The issue of texture specific fermion mass matrices have been examined briefly from the `bottom-up' perspective. In case no conditions are imposed, the texture ansatze leads to a large number of viable possibilities. However, besides textures, if in case one incorporates the ideas of `natural mass matrices' and uses the facility of Weak Basis Transformations, then one is able to arrive at a minimal finite set of viable mass matrices in the case of quarks.
A detailed investigation of all possible textures of Fritzsch-like and non-Fritzsch like, 144 for texture 6 zero and 432 for texture 5 zero mass matrices, have been carried out to ascertain their compatibility with the existing quark mixing data. It seems that all the texture 6 zero possibilities are completely ruled out whereas in the case of texture 5 zero mass matrices the only viable possibility looks to be that of Fritzsch-like.
The triangular basis is proposed as an efficient way of analyzing general quark mass matrices. Applying the method to hermitian hierarchical matrices with five texture zeros, analytic predictions for quark mixing can be readily obtained. One unique texture pair is found most favorable with present data. Some remarks are also made concerning parallel textures between the up and down quark mass matrices with four zeros.
We perform a systematic analysis of all possible texture zeros in general and symmetric quark mass matrices. Using the values of masses and mixing parameters at the electroweak scale, we identify for both cases the maximally restrictive viable textures. Furthermore, we investigate the predictive power of these textures by applying a numerical predictivity measure recently defined by us. With this measure we find no predictive textures among the viable general quark mass matrices, while in the case of symmetric quark mass matrices most of the 15 maximally restrictive textures are predictive wit…
The so called ``Texture 2(4) zero mass matrices'' were first introduced in a Wayne State University preprint to accommodate the "yet to be discovered" heavy top quark. The preprint in its entirety is reproduced here after a brief commentary.
In the light of refined and large reactor mixing angle $θ_{13}$, we have revisited the texture three and two zero neutrino mass matrices in the flavor basis. For Majorana neutrinos, it has been explicitly shown that all the texture three zero mass matrices remain ruled out. Further, for both normal and inverted mass ordering, for the texture two zero neutrino mass matrices one finds interesting constraints on the Dirac-like CP violating phase $δ$ and Majorana phases $ρ$ and $σ$.
Implications of texture specific mass matrices have been investigated for both quarks and neutrinos. Interestingly, for the case of quarks Fritzsch-like texture 4 zero mass matrices have been found to be compatible with the present precisely known sin2βas well as other precise CKM matrix elements. In the case of leptonic mass matrices, for both Majorana and Dirac neutrinos we find that for texture 4, 5, 6 zero mass matrices the inverted hierarchy and degenerate scenarios of neutrino masses are ruled out by the present data.
Texture specific fermion mass matrices have played an important role in understanding several features of fermion masses and mixings. In the present work, we have given an overview of all possible cases of Fritzsch-like as well as non Fritzsch-like texture 6 and 5 zero fermion mass matrices. Further, for the case of texture 4 zero Fritzsch-like quark mass matrices, the issue of the hierarchy of the elements of the mass matrices and the role of their phases have been discussed. Furthermore, the case of texture 4 zero Fritzsch-like lepton mass matrices has also been discussed with an emphasis on…
We investigate the texture of fermion mass matrices in theories with partial unification (for example $ SU(2)_L\times SU(2)_R\times SU(4)_c$) at a scale $\sim 10^{12}$ GeV. Starting with the low energy values of the masses and the mixing angles, we find only two viable textures with atmost four texture zeros. One of these corresponds to a somewhat modified Fritzsch textures. A theoretical derivataion of these textures leads to new interesting relations among the masses and the mixing angles.
A comprehensive review of several aspects of fermion mixing phenomenon and texture specific mass matrices have been presented. Regarding fermion mixings, implications of unitarity and certain new developments for the CKM paradigm have been discussed. In the leptonic sector, the question of possibility of CP violation has been discussed in detail from the unitarity triangle perspective. In the case of texture specific mass matrices, the issues of viability of Fritzsch-like as well as non Fritzsch-like mass matrices have been detailed for both the quark and leptonic sectors. The relationship of …
Within the Standard Model, starting with the most general mass matrices we have used the facility of making weak basis transformations and have imposed the condition of `naturalness' to carry out their analysis within the texture zero approach. Interestingly, our analysis reveals that a particular set of texture 4 zero quark mass matrices can be considered to be a unique viable option for the description of quark mixing data.
There are many viable combinations of texture zeros in lepton mass matrices. We propose an economical and stable mass texture. Analytical and numerical results on mixing parameters and the effective mass of neutrinos are obtained. These results satisfy new constraints from neutrinos oscillation experiments and cosmological observations. Our proposition reveals that in the complex forest of neutrinos mixing models, a simple and robust one is still possible.
We provide a complete and systematic analysis of hermitian, hierarchical quark mass matrices with four texture zeros. Using triangular mass matrices, each pattern of texture zeros is readily shown to lead to a definite relation between the CKM parameters and the quark masses. Nineteen pairs are found to be consistent with present data, and one other is marginally acceptable. In particular, no parallel structure between the up and down mass matrices is found to be favorable with data.
The recent T2K, MINOS and Double Chooz oscillation data hint a relatively large $θ_{13}$, which can be accommodated by some general modification of the Tribimaximal/Bimaximal/Democratic mixing matrices. Using such matrices we analyze several Majorana mass matrices with texture one-zero and show whether they satisfy normal or inverted mass hierarchy and phenomenologically viable or not.
A systematic analysis on the phenomenologically allowed textures in Hermitian quark mass matrices with four texture-zeros is presented. The current data allow a full determination of the mass matrix elements, provided that the actual number of the parameters in the matrices is less than or equal to ten. Besides the standard texture with zeros located in (1,1) and (1,3) positions, we find four new type of parallel mass matrices. All of them are found to have similar hierarchical structures: three of the nonzero matrix elements are at the same order of magnitude with a small geometric hierarchy,…
Several popular Ansätze of lepton mass matrices that contain texture zeros are confronted with current neutrino observational data. We perform a systematic $χ^2$-analysis in a wide class of schemes, considering arbitrary Hermitian charged lepton mass matrices and symmetric mass matrices for Majorana neutrinos or Hermitian mass matrices for Dirac neutrinos. Our study reveals that several patterns are still consistent with all the observations at 68.27% confidence level, while some others are disfavored or excluded by the experimental data. The well-known Frampton-Glashow-Marfatia two-zero textu…
Against the conventional picture that the mass matrix forms in the quark sectors will take somewhat different structures from those in the lepton sectors, on the basis of an idea that all the mass matrices of quarks and leptons have the same texture, a universal texture of quark and lepton mass matrices is proposed by assuming a discrete symmetry Z_3 and an extended flavor 2\leftrightarrow 3 symmetry. The texture is described by three parameters (including phase parameter). According to this ansatz, the neutrino masses and mixings are investigated.
It has been shown that the neutrino mass matrices with two texture zeros in the charged lepton basis predict non-zero 1-3 mixing and are necessarily CP violating with one possible exception in class C for maximal mixing.
In an attempt to find minimal scenarios we study the implications of Dirac and Majorana mass matrices with texture zeros within the type I seesaw mechanism. For the Dirac mass matrices we consider 5 zero textures which we show to be the most minimal form that can successfully account for low energy phenomenology if the Majorana mass matrices are chosen minimal as well. For those, we consider both diagonal and even more minimal non-diagonal forms. The latter can be motivated e.g. by simple U(1) flavour symmetries and have two degenerate eigenvalues. We classify the allowed textures and discuss …
The full parameter space of Hermitian quark mass matrices with four texture zeros is explored by using current experimental data. We find that all ten free parameters of the four-zero quark mass matrices can well be constrained. In particular, only one of the two phase parameters plays an important role in CP violation. The structural features of this specific pattern of quark mass matrices are also discussed in detail.
Starting with the most general mass matrices, within the context of Standard Model and some of its extensions, incorporating the ideas of weak basis transformations and naturalness, we find that there exists a particular set of texture specific quark mass matrices which can be considered to be the minimal viable option.
A way of counting free parameters in the quark mass matrices of the standard model, including the constraints coming from weak basis transformations, is presented; this allow to understand the exact physical meaning of the parallel and non-parallel texture zeros which appear in some "ansätz" of the $3\times 3$ quark mass matrices, including the CP violation phenomena in the analysis, it is shown why the six texture zeros are ruled out. Finally, a five texture zeros "ansätze" which properly copes with all experimental constrains, including the angles of the unitary triangle, is presented.
Out of the fifteen 3 x 3 neutrino mass matrices with two texture zeros seven are compatible with the neutrino oscillation data. While 2 of them correspond to hierarchical neutrino masses and 1 to an inverted hierarchy, the remaining 4 correspond to degenerate masses. Moreover only the first 3 of the 7 mass matrices are compatible with the maximal mixing angle of atmospheric neutrino and hence favoured by data. We give compact expressions for mass matrices in terms of mass eigenvalues and study phenomenological implications for the 7 cases. Similarity of the textures of the neutrino, charged-le…
The phenomenology of the five independent sets of $3\times 3$ quark mass matrices with five texture zeros is carried through in full detail, including predictions for the CP violation asymmetries. Our study is done without any approximation, first analytical and then numerical.
In view of the precise measurement of the leptonic mixing angle θ_{13}, implications of the latest mixing data have been investigated for lepton mass matrices pertaining to Dirac neutrinos.These texture specific lepton mass matrices have been examined for their compatibility with the latest data in the cases of normal hierarchy, inverted hierarchy and degenerate scenario of neutrino masses.
We have carried out an extensive analysis of all possible minimal texture quark mass matrices implying 169 texture 6 zero combinations. One finds that all these combinations are ruled out, a good number of these analytically, the other possibilities are excluded by the present quark mixing data. Interestingly, even if in future, there are changes in the ranges of the light quark masses, these conclusions remain valid.
We study a variety of different texture patterns in the basis in which the charged lepton mass matrix or neutrino mass matrix or neither are diagonal. The experimental results on the neutrinos provide sufficient restrictions to allow only a small number of simple patterns. We discuss particularly the texture zeroes which provide important relations among the mass eigenvalues and the mixing matrix.
We show that the parameters of the quark mass matrices M_u and M_d of a 4 texture zero model, exhibit an interesting hierarchical regularity we have called equal spacing rule, and that this regularity leads us to a further observation that the quark mass matrices (M_u, M_d) appear to exist in a plurality of states, each state labelled by two numbers (N,k). We give interpretation to these observations.
In pursuance of finding a viable set of mass matrices, keeping in mind recent precision measurement of quark masses and CKM parameters, we have carried out a detailed and comprehensive analysis of hermitian texture 4 zero quark mass matrices. Our analysis reveals that only Fritzsch like texture 4 zero combination provides a viable set of mass matrices for the present quark mixing data and all other texture 4 zero combinations are ruled out. A good number of these possibilities can be ruled out analytically, the other possibilities are excluded by the present quark mixing data. Interestingly, o…
We construct the $CP$-odd weak basis invariants in the flavor basis for all the phenomenologically viable neutrino mass matrices with a texture zero and a vanishing minor and, also, find the necessary and sufficient conditions for $CP$ invariance . We examine the interrelationships between different $CP$-odd weak basis invariants for these texture structures and investigate their implications for Dirac- and Majorana-type $CP$ violation.
In the context of texture 4 - zero and texture 5 - zero hierarchical quark mass matrices, CP violating asymmetry in $B^o_d({\bar B}^o_d) \to ψK_S$ (sin2$β$) has been evaluated by considering quark masses at $m_Z$ scale. For a particular viable texture 4 - zero mass matrix the range of sin2βis: 0.27 - 0.60 and for the corresponding texture 5 - zero case it is 0.31 - 0.59. Further our calculations reveal a crucial dependence of sin2$β$ on light quark masses as well as the phase in this sector.
We reanalyse Majorana-neutrino mass matrices M_nu with two texture zeros, by searching for viable hybrid textures in which the non-zero matrix elements of M_nu have simple ratios. Referring to the classification scheme of Frampton, Glashow and Marfatia, we find that the mass matrix denoted by A1 allows the ratios (M_nu)_{mu mu} : (Mnu)_{tau tau} = 1:1 and (M_nu)_{e tau} : (Mnu)_{mu tau} = 1:2. There are analogous ratios for texture A2. With these two hybrid textures, one obtains, for instance, good agreement with the data if one computes the three mixing angles in terms of the experimentally d…
Using the triangular matrix techniques of Kuo et al and Chiu et al for the four and five texture zero cases, with vanishing (11) elements for U and D matrices, it is shown, from the general eigenvalue equations and hierarchy conditions, that the quark mass matrices, and the CKM matrix can be expressed (except for the phases) entirely in terms of quark masses. The matrix structures are then quite simple and transparent. We confirm their results for the five texture zero case but find, upon closer examination of all the CKM elements which our results provide, that six of their nine patterns for …
An attempt has been made to carry out a detailed analysis of quark mass matrices having structure beyond the minimal texture. In particular, keeping in mind, precision measurements of CKM parameters as well as refinements in the ranges of light quark masses, we have examined the viability of all possible combinations of hermitian texture 5 zero quark mass matrices. Interestingly, one finds that all these possibilities are now excluded by the present quark mixing data, thereby, having important implications for model building.
We reanalyze the mass matrices model of quarks and leptons which gives a unified description of quark and lepton mass matrices with the same texture form. By investigating possible types of the assignment for the texture's components of this mass matrix form, we find that a different assignment for up-quarks from one for down-quarks can lead to consistent values of CKM mixing matrix. This finding overcomes a weak point of the previous analysis of the model. We also obtain some relations among the CKM mixing matrix parameters, which are independent of evolution effects.
We review previous work on neutrino mass textures in gauge theories. Such textures may arise as a result of flavour symmetries. In a given theory, it is possible to give a classification of heavy Majorana neutrino mass matrices, assuming the Dirac masses of the neutrinos to be of the same form as the ones of the up-quarks. Heavy Majorana neutrino mass matrices leading to large neutrino mixing, are tabulated as an example. Such solutions are now of interest, in the light of the Super-Kamiokande data.
We give a classification of heavy Majorana neutrino mass matrices with up to three texture zeroes, assuming the Dirac masses of the neutrinos to be of the same form as the ones of the up-quarks in the five texture zero solutions for the quark matrices. This is the case for many unified and partially unified models. We find that it is possible to have solutions which account for the solar and atmospheric neutrino problems as well as the COBE observations simultaneously, and we motivate the existence of such solutions from symmetries.
The generic predictions of two-texture zero neutrino mass matrices in the flavor basis have been examined especially in relation to the degeneracies between mass matrices within a class and interesting constraints on the neutrino parameters have been obtained. It is shown that the knowledge of the octant of $θ_{23}$, the sign of $\cosδ$ and neutrino mass hierarchy can be used to lift these degeneracies.
A class of neutrino mass matrices with texture zeros realizable using the group $Z_3$ within the framework of type (I+II) seesaw mechanism naturally admits a non-zero $θ_{13}$ and allows for deviations from maximal mixing. The phenomenology of this model is reexamined in the light of recent hints for non-zero $θ_{13}$.
In the context of Fritzsch-like texture 4 zero Hermitian quark mass matrices, we have attempted to find an `exact' formula for sin2βwherein the dependence of βon the quark masses and the elements of the quark mass matrices is visible in a simple and clear manner. This has been achieved keeping in mind the strong hierarchy of the quark masses and assuming the weak hierarchy amongst the elements of the mass matrices. This `exact' formula represents a vast improvement over the leading order formula based on strong hierarchy of the elements of the mass matrices. Apart from showing the compatibilit…
Hermitian mass matrices for the up and down quarks with texture zeroes but with the minimum number of parameters, ten, are investigated. We show how these {\em minimum parameter} forms can be obtained from a general set of hermitian matrices through weak basis transformations. For the most simple forms we show that one can derive exact and compact parametrizations of the CKM mixing matrix in terms of the elements of these mass matrices (and the quark masses).
Taking into account the latest neutrino oscillation data, we study texture zeros of the lepton mass matrices. Assuming the Dirac neutrino mass matrix M_D, the charged-lepton mass matrix M_l and the mass matrix of heavy right-handed Majorana neutrinos M_R to have three texture zeros, we show that the observed neutrino mixing angles can naturally be obtained. The phenomenological implications for the neutrino mass spectrum, the CP-violating phases, the tritium beta decay and the neutrinoless double-beta decay are explored.
We show that the four-zero texture of Hermitian quark mass matrices can survive current experimental tests: it is able to yield sufficiently large predictions for the flavor mixing parameter $|V_{ub}/V_{cb}|$ and the CP-violating parameter $\sin 2β$, without fine-tuning of the input values of quark masses, provided the (2,2), (2,3) and (3,3) elements of up and down mass matrices roughly satisfy a geometrical hierarchy. The successful relations $|V_{us}| \approx \sqrt{m_u/m_c + m_d/m_s}$ and $|V_{td}/V_{ts}| \approx \sqrt{m_d/m_s}$ obtained previously from the six-zero texture of Hermitian quar…
We demonstrate that Abelian family symmetries allow one to enforce texture zeros in arbitrary entries of the fermion mass matrices. Placing zeros in any number of elements of all occurring mass matrices can be done with two alternative methods; one of them utilizes the group Z_n with n sufficiently high. Concentrating on the lepton sector and on neutrino masses, we discuss the methods in the case of seesaw models and scalar triplet models. As an illustration, we present an example for each type of model.
We perform an analysis of general quark mass matrices in the general nearest neighbor interaction form. Excellent agreement with experiment is realized with this general texture, which is neither hermitian nor real-symmetric. We then propose a new class of quark mass matrices that contain no additional parameters other than the quark masses themselves, and thus possess calculability, i.e., ensure a relationship between the six quark masses and four flavor-mixing parameters of the Standard Model.
We study the implications of the simultaneous existence of a texture zero and a vanishing minor in the neutrino mass matrix. There are thirty six possible texture structures of this type, twenty one of which reduce to two texture zero cases which have, already, been extensively studied. Of the remaining fifteen textures only six are allowed by the current data. We examine the phenomenological implications of the allowed texture structures for Majorana type CP-violating phases, 1-3 mixing angle and Dirac type CP-violating phase. All these possible textures can be generated through the seesaw me…
We attempt the integration of the phenomenologically successful four zero texture of fermion mass matrices with the renormalizable SO(10) GUT. The resulting scenario is found to be highly predictive. Firstly, we examine the phenomenological implications of a class of the lepton mass matrices with parallel texture structures and obtain interesting constraints on the parameters of the charged lepton and the neutrino mass matrices. We combine these phenomenological constraints with the constraints obtained from SO(10) GUT to reduce the number of the free parameters and to further constrain the al…
All quark mass matrices with texture zeroes obtained through weak basis transformations are confronted with the experimental data. The reconstruction of the quark mass matrices M_u and M_d at the electroweak scale is performed in a weak basis where the matrices are Hermitian and have a maximum of three vanishing elements. The same procedure is also accomplished for the Yukawa coupling matrices at the grand unification scale in the context of the Standard Model and its minimal supersymmetric extension as well as of the two Higgs doublet model. The analysis of all viable power structures on the …
In the Standard Model, we obtain a non-Fritzsch like configuration with five texture zeros for the quark mass matrices. This matrix generates the quark masses, the inner angles of the CKM unitary triangle, and the CP-violating phase in the quark sector. This work can be applied to the PMNS matrix in the lepton sector, by assuming Dirac masses for the neutrinos, where non-trivial predictions for the neutrino masses and mixing angles are expected.
We study predictive textures for the lepton mass matrices in which the charged-lepton mass matrix has either four or five zero matrix elements while the neutrino Majorana mass matrix has, respectively, either four or three zero matrix elements. We find that all the viable textures of these two kinds share many predictions: the neutrino mass spectrum is inverted, the sum of the light-neutrino masses is close to 0.1 eV, the Dirac phase $δ$ in the lepton mixing matrix is close to either $0$ or $π$, and the mass term responsible for neutrinoless double-beta decay lies in between 12 and 22 meV.
In the quark sector, Jarlskog rephasing invariant parameter $J_{CP}$ has important implications for the CP violation as well as phase structure of the quark mass matrices. In fact all CP violating effects in this sector are proportional to the magnitude of the imaginary part of $J_{CP}$ . With the observation of non-zero and large "reactor mixing angle", it is widely believed that CP might be violated in the leptonic sector. In this context, we have examined in detail the relationship of CP odd invariants for texture specific mass matrices. In particular, we have calculated the predicted range…
Aiming to relate leptonic CP violating phase $δ$ to the cosmological CP asymmetry, we study the extension of MSSM by two quasi-degenerate (strictly degenerate at tree level) right-handed neutrinos and consider all possible two texture zero 3x2 Yukawa matrices plus one $ΔL=2$ dimension five (d=5) operator contributing to the light neutrino mass matrix. We classify all experimentally viable mass matrices, leading to several predictions, and analytically derive predictive relations. We also relate the CP violating $δ$ phase to the CP phase of the thermal leptogenesis.
We analyse the parallel hybrid texture structures in the charged lepton and the neutrino sector. These parallel hybrid texture structures have physical implications as they cannot be obtained from arbitrary lepton mass matrices through weak basis transformations. The total sixty parallel hybrid texture structures can be grouped into twelve classes, and all the hybrid textures in the same class have identical physical implications. We examine all the twelve classes under the assumption of non-factorizable phases in the neutrino mass matrix. Five out of the total twelve classes are found to be p…
We use the permutational symmetry group $S_{3}$ as a symmetry of flavour, which leads to a unified treatment of masses and mixings of the quarks and leptons. In this framework all mass matrices of the fermions in the theory have the same form with four texture zeroes of class of I. Also, with the help of six elements of real matrix representation of $S_ {3}$ as transformation matrices of similarity classes, we make a classification of the sets of mass matrices with texture zeroes in equivalence classes. This classification reduce the number of phenomenologically viable textures for the non-sin…
Texture six zero Fritzsch like as well as non Fritzsch like hermitian lepton mass matrices (144 combinations in all) have been investigated for both Majorana and Dirac neutrinos for their compatibility with the current neutrino oscillation data, keeping in mind the hierarchy of neutrino masses. All the combinations considered here for Majorana neutrino masses are ruled out by the existing data in the case of inverted hierarchy and degenerate scenario. For Majorana neutrinos with normal hierarchy, only 16 combinations can accommodate the experimental data. Assuming neutrinos to be Dirac particl…
The hierarchical quark masses and small mixing angles are shown to lead to a simple triangular form for the U- and D-type quark mass matrices. In the basis where one of the matrices is diagonal, each matrix element of the other is, to a good approximation, the product of a quark mass and a CKM matrix element. The physical content of a general mass matrix can be easily deciphered in its triangular form. This parameterization could serve as a useful starting point for model building. Examples of mass textures are analyzed using this method.
The issue of texture specific mass matrices has been discussed by incorporating Weak Basis transformations and the concept of `naturalness'. Interestingly, we find that starting from the most general mass matrices, one can arrive at texture four zero mass matrices which can fit both quark as well as lepton mixing data and are similar to the original Fritzsch ansatze.
We reanalyze the mass matrix model of quarks and leptons that gives a unified description of quark and lepton mass matrices with the same texture form. By investigating possible types of assignment for the texture components of the lepton mass matrix, we find that a different assignment for neutrinos than for charged leptons can also lead to consistent values of the MNSP lepton mixing matrix. We also find that the predicted value for the lepton mixing matrix element $U_{13}$ of the model depends on the assignment. A proper assignment will be discriminated by future experimental data for $U_{13…
We consider a modification of the Fukuyama-Nishiura texture and compare it to the precision quark flavour data, finding that it fits the data very well but at the cost of accidental cancelations between parameters. We then propose different viable textures for quarks, where only the Cabibbo mixing arises from the down sector, and extend to the charged leptons while constructing a complementary neutrino structure that leads to viable lepton masses and mixing.
