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MINIMALITY AND SUPERSYMMETRY -
DYNAMICAL SYMMETRY BREAKING THROUGH PREONS
J. Pati
To cite this version:
J. Pati. MINIMALITY AND SUPERSYMMETRY - DYNAMICAL SYMMETRY BREAK- ING THROUGH PREONS. Journal de Physique Colloques, 1982, 43 (C3), pp.C3-297-C3-302.
�10.1051/jphyscol:1982359�. �jpa-00221914�
MINIMALITY A N D SUPERSYMMETRY - D Y N A M I C A L S Y M M E T R Y B R E A K I N G T H R O U G H P R E O N S
J . C . P a t i
Department of P h y s i c s , U n i v e r s i t y o f Maryland, CoZZege Park, MD 20742, U . S.A.
I . I n t r a d u c t o r v Remarks: The h y p o t h e s i s of grand u n i f i c a t i o n s e r v i n g t o u n i f y a l l
" b a s i c " p a r t i c l e s - q u a r k s and l e p t o n s
-
and t h e i r f o r c e s-
weak, e l e c t r o m a g n e t i c a s w e l l a s s t r o n g-
s u g g e s t e d a l m o s t a decade-
s t i l l h o l d s i t s own a e s t h e t i ca p p e a l . I t g i v e s t h e f l a v o r of s y n t h e s i s i n t h a t i t p r o v i d e s a r a t i o n a l e f o r t h e e x i s t e n c e of q u a r k s and l e p t o n s by a s s i g n i n g t h e two s e t s of p a r t i c l e s t o o n e m u l t i - p l e t of a gauge symmetry G. I t d e r i v e s t h e i r f o r c e s through one p r i n c i p l e
-
gaugeu n i f i c a t i o n . And i t e x p l a i n s t h e q u a n t i z a t i o n of e l e c t r i c c h a r g e s . On t h e e x p e r i - m e n t a l f r o n t , i t i s s t r e n g t h e n e d by t h e o b s e r v e d v a l u e of s i n 2 e W . Furthermore, i t i s e s p e c i a l l y e x c i t i n g t h a t t h r e e c o n f i n e d e v e n t s w i t h v i s i b l e energy of a b o u t 1 GeV have b e e n r e p o r t e d a t t h i s c o n f e r e n c e by t h e K o l a r Gold F i e l d group; t h e s e e v e n t s a p p e a r t o b e s t r o n g c a n d i d a t e s f o r proton-decay; t h e y s u g g e s t a l i f e t i m e f o r t h e p r o t o n of about 7 x y e a r s . I f a l l t h i s i s f i r m l y e s t a b l i s h e d , i t w i l l g i v e a s t r o n g b o o s t t o t h e i d e a o f quark-lepton-unificationf and second i t would s e l e c t o u t a c l a s s of grand u n i f i c a t i o n - s y m m e t r i e s c h a r a c t e r i s e d by t h e p r e d i c t i o n s : s i n 2 e W 0 . 2 1 and T~ 1030+1.5 y e a r s . T h l s c l a s s would i n c l u d e SU(5), SO(10) and t h e "maximal" one-family-symmetry SU(16), w i t h t h e p r o v i s i o n t h a t t h e symmetry i n q u e s t i o n b r e a k s s p o n t a n e o u s l y i n o n e s t e p t o SU(2) x U(1) x S U ( ~ ) ' .
D e s p i t e t h e s e s u c c e s s e s , t h e p r a c t i c a l i m p l e m e n t a t i o n of t h e grand u n i f i c a t i o n h y p o t h e s i s r e q u i r e s , however, a n a r b i t r a r y p r o l i f e r a t i o n i n t h e c h o i c e of s p i n - 1 / 2 and spin-0 m a t t e r and what i s worse, i n t h e p a r a m e t e r s a s s o c i a t e d w i t h t h e spfn-0 H i g g s - s e c t o r . For t h e s e r e a s o n s , i t a p p e a r s d i f f i c u l t t o b e l i e v e t h a t a s t a n d a r d grand u n i f i c a t i o n - m o d e l (SU(5), SO(10) o r SU(16)) c a n b e p a r t of a fundamental t h e o r y w i t h t h e a s s o c i a t e d spin-112, s p i n - l & spin-0 m a t t e r a l l b e i n g e l e m e n t a r y .
I b e l i e v e t h a t a fundamental t h e o r y ought t o b e v i s i b l y economical i n i t s b u i l d - i n g b l o c k s
&
p a r a m e t e r s-
e q u a l l y i m p o r t a n t , i t s h o u l d b e somehow "unique." I n l i n e w i t h t h i s b e l i e f , i t seems i n e v i t a b l e t h a t q u a r k s , l e p t o n s , t h e a s s o c i a t e d Higgs and p e r h a p s even t h e gauge p a r t i c l e s ( i . e . W's, Z ' s , and g l u o n s , e t c . ) a r ecomposites of more e l e m e n t a r y o b j e c t s , which Salam and I c a l l "preons." The p r e o n s themselves may b e composites of s t i l l more e l e m e n t a r y o b j e c t s , which we c a l l "Pre- preons." T h i s c h a i n of i n c r e a s i n g e l e m e n t a r i t y must e n d , b u t n o t u n t i l one r e a c h e s a s t a g e , which i s m a n i f e s t l y minimal, e l e g a n t and "unique." One c o u l d c o n c e i v e of t h e p o s s i b i l i t y t h a t grand u n i f i c a t i o n through e.g. SU(16), SO(10) o r SU(5) emerges a s a n e f f e c t i v e gauge t h e o r y a t a composite l e v e l 4 from t h e u n d e r l y i n g minimal p r e o n i c o r p r e - p r e o n i c t h e o r y , w i t h t h e p a r a m e t e r s of t h e a s s o c i a t e d comuosite Higgs b e i n g determined i n t e r m s of t h o s e of t h e minimal u n d e r l y i n g t h e o r y . Such a n approach s h o u l d p r o v i d e a guidance on ( a ) t h e number of composite q u a r k - l e p t o n f a m i l i e s , which s h o u l d form and, (b) t h e p a t t e r n of spontaneous b r e a k i n g of t h e e f f e c t i v e grand u n i f y i n g symmetry t o b e e x p e c t e d . I t s h o u l d p r o v i d e a r e a s o n f o r t h e observed f e r m i o n mass-hierarchy ( i . e . me << m,, << q). I d e a l l y i t s h o u l d h e l p d e t e r m i n e o r a t l e a s t s u b s t a n t i a l l y r e d u c e t h e p a r a m e t e r s of t h e Fermi mass-matrix ( i . e . masses, Cabibbo-like a n g l e s and p h a s e a n g l e s ) . Such i s t h e n a t u r e of t h e g o a l and dream of a p r e o n i c t h e o r y .
11. M i n i m a l i t y and Supersymmetry: I n t h i s t a l k , I f i r s t c o n s i d e r t h e q u e s t i o n of m i n i m a l i t y a t a fundamental l e v e l . I p r e s e n t some p r e l i m i n a r y a t t e m p t s by Salam and myself5 i n a r r i v i n g a t a minimal system of fundamental s u b s t r u c t u r e s (pre-preons) which c o u l d g i v e r i s e t o p r e o n s of t h e flavon-chromon-type proposed some t i m e ago:6
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982359
JOURNAL DE PHYSIQUE
W i t h i n our a p p r o a c h , i n t h e i n t e r e s t of a c h i e v i n g economy i n b u i l d i n g b l o c k s and p a r a m e t e r s , we g i v e up t h e i d e a t h a t f l a v o r and c o l o r a r e b a s i c . They do n o t e x i s t , i n o u r view, even a s g l o b a l symmetries a t t h e b a s i c pre-preon o r pre-pre- preon l e v e l . They a r i s e d y n a m i c a l l y a s e f f e c t i v e symmetries i n t h e i r g l o b a l and s i m u l t a n e o u s l y l o c a l form o n l y a t a composite l e v e l . F l a v o r c o l o r gauge f o r c e s a r e t h u s viewed a s e f f e c t i v e r e s i d u a l f o r c e s 7 of t h e p r i m o r d i a l pre-preon-force, w i t h W , 2, g l u o n s e t c . b e i n g composites of s m a l l s i z e << ( 1 T ~ v ) - ~ ( i . e . t h e i r i n v e r s e s i z e s Mo z l / r o f a r exceeds t h e i r m a s s e s ) . One c a n a r g u e on c o n s i s t e n c y grounds t h a t t h e e f f e c t i v e i n t e r a c t i o n s of s u c h c o m p o s i t e s , a t low momenta << Mo, must b e d e s c r i b a b l e by a r e n o r m a l i z a b l e t h e o r y . I n t h e p r e s e n t c a s e , s u c h a t h e o r y must b e g i v e n by a Yang-?tills t h e o r y , which i s broken i f a t a l l , o n l y s p o n t a n e o u s l y .
The g e n e r a t i o n of m a s s l e s s spin-112 f e r m i o n s a s w e l l a s spin-0 and even s p i n - 1 b o s o n i c composites ( v i z . composites w i t h masses which a r e z e r o o r s m a l l compared t o t h e i r i n v e r s e s i z e s ) , we b e l i e v e , a r i s e s due t o t h e i n t e r p l a y of c h i r a l symmetry and extended supersymmetry, though a d e t a i l e d model of t h i s k i n d i s n o t y e t i n hand.
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The Po s i s t e n c y of t h e p i c t u r e o u t l i n e d above h a s b e e n d i s c u s s e d i n more d e t a i l elsewhere!" I n p a r t i c u l a r , n o t e t h a t t h e g e n e r a t i o n of m a s s l e s s s p i n - 1 composites s e r v i n g a s f l a v o r and color-gauge p a r t i c l e s does n o t i n any way c o n f l i c t w i t h t h e Weinberg-Witten c o n s t r a i n t , s i n c e i n our p i c t u r e t h e c o r r e s p o n d i n g g l o b a l symmetries a r e n o n - e x i s t e n t a t t h e u n d e r l y i n g l e v e l .
Our approach, t i e d t o t h e demand of m i n i m a l i t y , n a t u r a l l y s u g g e s t s t h e need f o r a c e r t a i n Fermi-Bose Symmetry a t t h e b a s i c preon o r pre-preon l e v e l . Consider t h e s i m p l e s t flavon-chromon,preonic modesG i n which q u a r k s and l e p t o n s . a r e compos- i t e s of spin-112 f l a v o n s ( f ; ) ~ , ~ = ( u , d ,
. .
.): and spin-0 chromons ( c i )*
=( r , y , b , l ,
. . f
i)*. Here "i" d e n o t e s r e p r e s e n t a t i o n - c o n t e n t w i t h r e g a r d t o t h e p r i m o r d i a l gauge symmetry; "a" and "a" d e n o t e f l a v o r and c o l o r - i n d i c e s r e s p e c t i v e l y . The f l a v o n s and chromons a p p e a r t o r e c e i v e t h e i r s i m p l e s t i n t e r p r e t a t i o n a s Fermi- Bose p a r t n e r s of a supersymmetric t h e o r y ; t h e emergence of t h e c o n c e p t s of f l a v o r and c o l o r , i n t h i s p i c t u r e , i s synonymous w i t h supersynrmetry-breaking. Ana l t e r n a t i v e p i c t u r e , i n which f l a v o n s and chromons a r i s e a s Fermi and Bose Compon- e n t s of d i f f e r e n t s u p e r f i e l d s and t h e r e b y p e r m i t t h e emergence of t h e c o n c e p t s of f l a v o r and c o l o r p r i o r t o supersymmetry-breaking, r e q u i r e s f o u r f l a v o n i c p l u s e i g h t chromonic s u p e r f i e l d s . We p r o p o s e minimal-pre-preon models w i t h Fermi and Bose- components ( b u t w i t h and w i t h o u t supersymmetry), which g i v e r i s e t o a d e s i r a b l e set of f l a v o n s and chromons a t a composite l e v e l . S t a r t i n g w i t h a s i m p l e p r e - p r e o n i c model, we o b t a i n t h r e e q u a r k - l e p t o n f a m i l i e s w i t h T b e i n g d i s t i n c t from e and p i n some of i t s i n t e r a c t i o n s . We s u g g e s t t h a t pre-preons a r e t h e n a t u r a l b u i l d i n g b l o c k s f o r supersymmetric Yang-Mills t h e o r i e s and o b s e r v e t h a t N=8 s u p e r g r a v i t y - t h e o r y may b e viewed a s a composite t h e o r y of p r e o n s b u i l t of s u c h pre-preons ( p a r t i c u l a r l y y i t h pre-preons b e l o n g i n g t o t h e f i n i t e N=4 supersymmetric Yang-1Iil.l~
t h e o r y ) . More d e t a i l s o n t h i s p a r t of my t a l k may be found i n Ref. 5. I now t u r n t o some remarks r e g a r d i n g t h e v i r t u e s of dynamical symmetry-breaking t h r o u g h p r e o n s . T h i s i n v o l v e s some work of mine t o b e p u b l i s h e d .
111. Dynamical Symmetry Breaking Through P r e o n s : There i s no q u e s t i o n t h a t t h e Higgs p a r t i c l e s
-
r e g a r d e d e l e m e n t a r y - a r e t h e most u n a e s t h e t i c components of a grand u n i f i e d t h e o r y i n t h a t t h e c h o i c e of t h e i r r e p r e s e n t a t i o n s , t h e i r masses and t h e i r q u a r t i c and Yukawa c o u p l i n g p a r a m e t e r s i s l a r g e l y a r b i t r a r y . The t e c h n i c o l o r h y p o t h e s i s 8 (TC) a t t e m p t s t o remove t h i s unwanted f e a t u r e and s i m u l t a n e o u s l y pro- v i d e a t e c h n i c a l l y " n a t u r a l " r e a s o n f o r t h e s c a l e of e l e c t r o w e a k symmetry-breaking t o b e around 112 TeV by assuming t h a t t h e r e l e v a n t Higgs p a r t i c l e s a r e composites of a new s e t of f e r m i o n s c a l l e d " t e c h n i f e r m i o n s " ( Q ' s ) , which p o s s e s s n o t o n l y t h e e l e c t r o w e a k gauge f o r c e of SU(Z)L x U(1) b u t a l s o a new QCD-like n o n a b e l i a n gauge f o r c e , c a l l e d " t e c h n i f o r c e " (FT) w i t h a s c a l e - p a r a m e t e r (AT) of o r d e r 1 TeV.R e a l i s t i c models of t e c h n i c o l o r a p p e a r t o s u f f e r , however, from a n e x c e s s i v e magnitude f o r f l a v o r changing n e u t r a l - c u r r e n t (FCNC) p r o c e s s e s
-
n o t t o mention t h e a r b i t r a r y p r o l i f e r a t i o n i n b u i l d i n g b l o c k s , which t h e y i n v a r i a b l y i n t r o d u c e . The d i f f i c u l t y w i t h r e g a r d t o FCNC-
p r o c e s s e s i s s k e t c h e d below.Under t h e i n f l u e n c e of FT, t h e t e c h n i q u a r k s a r e assumed t o form c o n d e n s a t e s i n p a i r s , w i t h a magnitude A ~ : <QQ> E h 3 f 0; r o u g h l y s p e a k i n g A i s g i v e n by t h e r e n o r m a l i z a t i o n s c a l e - p a r a m e t e r 9 AT of F
.
The f o r m a t i o n of t h e c o n d e n s a t e b r e a k s t h e f l a v o r gauge-
symmetry SU(Z)L x U(17 d n a m i c a l l.
From t h e mass of WL- t ( o r e q u i v a l e n t l y t h e observed v a l u e s of t h e F e A i c o u p l i z g c o n s t a n t and s i n 2 e W ) , o n e ,deduces A T ' - A 2 112 TeV. But a n o n v a n i s h i n g<Qn>
d o e s n o t n e c e s s a r i l y b r e a k c h i r a lsymmetry of o r d i n a r y f e r m i o n s
-
i . e . normal q u a r k s and l e p t o n s . To g i v e masses t o t h e l i g h t q u a r k s and l e p t o n s , one ends up i n t r o d u c i n g new extended t e c h n i c o l o r gauge i n t e r a c t i o n s (ETC), which c o u p l e l i g h t q u a r k s (and l e p t o n s ) t o t e c h n i f e r m i o n s( 4 ' s ) - Lhese g i v e r i s e , i n second o r d e r , t o a n e f f e c t i v e a m p l i t u d e of t h e t y p e gg (qq) (QQ)
1%.
2 where mE i s t h e mass of ETC-
ga g e bosons and g ~ t h e i r e f f e c t i v e c o u p l i n g-
c o n s t a n t . Wlth <QQ>[
A:'
(112 TeV)Y, gE 1 and m 5 HeV, 300 MeV and 1 0 GeV r e p r e s e n t i n g t y p i c a l average" mass of t h e e , p and ? - f a m i l i e s , we o b t a i n mE 1: 150 TeV, 20 TeV and 3 TeV f o r t h e e , p and T - f a m i l i e s r e s p e c t i v e l y . Taking a t y p i c a l ETC-
m u l t i p l e t (Ql, Q 2 ,---
QN, qd, q s ) , which i s c a p a b l e of giv- i n g d i a g o n a l a s w e l l a s Cabibbo-mixed n o n d i a g g n a l masses t o t h e (qd, qs) - system, we o b t a i n i n second o r d e r a n a m p l i t u d e-
g g r ( q d qs) (qs q d ) / m i t , where qd and qs d e n o t e c u r r e n t e i g e n - s t a t e s . Note t h a t t h i s a m p l i t u d e does n o t have a GIM-invari- enf form. E x p r e s s i n g (qd, qs) i n terms of t h e Cabibbo-rotated mass e i g e n - s t a t e s (qqi),
one, t h e r e f o r e , o b t a i n s from t h e above a m p l i t u d e a 1AS[ = 2-amplitude=
:;I
( q ~ q ~ ) 2 c o s 2 ~ c s i n 2 ~ C / m ~ t w i t h a magnitude M (112) (10-9 G ~ v - ~ ) f o r m ~ ' 1 20 TeV, gzlE2 1 and s i n 2 8 ,"
1 / 1 6 . T h i s i s a b o u t 1000 t i m e s b i g g e r t h a n t h a t p e r m i t t e d by t h e o b s e r v e d v a l u e of t h e E KL - KS m a s s - d i f f e r e n c e . G e n e r a t i o n of e x c e s s i v e FCNC-processes t h u s a p p e a r s t o b e one of t h e major d i f f i c u l t i e s of t e c h n i c o l o r models.It h a s a l r e a d y b e e n remarked1' t h a t p r e o n i c models, i n which, n o t o n l y Higgs b u t a l s o q u a r k s and l e p t o n s a r e composites of p r e o n s , s c o r e o v e r s t a n d a r d t e c h n i - c o l o r models a t l e a s t o n grounds of economy: t h e same o b j e c t s ( p r e o n s ) , which make q u a r k s and l e p t o n s , o r t h e i r s u i t a b l e c o m p o s i t e s , s e r v e a s t e c h n i f e r m i o n s ; w h i l e
t h e same f o r c e which b i n d s p r e o n s o r e f f e c t i v e r e s i d u a l f o r c e s g e n e r a t e d by t h e p r e o n i c b i n d i n g f o r c e s e r v e a s t h e t e c h n i f o r c e . No new i n g r e d i e n t s need t o b e p o s t u l a t e d . I now wish t o p o i n t o u t t h a t a c l a s s of p r e o n i c models have t h e added a d v a n t a g e t h a t t h e y p e r m i t t h e i m p l e m e n t a t i o n of dynamical symmetry-breaking with- o u t r u n n i n g i n t o t h e problem of FCNC - p r o c e s s e s . These c o n s i d e r a t i o n s l e a d u s t o p r e d i c t t h a t q u a r k s and l e p t o n s must h a v e a s i z e i n t h e r a n g e o f (3 t o 1 0 T ~ v ) - ~ .
We s h a l l i l l u s t r a t e t h e s e remarks i n t h e c o n t e x t of t h e s i m p l e s t v e r s i o n of t h e flavon-chromon preon-models mentioned b e f o r e , though t h e mechanism p r e s e n t e d h e r e f o r evading e x c e s s i v e FCNC-processes i s more g e n e r a l . I n t h e s e models,
q u a r k s and l e p t o n s a r e made of a s e t of spin-112 f l a v o r c a r r y i n g e n t i t i e s ( f p ) ) L , R
= ( u , d , c , s , - - - ) & i & c a l l e d " f l a v o n s " and a s e t of spin-o c o l o r c a r r y i n g e n t i t i e s c i i ) ( r , y ,b ,l;--I-) (i) c a l l e d "chromons". The s u p e r s c r i p t "in d e n o t e s e i t h e r t h e common c h a r g e of f l a v o n s and chromons w i t h r e s p e c t t o a n a b e l i a n p r i m o r d i a l f o r c e Fb, o r t h e r e p r e s e n t a t i o n of f l a v o n s and chromons w r t a n o n a b e l i a n p r i m o r d i a l f o r c e (Fb) g e n e r a t e d by a l o c a l gauge symmetry
%
l i k e SU(N). The composites fC*i d e n t i f i e d w i t h q u a r k s and l e p t o n s a r e s i n g l e t s of
(+,
= U ( l ) b o r SU(NIb.Assume a t a s e t of s p i n 112 f l a v o r c a r r i n e n t i t i e s $ L , R form c o n d e n s a t e s i n p a i r s (
<Z$iSp> H4
) under t h e i z f l z e n c e of a n a t t r a c t i v e f o r c e Yc.The condensing f e r m i o n s
f
s may b e t h e p r i m o d i a l f l a v o n s f ' s t h e m s e l v e s ; o r , a l t e r n a t i v e l y t h e y may b e s u i t a b l e composites of f ' s and a s e t of primed chromons ( c ' ) l l . The f o r c e Fc, which we s h a l l r e f e r t o a s t h e "condensing f o r c e " may i n g e n e r a l b e d i s t i n c t from t h e f o r c e Fb which b i n d s t h e c o n s t i t u e n t s of q u a r k s and l e p t o n s , though under c e r t a i n c i r c u m s t a n c e s Fc and Fb may b e o n e and t h e same f o r c e ( I f Fc 5 Fb, t h e s c a l e A of t h e c o n d e n s a t e and t h e i n v e r s e s i z e of t h e composites s h o u l d b e of t h e same o r d e r-
b u t t h e y n e d n o t b e e q u a l , s e e R e f . 1 2 ) . What concerns u s h e r e i s t h a t t h e c o n d e n s a t e<gLfi)
5%
b r e a k s t h e gauge symmetry SU(2)L x U(1). Using t h e s c a l e of WL - mass, A $=
112 TeV a s i n t h e TC-models.
L e t us examine how o r d i n a r y q u a r k s and l e p t o n s , which w e r e m a s s l e s s i n t h e l i m i t of SU(Z)L x U(1) and which a r e s i n g l e t s of b o t h t h e condensing f o r c e Fc and
JOURNAL DE PHYSIQUE
t h e b i n d i n g f o r c e Fb a c q u i r e mass. I f q u a r k s and l e p t o n s w e r e p o i n t p a r t i c l e s and were n o t l i n k e d e f f e c t i v e l y i n any way t o t h e condensing f e r m i o n s $ I s , t h e y would s t i l l remain m a s s l e s s . However, w i t h compo i e qu r k s , d e s p i t e t h e i r n e u t r a l i t y , t h e
G; qe -
p a i r c a n make a t r a n s i t i o n t oyc 9: -
p a i r u t i l i s i n g t h eb i n d i n g f o r c e c o n s i s t e n t w i t h a l l c o n s e r v a t i o n - laws; t h e a m p l i t u d e , we e x p e c t , would b e governed by t h e i n v e r s e s i z e A. of t h e r e l e v a n t q u a r k s . Here alb d e n o t e f a v o r - i n d i c e s . (qa qb) (
FL i f :
)/A;,+
h c , where T h i s would l e a d t o a n e f f e c t i v e i n t e r a c t i o nR
i s a n e f f e c t i v e c o u p l i n g c o n s t a n t"
o y o r d e r un!tyL T h ~ s g i v e s r i s e t o quark massm i
=(H
)(A! /A;). I f we s e tRq
= 1 and mq-
5 MeV, 300 MeV and 1 0 CeV f o r t y p i c a l avegage%ass of e ,u
and T - f a m i l y r e s p e c t i v e l y , we o b t a i n A, = 150 TeV, 20 TeV and 3 TeV r e p r e s e n t i n g t y p i c a l a v e r a g e i n v e r s e s i z e of e ,u
and T-fermions r e s p e c t i v e l y . So f a r t h e r e i s one-one c o r r e s - pondence between t h e p r e o n i c and t e c h n i c o l o r - a p p r o a c h e s e x c e p t t h a t t h e masses of t h e ETC gauge bosons a r e now r e p l a c e d by t h e i n v e r s e s i z e s o f t h e r e s p e c t i v e com- p o s i t e f e r m i o n s . The i n v e r s e s i z e s o f e , p and T f e r m i o n s have t u r n e d o u t t o b e d i f f e r e n t b e c a u s e of t h e assumption t h a t t h e s c a l e s of c o n d e n s a t e s( sk $&)
i n v o l v e d i n t h e g e n e r a t i o n of masses of e , and T a r e e q u a l . I t i s p e r f e c t l y p o s s i b l e , e s p e c i a l l y i n a p r e o n i c c o n t e x t , t h a t t h e i n v e r s e s i e s of e ,
u
and T a r e e q u a l , b u t t h e c o n d e n s a t e s< & &>
and< $&>
d i f f e r from each o t h e r by r a d i a t i v e f a c t o r s of o r d e r a d e s p i t e t h e condensxng f o r c e i n a l l t h r e e c h a n n e l s b e i n g t h e same.12F o r examining t h e s t r e n g t h of ] A S ] = 2 n e u t r a l c u r r e n t p r o c e s s e s , we s h a l l proceed by t a k i n g t h e i n v e r s e s i z e of t h e u-fermions t o b e around 1 0 t o 20 TeV, which i s what i s most r e l e v a n t f o r o u r purposes.
The mechanism f o r g e n e r a t i o n of quark-masses o u t l i n e d above p r o v i d e s d i a g o n a l masses ( f o r a = b ) , a s w e l l a s non-diagonal ones ( f o r a
#
b ) . For example t h ec o n d e n s a t e
<$d 9s)
would p r o v i d e Cabibbo mixing and t h e r e b y g e n e r a t e f a m i l i a r s t r a n g e n e s s changing charged current-weak i n t e r a c t i o n s . S i n c e t h e b i n d i n g f o r c e i s f l a v o r - i n d e p e n d e n t,
we e x p e c t< $ fs)
t o b e a t most of same o r d e r a s,
where A $ 2 112 TeV.<El it&
Now c o n s i d e r t h e a m p l i t u d e f o r t h e p r o c e s s : qd
+
qd + qS+
qs, which mani- f e s t l y l e a d s t o A s = 2 NC-processes even a f t e r Cablbbo-rotation. L e t u s r e c a l l t h a t each i n d i v i d u a l flavon-number ( l i k e w i s e chromon number) i s conserved by t h e p r i m o d i a l f o r c e . Now o b s e r v e t h a t i f t h e s t r a n g e q u a r k qs were j u s t a quantum-pair e x c i t a t i o n of t h e down quark qd, a s s u g g e s t e d by s e v e r a l a u t h o r s o n grounds of economy, o n e c o u l d e a s i l y e x c i t e a n e u t r a l p a i r through t h e e m i s s i o n of p r i m o d i a l g l u o n s by p r o b i n g i n s i d e t h e s i z e of q u a r k s (See F i g . 1 ) ; t h i s would i n d u c e t h ep r o c e s s qd
+
qd ++
qs w i t h n a m p l i t u d e of ' o r d e r ( 1 1 ~ 2 ) % 10-Is- 10-9 CeV-I, which i s t o ol a r g e t o b e c o m p a t i b l e w i t h KL
-
Ks mass d i f f e r -I f , on t h e o t h e r hand, qs d i f f e r s from qd by a n a t t r i b u t e , f o r example
-
by i t s f l a v o n - c o n t e n t w i t h s f d, t h e1
A S \ = 2 NC-process qd+
qd + qs+
qs c a n o s u r o n l y by u t i l i s i n g t h e I A s I = I -%
c o n d e n ~ a t e < $ ~ * ~ > , g e n e r a t e d n o n - p e r t u r b a - t i v e l y , t w i c e . The c o r r e s p o n d i n g a m p l i t u d e s h o u l d F i g . 1 t h e n b e p r o p o r t i o n a l t o A 6 From d i m e n s i o n a l6 c o n s i d e r a t i o n s , t h e ampli%e f o r q d + qd + (Is+
qs would t h e n - b e of o r d e r (A* /A:) which i s l e s s t h a n o r of o r d e r l n - I 5 G ~ V - 2 f o r A
=
112 TeV and A, 2 10-20 TeV. T h i s i s c e r t a i n l y s a f e f o r KL-
Ks mass d i f f e r -e k e .
L e t u s , t h e r e f o r e , t a k e d and s f l a v o n s t o b e d i s t i n c t . S t i l l , what a b o u t t h e A S 0
-
p r o c e s s qd+
qs + qd+
q s , i n v o l v i n g c u r r e n t q u a r k - f i e l d s , which i s what c a u s e s t h e problem f o r t e c h n i c o l o r models, s u b s e q u e n t t o C a b i b b o - r o t a t i o n ? Such a p r o c e s s c a n i n d e e d o c c u r w i t h i n o u r p r e z n i c model through t h e i n t e r m e d i a c y of p r i m o r d i a l g l u o n s ; s e e e.g. F i g . 2, where f u f C-
composite p l a y s t h e r o l e of t h e ETC gauge boson. S i n c e t h e p r i m o r d i a l f o r c e 1s i n v a r i ~ n t under r o t a t i o n s i n t h e( e , p)
-
f l a v o r - s p a c e however, t h e above ampli- t u d e i s q e c e s s a r _ i l y p a r t of a GIN-
i n v a r i a n t form a (q q+
q qs)? w h i c h - a r i s e s v i a G I Md d . s
i n v a r i a n t p r e o n l c a m p l i t u d e ( f d f d
+ Ts
f s ) 2 . T h i s i s what makes t h e combined s e t of p r o c e s s e s( i ) 9d + q s + qd + qs, ( i i ) 4d + qd + 9d + 4d and ( i i i ) qs
+
qs + qs+
qs s a f e w r t Cabibbo--
r o t a t i o n w i t h i n t h e c l a s s of p r e o n i c models pre- s e n t e d h e r e . Note t h a t t h e a n a l o g of GIN-
i n v a r - i a n c e i s n o n - e x i s t e n t f o r t h e h i t h e r t o-
proposedF i g . 2 ETC models.
To summarise, we s e e t h a t t h e n o t i o n of dynamical symmetry b r e a k i n g can l i v e f r u i t f u l l y through p r e o n s w i t h o u t e n c o u n t e r i n g t h e problem of FCNC
-
p r o c e s s e s . B e l i e v i n g i n DSB, t h i s a p p e a s t o c a l l f o r a need f o r P r e o n s . Our mechanism t o a v o i d FCPJC-
p r o c e s s e s i n t h e c o n t e x t of DSB i s more g e n e r a l t h a n t h e p r e o n i c model c o n s i d e r e d h e r e . Two i n g r e d i e n t s a r e e s s e n t i a l : F i r s t , t h e muon-
f a m i l y must d i f f e r from t h e e l e c t r o n-
f a m i l y i n r e s p e c t of some a t t r i b u t e s ( 1 i k e ( c , s ) (u,d)).[ T h i s i n c i d e n t a l l y l e a v e s t h e door open t h a t T may e i t h e r b e a quantum p a i r
-
e x c i t - a t i o n of e o r p o r t h a t i t t o o many h a v e i t s own d i s t i n c t i v e a t t r i b u t e . It w i l l b e w o r t h w h i l e t o s t u d y T + ey and py - b r a n c h i n g r a t i o s up t o a l e v e l of a b o u t 10-6 t o judge on t h i s i s s u e ] . Second, t h e p r e o n i c dynamics must l e a d t o a GIM-invariant form f o r four-quark t r a n s i t i o n s . One consequence of r e a l i s i n g DSB through p r e o n s i s t h a t i n v e r s e s i z e s of q u a r k s and l e p t o n s o r e f f e c t i v e masses of some of t h e c o n s t i t u e n t s ( l i k e t h e chromons) must b e i n t h e r a n g e of few t o 1 0 ~ e ~ 1 3 . T h i s g e n e r a t e s e x c i t i n g new p o s s i b i l i t i e s f o r a c c e l e r a t o r s of t h e n e x t two d e c a d e s . REFERENCES AND FOOTNOTES1. J. C. P a t i and Abdus Salam, P r o c . B a t a v i a Conf. Vol. 2, p. 304, S e p t . 1972 ( r e p o r t e d by J . D. B j o r k e n ) ; Phys. Rev. D
3,
1240 (1973); Phys. Rev. D10,
275 (1974); Phys. L e t t .s,
333 (1975); J . C. P a t i , Abdus Salam and J . S t r a t h d e e , I1 Nuovo C i m .a,
77 (1975); Nucl.Phys. Bm, 445 (1981).2. H. Georgi and S. L. Glashow, Phys. Rev. L e t t . 32, 438 (1974).
3. H . G e o r g i , H. Quinn and S. Weinberg, Phys. Rev. L e t t .
33,
451 (1974).4. I n t h i s c a s e , i n o r d e r t h a t t h e s t a n d a r d a p p l i c a t i o n s of RGE f o r r u n n i n g c o u p l i n g c o n s t a n t s and t h e r e f o r e t h e s t a n d a r d p r e d i c t i o n s f o r grand u n i f i c a t i o n mass M, s i n 2 e W and proton-decay, s h o u l d h o l d , d e s p i t e t h e composite-natur of t h e e f f e c t i v e t h e o r y , t h e gauge p a r t i c l e s s h o u l d h a v e i n v e r s e s i z e s < M z 10'' GeV.
However, t h e composite f e r m i o n s ( i . e . q u a r k s and l e p t o n s ) , which do n o t c o n t r i b u t e anyway i n t h e l e a d i n g o r d e r t o t h e r e l e v a n t d i f f e r e n c e - e q u a t i o n s , c a n h a v e i n v e r s e s i z e s a s s m a l l a s few TeV ( s e e remarks l a t e r ) . Some of t h e Higgs p a r t i c l e s may a l s o have s i m i l a r " l a r g e " s i z e s .
5. J. C. P a t i and Abdus Salam, T r i e s t e P r e p r i n t IC/82/89 ( J u l y , 1982).
6. J . C. P a t i and Abdus Salam, Phys. Rev. D l O , 275 (1974); P r o c . Palermo Conf.
J u n e 1975, P. 171; J. C. P a t i , Abdus Salam, and J . S t r a t h d e e , Phys. L e t t .
z,
265 (1975).
7. J . C. P a t i , Proc. Grand Unif. Workshop, E r i c e , Plarch 1980, P. 267; Phys. L e t t . 90B 40 (1981); Proc. N e u t r i n o Conf. J u n e 1980, P. 275; J. C. P a t i , Abdus Salam and
-
J . S t r a t h d e e , Nuc. Phys. Bm,416 (1981).8. See e . g . E. F a r h i and L. S u s s k i n d , Phys. Rep. ( 1 9 8 1 ) f o r a r e v i e w and r e l e v a n t r e f e r e n c e s
.
9. A s i n QCD, by d e f i n i t i o n , A i s t h a t s c a l e of momentum f o r which t h e e f f e c t i v e t e c h n i c o l o r c o u p l i n g c o n s t a n t (:$!4n) i s u n i t y .
1 0 . J . C. P a t i (Ref. 7 ) ; H. H a r a r l , SLAC summer s c h o o l l e c t u r e s (1981); E. F a r h i and L. S u s s k i n d (Ref. 8)
.
11. I f t h e b a s i c c o l o r gauge symmetry a t p r e o n i c l e v e i s s a y Sl&f)C d e f i n e d i n t h e s p a c e of e i g h t chromons ~ 2 ' ) = ( r , y , b , l ; r ' , y l , l ' , l ' ) t i ) , SU(8) could b r e a k through c c ~ k >
-
c o n d e n s a t e f o r v e d bv t h e p r i m o d i a l b i n d i n g f o r c e Fb a c t l n g o n t h e i n d e x i t o S U ( ~ ) x ~ ~ ( 4 1 x U(1) ; S U ( ~x S U ( ~ ) c o u l d b r e a k hrough ) ~ ~ ~ ~ a d d i i t o n a l c o n d e n s a t e s l i k e <fRfRC*C*> t o u ( l T x x ~ ~ ( 3 ) c o l , w h i l e SU(4)C0f c o u l d remain unbroken and p r o v i d e a new e f f e c t i v e h y p e r c o l o r f o r c e w i t h a s c a l e - p a r a m e t e r A c t >> (Ac)QCD. The condensing f e r m i o n s&'
s could b e composites of ( f c ' ),
whichJOURNAL DE PHYSIQUE
a r e n e u t r a l w i t h r e s p e c t t o t h e b i n d i n g f o r c e Fb, b u t n o n - n e u t r a l w r t b o t h f l a v o r and SIT(^)''. I n t h i s c a s e t h e condensing f o r c e could b e p r o v i d e d by S U ( ~ ) ~ ' . With flavon-chromon-preons b e i n g composites of pre-preons ( s e e e a r l i e r d i s c u s s i o n ) , we would, of c o u r s e , i n t e r p r e t t h e e n t i r e S U ( ~ ) c o l gauge-force a s a n e f f e c t i v e r e s i d u a l f o r c e , g e n e r a t e d a t t h e l e v e l of composite p r e o n s , from a n u n d e r l y i n g pre- p r e o n i c p r i m o r d i a l f o r c e .
12. Drawing t h e a n a l o g y between composite Kiggs-mechanism and condensate-formation, Miriam C v e t i c and I h a v e r e c e n t l y showncto b e p u b l i s h e d ) t h a t t h e e f f e c t i v e p o t e n t i a l V(9e.9v,9T) c a n p e r m i t t h e s o l u t i o n
<4,>
0 with'<.$,> ( 4 > = 0 a t t r e e - l e v e l ; t h e one l o o p r a d i a t i v e c o r r e c t i o n s c a n i n d u c e < + > = ( g . ( ~ , ) < ~ $ ~ ) > w i t h <$,> s t i l l z e r o . These r e s u l t s f o l l o w d e s p i t e t h e e ++ p ++ !J T d i s c r e t e symmetry of t h e e f f e c t i v e p o t e n t i a l V. I n s u c h a p i c t u r e , w i t h <$,> b e i n g t h e d r i v i n g c o n d e n s a t e , we would e x p e c t , on t h e b a s i s of d i s c u s s i o n s i n t h e t e x t , t h a t t h e e , !J&
Tf e r m i o n s
-
a l l h a v e a n i n v e r s e s i z e of o r d e r 3 TeV, which i s only a f a c t o r of 6 b i g g e r t h a n A 9-
112 TeV. I n t h i s c a s e , i t becomes p o s s i b l e t o imagine t h a t t h e condensing f o r c e Fc and t h e p r e o n b i n d i n g f o r c e Fb b i n d i n g p r e o n s t o make q u a r k s and l e p t o n s a r e o n e and t h e same f o r c e .1 3 . Note t h a t s u c h " l a r g e ? s i z e s f o r q u a r k s and l e p t o n s may s t i l l b e c o m p a t i b l e w i t h t h e emergence of a n e f f e c t i v e grand u n i f i e d t h e o r y w i t h composite gauge bosons having i n v e r s e s i z e s > 1014 GeV ( s e e remarks i n Ref. 4 ) . An u n d e r l y i n g model, which c o u l d g i v e f l a v o r - c o l o r gauge bosons of s m a l l s i z e , b u t composite q u a r k s and l e p t o n s of much l a r g e r s i z e , i s t h e flavon-chromon-somen model ( s e e Ref. 7) w i t h , f o r example, f , C and S b e l o n g i n g t o r e p r e s e n t a t i o n s (nl, n;, I ) , ( 1 , n2, n;) and (n* 1, n3) of a l o c a l gau symmetry SU(nl) x SU(n2) x SU(n3), w i t h A1 and A3
