UNIFIED MODELS OF PARTICLES AND INTERACTIONS

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UNIFIED MODELS OF PARTICLES AND INTERACTIONS

P. Fayet

To cite this version:

P. Fayet. UNIFIED MODELS OF PARTICLES AND INTERACTIONS. Journal de Physique Collo-

ques, 1982, 43 (C3), pp.C3-673-C3-703. �10.1051/jphyscol:1982383�. �jpa-00221939�

JOURNAL DE PHYSIQUE

Colloque CS, supplément au n° 12, Tome 43, décembre 1982 page C3-673

UNIFIED M O D E L S OF P A R T I C L E S A N D I N T E R A C T I O N S

P. Fayet

Laboratoire de Physique Théorique de l'Eoole normale Supérieure, Paris, France

Résumé. - Nous discutons diverses approches d'une description unifiée des particules et de leurs interactions : la technicouleur, les modèles composés de quarks et de leptons e t , de manière plus d é t a i l l é e , les théories super- symétriques et leurs conséquences phénoménologiques.

Abstract. - We discuss various approaches towards a unified description of particles and their interactions : technicolor, composite models of quarks and leptons, and in a more detailed way, supersymmetric theories and their phenomenological consequences.

INTRODUCTION

The standard model of strong, electromagnetic and weak interactions gives, presently, a satisfactory description of the interactions of particles . These interactions are due to the exchanges of spin-1 gauge bosons between spin-1/2 matter fermions, leptons and quarks. These gauge bosons are the eight gluons of the color SU(3) gauge group ; the photon y, and the charged and neutral intermediate bosons

± 2 W and Z. The latter acquire large masses of the order of 80 or 90 GeV/c by the

Englert-Brout-Higgs mechanism while the SU(2) x U(l) electroweak gauge group is T21 spontaneously broken down to the U(l) subgroup of quantum electrodynamics. At least one neutral spin-0 Higgs boson is present in the theory, and plays an essential role in its renormalizability.

What are the experimental indications in favor of this scheme ? There is indirect evidence for the existence of gluons, and quantum chromodynamics is in good agreement with experimental data while spin-0 gluons, for example, can be excluded. Weak interactions are well represented by a current-current effective Lagrangian density

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982383

2 2

gff

^{= 2 G~}

^i~

^{[J;J~+ + (J"} - s i n 8 ~ " ~ ~ )

I

Recent experimental r e s u l t s , l i k e measurements o f t h e forward-backward asymmetry i n

+ -

e+e- ⁺ p+v- o r r r a n n i h i l a t i o n s , and o f p a r i t y v i o l a t i o n e f f e c t s i n atomic physics, are w e l l i n agreement w i t h formula (1) ( c f . D a v i e r ' s t a l k a t t h i s conference [31 ) .

This, however, does no* imply t h a t t h e gauge bosons

' W

and Z must e x i s t , n o t t o mention t h e Higgs p a r t i c l e ( s ) . We hope t o know soon, from p

p

s c a t t e r i n g e x p e r i - ments, about t h e existence o f t h e Z. The

' W

and Z may a l s o e x i s t w i t h d i f f e r e n t p r o p e r t i 0s from those common1 y expected. Moreover, t h e r e may be several Z' s i n s t e a d o f a s i n g l e one, and a d d i t i o n a l ~ " s , even i f ( 1 ) g i v e s a good d e s c r i p t i o n o f t h e present phenomenology.

I f t h e standard model i s phenomenologically very successful i t leaves, on t h e o r e t i c a l grounds, many questions unanswered. I n c l u d i n g t h e tau n e u t r i n o and t h e as-yet undiscovered t o p quark we have t h r e e generations o f l e p t o n s and quarks,

(ve, e, u, d), (vv,

u ,

c, s), (vr, T, t, b). Why t h i s r e p l i c a t i o n o f fermion families, and how c o u l d t h e corresponding masses and Cabibbo-like m i x i n g angles be determined ? This i s t h e " f a m i l y problem".

One can a l s o ask many o t h e r questions concerning f o r example t h e

P

and CP conservation

,

o r non-conservation, by t h e v a r i o u s i n t e r a c t i o n s ; charge quantization;

and t h e existence and masses o f s c a l a r Higgs bosons. What i s t h e r o l e o f g r a v i t a t i o n , and can one f i n d a f i n i t e quantum t h e o r y o f g r a v i t a t i o n ?

I f most o f these questions have n o t y e t received a s a t i s f a c t o r y answer, t h e y have l e d p h y s i c i s t s t o develop a v a r i e t y o f ideas t o go beyond t h e standard model o f i n t e r a c t i o n s . These ideas go i n two general d i r e c t i o n s : i ) search f o r subconsti- t u e n t s o f p a r t i c l e s p r e v i o u s l y considered as "elementary" and i i ) search f o r new symmetries t o r e l a t e p a r t i c l e s and t h e i r i n t e r a c t i o n s .

T h i s i s a v e r y wide s u b j e c t on which a considerable amount o f work has been done. 9ue t o l a c k o f time t h e r e a r e many i n t e r e s t i n g ideas and r e s u l t s t h a t I w i l l n o t be a b l e t o mention.

A f t e r mentioning some r e c e n t r e s u l t s concerning l e f t - r i g h t symmetric theories, and searches f o r axions, we s h a l l discuss, r e l a t i v e l y b r i e f l y , some o f t h e ideas u n d e r l y i n g t h e " t e c h n i c o l o r " t h e o r i e s i n which elementary Higgs bosons a r e rep1 aced by bound s t a t e s o f "technifermions", and t h e "composite models", i n which t h e quarks and l e p t o n s themselves a r e no l o n g e r elementary p a r t i c l e s , b u t bound s t a t e s o f preons.

The search f o r new symmetries o f p a r t i c l e s and i n t e r a c t i o n s has l e d t o t h e idea o f g r a n d - u n i f i c a t i o n c41

.

Quarks a r e r e l a t e d t o leptons, and weak, e l e c t r o - magnetic and s t r o n g i n t e r a c t i o n s appear as t h r e e d i f f e r e n t aspects o f a s i n g l e i n t e r a c t i o n . Such a program, discussed i n G e o r g i ' s t a l k , a l l o w s one t o compute t h e value o f t h e electroweak m i x i n g angle 8, and leads t o t h e p o s s i b i l i t y o f proton decay. But g r a n d - u n i f i e d t h e o r i e s s t i l l i n v o l v e many a r b i t r a r y parameters, masses and c o u p l i n g constants, t h e s e c t o r o f spin-0 Higgs p a r t i c l e s i s q u i t e ugly, and they

P. Fayet

leave gravity out of the game.

One can a l s o consider a symmetry between bosons and fermions, namely super- symmetry 15] . A1 though supersymmetry i s almost a decade old by now, i t was only recently brought t o t h e general a t t e n t i o n , and the l a r g e r part of t h i s t a l k will be devoted t o i t .

Supersymmetry i s p a r t i c u l a r l y a t t r a c t i v e due t o i t s connection with gravitation ( a locally supersymmetric theory automatically includes general r e l a t i v i t y )

;

the new r e l a t i o n i t establishes between massive gauge bosons, such a s the

W'

and the

Z ,

and Higgs bosons

;

and the improved convergence properties of supersymmetric f i e l d theories.

While the grand-unification symmetry i s presumably broken a t a very high scale, t y p i c a l l y

^.L

10 GeV 15 or so, supersymmetry may be apparent a t r e l a t i v e l y low values of t h e energy of the order of the

W

mass and possibly less. This makes supersymmetry very a t t r a c t i v e f o r experimentalists, who might discover, r e l a t i v e l y soon, a large variety of new p a r t i c l e s .

LEFT-RIGHT SYMMETRY

Why do weak interactions v i o l a t e parity, and, more precisely, why a r e charged currents

V

-

A ?

One can think of a p a r i t y operation which would be a symmetry of the electroweak theory a t high energy. This leads t o two general classes of l e f t - r i g h t symmetric theories (see f o r example r e f . [61 f o r a review and references there- i n ) .

One may keep SU(2) x U(l) as the electroweak gauge group

b u t

use equal numbers of left-handed and right-handed doublets and s i n g l e t s , ordinary leptons and quarks being associated with mirror p a r t i c l e s . Mirror p a r t i c l e s , which would have (V + A) couplings, can only e x i s t i f they a r e s u f f i c i e n t l y heavy ( i . e . m

>

18 GeV/c f o r 2 mirror 1 eptons) .

Another p o s s i b i l i t y i s t h a t t h e l e f t - r i g h t symmetry a c t s on the gauge group, extended t o include SU(3) x SU(2IL x SU(2)R x U(l) a t l e a s t . (Further i n t e r e s t in t h i s group comes from the f a c t t h a t i t appears as a subgroup of a grand unification group SO(10)). This suggests the possible existence of another charged boson,

WkR,

coupled t o a

V

+

A

current, which would be the mirror image of t h e usual w ' ~ .

The w ' ~ and w ' ~ may nix. This would lead t o a small

( V

+ A) part i n the mostly

( V

- A) charged current. Improved l i m i t s on t h e mixing have been obtained recently

:

i t should be 6 10

%,

from neutrino scattering experiments C71 , or even smaller 181

2

16j The charged

W'

which has mostly

V

+

A

couplings should be heavier than ~ 2 2 0 GeV/c .

This bound may be ir.iproved by studying t h e KL - KS mass difference .

^P

stronger l i m i t

^.L 4

TeV/c could be obtained from the helium abundance i n the universe, 2 assuming t h a t ve, v andvT are three l i g h t Dirac neutrinos

C

101

P AX

IONS

Why i s

CP

conserved by strong interactions, while i t i s violated by weak i n t e r -

a c t i o n s ? The s o l u t i o n proposed by Peccei and Quinn, which makes use o f a g l o b a l U ( l ) p Q symmetry t o r o t a t e away t h e C P - v i o l a t i n g phase €I o f QCD

,

leads t o t h e existence o f a very l i g h t n e u t r a l spin-0 boson, t h e axion

.

Various experiments have e s t a b l i s h e d s t r o n g l i m i t s on t h e existence o f such a p a r t i c l e , and i t i s now c l e a r t h a t the o r i g i n a l axion o f r e f s . [ll, 121 does n o t e x i s t . One expects, f o r example, t h i s axion t o be produced i n r a d i a t i v e decays o f t h e $ and T w i t h t h e r a t e s

B ($ ⁺ ya) = 6 x2

-4

1

B (T + ya) = 3 10

X

The SPEAR experiment found t h e f i r s t branching r a t i o t o be < 1.4 10 -5 [I3]

.

^combi-

n i n g t h i s r e s u l t w i t h t h e CORNELL l i m i t on t h e second branching r a t i o , one f i n d s ^[ 141 B($ ⁺ ya) x B(T ⁺ ya) < (%5 %) x expected v a l u e (3) r u l i n g o u t t h e existence o f a standard axion.

The axion c o u l d s t i l l e x i s t as an " i n v i s i b l e " p a r t i c l e having v e r y small couplings w i t h o r d i n a r y l e p t o n s and quarks [I5]

.

There i s , however, a d i f f i c u l t y i n t h i s scheme : one c o u l d have t h e formation o f d i f f e r e n t domains i n t h e universe separated by w a l l s ; t h i s would be incompatible w i t h t h e standard cosmology [ 161 How t h i s problem c o u l d be solved, and f u r t h e r d i f f i c u l t i e s r e l a t e d w i t h i n v i s i b l e axions, i s discussed by Georgi i n h i s t a l k .

TECHNICOLOR

I n t e c h n i c o l o r t h e o r i e s , t h e r e are no elementary Higgs s c a l a r s . They a r e replaced by bound s t a t e s o f new fermions c a l l e d technifermions. Since t h e r e have been many good l e c t u r e s and review a r t i c l e s on t h e s u b j e c t [I7' we can be r e l a t i v e l y b r i e f . The most important new r e s u l t i s t h e non-observation o f t h e charged t e c h n i - pions P- ⁺

,

which had been p r e d i c t e d i n t h e 5 t o 14 GeV/c 2 mass range.

The m o t i v a t i o n f o r t e c h n i c o l o r i s t o a v o i d t h e elementary spin-0 f i e l d s used t o t r i g g e r t h e spontaneous breaking o f t h e gauge symmetry [ l g l

.

This i s because o f t h e a r b i t r a r i n e s s e x i s t i n g i n t h e spin-0 s e c t o r o f gauge theories, and t h e f a c t t h a t spin-0 f i e l d s tend t o a c q u i r e l a r g e masses comparable t o t h e heaviest s c a l e i n t h e t h e o r y considered, namely t h e compositeness scale, o r t h e g r a n d - u n i f i c a t i o n scale ; o r even t h e Planck mass i f one considers a l s o g r a v i t a t i o n . It i s then d i f f i c u l t t o understand how t h e ~ " n d Z can be l i g h t , compared t o t h i s heavy scale;

t h i s i s t h e well-known h i e r a r c h y problem r201

.

Therefore t h e o r e t i c i a n s do n o t l i k e elementary s c a l a r s . (Except, o f course, i n supersymmetric t h e o r i e s , where spin-0 f i e l d s a r e r e l a t e d t o spin-1/2 and s p i n - 1 f i e l d s and can be p r o t e c t e d from acquiring v e r y l a r g e masses).

I n t e c h n i c o l o r t h e o r i e s b i l i n e a r products o f fermion f i e l d s , r a t h e r than elementary Higgs f i e l d s , a c q u i r e non-vanishing vacuum e x p e c t a t i o n values <FF>, generating t h e spontaneous breaking o f SU(2) x U(1) However, t h e F ' s cannot be

P. Fayet C3-677

o r d i n a r y quark f i e l d s i f t h e

' W

and Z a r e t o a c q u i r e l a r g e masses % 80 ~ e ~ / c ~ . They w i l l be new fermion f i e l d s c a l l e d technifermions, bound by a new force, t e c h n i c o l o r , which becomes s t r o n g a t a s c a l e ATC 1 TeV.

This mechanism i s a p p r o p r i a t e f o r generating t h e W' and Z masses b u t unfortuna- t e l y i t leaves l e p t o n s and quarks massless. To generate l e p t o n and quark masses one can enlarge t h e t e c h n i c o l o r group t o extended t e c h n i c o l o r (ETC) [211

.

ETC gauge bosons couple usual fermions ( f ) t o technifermions (F), so t h a t t h e condensation o f technifermions generates masses f o r o r d i n a r y fermions :

2 < F F >

mf % ETC 2

ETC (see F i g . 1 )

Heavy ETC gauge boson

F i g . 1 : Generation o f fermion masses i n extended t e c h n i c o l o r - t h e o r i e s . The masses mf o r i g i n a t e from t e c h n i f e r m i o n c o n d e n s a t e s ~ F F > t h r o u g h exchanges o f very heavy ETC gauge bosons.

3 F a m i l i e s n T e c h n i f a m i l i e s

GENERATION GROUP TECHNICOLOR GROUP

k \-

The f i e l d content o f a t y p i c a l extended t e c h n i c o l o r t h e o r y i s represented i n F i g . 2

r

²²¹

4 u c t U1

- -

_'n

EXTENDED TECHNICOLOR S'J(3)

X

Fig. 2 : Fermion c o n t e n t o f a t y p i c a l ETC theory, w i t h 3 f a m i l i e s o f fermions, and n f a m i l i e s o f technifermions t r a n s f o r m i n g under t h e t e c h n i c o l o r group. Extended t e c h n i c o l o r i m p l i e s a gauging o f t h e generation group and leads t o flavor-changing n e u t r a l c u r r e n t amplitudes.

d s b

Dl - -

_Dn

ve "7 N1

- -

su(2) X U(1)

,

^V

_u

^{U T} _El

_{- -}

_En

+ + + .+

The existence of ETC gauge bosons c o u p l i n g o r d i n a r y f a m i l i e s o f l e p t o n s and quarks t o t e c h n i f a m i l i e s i m p l i e s , also, t h e e x i s t e n c e of ETC gauge bosons c o u p l i n g one f a m i l y t o another. Extended t e c h n i c o l o r i m p l i e s f a m i l y u n i f i c a t i o n . Since t h e fermions of t h e d i f f e r e n t f a m i l i e s mix through Cabibbo-like angles, t h e exchanges o f t h e ETC gauge bosons o f t h e generation group l e a d t o flavor-changing n e u t r a l c u r r e n t amplitudes, i.e; t o as-yet unobserved processes such as p ⁺ ey ( t h e present 1 im i t on t h e branching r a t i o i s 2 lo-''), K ^-t pe, o r AS = +2 (KOKO) and AC = ?2 (DODO) n i x i n g amp1 i t u d e s .

These amplitudes can be made small enough i f t h e corresponding ETC gauge bosons a r e s u f f i c i e n t l y h e a v y . H o w e v e r one a l s o n e e d s mETC ^% gETC (few TeV t o 100TeV) t o generate l e p t o n and quark masses. P.s a r e s u l t ETC nodels p r e d i c t KORO and m i x i n g amplitudes which a r e u s u a l l y t o o large, by a t l e a s t two orders o f magnitude. This i s a serious problem f o r extended t e c h n i c o l o r t h e o r i e s . Various suggestions, which a r e n o t discussed here, have been made t o s o l v e it, and i t i s s t i l l p o s s i b l e t o imagine t h a t t h i s can be done by b u i l d i n g more complex - o r more ingenious- models.

Extended t e c h n i c o l o r t h e o r i e s a l s o p r e d i c t the existence o f bound s t a t e s o f technifermions named technipions. While most of them would have l a r g e masses >s 50

~ e ~ / c ' , two n e u t r a l ones c o u l d by l i g h t (6 2 GeV/c 2 ) ; as w e l l as two charged ones, P', which g e t t h e i r masses from electroweak i n t e r a c t i o n s , and have been p r e d i c t e d i n the 5 t o 1 4 GeV/c mass range 2 [22, 233

The P' would decay p r e f e r e n t i a l l y towards heavy l e p t o n s and quarks, e.g. P- -+

- - ₊ -

v T

, c

^{b o r}

7

s. One can search f o r t h e i r p a i r production, and decay, i n e e

'r

a n n i h i l a t i o n , and discuss i t i n terms o f the hranching r a t i o BT r 1

-

Bhadrons.

The new experimental r e s u l t s presented a t t h i s conference by the TASSO c o l l a b o r a t i o n complete t h e i n f o r m a t i o n already obtained by JADE, CELLO, MARK J and MARK 11 [''I. No charged t e c h n i p i o n can e x i s t i n t h e 5 t o 13 GeV/c 2 mass i n t e r v a l . I n t h e plane (mp+

,

BT) most of the 5 t o 14 GeV/c 2 r e g i o n where technipions c o u l d be expected i s now excluded. Together w i t h the q u e s t i o n o f flavor-changing n e u t r a l currents, t h i s appears as an i m p o r t a n t source o f concern f o r extended t e c h n i c o l o r t h e o r i e s . COMPOSITE MODELS

The already l a r g e number of leptons and quarks, as w e l l as t h e d e s i r e t o e x p l a i n t h e i r mass spectrum, may be m o t i v a t i o n s f o r c o n s i d e r i n g t h e p o s s i b i l i t y t h a t leptons and quarks a r e composite. This approach has been described a t t h i s conference by Farhi, P r e s k i l l and ~ a t i ' ~ ~ '

.

(See a l s o r e f . [ 251 f o r a review and references .)

Quarks and leptons could be made o f subconstituents

,

which we s h a l l c a l l preons, bound t o g e t h e r by a new s t r o n g f o r c e c a l l e d metacolor. This i s analogous t o t h e QCD d e s c r i p t i o n o f hadrons, formed o f quarks bound by a s t r o n g c o l o r f o r c e due t o gluon exchanges. E x a c t l y 1 i ke c o l o r i s confined w i t h i n hadrons, metacol o r would be confined i n s i d e l e p t o n s and quarks. T h i s i s i l l u s t r a t e d , very nai'vely, i n Fig. 3, which repre- sents a p o s s i b l e view o f a p r o t o n made o f composite quarks. Since b o t h c o l o r and meta-

P. Fayet C3-679

color are confined, electromagnetism and gravitation are, s t i l l , the only two long range forces.

Proton made of three quarks

Metacolor

Fig.

3 : A

nai've view of a proton made of composite quarks. Fletacolor i s confined inside quarks ( o r leptons), while color i s confined inside hadrons .

One can a l s o ask whether the spin-1 bosons themselves should be elementary or composite. There a r e d i f f e r e n t points of view, but one generally considers t h a t the photon and gluons, which are massless gauge bosons, should be elementary. The s i t u a t i o n i s d i f f e r e n t f o r the intermediate bosons

W'

and Z. They may be elementary gauge bosons of a spontaneously broken local electroweak gauge symmetry. B u t they may a l s o be com- p o s i t e , i n which case one would only have a global weak interaction symmetry. Or they may even not e x i s t a t a l l .

Many d i f f e r e n t p o s s i b i l i t i e s have been explored ( s e e , e.g. r e f s . [24,25]). There a r e , f i r s t , scenarios with nearby compositeness. One of the f i r s t examples i s the model of Abbott and ~ a r h i ' ~ ~ ] , i n which right-handed leptons and quarks a r e elementary while left-handed ones appear as spin-1/2 spin-0 bound s t a t e s . In such scenarios the compo- s i t e n e s s s c a l e

Ac

i s r e l a t i v e l y low and the new phenomena associated with compositeness may appear i n the 100 t o 10 GeV energy s c a l e . The physics of W's and Z's may be d i f f e r -

3

e n t . These could be bound s t a t e s , and have masses d i f f e r e n t from what i s usually

expected. There could be several of them, possibly strongly interacting a t high energy.

One may see a structure of the Z resonance, e t c . . .

We s h a l l not discuss the phenomenological properties of these models. B u t we note t h a t i n such schemes with nearby compositeness one usually has a t r i v i a l replication of families, and therefore no new i n s i g h t on the family problem.

If one wants t o deal with t h i s question, ( i . e . t o have the electron and muon, f o r

example, b u i l t of the same constituents) one faces the p o s s i b i l i t y of unwanted flavor

changing neutral current processes, such as

y +

ey,

K +

we, e t c . This requires the

compositeness s c a l e t o be s u f f i c i e n t l y high ( t y p i c a l l y

Ac

3 100 TeV). One then has t o

explain why the bound s t a t e s -leptons and quarks- would be so l i g h t , compared t o the

1

arge composi teness s c a l e .

This can be done by invoking, i n the approximation i n which l e p t o n and quark masses a r e neglected, a c h i r a l symmetry t o p r o t e c t them. O f course t h i s c h i r a l symmetry should remain unbroken ( i n c o n t r a s t w i t h the c h i r a l symmetry o f QCD). How can we know something about t h e massless bound s t a t e s which appear i n the t h e o r y ? By u s i n g t h e ' t Hooft anomaly matching argumentr2", which says t h a t t h e t r i a n g l e anomaly o f t h r e e c u r r e n t s can be computed, e i t h e r i n terms o f elementary preons, or, e q u i v a l e n t l y , i n terms o f the massless composite bound s t a t e s which appear i n the theory. This anomaly matching c o n d i t i o n , t o g e t h e r w i t h o t h e r c o n d i t i o n s t h a t bound s t a t e s should s a t i s f y , t u r n s o u t t o c o n s t r a i n very s t r o n g l y t h e c l a s s o f models which can be considered.

I n t h i s framework, one can t h e n address the q u e s t i o n o f t h e l e p t o n and quark spectrum,and generation mixing. Considerable work has been done on t h i s s u b j e c t . How- ever, as P r e s k i l l t o l d us, no model w i t h a very r e a l i s t i c l o o k i n g mass spectrum has been found y e t . I n any case we apparently need a l a r g e number o f preons. We even have heard about t h e possi b i li t y o f one more l a y e r o f composi teness, "prepreons"

,

^discussed

by P a t i . While leptons and quarks may w e l l be composite objects, t h i s i d e a does n o t seem t o h e l p us, p r e s e n t l y , t o understand them b e t t e r .

PRESENT MOTIVATIONS FOR SUPERSYMHETRY

There are several s t r o n g m o t i v a t i o n s f o r c o n s i d e r i n g a symmetry between bosons and fermions -supersymmetry 15]- i n p a r t i c l e physics.

( a ) one would l i k e t o go beyond t h e electroweak o r grand u n i f i c a t i o n o f i n t e r - a c t i o n s by e s t a b l i s h i n g new r e l a t i o n s between p a r t i c l e s , and t o have a b e t t e r under- standing of the Higgs s e c t o r o f gauge t h e o r i e s . This program has l e d t o t h e i n t r o d u c t i o n o f spin-0 leptons and quarks, spin-1/2 g l u i n o s and photino, as the superpartners o f

[ 281 t h e o r d i n a r y p a r t i c l e s . It a l s o leads t o a r e l a t i o n between gauge and Higgs bosons

.

Although t h e l a t t e r i s n o t a necessary f e a t u r e of supersymmetric gauge t h e o r i e s i t does p r o v i d e much o f the m o t i v a t i o n f o r s t u d y i n g them.

( b ) L o c a l l y supersymmetric t h e o r i e s a r e n e c e s s a r i l y i n v a r i a n t under l o c a l c o o r d i - nate t r a n s f o r m a t i o n s . They a u t o m a t i c a l l y i n c l u d e general r e l a t i v i t y and describe g r a v i - t a t i o n a l i n t e r a c t i o n s ( s u p e r g r a v i t y ) , suggesting a promising connection between g r a v i -

[291 t a t i o n and p a r t i c l e physics

.

( c ) Supersymmetric f i e l d t h e o r i e s have remarkable c o n v e r g e n c e p r o p e r t i e s . Q u a d r a t i c r e n o r m a l i z a t i o n s o f parameters a r e usual 1 y absent'30'

.

This may u l t i m a t e l y p r o v i d e a s o l u t i o n t o t h e h i e r a r c h y problemr201 o f grand u n i f i e d t h e o r i e s ( c f . Georgi's t a l t[41). Supersymmetry may a l s o p r o v i d e us w i t h a f i n i t e quantum f i e l d theory : t h e Yang-Mills theory w i t h N = 4 supersymmetry generatorsZ311 has a vanishing B f u n c t i o n , n o t o n l y a t the three-loop levelE321 b u t a l s o t o a l l ordersi331. Extended s u p e r g r a v i t y t h e o r i e s r a i s e the hope f o r a completely f i n i t e quantum theory o f g r a v i t a t i o n (see, e.g., r e f . [341).

(d) I n a more ambitious way one might hope t h a t an extended s u p e r g r a v i t y theory, such as the one w i t h N = 8 supersymmetry generators[351 w i l l u l t i m a t e l y appear as a completely u n i f i e d theory o f a1 1 i n t e r a c t i o n s , provided the c o r r e c t spectrum o f leptons, quarks, gauge bosons, e t c . i s obtained, as bound s t a t e s o f preons belonging t o t h e

fundamental multiplet of the graviton [36,371

For a long time supersymmetry appeared t o most physicists as a beautiful symmetry

w i t h

presumably no connection

w i t h

r e a l i t y . Many now accept the idea t h a t supersymmetry nay be relevant, not only a t superhigh energies of the order of the Planck mass

19 2

(10 GeV/c

),

but already a t moderate energies comparable t o the

!J

mass. Uhile there i s no experimental indication i n favor of supersymmetry, theoretical and aesthetical motivations a r e s u f f i c i e n t l y strong t o j u s t i f y a systematic search f o r i t s consequences.

Supersymmetric theories a r e invariant under a spin-1/2 symmetry generator

Q

which changes the spin of p a r t i c l e s by 1/2 unit, transforming bosons i n t o fermions and con- versely. This supersymmetry generator

Q

obeys the a1 gebra 151

The appearance of the space-time t r a n s l a t i o n generator

P%

n the right-hand side of eq.

( 5 )

indicates a connection between supersymmetry and space time, and therefore, ultimately, gravitation.

Any ( l i n e a r ) representation of supersymmetry contains an equal number of bosonic and fermionic degrees of freedom. Those can be described simultaneously

i n

terms of superfields, which are functions of a superspace point (x? ea),

Ba

being a spin-l/2 a n t i commuti ng Grassman coordi nate[38' Massless gauge superfiel ds describe both a spi n-1 gauge boson and a spin-1/2 Majorana fermion (sometimes called gaugino). Chiral super- f i e l d s describe a two-component Di rac fermion, together with a complex spin-0 boson.

HOW COULD NATURE BE

SUPERSYMMETRIC

?

Supersymmetry may be, a t best, a spontaneously broken invariance. Spontaneous breaking of global supersymmetry generates a massless neutral spin-1/2 Goldstone fermi on [39s401, and t h i s seemed a t f i r s t very a t t r a c t i v e since t h i s fermion might have been interpreted as a neutrino[41'. However, f o r various reasons such as low-energy theoremsC421, quark-lepton symmetry, e t c . t h i s idea i s not tenable. In t h a t case, why has no Goldstone fermion been observed

?

I t i s audacious t o imagine t h a t Nature could be supersymmetric. Where are the bosons and fermions t h a t could be r e l a t e d

?

How could lepton and baryon numbers be conserved

?

Why a r e weak, e l e c t r o m a g n e t i c and strong interactions mediated by spin-1 particles, and not by the many spin-0 p a r t i c l e s present i n supersymmetric theories

?

Can one generate large masses f o r most of the new p a r t i c l e s , and why would the l i g h t ones remain unobserved

?

I t turns out t h a t the simplest answer t o these questions i s obtained by i n t r o -

ducing near p a r t i c l e s as the superpartners of the ordinary ones. The photon i s associated

with a spin-1/2 photino while the gluons a r e associated with an o c t e t of spin-1/2

gl uinos. Leptons and quarks a r e associated with spi n-0 partners. The spi n-1/2 partners

of the

W'

and Z bosons a r e new fermions, which acquire masses of the order of inW and

mZ (unless supersymmetry were badly broken i n t h i s s e c t o r ) . Before symmetry breaking

t h e p h y s i c a l c o n t e n t o f t h e t h e o r y can be summarized as i n Table lEZ8]

I

S u p e r f i e l d

(

^{Spin 1}

1

^{Spin 1/2}

I

S p i n 0

I

Gauge superf i e l d s Photon, gluons Photino, g l u i n o s

w',

Z, e t c

1

^and

I

⁺ o t h e r "gauginos"

-

Higgs superf i e l ds

Table 1 : Content o f a supersymmetric t h e o r y o f p a r t i c l e s , i n d i c a t i n g R - p a r i t y characters : + f o r o r d i n a r y f i e l d s ,

-

f o r t h e i r superpartners.

Lepton and quark s u p e r f i e l d s

I n many o f these t h e o r i e s one can d e f i n e a conserved quantum number, R, which i s c a r r i e d by t h e supersymmetry generator [ 28y 41

,

43

.

Gauge bosons, Higgs bosons

,

leptons and quarks a l l have R = 0, w h i l e t h e i r superpartners, photino, gluinos, spin-0 l e p t o n s and quarks, etc., have R = c 1. Even i n t h e absence o f a continuous R-invariance (as i s t h e case when g r a v i t a t i o n i s considered), one can s t i l l d e f i n e a conserved R-parity. I t ensures t h a t new, R-odd p a r t i c l e s can o n l y be pair-produced.

I t e x p l a i n s why n e u t r a l p a r t i c l e s which may remain massless o r light,such as t h e p h o t i n o and t h e g o l d s t i n o , have n o t been observed. (The g o l d s t i n o , which i s necessa- r i l y d i s t i n c t from t h e p h o t i n o [ 441

,

i s t h e Goldstone fermion a r i s i n g from t h e spontaneous breaking o f g l o b a l supersymmetry). T h i s scheme describes, i n general, supersymmetric t h e o r i e s o f p a r t i c l e s , i r r e s p e c t i v e l y o f t h e way t h e symmetry i s broken.

I f t e c h n i c o l o r were used t o t r i g g e r t h e electroweak symmetry breaking t h e s p i n - 0 Higgs f i e l d s i n Table 1 would be techniquark condensatesC451

.

T h i s approach faces problems f o r l e p t o n and quark mass generation, and symmetry breaking. I n any case the m o t i v a t i o n s f o r t e c h n i c o l o r and supersymmetry are r a t h e r opposite.

One can wonder about t h e i n t e r e s t o f supersymmetry, s i n c e Table 1 i n d i c a t e s t h a t a l l p a r t i c l e s have been d u p l i c a t e d . However, i f Higgs s u p e r f i e l d s a r e s u i t a b l y matched w i t h gauge s u p e r f i e l d s one gets, a f t e r gauge symmetry breaking, r e l a t i o n s between massive s p i n - 1 gauge bosons and spin-0 Higgs bosons : they belong t o t h e same m u l t i p l e t s o f supersymrnetry (see Table 2) ^[ 28, 461

Spin 1/2 p a r t n e r s o f Higgs bosons

-

Higgs bosons

+

Leptons and quarks

+

Spin-0

l e p t o n s and quarks

-

P. Fayet

Lepton and quark superf i e l ds

Superf i e l d Massless gauge s u p e r f i e l d Massive gauge superf i e l ds

Spin 1/2 Photino, g l u i n o s

-

Spin 1 Photon, gluons

+

Table 2 : P a r t i c l e content o f a supersymmetric spontaneously broken

gauge theory, i n d i c a t i n g t h e R - p a r i t y characters and t h e r e l a t i o n s between massive gauge bosons and Higgs bosons.

Spin 0

W*

,

Z,

....

+

Leptons, quarks

I ⁺

SPONTANEOUS SUPERSYMMETRY BREAKING

Spin-0 l e p t o n s and quarks

-

Supersymmetry i s hard t o break spontaneously, due i n p a r t i c u l a r t o t h e f a c t t h a t any supersymrnetric s t a t e , i f i t e x i s t s , i s n e c e s s a r i l y s t a b l e . There a r e two known methods t o o b t a i n a spontaneous breaking o f g l o b a l supersyrinetry i n f o u r dimensions. The f i r s t one makes use o f an a b e l i a n U(1) gauge group [391

.

The second one, which can be a p p l i e d t o semi-simple gauge groups, r e l i e s on a system o f spin- 112 and spin-0 p a r t i c l e s , having i n t e r a c t i o n s c a r e f u l l y chosen i n such a way t h a t no supersymmetric vacuum s t a t e e x i s t s [401

.

T h i s i s a r a t h e r exceptional s i t u a t i o n . The best way t o have i t i s t o impose t o t h e t h e o r y R-invariance as an a d d i t i o n a l symmetry, R denoting t h e new quantum number c a r r i e d by t h e supersymmetry

generator [28y 41, 431

.

( I f R-invariance i s n o t used, s u p e r s y m e t r y breaking occurs o n l y i f c e r t a i n terns, although allowed by t h e symmetries o f t h e t h e o r i e s , a r e o m i t t e d from t h e Lagrangian d e n s i t y ; w h i l e t h i s i s t e c h n i c a l l y j u s t i f i e d , owing t o t h e s o - c a l l e d "non-renormalization theorems"C301, i t looks r a t h e r u n n a t u r a l ) .

The p o s s i b i l i t y o f a dynamical breaking o f t h e supersymmetry has a l s o been considered, although t h i s i s n o t l i k e l y t o occur r 4 5 7 47-491. The naTve reason i s t h a t , due t o t h e special r o l e o f t h e energy, o n l y those condensates which preserve supersymmetry can form ( t h e s i t u a t i o n , however, may be d i f f e r e n t i n s u p e r g r a v i t y [491).

I n c e r t a i n cases, t h e "index theorem" a l s o i n d i c a t e s t h a t no dynamical supersymmetry breaking should occur1471

.

I n s t a n t o n e f f e c t s , f i n a l l y , m i g h t break t h e supersymme- t r v r47, 501

Charged and n e u t r a l heavy fermions

-

L o c a l l y supersymmetric t h e o r i e s

-

s u p e r g r a v i t y -C291 o f f e r s a t t r a c t i v e new p o s s i b i l i t i e s f o r symmetry breaking. The super-Higgs mechanism, which generates a mass f o r t h e spin-3/2 gravitinor51'can a l s o generate l a r g e mass s p l i t t i n g s between bosons and fermions i n t h e m u l t i p l e t s o f supersymmetry, provided t h e g r a v i t i n o i t s e l f i s heavy 152, 531

Charged and n e u t r a l Higgs bosons :

w*

,

2,

...

-k

Depending on which method of symmetry breaking is used, different classes of models can be obtained. They all describe, as in [281 , spin-0 leptons and quarks, gluinos, etc., and share many properties. How the supersymmetry is spontaneously broken is only relevant to have information on the mass spectrum, mass relations, etc.

An extra U(l)

?

If one wants to make all spin-0 leptons and quarks heavy at the tree approxima- tion, in a globally supersymmetric theory, the gauge group must include an extra U(1) factor at least IZ8' 441 e.g. it can be SU(3) x SU(2) x U(l) x U(l), or SU(5) x U(1), etc. The extra neutral gauge boson U is related by supersymmetry both to the spin-1/2 goldstino (or, in supergravity, to the spin-3/2 gravitino) , and to the usual dilaton-like Higgs boson u of the standard model. It should have essentially axial couplings to usual leptons and quarks. One finds mass relations which read, in the simplest case

:

2 2 2 2

(

m2(w') - ^m2(w')

⁼

^{m (Z)} - m (z)

=

- ^{(m (U)} - m (u))

=

4p 2 m2(spin-0 lepton or quark) - m (lepton or quark)

2 = p

2

m (with

4

- 2y 1.

wk,z and u are the Higgs Bosons associated with the gauge bosons w', Z and U under supersymmetry. The above relations imply that spin-0 leptons and quarks should be lighter that

%

m - ^{40 ~ev/c',} otherwise the charged Higgs w ' would have too small a mass or even a negative one. (See Fig. 4).

2

Extending the gauge group usually leads to unacceptable deviations from the neutral current phenomenology of the standard model. It should be noted, however, that if the new gauge boson U is light, the new neutral current amplitudes, propor-

0

[541 tional to GF , are essentially negligible for momentum transfer /ql>>mU .

mu + q

Experimentalists should therefore be very attentive to deviations from the standard phenomenology which would only be apparent at lower values of q2

;

as,in particular, in parity-violation atomic physics experimentsC3'. Neutral current processes (neu- trino scatterings, asymmetry in e - ' e annihilation, atomic physics)

;

searches for narrow resonances in e ' e - annihilation

;

searches for new particle production in kaon,

J,

and

T

decays, ... already impose very strong constraints on the existence of a new neutral gauge boson, assuming of course it is coupled with normal strength r54-

561

. If, on the other hand, an extra Higgs singlet is present the effects of the new boson may be extremely small, this particle being almost "invi- sible".

The mass relations (7) automatically ensure that the spin-0 u and c quarks, for example, are nearly degenerated in mass. This also occurs in other types of supersymmetric models.

As

a result a super-GIM cancellation operates to suppress unwanted flavor-changing neutral current amplitudes induced by the exchange of a

[57 1

pair of spin-0 particles .

photon p h o t i n o

v

, New heavy

/ /

/ fermions

-I /

/ /

I

z

^/

/ L/

/

Standard Higgs

/ -

^IC

^,

^boson

w' d - --

- ^{- -}

gluons gl uinos

u

\ ^I

(New gauge

: ^3.

boson)

2.

I S 1-

I i I

\

Spi n-0 Leptons and quarks

go1 d s t i n o Leptons and quarks (+ g r a v i ti no)

F i g . 4 : Typical mass spectrum o f a supersymmetric t h e o r y o f p a r t i c l e s w i t h an e x t r a U(1) 1281

.

^The

m,- ,

and

---

stand f o r spin-1, s p i n - l / 2 and spin-0 p a r t i c l e s , r e s p e c t i v e l y . Note t h e r e l a t i o n between t h e new s p i n - 1 gauge boson, t h e spin-1/2 g o l d s t i n o (or, i n supergravity, t h e spin-3/2 g r a v i t i n o ) and t h e usual d i l a t o n - l i k e spin-0 Higgs boson.

An a t t r a c t i v e feature of t h e e x t r a

U(l)

i s t h a t g l o b a l conservation laws B, L, R, appear as automatic consequences o f gauge invariance. Moreover, t h e l o c a l U(1) ensures t h a t i n g r a n d - u n i f i e d versions o f such t h e o r i e s p r o t o n decay amplitudes are a u t o m a t i c a l l y suppressed by two powers of t h e grand-unif i c a t i o n massT 581

,

w h i l e

C

591 R-invariance a l l o w s f o r a c o u p l i n g o f t h e t h e o r y t o s u p e r g r a v i t y

.

I n i t s minimal v e r s i o n t h e t h e o r y i s n o t anomaly-free. Although anomalies are n o t easy t o cancel if one wants t o keep a s e n s i b l e mass spectrum, t h i s does n o t appear t o me as a serious problem, s i n c e one can envisage anomaly-free extensions w i t h a m i r r o r s e c t o r o f l e p t o n s and quarks heavier than t h e i r spin-0 p a r t n e r s 1561 (see a l s o [60] ). I n any case anomalies a r e e s s e n t i a l l y i r r e l e v a n t i f t h e new U(1) c o u p l i n g constant g" i s v e r y small ( o r a l s o i f t h e new boson mass i s made v e r y

large[611)- In the limit g"+

0[541,

the parameter

p2

appearing in eq. (7) being fixed, the goldstino gets "invisible" and decouples (cf. refs.146, 621

) ,

the para- meter d (which fixes at the same time the supersymmetry breaking scale and the strength of the goldstino interactions, or equivalently the gravitino mass in a locally supersymmetric theory [633641),proportional to L, 2 becoming very large.

4"

The limiting theory has only SU(3) x SU(2) x U(l) as the local gauge group, while the supersymmetry is softly broken by a single dimension-2 operator.

No extra U(l)

There exist alternatives to an enlargement ofthe gauge group. One appealing possibility, developed recently, is to consider the coupling of supergravity to gauge and matter ~u~erfields'~~'

65'

661and to rely on the super-Higgs mechanism[511 to generate large masses for spin-0 leptons and quarks, comparable to the gravitino mass m

3/2

^[52y

531. By disregarding gravitation, keeping fixed, one finds, in flat space, ~ o f t [ ~ ~ ~ s u ~ e r s y m m e t r y breaking terms of dimension

,<

3

[531.

In this approach the gravitino mass

=

&=e ^G~:$E~~ d should be relatively large.

6

Not too large, however, otherwise one would have difficulty to understand how the W mass can be small compared to the gravitino mass. Since the supersymmetry breaking scale d1I2 is given by

6112 ;(L) 1/4 ^dm

48 Planck m3/2

the term "geometrical hierarchy" is sometimes used to refer to models with a heavy gravitino having a mass comparable to the

W

mass. One has then

d1I2

%

JG

^%

^{10 lo-'' ~ev/c'.} Supergravity may be used, a1 so, as a possi- ble way to resolve the ambiguity existing between different vacua in supersymmetric theories C66,

681

Another popular method is to use radiative corrections to make spin-0 leptons and quarks heavy

[69y701.

One first considers (cf. ref .C401), a sector of spin-112 and spin-0 particles with carefully chosen interactions so that supersymmetry gets spontaneously broken at a relatively high scale. This generates masses for gluinos and other gauge fermions at the two-loop level, and subsequently, masses for spin-0 leptons and quarks, at the three loop level.

These models look, however, somewhat complicated. While spin-0 leptons should be relatively light

(6 $),

spin-0 quarks, which acquire their masses through strong rather than electroweak interactions, may be heavier

;

gluinos could have a mass in the 1 to 100 TeV/c range. One neutral spin-1/2 particle (Higgsino) may remain light, 2 and could possibly be the lightest R-odd particlet691.

SPIN-0 LEPTONS AND QUARKS AND PHOTINOS

Spin-0 leptons and quarks are unstable and decay extremely quickly into the

[

281 corresponding lepton or quark by emission of a photino, goldstino or gluino .

(see Fig.

5).

(However, if these decays were kinematically forbidden, one would

have i n s t e a d three-body decay modes such as spin-0 muon + spin-0 e l e c t r o n ;e vu, e t c . induced by spin-1/2 W' exchanges ; see F i g . 6).

spin-0

l e p t o n

\

p h o t i no o r g o l d s t i n o

s p i n-0

quark

\

photino, go1 d s t i no o r g l u i no F i g . 5 : Two-body decay modes o f spin-0 l e p t o n s and quarks. The p h o t i n o couplings

(eQ,,

J;I)

a r e f i x e d by t h e e l e c t r i c a l charge, those o f t h e g l u i n ~ s by c o l o r .

b B

The couplings o f t h e massless spin-1/2 g o l d s t i n o a r e eq

f i

=

qfl ^,

^{i n}

which am' i s t h e m a s s L - s p l i t t i n g between spin-0 and spin-1/2 l 6 t o n s and quarks, and d i s t h e parameter which f i x e s t h e scale o f supersymmetry breaking [63, 641

.

When supersymmetry i s r e a l i z e d l o c a l l y t h e massless, s p i n - l / 2 g o l d s t i n o i s replaced by a spin-312 g r a v i t i n o o f mass

4/2

= T h i s one i s almost n o n - i n t e r a c t i n g unless i t i s v e r y l i g h t , i n which case i t behaves l i k e a massless spin-1/2 g o l d s t i n o .

F i g . 6 : Example o f a three-body decay mode s -t S

;

v (assuming m(su) > m(se)) due

v

e e u

t o t h e exchange o f t h e f e r m i o n i c p a r t n e r o f t h e

w'.

Spin-0 l e p t o n s and quarks can be p a i r produced i n e'e- a n n i h i l a t i o n , as shown i n Fig. 7 : ^{l 7 1 1}

- ^-

e e - - -

^s

,'

s ~ , q

e

/

photi no

or goldstino

\

\ -

- - _ - - -

e + s e+ s

8 4

e

Fig.

7 :

Pair production of spin-0 leptons and quarks i n e+e- annihilation. Photino and goldstino exchanges contribute only in the case of spin-0 electrons.

Assuming a two-body decay mode f o r spin-0 leptons, we have the process

:

e+e-

^-t

Pair of spin-0 leptons

+ - + -

-t

Non-coplanar pair ( e e ,p p or,T+T-)

+

2

unobserved photinos or goldstinos

Systematic searches f o r spin-0 leptons have been carried out a t

PETRA

and,more recently, a t PEP[^^'. The r e s u l t s a r e shown i n Table

3 .

Table

3 :

Limits on the masses of spin-0 leptons.

In short, one has CELLO

JADE

MARK

J MARK I 1 PLUTO

TASSO

(2 spin-0 leptons)

m (spin-0 electron o r muon)

>

16

G ~ V / C '

m

(spin-0 tau)

z 15

GeV/c

²

T h e s e l i m i t s a r e close t o the maximum beam energy available. I t i s , also,possible t o produce a s i n g l e spin-0 lepton in association with i t s spin-1/2 partner and a photino or goldstino~71' . This may allow one t o get b e t t e r l i m i t s on spin-0 lepton

C731

masses

:

up t o 25

%

above the beam energy, in the case of spin-0 electrons .

Constraints on the mass matrix of spin-0 p a r t i c l e s may a l s o be obtained by studying Excluded mass r a n g e f o r s p i n - 0 l e p t o n s

ST

{>

^{-+ -t}

15.3

^{3 . 8} 4

+ 1 3 mT

⁺ 14 mT ⁺ 9 . 9

- -

e 2-t

16.8

4 6

- -

<13

<16.6

S li ^I

3 . 3 +

16

-

3

+

15

- -

d 6 . 4

f lavor-changing t i e u t r a l c u r r e n t amp1 i t ~ d e s [ ~ ~ ' a n d p a r i t y v i o l a t i o n e f f e c t s i n nuclear [741

physics

.

I n t h e f u t u r e a good way t o l o o k f o r spin-0 p a r t i c l e s would be t o search f o r t h e i r p a i r p r o d u c t i o n i n e'e- a n n i h i l a t i o n a t t h e Z p o l e : see F i g . 8

F i g . 8 : P a i r p r o d u c t i o n o f spin-0 l e p t o n s and quarks i n e'e- a n n i h i l a t i o n . This assumes, o f course, t h a t t h e new spin-0 p a r t i c l e s a r e l i g h t e r than mZ/2 Supersymmetry would then l e a d t o an increase o f t h e Z w i d t h by a t most % 50 %. If spin-0 l e p t o n s and quarks a r e s u f f i c i e n t l y l i g h t compared t o

3

and can indeed

L

decay i n t o photinos, g o l d s t i n o s o r gluinos, one expects t h a t i) about 3 % o f t h e Z decays w i l l have a non-coplanar e'e-, p'u- o r T'T- p a i r i n t h e f i n a l s t a t e w i t h h a l f t h e energy missing on average, i i ) about one f o u r t h o f t h e Z decays w i l l l e a d t o f o u r j e t events ( f r o m spin-0 quarks decaying i n t o g l u i n o s ) , and a v e r y small f r a c t i o n t o non-coplanar t h r e e - j e t events w i t h l a r g e energy m i s s i n g (from one spin-0 quark decaying i n t o a g l u i n o , t h e o t h e r i n t o a p h o t i n o o r a g o l d s t i n o ) (see e.g. ref.1751 ) .

tloreover, w h i l e a Z can decay i n t o neutrinos, spin-0 neutrinos, etc., i t does n o t couple t o photinos. The " n e u t r i n o counting" r e a c t i o n e'e- -. yZ (+ unobserved neutrals)[761 i n which one looks f o r t h e peak i n t h e photon spectrum corresponding t o t h e p r o d u c t i o n o f a Z, can g i v e i n f o r m a t i o n on n e u t r a l bosons and fermions coupled t o t h e Z (e.g. r e f . [ 7 7 1 ) b u t n o t on photinos.

I f spin-0 e l e c t r o n s a r e n o t t o o heavy, photinos i n t e r a c t w i t h e l e c t r o n s more s t r o n g l y than n e u t r i n o s As a r e s u l t t h e r e may be a way t o know, r e l a t i v e l y soon, about spin-0 e l e c t r o n s and photinos, by searching f o r t h e r a d i a t i v e p a i r

[ 791 p r o d u c t i o n o f photinos i n e'e- a n n i h i l a t i o n (see F i g . 9)

.

-

^[801, b u t i t s cross s e c t i o n i s s i g n i f i - This process i s s i m i l a r t o e'e- + yvv

c a n t l y l a r g e r i f spin-0 e l e c t r o n s a r e between 16 and 40 ~ e v / c ' , and i f photinos are n o t t o o heavy. I t may be measurable a t PETRA/PEP energies. I f no s i g n a l i s found a t t h e r e q u i s i t e l e v e l , t h e existence o f l i g h t photinos coupled t o spin-0 e l e c t r o n s l i g h t e r than % 40 ~ e ~ / c ' would be excluded.

F i g . 9 : R a d i a t i v e p r o d u c t i o n o f photinos i n e'e- a n n i h i l a t i o n , induced by t h e exchange o f a spin-0 e l e c t r o n .

GLUINOS AND R-HADRONS

Gluinos are a c o l o r o c t e t o f n e u t r a l spin-112 p a r t i c l e s associated w i t h t h e gluons under supersymmetry. I n g l o b a l supersymmetry they are always massless a t the t r e e approximation, b u t they may acquire a mass by r a d i a t i v e c o r r e c t i o n s . However, s i n c e R-invariance acts on gluinos i n a c h i r a l way t h e generation o f mass f o r g l u i n o s i s n e c e s s a r i l y r e l a t e d w i t h an ( e x p l i c i t o r spontaneous) breaking o f

inva variance[^^,^^].

(Unless t h e r e e x i s t s a second o c t e t o f spin-112 p a r t i c l e s having opposite R-transform- a t i o n p r o p e r t i e s , i n which case one can c o n s t r u c t a mass term f o r Dirac gluinos i n an R - i n v a r i a n t way). From the t h e o r e t i c a l p o i n t of view g l u i n o s could be massless, l i g h t , o r heavy.

Gluinos may combine w i t h quarks, antiquarks and gluons t o g i v e new c o l o r s i n g l e t hadronic s t a t e s named R-hadrons ( q q q g l u i n o , q

q

g l u i n o , etc.)C821. R-hadrons should i n p r i n c i p l e be unstable and decay i n t o o r d i n a r y hadrons by e m i t t i n g a p h o t i n o o r g o l d s t i n o , w i t h o u t charged accompanying l e p t o n . A t y p i c a l R-hadron decay mode i s represented i n F i g . 10.

spin-0 quark

p h o t i n o o r g o l d s t i n o g l u i n o

R-pi on

hadrons

F i g . 10 : Decay of an R-pion i n t o a p h o t i n o ( o r g o l d s t i n o ) t hadrons.

I f the p h o t i n o i s l i g h t compared t o R-hadrons we have : a Q

r(R-hadron ^-t hadron

+

p h o t i n o ) ^%

7

m5 (R-hadron)

"'s q

A s i m i l a r formula i n v o l v i n g t h e supersymmetry breaking scale parameter d can be w r i t t e n f o r t h e g o l d s t i n o . I n l o c a l supersymmetry, as we s h a l l see, t h e massless spin-112 g o l d s t i n o i s replaced by a spin-3/2 g r a v i t i n o o f mass m

3/2 r641 and one f i n d s

R-hadrons are presumably s h o r t l i v e d , b u t m i g h t a l s o be l o n g - l i v e d , i f spin-0 quarks were very heavy (see r e f . [831 f o r c o n s t r a i n t s on quasi s t a b l e R-hadrons). I t i s then important t o be a t t e n t i v e t o t h e p o s s i b l e existence o f these p a r t i c l e s , w i t h o u t having too much t h e o r e t i c a l p r e j u d i c e about t h e i r masses and l i f e t i m e , which a r e model- dependent. One can search f o r missing energy c a r r i e d away by the unobserved n e u t r a l s i n c a l o r i m e t e r experiments [82y841. T h i s leads t o a lower

-

l i m i t on R-hadron masses, mR

3

1.5 o r 2 G~v/c'. Much s t r o n g e r l i m i t s can be obtained from beam dump experiments, provided spin-0 quarks are n o t t o o heavy [82,85,56,86,87]

From beam dump experiments one gets an upper l i m i t on the product up

oi ,

i n which o i s the p a i r p r o d u c t i o n cross s e c t i o n o f gluinos, and

ai

denotes a weighted average o f t h e r e i n t e r a c t i o n cross sections o f the photinos and g o l d s t i nos ( g r a v i ti nos) produced P

i n R-hadron decays. I t i s u s u a l l y s u f f i c i e n t t o t a k e o n l y the photinos i n t o consider- a t i o n . They r e i n t e r a c t w i t h m a t t e r by e x c i t i n g again R-hadrons i n t h e f i n a l s t a t e , w i t h a cross s e c t i o n oi p r o p o r t i o n a l t o (ms )-4, ms b e i n g t h e mass o f t h e spin-0 quark exchangedt781. This leads t o an upper l i m i t q on a

7

which can be transformed i n t o a

P

lower l i m i t on t h e R-hadron mass mR

,

as a f u n c t i o n o f m : see F i g . 11.

s C1

Given t h e present agreement between QCD p r e d i c t i o n s and experimental data one might t h i n k t h a t r e l a t i v e l y l i g h t gluinos would be forbidden. This, however, i s n o t t h e case,

5

since the p r e d i c t i o n s o f QCD w i t h (Majorana o r even Di r a c ) g l u i nos a r e very close t o t h e p r e d i c t i o n s o f standard QCD (provided o f course a s u i t a b l e r e d e f i n i t i o n o f the scale parameter A i s made)t881, w h i l e l a r g e r e f f e c t s m i g h t have been expected[891. Present data cannot d i s t i n g u i s h between standard QCD and QCD w i t h gluinos. The main e f f e c t o f g l uinos i s t o c a r r y some o f the momentum u s u a l l y a t t r i b u t e d t o gluons.

Gluinos may be produced i n processes such as ete- a n n i h i l a t i o n , quarkonium decays[891, p p s c a t t e r i n g s , and, o f course, p a n n i h i l a t i o n s a t h i g h energy. (See t h e proceedings o f the CERN workshop on supersymmetry as a reference f o r g l u i n o searches and, more generally, t h e phenomenology o f supersymmetryrgo1).

R-INVARIANCE, THE CP PROBLEM, AND BACKMARD HIERARCHY

The f a c t t h a t experiments p o i n t i n t h e d i r e c t i o n o f massive g l u i n o s i n d i c a t e t h a t ( i f t h e r e i s a s i n g l e o c t e t o f Majorana g l u i n o s ) , R-invariance should be broken, e x p l i - c i t l y o r spontaneously. I n t h e l a t t e r case one would have a Goldstone boson i n the theory.

1

-

excluded

I 1 L

F i g . 11 : Lower l i m i t on R-hadron masses from Fermilab (a)[861 and CHARM (b, p r e l i m i n a r y ) [ 8 7 1 beam dump experiments, as a f u n c t i o n o f the spin-0 quark masses mS

.

For mS < 40 (resp. 100) GeV/c one has

2

9 2 9

mR > 5 (resp. 3.5) GeV / c .From t h e r e one can deduce a lower l i m i t on the g l u i n o mass by s u b t r a c t i n g about 1 GeV/c 2 ( ? ) t o take i n t o account t h e e f f e c t o f the s t r o n g b i n d i n g f o r c e s .

I n f a c t the R-symmetry c u r r e n t u s u a l l y has a non-zero s t r o n g i n t e r a c t i o n anomaly.

This may be a t t r a c t i v e since, by means of an R-transformation one can r o t a t e away t h e CP-violating parameter 8 o f QCD. R-invariance, t h e r e f o r e , c o u l d be used as a Peccei- Quinn symmetry t o s o l v e t h e s t r o n g CP problem[911.

However, as i s w e l l known, the breaking o f a U ( l ) p Q symmetry leads t o a l i g h t axion.

This one c o u l d be a fundamental s c a l a r ; o r a bound s t a t e o f gluinos ( o r o f some s o r t o f " t e c h n i g l u i n o s " ) , i f t h e R-symmetry were dynamically broken. Since no axion has been found the i d e a i s tenable o n l y i f t h i s p a r t i c l e i s s u f f i c i e n t l y weakly i n t e r a c t i n g . This would be the case i f R-invariance were broken a t a s u f f i c i e n t l y h i g h scale

(3

1 TeV). This i s probably t o o h i g h a scale f o r a g l u i n o condensate (even i f we con- s i d e r the f a c t t h a t gluinos, which a r e o c t e t s , i n t e r a c t more s t r o n g l y than quarks, which a r e t r i p l e t s ) . I f we do n o t want t o i n t r o d u c e new s t r o n g c o l o r l i k e forces t o t r i g - g e r a dynamical R-symmetry breaking, we would have t o r e l y on a l a r g e vacuum e x p e c t a t i o n value f o r a t l e a s t one o f the R = i 2 spin-0 f i e l d s which are u s u a l l y present i n super- symmetric t h e o r i e s .

It i s a l s o p o s s i b l e t h a t t h e R-current i s f r e e o f s t r o n g i n t e r a c t i o n anomaly, i n which case one would have e i t h e r a t r u e massless Goldstone boson o r a verynearlymass-

P. Fayet C3-693

less pseudo-Go1 dstone boson f o r R-i nvariance. I t s existence can be excluded experiment- ally[921 unless, again, R-invariance i s broken a t a h i g h s c a l e .

A t

t h i s point i t i s i n t e r e s t i n g t o return t o the method introduced i n r e f . 1931, which shows how t o generate spontaneous Supersymmetry breaking, i

n

a non-Abel i an gauge the-

ory, by using the interactions of a s i n g l e t , an adjoint and two fundamental chiral superfields. Both the adjoint and the s i n g l e t carry R = 2, and have undetermined vacuum expectation values a t the t r e e approximation. Once the v.e.v. of the adjoint (which may be, f o r example, a 24 of SU(5)) i s fixed by the r a d i a t i v e corrections, the v.e.v. of the s i n g l e t adjusts i n such a way that the two spin-0 f i e l d s i n the fund- amental representations (those may be a 5 and

5

of SU(5), which would be responsible f o r the electroweak symmetry breaking) can be translated ( " s l i d i n g s i n g l e t " mechanism).

I f one does not consider the gauge i n t e r a c t i o n s , both the a d j o i n t and the s i n g l e t have vanishing vacuum expectation values, and R - i nvariance i s preserved [941. When the gauge interactions are taken into account i n the calculation of the e f f e c t i v e p o t e n t i a l , one finds t h a t both the adjoint and the s i n g l e t can have a runaway behavior a t the o r i g i n , and acqui re huge vacuum expectation values determined by the radiative correct- i o n ~ ' ~ ~ ] . This method of using radiative corrections t o f i x the value of the grand- unification mass i s known as "backward hierarchy".

A t

the same time i t can provide us, automatically, with an R-invariance spontaneously broken a t a very high s c a l e , namely the grand unification s c a l e , the corresponding Goldstone p a r t i c l e , or axion, being then " i n v i s i b l e " , as in r e f . [15].

Finally i t i s useful t o remind the reader t h a t i n a (simple) spontaneously broken supergravity theory the superHiggs me~hanism[~~'which provides a mass

m3/2

f o r the spin-3/2 gravi t i n o , necessari ly implies a breaking of R-invariance, leading therefore, e i t h e r t o the t r e e approximati on or by radiative corrections, t o massive gl ui nos and photinos[631. While they a r e negligible i f the gravitino mass i s small, such super- gravity e f f e c t s are obviously important as soon as the gravitino i s heavy.

SUPERGRAVITY, AND THE EFFECTS OF ME GRAVITINO IN PARTICLE PHYSICS AND ASTROPHYSICS When the supersymmetry algebra i s realized locally the spi n-2 gravi ton couples t o the energy momentum tensor T ~ ' while i t s partner, the spin-3/2 gravitino, couplCs

1291.

This i s the theory of supergravity.

t o the conserved vector-spinor current J a

The gravitino couples the electron t o spin-0 electrons, the photon t o the photino, e t c . All couplings a r e fixed by

K =

4

^{871 GNewton =} 4.11 10-l'

G ~ v - '

(13) When local s u p e r s y m t r y i s spontaneously broken, the super-Higgs mechanismr511 operates t o eliminate t h e massless spin-1/2 goldstino i n favor of new degrees of freedom f o r the spin 3/2 gravi tino. This one acquires a mass,

m3/2

= 'C d / ~ %

,

^{i n}

which the parameter d, which has the dimension of a mass2, measures the s c a l e of super- symmetry breaking (exactly as one has

$

=

% ^,

i n which v measures the s c a l e of the SU(2)

x

U ( l ) breaking). d1l2 i s often called the supersymmetry breaking s c a l e , but i t may be vastly d i f f e r e n t from the order of magnitude of the mass s p l i t t i n g s between