PHYSICAL REVIEW D VOLUME 28, NUMBER 5 1 SEPTEMBER 1983

Photino and gluino production from quarkonium decay

Wai-Yee Keung Physics Department, Brookhaven National Laboratory, Upton, New York 11973

(Received 1 1 April 1983)

The branching ratios of T ( V+g g g ) / T ( V-3g ) and r( V-g g7 )/r( V-gg y ) could be larger than 10% for the scalar-quark mass less than 1.3 times the mass of the quark in the quarkonium V. The signature of these events would be the large momentum imbalance, especially for the case of the photino production.

I. INTRODUCTION

Rare decays of the heavy quarkonium V could provide interesting physics, such as the productions of glueballs, axions, Higgs bosons, etc. Here we study the decays of heavy quarkonium into photinos and gluinos, which are the spin-half superpartners of photons and gluons, respec- tively, in the framework of supersymmetric theories.'

With supersymmetry spontaneously broken to explain the known elementary-particle spectrum, both the gluino and the photino are usually protected by the gauge invari- ance to remain massless at the tree level. They acauire - m

small masses only through radiative corrections. Because a <<as, one expects the photino mass is far less than the gluino mass. Experimental data are consistent with a massless photino, as its interactions with the ordinary matter are quite weak.2 On the other hand, gluinos carry colors, and thus they could have already been produced and observed if they were too Beam-dump experi- m e n t ~ ~ . ~ set a lower limit for the gluino mass of about a few GeV. In the present paper, we neglect the photino mass and also assume the gluino is not too heavy.

Campbell, Ellis, and ~ u d a z ~ studied the gluino pair pro- duction from a massive virtual gluon accompanied by two gluon jets in the quarkonium decay. Their calculation is independent of the mass of the scalar quark, which is sup- posed to be heavy. However, the partial width of this pro- cess (V- two gluon + two gluinos) is of order as4. Also, the similiar process cannot occur for the photino

production. We complement their work by studying the processes of order as3 (aaS2) with the scalar-quark ex- changes which are usually suppressed by their propaga- tors. From our study we learn that the suppression would not be severe for the case where the corresponding scalar quark is not twice as heavy as the quark in V. This scenario could possibly be realized for the presumed top- quarkonium. The signature of these events would be the large momentum imbalance, especially for the case of the photino production.

11. DECAY AMPLITUDES AND RATES

Figure 1 illustrates the Feynman diagrams for the pro- duction of gauge fermions from the decay of a vector quarkonium. The process proceeds via the exchange of scalar quarks. The final state includes a gluon g, a gluino g, and a second gauge fermion E, which can either be a photino 7 or another gluino The contributions from di- agrams with the gluon legs attached to the outgoing lines cancel each other when the overall amplitude is antisym- metrized. As suggested by most supersymmetric models we assume both the scalar partners of the right-handed and left-handed quarks have a common mass 6, which is usually larger than the quark mass m. The resulting am- plitude is

with

Here the symbols V, g, g, and Ealso denote the momenta of the corresponding particles. fl represents the quarkoni- um vertex and is related to the wave function +(?=O) at the origin,

in the nonrelativistic approximation7 in which the quar- konium mass is 2m. The polarizations of the quarkonium and the gluon are 6, and E,, respectively. The coupling

constants and the color factors are lumped toggher into G in Eq. (1). Let i,j, k be the color index of g,g, k. Then we obtain

1129 @ 1983 The American Physical Society

WAI-YEE KEUNG - 28

The energies E above are measured in the rest frame of V. We also define

n = m E / m , (7)

h =(% 2 / m 2 - 1 - n 2 ) / 2 . For the case of V+ggT, the corresponding allowed region is

k 0 < z < 1 - n 2 , (8)

y $ 1 - z / 2 + ( ~ / 2 ) [ 1 - n 2 / ( 1 - z ) ] " ~ .

FIG. 1. Diagrams for the process V+ggE. Ecan either be a For the other case V-gg7, the corresponding allowed re- photino or a gluino. Dashed lines represent the exchanges of gion is scalar quarks. The conjugate diagrams with and g inter- changed are not shown here. O < Z < 1 - n 2 / 4 ,

(9)

The kinematics for the decay process v - ~ ~ K can be with the assumption of a negligible photino mass studied in terms of the scaling variables m,=O . (10)

Using the computer program SCHOONSCHIP we are able to

(6) carry though the trace algebra defined in Eqs. (1)-(3). The resulting rates for v - ~ ~ E , normalized with respect to V-ggk, are given below:

Here 6= 1 for k = y, otherwise zero. Rk includes the effects due to the mass of the gluino. For case k =g or y, they are

Rg=[2+2(1-z ) ( l+xy) -3 (x +y)2 /2]n2-z2n2(n2-2h + h 2 ) / 2 , (12)

~ ~ = ( n ~ / 6 4 ) [ 2 n ~ ( 3 + 8 ~ - 4 y -2xy -2x2)+ 16h2(x -y ) (2+z) - -n2(n4+4n2h +8h2)

+ 1 6 h n ~ ( l - ~ +3x -xy -x2)+4n2(18-16y+12xy +y2+4x2y -21x2+4x3)

mg/m m ~ / m

FIG. 2. The branching ratio T ( V + g s ) / T ( V-ggg vs the FIG. 3. The branching ratio r( V-ggj ; ) / r ( V-ggy) vs the gluino mass for the cases that the scalar-quark mass m" = m , gluino mass for the cases that the scalar-quark mass E =m, 1.2m, 1.5m, and 2m. 1.2m, 1.5m, and 2m.

PHOTINO AND GLUINO PRODUCTION FROM QUARKONIUM . . . 1131

FIG. 4. The energy distribution of the gluon jet measured in the rest frame of V. Here z = E, / m . The cases A = 1.2m, 1.5m, and 2m with a negligible gluino mass are illustrated.

111. NUMERICAL ANALYSIS AND DISCUSSION

With formulas presented in the previous section we cal- culate the branching ratios Ti ~ - ~ g E ) / r i V-ggk ) for the cases of k =g and y, as shown in Figs. 2 and 3. The scalar-quark mass 6 is varied within the range of i n t e r ~ t s between rn and 2rn. The branching ratios r ( V - g g k ) / T ( V-ggk) are larger than 10% for f i < 1.3rn with a light gluino rng < 0.2rn.

The process V-ggg gives rise to events with three jets with one from the gluon and two from the gluinos. The energy distributions of the gluon and the gluinos are illus- trated in Figs. 4 and 5, from which we know they are all energetic in general. To distinguish these events from the ordinary ones, V-ggg, it requires accurate measurements of the missing energy carried away either by the photinos or by the Goldstone fermions from the subsequent decays of the gluinos.

The other process V-ggy offers better detection signa- tures as it looks like a two-jet event with the primary pho-

I J',' I 0 0 'I 1 1 I I I L L

0 0 0.2 0 4 0.6 0 8 I .O

Y

FIG. 5. The energy distribution of the gauge fermion (7 or g7 measured in the rest frame of V. Here y = E / m or Ez /m. The

Y cases f i = 1.2m, l.Sm, and 2m with a negligible mass are illus- trated.

tino unregistered in the experiment, thus resulting in about one third of the total energy missing. This process, unlike V--+ggg, is kinematically allowed even for a rather heavy gluino: rn 5 rng <2m, assuming m y =O. Therefore, it pro- vides a possible source for heavy gluinos in the e + e - col- lision. The rate is unfortunately suppressed by cr/cr,, hence higher statistics are required for the detection. There exists a background from the r pair production

r - 1 V - r f r - , followed by 7'- hadrons + v ,, with con- siderable missing energy. Unlike the signal, it gives events of two jets almost back to back. The missing momentum transverse to the hadron axis is limited below rn, for this background and not for the signal V-ggY in general.

ACKNOWLEDGMENT

This work was supported in part by the U.S. Depart- ment of Energy under Contract No. DE-AC02- 76CH00016.

'For the phenomenology of the supersymmetry, see review arti- cles by I. Hinchliffe and L. Littenberg, in Proceedings of the 1982 DPF Summer Study on Elementary Particle Physics and Future Facilities, Snowmass, Colorado, edited by R. Donald- son, R . Gustafson, and F. Paige (Fermilab, Batavia, Illinois, 19821, p. 242; P. Fayet, in Proceedings of the 21st Znternation- a1 Conference on High Energy Physics, Paris, 1982, edited by P. Petiau and M. Pornuef [J. Phys. (Paris) Colloq. &3 (1982)l.

2P. Fayet, Phys. Lett. m, 272 (1979). 3G. Farrar and P. Fayet, Phys. Lett. m, 442 (1978).

4G. L. Kane and J. P. Leveille, Phys. Lett. m, 227 (1982). 5F. Bersma et al. (CHARM Collaboration), Phys. Lett. m,

429 (1983). 6B. A. Campbell, J. Ellis, and S. Rudaz, Nucl. Phys. m, 1

(1982). 'For a summary, see W.-Y. Keung, in Proceedings of Z0 Physics

Workshop, Zthaca, New York 1981, edited by M . Peskin and S.-H. H. Tye (Laboratory of Nuclear Studies, Cornell Univer- sity, Ithaca, 1981), p. 276.