Single squark production at e+e- colliders

Volume 171, number 4

PHYSICS LETTERS B

1 May 1986

SINGLE SQUARK P R O D U C T I O N AT e + e - C O L L I D E R S A. B A L L E S T R E R O 1NFN, Sezione di Torino, 1-10125 Turin, Italy

and E. M A I N A Istituto di Fisica Teorica, Unioersiti~ di Torino and INFN, Sezione di Torino, 1-10125 Turin, Italy

Received 6 December 1985

Single squark production is examined at present and next-generation e+e - machines. In addition to total cross sections, missing energy and angular distributions are discussed which could allow detection of these events despite rather small rates.

In recent years much attention has been devoted to the search for experimental evidence of supersymmetric particles [1,2]. As is obvious, if supersymmetry has anything to do with the real world it must be broken by some, so far unknown, mechanism. On the other hand, the scale of supersymmetry breaking should not be too far from the weak scale if the theory is to solve the hierarchy problem. Available data indicate that no charged partner of known particles exists with mass lighter than about 20 GeV [3]. Recent analyses of collider results from UA1 and UA2 have strenghtened these limits for gluinos and squarks leading to three possible "scenarios" [4] : (i) rn-g > m -q > 4 0 - 5 0 GeV, (ii) m~ > m~- > 4 0 - 5 0 GeV, (iii) m~" = 3 - 7 GeV with m z > 6 0 - 8 0 GeV. These analyses rely on Monte ~arlo simulation of experimental cuts and of sparticle fragmentation and hence the limits are subject to uncertainties which are not easy to assess. e+e - colliders provide a much cleaner environment for particle searches. Therefore it is of interest to give detailed predictions of supersymmetric particles production at e+e - machines. Several possibilities have been explored in the literature. If sparticles have mass smaller than the beam energy the main production mechanism is in pairs [5]. Otherwise they can be produced singly in a three-body final state, with a sizeable cross section if they are not too heavy. In particular single scalar electron production in a wide range of energies [6] and sleptons and squarks production at the Z 0 peak [7] have been studied. In this letter we examine single squark production at present and next generation e+e - machines. In addition to total cross sections we discuss missing energy and angular distributions with various sparticle masses which can possibly lead to nice experimental signatures. In our calculation we assume that both the photino and the zino correspond to mass eigenstates and neglect possible rnixings. Our conventions are those of Haber and Kane [1 ]. Sparticles o f R- and L-chirality are taken to be degenerate in mass and their contributions are summed over. The photino mass is neglected. All squark masses are assumed to be equal and we sum over the contributions of five flavours. We choose sin20 w = 0.23, m Z = 92 GeV, F z = 3 GeV,t~ s = 0.15 and Ctem = 1/128. In fig. 1 we show the relevant graphs. Obviously the diagrams with photino or zino in the intermediate state do not contribute to the squark-gluino production. 0370-2693/86/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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Volume 171, numbez 4

1 May 1986

PHYSICS LETTERS B

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Fig. 1. Feynman diagrams for single squark production at e e machines. As a sample of our calculations we report the amplitude squared of diagram I (T1), II (T2) and their inter. ference (7"3). We take Z 0 as intermediate vector boson, q(~" as final state and sum over the squark chiralities. Defining: Xl = P l " k 2 ,

Yl = P l " k l ,

s = 2p I ° P2,

u = k 1 • k 2,

o 2 = [(s _ m2)2 + r 2 m 2 ] - i

Zl = P l " k 3 , v = k 2 • k3 , ,

x2=P2" k2

Y2=P2"kl,

z2=P2"

k3,

w = k1 • k3 ,

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q

q

,

where P l , P2, k l , k2 and k 3 are the four-momenta o f e - , e +, q', q and ~ respectively, we have: T1 = 64gs2g4 [Oz/(m 2 ff2 + 2w)2] {(K 2 + b 2 ) ( a 2 +b2)[2W(XlY2 +x2Y 1) - m 2 ( x l z 2

+X2Zl)]

+ 4Kbab [ws(x 1 - x2) - (m 2 + 2 w ) ( x l z 2 - X2z 1)]) , 2 ~ 2 D 2~ (-c 2R + C2L)(a2 +b2)v(4YlY2_'- m 2 s ) , T2 = ~ J'~gsg4Uz

T3 = 649394Dz22 [1/(m~.2 + 2w)]D2[(2u

_ m2){(a2+b2)[CR(ff+-~)+CL(-ff _ ~)1

X [W(XlY 2 +X2Yl) - U ( Z l y 2 + Z2Yl) + 2 v y l y 2 - m2vs/2] 2

+ 2 [CR(a + b-) - eL(a- - b)]ab [W(XlY 2 - X2Yl) + U(YlZ 2 - Y2Zl) + mff (ZlX 2 - Z2Xl)]}

+ F ~ m f f e u v p t r p ul P 2~'k lpk 2 o( [ C R ( ~ + b-) - c L ( a - b ) ] (a 2 + b2)CVl - Y2) - 2 [CR(~- + b-) + CL(~- -- b ) ] a b ( u + w)}] . 48O

Volume 171, number 4

PHYSICS LETTERS B

1 May 1986

102

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Fig. 2. Total cross section for e+e - ~ q~'~ (a) and e+e - ~ qff~ (b) with mff = 1.1Eb and rn~, = my -=0, Eb = beam energy. In (b) th~ lowest continuous line is for m z ~" x/~, and the upper one for rn~ = 120 Ge'V (the two coin~de at the peak). The dashed line is for m~ ~ 95 GeV and the dot-dashed line refers to m~ = 60 GeV.

The appropriate coefficients for electrons, up- and down-type quarks are (s w = sin 0w, c w = cos a = ( - 1 / 4 C w ) ( 1 - 4S2w),

a u = (1/4Cw)(1 - ~ s 2 ) ,

0w):

a d = (--1/4Cw)(1 -- I s 2 ) ,

b = b-d = -b-u = 1/4Cw, Cu R = - - ~Sw/C 22 w,

CR = 1~ S w 2 /C w,

Cu L =(1/2Cw)(1 - ~S2w),

22 CdL = ( _ l / 2 c w ) ( 1 -- ~Sw).

Fig. 2a shows the total cross section for e+e - ~ q q ' ~ with m~- = 1.1E b and rng = 0, E b being the beam energy. In the first c o l u m n o f table 1 we report the value o f the cross section for different choices of the squark mass at the Z 0 peak. The cross section can be rather large, b u t if we limit ourselves to the mass range of scenario (iii) it falls dramatically. The second scenario leads to m u c h smaller cross sections. F u r t h e r m o r e in either case, since b o t h the squark and the gluino in general decay, the signature is rather complicated (four or more jets in the final state) and it is quite difficult to distinguish these processes from background. Therefore we concentrate on the first scenario. In fig. 2b and in the second c o l u m n of table 1 we show the total cross section for e+e - ~ q ~ ' ~ . The selectron mass, for simplicity, is p u t equal to the squark mass. The total cross sections are o b t a i n e d numerically integrating the full differential cross section da/dEq dE~-× d cos 0q d cos 0 ~ over the kinematical ranges of the variables. For m ~ = 50.6 GeV and w i t h o u t including the zino c o n t r i b u t i o n (rnff >> x/s) we find a cross section of 0.5 pb at V ~ = 92 GeV. With t h e p r o j e c t e d l u m i n o s i t y for LEP of 1.4 × 1031 c m - 2 s - 1 , this means roughly 55 events in an ideal three-months run. Table 1 rn~- (GeV)

o(g"~ ~) (pb)

o(~"'qq) (pb)

48 60 70 80

116.9 9.14 1.21 5.5 × 10 -2

1.01 0.08 1.1 X 10 -2 0.5 X 10 .3

481

Volume 171,

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PHYSICS LETTERS B 1

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Fig. 3. Distributions for the angle between the two quarks. (a) refers to x/~: m Z. The •continuous line is for m~ ~- x/~. The dashed line is for rn~ : 60 GeV and the dot-dashed line for m~" : 80 GeV. (b) shows the cases x/s ~ 80 GeV, m~ = 60 GeV (continuous line) and x~Zs: 95 GeV (dashed line).

Zinos with relatively low mass could yield a reasonably large cross section as soon as the beam energy is sufficient to produce them on mass shell. This effect could be m u c h larger than the contribution o f the Z 0 at the peak and could allow the detection o f singly produced sparticles even outside the peak where otherwise the signal would be hopelessly small. The contribution of the zino to the total cross section is cl~ite sensitive to its total width, w h i c h is m o d e l dependent. We assume that the Z can o n l y decay into q~" or ££ pairs. For each channel the partial width is 2 1-' = (1/8rO(g2/C2w)(1/M~z) (M 2~ - m.~,~)2 [(T3 £,q

2 ) 2 + e£,qSw]. 2 4 e~,qSw

_

If one assumes, for instance, a constant w i d t h o f 3 GeV the m a x i m u m cross section with a 60 GeV zino is 0.85 pb. Under the present assumptions squarks can o n l y decay into a quark and a photino. In figs. 3 and 4 we give the probability distribution for the angle between the two quarks and for the missing energy. Such distributions have been calculated with a Monte Carlo based on the Metropolis algorithm, from the convolution o f the differential production cross sections with the isotropic decay of the squark in its own rest frame. The events are characterized by large missing energy and two strongly acollinear jets providing a good signature to l o o k for. The distribuoo5 ~

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Fig. 4. Missing energy distributions. (a) refers to x/~-= mZ. The continuous line is for m~" ~. x~. The dashed line is for m~'~ 60 GeVand the dot-dashed line for m~" = 80 GeV. (b) shows the eases V~ = 80 GeV, rn~" = 60 GeV (continuous line) and x/3 = 130 GeV, rn~" = 96 GeV (dashed line). 482

Volume 171, number 4

PHYSICS LETTERS B

1 May 1986

tions obtained for rn Z >>x/~do not significantly differ from the ones we compute taking into account possible zino contributions. Reasonable cuts in missing energy and coUinearity should allow a clean separation of signal from the background, without decreasing the expected number of events in a significant way. In conclusion we have shown that, although the cross sections involved are rather modest, the events signature can allow detection of single squarks in e÷e - ~ q~'~ if the squark mass is not too heavy and the gluino mass is larger than the squark mass. We gratefully acknowledge several useful discussions with F. Bianchi, M. Caselle and F. Gliozzi.

References [1] H.E. Haber and G.L. Kane, Phys. Rep. 117 (1985) 75. [2] H.P. Nilles, Phys. Rep. 110 (1984) 1. [3] R. Prepost, in: Perspectives in eleetroweak interactions, ed. J. Tran Thanh Van (Editions Fronti~res, Dreux, 1985) p. 131; A. B6hm, in: Perspectives in electroweak interactions, ed. J. Tran Thanh Van (Editions Frontidres, Dreux, 1985) p. 141. [4] J. Ellis and H. Kowalski, Phys. Lett. B 157 (1985)437; A. De Rujula and R. Petronzio, Nuel. Phys. B261 (1985) 587, and references therein. [5] G.R. Farrar and P. Fayet, Phys. Lett. B 89 (1980) 191; M. Gliick and E. Reya, Phys. Lett. B 130 (1983) 423; T. Kobayashi and M. Kuroda, Phys. Lett. B 134 (1984) 271. [6] M.K. Gaillard, L. HaU and I. Hinehliffe, Phys. Lett. Bl16 (1982) 279; M. Kuroda, K. Ishikawa, T. Kobayashi and S. Yamada, Phys. Lett. B 127 (1983) 467; I. Hayashibara, F. Takasaki, Y. Shimizu and M. Kuroda, Phys. Lett. B 158 (1985) 349. [7] K. Hidaka, H. Komatsu and P. Rateliffe, Phys. Lett. B 150 (1985) 399.

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