Mass of photino and scalar lepton production in e+e− annihilation

Volume 134B, number 3,4

PHYSICS LETTERS

12 January 1984

MASS OF PHOTINO AND SCALAR LEPTON PRODUCTION IN e+e - ANNIHILATION

T. KOBAYA:~I~i

Laboratory of International Collaboration on Elementary Particle Physics, University of Tokyo, Japan and M. KURODA

Institut fur Theoretisehe Physik, Universith't Regensburg, Fed. Rep. Germany Received 13 October 1983

The scalar lepton production in e+e- annihilation is reconsidered with the specific emphasis on the effect of the finite photino mass.

One of the most direct confirmations of supersymmetric theories (SUSY) is the detection of the new kind of particles inherent to the theories, i.e., the supersymmetric partners of the usual particles, such as scalar leptons (V), scalar quarks ('~), photino (~'), etc.. For the detection of such particles, it is crucial to know the possible range of their masses. Theoretical situation on this issue is still quite unsatisfactory and there is considerable flexibility in the possible spectrum [1]. This is because, although couplings are determined unambiguously by the supersymmetry principle, masses and mixing angles are dependent on the symmetry breaking used in the model. There are mainly two classes of models for the symmetry breaking of SUSY. One class [2] predicts almost massless photino, while the other class [3] predicts heavy photino and heavy scalar leptons of the mass of order row~2. Since there is such a wide range of possibility for the spectrum, it would be an appropriate attitude, in the phenomenological analysis of SUSY, not to be too much biased by the specific symmetry breaking pattern of the model. In this paper we consider the scalar lepton production in e+e - annihilation with general finite masses of photino and scalar leptons.

Scalar lepton pair production. There are two kinds of scalar leptons ~:1 '~e and ffL, whose masses are in general different. Especially in several models [3], the mass o f ~ L is heavier than the mass o f ~ R because the former may get an extra contribution from the left-handed SU(2) weak interactions. In this case, the process e+e - ~ ~R~'R is the energetically most feasible process to detect the scalar leptons. The relevant diagrams for the process are shown in fig. 1. The case of massless photino is discussed by Farrar and Fayet [4]. Keeping the photino mass ( m @ and the scalar lepton mass (m~re) , the matrix element for the process e+e ->~R"{R is modified as follows c/~ = o(P2) {e2(~l - ~2)/(Pl +P2 )2 + ½(1 -- q,S)[-2e2K/(3b 1 - ~1 -- my)] -~(1 + 75)}u(Pl),

(1)

where K = 0 (1) for scalar muon (electron) pair production ,z. The differential cross section then becomes do/d cos0 = (n~2/32E2eam)[33sin20 (1 + [1 - 4K/(1 - 2/3 cos0 +/32 + U2)] 2),

(2)

+1 The symbols t~ and s• are also used in the literature in place of ~YRand ~rL for right-handed and left-handed scalar leptons. +2 Here we neglect the contribution from goldstino, which is eaten by gravitino in the local SUSY. 0.370-2693/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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Volume 134B, number 3,4

~R(k2 )

eR(k~ )

PHYSICS LETTERS

~R

12 January 1984

/eR pb

o -

100

e*(P2)

e-(p~)

e"

72'2'

e+

,~

Fig. l. Feynman diagrams for e e--+ ~R~R .

.....

.mi---

10

.,), \\

Y\l

l:ig. 2. Total cross section a(e+e --+ ~R'~'R at Ebeam = 20 GeV for the photino mass my =_0, 10 and 20 GeV/c 2, and total cross section a(e+e - -~ ~'R~'R) at Ebeam = 20 GeV, which is independent of m~, and which corresponds to the ms~ = ~,, case of the ~rRgR pair production cross section.

5

10

15

20

m~, [6eV/cq

where ~ = m T / E and 132 = i -- m 2 /E 2. The threshold behaviour 133 = (1 - m 2 /E2) 3/2, and sin20 behaviour reR . . .R . . . . flect the p-wave nature of the process and result from the spin o f g and its chlral couphng. This behavIour as common to other SUSY particle productions e+e - -+ u u [5], and e+e - -+ ~'~" [6]. Fig. 2 shows the total cross section for'gR~"R pair p r o d u c t i o n at b e a m energy E = 20 GeV as a function o f the scalar electron mass, rn~ , for several values o f the photino mass, m9,. The cross section becomes smaller as the photino mass increases. Th~s implies that even if the scalar electron pair production is not detected by P E T R A experiments, there is still a possibility of scalar electron mass being slightly lighter than the b e a m energy if the photino mass is heavy. F o r comparison, we include in fig. 2 the total cross section for ~'R~"R pair production, for which the photino exchange diagram does not contribute [K = 0 in eqs. (1) and (2)] and which corresponds to the mN = oo case o f the "ge~R pair production. ReCently, GlOck and Reya have calculated o(e+e - -+~R'gR + ~Lg'L + ffR'gL + ~L'gR) with the assumption rn~, + - + ~ ~ . . . . . . . R = m,~ , and found that o(e e eRe L + eLeR), which vanishes m the massless p h o t m o hrmt, Induces an enhancementLnear the threshold. When m~ 4= m~ , however, (most probably m~ > m~ ), although this enhancement near tile eRe L threshold persists, t~e sltuah_on is more subtle. Firstly the process e e - ~ e r e L + eLe R has a higher threshold than the process e + e - _ ~ ~RTR . Secondly, even if the b e a m energy i s h i g h enough to produce e~Re~L pair, the cross section o(e+e - ~ ~RTR) might be larger than a(e+e - ~ TR'~L + ~L~R), simply because of the large phase space for the former process. F r o m the experimental point of view, the enhancement near the threshold is o f practical help only when rnw = m . ~ . The differential and the total cross sectmns fore'he process e+e -+ e r e L are given as •

do(e+e o(e+e

.

. R

--

-+ eR~L)/d Cos 0 : (rra213'/2E2eam)#2/(1 -- 213'cos0 + 13,2 + ~2 _ A2)2, _+~R,~t) -_t i.rrct2o,,E2 . 2,/[(1 +13,2+ /./2 _ A2)2 _413,2], p / beam)/./

where ~'

= final m o m e n t u m / E = { [1

/_.X= (rn2 R

(m~R + m~,L)2/4E 2 ]

[1 - (rng R - m,gL)Z/4E2 ] } l/2,

m2L)t4E2.

Eqs. (3) and (4) reduce to the result obtained in ref. [7] when rn~R = m~.L (A = 0). 2'72

(3) (4)

e-

e +

12 January 1984

PHYSICS LETTERS

Volume 134B, number 3,4

e*

Fig. 3. Dominant Feynman diagrams for e÷e- ~ e+'~R~"when the final e÷ is not detected.

e-

Single scalarelectron production. When the scalar electron is heavier than the beam energy (but still mg + m~, < 2Ebeam), the single scalar electron production, e+e - ~ e +- + photino + scalar electron, takes place. The complete calculation with massless photino is given in ref. [8] in the case when final e -+ is also detected. When final e -+ is not detected, the one photon exchange diagrams dominate (see fig. 3) and the equivalent photon approximation works quite well [8,9 ]. Using the equivalent photon approximation, the cross section Otot(e+e- ~ e+~'R7 -'') is given as 1

a2rr[X(g,m2,m2 3"

Otot = f dy F(y) x (

)] 1/2

32E4y 2

m2 _ m 2 eR 3'

X 1+7

eR

4(m 2 eR

g

+

-m2)(g+m 2 - m 2 )

[~/-X--g--m2R+m21)

eR

g[X(g,m2,m2R)]l/2

..........

in V~+§+m2R_m2

,

(5)

where x =(m?. R

+rn~.)2/4E2,

F(y) =-~- [1 +(1 _ y ) 2 ] ,

X(a2,b2,c2) = [a2-(b+c) 2] [a2-(b-c)2],

§ = 4 y E 2.

(6)

Fig. 4 shows ato t as a function of the photino mass, m z , at Ebeam = 20 GeV and m~, = 20, 22 and 24 GeV/c 2. / K The cross section is of order 0.1 pb and decreases with increasing photino mass or scalar electron mass. In order to reduce the background, it is necessary to make a cut on the energy and the scattering angle of the electron coming from the scalar electron. The experimentally important quantity is, therefore, the differential cross section, which is expressed as follows 1

da(e+e - -+ e+~'R~)/d cos0

=f

dyF(y)

Ymin (

/+m2R--2m 2

a27r,x/a_'~-J ( c o s 0 ,y) 32E4yZ

2(m2 R - m 2 ) ( g + m 2

3"~

X

l+

R - m 2) 2m2 (m2 --m2)\ m°R

s(f-m2R)

g

+

,

if-m2. )2

|, !

(7)

where cos 0 is a scattering angle of the scalar electron in the laboratory frame and J(cos0 ,y) = (4V~g k2/x/'X) [(1 +y)co + (1

t=m 2 - 2yE(co "R

k cos0),

-y)k

cos0] - 1 ,

co 2 = k 2 + m 2 eR"

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Volume 134B, number 3,4

PHYSICS LETTERS

12 January 1984 1

i

do

o(e'e----~ e*gR~)

pb

ggTg

pb

= L~OGeV

r n ~ .

1

(e.e____. e.ERi)

=~0 5eV = 22 GeV/c

0.1

m~ = 10

0.01

0.01

5

I0

I

0

cos 0

I.ig. 5. Differential cross section do(e+e- --+ e+gR~')/d cos 0 at Ebeam = 20 GeV, mzfR = 22 GeV/c 2 and rn~. = 0 and 10 GeV/e 2 .

15

l'ig, 4. Total cross section atot(e+e - ~ C+VR~') at £beam = 20 GeV for the scalar electron mass ~ = 20, 22 and 24 GcV/c 2" meR k is the m o m e n t u m o f t h e scalar e l e c t r o n in the l a b o r a t o r y frame and is given b y 2 ) 2XFy(1 -y)COcCOS0 -+ (1 + y ) [4y(co~ - rn~R k

(1

y ) 2 m 2 R s i n 2 0 ] 1/2

--

(l +y)2

(1

y ) 2 cos20

w i.t h co,, =. (7 + m 2e R - m 23 ') / 2 .V ' 7 . The o t h e r q u a n t i t i e s F ( y ) , X a n d g are defined in eq. (6). The typical angular dis, ~ t r l b u t l o n is s h o w n m fig. 5 t o r m,r = 22 G e V / c 2 and r n - = 0 a n d 10 G e V / c 2. It has n o p r o m i n e n t s t r u c t u r e except near c o s 0 = - 1. R y In c o n c l u s i o n , we w o u l d like to p o i n t o u t t h a t the effect o f the p h o t i n o mass is fairly s u b s t a n t i a l in scalar elect r o n p r o d u c t i o n . Even w h e n the scalar e l e c t r o n is n o t f o u n d at P E T R A e x p e r i m e n t s , o n c e the mass o f the p h o t i n o is k n o w n or its u p p e r or l o w e r b o u n d is well d e t e r m i n e d , we can set a b e t t e r b o u n d for scalar e l e c t r o n mass in the process discussed in this paper. The a u t h o r s w o u l d like to t h a n k Professor E. Reya and Professor S. Y a m a d a for useful c o m m u n i c a t i o n . T.K. t h a n k s the DESY d i r e c t o r i u m for the k i n d h o s p i t a l i t y e x t e n d e d to h i m at DESY a n d he is grateful to Professor M. K o s h i b a for s u p p o r t .

References [ t F For example, see, C.1t. Llewellyn Smith, talk at the CERN supersymmetry workshop (1982), Oxford preprint ref. 44/82. [2] P. Fayet, in: Unification of the fundamental particle interactions, eds. S. Ferrara, J. Ellis and P. vna Nieuwenhuizen (Plenum Press, New' York, 1980). [3] J. Ellis, L.l:. Ibanez and G.G. Ross, Phys. Lett. l13B (1982) 283; J. Ellis, J.S. Hagelin and D.V. Nanopoulos, Phys. Lett. 116B (1982) 283. [41 G.R. Farrar and P. lrayet, Phys. Lett. 89B (1980) 191. [5] R.M. Barnett, K.S. Ladencr and H.E. Haber, SLAC preprint SLAC-PUB-3105. [6] J. Ellis and J.S. Hagelin, Phys. Lett. 122B (1983) 303. [7] M. Glfick and t'. Reya, Phys. Lett. 130B (1983) 423. [8] M. K uroda, K. lshikawa, T. Kobayashi and S. Yamada, Phys. Lett. 127B (1983) 467. [9] M.K. Gaillard, L. Hall and 1. Hinchliffe, Phys. Lett. l16B (1982) 279. 274