Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://nuclphys.sinp.msu.ru/conf/lpp14/220809/Mankoc.pdf Äàòà èçìåíåíèÿ: Wed Sep 16 16:31:16 2009 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 00:40:06 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: universe

Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

The approach unifying spins and charges is offering a new way beyond the Standard model: A simple action, in which in d > 1 + 3 spinors carry only two kinds of spins, no charges, manifests in d = 1 + 3 the Standard model effective Lagrangean--with the families, Higgs and Yukawa couplings included--predicting the fourth family and the Dark matter candidate.
N.S. Manko Bor c stnik, Moscow 2009, 19-25 August
N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Collab orators in this project, which SNMB has started almost 15 years ago: Anamarija Pika Bortnik Bra , Gregor Bregar, Matja s cic z Breskvar, Dragan Lukman, Holger Bech Nielsen (first of all), Jo Vrab ec, others. ze

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

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), hep-th/0311037, hep-th/0509101, with H.B.N. hep-ph/0401043, hep-ph/0401055, hep-ph/0301029, Phys. Rev. , D 74 073013-16 (2006), hep-ph/0512062, with A.B.B.. hep-ph/0606159, with M.B., D.L.. New Jour. of Phys. 10 (2008) 093002, hep-ph/0606159, hep/ph-07082846, with G.B., M.B., D.L. astro-ph¿arXiv: 0907.0196, with G.B.
N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

INTRODUCTION

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

N.S.

The approach unifying spins and charges is offering a new way b eyond the Standard model of the electroweak and colour interactions: Spinors carry in d > 4 only two kinds of the spin, no charges. The Dirac spin manifests in d = 1 + 3 the spin and all the charges of quarks and leptons, the second kind of spin generates families. A spinor interacts in d = 1 + 13 with the vielb eins and the (two kinds of ) the spin connections. A simple action in d = 1 + 13 manifests in d = 1 + 3, after the break of the starting symmetry, all the properties of families of quarks and leptons, as assumed by the Standard model. It is a part of the simple starting action, which manifests the Yukawa coupling, the Higgs are a part of Manko Bor c vielb eins. 009, 19-25 August stnik, Moscow 2

The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

I am looking for general pro ofs that this Approach does lead in the observable (low) energy region to the observable phenomena, how many of the op en questions of the standard mo dels do es the Approach answer.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

The open questions, which I am trying to answer, together with my collaborators, are: 1 Where do families of quarks and leptons come from? 2 What do es determine the strength of the Yukawa couplings and accordingly the weak scale? 3 Why do only the left handed spinors carry the weak charge, while the right handed are weak chargeless? 4 How many families app ear at (so on) observable energies? 5 Are among the memb ers of the families the candidates for the dark matter? 6 How do es the evolution of the universe determine the to day observable matter and energy? 7 Where do charges come from? 8 And several other questions.
N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

N.S. The

The approach unifying spins and charges offers the answers to these questions: The representation of one Weyl spinor of the group SO(1,13), manifests the left handed weak charged quarks and leptons and the right handed weak chargeless quarks and leptons. There are two kinds of the Clifford algebra objects. One kind takes care of the spin and the charges, the other generates families. It is a part of a simple starting Lagrange density for a spinor in d = 1 + 13 (which carries nothing but two kinds of spins, no charges) and interacts with the gravitational fields only­the vielb eins and the spin connections of the two kinds­which manifests in d=1+3 the Lagrange density for spinors as assumed by the Standard model before the break Manko Bor the electroweak symmetry, manifesting the hyp er , the c of stnik, Moscow 2009, 19-25 August Approach unifying spins and the weak charge and coupling the spinor to colour and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

It is a part of a simple starting Lagrange density for a spinor in d = (1 + 13), which manifests in d=1+3 the Yukawa couplings, playing the role of the Higgs field of the Standard model. The way of breaking symmetries determines the charges and the prop erties of families, as well as the coupling constants of the gauge fields. There are two times four families with zero Yukawa matrix elements among the members which do not belong to the same four families' group. The three from the lowest four families are the observed ones, the fourth family might (as the first rough estimations show) b e seen at LHC. The lowest among the decoupled four families is the candidate for forming the Dark matter clusters.
N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

ACTION

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

There are two kinds of the Clifford algebra objects: The Dirac a op erators (used by Dirac 80 years ago), ~ The second one: a , which I recognized in Grassmann space

{ a , b }+ = 2 { a , b }+ = 0, ~

ab

= { a , b }+ , ~~

a B : = i(-)nB B a , ~

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Sab := (i/4)( a b - b a ), ~ Sab := (i/4)( a b - b a ), ~~ ~~ ab , Scd } = 0. ~- {S I recognized: If a describe the spins and the charges of spinors, describ e a their families. ~

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

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 ) + h.c . 2 = f a p0 , 1 1~ - Sab ab - Sab ab ~ 2 2 =



N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

e a f b = ab , e a f a = Latin indices a, b , .., m, n, .., s , t , .. denote a tangent space (a flat index), Greek indices , , .., µ, , .., .. denote an Einstein index (a curved index). Letters from the b eginning of both the alphabets indicate a general index (a, b , c , .. and , , , .. ), from the middle of b oth the alphabets the observed dimensions 0, 1, 2, 3 (m, n, .. and µ, , ..), indices from the b ottom of the alphabets indicate the compactified dimensions (s , t , .. and , , ..).

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

The Einstein action for a free gravitational field is assumed to be linear in the curvature Lg = E ( R + R ), ~~
[a b ]

R=f ~ R=f with E = det(e a ) and f [a f b] = f a f
b

f

( ( ~

ab , ab ,

- - ~

ca ca

~

c c

b b

), ),

[a b ]

f

-f

b f a

.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Variation of the action brings for ab ab




=-

1 ee eb (Ef 2E - ee e
e

[e

f

a]

) + ee ea (Ef
[a



[b

f

e ]

)

Ef



f



b]

- -

3i e ee ¯ e e Sab + (b a - a b ) 4 2 1¯ 1 1d e Ef [d f b] + d Sdb ea d -2 E 2 1d 1¯ - eb e Ef [d f a] + d Sda E 2

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

and for ~ ab ~


ab

=-

1 ee eb (Ef 2E - ee e
e

[e

f

a]

) + ee ea (Ef
[a



[b

f

e ]

)

Ef



f



b]

- -

ee ¯ e 4 1 ea d -2 -e
b

3i e e ~ Sab + (b a - a b ) 2 1d 1¯ e Ef [d f b] + d E 2 1¯ 1d e Ef [d f a] + d E 2

~ Sdb ~ Sda

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

The action for spinors can formally be rewritten as ¯ = m (pm -
A ,i

Lf

g A Ai AAi ) + m
0s

{
s =7,8

¯ s p

} +

the rest
Ai Ai

=
a ,b

c

Ai

ab

S ab ,

{ , }- = i

Bj

AB Aijk Ak

f

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

There are particular breaks --the particular isomertries-- of the starting symmetries which make that only the measured gauge fields manifest at low energies: the spin connections st µ are expressible with the vielb eins e s µ in d = 1 + 3 and the present spinor fields.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

A=1 A=2 A=3

U (1) hyper charge i = {1} SU (2) weak charge i = {1, 2, 3} SU (3) colour charge i = {1, · · · , 8}

usual not. Y , usual not. i , usual not. i /2,

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

One can see that: one Weyl spinor representation in d = (1 + 13) with the spin as the only internal degree of freedom manifests, if analyzed in terms of the subgroups SO (1, 3) â U (1) â SU (2) â SU (3), in four-dimensional "physical" space as the ordinary (SO (1, 3)) spinor with all the known charges of one family of the left handed weak charged and the right handed weak chargeless quarks and leptons of the Standard model.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

~ The second kind of the Clifford algebra objects S ab takes care of the families by generating the equivalent representations with respect to S ab , which generate spin and charges.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

THE YUKAWA COUPLINGS and HIGGS' FIELDS

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

It is a part of the simple starting action for spinors in d = 1 + 13 which manifests in d = 1 + 3 the Yukawa couplings. It is a part of the simple starting vielb eins in d = 1 + 13 which manifests in d = 1 + 3 the scalar (Higgs') fields. The symmetry SO (1, 7) â U (1) breaks twice: SO (1, 7) â U (1) into SO (1, 3) â SU (2) â U (1) leading to the Standard model massless quarks and leptons of four (not three families) and massive, decoupled in the Yukawa couplings from the lower mass families, four families. Accordingly there are two kinds of Higgs fields.
N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

The Yukawa couplings

-LY

= 0 s p0s = 0 {(+) p0+ + (-) p0- } , p = (p7 i p8 ) - 1 ab S ab± - 2 = ab7 i ab8 = ab ~
7 78 78

0±

ab ab ~

± ±

1 ~ ab S ab± , ~ 2 ,

i ab ~

8

We put p7 = p8 = 0.
N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

The vielb eins in d > (1 + 3) manifest the Higgs. e E
a



=

e

s

µ

m µ = es E

e
Ai Ai Aµ

m

e

s

=0


Ai

=

Ai

x,

A= 1 · · · the U(1) field, A= 2 · · · the weak field.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

LSB

=

1 µ (p0µ g )(p0 g ) + 2 µ similar terms with p0 - V (g )

p0µ is the covariant momentum concerning the U (1) and SU (2) charge g


=e

s

es

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Our technique

OUR TECHNIQUE TO REPRESENT SPINOR STATES

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

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, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Our technique

S

ab

ab

(k) =
ab

~ Sab (k) =
ab

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

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

ab

[k] =

a (k) = aa [-k], a [k] = (-k), ~ a (k) = -i aa [k], ~ a [k] =
The Approach unifying spins and charges

b (k) = -ik [-k], b [k] = -ik aa (-k)
ab ab

ab

ab

ab

ab

ab

ab

~ b (k) = -k [k], ~ b [k] = -k aa (k).
ab ab

ab

ab

ab

ab

i (k),

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

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, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Our technique

ab ab ab ab ab ab ab

ab

ab

(k )(k ) = 0, (k )(-k )=
ab ab ab ab

aa

ab

ab ab ab

ab

[k ], [k ][k ]=[k ],

ab ab

[k ][-k ] = 0, (k )[k ]= 0, (k )[-k ] = (k ), ~ (k )(k ) = 0,
ab ab ab ab ab

[k ](k )=(k ),

[k ](-k )= 0.
ab ab

~ (-k )(k )= -i
ab

ab

aa

ab

[k ],

~ (k )[k ] = i (k ), 1 ~ (±i )= ( ~ 2
The Approach unifying spins and charges

~ (k )[-k ]= 0.
ab

ab

a

b ), ~

1 ~ (±1)= ( a ± i b ), ~ ~ 2

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

THE REPRESENTATION OF A SPINOR IN d = 1 + 13 ANALYZED IN TERMS OF THE STANDARD MODEL SYMMETRIES

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Cartan subalgebra set of the algebra S S 03 , S 12 , S 56 , S 78 , S A left handed ((1 Cartan subalgebra
03 ,13) 9 10

ab

,S

11 12

,S

13 14

.

= -1) eigen state of all the members of the
56 78 9 10 11 1213 14

12

(+i )(+) | (+)(+) || (+) (-) (-) | = 10 ( - 3 )( 1 + i 2 )|( 5 + i 6 )( 7 + i 8 )|| 27 ( 9 + i 10 )( 11 - i 12 )( 13 - i 14 )| .

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

S ab generate a representation--the members of one family. The eightplet (the representation of SO (1, 7)) quarks of a of particular color charge ( 33 = 1/2, 38 = 1/(2 3), and 41 = 1/6)
i |a i > Octet, (1,7) = 1, (6) = -1, of quarks
c uR1 c uR1 c dR1 c dR1 c dL 1 c dL 1 c uL1 c uL1 03 03 03 03 03 03 03 03 12 12 12 12 12 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

21

Y

Y

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 3 -1 3
2 3 2 3 1 6 1 6 1 6 1 6

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

-
1 2

1 1 1 -1

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

-

-

1 3

-1 2
1 2

-1 2 0 0 0 0

1 -3 1 6 1 6 1 6 1 6

-
1 2

1 2

-1 -1

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

-

1 2

-1

-LY = 0 {(+) p0+ + (-) p0- } , 0 (-) transforms uR of the 1st row into uL of the 7th row, while 0 (+) transforms dR of the 3rd row into dL of the 5th row, doing what the Higgs and 0 do in the Standard ab N.S. Manko Bor ab Moscow 2009,ab 9-25 August ab c stnik, 1 ab model. a (k )= aa [-k ], (-k )(k )= aa [-k ], The Approach unifying spins and charges
78


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

~ S ~ S

ab 03

generate families.
03 12 03 12 03 12 03 12 i ~~ ~~ ~~ ~~ = 2 [(+i )(+) + (-i )(+) + (+i )(-) + (-i )(-)]

Both vectors bellow describe a right handed u -quark of the same colour.
03 12

~~ (-i )(-)

03 03

12 12

56 56

78 78

910 11121314 910 11121314

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

ab 1 ~ (±i )= 2 ( ~ a

ab 1 ~ b ), (±1)= 2 ( a ± i b ), ~ ~ ~

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Raising and lowering operators:
ac b d

(k )(l ) and
ac b d

~l (k )(~) 0 (-) transforms the right handed weak chargeless uR -quark into the left handed weak charged uL -quark: 0 (-)
78 03 03 12 12 56 78 9 10 11 1213 14 9 10 11 1213 14 78

(+i )(+) | (+)(+) || (+) (-) (-) =
56 78

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

~l (k )(~) transform one family into another.
N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

BREAKING THE STARTING SYMMETRY SO(1,13)

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Breaks of symmetries
SO (1, 13) SO (1, 7)â ? SO (1, 3) â SO (4) â U (1) ? SO (1, 3) â SU (2) â U (1) ? SU (3) SU (3) SU (3) â U (1)

? SO(1, 3) â U(1) â SU(3)

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Breaking symmetries from SO (1, 13) to SO (1, 7) â U (1) â SU (3) occurs at very high energy scale (E > 1016 GeV) and leaves very heavy all the families except one which is left massless. With H.B. Nielsen we studied possibilities of such way of breaking on the toy model of d = 1 + 5. There are 28/2-1 = 8 families--the symmetry SO (1, 7)(âU (1)) determines them.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

There are two further breaks: From SO (1, 7) â U (1) to SO (1, 3) â SU (2) â U (1) (at E around 1013 GeV) which leaves four of the families massless and mass protected (since only the left handed carry the weak charge), while four of the families obtain the Yukawa couplings determined by the scale of break. From SO (1, 3) â SU (2) â U (1) to SO (1, 3) â U (1) (the Standard model type of breaking) bringing the masses to the light four families. All the members of eight families have after the second break the same quantum numbers, that is the same quarks and leptons, coupling to the same gauge fields, but differing in Yukawa couplings.
N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

There are the vielbeins e spinors fields too).

a



which manifest the breaking (caused by

There are vielbeins which manifest the gauge fields e s µ = e s E Ai AAi µ E Ai = Ai x . e s µ are expressible by ab (and influenced by ab ). ~ Accordingly do
st µ

appear as gauge fields, while ~

ab µ

do not at al.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Break I The first break from SO (1, 7) â U (1) â SU (3) to SO (1, 3) â SU (2) â U (1) â SU (3) leads to the symmetries of the hyp er charge and the weak charge U (1), SU (2), (together with SO (1, 3) and SU (3)) as good quantum numbers. There app ears Higgs, determined by vielbeins e s , coupled to the gauge field AY , µ to which it brings the mass, while AY , A1i , i = 1, 3 stay massless. µ µ s , = 5, 6, 7, 8; m, µ = 0, 1, 2, 3.
N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

The eight families break into two decoupled four families: Four massless and four (very) massive, provided that the angle ~ 2 = 0. We take also 2 = 0. ~s ~s At the break new fields AY and AY are formed: ~s ~s ~ ~s ~ A23 = AY sin 2 + AY cos 2 , 41 Y Y ~ ~ ~ ~ ~ As = As cos 2 - As sin 2 , with indices = only, these are the scalar fields of the new operators: ~ Y = 41 + 23 , ~ ~
1~ with 23 = 2 (S ~ 56

(1)

~ ~ Y = 23 - 41 tan 2 , ~ ~ ~ 41 = - 1 (S ~ 3
9 10

~ + S 78 ),

~ +S

11 12

~ +S

13 14

).

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

In the S ab sector appear massless gauge fields of Y = 4 + 23 , and 1i 1 1 = ( 2 (S 58 - S 67 ), 1 (S 57 + S 68 ), 1 (S 56 - S 78 )) 2 2 and massive of Y = 23 . ~ 23 = 1 (S 56 + S 78 ), 23 = 1 (S ~ 2 2 4 + 23 , Y = 23 . ~ ~ Y = ~ ~ ~
56

~ + S 78 )

4 is from SO (6) after breaking into SU (3) â U (1), 1~ ~ ~ 41 = - 3 (S 9 10 + S 11 12 + S 13 14 ) ~ 23 is from one of the two SU (2) contained in SO (4) after breaking into SU (2) and (together with 4 ) into U (1).

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Let us point out that S ab transforms one member of the spinor representation of one family into another memb er of the same representation (and the same family). ~ S ab transforms one member of the spinor representation of a particular family into the same memb er but of a different family.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

There appear nonzero Yukawa couplings due to the term 0 s p0s and nonzero f s ab . ~ It is easy to understand, why there are four massless and four massive families. There are twice four families: Half of them are singlets with respect to 2i , i = 1, 2, 3, ~ accordingly 2i A2i give to them no contribution. ~ ~s Half of them are triplets with respect to 2i , i = 1, 2, 3, ~ 2i A2i contribute to their mass. ~s ~ ~s ~ where A2i is expressible with st .

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Eight families of quarks and leptons of a right handed quark or lepton with the spin 1/2. S ab , a, b {0, 1, 2, 3, 5, 6, 7, 8} reach all the members of one family of a particular colour charge.
03 12 56 78

IR IIR IIIR IVR VR VIR VIIR
N.S. Manko Bor c stnik, Moscow 2009, 19-25 August R The Approach unifying spins and charges

[+i ](+)(+)[+]
03 03 03 03 03 03 03 12 56 78 12 56 78 12 56 78 12 56 78

(+i )[+][+](+) [+i ](+)[+](+) (+i )[+](+)[+] (+i )(+)(+)(+)
12 56 78 12 56 78

(+i )(+)[+][+] [+i ][+](+)(+)
12 56 78

VIII

[+i ][+][+][+]


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

The Yukawa couplings

-LY with p
0±

= 0 {(+) p0+ + (-) p0- } ,

78

78

= (p

5

~~ ~~ ~~ ~ g A23 - 2- g A2- - 2+ g A2+ . (2) ip6 ) - Y ~ ~ ± ± c± 2c 2c

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

The Yukawa couplings for u -quarks after the break of SO (1, 7) â U (1) into SO (1, 3) â SU (2) â U (1).
I I II III IV V VI VII VIII 0 0 0 0 0 0 0 0 II 0 0 0 0 0 0 0 0 III 0 0 0 0 0 0 0 0 IV 0 0 0 0 0 0 0 0 V 0 0 0 0
~~ - g A23 c- g ~ ~ - A2+ 2c -

VI 0 0 0 0
g ~ 2c ~ -g c

VII 0 0 0 0 0 0
g ~ 23 ~ A c- g ~ ~ A2+ 2c -

VIII 0 0 0 0 0 0
g ~ ~ A2- 2c - g ~ 23 ~ A- c

~ A2- - ~ A23 -

0 0

0 0 -

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

After the break of SO (1, 7) â U (1) into SO (1, 3) â SU (2) â U (1) the four lower families are massless and mass protected, the left handed u -quarks carry the weak charge, the right handed do not.
~~ ~~ If | g A23 | >> | g c A2- |, - c- 2 the four massive families have all approximately the same mass. ~~ ~~ If the | g A23 | | g c A2- | - c- 2 then two families have much lower mass than the other two.

Since 2± do not distinguish between quarks and leptons, the masses of quarks and leptons are the same.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Break II. At the weak scale SU (2) â U (1) breaks into U (1) in both sectors. In the ~s A13 = ~s AY = ~ S ab sector ~ ~ As sin 1 + ~ ~ As cos 1 - ~~ new fields As , Zs appear ~s cos 1 , ~ Z ~ ~ Zs sin 1 ,

the gauge fields of ~ ~ ~ Q = 13 + Y = S 56 + 41 , ~ ~ 2 + 13 , ~ ~ Q = -Y tan ~1 ~ ~~ ~ ~ with e = g Y cos 1 , g = g 1 cos 1 , tan 1 = ~~ ~
N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges

gY ~ g1 ~

.


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

The Yukawa couplings

-LY

= 0 s p0s = 0 {(+) p0+ + (-) p0- } ,
78 78

can be rewritten as follows

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

LY

= 0 {(+) (
y =Y , Y 78

78

yAy + + yAy + - -1 2

-1 2

~~ S ab
(ab ) ab -

ab +

)) +

(-) (
y =Y ,Y 78

~~ S ab
(ab )

)

ac b d

(+)
{(ac )(bd )},k ,l 78

~l~ (k )(~) Akl ((ac ), (bd )) + +
ac b d

(-)
{(ac )(bd )},k ,l

~l~ (k )(~) Akl ((ac ), (bd ))} , -

with k , l = ±1, if aa bb = 1 and ±i , if aa bb = -1, while Y = 21 + 41 and Y = - 21 + 41 , (ab ), (cd ), · · · Cartan only.
N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

There are several possibilities how to further break the symmetries ~ in the S ab sector, which occurs when the weak scale break occurs. One can make that on the tree level the massless four families break into twice two families, the lower two (almost) massless, which for neutrinos leads to three almost massless families, but not for electrons and quarks. This work is in progress and is in need of collaborators.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

There is a progress made also in the understanding how are the vielbeins connected with the scalar fields (Higgs), gauge fields and the Yukawa couplings. Also this is in progress and calls for collaborators.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

I am presenting the old numerical results, when a particular way of breaking symmetries has led to some predictions (Gregor's diploma work). The ab -s and ab -s, determining the Yukawa couplings for the ~ lower four families, and correspondingly influencing the upper four families as well, are assumed to be different for u -quarks, d -quarks, and e , having in mind that going beyond the tree level would take care of these differences.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

NUMERICAL RESULTS FOR THE LOWER FOUR FAMILIES

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

The second break influences the massive (upper) four families as well. We have not yet studied the properties of the upper four families after the second break. Partly because the calculations bellow the tree level for the lower four families must be done first.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

IR IL IIL I I IL IVL VL VIL VIIL VIIIL XXXX
~ -- -A - ((03),(12)) ~ -- A - ((56),(78))

IIR ~ -A++ - ((03),(12)) XXXX 0
~ -- A - ((56),(78))

I I IR ~ -A++ - ((56),(78)) 0 XXXX
~ -- -A - ((03),(12))

IVR 0
~ -A++ - ((56),(78)) ~ ++ -A - ((03),(12))

VR 0 0 0 0 XXXX 0
~ -+ A - ((56),(78)) ~ +- -A - ((03),(12))

VIR 0 0 0 0 0 XXXX
-+ - ((03),(12)) ~ +- -A - ((56),(78)) ~ -A

VIIR 0 0 0 0
~ +- -A - ((56),(78)) ~ +- -A - ((03),(12))

VIIIR 0 0 0 0
~ -A

0 0 0 0 0

XXXX 0 0 0 0

0 0 0 0

0 0 0 0

-+ - ((03),(12) ~ -+ A - ((56),(78)

XXXX 0

0 XXXX

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

The new fields determine the mass matrices, which have the form
I I II III IV a±
g m ~ - N+ ~ A 2± g1 ~ ~ A1- 2±

II
g m ~ +N+ ~ A 2± 1 g m ( A 3 N- ~ ~± 2

III
g~ ~ - A1+ 2± 1

IV 0
g1 ~ ~ - A1+ 2± g m ~ + N+ ~ A 2±

a± +

~ 3N + A± + )
gm ~ 2

0 ~~ a± + e A ± + g Z ± ~~ ~ -N A± +

0
g1 ~ 2

0

~ A1- ±

~~ a± + e A± + g Z± ~~
3N 1~ ~ ~ 3N + 2 g m (A ± - + A± + )

The mass matrix for the lower four families of u -quarks (-) and d -quarks (+) is symmetric. We parameterize a± b± -c± 0 b± a± + d1± 0 -c± c± 0 a± + d2± b± 0 c± b± a± + d3±

not assumed to be real and

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Fitting these parameters with the Monte-Carlo program to the experimental data within the known accuracy and to the assumed values for the fourth family masses we get for the u -quarks the mass matrix
(9, 22) (-150, -83) 0 (-306, 304) (-150, -83) (1211, 1245) (-306, 304) 0 0 (-306, 304) (171600, 176400) (-150, -83) (-306, 304) 0 (-150, -83) 200000

and for the d -quarks the mass matrix (5, 11) (8.2, 14.5) 0 (174, 198)
The Approach unifying spins and charges

(8.2, 14.5) (83, 115) (174, 198) 0

0 (174, 198) (4260, 4660) (8.2, 14.5)

(174, 198) 0 (8.2, 14.5) 200000

.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

This corresponds to the following values for the masses of the u and the d quarks mui /GeV mdi /GeV = (0.005, 1.220, 171., 215.), = (0.008, 0.100, 4.500, 285.), quarks -0.00412 0.00218 -0.0421 -0.000207 . 0.999 0.00294 -0.00293 0.999

and the mixing matrix for the -0.974 -0.226 0.226 -0.973 0.0055 -0.0419 0.00215 0.000414

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

DO I HAVE THE RIGHT ANSWER TO THE QUESTIONS WHAT ARE THE DARK MATTER CONSTITUENTS?

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

The candidate for the Dark matter constituent must have the following properties:
1 2

It must be stable in comparison with the age of the Universe. Its density distribution within a galaxy is approximately spherically symmetric and decreases approximately with the second power of the radius of the galaxy. The scattering amplitude of a cluster of constituents with the ordinary matter and among the Dark matter clusters must be small enough and the properties of the clusters must be such that all the predictions are in agreement with the observations. The Dark matter constituents and accordingly also the clusters had to have a chance to be formed during the evolution of our Universe so that they agree with the today observed properties of the Universe.

3

4

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

We study the possibility that the Dark matter constituents are clusters of the stable fifth family of quarks and leptons, which due to the Approach has the matrix elements in the Yukawa couplings to the lower four families zero (in comparison with the age of the universe). The masses of the fifth family lie much above the known three and the predicted fourth family masses--at around 10 TeV or higher--and much bellow the break of SO (1, 7) to SO (1, 3) â SU (2) â SU (2), which occurs bellow 1013 TeV . The baryons made out of the fifth family are heavy, forming small enough clusters with small enough scattering amplitude among themselves and with the ordinary matter to have the chance to form the Dark matter constituents.
N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

We estimate the properties of the fifth family memb ers (u5 , d5 , 5 , e5 ) and of the fifth family baryons . Due to what I have presented and discussed, the approach unifying spin and charges predicts that the fifth family has all the properties of the lower four families: the same family memb ers and the interactions with the same gauge fields, AFTER the last break, but not during the evolution of the universe, when the phase transitions of SU (3) and very probably also for SU (2) is felt differently for the fifth than for the first family.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Properties of the fifth family baryons

Prop erties of the fifth family baryons

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Properties of the fifth family baryons

We use a simple (the Bohr like) model to estimate the size and the binding energy of the fifth family neutron (u5 d5 d5 ), assuming that the differences in masses of the fifth family quarks makes the n5 stable. We estimate the behavior of such clusters in the evolution of the Universe as candidates for the Dark matter constituents, which do not contradict all the cosmologic observations. We estimate the behavior of such clusters when hitting our Earth and in particular the DAMA/NaI and DAMA-LIBRA experiments in dependence of the mass of the fifth family and when hitting the CDMS experiment.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Properties of the fifth family baryons

The Bohr (hydrogen)-like model for three heavy enough quarks gives the binding energy E
c

5

1 -3 2

2 c 3

2

m q5 2 c, 2

rc5

c
2 3



mq5 2 c2c

.

(3)

The mass of the cluster is approximately 1 mc5 c 2 3mq5 c 2 (1 - ( c )2 ) 3 . We use the factor of 2 for a two quark pair potential and of 3 an quark and anti-quark pair potential.
4 3

(4) for

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Properties of the fifth family baryons

It follows for a cluster of the fifth family baryon n
mq5 c TeV
2

5



c

Ec5 mq5 c

2

rc5 10-6 fm

mud c GeV

2

1 10 102 103 104 105

0.16 0.12 0.10 0.08 0.07 0.06

-0.016 -0.009 -0.006 -0.004 -0.003 -0.003

3.2 · 103 4.2 · 102 52 6.0 0.7 0.08

0.05 0.5 5 50 5 · 102 5 · 103

Table: The properties of a cluster of the fifth family quarks within the extended Bohr-like (hydrogen-like) model from Appendix I. mq5 in TeV/c2 is the assumed fifth family quark mass, c is the coupling constant of the colour interaction at E (-Ec5 /3) (Eq.3) which is the kinetic energy of quarks in the baryon, rc 5 is the corresponding average 2 radius. Then c5 = rc5 is the corresponding scattering cross section.
N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Properties of the fifth family baryons

The binding energy is approximately
2 c 3

1 100

of the mass of the cluster

(it is ). The baryon n5 (u5 d5 d5 ) is lighter than the baryon p5 , (uq5 dq5 dq5 ) if mud = (mu5 - md5 ) is smaller than (0.05, 0.5, 5, 50, 500, 5000) GeV for the six values of the mq5 c 2 on Table 1, respectively. The nucleon-nucleon cross section is for the fifth family nucleons obviously for many orders of magnitude smaller than for the first family nucleons. The binding energy is of the two orders of magnitude smaller than the mass of a cluster at mq5 10 TeV to 106 TeV.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Evolution

Evolution of the abundance of the fifth family memb ers in the universe: (S. Dodelson, Modern Cosmology, Academic Press Elsevier 2003)

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Evolution

To estimate the behaviour of our stable heavy family quarks and anti-quarks in the expanding universe we need to know: i.) the masses of our fifth family members, ii.) their particle--anti-particle asymmetry. We need to evaluate: i.) their thermally averaged scattering cross sections (as the function of the temperature) for scattering i.a.) into all the relativistic quarks and anti-quarks of lower families (< v >qq ), i.b.) into gluons (< v >gg ), i.c.) into ¯ (annihilating) bound states of a fifth family quark and an anti-quark (< v >(qq)b ), i.d.) into bound states of two fifth ¯ family quarks and into the fifth family baryons (< v >c5 ) (and equivalently into two anti-quarks and into anti-baryons), ii.) the probability for quarks and anti-quarks of the fifth family to annihilate at the colour phase transition (Tkb 1 GeV).
N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Evolution

The quarks and anti-quarks start to freeze out when the temperature of the plasma falls close to mq5 c 2 /kb (kb is the Boltzmann constant). They are forming clusters (bound states when the temperature falls close to the binding energy. When three quarks or three anti-quarks of the fifth family form a colourless baryon (or anti-baryon), they decouple from the rest the plasma due to small scattering cross section manifested by average radius presented in Table.

) the of the

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Evolution

We assume no asymmetry between the fifth family quarks and anti-quarks. To see how many fifth family quarks and anti-quarks succeed to form the fifth family baryons and anti-baryons we solve the Boltzmann equations as a function of time (or temperature). needed in the Boltzmann equations 16 c c 2 ( ), < v >qq = ¯ 9 mq5 c 2 37 c c 2 < v >gg = ( ) 108 mq5 c 2 < v >c < v >(q
5

=

c5

10

c c mg5 c 2 10

2

c
2

Ec 5 Ec ln 5 , Tkb Tkb c Ec 5 Ec ln 5 , Tkb Tkb

q )b ¯

=

(q q )b ¯

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges

c c mg5 c 2
2


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Evolution

Let T0 is the today's black body radiation temperature, T (t ) the actual (studied) temperature, a2 (T 0 ) = 1 and a2 (T ) = a2 (t ) is the metric tensor component in the expanding flat universe--the Friedman-Robertson-Walker metric: a diag gµ = (1, -a(t )2 , -a(t )2 , -a(t )2 ), ( a )2 = 8G , with 3 2 = g T 4 , T = T (t ), g measures the number of degrees of 15 freedom of those of the four family members (f ) and gauge bosons (b), which are at the treated temperature T ultra-relativistic (g = i b gi + 7 i f gi ). H0 1.5 10-42 GeVc is the present 8 c 2 Hubble constant and G = c /(mpl ), mpl c 2 1.2 · 1019 GeV.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Evolution

We solve the Boltzmann equation, which treats in the expanding universe the number density of all the fifth family quarks as a function of time t . The fifth family quarks scatter with anti-quark into all the other relativistic quarks and anti-quarks (< v >qq ) and into gluons ¯ (< v >gg ). At the beginning, when the quarks are becoming non-relativistic and start to freeze out, the formation of bound states is negligible.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Evolution

a

-3

d (a3 nq5 ) dt

= < v >q

q ¯

nq5 n

(0) (0) q5 ¯

-

nq5 nq5 ¯ n
(0) (0) q5 nq5 ¯

+

nq nq ¯ (0) (0) nq nq ¯ ng ng (0) (0) ng ng

+

< v >gg nq5 nq5 ¯
-
mi c 2 Tkb

(0) (0)

-

nq5 n n

q5 ¯ (0) (0) q5 nq5 ¯

+

.

n

(0) i

= gi (

and to

mi c 2 Tkb ( c )2 gi Tkb 3 ( c) 2

)2 e

3

for mi c 2 >> Tkb (which is our case

for mi c 2 << Tkb ).

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Evolution

Since the ultra-relativistic quarks and anti-quarks of the lower families are in the thermal equilibrium with the plasma and so are nq n ¯ ng n gluons, it follows (0) q = 1 = (0) g . (0) (0)
n
q

n

q ¯

Taking into account that (a T quantity Yq5 = nq5 (
dx dt c3 kb T )

ng ng 3 g (T )

) is a constant it is
mq5 c kb T
2

appropriate to introduce a new parameter x = ,
(0) Yq5

and the

=n


(0) c3 q5 ( kb T )
2

.

=

hm mq5 c x

2

, with hm =

4 3 g 45

c c mpl c

, Eq. 5 transforms into

dYq5 q (0)2 2 = 25 (Yq5 - Yq5 ), dx x
q
5

=

(< v >q q +< v >gg ) mq5 c ¯ hm ( c )3

2

.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Evolution

When the temperature of the expanding universe falls close enough to the binding energy of the cluster of the fifth family quarks (and anti-quarks), the bound states of quarks (and anti-quarks) and the clusters of fifth family baryons (in our case neutrons n5 ) (and anti-baryons n5 --anti-neutrons) start to be formed.// ¯

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Evolution

The corresponding Boltzmann equation for the number of baryons nc5 reads 2 3n ) nq5 d (a c5 nc5 (0)2 a-3 = < v >c5 nq5 (0) - (0) . dt nq5 nc5 Again Yc Yc
< v > mc
2 5 5

= nc5 ( =n
(0) c5

(0)

c3 ), kb T kb T 3 ( ), c

c and c5 = hm (5 c )q5 , 3 with the same x and hm as above.

N.S. Manko Bor c stnik, Moscow

dYc5 c (0) Yq5 2 = 25 (Yq5 - Yc5 Yq5 ). (0) dx x Yc5 2009, 19-25 August

(0)

The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Evolution

The number density of the fifth family quarks nq5 (and correspondingly Yq5 ), which has above the temperature of the binding energy of the clusters of the fifth family quarks (almost) reached the decoupled value, starts to decrease again due to the formation of the clusters of the fifth family quarks (and anti-quarks) as well as due to forming the bound state of the fifth family quark and an anti-quark, which annihilates into gluons.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Evolution

a

-3

d (a3 nq5 ) = dt
(0) (0) q5 nq5 (0) (0) q5 ¯

< v >c5 n < v >q
q ¯

- (-

nq nq5 n

2
5

(0) nq5 q5 ¯ (0) (0) q5 nq5 ¯

+ + +

c5 (0) nc5

n

-



(q q ) ¯

b

nq

2
5

+

c

5

(0) nq5

nq5 n

< v >gg nq5 nq5 (- ¯ with
(q q )b ¯

(0) (0)

q5 ¯ (0) (0) nq5 nq5 ¯

n nq5 n

nq nq ¯ (0) (0) nq nq ¯ ng ng (0) (0) ng ng

)+ ),

and

c5

defined above.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Evolution

There follow the coupled equations for Yq5 and Yc dYq dx
5

5

= +

(0) (q c5 (0) Yq5 2 )+ (-Yq5 + Yc5 Yq5 2 (0) x x Yc5 q5 (0)2 2 (Yq5 - Yq5 ), x2
qq) ¯

q )b ¯ 2

2 (-Yq5 )

5 b (qq)b = Gregor solved this equation together with ¯ hm ( c )3 the above equation for Yc5 .

< v >(

mq c

2

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Evolution

We obtain
mq5 c 2 TeV

(

q q )b ¯

=1

(

q q )b ¯

c5 c5 c5 c5 c5 c5

=1 =3 1 =3 = 10 1 = 10 1 = 50

19 15 25 13 39 71

= 11 9.5 14 ­ 20 ­

1 3



(q q )b ¯

=3



(q q )b ¯

= 10

37 27 54 22 84 ­

417

Table: The fifth family quark mass is presented, calculated for different choices of c5 (which takes care of the probability that a colourless cluster of three quarks (anti-quarks) instead of two are formed) and of (qq)b (which takes care of the annihilation of a bound state of ¯ quark--anti-quark). .
N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Evolution

Figure:

The dependence of the two number densities nq5 (of the fifth family quarks) and nc5 (of the fifth
mq c 2 5 Tkb 1 is presented for the values mq5 c 2 = 71 TeV, c5 = 50 and

family clusters) as the function of (q q ) = 1. We take g ¯b = 91.5.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Evolution

We read from Table the mass interval for the fifth family quarks' mass 10 TeV < mq5 c 2 < 4 · 102 TeV. (5)

From this mass interval we estimate the cross section for the fifth family neutrons (rc5 )2 : 10-8 fm2 < c5 < 10-6 fm2 . (It is at least 10-6 â smaller than the cross section for the first family neutrons.) (6)

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Dynamics of baryons

Dynamics of the heavy family baryons in our galaxy:

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Dynamics of baryons

Our Sun's velocity: vS (170 - 270) km/s. Locally dark matter density dm is known within a factor of 10 accurately: dm = 0 , 0 = 0.3GeV /(c 2 cm3 ), we put 1 < < 3. 3 The local velocity of the dark matter clusters vdm is unknown, the estimations are model dependant. The velocity of the Earth around the center of the galaxy is equal to: vE = vS + vES , vES = 30 km/s, vS ·vES 0 vS ves cos sin t , = 60 .

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Dynamics of baryons

The flux per unit time and unit surface of our dark matter clusters hitting the Earth: dm = i dmi |vdm i - vE | to be equal to mc
5



dm


i

dmi vdmi - vS {|vdm i - vS | - vES · }. m c5 |vdmi - vS |

We assume i |vdmi - vS | dmi = vdmS vS 0 , and correspondingly i vES · |vdmi -vS | = vES vdmES cos sin t , with vdmi -vS for our Earth rotation around our. vdmS 1 1 < 3. 3 < vdmS < 3 and 3 < v
dmES

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Dynamics of baryons

The cross section for our heavy dark matter baryon n5 to elastically scatter on an ordinary nucleus with A nucleons in the Born approximation: 2 c5 A = 1 2 < |Mc5 A | >2 mA , 2 · · · the mass of the ordinary nucleus, mA = mn1 A (A) = 0 A4 ,
1 2 0 = 9 rc5 nucl , 30 < nucl < 30, when the "nuclear force" dominates, mn G 0 = 12F ( A-Z )2 weak (= (10-6 fm A-Z )2 weak ), A A weak 1, when the weak force dominates (mq5 > 104 TeV). The scattering cross section among our heavy neutral baryons n5 is determined by the weak interaction: mc5 c5 (10-6 fm)2 GeV .
N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Direct measurements

Direct measurements of the fifth family baryons as dark matter constituents:

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Direct measurements

Let us assume that DAMA/NaI and CDMS measure our heavy dark matter clusters. We lo ok for limitations these two exp eriments might put on properties of our heavy family memb ers. Let an experiment has NA nuclei per kg with A nucleons. At vdmE 200 km/s are the 3A scatterers strongly bound in the nucleus, so that the whole nucleus with A nucleons elastically scatters on a heavy dark matter cluster. The number of events per second (RA ) taking place in NA nuclei is equal to (the cross section is at these energies almost independent of the velocity)

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Direct measurements

RA = NA

0 (A) vS mc5

v

dmS

(1 +

vdmES vES cos sin t), vdmS vS
vdmES vES vdmS vS

RA = RA ( t = ) - RA ( t = 0) = NA R0 A4 2 R0 = 0 0 3 mq5 vS .

cos ,

= vdmES , 10-3 < < 102 , for the "nuclear-like force" dominating 10-2 < < 101 , for the weak force dominating

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Direct measurements

For vdmES vvES cos small and cut A determining the efficiency of a S dmS particular experiment to detect a dark matter cluster collision.
v



R

A exp

NA R0 A4

cut A

= RA

cut A

vdmS vS . vdmES vES cos

If DAMA/NaI is measuring our heavy family baryons scattering mostly on I ( AI = 127, we neglect Na, with A = 23), then R
I dama

Rdama

vdmS vS vdmES vSE cos 60

0

.
vdmS vdmES

Most of unknowns except vS , the cut off procedure and hidden in Rdama .

are

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Direct measurements

For Sun's velocities vS = 100, 170, 220, 270 km/s, S we find vSEvcos = 7, 10, 14, 18, respectively. DAMA/NaI publishes RI dama = 0, 052 counts per day and per kg of NaI. v S Then RI dama = 0, 052 v dmS vSEvcos counts per day and per kg. dmES CDMS should then in 121 days with 1 kg of Ge (A = 73) cut cdms v 73 S detect RGe cut cdms 8.3 ( 127 )4 cut dama v dmS vSEvcos 0.052 · 121 4.0 dmES , which is for vS = 100, 170, 220, 270 km/s equal too cut cdms v (10, 16, 21, 25) cut dama v dmS .
dmES

CDMS has found no event.
N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Direct measurements

cut cdms If cut dama v dmS is small enough, CDMS will measure our fifth dmES family clusters in the near future.

v

DAMA limits the mass of our fifth family quarks 200TeV < mq5 c 2 < 105 TeV . Cosmological evolution requires that masses of the fifth family quarks are not larger than a few 100 TeV.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Concluding remarks:

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

The approach unifying spin and charges is offering the new way beyond the Standard mo dels: It explains the origin of the charges, of the gauge fields and of the scalar fields (Higgs). It is offering the mechanism for generating families (the only mechanism in the literature, to my knowledge) and correspondingly explains the origin of the Yukawa couplings.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

It predicts: Four families (connected by the Yukawa couplings), the fourth to b e p ossibly seen at the LHC and correspondingly the masses and the mixing matrices. The stable fifth family which is the candidate to form the dark matter.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

We evaluated: The prop erties of the lower four families. The prop erties of the fifth family quarks:
Their Their of the 3 Their family
1 2

forming the neutral clusters. decoupling from the rest of plasma in the evolution universe. interaction with the ordinary matter (with the first baryons) and among themselves.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

I am concluding: There are more than the observed three families, the fourth family will possibly be seen at the LHC. The fifth family, decoupled from the lower four families (no Yukawa couplings to the lower four families) is the candidate to form the dark matter, provided that the mass of the fifth family quarks is a few hundred TeV. We also predict, that if DAMA exp eriments measure our fifth family neutrons, the other direct experiments will "see" the dark matter in a few years.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges


Collaborators and some publications Introduction Action Yukawa couplings and scalar fields The spinor representation Breaking

Op en problems to b e solved although the main steps are done: The way how does the breaking of symmetries o ccur and define the scales. The b ehaviour of quarks and leptons (neutrinos in particular) and gauge fields at the phase transitions of the plasma (SU (2) and SU (3)). The way how do the loop corrections influence the Yukawa couplings evaluated on the tree level and define corresp ondingly the differences in masses and mixing matrices. Many other not jet solved problems.

N.S. Manko Bor c stnik, Moscow 2009, 19-25 August The Approach unifying spins and charges