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Submitted on 1 Jan 1982
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H. Georgi
To cite this version:
H. Georgi. GRAND UNIFICATION. Journal de Physique Colloques, 1982, 43 (C3), pp.C3-705-C3-
721. �10.1051/jphyscol:1982384�. �jpa-00221940�
JOURNAL DE PHYSIQUE
CoZZoque C3, suppzdrnent a u n o 12, Tome 43, ddcernbre 1982 page C3-705
G R A N D UNIFICATION
H. G e o r g i
Department of P h y s i c s , Lyman Laboratory o f P h y s i c s , Harvard U n i v e r s i t y , hl.4 02138, U.S.A.
Today I w i l l t a l k a b o u t t h e p r o g r e s s t h a t h a s b e e n made i n t h e l a s t y e a r o r two i n u n i f y i n g t h e i n t e r a c t i o n s o f p h y s i c s . The s h o r t summary i s t h a t t h e r e h a s n ' t b e e n a n y . T h i s i s a f i e l d which i s s t r a n g l i n g f o r want o f e x p e r i m e n t a l i n p u t . But some t h i n g s h a v e h a p p e n e d . I f we h a v e n ' t made p r o g r e s s , we h a v e a t l e a s t l e a r n e d a t h i n g o r two. And who knows, t h e y may t u r n o u t t o b e u s e f u l when e x p e r i m e n t d o e s f i n a l l y p o i n t u s i n t h e r i g h t d i r e c t i o n .
UNIFICATION OF OBSERVED INTERACTIONS
L e t me b e g i n by b r i e f l y d i s c u s s i n g t h e u n i f i c a t i o n o f t h e o b s e r v e d ( o r a l m o s t o b s e r v e d ) S U ( 3 ) xSU(2) x U ( 1 ) gauge i n t e r a c t i o n s . N o t h i n g r e v o l u t i o n a r y h a s
happened l a t e l y , w h i c h is n o t s u r p r i s i n g s i n c e t h e m a i n t h e o r e t i c a l i d e a s h a v e been i n p l a c e f o r 8 But t h e r e h a s b e e n some e v o l u t i o n i n o u r i d e a s . The most i n t e r e s t i n g r e c e n t d e v e l o p m e n t s h a v e b e e n i n t h e p r e d i c t i o n s o f s i n 2 OW a n d o f t h e p r o t o n d e c a y r a t e . The p r e d i c t i o n o f s i n 2
eW
i n t h e s i m p l e s t SU(5) model h a s now b e e n r e f i n e d a b o u t a s f a r a s i t i s w o r t h r e f i n i n g i t . 2 And i t a g r e e s p e r f e c t l y w i t h t h e d a t a . At t h i s p o i n t , improvement i n t h e d a t a would b e m o s t welcome.The s i t u a t i o n w i t h r e s p e c t t o p r o t o n d e c a y i s more i n t e r e s t i n g . On t h e t h e o r e t i c a l s i d e , two t h i n g s have happened. One i s t h a t t h e e x p e r i m e n t a l d e t e r - m i n a t i o n o f A h a s e v o l v e d . As David P o l i t z e r w i l l d i s c u s s i n t h e n e x t t a l k , t h e
QCD
b e s t ( o r a t l e a s t t h e c u r r e n t f a v o r i t e ) v a l u e o f A i s s o m e t h i n g l i k e 1 5 0 M e V , down a f a c t o r o f two o r more from e a r l i e r e s t i m a t e s .
The s e c o n d d e v e l o p m e n t i s a n improvement i n t h e q u a r k model e s t i m a t e s o f t h e s t r o n g i n t e r a c t i o n m a t r i x e l e m e n t s i n v o l v e d i n t h e p r o t o n d e c a y p r o c e s s . I t h a s b e e n f o u n d 3 t h a t t h e t h r e e - q u a r k f u s i o n p r o c e s s , o r t h e p o l e d i a g r a m c a n n o t b e i g n o r e d . The i n c l u s i o n o f t h i s e f f e c t b r i n g s t h e q u a r k model r e s u l t s i n t o a g r e e - ment w i t h r e s u l t s from complementary a p p r o a c h e s ( s u c h a s c u r r e n t a l g e b r a ) .
But b o t h t h e c h a n g e i n A a n d t h e e x t r a d i a g r a m have t h e e f f e c t o f i n c r e a s i n g QCD
t h e p r e d i c t e d p r o t o n d e c a y r a t e i n a n y g i v e n model. I n t h e s i m p l e s t SU(5) model, t h i s b r i n g s t h e p r e d i c t i o n t o t h e v e r y e d g e of d i s a g r e e m e n t w i t h t h e p r e s e n t e x p e r i - m e n t a l bound. On t h e o t h e r hand, t h e r e a r e " c a n d i d a t e " n u c l e o n d e c a y e v e n t s from t h e K o l a r Gold F i e l d a n d NUSEX
group^.^
T h i s is v e r y e x c i t i n g . E i t h e r we w i l l s e e more s o o n , o r t h e s i m p l e s t ( a n d t h u s o n e o f t h e most a t t r a c t i v e ) GUTS w i l l b e r u l e dArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982384
out.
SU(5) VERSUS SO(10)
Alas, it doesn't take much of a modification of the simplest GUT to drasti- cally increase the uncertainty in the prediction of the proton decay rate. In SU(5), many more light fermions would increase the lifetime (although one extra family doesn't do,much). After SU(5), the next simplest GUT is based on an SO(10) gauge group. In SU(5), the unification scale is unique, because there is no larger subgroup of SU(5) that contains SU(3) xSU(2) xU(1). But in S0(10), there are many possible routes from the full SO(10) symmetry to SU(3) xSU(2) xU(1). Some of them involve several different scales and many more parameters than in SU(5) (see Table 1). In this theory (or perhaps I should say "set of theories") it is easy to change the proton decay rate prediction by a factor of almost 10 3
.
Let's hope that Nature is Simple.TABLE 1 SO(10) Breakdown Schemes
+ SU(3) x SU(2) x U(1) = H
+ SU(5) + H
+ SU(5)' x U(l)(anti SU(5)) + H
-.
SO(6) x SU(2) x U(1) + HRef. T -P
There has'also been a development in technical quantum field theory which has potentially extremely important application to GUTS. This is the suggestion by Rubakov and Callan (and the related work by Wilczek) that SU(5) monopoles may catalyze baryon number violating processes with a typical strong interaction cross section.* I say "potentially important" only because I do not fully understand the argument. If it is correct, it is certainly one of the most exciting ideas to come along in some time.
THE GRAND MYSTERIES
There may be good reasons to embellish the simple SU(5) GUT. Although the SU(3) xSU(2) xU(1) interactions of quarks and leptons fit into SU(5) like the proverbial hand into a (fivc fingered) glove, this unification does little to demystify two old puzzles: hierarchy and flavor. The large scales, the Planck
H. G e o r g i
mass
%
and t h e g r a n d u n i f i c a t i o n s c a l e MG a r e s o much l a r g e r t h a n t h e s m a l l s c a l e s Mu, AQCD and q u a r k and l e p t o n masses--the hand is a t t h e end o f a v e r y , v e r y l o n g arm. And why is ttgere more t h a n one g e n e r a t i o n of q u a r k s and l e p t o n s ? I s n ' t one hand enough?Some t h i n g s g e t l e s s m y s t e r i o u s w i t h t i m e , s i m p l y b e c a u s e we g e t u s e d t o them.
We have grown accustomed t o r e n o r m a l i z a t i o n , c o n f i n e m e n t , e v e n income t a x l a w s . But h i e r a r c h y and f l a v o r seem more m y s t e r i o u s a s t i m e p a s s e s , b e c a u s e o u r a t t e m p t s t o u n d e r s t a n d them d o n ' t seem t o l e a d anywhere.
UNIFICATION OF IMAGINED INTERACTIONS
Here I w i l l d i s c u s s t h r e e t y p e s of unobserved i n t e r a c t i o n s which, i f t h e y e x i s t , might h e l p u n r a v e l t h e s e p u z z l e s : T e c h n i c o l o r , Supersymmetry and Family Symmetry. A l l o f t h e s e s u b j e c t s go f a r beyond g r a n d u n i f i c a t i o n , b u t I w i l l t a l k o n l y a b o u t t h o s e a s p e c t s which impinge on GUTS and t h e h i e r a r c h y and f l a v o r p u z z l e s .
T e c h n i c o l o r and Supersymmetry might a d d r e s s t h e h i e r a r c h y p u z z l e w h i l e Family Symmetry may have s o m e t h i n g t o d o w i t h f l a v o r .
TECHNICOLOR
I t is e a s y t o u n d e r s t a n d why M
>>%
i f t h e W mass i s due t o d y n a m i c a l b r e a k i n g of t h e SU(2) x U ( 1 ) symmetry. I f t h e r e i s a t e c h n i c o l o r (TC) i n t e r a c t i o n of ( a s y e t u n o b s e r v e d ) t e c h n i f e r m i o n s . weak a t MG, M may be -eATC/sin8 where ATC i s t h eW
a n a l o g o f A f o r t h e t e c h n i c o l o r i n t e r a ~ t i o n . ~ T h i s i s a u t o m a t i c a l l y exponen- OCD
t i a l l y s m a l l compared t o MG. T h i s k i n d of d y n a m i c a l mechanism f o r b r e a k i n g S U ( 2 ) x U ( l ) a l m o s t s u r e l y makes s e n s e , b e c a u s e i t i s based o n a s i m p l e and d i r e c t a n a l o g y w i t h c h i r a l symmetry b r e a k i n g i n QCD. I t i s v e r y s i m p l e and e l e g a n t . And i t r e q u i r e s no f u n d a m e n t a l Higgs mesons w i t h m a s s e s l e s s t h a n M T h i s i s impor-
G '
c a n t , b e c a u s e i n o r d i n a r y quantum f i e l d t h e o r i e s , i t t a k e s one u n n a t u r a l f i n e t u n i n g f o r e a c h Higgs m u l t i p l e t t h a t must be k e p t l i g h t . The t r o u b l e w i t h TC i s t h a t by i t s e l f , i t c a n n o t g i v e q u a r k and l e p t o n m a s s e s . T h e r e must be o t h e r i n t e r a c t i o n s , c a l l e d e x t e n d e d t e c h n i c o l o r , ETC, which c o u p l e q u a r k s and l e p t o n s t o t e c h n i - fermions.1° Of c o u r s e , i f TC is embedded i n a GUT, t h e r e
are
o t h e r i n t e r a c t i o n s . But s i n c e t h e s e a r e i n t e r a c t i o n s w i t h p a r t i c l e s of mass "M i f TC i s a s y m p t o t i c a l l yG '
f r e e (AF), t h e y d o n ' t do much. I t would seem t h a t t h e r e a r e f o u r p o s s i b i l i t i e s f o r implementing ETC:
( a ) Have s p i n l e s s b o s o n s w i t h a mass *METC n o t much l a r g e r t h a n A ' TC' (b) Have gauge bosons w i t h a mass -M ETC
. '
( c ) Give up t h e a s y m p t o t i c freedom o f TC and push up METC;
( d ) Rely on i n t e r a c t i o n s a t MG.
I t i s e a s y t o c o n s t r u c t r e a l i s t i c models i n ( a ) , b u t t h i s p o s s i b i l i t y i s v e r y u n a t t r a c t i v e b e c a u s e i t r e q u i r e s f i n e t u n i n g s t o keep t h e s p i n l e s s bosons l i g h t . The most of t h e m o t i v a t i o n f o r TC i s l o s t .
( b ) i s t h e c l a s s i c ETC i d e a . It r e q u i r e s no l i g h t s c a l a r s . I t i s v e r y a m b i t i o u s . A s u c c e s s f u l g r a n d u n i f i e d ETC scheme would d e s c r i b e a l l of low e n e r g y p a r t i c l e p h y s i c s i n t e r n s of a s m a l l number of gauge c o u p l i n g c o n s t a n t s . The problem i s t h a t i t i s h a r d , and p e r h a p s i m p o s s i b l e , t o g e t enough s t r u c t u r e . And t h e r e a r e phenomenological d i f f i c u l t i e s . G e n e r a l a r g u m e n t s ( s u p p o r t e d by t o y examples) s u g g e s t t h a t t h e s e ETC models w i l l have p o t e n t i a l l y s e r i o u s f l a v o r c h a n g i n g n e u t r a l c u r r e n t i n t e r a c t i o n s . l1 Not much h a s happened r e c e n t l y t o s u g g e s t t h a t t h e s e d i f f i c u l t i e s c a n b e overcome w i t h AF TC.
( c ) h a s i t s r o o t s i n Holdom's comment t h a t i f t h e TC t h e o r y were a c o n f i n i n g phase of a non AF t h e o r y w i t h a n o n t r i v i a l u l t r a v i o l e t f i x e d p o i n t (UVFP),
t h e %TC s c a l e c o u l d be r a i s e d and t h e phenomenological problems w i t h ETC c o r r e s p o n d i n g l y a l l a y e d . 1 2 But i t i s s t i l l h a r d t o b u i l d r e a l i s t i c models. ( d ) is t h e s u g g e s t i o n by Glashow and m e . t h a t i f we c o u l d r a i s e M t o MG, we w o u l d n ' t need ETC i n t h e
ETC
u s u a l s e n s e a t a l l , b u t c o u l d u s e t h e heavy s p i n l e s s mesons which a l w a y s a p p e a r i n GUTS t o p r o d u c e q u a r k and l e p t o n mass.13 I a n MacArthur and I t h e n found a p l a u s i b l e dynamical scheme t h a t c o u l d g i v e t h e r i g h t p h y s i c s . 14 B r i e f l y , t h e i d e a i s i n t h e c o n f i n i n g p h a s e , a TC t h e o r y w i t h a n o n t r i v i a l UVFP might be e q u i v a l e n t t o a n AF e f f e c t i v e TC (eTC) t h e o r y w i t h f u n d a m e n t a l Higgs s c a l a r s c o u p l e d t o t h e t e c h n i - f e r m i o n s . I n t h i s e f f e c t i v e t h e o r y , t h e s c a l a r would b e l i g h t f o r d y n a m i c a l r e a s o n s . Assuming t h a t t h i s i d e a i s c o r r e c t , I was a b l e t o c o n s t r u c t a r e a l i s t i c GUT based o n a n SO(10) 5 symmetry. 15
U n f o r t u n a t e l y , w h i l e t h i s r e a l i z a t i o n of t h e eTC i d e a h a s some i n t e r e s t i n g f e a t u r e s , 1 6 i t seems u n r e a s o n a b l y c o m p l i c a t e d and c o n t r i v e d . Even i f eTC works j u s t a s I e x p e c t , i t seems h a r d t o b u i l d a c o m p e l l i n g model.17 Something i s o b v i o u s l y s t i l l m i s s i n g . But t h e TC d i r e c t i o n i s n o t ( I t h i n k ) r u l e d o u t e n t i r e l y . It i s s t i l l a n a t t r a c t i v e i d e a , and t e c h n i f e m i o n s s h o u l d b e one of t h e p r i m a r y q u a r r i e s f o r t h e f u t u r e g e n e r a t i o n of a c c e l e r a t o r s .
SUPERSYMMETRY
Supersymmetry (SS) h a s been d i s c u s s e d e x t e n s i v e l y i n t h e p a r a l l e l s e s s i o n d e v o t e d t o i t and i n F a y e t ' s t a l k . Here I w i l l d i s c u s s o n l y a v e r y s p e c i f i c a p p l i - c a t i o n o f supersymmetry, t o t h e h i e r a r c h y p u z z l e i n GUTS.
One c a n imagine v a r i o u s ways i n which supersymmetry m i g h t s o l v e t h e f i n e t u n i n g problem o f k e e p i n g Higgs d o u b l e t s much l i g h t e r t h a n t h e u n i f i c a t i o n s c a l e . The s i m p l e s t and l e a s t s u b t l e p o s s i b i l i t y i s t o have t h e f e n n i o n s u p e r p a r t n e r s of t h e Higgs c a r r y a n unbroken c h i r a l symmetry. But i t i s a l . s o p o s s i b l e t o make u s e o f s o c a l l e d " s u p e r m i r a c l e s " ( w h i c h F a y e t c a l l e d n o n r e n o r m a l i z a t i o n t h e o r e m s ) . I f t h e Higgs d o u b l e t i s m a s s l e s s i n t r e e a p p r o x i m a t i o n , i t s t a y s m a s s l e s s u n t i l t h e s u p e r - symmetry i s broken. Thus a l l we need do i s t o a v o i d f i n e t u n i n g i n t h e t r e e ap- p r o x i m a t i o n . 1 8 T h i s c a n be done i n s e v e r a l ways. 1 9 , 2 0
I t i s n o t s o o b v i o u s how SS c a n h e l p w i t h t h e e x p l a n a t i o n o f t h e l a r g e r a t i o of
H . Georgi
MG t o
\.
At f i i - s t it was hoped t h a t TC and SS could be combined i n t o " s u p e r c o l o r " . Dimopoulos and Raby and Dine, F i s c h l e r and S r e d n i c k i c o n s t r u c t e d models i n which t h e y hoped t h a t t h e small s c a l e would be produced by t h e d y n a a i c a l breaking o f supersymmetry. 2 1There a r e arguments which suggest t h a t t h i s kind o f dynamical S S breaking w i l l not work." But W i t t e n has i n v e n t e d another way o f g e t t i n g a l a r g e h i e r a r c h y . 2 3 Introduce t h e small s c a l e e x p l i c i t l y i n an O I R a i f e a r t a i g h model which spontaneously b r e a k s S S a t -1 TeV, b u t i n such a way t h a t t h e l a r g e s c a l e i s c o m p l e t e l y u n d e t e r - mined i n t r e e approximation. W i t t e n showed t h a t r a d i a t i v e c o r r e c t i o n s can produce an e x p o n e n t i a l l y l a r g e vacuum e x p e c t a t i o n v a l u e (VEV). T h i s i s t h e so c a l l e d
" i n v e r t e d " or "backwards" h i e r a r c h y i n which t h e small s c a l e i s fundamental and t h e l a r g e s c a l e i s dynamically induced.
There a r e s e v e r a l p r a c t i c a l d i f f i c u l t i e s w i t h t h e i n v e r t e d h i e r a r c h y . One must be c a r e f u l n o t t o break t h e gauge symmetry a t t h e l a r g e s c a l e down beyond
SU(3) x S U ( 2 ) x U ( 1 ) . T h i s i s not t r i v i a l because t h e l a r g e s c a l e symmetry breakdown i s d r i v e n by t h e symmetry breaking a t 1 TeV which r e s p e c t s o n l y SU(3) x U ( 1 ) . There i s a tendency f o r S S breaking i n t h e s e t h e o r i e s t o " d e c o u p l e " , which means t h a t o n l y t h e v e r y h e a v y , mass -M p a r t i c l e s f e l l S S breaking i n t r e e approximation. The
G'
e f f e c t s o f supersymmetry breaking on l i g h t p a r t i c l e s i s s u p p r e s s e d , o f o r d e r
V M G . Then t h e s u p e r p a r t n e r s o f t h e observed p a r t i c l e s a r e n o t s u f f i c i e n t l y heavy t o have escaped d e t e c t i o n . F i n a l l y , thr.re a r e o f t e n many l i g h t s u p e r m u l t i p l e t s i n such t h e o r i e s , o f t e n so many t h a t t h e gauge c o u p l i n g s g e t v e r y l a r g e b e f o r e u n i f i c a t i o n .
The f i r s t two o f t h e s e problems are e l i m i n a t e d i f t h e S S breaking s c a l e i s p "
q.
I n s u c h a so-called geometric h i e r a r c h y model, decoupling i s a v i r t u e , because t h e e f f e c t o f S S breaking on t h e l i g h t p a r t i c l e s i s o f o r d e r U 2 / M G-
M W'S t i l l , d e s p i t e some c l e v e r model b u i l d i n g by Dimopoulos and ~ a bno t o t a l l y ~ , ~ ~ s a t i s f a c t o r y backwards geometric h i e r a r c h y model has been c o n s t r u c t e d . T h i s i s b a s i c a l l y because spontaneous supersymmetry breaking i s v e r y cumbersome.
Sakai and Dimopoulos and I two years ago demonstrated t h a t i t i s e a s y t o b u i l d r e a l i s t i c GUTS i n which t h e S S i s s o f t l y broken a t 1 T ~ v . ' ~ These e a r l y e f f o r t s d i d not address t h e q u e s t i o n o f t h e l a r g e s c a l e d i f f e r e n c e . But i n t h e l a s t few w e e k s , Dimopoulos and I have disoovered t h a t an i n v e r t e d h i e r a r c h y can be d r i v e n by
s o f t S S breaking a t 1 TeV .26 The i d e a i s t h a t i f t h e supersymmetric vacuum has d e g e n e r a c i e s a s s o c i a t e d w i t h s c a l e t r a n s f o r m a t i o n s , t h e s o f t SS breaking terms can d e s t a b i l i z e t h e vacuum, l e a d i n g t o a t r e e approximation Hamiltonian which i s unbounded below. C l a s s i c a l l y t h e r e a r e tachyons and t h e t h e o r y i s s i c k . Quantum c o r r e c t i o n s ( p r o p o r t i o n a l t c t h e s o f t b r e a k i n g ) can r e s t a b i l i z e t h e vacuum f o r l a r g e v a l u e s o f t h e VEVs, t h u s r e s u s c i t a t i n g t h e c l a s s i c a l l y s i c k t h e o r y . Amazingly enough, t h i s e f f e c t , which we c a l l QMR, f o r "quantum mechanical r e s u s c i t a t i o n " , c a n a l l happen i n t h e regime o f v a l i d i t y o f p e r t u r b a t i o n t h e o r y .
I t i s s t r a i g h t f o r w a r d t o c o n s t r u c t r e a l i s t i c models based on t h i s i d e a
Dimopoulos d e s c r i b e d two t y p e s i n h i s t a l k i n t h e p a r a l l e l s e s s i o n on U n i f i e d Gauge T h e o r i e s . N e i t h e r r e q u i r e s a n y f i n e t u n i n g o f p a r a m e t e r s o f o r d e r M The
G'
o n l y u n n a t u r a l n e s s i n v o l v e s l o w e n e r g y p a r a m e t e r s . When we b r e a k t h e SS s o f t l y , we must t a k e c a r e t o p r e s e r v e a s u p e r GLM mechanism, f o r e x a m p l e by a d d i n g t h e same s o f t b r e a k i n g t e r m s f o r e a c h f a m i l y of q u a r k s a n d l e p t o n s . The p r o b l e m w i t h t h i s i s t h a t i t i s n o t n a t u r a l i n t h e m o d e l s we h a v e c o n s t r u c t e d . T h e s o f t b r e a k i n g t e r m s a r e r e n o r m a l i z e d d i f f e r e n t l y . But we e x p e c t t h a t t h i s e m b a r r a s s m e n t c a n b e a v o i d e d i n m o d e l s i n w h i c h m u l t i p l e f a m i l i e s a p p e a r n a t u r a l l y .
So f a r , I h a v e n ' t m e n t i o n e d g r a v i t y . T h a t ' s b e c a u s e i t i s b e s t t o t h i n k a b o u t i n v e r t e d h i e r a r c h i e s w h i l e s t a n d i n g o n y o u r h e a d , which is easier i f you t u r n o f f g r a v i t y . But t h e r e i s a p h i l o s o p h i c a l p r o b l e m h e r e . I n a TC m o d e l , i t may make s e n s e t o i g n o r e g r a v i t y .
5
i s b i g g e r t h a n t h e f u n d a m e n t a l s c a l e M b u t n o t s oG '
much b i g g e r t h a t t h e r a t i o %/MG i s e m b a r r a s s i n g l y l a r g e . But i f t h e s m a l l s c a l e
%
( o r t h e g e o m e t r i c s c a l e p) is f u n d a m e n t a l a s i n a n i n v e r t e d h i e r a r c h y , a n d M i s G d y n a m i c a l l y i n d u c e d , t h e n u n l e s s M p i s a l s o d y n a m i c a l l y i n d u c e d , t h e r e i s s t i l l a h i e r a r c h y p u z z l e . Why isMp
>>\? T h u s we s h o u l d r e a l l y b u i l d i n v e r t e d h i e r a r c h y m o d e l s i n which g r a v i t y i s i n c l u d e d , a n d M a n d M a r e n e c e s s a r i l y a b o u t e q u a l .P G
T h e s e w o r d s a r e s p o k e n t r i p p i n g l y o n t h e t o n g u e . But i t i s n o t s o e a s y t o a s s i g n them a n y meaning.
It may b e i n t e r e s t i n g t o n o t e , however, t h a t t h e i n v e r t e d h i e r a r c h y m o d e l s do n o t seem t o s u f f e r f r o m t h e c o s m o l o g i c a l p r o b l e m p o i n t e d o u t by ~ e i n b e r g . ~ ' He f o u n d t h a t t e r m s i n t h e e f f e c t i v e p o t e n t i a l i n d u c e d b y g r a v i t y a n d p r o p o r t i o n a l t o t h e s u p e r p o t e n t i a l t e n d t o d r i v e t h e t h e o r y i n t o t h e wrong vacuum. B u t i n
c l a s s i c a l l y s c a l e i n v a r i a n t s u p e r s y m m e t r i c t h e o r i e s , t h e s u p e r p o t e n t i a l v a n i s h e s f o r a l l v a c u a . T h a t is p r o b a b l y e n o u g h t o e l i m i n a t e , t h e p r o b l e m .
T h e r e i s a r i g h t - s i d e - u p a p p r o a c h t o t h e h i e r a r c h y p u z z l e i n a SS t h e o r y , i n w h i c h t h e r a t i o
% / M ~
is j u s t a l a r g e power o f a s m a l l c o u p l i n g c o n s t a n t . 28 The i d e a i s t o b r e a k SS a t MG, b u t a r r a n g e t h e t h e o r y s o t h a t SS p e r c o l a t e s i n t o t h e i n t e r e s t i n g s e c t o r s of t h e t h e o r y o n l y i n h i g h o r d e r p r o c e s s e s .The o r i g i n a l SU(5) model i s s o s i m p l e a n d e l e g a n t t h a t it h a s t o b e r i g h t - - a t l e a s t p a r t o f t h e t r u t h . I t h o u g h t s o e i g h t y e a r s a g o when I f i r s t w r o t e i t down, and I s t i l l t h i n k s o t o d a y . None o f t h e s o l u t i o n s I h a v e d i s c u s s e d t o t h e h i e r a r c h y p u z z l e h a v e t h a t c h a r a c t e r . But t h a t d o e s n ' t mean t h a t t h e y a r e a l l wrong. J u s t t h a t we d o n ' t h a v e e n o u g h o f t h e p i c t u r e t o s e e i t c l e a r l y . We n e e d some g u i d a n c e from e x p e r i m e n t . Where s h o u l d we l o o k ? A l l t h e s e m o d e l s p r e d i c t new t y p e s of h e a v y e l e m e n t a r y p a r t i c l e s i n t h e TeV r e g i o n . I t seems i m p o s s i b l e t o g e t a n a t u r a l h i e r a r c h y w i t h o u t them. E v e n t u a l l y , t h i s w i l l b e v e r y i n t e r e s t i n g . But p r o b a b l y o f more i m m e d i a t e i n t e r e s t i s t h e d i f f e r e n t p r e d i c t i o n s o f t h e s e m o d e l s f o r p r o t o n d e c a y .
T h e r e a r e n o r e a l e x a m p l e s o f ETC GUTS, b u t i n my SO(10) 5 ETC m o d e l , p r o t o n d e c a y i s s i m i l a r t o t h a t i n t h e s i m p l e s t SU(5) model.
H . Georgi
The supersymmetric models are very d i f f e r e n t . The u n i f i c a t i o n s c a l e M i n S S G GUTS i s t y p i c a l l y l a r g e r by an order o f magnitude or so than t h e s c a l e i n an analogous non S S t h e o r y . The d i f f e r e n c e i s t h e l i g h t gauge f e r m i o n s , which
decrease t h e r a t e a t which t h e S U ( 3 ) , SU(2) and U ( 1 ) coupling c o n s t a n t s converge. 2 9 The old M could be restored i f a pair charge ' 1 , SU(2) xSU(3) s i n g l e t super-
G
m u l t i p l e t s remain l i g h t below nF.30 but 1 cannot t h i n k o f 9 reason why t h i s should occur. Thus I expect t h a t i f supersymmetry i s unbroken below M t h e u s u a l
G' gauge boson exchange c o n t r i b u t i o n w i l l be so suppressed as t o b e i n a c c e s s i b l e e x p e r i m e n t a l l y (and t h e r e f o r e b o r i n g ) . For example, i n t h e SU(6) model b u i l t by Dimopoulos and me, t h e proton l i f e t i m e i s something l i k e years.
Two t h i n g s can happen t c change t h i s p i c t u r e . Supersymmetric t h e o r i e s can v i o l a t e baryon number i n a d i f f e r e n t way, so t h a t t h e proton l i f e t i m e i s propor- t i o n a l t o o n l y two powers o f M G , not f o u r as i n t h e nonsupersymmetric SU(5) model.31 The d i f f e r e n c e i s t h e e x i s t e n c e o f s c a l a r partners o f t h e l i g h t p a r t i c l e s which a l l o w s baryon number v i o l a t i n g dimension 5 o p e r a t o r s i n t h e e f f e c t i v e low energy t h e o r y . These can lead t o proton decay i n t o K+; (and N-tK 0- V) a t an
observable r a t e i n some t h e o r i e s . 3 2 T h i s d o e s n ' t happen, however, i n t h e o r i e s ( l i k e t h e SU(6) model above) i n which t h e Higgs doublet s u p e r m u l t i p l e t s a r e l i g h t because t h e y carry a c h i r a l symmetry which i s unbroken a t M
G'
In t h e i n t e r m e d i a t e s c a l e backwards hierarchy model o f Dimopoulos and Raby, proton decay occurs due t o scalar boson exchange.24 T h i s i s much more important
( i n t h i s model) than gauge boson exchange because t h e color t r i p l e t s c a l a r s i n t h e 5 and
5
get a mass o f t h e order o f t h e i n t e r m e d i a t e s c a l e , r a t h e r than M G . Scalar+-
0+
t r i p l e t exchange causes proton decay primarily i n t o K
v
o r K p,
because t h e!J Higgs m u l t i p l e t s couple more t o heavier p a r t i c l e s .
0
+
Thus i f proton decay i s seen w i t h ~r e as t h e primary decay mode, i t i s reasonable t o assume t h a t supersymmetry ( i f i t i s r e l e v a n t a t a l l ) i s broken a t M
G or M
.
On t h e o t h e r hand, i f t h e l i m i t on t h e proton l i f e t i m e i s pushed beyond 1033Pyears or s o , or i f t h e r a t e i s years and t h e dominant modes i n v o l v e K ' s , t h e n some form o f low energy supersymmetry may be t h e most reasonable e x p l a n a t i o n . I should s t r e s s t h a t i n none o f t h e s e models i s t h e r e a f i r m p r e d i c t i o n f o r TP '
A l l o f them have many more parameters which go i n t o T than simple S U ( 5 ) .
P
FAMILY SYMMETRY
The f a m i l y p u z z l e , a t l e a s t t o me, i s even more mysterious than t h e hierarchy p u z z l e . Here many i d e a s have been t r i e d , some o f which seemed q u i t e c l e v e r and i n t e r e s t i n g a t t h e o u t s e t . But none o f them have led anywhere, or a t l e a s t not t o anything we can recognize a s progress without more experimental guidance.
S t i l l i t may be u s e f u l t o recount here t h i s f r u s t r a t i n g h i s t o r y . Some o f i t may even be r i g h t , f o r reasons which we dc not yet see c l e a r l y . At any r a t e , i t may serve t o s t e e r people away from s t a l e , f l a t and u n p r o f i t a b l e d i r e c t i o n s .
I s h o u l d s a y t h a t t h e r e i s o n e f a s h i o n a b l e a p p r o a c h t o t h e f l a v o r p u z z l e t h a t I w i l l n o t d i s c u s s - - t h e n o t i o n of c o m p o s i t e q u a r k s and l e p t o n s . I won't t a l k a b o u t i t h e r e b e c a u s e i t d o e s n ' t seem t o have much t o d o w i t h u n i f i c a t i o n ( i n d e e d , many of t h e s e models undo e v e n t h e p a r t i a l u n i f i c a t i o n of SU(2) x U ( 1 ) ) . F o r what i t i s w o r t h , though, I t h i n k t h a t s e n s i b l e models of t h i s kind33 w i l l n o t l e a d t o any r e a l improvement i n o u r u n d e r s t a n d i n g of f l a v o r , b e c a u s e t h e y w i l l b e a t l e a s t a s c o m p l i c a t e d and a r b i t r a r y a s t h e m u l t i p l e f a m i l i e s t h e y s e e k t o e x p l a i n .
I w i l l o r g a n i z e t h e d i s c u s s i o n o f a p p r o a c h e s t o t h e f a m i l y q u e s t i o n i n t h r e e broad c a t e g o r i e s : D i s c r e t e u n i f i c a t i o n , u n i t a r y u n i f i c a t i o n and o r t h o g o n a l u n i f i c a t i o n . A l l of t h e schemes t h a t I d i s c u s s w i l l i n v o l v e complex r e p r e s e n t a - t i o n s o f t h e u n i f y i n g group. Only i f t h e r e p r e s e n t a t i o n o f t h e Weyl f e r m i o n s i s complex c a n t h e gauge i n t e r a c t i o n s n a t u r a l l y d i s t i n g u i s h f e r m i o n s w i t h V-A
i n t e r a c t i o n s from t h o s e w i t h V+A weak i n t e r a c t i o n s . A l l t h e q u a r k s and l e p t o n s we have s e e n s o f a r a r e c l e a r l y V-A. Some w o r k e r s , s u c h a s P a t i , Salam, and
S t r a t h d e e , b u i l d models which have r e a l r e p r e s e n t a t i o n s , s o t h a t t h e y h a v e " m i r r o r f e r m i o n s " w i t h t h e wrong h a n d e d n e s s f o r t h e weak
interaction^.^^
T h i st e c h n i c a l l y p o s s i b l e . But i f i t i s r i g h t , t h e n n a t u r e h a s been d e l i b e r a t e l y mis- l e a d i n g u s i n e x p o s i n g o n l y t h o s e q u a r k s and l e p t o n s w i t h V-A weak i n t e r a c t i o n s .
The p r i m a r y enemy of any d e e p u n d e r s t a n d i n g of f l a v o r s i s t h e Glashow, I l i o p o u l o s , M a i a n i (GIM) mechanism. 35 T h i s w o n d e r f u l mechanism f o r s u p p r e s s i n g f l a v o r c h a n g i n g n e u t r a l c u r r e n t e f f e c t s works when t h e g a u g e i n t e r a c t i o n s a c t t h e same way o n e a c h f a m i l y . Of c o u r s e a t low e n e r g i e s , t h i s seems t o b e t h e c a s e . The SU(3) xSU(2) x U ( 1 ) gauge i n t e r a c t i o n s do n o t d i s t i n g u i s h between t h e d i f f e r e n t f a m i l i e s . I f , on t h e o t h e r hand, t h e r e a r e a d d i t i o n a l gauge i n t e r a c t i o n s which a c t d i f f e r e n t l y o n t h e d i f f e r e n t f a m i l i e s , t h e f a m i l y p u z z l e w i l l b e a l o t l e s s
p u z z l i n g . I t is t h e g a u g e symmetries a s s o c i a t e d w i t h t h e s e h y p o t h e t i c a l gauge i n t e r a c t i o n s t h a t I r e f e r t o a s f a m i l y symmetry.
The r o l e of t h e s e i n t e r a c t i o n s i s t o e l i m i n a t e t h e G I M mechanism and d i s t i n - g u i s h t h e d i f f e r e n t f a m i l i e s . It f o l l o w s t h a t t h e y p r o d u c e f l a v o r c h a n g i n g n e u t r a l c u r r e n t e f f e c t s . We know t h a t t h e s e e f f e c t s a r e v e r y weak, and t h u s we know t h a t t h e f a m i l y s y m m e t r i e s ( i f t h e y e x i s t ) a r e b r o k e n a t an e n e r g y h i g h e r t h a n t h e 300 GeV of SU(2) x U ( 1 ) b r e a k i n g . How much h i g h e r we d o n o t know. I f t h e
f a m i l y s y m m e t r i e s a r e broken a t M t h e y a r e n o t v e r y i n t e r e s t i n g p h e n o m e n o l o g i c a l l y . G '
But i t i s p o s s i b l e t h a t t h e y p e r s i s t down t o l o w e r e n e r g i e s , i n which c a s e t h e y may p r o d u c e o b s e r v a b l e f l a v o r c h a n g i n g n e u t r a l c u r r e n t e f f e c t s . E x p e r i m e n t s t o s e e r a r e decay modes produced by s u c h i n t e r a c t i o n s must n o t be f o r g o t t e n i n o u r r u s h t o
- +
h i g h e r e n e r g y and more e x o t i c p r o c e s s e s . The d i s c o v e r y ( f o r example) of KL->lJ e would b e j u s t a s i m p o r t a n t a s ( s a y )
N-N
m i x i n g . And I t h i n k t h a t t h e f o r m e r i s much more l i k e l y t o e x i s t a t a n o b s e r v a b l e r a t e .0 n e . v e r y amusing s u g g e s t i o n i s t h a t t h e o b s e r v e d CP v i o l a t i o n i n t h e K meson system may a r i s e from s u c h G I M v i o l a t i n g
interaction^.^^
T h i s g i v e s a much more n e a r l y superweak t h e o r y of CP v i o l a t i o n t h a n t h e s t a n d a r d s i x q u a r k SU(2) x U ( 1 )H. G e o r g i
model. F o r example, f a i l u r e t o o b s e r v e E ' / E a t t h e l e v e l p r e d i c t e d by Gilman a n d might c o n s t i t u t e e v i d e n c e f o r new i n t e r a c t i o n s o f t h i s k i n d .
DISCRFPE UNIFICATION
Here t h e i d e a is t h a t t h e r e may b e a f a m i l y symmetry g r o u p w i t h t h e same s t r u c t u r e a s t h e o r d i n a r y u n i f y i n g g r o u p , f o r example SU(5), and t h a t t h e f u l l symmetry i s a p r o d u c t of t h e two w i t h a d i s c r e t e symmetry u n d e r w h i c h t h e f a c t o r s a r e i n t e r c h a n g e d . A s i m p l e example i s a f i v e f a m i l y model i n which t h e LH
f e r m i o n s t r a n s f o r m u n d e r SU(5) x SU(5) l i k e ( 1 0 , 5 ) + ( 5 , 1 0 ) + ( 5 , 5 ) , where t h e f i r s t f a c t o r i s o r d i n a r y SU(5) and t h e s e c o n d i s a " f a m i l y SU(5)". T h i s i s t y p i c a l of s u c h models i n t h a t i t h a s f e r m i o n s , i n t h i s c a s e f i v e 5 ' s a n d f i v e 5 ' s which g e t a n SU(3) x S U ( 2 ) x U ( 1 ) i n v a r i a n t mass o f t h e o r d e r of t h e f a m i l y symmetry b r e a k i n g s c a l e , Only t h e f i v e 1 0 ' s and f i v e o f t h e
5's
s u r v i v e below M t o form f i v eF o r d i n a r y f a m i l i e s w i t h V-A weak i n t e r a c t i o n s .
Ramond h a s had some f u n i m a g i n i n g what h a p p e n s i f some of t h e "heavy" p a r t i - c l e s w i t h mass o f o r d e r
%
a r e a c t u a l l y l i g h t f o r d y n a m i c a l o r j u s t p l a i n a c c i - d e n t a l r e a s o n s . 3 8 F o r example, t h e SU(2) d o u b l e t s i n t h e heavy 5 ' s a r e r e a l l y s p l i t e l e c t r o m a g n e t i c a l l y .UNITARY FLAVOR UNIFICATION
I t is a l s o p o s s i b l e t o embed b o t h SU(5) a n d f a m i l y symmetry i n t o a s i n g l e s i m p l e u n i t a r y group.39 An example is my SU(11) model i n which
- - -
SU(11) +SU(5) x S U ( ~and t h e LH f e r m i o n s a r e 330 + I 6 5 + 5 5 ) ~ ~ ~ ~ ~ ~ +11 ( t h e s e a r e SU(11) t e n s o r s w i t h 4 u p p e r i n d i c e s and 3 , 2 a n d 1 l o w e r i n d i c e s r e s p e c t i v e l y ) . When the d u s t s e t t l e s i n t h i s model, t h e r e a r e t h r e e normal f a m i l i e s p l u s heavy s t u f f . Of c o u r s e , t h e r e
2
a l o t of d u s t . So much t h a t some of t h e f a m i l ysymmetry must b e b r o k e n a t v e r y h i g h e n e r g y , a t o r n e a r MG, t o p r e v e n t t h e o r d i n a r y c o u p l i n g c o n s t a n t s from g e t t i n g l a r g e b e f o r e u n i f i c a t i o n .
D i s c r e t e and u n i t a r y u n i f i c a t i o n a r e amusing n u m e r o l o g i c a l games. But t h e r e i s o b v i o u s l y s o m e t h i n g m i s s i n g . T h e r e i s j u s t no c o m p e l l i n g r e a s o n t o p r e f e r a n y one o f t h e s e m o d e l s o v e r a l l t h e o t h e r s . But t h a t c o u l d change. F o r example, we m i g h t f i n d some t h e o r e t i c a l c o n t e x t i n which some p a r t i c u l a r t y p e of r e p r e s e n t a t i o n l o o k s e s p e c i a l l y a p p e a l i n g . At a n y r a t e , k e e p l o o k i n g f o r t h o s e r a r e d e c a y modes. The GLM mechanism is bound t o b r e a k dcwn. The o n l y q u e s t i o n i s "Where?" and "How Much?"
ORTHOGONAL UNIFICATION
The l a s t u n i f i c a t i o n of f a m i l y symmetry t h a t I w i l l d i s c u s s i s b a s e d on t h e s i m p l e s t and most a p p e a l i n g i d e a : t h a t a l l t h e f e r m i o n s m i g h t b e d e s c r i b e d by a s i n g l e s p i n o r r e p r e s e n t a t i o n (SR) of a n o r t h o g o n a l g r o u p . T h i s s o u n d s g r e a t
i n i t i a l l y , s i n c e a s i n g l e f a m i l y f i t s w e l l i n t o t h e 1 6 d i m e n s i o n a l SR o f s ) ( 1 0 ) . And t h e SRs o f t h e l a r g e r o r t h o g o n a l s a r e b u i l t o u t o f c o p i e s o f SRs o f s m a l l e r o n e s . I t i s n o t s o s i m p l e t h o u g h , b e c a u s e a l l l a r g e r o r t h o g o n a l g r o u p s h a v e a s many
16's
as 1 6 ' s i n t h e i r SRs, a n d t h u s a s many q u a r k s a n d l e p t o n s w i t h V+A weaki n t e r a c t i o n s a s w i t h V-A weak i n t e r a c t i o n s . U n l e s s we want t o d e g e n e r a t e t o a m i r r o r f e r m i o n scheme, we need s o m e t h i n g t o d i s t i n g u i s h t h e two. T h i s i s p o s s i b l e f o r S0(4n+2) w h i c h h a s complex SRs. The o b v i o u s p o s s i b i l i t y i s t e c h n i c o l o r . F o r e x a m p l e , t e c h n i c o l o r SU(2) c a n b e embedded i n SO(14) s o t h a t t h e SR c o n s i s t s o f two n o r m a l f a m i l i e s and a t e c h n i c o l o r d o u b l e t of V+A f a m i l i e s . T h i s is t h e F a r h i - S u s s k i n d model.40 H e r e t h e TC i s no good f o r s o l v i n g t h e h i e r a r c h y p u z z l e b e c a u s e i t i s n o t s u f f i c i e n t l y AF.
4 1 The SO(18) SR c a n g i v e t h r e e n o r m a l f a m i l i e s w i t h a t e c h n i c o l o r S 0 ( 5 ) ( = S p ( 4 ) ) . A l a s , t h e r e a r e s o many f e r m i o n s i n t h e SR ( 8 V-A and 8 V+A f a m i l i e s ) t h a t t h e g a u g e c o u p l i n g s g e t v e r y l a r g e b e f o r e u n i f i c a t i o n . P e r t u r b a t i v e u n i f i c a t i o n is l o s t a n d t h e a p p a r e n t s u c c e s s o f t h e s i n 2 OW p r e d i c t i o n would h a v e t o b e r e g a r d e d a s a c c i d e n t a l . S t i l l , t h i s model i s a p p e a l i n g . No d o u b t , t h e r e w i l l b e f u r t h e r a t t e m p t s t o make i t work.
L a r g e r u n i t a r y g r o u p s a r e e v e n w o r s e . The t r o u b l e i s t h a t o n l y t h e S0(4n+2) g r o u p s h a v e complex SRs, and when n i n c r e a s e s b y 1, t h e s i z e o f t h e SR i n c r e a s e s by a f a c t o r of 4. They g e t w o r s e e x p o n e n t i a l l y .
FUNNY CHARGES
A l l t h e e x t r a g a u g e s y m m e t r i e s I h a v e d i s c u s s e d s o f a r h a v e b e e n t r i v i a l e x t e n s i o n s o f SU(5) i n t h e s e n s e t h a t a l l o f t h e l o w e n e r g y SU(3) x S U ( 2 ) x U ( 1 ) r e s i d e d i n t h e SU(5) s u b g r o u p . But l o t s more b i z a r r e e m b e d d i n g s of SU(3) x S U ( 2 ) x U(1) a r e p o s s i b l e . I n g e n e r a l , i f you d o s o m e t h i n g b i z a r r e , you g e t a t h e o r y t h a t d o e s n ' t make s e n s e b e c a u s e y o u r f e r m i o n s a r e n o t e v e n r e a l u n d e r SU(3) x U ( 1 ) . T h i s mucks up QED a n d QCD. But t h e SRs o f t h e S0(4n+2) g r o u p s a r e a l m o s t r e a l , and i t i s v e r y e a s y t o make i t work. To me, t h e m o s t a m u s i n g e x a m p l e o f a n o n t r i v i a l
embedding i s Kim's SO(14) ( o r SU(7)) I n t h e s i n g l e SR i n Kim's model, t h e r e a r e two n o r m a l V-A f a m i l i e s b u t t h e two V+A f a m i l i e s a r e d i s p l a c e d by o n e u n i t i n c h a r g e i n o p p o s i t e d i r e c t i o n s . T h i s p r o d u c e s a n o t h e r l e p t o n d o u b l e t w i t h n o r m a l V-A i n t e r a c t i o n s b e c a u s e o n e o f t h e V+A l e p t o n d o u h l e t w i t h f u n n y c h a r g e c a n b e r e i n t e r p r e t e d as a n a n t i l e p t o n d o u b l e t . Thus t h e r e i s room i n t h e m o d e l f o r t h e T, a s w e l l a s f o r t h e e and t h e U. V e r y c l e v e r !
The f u n n y c h a r g e s a l s o muck up c o u p l i n g c o n s t a n t r e n o r m a l i z a t i o n . To g e t a n a c c e p t a b l e s i n 2 OW, you m u s t p r e s e r v e a n SU(4) xSU(3) s u b g r o u p u n b r o k e n down t o low e n e r g i e s . A l l of what e v e n t u a l l y becomes e l e c t r i c c h a r g e r e s i d e s i n t h i s semi- s i m p l e SU(4) x S U ( 3 ) s u b g r o u p . T h u s t h e m o n o p o l e s i n t h i s m o d e l a r e l i g h t . T h i s i s a n o t h e r a m u s i n g f e a t u r e o f t h e m o d e l .
A l a s , t h e K i m model w i t h a s i n g l e SR i s a l r e a d y r u l e d o u t by e x p e r i m e n t . The
H. G e o r g i
b q u a r k i n t h i s model i s p e c u l i a r . I t i s ( a t l e a s t ) p r i m a r i l y p a r t o f a V+A SU(2) d o u b l e t w i t h c h a r g e s -113 and -413. Manohar h a s shokm t h a t d a t a on b d e c a y from CESR, t o g e t h e r w i t h what we know from c o u p l i n g c o n s t a n t r e n o r m a l i z a t i o n and t h e s t a b i l i t y of t h e p r o t o n , is n o t c o n s i s t e n t w i t h t h e Of c o u r s e , one c o u l d a l w a y s u s e two SR's i n s t e a d o f o n e , b u t t h e n you g i v e up t h e n i c e s t f e a t u r e , s o why b o t h e r .
F i n a l l y , I w i l l m e n t i o n a p e c u l i a r v a r i a n t o f t h e Kim model proposed t o a c c o u n t f o r t h e a l l e g e d o b s e r v a t i o n o f f r a c t i o n a l l y c h a r g e d p a r t i c l e s . 4 4 I n t h e SR of S 0 ( 1 4 ) , one c a n d i s p l a c e t h e V+A f a m i l i e s by a n '113 u n i t o f c h a r g e , p r o d u c i n g a h o s t of c o l o r l e s s p a r t i c l e s w i t h c h a r g e s '213, '113, e t c . Goldberg h a s worked o u t a n e n t e r t a i n i n g c o s m o l o g i c a l and a s t r o p h y s i c a l s c e n a r i o i n which t h e s e f r a c t i o n a l l y c h a r g e d p a r t i c l e s a n n i h i l a t e i n e a r l y s u p e r n o v a e enough t o be p r e s e n t t o d a y o n l y i n t h e v e r y s m a l l c o n c e n t r a t i o n which may have been o b s e r v e d . 4 5
F i n a l l y , l e t me n o t e t h a t by e n l a r g i n g t h e low e n e r g y symmetry g r o u p t o c o n t a i n a n e x t r a unbroken U(1) f a c t o r , s o t h a t t h e r e i s a funny photon which d o e s n o t c o u p l e t o normal m a t t e r , one c a n b u i l d o r t h o g o n a l u n i f i c a t i o n s which
s i m u l t a n e o u s l y d e s c r i b e f r a c t i o n a l l y c h a r g e d c o l o r s i n g l e t p a r t i c l e s m a g n e t i c monopoles w i t h D i r a c ' s v a l u e f o r t h e m a g n e t i c c h a r g e . 4 6
INVISIBLE AXIONS
I n e x t t u r n t o t h e h i s t o r y o f a n odd c h a p t e r i n p a r t i c l e t h e o r y : t h e s t o r y of t h e I n v i s i b l e Axion. The a x i o n was a n a t t r a c t i v e s o l u t i o n t o t h e p u z z l e o f why CP v i o l a t i o n i n QCD is s o s m a l l . The i d e a was t o b u i l d a t h e o r y i n which a l l t h e i n t e r a c t i o n s i n t h e SU(3) xSU(2) x U ( 1 ) t h e o r y e x c e p t QCD i n s t a n t o n e f f e c t s had a Peccei-Quinn (PQ) symmetry which changed t h e p h a s e of t h e d e t e r m i n a n t o f t h e q u a r k mass m a t r i x . 4 7 Then t h e r e i s a pseudo-Goldstone b o s o n , (PGB) t h e a ~ i o n . ~ ~ The VEV
of t h e a x i o n a d j u s t s i t s e l f t o make t h e s t r o n g CP v i o l a t i o n s m a l l .
T r o u b l e was t h e a x i o n w a s n ' t t h e r e . I f i t had been a PGB a s s o c i a t e d w i t h SU(2) x U ( 1 ) b r e a k i n g , a s o r i g i n a l l y p r e d i c t e d , i t s h o u l d h a v e had i n t e r a c t i o n s s u p p r e s s e d by a p p r o p r i a t e powers of G and s h o u l d have shown up i n v a r i o u s
F' e x p e r i m e n t s .
These e x p e r i m e n t a l d i f f i c u l t i e s c a n be a v o i d e d i f t h e a x i o n i s a s s o c i a t e d w i t h a h i g h e r symmetry b r e a k i n g s c a l e , b e c a u s e i t s c o u p l i n g s would b e weaker. 49,50
But l o t s of p e o p l e r e a l i z e d t h a t i n t h e c o n t e x t of SU(3) x S U ( 2 ) x U ( 1 ) , Kim's s o l u t i o n was r e a l l y j u s t t r a d i n g o n e problem f o r a n o t h e r . The VEV which b r e a k s t h e PQ symmetry had t o be l a r g e r t h a n 10' GeV t o a v o i d problems w i t h a x i o n e m i s s i o n from t h e c o r e s of h o t s t a r s . 5 1 But t h e n t h e l a r g e s c a l e i s s o much l a r g e r t h a n
%
t h a t t h e r e i s a h i e r a r c h y . But when t h e i d e a i s a d a p t e d t o GUTS i t r e a l l y l o o k s n i c e , b e c a u s e t h e PQ symmetry c a n be broken a t t h e GUT s c a l e which i s known t o be l a r g e anyway. T h i s g i v e s t h e i n v i s i b l e a x i o n : w i t h c o u p l i n g s s u p p r e s s e d by powers of MC, i t c a n ' t be s e e n i n any c o n v e n t i o n a l p a r t i c l e p h y s i c s e x p e r i m e n t s . 50.52
The
PQ symmetry c a n be imposed by hand, b u t i t i s a l s o p o s s i b l e t o c o n s t r u c t t h e o r i e s i n which t h e PQ symmetry i s " a u t o m a t i c " i n t h e s e n s e t h a t i t f o l l o w s from t h e gauge s t r u c t u r e and r e n o r m a l i z a b i l i t y of t h e t h e o r y . 5 3
The i n v i s i b l e a x i o n i s a n t i p h y s i c s , i n a way, b e c a u s e you c a n ' t s e e i t d i r e c t l y . I t is, t h e r e f o r e , n o t t o o d i s a p p o i n t i n g t h a t t h e r e a r e c o s m o l o g i c a l d i f f i c u l t i e s a s s o c i a t e d w i t h t h e o r i e s of t h i s k i n d .
S i k i v i e s t a r t e d u s t h i n k i n g a b o u t c o s m o l o g i c a l p r o p e r t i e s of i n v i s i b l e a x i o n s by p o i n t i n g o u t t h a t many s u c h m o d e l s h a v e s e v e r a l d e g e n e r a t e v a c u a . T h i s c a n l e a d t o f o r m a t i o n of d i f f e r e n t domains i n t h e e a r l y u n i v e r s e , s e p a r a t e d by domain w a l l s which f o u l up s t a n d a r d cosmology. 5 4
T h i s problem ( i f i t is a problem) i s e a s y t o f i x . Many p e o p l e s u g g e s t e d ways t o f i x any t h e o r y t o make t h e vacuum unique.55 The s o l u t i o n s a r e i n t e r e s t i n g o n l y b e c a u s e none of them i n v o l v e s i m p l e r e p l i c a t i o n of i d e n t i c a l f a m i l i e s . I t i s even p o s s i b l e , i n f a m i l y symmetry t h e o r i e s , t o f i n d models i n which t h e PQ symmetry i s a u t o m a t i c and i n which t h e r e a r e n o domains. 5 6
But r e c e n t l y P r e s k i l l , W i s e and Wilczek and Abbott and S i k i v i e have i d e n t i f i e d a c o s m o l o g i c a l problem which seems t o be more d i f f i c u l t t o e x o r c i z e . 5 7 I c a l l i t t h e Axion e n e r g y c r i s i s . They n o t e t h a t when t h e c h i r a l symmetry b r e a k i n g p h a s e t r a n s i t i o n i n QCD o c c u r s , a t a t e m p e r a t u r e of a b o u t a GeV, t h e a x i o n f j e l d i n any g i v e n r e g i o n h a s some random vacuum v a l u e , l e f t o v e r from t h e e a r l i e r h i s t o r y of
t h e u n i v e r s e . I n g e n e r a l , t h i s v a l u e w i l l n o t be n e a r t h e minimum of t h e PQ symmetry b r e a k i n g p o t e n t i a l , which i s t h e t r u e VEV.
A normal f i e l d would q u i c k l y s e t t l e down tc, t h e minimum, l o s i n g i t s e x t r a p o t e n t i a l e n e r g y by p r o d u c i n g p a r t i c l e s and r e h e a t i n g t h e u n i v e r s e . But h e r e , t h e same weakness of c o u p l i n g s which makes t h e a x i o n i n v i s i b l e makes t h i s p r o c e s s s l o w compared t o t h e e x p a n s i o n of t h e u n i v e r s e . The r e s u l t i s t h a t t h e a x i o n j u s t s i t s t h e r e and l o s e s e n e r g y t o e x p a n s i o n . U n l e s s t h e f i e l d i s c l o s e t o i t s VEV by a c c i d e n t , t h e r e s u l t i n g u n i v e r s e i s dominated by t h e e n e r g y i n t h e e x c i t e d a x i o n f i e l d . It c l o s e s t h e u n i v e r s e by many o r d e r s o f m a g n i t u d e . Thus t h e a x i o n e n e r g y c r i s i s is t h a t t h e a x i o n f i e l d i n g e n e r a l h a s t o o much e n e r g y and c a n n o t g e t r i d o f i t . I f t h i s problem is a s s e r i o u s a s i t s o u n d s t o me, we w i l l have t o g i v e up t h e i n v i s i b l e & i o n o r s u b s t a n t i a l l y modify i t . T h a t i s n o t s u c h a bad t h i n g . The a l t e r n a t i v e s may b e more e x p e r i m e n t a l l y a c c e s s i b l e .
B e f o r e c l o s i n g l e t me r e t u r n b r i e f l y t o t h e u n i f i c a t i o n of g r a v i t y . F r a n k l y , I b e l i e v e t h a t t h e u n i f t c a t i o n o f g r a v i t y i s p r e m a t u r e . Contemporary t h e o r i e s of quantum g r a v i t y a r e p r o b a b l y a n a l o g o u s t o t h e f o u r - f e r m i o n t h e o r y of c h a r g e d c u r r e n t weak i n t e r a c t i o n s ; a u s e f u l d e s c r i p t i o n a t d i s t a n c e s l a r g e compared t o t h e a p p r o p r i a t e s c a l e , b u t i r r e l e v a n t a t s h o r t e r d i s t a n c e s . I f s o , t r y i n g t o u n i f y g r a v i t y and p a r t i c l e f o r c e s i s l i k e t r y i n g t o u n i f y e l e c t r o m a g n e t i s m w i t h t h e Fermi t h e o r y . I t w i l l have t o w a i t u n t i l we push o u r u n d e r s t a n d i n g of g r a v i t y down t o s h o r t e r d i s t a n c e s .
H. G e o r g i
One s u g g e s t i o n i n t h i s d i r e c t i o n i s " i n d u c e d g r a v i t y " , i n which t h e s h o r t d i s t a n c e t h e o r y i s c l a s s i c a l l y s c a l e i n v a r i a n t , a n d Newton's c o n s t a n t i s
d y n a m i c a l l y i n d u c e d . 5 8 P e r s o n a l l y , I s u s p e c t t h a t e v e n w i l d e r i d e a s a r e g o i n g t o b e r e q u i r e d , p e r h a p s t h e k i n d of t h e o r y c o n j u r e d up by H o l g a r N i e l s e n , i n which L o r e n t z i n v a r i a n c e ( a n d p e r h a p s g e n e r a l c o o r d i n a t e i n v a r i a n c e ) i s o n l y a p p r o x i m a t e , v a l i d a t l o n g d i s t a n c e s b u t v i o l a t e d a t s h o r t e r
distance^.^'
T h e s e t h e o r i e s do n o t y e t e x i s t , b u t p e r h a p s t h e d i s c i p l i n e o f u n i f i c a t i o n c a n h e l p u s t o f i n d them.T h e r e i s o n e p o p u l a r a t t e m p t t o u n i f y g r a v i t y w i t h p a r t i c l e f o r c e s i n t h e c o n t e x t o f s u p e r s y m m e t r y . T h i s i s N=8 s u p e r g r a v i t y . 6 0 I t h i n k t h a t t h e m o t i v a t i o n f o r t h i s i s a s f o l l o w s . I n c o n v e n t i o n a l r e n o r m a l i z a b l e g a u g e t h e o r i e s , o n e h a s a s e r i e s o f d i s c r e t e a n d c o n t i n u o u s c h o i c e s t o make. One must c h o o s e g a u g e g r o u p , f e r m i o n a n d b o s o n r e p r e s e n t a t i o n s , and u s u a l l y many c o u p l i n g c o n s t a n t s . On t h e o t h e r h a n d , o n e c a n a r g u e t h a t t h e N=8 s u p e r g r a v i t y i s t h e u n i q u e s u p e r s y m m e t r i c u n i f i c a t i o n o f s in stein's g r a v i t y a n d p a r t i c l e f o r c e s . U n f o r t u n a t e l y , t h i s
u n i q u e n e s s i s i t s o n l y o b v i o u s v i r t u e . W h i l e t h e c l a s s i c a l f i e l d t h e o r y p r e s u m a b l y makes s e n s e , i t is n o t a t a l l c l e a r t h a t t h e r e i s a c o r r e s p o n d i n g quantum t h e o r y . Even i f i t makes s e n s e , i t i s n o t c l e a r how t o e x t r a c t a n y i n f o r m a t i o n a b o u t t h e w o r l d f r o m i t .
T h e r e h a v e b e e n a t t e m p t s t o e x t r a c t i n f o r m a t i o n a b o u t p a r t i c l e i n t e r a c t i o n s below
%
u s i n g symmetry c ~ n s i d e r a t i o n s a l o n e , f i n e s s i n g a l l t h e d y n a m i c a l d e t a i l s . 61 Even t h i s d o e s n ' t a p p e a r t o work.62 The s p i n 1. 1 / 2 , and 0 s t a t e s seem t o b e t o o i n t i m a t e l y mixed up w i t h h i g h e r s p i n s t a t e s t o s u r v i v e a t low e n e r g i e s a n d g i v e a s e n s i b l e d e s c r i p t i o n o f p a r t i c l e p h y s i c s .I t s e e m s t o me t h a t t h i s is t o o h i g h a p r i c e t o pay f o r u n i q u e n e s s . I would r a t h e r b e a b l e t o c a l c u l a t e e v e r y t h i n g i n t e r m s o f 2 3 p a r a m e t e r s t h a n t o b e a b l e t o c a l c u l a t e n o t h i n g i n t e r m s o f two p a r a m e t e r s .
I w i l l c l o s e w i t h a p a r a b l e which I l e a r n e d from A l v a r o De ~ G j u l a . C o n s i d e r t h e s i m i l a r i t i e s a n d d i f f e r e n c e s b e t w e e n t h e f o l l o w i n g two sets: A f a r m e r , h i s p i g a n d t r u f f l e s o n t h e o n e hand and t h e t h e o r i s t , t h e e x p e r i m e n t o r a n d d i s c o v e r i e s o n t h e o t h e r . The s i t u a t i o n i s t h i s . The f a r m e r l e a d s h i s p i g i n t o t h e woods. The p i g s n i f f s a n d r o o t s a r o u n d u n t i l h e f i n d s t h e t r u f f l e s . Then t h e f a r m e r h i t s t h e p i g o v e r t h e h e a d w i t h a s t i c k and t a k e s t h e t r u f f l e s away. T h e s e a r e t h e s i m i - l a r i t i e s . The d i f f e r e n c e i s t h a t t h e f o r e s t i n t o which t h e f a r m e r l e a d s t h e p i g a l w a y s c o n t a i n s t r u f f l e s .
T h i s i s t h e n a t u r e o f t h e game. I c a n ' t t e l l you w h e t h e r t h e b e s t p l a c e t o l o o k f o r t h e n e x t i m p o r t a n t c l u e i s i n p r o t o n d e c a y , r a r e meson o r l e p t o n d e c a y modes, new heavy p a r t i c l e s , o r w h a t e v e r . G e n e r a l l y , you o n l y f i n d o u t w h e t h e r you h a v e f o u n d t h e c r u c i a l p i e c e t o a p u z z l e a f t e r you h a v e b e e n h i t o v e r t h e h e a d w i t h a s t i c k . But k e e p l o o k i n g . O t h e r w i s e , p a r t i c l e p h y s i c s d e g e n e r a t e s i n t o
p h i l o s o p h y . A f t e r a l l t h e r e is a n o t h e r d i f f e r e n c e b e t w e e n t r u f f l e s and d i s c o v - eries. To t h e f a r m e r a n d t o t h e p i g , t r u f f l e s are o n l y a l u x u r y .
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