ϒ decay into two gluinos

Volume 134B, number 3,4

PHYSICS LETTERS

12 January 1984

T DECAY INTO TWO GLUINOS Gad EILAM 1 and Avinash KHARE 2 Department o f Physics, Brookhaven National Laboratory, Upton, N Y 11973, USA

Received 13 September 1983 Mass splitting between the superpartners of the b quark may induce a substantial branching ratio for T ~ ' ~ ' if m~' < 5 GeV.

Heavy quarkonia can decay into a gluino pair plus two gluons via an ~4s process [1] (see fig. la). It was shown that for zero gluino mass [2] R a =-

F(3S 1 ~ gg~'~)/F(3S1 -~ ggg) ~" 0.3

(m~, = 0),

(1) if we use a s = 0.2 in the results of ref. [2]. drops fast as m~. increases [1], with 6% ~ B R ( T - ~ g g ~ ) ,5< 0.04%

R a

then

for 1 ~
(2) These values are independent of the masses of the scalar superpartners of quarks. A gain o f one power in as and larger phase space are typical of the squark mediated process [3,4] 3 S1 -+ g ~ (see fig. lb). Although possibly important for toponium, squark masses of 20 GeV or higher mean a negligible rate for T ~ g ~ . A 3S l particle can also decay directly into two gluinos (see fig. lc). Parity is obviously violated in this 1 Permanent address after 1 September 1983: Physics Department, Technion, Haifa, Israel. 2 Permanent address after 1 september 1983: Institute of Physics. Bhubaneswar, India.

decay, as is also the case for the one-loop process [5] e+e - ~g~" (for Z 0 -+g~" see refs. [6] and [7] ). This is possible in broken supersymmetric QCD when the two spin zero chiral squarks may have different masses [8]. Toponium ~ g g was considered in ref. [9] and it was found that for various values of the relevant parameters the rate for this process could be substantially larger than that for toponium -+ e+e . Here we complement the results of ref. [9] by focusing on T -+ g g. Unlike the case of the top quark which may well be O(mw) or larger the smallness of m b leads to small mixing between the scalar partners of b. Furthermore, whereas the lightest between the two stops may obey rn,r~ < mt, the case is opposite for b quarks. One would therefore not expect a very large enhancement for T -+ g ~. This advantage may be compensated by the fact that T is a well established particle and absence of its decay into a gluino pair may restrict m~, to be higher than 4.5 GeV or so, while toponium has yet to be discovered. As in ref. [9] we find F ( T _ + . ~ ) / F ( T ~ e + e _) = 4(O~s/a)2 C2(1 - ,,,,.~/,,Ob ,..2/.,2~3/2 j ,

with C = [(m 2 - m 2g +m~)2 - 1

(3) (m b 2 _ m 2g +m22)-1]//,/2.

(4) g ~

~

QI I

(a)

(b)

(c)

Fig. 1. Representative diagrams contributing to gluino production in 1 decays.

0.370-2693/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

Since there is a wide possible range of masses m ~ ' , rn~-2 and m~, we present the branching ratios for T - + ~ in fig. 2 as a function ofm~, in two cases: m~"2 = m~"1 + 2m b (fig. 2a) as advocated in ref. [11], and a larger splitting with an arbitrary fixed value [5] m~"2 = 120 GeV. We obtain substantial branching ratios 269

Volume 134B, number 3,4

rc I

t

I

PtIYSICS LETTERS

OGe ' t

I

m'6"Z=m'~l+ 2m b

GeV

~'

I

3 0 GeV

0.1

~

GeV

I

12 January 1984

is the photino (which is presumably stable), 1/3 of" the energy should he missing, and a m o m e n t u m imbalance will show up. Detailed Monte Carlo simulations are o f course needed since a jet structure is not that p r o n o u n c e d in q~ decays [13]. We are unaware o f any study o f missing energy under the T, and hope that the results presented here will encourage such analyses. We would like to thank the members of" the BNL T h e o r y G r o u p for their warm hospitality, and Yee Keung and Laury Littenberg for helpful discussions. One o f us (G.E,) thanks the Lewes Center for Physics for excellent atmosphere and Serge Rudaz for good advice.

References [b) i

i

2

5

4

rn~(GeV)

5

2

i

I

4 m'~lGeV) 3

I

5

Fig. 2. Branching ratios for 'i' -+ ~'~" as a function of m~" for various values o f m g . (a) mg = mg"1 + 2rn b. (b) rn'~2= 120 GeV. We use c~s = 0.3, m b = 5~GeV and [10] BR(q~ ~ e+e-) = 5.1%.

which for large m~, are usually larger than B R ( T -+ g g g g). We considered here values o f m,g larger than 1 GeV since lower limits on m~, from beam d u m p experiments [12] are m~, > 1 to 4 GeV, depending on various assumptions. There are however arguments in favor o f a higher value for m~- [9,11]. Since gluinos are expected to decay into qgl'~ where

270

[ 1 I B.A. Campbell, J. Ellis and S. Rudaz, Nucl. Phys. B 198 (1982) 1. [21 G. Eilam and M. Gliick, Technion preprint PHYS-83-7 (1983). [ 3 ] W.-Y. Keung, Brookhaven preprint BNL-32961 (1983). [4J M. Gliick, Phys. Lett. 129B (1983) 257. [5] P. Nelson and P. Osland, Phys. Lett. I15B (1982) 407. [6] G.L. Kane and W.B. Rolnick, Nucl. Phys. B217 (1983) 117. [71 B.A. Campbell, J.A. Scott and M.K. Sundaresan, l'hys. Left. 126B (1983) 376. [8[ J. Ellis, J.S. 11agelin, D.V. Nanopoulos and K. Tamvakis, Phys. Lett. 125B (1983) 275. [91 J. Ellis and S. Rudaz, Phys. Lett. 128B (1983) 248. [10] C. Berger et al., Phys. l,ett. 93B (1980) 497. [11] P. Fayet, Phys. Lett. 125B (1983) 178. [12] E. Bergsma et al., Phys. Lett, 121B (1983) 429. [ 13 [ K, Berkelman, Cornell preprint, CLNS-83/564 (1983).