Empirically Consistent “Calculable” Quark Mass Matrices in the Approximately “Flavour Democratic” Basis

The empirically consistent calculable schemes, discovered among the modified Fritzsch-Plankl type quark mass matrices, and their predicted topquark masses and KM properties are presented

The empirically consistent "calculable" schemes, discovered among the modified Fritzsch-Plankl type quark mass matrices, and their predicted topquark masses and KM properties are presented.
In the previous papers, !)-3) accepting the discrepancies between the Fritzsch type quark mass matrices 4 ) -the only "calculable" quark mass matrices survived until recently -and the recent KM phenomenology as serious one, we have searched for and presented new types of quark mass matrices consistent with the KM phenomenology in the approximately "flavour democratic" as well as approximately diagonal bases. We advocated!) there that the realistic quark mass matrix must have the following structure, in the approximately diagonal basis, and further we presented!) a "calculable" scheme having such structure as hu bu predicting 2 ) mrys=110~ 150 GeV. We have also searched for and presented 3 ) the desirable approximately "flavour democratic" quark mass matrices.
The purpose of this paper is to correct some incompleteness of the previous papers 3 ) and to present the results of more comprehensive considerations on the empirically consistent "calculable" quark mass matrices in the approximately "flavour democratic" basis.
We would like to start our dicussion by presenting the empirically consistent "calculable"schemes, predicting 0 between 0° and 180", discovered among the modified Fritzsch-Plankl type quark mass matrices. They are given as*) ~ ~. [ : 1 :]+(-lH: where the ±'s in (3) are the same sign in the same order.*) The Mtll and Mtn(~= U, d) are the "calculable" quark mass matrices, consistent with the present KM data,6)-8) the indirect KM informations through the formulas 9 ),lO) on the KO-Ko and EO-Bo mixings and the knowledge on the quark masses.ll),12) They are selected from the following class of quark mass matrices, that is The M«E<, P<, If<) come to belong to the Fritzsch-Plankl typeS) quark mass matrices, that is It ~rl c<~la<I~I.8<I~I/<I, (~=u and d) (5) when p<=l. On the other hand, the Mlp come to belong to the M«E<, p<, cP<), when at The third term of the M1ilm(PU) given in (3) The UMfn(2)(Pu) U t take the following form, for pu=OO, l(Fritzsch.-Plankl's case 5 ») and 0, - -respectively. It should be noted here that these quark mass matrices, (7)~(9), have the structure (1) advocated by us, I) and that, unlike the quark mass matrix given in (2) where ,ulu=lmu/mci, ,u2 u =lmc/mtl, ,uld=lmd/msl and ,u2d=lms/mbl. Among the schemes belonging to the M~(E~, P~, rf;~), we searched for the ones which were "calculable"*) and made the predicted formulas (10), the knowledge on the quark masses (11)11) (12)12) (13) in this work, to be mutually consistent, and found the Mif! and Mi12, given in (3), as the solutions. In these analyses, we used the following approximate relations (in units of GeV) extracted from Fig. 13 in Nir's paper l3 ) (14) for the range of 90 Ge V < mr yS < 400 Ge V.
The values of 0= -arg( VUb ) and I Vubl/VCb predicted from the Min(2) concentrate in the following ranges: We can further obtain the predicted ranges of the mr yS in the Min(2)' by taking into consideration the €-bound in the KO-Ko mixing and the xd-bound in the BO-Bo mixing. We use the following formulas, 9)