The spin-charge-family theory is explaining the origin of families, of the Higgs and the Yukawa couplings

The spin-charge-family theory offers a possible explanation for the assumptions of the standard model - for the charges of a family members, for the gauge fields, for the appearance of families, for the the scalar fields - interpreting the standard model as its low energy effective manifestation. The spin-charge-family theory predicts at the low energy regime two decoupled groups of four families of quarks and leptons. The predicted fourth family waits to be observed, while the stable fifth family is the candidate to form the dark matter. The Higss and Yukawa couplings are the low energy effective manifestation of several scalar fields, all with the bosonic (adjoint) representations with respect to all the charge groups, with the family groups included. Properties of the families are analysed and relations among coherent contributions of the loop corrections to fermion properties discussed, including the one which enables the existence of the Majorana neutrinos. The appearance of several scalar fields is presented, their properties discussed, it is explained how these scalar fields can effectively be interpreted as the {\em standard model} Higgs (with the fermion kind of charges) and the Yukawa couplings, and a possible explanation why the Higgs has not yet been observed offered. The relation to proposals that the Yukawas follow from the SU(3) family (flavour) group, having the family charges in the fundamental representations of these groups, is discussed. The spin-charge-family theory predicts that there are no supersymmetric partners of the observed fermions and bosons.


I. INTRODUCTION
The standard model offered more than 35 years ago an elegant next step in understanding the origin of fermions and bosons. It is built on several assumptions leaving many open questions to be answered in the next step of theoretical interpretations. A lot of proofs and calculations have been done which support the standard model.
The measurements so far offer no sign which would help to make the next step beyond the standard model. There are many proposals in the literature [1][2][3][4][5][6][7][8][9]  The theory unifying spin and charges and predicting families [10][11][12][13][14]19], to be called the spin-charge-family theory, seems promising in answering these, and several other questions, which the standard model leaves unanswered.
The spin-charge-family theory assumes in d = (1 + (d − 1)), d = 14 (or larger), a simple starting action for spinors and the gauge fields: Spinors carry only two kinds of the spins (no charges), namely the one postulated by Dirac 80 years ago and the second kind proposed by the author of this paper. There is no third kind of a spin. Spinors interact with only vielbeins and the two kinds of the corresponding spin connection fields.
After the breaks of the starting symmetry, leading to the low energy regime, the simple starting action (Eq.(4)) manifests two decoupled groups of four families of quarks and leptons, with only the left handed (with respect to d = (1+3)) members of each family carrying the weak charge while the right handed ones are weak chargeless. The fourth family is pre-dicted [11,13] to be possibly observed at the LHC or at somewhat higher energies, while the stable fifth family members, forming neutral (with respect to the colour and electromagnetic charge) baryons and the fifth family neutrinos are predicted to explain the origin of the dark matter [14].
The spin connections, associated with the two kinds of spins, together with vielbeins, all behaving as scalar fields with respect to d = (1 + 3), are with their vacuum expectation values at the two SU(2) breaks responsible for the nonzero mass matrices of fermions and also for the masses of the gauge fields. The spin connections with the indices of vector fields with respect to d = (1 + 3), manifest after the break of symmetries as the known gauge fields.
Although the properties of the scalar fields, that is their vacuum expectation values, coupling constants and masses, can not be calculated without the detailed knowledge of the mechanism of breaking the symmetries, and have been so far only roughly estimated, yet one can see, assuming breaks which lead to observable phenomena at the low energy regime, how properties of the scalar fields determine the fermion mass matrices, manifesting effectively as the standard model Higgs and its Yukawa couplings.
Four of the eight families are doublets with respect to the generators (Eqs. (14,15,16)) τ 2 and with respect to Ñ R , while they are singlets with respect to τ 1 and Ñ L . The other four families are singlets with respect to the first two kinds of generators and doublets with respect to the second two kinds ( τ 1 and Ñ L ) of generators.
Analysing properties of each family member with respect to the quantum numbers of the spin and the charges subgroups, SO (1,3), SU(2) I , SU(2) II , U(1) II and SU(3), we find that each family includes left handed (with respect to SO(1, 3)) weak SU(2) I charged quarks and leptons and right handed (again with respect to SO(1, 3)) weak SU(2) I chargeless quarks and leptons. While the right handed members (with respect to SO (1,3)) are doublets with respect to SU(2) II , the left handed fermions are singlets with respect to SU(2) II .
Each member of eight massless families of quarks and leptons carries the SU(2) II charge, in addition to the family quantum number and the quantum numbers of the standard model. The upper four families, which are doublets with respect to these two SU(2) groups, become massive and so does the SU(2) II gauge vector field (in the adjoint representation of SU(2) II in the S ab sector with τ 2i = c 2i ab S ab , {τ 2i , τ 2j } − = ε ijk τ 2k ). The lower four families, which are singlets with respect toτ 2i andÑ i R , the two SU(2) subgroups in theS ab sector, stay massless. This is assumed to happen below the energy scale of 10 13 GeV, that is below the unification scale of all the three charges, and also pretty much above the electroweak break.
The lower four families become massive at the electroweak break, when SU(2) I × U(1) I breaks into U (1). To this break the vielbeins and the scalar part of both kinds of the spin connection fields contribute, those which are triplets with respect to the two remaining invariant SU(2) subgroups in theS ab sector,τ 1i (τ 1i = c 1i abS ab ) andÑ i L (Ñ i L = c Li abS ab ), as well as the scalar gauge fields of Q, Q ′ and Y ′ (all expressible with S ab ). In this break also the SU(2) I weak gauge vector field becomes massive [28].
Although the estimations of the properties of families done so far are very approximate [13,14], yet the predictions give a hope that the starting assumptions of the spincharge-family theory are the right ones: i. Both existing Clifford algebra operators determine properties of fermions. The Dirac The project to come from the starting action through breaks of symmetries to the effective action at low (measurable) energy regime is very demanding. Although one easily sees that a part of the starting action manifests, after the breaks of symmetries, at the tree level the mass matrices of the families and that a part of the vielbeins together with the two kinds of the spin connection fields manifest as scalar fields, yet several proofs are still needed besides those done so far [16,17] to guarantee that the spin-charge-family theory does lead to the measured effective action of the standard model. Very demanding calculations in addition to rough estimations [11,13,14] done so far are needed to show that predictions agree also with the measured values of masses and mixing matrices of the so far observed fermion families, explaining where do large differences among masses of quarks and leptons, as well as among their mixing matrices originate.
Let us point out that in the spin-charge-family theory the scalar (with respect to (1 + 3)) spin connection fields, originating in the Dirac kind of spin, couple only to the charges and   spin, contributing on the tree level equally to all the families, distinguishing only among   the members of one family (among the u-quark, d-quark, neutrino and electron, the left and right handed), the other scalar spin connection fields, originating in the second kind of spin, couple only to the family quantum numbers. Both kinds start to contribute coherently only beyond the tree level and a detailed study should manifest the drastic differences in properties of quarks and leptons: in their masses and mixing matrices [10,19]. It is a hope that the loop corrections will help to understand the differences in properties of fermions, with neutrinos included and the calculations will show to which extent are the Majorana terms responsible for the great difference in the properties of neutrinos and the rest of the family members.
In this work the mass matrices of the two groups of four families, the two groups of the scalar fields giving masses to the two groups of four families and to the gauge fields to which they couple, and the gauge fields are studied and their properties discussed, as they follow from the spin-charge-family theory. Many an assumption, presented above, allowed by the spin-charge-family theory, is made in order that the low energy manifestation of the theory agrees with the observed phenomena, but not (yet) proved that it follows dynamically from the theory.
This paper manifests that there is a chance that the properties of the observed three families naturally follow from the spin-charge-family theory when going beyond the tree level, although on the tree level the mass matrices of leptons and quarks are (too) strongly related. A possible explanation is made why the observed family members differ so much in their properties. It is also explained why does the spin-charge-family theory predict two stable families, and why and how much do the fifth family hadrons differ in their properties from the first family ones, offering the explanation for the existence of the dark matter.
In the refs. [11,13] we studied the properties of the lower four families under the assumption that the loop corrections would not change much the symmetries of the mass matrices of the family members, as they follow from the spin-charge-family theory on the tree level, but would take care of differences in properties among members. Relaxing strong connections between the mass matrices of the u-quark and neutrino and the d-quark and electron, we were able to predict some properties of the fourth family members and their mixing matrix elements with the three so far measured families. This paper is bringing a possible justification for these relaxation. The concrete evaluations of the properties of the mass matrices beyond the tree level are in progress. First steps are done in the contribution with A. Hernández-Galeana [15], while more detailed analyses of the mass matrices with numerical results are in preparation.
The standard model is presented as a low energy effective theory of the spin-charge-family theory. Also some attempts in the literature to understand families as the SU (3)  There is no third kind of the Clifford algebra objects. The appearance of the two kinds of the Clifford algebra objects can be understood as follows: If the Dirac one corresponds to the multiplication of any spinor object B (any product of the Dirac γ a 's, which represents a spinor state when being applied on a spinor vacuum state |ψ 0 >) from the left hand side, the second kind of the Clifford objects can be understood (up to a factor, determining the Clifford evenness (n B = 2k) or oddness (n B = 2k + 1) of the object B as the multiplication of the object from the right hand sidẽ with |ψ 0 > determining the spinor vacuum state. Accordingly we have More detailed explanation can be found in appendix . The spin-charge-family theory proposes in d = (1 + 13) a simple action for a Weyl spinor and for the corresponding gauge Here [30] f α[a f βb] = f αa f βb − f αb f βa . To see that the action (Eq.(4)) manifests after the break of symmetries [11,13,19] all the known gauge fields and the scalar fields and the mass matrices of the observed families, let us rewrite formally the action for a Weyl spinor of (Eq.(4)) as follows where n = 0, 1, 2, 3 with All the charge (τ Ai (Eqs. (6), (15), (16)) and the spin (Eq. ( 14)) operators are expressible with S ab , which determine all the internal degrees of freedom of one family.
Index A enumerates all possible spinor charges and g A is the coupling constant to a particular gauge vector field A Ai n . Before the break from SO(1, (3), τ 3i describe the colour charge (SU(3)), τ 1i the weak charge (SU(2) I ), τ 2i the second SU(2) II charge and τ 4 determines the U(1) II charge. After the break of SU(2) II × U(1) II to U(1) I stays A = 2 for the U(1) I hyper charge Y and after the second break of SU(2) I × U(1) I to U(1) stays A = 2 for the electromagnetic charge Q, while instead of the weak charge Q ′ and τ ± of the standard model manifest.
The breaks of the starting symmetry from SO (1,13)  Accordingly the first row of the action in Eq. (5) manifests the dynamical fermion part of the action, while the second part manifests, when ω abσ andω abσ (σ ∈ (7, 8)) fields gain nonzero vacuum expectation values, the mass matrices of fermions on the tree level. Scalar fields contribute also to masses of those gauge fields, which at a particular break lose symmetries. It is assumed that the symmetries in theS abω abc and in the S ab ω abc part break in a correlated way, triggered by particular superposition of scalar (with respect to the rest of symmetry) vielbeins and spin connections of both kinds (ω abc andω abc ). I comment this part in sections II B, III. The Majorana term, manifesting the Majorana neutrinos, is contained in the second row as well (III A 1). The third row in Eq. (5) stays for all the rest, which is expected to be at low energies negligible or might slightly influence the mass matrices beyond the tree level.
Correspondingly the action for the vielbeins and the spin connections of S ab , with the Lagrange density α E R, manifests at the low energy regime, after breaks of the starting symmetry, as the known vector gauge fields -the gauge fields of U(1), SU(2), SU(3) and the ordinary gravity, contributing also to the break of symmetries and correspondingly to the masses of the gauge fields and fermions, whileα ER are responsible for off diagonal mass matrices of the fermion members and also to the masses of the gauge fields. Beyond the tree level all the massive fields contribute coherently to the mass matrices.
After the electroweak break the effective Lagrange density for spinors looks like The termψ M ψ determines the tree level mass matrices of quarks and leptons. The contributions to the mass matrices appear at two very different energy scales due to two separate breaks. Before the break of SU(2) II × U(1) II to U(1) I the vacuum expectation values of the scalar fields appearing in p 0s are all zero. The corresponding dynamical scalar fields are massless. All the eight families are massless and the vector gauge fields A Ai m , A = 2 ; in Eq. (5) are massless as well. To the break of SU(2) II × U(1) II to U(1) I the scalar fields from the first row in the covariant momentum p 0s , that is the two triplets ÃÑR s and Ã 2 s are assumed to contribute, gaining non zero vacuum expectation values. The upper four families, which are doublets with respect to the infinitesimal generators of the corresponding groups, namely Ñ R and τ 2 , become massive. No scalar fields of the kind ω abs is assumed to contribute in this break. Therefore, the lower four families, which are singlets with respect to Ñ R and τ 2 , stay massless. Due to the break of SU(2) II × U(1) II symmetries in the space ofS ab and S ab , the gauge fields A 2 m become massive. The gauge vector fields A 1 m and A Y m stay massless at this break.
To the break of SU(2) I × U(1) I to U(1) the scalar fields from the second row in the covariant momentum p 0s , that is the triplets ÃÑL s and Ã 1 s and the singletÃ 4 s , as well as the ones from the third row originating in ω abc , that is (A s , Z Q ′ s , A Y ′ s ), are assumed to contribute, by gaining non zero vacuum expectation values.
This electroweak break causes non zero mass matrices of the lower four families. Also the gauge fields Z Q ′ m , W 1+ m and W 1− m gain masses. The electroweak break influences slightly the mass matrices of the upper four families, due to the contribution of A s , Z Q ′ s , A Y ′ s and A 4 s and in loop corrections also Z Q ′ m and W ± m . To loops corrections of both groups of families the massive vector gauge fields contribute.
The dynamical massive scalar fields contribute only to families of the group to which they couple.
The detailed explanation of the two phase transitions which manifest in Eq. (7) is presented in what follows.

A. Spinor action through breaks
In this subsection properties of quarks, u and d, and leptons, ν and e, of two groups of four families are presented at the stage of The technique [18], which offers an easy way to keep a track of the symmetry properties of spinors, is used as a tool to clearly demonstrate properties of spinors. This technique is explained in more details in appendix . In this subsection only a short introduction, needed to follow the explanation, is presented. Mass matrices of each groups of four families, on the tree and below the tree level, originated in the scalar gauge fields, which at each of the two breaks gain a nonzero vacuum expectation values, will be discussed in section III.
Following the refs. [18] we define nilpotents ( (1 ± iγ a γ b ), for η aa η bb = 1 , as eigenvectors of S ab as well as ofS ab (Eq. (A.7) in appendix ) One can easily verify that γ a transform Correspondingly,S ab generate the equivalent representations to representations of S ab , and opposite. Defining the basis vectors in the internal space of spin degrees of freedom in d = (1 + 13) as products of projectors and nilpotents from Eq. (9) on the spinor vacuum state |ψ 0 >, the representation of one Weyl spinor with respect to S ab manifests after the breaks the spin and all the charges of one family members, and the gauge fields of S ab manifest as all the observed gauge fields.S ab determine families and correspondingly the family quantum numbers, while scalar gauge fields ofS ab determine, together with particular scalar gauge fields of S ab , mass matrices, manifesting effectively as Yukawa fields and Higgs.
Expressing the operators γ 7 and γ 8 in terms of the nilpotents 78 (±), the mass term in Eqs. (5,7) can be rewritten as follows After the breaks of the starting symmetry (from SO(1, Each family member carries also the family quantum number, which concernS ab and is determined by the quantum numbers of the two SU(2) from SO(1, 3) (with the generators Ñ (L,R) , Eq. (16)) and the two SU(2) from SO(4) (with the generators τ (1,2) , Eq. (15)).
Properties of families of spinors can transparently be analysed if using our technique. We arrange products of nilpotents and projectors to be eigenvectors of the Cartan subalgebra S 03 , S 12 , S 56 , S 78 , S 9 10 , S 11 12 , S 13 14 and, at the same time, they are also the eigenvectors of the correspondingS ab , that is ofS 03 ,S 12 ,S 56 ,S 78 ,S 9 10 ,S 11 12 ,S 13 14 .
Below the generators of the infinitesimal transformations of the subgroups of the group SO (1,13) in the S ab andS ab sectors, responsible for the properties of spinors in the low energy regime, are presented.
determine representations of the two SU(2) subgroups of SO(1, 3), Some justification for such an assumption can be found in the refs. [16,17].
At the stage of the symmetry of a family appears in eight massless families. Each family manifests at this symmetry eightplets of u and d quarks, left handed weak charged and right handed weak chargeless (of spin (± 1 2 )) in three colours, and the colourless eightplet of ν and e leptons, left handed weak charged and right handed weak chargeless (of spin (± 1 2 )). In Table I the eightplet of quarks of a particular colour charge (τ 33 = 1/2, τ 38 = 1/(2 √ 3)) and the U(1) II charge (τ 4 = 1/6) is presented in our technique [18], as products of nilpotents and projectors.
The vacuum state |ψ 0 >, on which the nilpotents and projectors operate, is not shown. The basis is the massless one. The reader can find the whole Weyl representation in the ref. [19].
Looking at Tables (I, II (13)) transforms the right handed u c1 R from the first row of Table I into the left handed u c1 L of the same spin and charge from the seventh row of the same table, and that it transforms the right handed ν R from the first row of Table II into Table I and that it transforms the right handed e R from the third row of Table II into the left handed one (of the same spin) presented in the fifth row of (+) 11 12 [−] 13 14 [−] ν R

03
[+i] (+) 11 12 (+) 13 14 (+) (+) 11 12 [−] 13 14 (+) 11 12 (+) 13 14 (+) 3)), and of the colourless right handed neutrino ν R of spin 1 2 are presented in the left and in the right column, respectively. All the families follow from the starting one by the application of the operators R of spin 1 2 and the chosen colour c1 to all the members of one family of the same colour. The same generators transform equivalently the right handed neutrino ν R of spin 1 2 to all the colourless members of the same family.
same member of another family, due to the fact that {S ab ,S cd } − = 0 (Eq. (2)). The eight families of the first member of the eightplet of quarks from Table I, for example, that is of the right handed u c1 R -quark with spin 1 2 , are presented in the left column of Table III. The generators (Ñ ± R,L ,τ (2,1)± ) (Eq. (A.19)) transform the first member of the eightplet from Table II, that is the right handed neutrino ν R with spin 1 2 , into the eight-plet of right handed neutrinos with spin up, belonging to eight different families. These families are presented in the right column of the same table. All the other members of any of the eight families of quarks or leptons follow from any member of a particular family by the application of the operators (N ± R,L , τ (2,1)± ) on this particular member. Let us point out that the break of SO(1, to leave all the eight families massless, allows to divide eight families into two groups of four families. One group of families contains doublets with respect to Ñ R and τ 2 , these families are singlets with respect to Ñ L and τ 1 . Another group of families contains doublets with respect to Ñ L and τ 1 , these families are singlets with respect to Ñ R and τ 2 . The scalar fields which are the gauge scalars of Ñ R and τ 2 couple only to the four families which are doublets with respect to this two groups. When gaining non zero vacuum expectation values, these scalar fields determine nonzero mass matrices of the four families, to which they couple.
These happens at some scale, assumed that it is much higher than the electroweak scale.
The group of four families, which are singlets with respect to Ñ R and τ 2 , stay massless unless the gauge scalar fields of Ñ L and τ 1 , together with the gauge scalars of Q , Q ′ and Y ′ , gain a nonzero vacuum expectation values at the electroweak break. Correspondingly the decoupled twice four families, that means that the matrix elements between these two groups of four families are equal to zero, appear at two different scales, determined by two different breaks.
To have an overview over the properties of the members of one (any one of the eight) family let us present in Table IV Tables I   and II share the family quantum numbers presented in Table V: The "tilde handedness" of the familiesΓ (1+3) (= −4iS 03S12 ),S 03 L ,S 12 L ,S 03 R ,S 12 R (the diagonal matrices of SO(1, 3) ),τ 13 (of one of the two SU(2) I ),τ 23 (of the second SU(2) II ).
We see in Table V that the first four of the eight families are singlets with respect to subgroups determined by Ñ R and τ 2 , and doublets with respect to Ñ L and τ 1 , while the rest four families are doublets with respect to Ñ R and τ 2 , and singlets with respect to Ñ L and τ 1 .
When the break from SU(2) I × SU(2) II × U(1) II to ×SU(2) I × U(1) I appears, the scalar fields, the superposition ofω abs , which are triplets with respect to Ñ R and τ 2 (are assumed to) gain a nonzero vacuum expectation values. As one can read from Eq. (5) these scalar fields cause nonzero mass matrices of the families which are doublets with respect to Ñ R and τ 2 and correspondingly couple to these scalar fields with nonzero vacuum expectation values. The four families which do not couple to these scalar fields stay massless. The whether the member is a triplet -the quark with the one of the charges determined by τ 33 and τ 38 , vacuum expectation value ofÃ 4 ± = 0 is assumed to stay zero at the first break. In this break also the vector (with respect to (1+3)) gauge fields of τ 2 (the generators of SU(2) II ) become massive.
In the successive (electroweak) break the scalar gauge fields of Ñ L and τ 1 , coupled to the rest of eight families, gain nonzero vacuum expectation values. Together with them also the scalar gauge fields A Y ′ s , A Q ′ s and A Q s (the superposition of ω sts ′ spin connection fields) gain nonzero vacuum expectation values. The scalar fields Ã 1 s , ÃÑL s , A Q s , A Q ′ s and A Y ′ s determine mass matrices of the last four massless families. At this break also the vector gauge fields of τ 1 become massive.
The second break, which (is assumed to) occurs at much lower energy scale, influences slightly also properties of the upper four families.
There is the contribution which appears in the loop corrections as the term bringing nonzero contribution only to the mass matrix of neutrinos, transforming the right handed neutrinos to the left handed charged conjugated ones. It looks like that (for a particular Let us end this subsection by admitting that it is assumed (not yet showed or proved) that there is no contributions to the mass matrices from ψ † L γ 0 γ s p 0s ψ R , with s = 5, 6. Such a contribution to the mass term would namely mix states with different electromagnetic charges (ν R and e L , u R and d L ), in disagreement with what is observed.
Masses of gauge fields of the charges τ Ai , which symmetries are unbroken, are zero, nonzero masses correspond to the broken symmetries. and potentials determining the dynamics of these scalar fields are also not known, and also the way how do scalar fields contribute to masses of the gauge fields, on the tree and below the tree level, waits to be studied.
Let us repeat that all the gauge fields, scalar or vectors, either originating in ω abc or iñ ω abc are after breaks in the adjoint representations with respect to all the groups, to which the starting groups break.

Scalar and gauge fields after the break from SU
for m = 0, 1, 2, 3 and a particular value of θ 2 . The scalar fields A Y ′ s , A 2± s , A Y ′ s , which do not gain in this break any vacuum expectation values, stay masses. This assumption guarantees that they do not contribute to masses of the lower four families on the tree level.
The corresponding operators for the new charges which couple these new gauge fields to fermions are The new coupling constants become In the break also the scalar fields originating inω abs contribute, and symmetries in both sectors,S ab and S ab , are broken simultaneously. The scalar fields Ã 2 s (which are the superposition ofω abs ,Ã 21 s =ω 58s +ω 67m ,Ã 22 s =ω 57s −ω 68s ,Ã 23 s =ω 56s +ω 78s ) gain a nonzero vacuum expectation values.
We have for the scalar fields correspondinglỹ contribute. The lower four families, which are singlets with respect to both groups, stay correspondingly massless.
The corresponding new operators are theñ New coupling constants are correspondinglygỸ =g 4 cosθ 2 ,gỸ ′ =g 2 cosθ 2 ,Ã 2± that is a superposition ofω abs , which is orthogonal to the one trigging the first break and ÃÑL s and a superposition of ω sts ′ s ∈ (7,8). While the superposition of Eqs. (23,24) couple to the lower four families only, since the lower four families are doublets with respect to τ 1 and ÑÑL , and the upper four families are singlets with respect to τ 1 and ÑÑL , the scalar fields A Q s , A Q ′ s and A Y ′ s (they are a superposition of ω sts ′ ; s, t ∈ (5, · · · , 14); s ′ = 7, 8) couple to all the eight families, distinguishing among the family members.
Correspondingly a superposition of the vector fields A 1 m and A 4 m , that is W ± m and Z m , become massive, while A m stays with m = 0. The new operators for charges are and the new coupling constants are correspondingly e = g Y cos θ 1 , g ′ = g 1 cos θ 1 and tan θ 1 = g Y g 1 , in agreement with the standard model. We assume for simplicity that in the scalar sector of ω stc -ω s,t,s ′ -the same θ 1 determines properties of the coupling constants as it does in the vector one -ω s,t,m .
In the sector of theω abs scalars the corresponding new operators arẽ Q =τ 13 +Ỹ =S 56 +τ 4 , with the new coupling constantsẽ =g Y cosθ 1 ,g ′ =g 1 cosθ 1 and tanθ 1 =g Ỹ g 1 . To this break and correspondingly to the mass matrices of the lower four families also the scalar fields ÃÑL s (orthogonal to ÃÑR s ) contribute. All the scalar fields presented in this and the previous subsection are massive dynamical fields, coupled to fermions and governed by the corresponding scalar potentials, for which we assume that they behave as normalizable ones (at least up to some reasonable accuracy). To loop corrections the gauge vector fields, the scalar dynamical fields originating in ω s ′ ts and inω abs contribute, those to which a particular group of families couple. Let us tell that there is also a contribution to loop corrections, manifesting as a very special products of superposition of ω abs , s = 5, 6, 9, · · · , 14 andω abs , s = 5, 6, 7, 8 fields, which couple only to the right handed neutrinos and their charge conjugated states of the lower four families.

CHARGE-FAMILY THEORY
This term might strongly influence properties of neutrinos of the lower four families. Table VI represents the mass matrix elements on the tree level for the upper four families after the first break, originating in the vacuum expectation values of two superposition of ω abs scalar fields, the two triplets of τ 2 and Ñ R . The notationãÃ i ± = −gÃ iÃÃi ± is used. The sign (∓) distinguishes between the values of the two pairs (u-quarks, ν-lepton) and (d-quark, e-lepton), respectively. The lower four families, which are singlets with respect to the two groups ( τ 2 and Ñ R ), as can be seen in Table IV, stay massless after the first break.
Masses of the lowest of the higher four family were evaluated in the ref. [14] from the cosmological and direct measurements, when assuming that baryons of this stable family I   II  III  IV  V  V I  V II  V III   I  0  0 TABLE VII: The mass matrix on the tree level for the lower four families of quarks and leptons after the electroweak break. Only the contributions coming from the termsS abω abs in p 0s in Eq. (7) are presented. The notationãÃ i ± stays for −gÃÃ i ± , where (∓) distinguishes between the values of the (u-quarks and d-quarks) and between the values of (ν and e). The terms coming from S ss ′ ω ss ′ t are not presented here. They are the same for all the families, but distinguish among the family members.
contribution from e QA Q s , g Q ′ Q ′ A Q ′ s and g Y ′ Y ′ A Y ′ s , which are diagonal and equal for all the families, but distinguish among the members of one family, are not present. The notatioñ aÃ i ± = −gÃ iÃÃi ∓ is used,τ Ai stays forτ 1i andÑ i L and correspondingly also the notation for the coupling constants and the triplet scalar fields is used.
The absolute values of the vacuum expectation values of the scalar fields contributing to the first break are expected to be much larger than those contributing to the second break The mass matrices of the lower four families were studied and evaluated in the ref. [13] under the assumption that if going beyond the tree level the differences in the mass matrices of different family members start to manifest. In this ref. we assumed the symmetry properties of the mass matrices from Table VII and fitted the matrix elements to the experimental data for the three observed families within the accuracy of the experimental data.
We were not able to determine masses of the fourth family. Taking the fourth family masses as parameters we were able to calculate matrix elements of mass matrices, predicting mixing matrices for all the members of the four lowest families.
In Table VIII we present quantum numbers of all members of a family, any one, after the electroweak break. It is easy to show that the contribution of complex conjugate to    Table IX presents the quantum numbersτ 23 ,Ñ 3 R ,τ 13 andÑ 3 L for all eight families. The first four families are singlets with respect toτ 2i andÑ i R , while they are doublets with respect toτ 1i andÑ i L (all before the break of symmetries). The upper four families are correspondingly doublets with respect toτ 2i andÑ i R and are singlets with respect toτ 1i andÑ i L .

A. Mass matrices beyond the tree level
While the mass matrices of (u and ν) have on the tree level the same off diagonal elements and differ only in diagonal elements due to the contribution of e QA Q s , where M α II (o) and M α I (o) have the structure with the matrix elements The values a 1 , a 2 , b and c are different for the upper (Σ = II) and the lower (Σ = I) four families, due to two different scales of two different breaks. One has For the upper four families (Σ = II) we have correspondinglyã 3 and for the lower four families (Σ = I ) we must takẽ To the tree level contributions of the scalarω ab± fields, diagonal matrices a ± have to be added, the same for all the eight families and different for each of the family member (u, d, ν, e), (â ∓ ≡ a α ∓ ) ψ, which are the tree level contributions of the scalar ω sts ′ fieldŝ Since the upper and the lower four family mass matrices appear at two completely different scales, determined by two orthogonal sets of scalar fields, the two tree level mass matrices M α Σ (o) have very little in common, besides the symmetries and the contributions from Eq. (32). Let us introduce the notation, which would help to make clear the loop corrections contributions. We have before the two breaks two times (Σ ∈ {II, I}, II denoting the upper four and I the lower four families) four massless vectors ψ α Σ(L,R) for each member of a family α ∈ {u, d, ν, e}. Let i, i ∈ {1, 2, 3, 4, } denotes one of the four family members of each of the two groups of massless families Let Ψ α Σ(L,R) be the final massive four vectors for each of the two groups of families, with all loop corrections included Then Ψ α (k) Σ(L,R) , which include up to (k) loops corrections, read Correspondingly we have Let us repeat that to the loop corrections two kinds of the scalar dynamical fields contribute, those originating inω abs (gỸ 1±Ã1± s ) and those originating in ω abs (eQ A s , g 1 cos θ 1Q To each family member there corresponds its own matrix M α Σ . It is a hope, however, that the matrices M α Σ Q Q ′ Y ′ k k ′ k ′′ might depend only slightly on the family mem- and that the eigenvalues of the operators (Q α ) k (Q ′α ) k ′ (Ŷ ′α ) k ′′ on the massless states ψ α Σ R make the mass matrices M α Σ dependent on α. To masses of neutrinos only the terms ( There is an additional term, however, which does not really speak for the suggestion of More about the mass matrices below the tree level can be found in the ref. [15].

Majorana mass terms in the spin-charge-family theory
There are mass terms within the spin-charge-family theory, which transform the right handed neutrino to its charged conjugated one, contributing to the right handed neutrino Majorana masses To include into Eq. (39) the scalar field and to point out all the relations -interactions -assumed by the standard model we could correspondingly rewrite Eq. (39) as follows The spin-charge-family theory starting symmetry group is with the action (Eq. (4)) which couples vielbeins and spin connection fields with spinors.
Since there are two kinds of spins (S ab andS ab ) there are also two kinds of the spin connection fields. To observe one kind of spin as the spin and all the charges of fermions, the break of the starting symmetry must occur. Accordingly it is meaningful to replace Eq. (41) with where the index (v, s) ⋄ points out that several particular breaks of the starting symmetry The operator  Tables I and II. The ∓ } on the lower four families is zero, since the lower four families are singlets with respect to Ñ R and τ 2 . In the loop corrections besides the massive scalar fields - mstart to contribute coherently.
We do not (yet) know the properties of the scalar fields, their vacuum expectation values, masses and coupling constants. We may expect that they behave similarly as the Higgs field in the standard model, that is that their dynamics is determined by potentials which make contributions of the scalar fields renormalizable. Starting from the spin connections and vielbeins we only can hope that at least effectively at the low energy regime, that is in the weak field regime, the effective theory is behaving as a renormalizable one.  Table X, which "dresses" u R and ν R in the way assumed by the standard model, and we simulate the part 78 (+) with the scalar field Φ I + from Table X, which "dresses" d R and e R . In the spin-charge-family theory mass matrices are determined on the tree level by 43)). Let this operator be calledΦ vI In the attempt to see the standard model as an effective theory of the spin-charge-family theory the standard model Higgs together with the Yukawa couplings can be presented as the product of Φ I ∓ andΦ vI ∓ . The role of Φ I ∓ in this product is to "dress" the right handed quarks and leptons with the weak charge and the appropriate hyper charge, whileΦ vI ∓ effectively manifests on the tree level as the Higgs and the Yukawa couplings together.
Masses of the vector gauge fields as well as the properties of the scalar fields should in the [+] 11 12 [+] 13 14 [+]

78
[+]|| 9 10 [−] 11 12 [−] 13 14 [ with θ 1 equal to θ W , with the electromagnetic coupling constant e = sin θ W , the charge Φ vI ∓ are determined in Eq. (45), while the states Φ I ∓ from Table X are normalized to unity as explained in the refs. [18] and in the appendix. Assuming, like in the standard model, that Let us therefore assume that the three so far observed families of quarks and leptons, neutrinos will be treated as ordinary family members, if all massless, manifest the "flavour"  [24,25] for the spin-charge-family theory as it manifests in the low energy region.

VI. CONCLUSIONS
The spin-charge-family theory [10][11][12][13][14]19] is offering the way beyond the standard model by proposing the mechanism for generating families of quarks and leptons and consequently predicting the number of families at low (sooner or later) observable energies and the mass matrices for each of the family member (and correspondingly the masses and the mixing matrices of families of quarks and leptons).
The spin-charge-family theory predicts the fourth family to be possibly measured at the LHC or at some higher energies and the fifth family which is, since it is decoupled in the mixing matrices from the lower four families and it is correspondingly stable, the candidate to form the dark matter [14].
The proposed theory also predicts that there are several scalar fields, taking care of mass matrices of the two times four families and of the masses of weak gauge bosons. At low energies these scalar dynamical fields manifest effectively pretty much as the standard model Higgs field together with Yukawa couplings, predicting at the same time that observation of these scalar fields is expected to deviate from what for the Higgs the standard model predicts.
To the mass matrices of fermions two kinds of scalar fields contribute, the one interacting with fermions through the Dirac spin and the one interacting with fermions through the second kind of the Clifford operators (anticommuting with the Dirac ones, there is no third kind of the Clifford algebra object). The first one distinguishes among the family members, the second one among the families. Beyond the tree level these two kinds of scalar fields and the vector massive fields start to contribute coherently, leading hopefully to the measured properties of the so far observed three families of fermions and to the observed weak gauge fields.
In the ref. [11,13] we made a rough estimation of properties of quarks and leptons of the lower four families as predicted by the spin-charge-family theory. The mass matrices of quarks and leptons turns out to be strongly related on the tree level. Assuming that loop corrections change elements of mass matrices considerably, but keep the symmetry of mass matrices, we took mass matrix element of the lower four families as free parameters. We fitted the matrix elements to the existing experimental data for the observed three families within the experimental accuracy and for a chosen mass of each of the fourth family member.
We predicted then elements of the mixing matrices for the fourth family members as well as the weakly measured matrix elements of the three observed families.
In the ref. [14] we evaluated the masses of the stable fifth family (belonging to the upper four families) under the assumption that neutrons and neutrinos of this stable fifth family form the dark matter. We study the properties of the fifth family neutrons, their freezing out of the cosmic plasma during the evolution of the universe, as well as their interaction among themselves and with the ordinary matter in the direct experiments.
In this paper we study properties of the gauge vector and scalar fields and their influence on the properties of eight families of quarks and leptons as they follow from the spin-chargefamily theory on the tree and below the tree level after the two successive breaks, from ( Correspondingly they cause nonzero mass matrices of the upper four families to which they couple and nonzero masses of vector fields, the superposition of the gauge triplet fields of τ 2 and of the gauge singlet field of τ 4 . Since these scalar fields do not couple to the lower four families (they are singlets with respect to Ñ R and τ 2 ) the lower four families stay massless at this break.
At the successive break, that is at the electroweak break, several other combinations of f σ sωabσ , the gauge triplets of Ñ L and of τ 1 (which are orthogonal to previous triplets), together with some combinations of scalar fields f σ s ω s ′ tσ , the gauge fields of Q, Q ′ and Y ′ , gain nonzero vacuum expectation values, contributing correspondingly to mass matrices of the lower four families and to masses of the gauge fields W ± m and Z m , influencing slightly, together with the massive vector fields, also mass matrices of the upper four families.
Although mass matrices of the family members are in each of the two groups of four families very much related on the tree level (u-quarks are related to ν-leptons and d-quarks to e-leptons), the loop corrections, in which the scalar fields of both kinds contribute, those distinguishing among the families and those distinguishing among the family members (u , d , ν , e), together with the massive vector gauge fields which distinguish only among family members, start to hopefully (as so far done calculations [15] manifest) explain why are properties of the so far observed quarks and leptons so different. Numerical evaluations of the loop corrections to the tree level are in preparation (the ref. [15]).
It might be, however, that the influence of a very special term in higher loop corrections, which influences only the neutrinos, since it transforms the right handed neutrinos into the left handed charged conjugated ones, is very strong and might be responsible for the properties of neutrinos of the lower three families.
To simulate the standard model the effective low energy model of the spin-charge-family theory is made in which the operator, which in the spin-charge-family theory transforms the weak and hyper charges of right handed quarks and leptons into those of their left handed partners, is replaced by a weak doublet scalar, colour singlet and of an appropriate hyper charge, while the scalar dynamical fields of the spin-charge-family theory determine the Yukawa couplings. This weak doublet scalar "dresses" the right handed family members with the appropriate weak charge and hyper charge behaving as the Higgs of the standard model. It is further tried to understand to which extent can the scalar fields originating inω abs and ω abs spin connection dynamical fields (all in the adjoint representations with respect to all the gauge groups) be replaced by a kind of a "bi-fundamental" (with respect to their several family groups) Yukawa scalar dynamical fields of the models presented in the refs. [24,25], in which fermion families are assumed to be members of several SU(3) family (flavour) SU(3) groups. It seems so far that it is hard to learn something from such, from the point of view of the spin-charge-family theory, very complicated models extending further the standard model assumption that the scalar (the Higgs) has charges in the fundamental representations. The so far very successful Higgs is in the spin-charge-family theory seen as an effective object, which can not very easily be extended to Yukawas. Let me add that if the spin-charge-family theory offers the right explanation for the families of fermions and their quantum numbers as well as for the gauge and scalar dynamical fields, then the scalar dynamical fields represent new forces, as do already -in a hidden way -the Yukawas of the standard model.
Let me point out at the end that the spin-charge-family theory, offering explanation for the appearance of spin, charges and families of fermions, and for the appearance of gauge vector and scalar boson fields at low energy regime, still needs careful studies, numerical ones and also proofs, to demonstrate that/whether this is the right next step beyond the standard model.
Appendix: Short presentation of technique [10,18] I make in this appendix a short review of the technique [18], initiated and developed by me when proposing the spin-charge-family theory [10][11][12][13][14]19] assuming that all the internal degrees of freedom of spinors, with family quantum number included, are describable in the space of d-anticommuting (Grassmann) coordinates [18], if the dimension of ordinary space is also d. There are two kinds of operators in the Grasmann space, fulfilling the Clifford algebra which anticommute with one another. The technique was further developed in the present shape together with H.B. Nielsen [18] by identifying one kind of the Clifford objects with γ s 's and another kind withγ a 's. In this last stage we constructed a spinor basis as products of nilpotents and projections formed as odd and even objects of γ a 's, respectively, and chosen to be orientates of a Cartan subalgebra of the Lorentz groups defined by γ a 's We assume the "Hermiticity" property for γ a 's andγ a 's γ a † = η aa γ a ,γ a † = η aaγa , (A. 3) in order that γ a andγ a are compatible with (A.1) and formally unitary, i.e. γ a † γ a = I and γ a †γa = I.
Recognizing from Eq.(A.2) that two Clifford algebra objects S ab , S cd with all indices different commute, and equivalently forS ab ,S cd , we select the Cartan subalgebra of the algebra of the two groups, which form equivalent representations with respect to one another One can proceed equivalently forγ a 's. We understand the product of γ a 's in the ascending order with respect to the index a: γ 0 γ 1 · · · γ d . It follows from Eq.(A.3) for any choice of the signature η aa that Γ † = Γ, Γ 2 = I. We also find that for d even the handedness anticommutes with the Clifford algebra objects γ a ({γ a , Γ} + = 0) , while for d odd it commutes with γ a ({γ a , Γ} − = 0).
To make the technique simple we introduce the graphic presentation as follows (Eq. Taking into account the above equations it is easy to find a Weyl spinor irreducible representation for d-dimensional space, with d even or odd.
For d even we simply make a starting state as a product of d/2, let us say, only nilpotents