Motivated by the first observation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-baryon decays, the search for baryonic decays exhibiting large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation will be a primary focus in the coming years. We propose that significant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math>-violating effects exist in the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mi>D</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math> denotes a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> eigenstate of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mtext>−</mtext><msup><mrow><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> system. The predicted <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> asymmetries for both the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math>-even and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math>-odd modes can reach magnitudes as large as 50%, making these decays promising targets for measurement at the LHCb experiment. Additionally, we predict for the first time several nonzero <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math>-violating observables associated with angular distribution parameters, providing valuable complementary information in the search for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> violation in baryon decays. Furthermore, we propose a novel strategy to extract the Cabibbo-Kobayashi-Maskawa angle <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math> by combining data on angular distribution parameters and decay rates from the relevant channels. We emphasize that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mi>D</mi></math> decays are among the most promising candidates for determining <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math> in the baryon sector. Our findings may offer new insights for future theoretical and experimental investigations.

China

Zhou Rui

Zhi-Tian Zou

Ya Li

Ying Li

Large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mi>D</mi></math> decays and extraction of the Cabibbo-Kobayashi-Maskawa angle <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math>

We clarify the structure of Yukawa couplings and mass matrices for matter fields in heterotic string theory on smooth Calabi-Yau threefolds with standard embedding. The topological structure of Calabi-Yau threefolds leads to interesting Yukawa textures that cannot be derived from group-theoretical symmetries, e.g., the so-called Weinberg texture in the case of two generations of matter fields. Furthermore, we find that a $\textit{U}$ (2) flavor symmetry, which plays an important role in controlling higher-dimensional operators in the Standard Model effective field theory, emerges at specific loci in the moduli space of multi-Higgs fields. Small perturbations around these loci generate semi-realistic patterns of quark masses and mixings.

Japan

Jun Dong

Tatsuo Kobayashi

Shuhei Miyamoto

Hajime Otsuka

Yukawa textures with enhanced symmetries in heterotic Calabi-Yau compactifications

The unsuppressed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation in QCD is a problem in the standard model. If we have some mechanism to guarantee real determinants of the quark mass matrices, the vanishing physical vacuum angle <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>θ</mi><mo stretchy="false">¯</mo></mover></math> indicates the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> invariance at the fundamental level. Thus, the small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>θ</mi><mo stretchy="false">¯</mo></mover></math> is technically natural, since we have an enhanced <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> symmetry in the limit of the vanishing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>θ</mi><mo stretchy="false">¯</mo></mover><mo>=</mo><mn>0</mn></math>. In fact, it was proved that the vacuum angle is never renormalized up to the four-loop level once it is fixed at 0 value at some high energy scale. The purpose of this paper is to construct a model that guarantees the real determinants of the quark mass matrices assuming a noninvertible symmetry. In the present model, we have only one <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violating phase and hence all observable phases such as phases in the Cabibbo-Kobayashi-Maskawa matrix, in the neutrino oscillation and in the leptogenesis are related. It should be remarkable that the correct sign of the baryon-number asymmetry in the present Universe is obtained and a narrow region for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violating phase <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mi mathvariant="italic">CP</mi></mrow></msub><mo>≃</mo><mn>19</mn><mn>2</mn><mi>°</mi><mi>–</mi><mn>19</mn><mn>7</mn><mi>°</mi></mrow></math> is predicted.

Morimitsu Tanimoto

Tsutomu T. Yanagida

GUT-motivated noninvertible symmetry as a solution to the strong <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> problem and the neutrino <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating phase

We study the origin of modular weights of wave functions in magnetized $\textit{T}$ models. It is explicitly demonstrated that the modular weights of the wave functions on magnetized $\textit{T}$ are equivalent to their mass level. We further extend this result to magnetized $\textit{T}$ models. As a result, we construct the wave functions of excited states in magnetized $\textit{T}$ models and show that their modular weights are likewise equivalent to the corresponding mass levels.

Tim Jeric

Maki Takeuchi

Hikaru Uchida

Modular weights of wave functions on magnetized torus

We clarify selection rules of conjugacy classes of several finite discrete groups where we deal with both gauged and ungauged cases. We find that the selection rules enjoy finite Abelian or non-Abelian discrete symmetries originating from the inner and/or outer automorphism of underlying discrete groups. Since the selection rules of conjugacy classes do not obey conventional grouplike selection rules, they open up new coupling selection rules of fields which are labeled by the conjugacy classes.

Ryusei Nishida

Discrete gauging and noninvertible selection rules

We investigate coupling selection rules in heterotic string theory on non-Abelian orbifolds. Since boundary conditions on the orbifolds are classified by conjugacy classes of space group elements, non-Abelian orbifolds give rise to non-invertible selection rules on couplings among twisted sectors as well as ones including untwisted sectors. Furthermore, we find that non-invertible selection rules lead to characteristic patterns of Yukawa matrices.

Non-invertible selection rules on heterotic non-Abelian orbifolds

We propose a three-zero texture for the down-quark mass matrix within a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>5</mn><mo stretchy="false">)</mo></math> grand unified theory (GUT)-inspired Standard Model, enforced by a noninvertible selection rule originating from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></math> gauging of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mi>N</mi></msub></math> symmetries. Assuming <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> invariance at the high-energy scale, our framework solves the strong <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> problem while reproducing a realistic quark mass matrix. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> symmetry is spontaneously broken down at an intermediate scale via complex vacuum expectation values of new scalar fields <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>i</mi></msub></math>, which generate the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> phase in the Cabibbo-Kobayashi-Maskawa matrix without inducing the quantum chromodynamics (QCD) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>θ</mi><mo stretchy="false">¯</mo></mover></math> term. The present model incorporates three generations of matter, Higgs, and additional scalars with a common structure under the noninvertible symmetry, which may be naturally embedded into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></math> GUTs at high energies.

Noninvertible symmetry as a solution to the strong <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> problem in a GUT-inspired standard model

In this letter, we construct an explicit rephasing transformation that converts an arbitrary unitary matrix into the Kobayashi–Maskawa (KM) parametrization and identify all independent CP phases in the mixing matrix as the arguments of its matrix elements. Furthermore, by applying this rephasing transformation to the fermion diagonalization matrices <inline-formula><tex-math id='TM0001' notation='LaTeX'>$U^{\nu , e}$</tex-math></inline-formula>, we show that the Majorana phases are represented by fermion-specific phases <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\delta ^{\nu , e}_{\rm KM}$</tex-math></inline-formula> and their relative phases. In particular, by neglecting the 3-1 elements <inline-formula><tex-math id='TM0003' notation='LaTeX'>$U_{31}^{\nu ,e}$</tex-math></inline-formula> of the diagonalization matrices for the two fermions, the KM phase <inline-formula><tex-math id='TM0004' notation='LaTeX'>$\delta _{\rm KM}$</tex-math></inline-formula> is concisely expressed as <inline-formula><tex-math id='TM0005' notation='LaTeX'>$\delta _{\rm KM} = \arg \left[1 + ({U^{e * }_{21} U^{\nu }_{21} / U^{e * }_{11} U^{\nu }_{11} }) \right] + \arg \left[ - { U_{32}^{e *} U_{32}^{\nu } / U^{e * }_{22} U^{\nu }_{22} } \right]$</tex-math></inline-formula> by fermion-specific rephasing invariants representing two relative phases.

Masaki J S Yang

Explicit Rephasing to Kobayashi–Maskawa Representation and Fundamental Phase Structure of CP Violation

We discuss the phenomenological implications of noninvertible selection rules in the framework of the supersymmetric standard model. We find that a remnant <inline-formula><tex-math id='TM0001' notation='LaTeX'>$\mathbb {Z}_2$</tex-math></inline-formula> symmetry of fusion algebras that holds at all-loop order plays the role of <italic>R</italic>-parity, forbidding baryon- and lepton-violating operators. In addition, a combination of Standard Model gauge symmetry and the noninvertible selection rules lead to baryon triality and proton hexality that can protect the proton from decay. In general, our selection rules cannot realize the same results as conventional <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\mathbb {Z}_N$</tex-math></inline-formula> symmetries in the supersymmetric standard model. We also clarify the assignments of matter fields under the fusion algebras that are consistent with <inline-formula><tex-math id='TM0004' notation='LaTeX'>$SU(4) \times SU(2) \times SU(2)$</tex-math></inline-formula>, <inline-formula><tex-math id='TM0005' notation='LaTeX'>$SU(5)$</tex-math></inline-formula>, and <inline-formula><tex-math id='TM0006' notation='LaTeX'>$SO(10)$</tex-math></inline-formula> grand unified theories.

Hironobu Mita

Riku Sakuma

Matter Symmetries in Supersymmetric Standard Models from Noninvertible Selection Rules

We apply non-invertible selection rules coming from a fusion algebra to radiative neutrino mass models where fields are labeled by the elements in the algebra. Since non-invertible selection rules only hold at tree level, radiative corrections naturally explain the origin of tiny neutrino masses. Furthermore, a remnant symmetry of the fusion algebra protects the stability of dark matter, which is conventionally imposed in radiative neutrino models. We also find that interesting neutrino mass textures are realized by assigning fields to family-dependent elements in the algebra.