W. Hayward, D. D. Hoppes, and R. P. Hudson, Phys. Rev. 105, 1413 (1957).
3. I. Y. Kobzarev, L. B. Okun, and I. Y. Pomeranchuk, Sov. J. Nucl. Phys. 3, 837 (1966)
4. E. W. Kolb, D. Seckel, and M. S. Turner, Nature 314, 415 (1985)
5. W. Tan, Phys. Lett. B 797, 134921 (2019)
6. W. Tan, Universe 9, 180 (2023)
7. W. Tan, Symmetry 15, 1415 (2023)