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Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Do we have the explanation for the families and their properties, for the scalar Higgs and Yukawa couplings and for the gauge vector fields?
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics

Moscow 22 - 28 of August, 2013
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Phys. Lett. B 292, 25-29 (1992), Modern Phys. Lett. A 10, 587-595 (1995), Int. J. Theor. Phys. 40, 315-337 (2001). Phys. Rev. D 62 (04010-14) (2000), Phys. Lett. B 633 (2006) 771-775, B 644 (2007) 198-202, B (2008) 110.1016, (2006), with H.B.N. Phys. Rev. , D 74 073013-16 (2006), with A.B.B.. New Jour. of Phys. 10 (2008) 093002, hep-ph/0606159, with G.B.,M.B., D.L. Phys. Rev. D (2009) 80.083534, astro-ph¿arXiv: 0907.0196, with G.B. New Jour. of Phys. (2011) 103027. J. Phys. A: Math. Theor. 45 (2012) 465401. J. of Modern Physics 4 (2013) 823-847.
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

More than 30 years ago the standard mo del offered an elegant new step in understanding the origin of fermions and bosons. It postulated, stimulated by the observations: The existence of the massless family members; coloured quarks and colourless leptons, the left handed memb ers distinguishing from the right handed ones in the weak and hyp er charges. The existence of families.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

name ui L d
i L

handedness -4iS03 S12 -1 -1 -1 -1

weak charge 13
1 2

hyper charge Y
1 6 1 6 1 -2

colour charge

elm charge Q
2 3

colour triplet colour triplet colourless colourless

-

1 2 1 2

-1 3 0 -1

i L

e

i L

-

1 2

-

1 2

ui R di R
i R

1 1 1 1

weakless weakless weakless weakless

2 3

colour triplet colour triplet colourless colourless

2 3

-1 3 0 -1

-1 3 0 -1

ei R

Memb ers of each of the i = 1, 2, 3 massless families before the electroweak break.

And the anti-fermions to each family and family member.
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Three massless vector fields, the gauge fields to the observed charges of the family memb ers, b efore the electroweak break.
name hyp er photon weak b osons gluons handedness 0 0 0 weak charge 0 triplet 0 hyp er charge 0 0 0 colour charge colourless colourless colour o ctet elm charge 0 triplet 0

They all are vectors in d = (1 + 3), in the adjoint representations with respect to the weak, colour and hyp er charges. Elm. charge = weak charge + hyp er charge.
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

The existence of one scalar field, the Higgs (and the anti Higgs), chosen to be a weak doublet, (like fermions) with the appropriate hyper charge in order to "dress" right handed family memb ers with the weak and the hyper charge of their left handed partners and to assure the appropriate mass ratios of weak b osons. The existence of the Yukawa couplings, v Y 2 taking care of the masses of fermions, together with the Higgs.
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

The Higgs field, the scalar in d = (1 + 3), with PR = (-1)2s +3B +L = 1.
name handedness 0 0 handedness 0 0 - - weak charge
1 2 1 2

hyp er charge
1 2 1 2

colour charge colourless colourless colour charge colourless colourless

elm charge 1 0 elm charge 0 -1

0· Higgs

u

< Higgs d > name

weak charge
1 2 1 2

hyp er charge - -
1 2 1 2

< Higgsu > 0· Higgsd
The Spin-Charge-Family-Theory

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Let us summarize the standard mo del assumptions All fermions have all the charges, which are not singlets, in the fundamental representations of the charge groups. All gauge b osons have all the charges, which are not singlets, in the adjoint representations of the corresp onding groups. The singlet values are all zero for all the gauge fields. Higgs scalars are doublets with respect to the weak charge. Yukawa couplings carry the family quantum numbers.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

The standard model assumptions have b een confirmed without offering surprizes. The last unobserved field, the scalar Higgs, detected in June 2012, was confirmed in March 2013.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

What questions should one urgently ask so that the answers would help to make the right next step b eyond the standard mo del? Why there exist families at all? Or rather: What is the origin of families? How many families are there? And what are their prop erties if there are more than the so far observed ones? Why family memb ers ­ quarks and leptons ­ manifest so different prop erties if they all start as massless?

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

How is the origin of the scalar field (the Higgs) and the Yukawa couplings connected with the origin of families? How many scalar fields determine properties of the so far (and others p ossibly to b e) observed fermions and masses of b osons? Why are all the scalar fields doublets with resp ect to the weak charge? What are their representations with resp ect to the family quantum numbers? Where does the dark matter originate? Where do the charges and correspondingly the so far (and others p ossibly be) observed gauge fields originate? What is the dimension of the space? (1 + 3)?, (1 + (d - 1))? What is d ?
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

What is the role of the symmetries: discrete, continues, global and gauge, fermion-antifermion asymmetry? And many others.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

My statement: Next trustable step beyond the standard mo del must offer answers to several op en questions not only to one. There exist not yet observed families, gauge fields, scalar fields. The app earance of Yukawa couplings sp eaks for several scalar fields. Dimension of the space is large than 4.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

In the literature NO explanation for the existence of the families can b e found. Several extensions of the standard mo del are, however, prop osed, like: A tiny extension: The inclusion of the right handed neutrinos into the family. The SU (3) group is assumed to describe ­ not explain ­ the existence of three families. Like Higgs has the charge in the fundamental representation of the group, also Yukawas are assumed to b e scalar fields, in the bi-fundamental representaion of the SU (3) group. Sup ersymmetric theories assuming the existence of partners to the existing fermions and b osons, with charges in the opp osite representations.
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

The spin-charge-family-theory do es offer a p ossible explanation for the existence of families, offering answers besides to the "urgent" op en questions also to many of the "not so urgent" op en questions, presented above.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Content of the talk A brief introduction into the spin-charge-family-theory. Achievements of the spin-charge-family-theory so far. Some new predictions for the measurements. Problems in this theory to be solved.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

The Spin-Charge-Family-Theory is offering the explanation for: The existence of families and family members. The origin of several scalar fields, which offer the (hopefully right) explanation for the origin of mass matrices of fermions, correspondingly for the origin of Yukawa couplings and masses of gauge fields. The origin of charges. The origin of gauge fields. The origin of dark matter. And...
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Is the spin-charge-family theory the right way at least as a first step b eyond the standard model?

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Introduction

Spinors carry in d (1 + 13) two kinds of the spin. No charges. In d = (1 + 3) the Dirac spin ( a ) takes care of the spin and the charges of quarks and leptons. The second kind of the spin ( a ) generates families. ~ Spinors couple correspondingly to vielbeins and to two kinds of spin connection fields. In d = (1 + 3) the spin-connection fields together with the vielb eins manifest as the gauge vector fields and the scalar fields. The vacuum exp ectation values of the scalar fields determine masses of fermions on the tree level.
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Introduction

A simple action in d = (1 + 13) for spinors and spin connections and vielb eins manifests in d = (1 + 3), after appropriate breaks of the starting symmetry, the standard mo del action
for fermions ­ predicting the fourth family coupled to the so far observed three and the dark matter family, 2 for gauge fields, predicting new ones, 3 for scalar fields, which take care of mass matrices of fermions and masses of weak b osons, predicting several ones.
1

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Introduction

All vector b oson fields have all the charges in the adjoint representations. The scalar fields have the family charges in the adjoint representations, while they are doublets with respect to the weak charge. All family members of all families have all the charges in the fundamental representations of the corresponding groups. No sup ersymmetry is predicted at low energy regime.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


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Introduction

d>1+13 =

d=1+3 and the fourth family and the fifth family the dark matter

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Clifford algebra

There are two kinds of the Clifford algebra objects (only two): The Dirac a op erators (used by Dirac 80 years ago). The second one: a , which I recognized. ~ { a , b }+ = 2 { a , b }+ = 0, ~ ( a B : = i(-)nB B a ) |0 >, ~ (B = a0 + aa a + aab a b + · · · + aa
1

ab

= { a , b }+ , ~~

···a

d

a1 . . . ad )|0 >

(-)nB = +1, -1, when the object B has a Clifford even or odd character, respectively. |0 > is a vacuum state on which the operators a apply.
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


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Clifford algebra

S ~ S

ab

:= (i/4)( a b - b a ), := (i/4)( a b - b a ), ~~ ~~

ab

~ {Sab , Scd }- = 0. ~ Sab define the equivalent representations with respect to Sab . My recognition: If a are used to describ e the spin and the charges of spinors, a can b e used to describ e families of spinors.. ~ Must b e used!!
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

The action

A simple action for a spinor which carries in d = (1 + 13) only two kinds of a spin (no charges) and for the gauge fields S= d d x E Lf + d d x E ( R + R ) ~~

Lf p0a p0 = p

=

1 ¯a (E p0a ) 2 1 = f a p0 + { 2E 1 - Sab ab - 2

+ h .c . p , Ef
a }-

1 ~ ab S ~ 2

ab

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

The action

The only internal degrees of freedom of spinors (fermions) are the two kinds of the spin. The only gauge fields are the gravitational ones ­ vielb eins and two kinds of spin connections.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


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The action

Breaks of symmetries when starting with massless spinors
SO(1, 13) BREAK SO(1, 7)â eight SO(1, 3) â SU(2)II â SU(2)I â U(1)II â (eight massless massless BREAK SO(1, 3) â SU(2)I â U(1)I â families families) II U(1) â SU(3) I

(four families stay massless,)

(four families obtain masses)

BREAK

I

The Standard Mo del typ e of breaking SO(1, 3) â U(1) â SU(3) N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

The action

The action for spinors at the low energy regime Lf ¯ = m (pm -
A ,i

g A Ai AAi ) + m
0s

{
s =[7],[8]

¯ s p

} +

the rest , p0
m µ = fm (pµ - A

g A A AA ) , µ g B B AB -
B B Ai ab

p0s

=

fs
Ai

(p - =
a ,b

g B B AB ) . ~ ~ ~ c ~
a ,b Ai

c

S

ab

, Ai = ~

ab

~ S

ab

,

N.S. Manko Bor Ai University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics c stnik, Bj AB Aijk Ak Ai Bj AB Aijk The Spin-Charge-Family-Theory

{ , }- = i

f

, { , }- = i ~~

f

Ak , ~


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The action

Before the last two breaks, BREAK II and Break I, of symmetries there are eight massless families of fermions. ¯ It is the term s p0s , s {[7], [8]} which determines massess of fermions on the tree level. Before the electroweak break ( BREAK I) the four out of eight families remain massless. Four of the eight gain masses. The lowest among the decoupled upper, massive after the SU (2)II â U (1)II break, four families is the candidate for forming the dark matter clusters.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


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Our technique

Our technique to represent spinors works elegantly. J. of Math. Phys. 43, 5782-5803 (2002), hep-th/0111257, J. of Math. Phys. 44 4817-4827 (2003), hep-th/0303224, both with H.B. Nielsen. (±i) : = 1a ( b ), 2 for aa bb = ab 1a ( ± i b ), (±) : = 2 for aa bb =
ab ab 1 [±i] := (1 ± a b ) 2 -1, ab 1 [±] := (1 ± i a b ), 2 1

with a which are the usual Dirac operators
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


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Our technique

S

ab

ab

(k) =
ab

~ Sab (k) =

k ab (k), 2 k ab (k), 2

k ab [k], 2 ab k ab ~ Sab [k] = - [k]. 2 S
ab

ab

[k] =

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Our technique

a transforms (k ) into [-k ], never to [k ]. ~ a transforms (k ) into [k ], never to [-k ].
ab ab ab

ab

ab

ab

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


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Family members and families

S ab generate all the memb ers of one family. The eightplet (the representation of SO (1, 7)) of quarks of a particular colour charge
i |a i > Octet, (1,7) = 1, (6) = -1, of quarks uc1 R
c uR1 c dR1 03 03 03 12 12 12 56 78 56 78 56 78 56 78 56 78 56 78 56 78 56 78 9 1011 1213 14

(1,3)

S 12

(4)

13

23

Y

4

1 2 3 4 5 6 7 8

(+i)(+) | (+)(+) || (+) (-) (-)
9 1011 1213 14

1 1 1 1 -1 -1 -1 -1

1 2

1
1 2

0 0 0 0 -1 2 -1 2
1 2 1 2

1 2 1 2

2 3 2 3 1 2 1 2

1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6

[-i ][-] | (+)(+) || (+) (-) (-)
9 1011 1213 14 9 1011 1213 14

-
1 2

1 1

(+i )(+) | [-][-] || (+) (-) (-)
03 12 03 12

- -

- -

1 3 1 3 1 6 1 6 1 6 1 6

d

c1 R

[-i][-] | [-][-] || (+) (-) (-)
9 1011 1213 14 9 1011 1213 14 9 1011 1213 14 9 1011 1213 14

-
1 2

1 2

1 -1 -1 -1

c dL 1

[-i ](+) | [-](+) || (+) (-) (-)
03 12 03 12 03 12

0 0 0 0

dc1 L u
c1 L

(+i)[-] | [-](+) || (+) (-) (-) [-i](+) | (+)[-] || (+) (-) (-) (+i )[-] | (+)[-] || (+) (-) (-)

-1 2
1 2

c uL1

-

1 2

-1

0 7 and 0 8 transform uR of the 1st row into uL of the 7th row, and dR of the 4rd row into dL of the 6th row, doing what the Higgs and 0 do in the Stan. model. N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Family members and families

In the standard mo del the families exist by assumption. In the spin-charge-family-theory the families are created. a transforms (k ) into [-k ], never to [k ]. S ab transform one family memb er into another one. ~ a transforms (k ) into [k ], never to [-k ]. ~ ab transform a family memb er into the same family S memb er of another family.
ab ab ab ab ab ab

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


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Family members and families

Eight families of uR with the spin 1/2 of a particular colour and of a colourless R :
IR IIR I I IR IVR VR VIR VIIR VIIIR
c uR1 c uR1 c uR1 c uR1 c uR1 c uR1 c uR1 c uR1 03 03 03 03 03 03 03 03 12 12 12 12 12 12 12 12 56 56 56 56 56 78 78 78 78 78 9 10 11 12 13 14 03 12 12 12 12 12 12 12 12 56 56 56 56 56 78 78 78 78 78 9 10 11 12 13 14

(+i ) [+] | [+] (+) || (+) [-] [+i ] (+) | [+] (+) || (+) [-] (+i ) [+] | (+) [+] || (+) [-] [+i ] (+) | (+) [+] || (+) [-] (+i ) (+) | (+) (+) || (+) [-]
56 78 56 78

[-] [-] [-] [-] [-] [-] [-] [-]

R R R R R R R R

(+i ) [+] | [+] (+) || (+) (+)
03 03 03 03 03 03 03

(+) (+) (+) (+) (+) (+) (+) (+)

9 10 11 12 13 14 9 10 11 12 13 14 9 10 11 12 13 14 9 10 11 12 13 14 9 10 11 12 13 14 9 10 11 12 13 14 9 10 11 12 13 14

9 10 11 12 13 14 9 10 11 12 13 14 9 10 11 12 13 14 9 10 11 12 13 14 9 10 11 12 13 14 9 10 11 12 13 14 9 10 11 12 13 14

[+i ] (+) | [+] (+) || (+) (+) (+i ) [+] | (+) [+] || (+) (+) [+i ] (+) | (+) [+] || (+) (+) (+i ) (+) | (+) (+) || (+) (+)
56 78 56 78

(+i ) (+) | [+] [+] || (+) [-] [+i ] [+] | (+) (+) || (+) [-]
56 78

(+i ) (+) | [+] [+] || (+) (+) [+i ] [+] | (+) (+) || (+) (+)
56 78

[+i ] [+] | [+] [+] || (+) [-]

[+i ] [+] | [+] [+] || (+) (+)

Before SO (1, SO (1, all the

the break of 3)â SU(2)I â SU(2)II âU(1)II â SU (3) into 3)â SU(2)I â U(1)I â SU (3) eight families are massless.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


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Family members and families

At the symmetry SO (1, 7) â U (1)II â SU (3) there are 2(1+7)/2-1 (= 8) massless families of fermions which stay massless also after the break into SO (1, 3) â SU (2)I â SU (2)II â U (1)II â SU (3).

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


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Scalars and mass term for fermions and gauge bosons

The scalar fields with resp ect to with resp ect to

~ ~s AAi and ABj , in adjoint representations s the family groups, are obviously doublets the weak charge group. The mass term

¯ L s (ps -
s=[7],[8] ~ A ,i

~~ gA Ai A ~~ ~

~ Ai s

-
B,j

gB

Bj

, ABj ) R s

namely do es what the standard model Higgs does: Transforms the right handed quarks and leptons into the left handed partners, generating the mass matrices.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


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Scalars and mass term for fermions and gauge bosons

To the break of symmetries from SU (2)I â SU (2)II â U (1) to SU (2)I â U (1)I only scalar fields which are triplets with ~ respect to 2 and NR (are assumed to) contribute. ~ ~s ~ A2i , A
~ NR i s

II

.

To the break of symmetries from SU (2)I â U (1)I to U (1) both kinds of scalar fields (are assumed to) contribute, ~ those which are triplets with respect to 1 and NL ~
~ ~s ~s A1i , ANL i and singlets Y As , AQ , AQ . s s

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


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Scalars and mass term for fermions and gauge bosons

Before the BREAK II the vielbeins (together with the spin connection fields of S ab ) manifest the massless gauge vector fields in (1+3) g 4 4 A4 , m g 1 1i A1i , m g 2 2i A2i , m g 3 3i A3i , m

~ and the vielbeins together with the spin connection fields of S ab st manifest in d = (1 + 3) the scalar gauge fields of Ai and S ~ and Ai ~
1 g1 1i A1i , s 1 g1 2i A2i , s

g 2 2i A2i , g 1 1i A1i , , ~ ~ ~s ~ ~ ~s ~ ~ ~ g NR NiR ANR i , g NL NiL A ~ ~ ~s ~ ~~
The Spin-Charge-Family-Theory

~ NL i s

.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics


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Scalars and mass term for fermions and gauge bosons

The spin-charge-family theory action resembles after the first of the two breaks the standard mo del action before the electroweak break. There are also many differences, like: There are several scalar fields, with the family charges in the adjoint representations, while they all are doublets with resp ect to the weak charge. There is the op erator 1 ( 7 8 ) = (±), which does, in the 2 ussual way, the "dressing" job of the Higgs. There are twice four families predicted at the low energy regime, four of them forming families out of which there are the measured ones. There is the dark matter family as well.
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory

78


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Achievements of the spin-charge-family-theory so far concerning: Families: Two decoupled groups of four families, three of the lowest four observed, the lowest of the upper four are expected to form the dark matter. Scalar fields: Two decoupled groups of scalar fields: contributing to the mass matrices of the twice four families. Massive vector boson fields: The SU (2)II and the SU (2)I (the weak) b osons.
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Mass matrices

The fifth family is stable. Its elm neutral baryons (neutrinos also contribute) form the dark matter. Direct measurements and cosmological evolution limit my fifth family mass to 10TeV < mq5 c 2 < 103 TeV . The dark matter baryons are opening an interesting new "fifth family nuclear" dynamics. hep-ph/0711.4681,p.189-194; Phys. Rev. D 80, 083534 (2009);

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Mass matrices

The lowest four families The mass matrix of any family member, of any quark and any lepton, ob eys the same symmetry ­ the symmetry required by the spin-charge-family theory on the tree level and (almost) proven to be kept in all loop corrections. We simplify the present study by assuming: The mass matrices are Hermitian and real. The mixing matrices are real unitary 4 â 4 matrices.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Mass matrices

The effective Lagrange density for spinors is after the electroweak break close to what the standard mo del assumes L p0
f

¯ = ( m p

0m

- M) ,

g1 1+ 1- = pm - {e Q Am + g1 cos Q ZQ + ( 1+ Wm + 1- Wm ) m 2 2 Y + g cos 2 Y Am } , ¯ M = s p0s ¯ g1 ~ ~ ~ ~ ~ p0s = ps - {g NL NL ANL + g Q Q AQ + ( 1+ A1+ + 1- A1- ) ~ ~ ~s ~ ~ ~s ~ ~s ~ ~s 2 + e Q As + g 1 cos 1 Q ZsQ + g 2 cos 2 Y AY } . s
m
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Mass matrices

Mass matrices of quarks and leptons have after the electroweak break after taking into account loop corrections in all orders a very determined symmetry -a1 - a e d b e -a2 - a b d . M = d b a2 - a e b d e a1 - a

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Mass matrices

We take the diagonal matrix elements M , = {u , d , , e } d and the mixing matrices V for the quark pair and the lepton pair from the experimental data, assuming that there is 4 â 4 mixing matrix which is unitary. The unitary conditions for the n â n matrix when applied on the (n - 1) â (n - 1) submatrix, determine for n 4 the n â n matrix uniquely. For an orthogonal matrix this is the case for any n. If assuming that (n - 1) â (n - 1) submatrix is unitary, we lose (2n - 1) informations, when the free choice of phases are taken into account (2n - 1) goes into (2n - 3). For an orthogonal matrix we lose in this case (n - 1) informations.
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Mass matrices

Taking into account the invariants mi ,
i =1,4 m1 m2 i >j =1,4 m3 m4 ,

mi mj ,
i >j >k =1,4

mi mj mk ,

determined by the masses of the three families and depending on the fourth family mass, we reduce the number of free parameters of each mass matrix from 6 (7) to 3 (4). The orthogonal mixing matrix, if known for three families exactly, determines all 6 = 3 + 3 free parameters of the two family members.
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Mass matrices

This would determine in the spin-charge-family theory the masses and the mixing matrices of the four families of quarks and leptons uniquely in the case, that i. b1 = b2 , that ii. all the experimental data would be measured accurately and that iii. orthogonality and reality of mixing matrices would be a good assumption. The measured values within the exp erimental accuracy enable to determine the intervals of the fourth family memb ers masses. The accurate enough exp eriments would confirm or exclude the fourth family.
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Mass matrices

We follow the pro cedure: The diagonalizing matrices S and S , each depending on 3 (for b1 = b2 otherwise 4) free parameters, are for real and symmetric mass matrices orthogonal. They follow from the procedure M M
d

= S M T d =(
m1 2



,

T = S F
4

S

F

T

,

,m ,m ,m ),

3

in two ways
A. : S = V S , A. : V S M S V = M , d

B . : S = V S ,

B . : V S M S V = M . d

We use both ways iteratively.
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Mass matrices

With Gregor Bregar we treat quarks and leptons in an equivalent way: Quarks (very preliminary, intervals are not yet determined): Mu /MeV /c d M /MeV /c
d d 2 2

= (1.24703, 620.141, 172 000., 650 000.?)) , = (2.92494, 54.793, 2 899., 700 000.?) ,
-0.2243 -0.0041 0.9737 -0.0409 0.0403 0.986 -0.0052 -0.162 0.0306 -0.0049 , 0.1616 0.9864 ij
104 497 315 176 315 198 -104 481 104 484 315 198 315 235 -104 497

0.9740 0.2242 |Vud |ij = 0.0084 -0.031
101 630 -46 077 M = -46 154 -94 733
u





-46 077 321 824 315 685 -46 154

-46 154 315 685 309 681 -46 077

-94 733 36 244 -46 154 d M = 104 497 104 484 -46 077 98 4880 -36 223

-36 223 -104 484 -104 497 36 304

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Mass matrices

Leptons (very preliminary, intervals are not yet determined): M /MeV /c d Me /MeV /c d
2 2

= (5 · 10-9 ? , 1 · 10

-8

? , 5. · 10-8 ? , 60? 000 ,

= (0.510998928? , 105.6583715? , 1776.82? 120 000)
-0.2243 -0.0041 0.9737 -0.0409 0.0403 0.986 -0.0052 -0.162 0.0306 -0.0049 , 0.1616 0.9864 ij
30 057 32 009 31 958 -29 762 29 762 31 958 32 009 -30 057 -27 207 -29 762 -30 057 28 933

0.9740 0.2242 |V e |ij = 0.0084 -0.031
M


14 021 14 968 = 14 968 -14 021



14 968 15 979 15 979 -14 968

14 968 15 979 15 979 -14 968

-14 021 28 933 -14 968 e M = 30 057 29 762 -14 968 14 021 -27 207

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Mass matrices

Summarizing prop erties of quarks and leptons following from the spin-charge-family theory and exp erimental data: We treat quarks and leptons in equivalent way. Differences in the properties of quarks and leptons are due to different couplings of family members to the scalars AQ , AQ and AY . s s s The theory predicts, so far very preliminary, masses of the fourth family memb ers within some intervals, due to the inaccuracy of the exp erimental data.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Scalar fields

Scalar fields at the electroweak break There are two triplets and three singlets with respect to the family quantum numbers. All are doublets with respect ~ ~N ~± ± ± ± ~ to the weak charge: Ai = [A±L i , A1i , AQ , AQ , AY ] The Lagrange density for scalars are so far assumed Lsb = V (Ai ) = p0
m

1 m (p0m Ai ) (p0 Ai ) - V (Ai ) , 2 1 1 { - (mAi )2 (Ai )2 + 2 4
A,i B ,j Ai

Ai Bj

(Ai )2 (Bj )2 } ,

= pm - g



Ai

AAi m

.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Scalar fields

The mass eigenstates : V ( ) =
V | vAi

Ai

=



C

Ai

.

1 1 { - (m )2 ( )2 + ( )4 } , 2 4

= 0,
78

The scalar fields 0 ( ) Ai Ai transform the right handed family memb ers into the the corresponding left handed partners 0 (-) Ai Ai (u, - 0 (+) Ai Ai (d, +
The Spin-Charge-Family-Theory

78

)R

Ai Ai -

(u, )L d,e)L

, .

78

e)R

Ai Ai ( +

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Scalar fields

(LkR) , ,

k (L,R)

,

= (u

L ,R

, dL,R , L,R , e

L,R

),

massless and massive k th and k th component of the four vectors, k and k are the family quantum numbers: We have
(L, R)

= S L, (


R)

S





M S = diag(m1 , · · · , m4 ) ,

S



M S



= . f

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Scalar fields

The (Yukawa!!) couplings of the scalar fields to the member of the k th family ( ) f
kk



k

= k

k

mk

k

.

The superposition of scalar fields in the mass eigenstates basis which couple to fermions
fk

=


D

k

.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Scalar fields

The scalar fields change, when gaining a nonzero vacuum expectation values, properties of the vacuum. At the electroweak BREAK I in the vacuum the new terms appear. In our technique it is
78 78 I 78 56 78 ) 1 ~ 56 78 9 10 11 1213 14

(-)
78

: = (-) TsNL |([+](+)) Td(- ~

|| [+] [+] [+] ,
9 10 11 1213 14

(+) I : = (+) TsNL |([-](-)) Td(+) 1 || [-] [-] [-] . ~ ~ ~ Here TsNL denotes a triplet with respect to the operators N ~
56 78 L

and a singlet with respect to NL , while ([+](+)) Td( ) 1 are ~ the two triplets with respect to 1 and doublets with respect ~ to 1 .
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Scalar fields

Due to
1+ 1- 78 78



(+) I =(+) I ,
78



1- 1+

78

78 I



(-)

=(-)

I

,

78

Q (+) I = 0 = Q (-) I , 78 1 1 Q (+) I = - , Q (-) I = , 2 cos2 1 2 cos2 1
78 ± the vector gauge fields A1± (= Wm ) and AQ (= Zm ) m m = cos 1 A13 - sin 1 AY become massive, while AQ (= Am ) m m m 13 + cos AY stays massless, if g 1 tan = 1. = sin 2 Am 1m 1 gY

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Scalar fields

Correspondingly the mass term of the vector gauge b osons is ^ ^ (p0m I ) (p0m I ) 1 1 ( )2 (g 1 )2 vI2 ( ZQ Z 2 (cos 1 )2 m

Qm

+ + 2 Wm W

-m

),

Tr (vI vI ) =

v2 . 2

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Scalar fields

What questions is the spin-charge-family theory able to answer?

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Scalar fields

The stated urgent questions the answers to which would help to make the right next step b eyond the standard model. Why there exist families at all? Or rather: What is the origin of families?... offering answers How many families are there? And what are their prop erties if there are more than the so far observed ones?... offering answers Why family memb ers ­ quarks and leptons ­ manifest so different prop erties if they all start as massless? ... offering answers

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Scalar fields

N.S. Manko c

How is the origin of the scalar field (the Higgs) and the Yukawa couplings connected with the origin of families? ... offering answers How many scalar fields determine properties of the so far (and others p ossibly to b e) observed fermions and masses of b osons? ... offering answers Why are all the scalar fields doublets with resp ect to the weak charge? What are their representations with resp ect to the family quantum numbers? ... offering answers Where does the dark matter originate? ... offering answers Where do the charges and correspondingly the so far (and others p ossibly be) observed gauge fields originate? ... offering answers 16th Lomonosov Conference on Elementary particle physics Bor stnik, University of Ljubljana,

The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

What predictions does the spin-charge-family theory offer?

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

There are four in the low energy regime, rather than three, coupled families of quarks and leptons. Careful measurments of the mixing matrices will show this up. Quarks and leptons manifest the same symmetries of mass matrices. The existence of four families explains the properties of neutrinos. The theory predicts the intervals for the masses of the fourth families, the more accurate are the measured properties of quarks and leptons, the narrower will be intervals. There are several scalar fields which will be observed at the LHC.
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

The dark matter origin in the fifth family. There are more than so far observed vector gauge fields. There is no supersymmetric partners, at least not to the observed ones.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

From Tr (vI vI ) = v2 we extract from the masses of gauge bosons one information about the vacuum expectation values of the scalar fields, their coupling constants and their masses.
2

Mass matrices of quarks and leptons offer additional information about the scalar fields of the spin-charge-family theory. Measuring charged and neutral currents, decay rates of hadrons, the scalar fields productions in the fermion scattering events and their decay properties provides us with additional in formations.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

What are not yet solved problems in the spin-charge-family theory?

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

The spin-charge-family theory offers the explanation for the assumptions of the standard mo del and several predictions. Yet there are several proofs needed and calculations to b e made. Although I see formally that SO (4) â U (1)II must break into SU (2)I â U (1)I leading to the SU (2)II massive vector gauge fields and the massless weak SU (2)I vector gauge field, this must be proven. Although I see that the symmetry is conserved whatever diagram I look at to see whether or not the symmetry of mass matrices on the tree level is conserved in all orders in loop corrections, this is not yet a proof.
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Although we have seen that the lo op corrections of all the contributions manifest coherence, this is not yet a proof that this coherence really leads to mass matrices, which manifest then the measured properties of quarks and leptons. Also the prop erties of scalar fields wait to be formally derived. Additional numerical evaluation of the mass matrices of the four families of quarks and leptons are needed. Carefull study of predictions of the properties of scalar fields, possibly measured at the LHC, are needed. And many additional problems to be solved and measurements to be predicted.
N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory


Some publications Open questions in elementary particle physics and cosmology Introduction Content of the talk About the spin-

Prediction for the LHC LHC will confirm the existence of several scalar fields. Yukawa couplings by themselves guaratee that there are several!! LHC will confirm the fourth family. NO desert in the future measurements.

N.S. Manko Bor c stnik, University of Ljubljana, 16th Lomonosov Conference on Elementary particle physics The Spin-Charge-Family-Theory