Quark Mass Matrices Research Articles

Solving the strong CP problem without axions

We formulate general conditions under which the strong CP problem is solved by spontaneous CP violation. Quark-mass matrix elements are polynomials in the CP-breaking order parameters, engineered such that their determinant is a real constant. This scheme permits only a limited number of textures. These conditions can be realized in supersymmetric theories with CP as an anomaly-free local flavor symmetry, suggesting a unified solution to the strong CP problem and the flavor puzzle. Our solution can be implemented using either modular invariance or a local U(1) symmetry. We present modular-invariant realizations where matter fields are assigned small modular weights ±2 (±1), utilising higher levels N = 2 (N = 3). Heavy quarks are in general not required, but their presence allows for models where colored particles fill non-singlet representations of the flavor group.

Nontriviality of dynamical Chern-Simons gravity and the standard model

Given the growing interest in gravitational-wave and cosmological parity-violating effects in dynamical Chern-Simons (dCS) gravity, it is crucial to investigate whether the scalar-gravitational Pontryagin term in dCS gravity persists when formulated in the context of the U(1)B−L anomaly in the standard model (SM). In particular, it has been argued that dCS gravity can be reduced to Einstein gravity after “rotating away” the gravitational-Pontryagin coupling into the phase of the Weinberg operator—analogous to the rotation of the axion zero mode into the quark mass matrix. We find that dCS gravity is nontrivial if the scalar field ϕ has significant spacetime dependence from dynamics. We provide a comprehensive consideration of the dCS classical and quantum symmetries relevant for embedding a dCS sector in the SM. We find that, because of the baryon/lepton number chiral gravitational anomaly, the scalar-Pontryagin term cannot be absorbed by a field redefinition. Assuming a minimal extension of the SM, we also find that a coupling of the dCS scalar with right-handed neutrinos induces both the scalar-Pontryagin coupling and an axionlike phase in the dimension-five Weinberg operator. We comment on the issue of gauging the U(1)B−L, the observational effects with these two operators present for upcoming experiments, and the origin of dCS gravity in string theory. Published by the American Physical Society 2024

Orbifold modular GUT of flavor

We discuss an SU(5) grand unified theory based on the 10d orbifold (T2)3/(Z4×Z2) plus three modular S4 groups with moduli at respective fixed points i,i+2,ω=e2iπ/3. The resulting model has hierarchical quark and charged-lepton mass matrices, arising from a double weighton mechanism, and reproduces the highly predictive littlest seesaw mechanism in the neutrino sector. The down-quark mass matrix has an upper triangular form, contributing to Cabibbo-Kobayashi-Maskawa mixing, while the charged-lepton mass matrix has a lower-triangular form with suppressed contributions to Pontecorvo-Maki-Nakagawa-Sakata mixing. The orbifold yields successful SU(5) breaking with doublet-triplet splitting of the Higgs multiplets. Published by the American Physical Society 2024

Tension between neutrino masses and gauge coupling unification in natural grand unified theories

The natural grand unified theories (GUT) solve various problems of the supersymmetric GUT and give realistic quark and lepton mass matrices under the natural assumption that all terms allowed by the symmetry are introduced with O(1) coefficients. However, because of the natural assumption, it is difficult to achieve the gauge coupling unification without tuning, while keeping neutrino masses at realistic values. In this paper, we try to avoid this tension between the neutrino masses and the gauge coupling unification, by introducing suppression factors for several terms. These suppression factors can be understood by approximate symmetries in some of the solutions. We show that one of the most important results in the natural GUT scenario, that the nucleon decay mediated by superheavy gauge fields is enhanced due to a smaller unification scale while the nucleon decay mediated by superheavy colored Higgs is suppressed, may change in those models proposed in this paper. Published by the American Physical Society 2024

A4 modular flavour model of quark mass hierarchies close to the fixed point τ = i∞

We study the possibility to generate the quark mass hierarchies as well as the CKM quark mixing and CP violation without fine-tuning in a quark flavour model with modular A4 symmetry. The quark mass hierarchies are considered in the vicinity of the fixed point τ = i∞, τ being the vacuum expectation value of the modulus. We consider first a model in which the up-type and down-type quark mass matrices Mu and Md involve modular forms of level 3 and weights 6, 4 and 2 and each depends on four constant parameters. Two ratios of these parameters, gu and gd, can be sources of the CP violation. If Mu and Md depend on the same τ, it is possible to reproduce the up-type and down-type quark mass hierarchies in the considered model for |gu| ~ mathcal{O} (10) with all other constants being in magnitude of the same order. However, reproducing the CP violation in the quark sector is problematic. A correct description of the quark mass hierarchies, the quark mixing and CP violation is possible close to τ = i∞ with all constant being in magnitude of the same order and complex gu and gd, if there are two different moduli τu and τd in the up-type and down-type quark sectors. We also consider the case of Mu and Md depending on the same τ and involving modular forms of weights 8, 4, 2 and 6, 4, 2, respectively, with Mu receiving a tiny SUSY breaking or higher dimensional operator contribution. Both the mass hierarchies of up-type and down-type quarks as well and the CKM mixing angles and CP violating phase are reproduced successfully with one complex parameter and all parameters being in magnitude of the same order. The relatively large value of Im τ, needed for describing the down-type quark mass hierarchies, is crucial for obtaining the correct up-type quark mass hierarchies.

CKM and PMNS mixing matrixes from SO(2) flavor symmetry

The relation between quark masses and CKM mixing is studied based on an approximate chiral flavor symmetry of quark mass matrix. In mass hierarchy limit, the mass ratio effect on CKM mixing is suppressed, which separates mass hierarchy and quark flavor mixing into two independent problems. We show that CKM mixing is dominated by two left-handed symmetries while mass hierarchy only provides slight corrections. The same mixing structure is generalized to lepton sector with extended Dirac neutrinos. The common flavor mixing provides a novel comprehension on the relation between quark CKM mixing and lepton PMNS mixing.

Texture zeros of quark mass matrices at fixed point tau =omega in modular flavor symmetry

We study systematically derivation of the specific texture zeros, that is the nearest neighbor interaction (NNI) form of the quark mass matrices at the fixed point tau =omega in modular flavor symmetric models. We present models that the NNI forms of the quark mass matrices are simply realized at the fixed point tau =omega in the A_4 modular flavor symmetry by taking account multi-Higgs fields. Such texture zero structure originates from the ST charge of the residual symmetry Z_3 of SL(2, Z). The NNI form can be realized at the fixed point tau = omega in A_4 and S_4 modular flavor models with two pairs of Higgs fields when we assign properly modular weights to Yukawa couplings and A_4 and S_4 representations to three generations of quarks. We need four pairs of Higgs fields to realize the NNI form in A_5 modular flavor models.

Soft breaking of the µ ↔ τ symmetry by S4 ⊗ Z2

The µ ↔ τ symmetry has been ruled out by its predictions on the reactor and atmospheric angles, nevertheless, a breaking of this symmetry might provide correct values. For that reason, we build a non-renormalizable lepton model where the mixings arise from the spontaneous breaking of the S4 ⊗ Z2 discrete group, subsequently the µ ↔ τ symmetry is broken in the effective neutrino mass matrix, that comes from the type II see-saw mechanism. As main result, the reactor and atmospheric angles are corrected and their values are in good agreement with the experimental data for the inverted hierarchy. Furthermore, we point out a link between the atmospheric angle and reactor one. In the quark sector, under certain assumptions, the generalized Fritzsch textures shape to the quark mass matrices so that the CKM matrix values are guaranteed.

A viable A_4 3HDM theory of quark mass matrices

It is known that a three Higgs doublet model (3HDM) symmetric under an exact A_4 symmetry is not compatible with nonzero quark masses and/or non-block-diagonal CKM matrix. We show that a 3HDM with softly broken A_4 terms in the scalar potential does allow for a fit of quark mass matrices. Moreover, the result is consistent with m_h=125,text {GeV} and the h rightarrow WW,ZZ signal. We also checked numerically that, for each point that passes all the constraints, the minimum is a global minimum of the potential.

Novel loop-diagrammatic approach to QCD θ parameter and application to the left-right model

When the QCD axion is absent in full theory, the strong CP problem has to be explained by an additional mechanism, e.g., the left-right symmetry. Even though tree-level QCD overline{theta} parameter is restricted by the mechanism, radiative corrections to overline{theta} are mostly generated, which leads to a dangerous neutron electric dipole moment (EDM). The ordinary method for calculating the radiative overline{theta} utilizes an equation overline{theta}=-arg det {m}_q^{textrm{loop}} based on the chiral rotations of complex quark masses. In this paper, we point out that when full theory includes extra heavy quarks, the ordinary method is unsettled for the extra quark contributions and does not contain its full radiative corrections. We formulate a novel method to calculate the radiative corrections to overline{theta} through a direct loop-diagrammatic approach, which should be more robust than the ordinary one. As an application, we investigate the radiative overline{theta} in the minimal left-right symmetric model. We first confirm a seminal result that two-loop level radiative overline{theta} completely vanishes (corresponding to one-loop corrections to the quark mass matrices). Furthermore, we estimate the size of a non-vanishing radiative overline{theta} at three-loop level. It is found that the resultant induced neutron EDM is comparable to the current experimental bound, and the expected size is restricted by the perturbative unitarity bound in the minimal left-right model.

Five texture zeros in the lepton sector and neutrino oscillations at DUNE

In this work, we have assumed special structures for the charged and neutral mass matrices in the lepton sector, inspired by structures for the up and down quark mass matrices that result by assuming a certain number of symmetrical zeros in their entries named texture zeros. A prediction of the lepton mixing matrix results from the rotation matrices that diagonalize the mass matrices in the neutral and charged lepton sectors. The use of texture zeros reduces the number of spurious parameters to the minimal ones needed to explain observations i.e., charged lepton masses and neutrino oscillation parameters. Specifically, we have considered the case of five texture zeros and we have confronted the resulting lepton mixing matrices with current measurements in the neutrino sector. Finally, sensitivities to the independent parameters in the mixing predicted by the nonequivalent forms were studied using simulated events at the DUNE neutrino oscillation experiment. We have found that DUNE is sensitive to nonzero $CP$ violation allowed in the models.

Flavor structures of quarks and leptons from flipped SU(5) GUT with A4 modular flavor symmetry

We propose to generate the flavor structures of the Standard Model plus neutrinos from flipped SU(5) GUT with A4 modular flavor symmetry. Possible way to assign different moduli values for quarks and leptons in modular GUT scheme is discussed. We propose to reduce the multiple modular symmetries to a single modular symmetry in the low energy effective theory with proper boundary conditions. We classify all possible scenarios in this scheme according to the assignments of the modular A4 representations for matter superfields and give the expressions of the quark and lepton mass matrices predicted by our scheme at the GUT scale. After properly selecting the modular weights for various superfields that can lead to better fitting, we can obtain the best-fit points with the corresponding χ2 values for the sample subscenarios. We find that the flavor structures of the Standard Model plus neutrinos can be fitted perfectly in such a A4 modular flavor GUT scheme with single or two modulus fields. Especially, the {chi}_{textrm{total}}^2 of our fitting can be as low as 1.558 for sample IX′ of scenario III even if only a single common modulus field for both quark and lepton sectors is adopted. The most predictive scenario III, in which all superfields transform as triplets of A4, can be fitted much better with two independent moduli fields τq, τl for quark sector and lepton sector ( {chi}_{textrm{total}}^2 ≈ 95) than that with the single modulus case ( {chi}_{textrm{total}}^2 ≈ 282.4).

Quark and lepton flavor structure in magnetized orbifold models at residual modular symmetric points

We study quark and lepton mass matrices derived from magnetized $T^2/\mathbb{Z}_2$ orbifold models. Quark and lepton masses have a large hierarchy. In addition, mixing angles are large in the lepton sector, while those are small in the quark sector. We find that this structure can be realized in certain flavor models, which are identified by the zero points of the zero-mode wave functions of fermions and Higgs modes. We classify such realistic flavor models. Fixed points $\tau=i$, $e^{2\pi i/3}$ and $i\infty$ of the modulus $\tau$ play a role in realizing a large mass hierarchy through our scenario, where residual $S$, $ST$, and $T$ symmetries remain and the lightest Higgs modes can correspond to eigenstates of residual symmetries at the leading order. As a result, we find that there are 24 flavor models in total which can be realistic in a vicinity of $S$-symmetric vacuum but no flavor models for $ST$ and $T$-symmetric vacua.

Mass matrices with CP phase in modular flavor symmetry

Abstract We study the CP violation and the CP phase of quark mass matrices in modular flavor symmetric models. The CP symmetry remains at τ = e2πi/3 by a combination of the T-symmetry of the modular symmetry. However, T-symmetry breaking may lead to CP violation at the fixed point τ = e2πi/3. We study such a possibility in magnetized orbifold models as examples of modular flavor symmetric models. These models, in general, have more than one candidate for Higgs modes, while generic string compactifications also lead to several Higgs modes. These Higgs modes have different behaviors under the T-transformation. The light Higgs mode can be a linear combination of those modes so as to lead to realistic quark mass matrices. The CP phase of the mass matrix does not appear in a certain case, which is determined by the T-transformation behavior. Deviation from this is important to realize the physical CP phase. We discuss an example leading to a non-vanishing CP phase at the fixed point τ = e2πi/3.

Constructing viable quark mass matrices in the flavor basis using S3 × Z3 symmetry

Non-Abelian discrete symmetry group [Formula: see text] has been used to construct quark mass matrices in the flavor basis. Interestingly, the case when [Formula: see text] is nondiagonal and [Formula: see text] is diagonal, is very much compatible with the presently refined data regarding the quark masses and mixing. However, the other case, when [Formula: see text] is nondiagonal and [Formula: see text] is diagonal, looks to be incompatible with the data.

Minimizing the phase structure of quark mass matrices

Fritzsch–Xing matrices are a particular class of texture 4 zero hermitian quark mass matrices, known to be successful in accommodating the quark mixing data. In the present work, it is shown that these texture 4-zero matrices with only one phase parameter, unlike the usually considered two phase parameters, are not only consistent with the latest experimental quark mixing data, but also predict the CP violation parameters, J and corresponding phase delta , in agreement with the recent global analyses. We also show that the mass matrix elements do not exhibit a strong hierarchy and there is a strong correlation between some of the mass matrix elements of up and down sector. A precision measurement of delta as well as small quark masses would have the potential to constrain the phase structure of the matrices further.

Flavourful axion and the Peccei-Quinn symmetry

A model is presented, where the Froggatt-Nielsen and Peccei-Quinn symmetries are identified. This provides a solution to the strong CP problem and an explanation to the fermion mass hierarchy. At leading order, the quark mass matrix possess a Nearest-Neighbour-Interaction structure, while the neutrino mass matrix has a Majorana A2 texture. From a thorough numerical analysis the viability of this model is asserted, by comparing against current measurements. The data obtained from this analysis is then used to study properties from the axion.

Flavor specific [formula omitted] gauge model for muon g − 2 and [formula omitted] anomalies

The muon (g−2)μ and b→sμ¯μ induced B anomalies as hints of new physics beyond the standard model (SM) have attracted much attention. These two anomalies indicate that there may exist new interaction specifically related to muon. A lot of theoretical ideas have been proposed to explain these anomalies. Gauged flavor specific U(1)Bq−Lμ is among the promising ones. The new gauge boson Z′ from U(1)Bq−Lμ interacts with muon and provides necessary ingredient to solve the (g−2)μ anomaly. The Z′-quark coupling can generate flavor changing interactions after diagonalization of quark mass matrix between weak eigen-state and mass eigen-state basis. We revisit challenges for such models attempting to explain the (g−2)μ and B anomalies separately or simultaneously. We find although for U(1)Bq−Lμ models there is still parameter space to provide solutions for separately explaining the (g−2)μ and B anomalies, there exists no parameter space for such models to solve both the anomalies simultaneously, after taking into account existing constraints from τ→μγ, τ→3μ, neutrino trident and Bs−B¯s data. Among them leptonic processes restrict Z′ mass to be less than a few hundred MeV if required to solve the (g−2)μ anomaly, which causes conflict between data from Bs−B¯s, D0−D¯0 mixing and also hadron decays with Z′ in the final states. The effects of U(1)Y and U(1)Bq−Lμ kinetic mixing on these anomalies are also studied. We find that neither can these effects do much to bring the two anomalies together to be solved simultaneously.

Yukawa textures in modular symmetric vacuum of magnetized orbifold models

Abstract We study quark mass matrices derived from magnetized $T^2/\mathbb {Z}_2$ orbifold models. Yukawa matrices at three modular fixed points, τ = i, e2πi/3, and i∞, are invariant under S-, ST-, and T-transformations. We study these invariances on the $T^2/\mathbb {Z}_2$ twisted orbifold. We find that Yukawa matrices have a kind of texture structure, although those at τ = i∞ are not realistic. We classify the Yukawa textures at τ = i and e2πi/3. Moreover we investigate the conditions such that the quark mass matrix constructed by Yukawa textures becomes approximately a rank-one matrix, which is favorable to lead to hierarchical masses between the third generation and the others. It is found that realistic quark mass matrices can be obtained around the S-invariant and ST-invariant vacua. As an illustrative example, we show the realization of the quark mass ratios and mixing based on Fritzch and Fritzch–Xing mass matrices.

Correlations between quark mass and flavor mixing hierarchies

We calculate the quark flavor mixing matrix V based on the Hermitian quark mass matrices Mu and Md with vanishing (1,1), (1,3) and (3,1) entries. The popular leading-order prediction |Vub/Vcb|≃mu/mc is significantly modified, and the result agrees with the current experimental value. We find that behind the strong mass hierarchy of up- or down-type quarks is the weak texture hierarchy of Mu or Md characterized by an approximate seesaw-like relation among its (2,2), (2,3) and (3,3) elements.