POLARIZATION AS A TOOL FOR REVEALING SUPERSYMMETRIC PARTICLES

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POLARIZATION AS A TOOL FOR REVEALING SUPERSYMMETRIC PARTICLES

F. Renard

To cite this version:

F. Renard. POLARIZATION AS A TOOL FOR REVEALING SUPERSYMMETRIC PARTICLES.

Journal de Physique Colloques, 1985, 46 (C2), pp.C2-23-C2-30. �10.1051/jphyscol:1985203�. �jpa-

00224512�

POLARIZATION AS A TOOL FOR REVEALING SUPERSYMMETRIC PARTICLES

F.M. Renard

Département de Physique Mathématique*, Université des Soienoes et Techniques du Languedoo, 34060 Montpellier Cedex, France •'

Résumé - Les particules supersymétriques diffèrent des particules ordinaires par une demi-unité de spin. Leur production dans les collisions de faisceaux polarisés présente donc des asymétries particulières qui devraient permettre de les identifier plus facilement. Des exemples typiques sont la production de gluinos dans les collisions proton-antiproton, de photons directs à grand moment transverse, de fermions scalaires dans les collisions e+e

. Nous pré- sentons les premiers résultats d'un travail en cours sur la production de particules supersymétriques dans les collisions e+e

polarisées.

Abstract - Supersymmetric particles differ from ordinary ones by half a unit of spin. This lead to special asymmetries in their production with polarized beams which should allow a better identification. Typical examples are gluino production in pp collisions, direct photon production at large pj, and sca- lar fermion production in e+e - collisions. We report on a work in progress about supersymmetric particle production in polarized e+e~ collisions.

I - INTRODUCTION

The idea of Supersymmetry (fermion-boson symmetry) is at least 13 years old j \ j . Applied to quantum field theory it leads to very interesting possibilities like extension of space-time symmetries by internal symmetries, reduction of divergences in perturbation theory, inclusion of gravity / 2 / . Phenomenological models however appeared difficult to construct / 3 / . Ordinary particles do not fall into supersym- metric multiplets unless one assumes that they are associated with new particles

(the Susy-partners) differing by half-a-unit of spin. Examples are (& ,t„ ; l) , (V% ' ^ ' ( H ± ; V™2 ; W ± ) > ( H ° ! \ ' \ ' Z ° ) • (~ 5 Y) , (g ! g). One can check that in each supermultiplet the number of fermionic degrees of freedom is equal to the number of bosonic ones. i T _ and q T _ are spin zero particles (scalar leptons and quarks associated to the left or right chiral leptons and quarks) ; H - and H are charged and neutral scalar bosons (Higgses) ; W. and W„

. f^J f^J t^U I^J

axe Dirac fermions (Winos) ; Z, ,Z„,Y and g are two-component majorana termions (Zinos, photino, gluinos). As none of them have yet been experimentally observed this means that Susy is broken in the particle spectrum, i.e. the partners have much higher masses.

In spite of that Susy got an impressive theoretical interest during the last ten years and which keeps growing /3,4/. The main reasons are that it gives a possibi- lity of constraining the scalar sector of the electroweak theory (Higgs mechanism).

The Fermi scale (W mass) can be found as a consequence of Susy breaking. Susy may solve the hierarchy problem in ttrand Unified Theories. Realized locally super- symmetric invariance describes gravity and gives a hope of establishing a unique

*Physique Mathématique et Théorique, Equipe de Recherche Associée au CNRS

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985203

C2-24 JOURNAL DE PHYSIQUE

d e s c r i p t i o n of a l l p a r t i c l e s and i n t e r a c t i o n s .

Various models of Susy b r e a k i n g have been proposed /3,4/. Most of them l e a d t o t h e minimal spectrum r e p r e s e n t e d i n F i g . I . A new quantum number ( R ) i s a l s o i n t r o d u c e d (R = 0 f o r u s u a l p a r t i c l e s and ' ¹ f o r t h e ~ u s ~ - ~ a r t n e r s ) . T h i s c o n s t r a i n s Susy p a r t i c l e s t o be produced i n p a i r s and t o decay by cascade down t o t h e l i g h t e s t s t a b l e one ( g e n e r a l l y t h e p h o t i n o y, which could e v e n t u a l l y decay very weakly i n t o

N N m N

-

a photon and a g r a v i t i n o ) . Examples : A * A+? ; q

q+g ; g * g+y o r qq + y ;

gauge bosons ( s p i n 1 )

i n o s l e p t o i l s s l e p t o n s Higgses q u a r k s s q u a r k s

( s p i n $) ( s p i n O)

F i g . 1 : Example of minimal spectrum i n Susy models /3,4/.

W N

G, ? ' (a2 _{o r qq)} + ( y o r g ) ; . . . e t c . T h i s l i g h t e s t p a r t i c l e w i l l escape detec- t i o n s o t h e ~ r o d u c t i o n of Susy p a r t i c l e s i s always c h a r a c t e r i z e d by m i s s i n g energy- momentum.

+ -

Negative experimental s e a r c h e s have been c a r r i e d - i n e e and i n hadronic c o l l i s i o n s /5,6/. From t h e absence of e+e- * A4 and - G qq a t Pep and P e t r a one can s e t % - 2 16 GeV. A t Pep t h e r e a c t i o n e'e- -. eey h a s been e s p e c i a l l y

17

q

s t u d i e d i n o r d e r t o push t h e l i m i t on t h e s e l e c t r o n mass s l i g h t l y h i g h e r

(mv 2 23 G ~ v ) . The r e a c t i o n e+e- ' y? i s even s e n s i t i v e t o h i g h e r v a l u e s through t h e i n f l u e n c e of t h e s e l e c t r o n propagator but i t s a n a l y s i s r e q u i r e s a good c o n t r o l of t h e background / 6 / . Beam dump experiments gave t h e l i m i t m > 3 GeV.

I \

W -

Various t e s t s have been proposed /7/ f o r c o l l i d e r s i n pa%icular i n connec-

t i o n w i t h W and Z production (decays of W ,Z i n p a i r s of Susy p a r t i c l e s O r

anomalous W,Z p r o d u c t i o n due t o Susy p r o c e s s e s ) . The r e c e n t UAl and UA2

e v e n t s showing m i s s i n g energy-momentum a s s o c i a t e d w i t h l a r g e pL photons o r j e t s

a r e sometimes taken a s a f i r s t h i n t f o r t h e production of Susy p a r t i c l e s . Obviously

c a r e f u l a n a l y s e s w i t h much more s t a t i s t i c s a r e r e q u i r e d . I n e+e- c o l l i s i o n s t h e

l i m i t a t i o n i s e s s e n t i a l l y due t o t h e a v a i l a b l e energy. SLC and LEP w i l l be welcome.

u s u a l p a r t i c l e s t h e p r o d u c t i o n of Susy p a r t i c l e s s h o u l d p r e s e n t d i f f e r e n t p o l a r i z a - t i o n asymmetries. A good Susy s i g n a t u r e i s m i s s i n g energy-momemtum a s s o c i a t e d t o a s p e c i a l p o l a r i z a t i o n asymmetry. Secondly p o l a r i z a t i o n a s u s u a l w i l l h e l p f o r ampli- tude a n a l y s i s and f o r t h e d e t e r m i n a t i o n of t h e b a s i c c o u p l i n g s of the new p a r t i c l e s . T h i s w i l l be n e c e s s a r y i n o r d e r t o prove t h a t t h e s e p a r t i c l e s a r e t h e ones p r e d i c t e d by t h e supersymmetric gauge t h e o r y and i n order t o choose among t h e v a r i o u s p o s s i b l e models.

We show t h a t a t y p i c a l f e a t u r e of Susy p a r t i c l e p r o d u c t i o n i s a change of s i g n of c e r t a i n p o l a r i z a t i o n asymmetries w i t h r e s p e c t t o t h e c a s e of o r d i n a r y p a r t i c l e pro- d u c t i o n . T h i s i s a v e r y profound p r o p e r t y of Supersymmetric i n v a r i a n c e r e l a t e d t o t h e s o - c a l l e d non-renormalization theorems / 2 , 3 / . T e s t s c o u l d e a s i l y be done a t

+ -

e e c o l l i d e r s .

I1 - TYPICAL ILLUSTRATIONS

A/ Gluino p r o d u c t i o n i n p o l a r i z e d p';' c o l l i s i o n s

The s u b p r o c e s s gg + E ( a s w e l l a s o t h e r gaugino p r o c e s s e s ) h a s been c o n s i d e r e d a s one of t h e most p r o m i s s i n g s o u r c e of Susy p d r t i c l e i n h a d r o n i c c o l l i s i o n s / 7 , 8 / . The p e c u l i a r h e l i c i t y dependence of t h i s p r o c e s s a s compared t o t h a t of t h e u s u a l p r o c e s s gg gg was n o t i c e d by C r a i g i e e t a 1 / g / .

N e g l e c t i n g m, t h e c r o s s - s e c t i o n s r e a d : R -

dU h h ' - ^{t u t+u 2 ' 2}

, ^{( g g - gg) = S* [ ( l - -$ t U ]} ( l - h h ' ) 4 S S

where h , h ' a r e t h e i n i t i a l gluon h e l i c i t i e s . The c o r r e s p o n d i n g asymmetries a r e shown i n F i g . 2 . The p e c u l i a r f a c t o r ( I -hht ), i . e . A = -1 f o r g l u i n o p r o d u c t i o n

LL

F i g . 2 : H e l i c i t y asymmetries i n gg

- gg and gg

gg / g / .

C2-26 JOURNAL DE PHYSIQUE

i s t y p i c a l of t h i s subprocess ( h e l i c i t y conservation along t h e fermion l i n e ) and should n o t s u r p r i s e t h o s e f a m i l i a r w i t h e+e- * yy o r yy qq /10/. The change of s i g n of hL w i t h r e s p e c t t o gg

gg s u r v i v e s g l u i n o mass e f f e c t s and convo-

I \

l u t i o n w i t h spin-dependent p a r t o n d i s t r i b u t i o n s i n s i d e p o l a r i z e d p and':) a s shown by C r a i g i e e t a l . These a u t h o r s considered a l s o t h e o t h e r subprocesses - -

gq * gq, gg * qq and qq * qq. T h e i r c o n c l u s i o n i s t h a t missing-energy-momentum e v e n t s due t o Susy p a r t i c l e p r o d u c t i o n should be c l e a r l y a s s o c i a t e d w i t h h e l i c i t y asymmetries i n p o l a r i z e d p';) c o l l i s i o n s .

B/ L i n e a r p o l a r i z a t i o n of d i r e c t photons produced i n p ( o ) c o l l i s i o n s

This i s an example of f i n a l p o l a r i z a t i o n produced w i t h u n p o l a r i z e d beams. The sub- processes q + g M q+y and q+q * g+y a r e t h e s t a n d a r d s o u r c e s of d i r e c t photons i n h a d r o n i c c o l l i s i o n s . QCD c a l c u l a t i o n s even by i n c l u d i n g heavy quark mass e f f e c t s / i f / p r e d i c t only a n e g l i g i b l e photon p o l a r i z a t i o n :

Antoniadis e t a 1 / 1 1 / remarked t h a t l a r g e r mass e f f e c t s a r i s e in supersymmetric

N W N N

c a l c u l a t i o n s which u s e the subprocesses q+g q+y and q+q g+y. The e s s e n t i ~ l difference- w i t h t h e effect- of massive t o p q u a r k s i n t h a t t h e p r o b a b i l i t y of f i n d i n g squarks q and g l u i n o s g i n s i d e proton s t r u c t u r e is much l a r g e r . According t o Kounnas and Ross /12/ f o r l a r g e (deep s t r u c t u r e ) 32% of proton momemtum i s c a r r i e d by Susy p a r t o n s . With such an i n p u t and m-= 20 GeV, 4 GeV, Antoniadis

9 g

e t a 1 g e t a l i n e a r p o l a r i z a t i o n approaching 1% f o r J s = 540 GeV and 30 GeV.

This i s a good i l l u s t r a t i o n of Susy e f f e c t s . However t h e r a t e of l a r g e pl photons i s s m a l l and a 1 % l i n e a r p o l a r i z a t i o n i s n o t an easy measurement t o do.

The Susy-parton c o n t e n t s of t h e proton c o u l d be t e s t e d i n e-p c o l l i s i o n s w i t h HERA. This was s t u d i e d by Jones and LleweLlyn Smith /12/ but t h e i r conclusions were not very o p t i m i s t i c . The a v a i l a b l e energy f o r the subprocesses w i l l be j u s t s u f f i - c i e n t and t h e i d e n t i f i c a t i o n of Susy p a r t i c l e s among t h e background w i l l be d i f - f i c u l t . F o r more d e t a i l s s e e t h e r e p o r t by P. SchmUser a t t h i s symposium.

+ -

C/ S c a l a r fermion p r o d u c t i o n i n e e c o l l i s i o n s

J. S o f f e r /13/ remarked t h a t t h e s i g n s of t h e cos 29 dependence f o r t r a n s v e r s a l l y p o l a r i z e d e' beams d i f f e r in e+e- * and i n e+e-

f ? .

P r e c i s e l y through one photon a n n i h i l a t i o n one has : 2 2 3

da - @ & f B 2

- (e'e- * Z) -

dR s i n 8 ( I - P+ P- cos zV)

8 s J.1

These e x p r e s s i o n s a r e e x a c t l y those of ete- * n+n- and e+e- - ^pp i n t h e point- l i k e l i m i t /10/. The t h i s change of s i g n i s v e r y g e n e r a l

(compare . l 2 o ) , independent of s i g n s of coupling c o n s t a n t s and

a n n i h i l a t i o n hidden i n a background of s p i n l e p t o n o r hadron production.

The preceding example motivated a more g e n e r a l s t u d y of t h e p o l a r i z a t i o n p r o p e r t i e s i n Susy p a r t i c l e production. I now r e p o r t on a work i n p r o g r e s s by P. C h i a p p e t t a , J. S o f f e r , P. Sorba, P. Taxi1 and myself /14/. We consider both l o n g i t u d i n a l ( P )

& //

and t r a n s v e r s e (P1) e beam p o l a r i z a t i o n s . We t r e a t s e v e r a l t y p e s of Susy p a r t i - c l e s (sfermions and gauginos) and i n c l u d e t h e decay d i s t r i b u t i o n e f f e c t s .

Cross-section i n e+e- c o l l i s i o n s have t h e g e n e r a l h e l i c i t y s t r u c t u r e /l 0/ :

+ (P~-P;)[X cosq + X sinrp] + ( P > P ~ ) [ x ~ cosq + X ' sinrp]

6 7 7

+ p l p i + [X3 cos 2 r p + X s i n 2 r p + X 1.

4 5

We d i s c u s s t h e f o l l o w i n g l o n g i t u d i n a l and t r a n s v e r s e asymmetries :

and

-

+ -+ N

-

a ) e e P= t9 pR % and decay W - W Y .

We compute t h e c r o s s - s e c t i o n due t o a n n i h i l a t i o n through y and Z 0 /14/.

It c o n t r i b u t e s t o X. ( i = 1 , 2 , 3 , 4 ) . F i g . 3 a shows t h e l o n g i t u d i n a l asymmetry which mainly r e s u l t s from t h e v e c t o r - a x i a l combination of t h e y-ZO i n t e r f e r e n c e and which

N N N

obviously changes sign from t o %. If % and % a r e not d e g e n e r a t e one h e r e has

N

a very good s i g n a l f o r s c a l a r l e p t o n production. I f and % a r e degenerate t h e sum of t h e i r c o n t r i b u t i o n s t o

A// e x a c t l y c o i n c i d e s w i t h t h e one of e+e-

p+@-.

F i g . 3b showsthe r e s u l t i n g t r a n s v e r s e asymmetry i n t h e case o f ^{m_ =} 20 and 40 GeV.

+ -

A s expected i t changes s i g n w i t h r e s p e c t t o t h e case of e e - ^. Even i f one could n o t d i s t i n g u i s h e+e- * from e+e-

p'p- G t h e ave;aged t r a n s v e r s e

+ -

asymmetry i s s t i l l v e r y d i f f e r e n t from t h e pure y )L case a s soon a s we stand above t h e ZO peak. For example a t J s = 100 GeV f o r mw = 20 GeV, A: i s equal

P

t o +0.40, t h e pure c a s e i s - 0.33 and t h e average i s - 0.1 6.

JOURNAL DE PHYSIQUE

+ -,-=

--

F i g . 3 : L o n g i t u d i n a l and Transverse asymmetries i n e e PP

(I p YY /14/.

.E .4-

2 a

-.4

-.a

.E

-

MI W N

b ) e+e- ' e e and decay e

e+y .

W W

-

I n a d d i t i o n t o a n n i h i l a t i o n through y and Z 0 which produce ALAL and Z& we a l s o have gaugino G, ?, . . .) exchanges which c o n t r i b u t e /l 5/ t o t h e 4 processes

+ -

L L , a\, ^2L2R, and g i v e s new X 1 terms. S i m i l a r l y t o t h e case of e e ' A A

192

photon exchange i n Bhabha s c a t t e r i n g t h e gaugino exchange p r o c e s s e s i n c r e a s e t h e r a t e s , peak t h e a n g u l a r d i s t r i b u t i o n s but do not d i r e c t l y c o n t r i b u t e t o t h e t r a n s v e r - s e asymmetry ( e x c e p t by t h e i r i n t e r f e r e n c e w i t h t h e a n n i h i l a t i o n terms).

,c--.

---

I \ 8 , -

---

- ---____-

8'

,

lln '

S

---,,"' ,

,

g

, e+e-- {p-

- - - - -- -

,

- -- --

^f --.--- - - I - - -

- --. .-. _'. , , ^{, , ,}

, .

- ^(a) '., _'.-.,' ^; '., .. -_________--- - PL -

Around t h e Z peak where t h e a n n i h i l a t i o n terms dominate t h e g r o s s f e a t u r e s of t h e

+ - + - F -

asymmetries a r e s i m i l a r t o those of e e y y . See f o r example t h e t r a n s v e r s e asymmetry i n Fig. 4 compared t o t h e one of e+e- ' e+e-. For J s = 100 GeV t h e d i f - f e r e n c e w i t h Bhzbha s c a t t e r i n g i s w e n very s t r o n g f o r t h e l o n g i t u d i n a l asymmetry e s p e c i a l l y i n t h e backward r e g i o n a s shown i n Fig. 5.

9e

,

-.K.

+ - -

Fig. 4 : Transverse asymmetry i n e'e- ' ee

e e y y , i n t e g r a t e d on 8 between

900 and 1400 a t i s = m z /l 4/.

+ -

+ - -

F i g . 5 : L o n g i t u d i n a l asymmetry i n e e

ee

e e yy a t J s = 100 GeV /14/.

+ - + - -

Even i f one could not e x p e r i m e n t a l l y d i s t i n g u i s h e+e-

efe- from e e

e e yy t h e r e s u l t i n g asymmetries a r e s t i l l d i f f e r e n t from t h e pure Bhabha c a s e . For example a t J s = m, t h e pure Bhabha t r a n s v e r s e asymmetry i s A? = - 0.66, t h e pure

L

l.

N C ;

e e one i s + 0.58 and t h e averaged one i s - 0.27.

c ) Other p r o c e s s e s . _{+ -} -

'W

A p p l i c a t i o n s t o e e

vv, qq a r e s t r a i g h f o r w a r d . Other i n t e r e s t i n g channels a r e

+ -

e e

2 gauginos o r h i g g s i n o s ( T , Y , ? , ~ , . . . ^). We s u s p e c t t h a t t h e p o l a r i z a t i o n e f f e c t on efe-

yG ^{w i l l} be n o t a b l y d i f f e r e n t from t h e one on i t s background e'e-

yvc s o t h a t much b e t t e r l i m i t s on mm and 4 - qould a l r e a d y be given w i t h

* ^{e Y}

p o l a r i z e d e beams. These c a l c u l a t i o n s ^are i n p r o g r e s s / l 4/.

I V - CONCLUDING REMPrRKS

I n t h e v a r i o u s examples t h a t we have t r e a t e d t h e s t r i k i n g f e a t u r e of Susy p a r t i c l e production i n p o l a r i z e d c o l l i s i o n s i s t h e change of s i g n of c e r t a i n p o l a r i z a t i o n asymmetries. T h i s i s not an a c c i d e n t b u t a very deep p r o p e r t y of Supersymmetry. T h i s change of s i g n between fermion and boson c o n t r i b u t i o n s i s the b a s i c i n g r e d i e n t of t h e s o - c a l l e d non r e n o r m a l i z a t i o n theorem /2,3/. For example i n -e+e- c o L l i s i o n s

-

NN N

G

one can e x p l i c i t e l y and very e a s i l y check (adding e'e-

fT, f L f L and f R f R ) t h a t when summing over a complete S u s y m u l t i p l e t and n e g l e c t i n g t h e mass d i f f e r e n c e s t h e t o t a l t r a n s v e r s e asymmetry ( i . e . X? term of do e x a c t l y c a n c e l s . When one remem- b e r s t h a t e'e- a n n i h i l a t i o n c r o s s - s e c t i o n i s r e l a t e d t o t h e r e n o r m a l i z a t i o n f a c t o r of boson propagators t h i s may not be a s u r p r i s e . P o l a r i z e d c o l l i s i o n s w i l l not only be of h e l p f o r d e t e c t i n g Susy p a r t i c l e s , it w i l l be a way of t e s t i n g one of t h e deepest p r o p e r t y of Supersymmetric i n v a r i a n c e .

.L

Azimuthal cos 2q dependence of t h e c r o s s - s e c t i o n f o r n a t u r a l l y p o l a r i z e d e- beams was a l r e a d y observed a t v a r i o u s efe- c o l l i d e r s . I e s p e c i a l l y remember t h e 1975 experiment / l 6/ a t Spear which c l e a r l y showed t h a t quarks have s p i n &.

Why not a s i m i l a r experiment a t h i g h e r e n e r g i e s r e v e a l i n g Supersymmetry ?

JOURNAL DE PHYSIQUE

F i g . 6 : Azimuthal dependence of o ( e + e - hadrons) measured by SLAC-LBL a t S p e a r (/S = 7.4 G ~ V ) i n 1975 /16/.

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