Volume 122B, number 5,6 PHYSICS LETTERS 17 March 1983

SELECTRON AND SNEUTRINO PRODUCTION IN ELECTRON-PROTON

AND ELECTRON-POSITRON COLLISIONS

P. SALATI 1 and J.C. WALLET 2

LAPP, Annecy-le- Vieux, France

Received 28 July 1982

We present a complete calculation of the total cross sections for selectron and sneutrino production in the following processes:

e - + p ~ s e - + g a u g i n o ° + X , e - + p ~sv+gaugino ° + X .

We find, if the mass of the gaugino is less than 30 GeV, a detectable number of these "super-particles" will be produced at HERA. In particular, from 0(0.5) (mselectro n = 60 GeV) to 0(20) (mselectro n = 20 GeV) selectrons and photinos will be produced per day.

We also give estimates of the total cross section for the processes:

e- + e + -~ se- + gaugino ° + e + , e- + e + ~ sv + gaugino ° + e ÷ .

It appears that one of the predictions of Fayet's model about the mass of the selectron (mselectro n < 0(40) GeV), will be testable at LEP.

One of the most excit ing aspects of low energy

supersymmetr ic models [1,2] is the predict ion o f a

rich spectroscopy of new particles. The supersymmet-

tic partners o f the fermions and of the Higgs and

Gauge bosons are predicted to have masses less than

a few hundred GeV [3,4] and thus could be de tec ted

( i f they exist) in the new generat ion o f colliders like

H E R A or LEP. So it is of great interest to have as

much in format ion as possible about processes in which

such "super-par t ic les" are expected to be produced. In

this paper, we calculate the total cross sections o f the processes

e - + p - + s e - + G 0 + X , e - + p - + s v + C , - + X , (1)

in the case o f quasi-elastic scattering (X = p) and in the

case o f inelastic (X 4= p) where X is a hadronic final state. Here, se and st, stand respectively for the scalar

sypersymmetr ic par tner o f the electron (selectron) and that of the neutr ino (sneutr ino) and 9 0, G - are the

fermionic partners o f the neutral and charged electro-

1 Also at Universit6 de Savoie, Chambdry, France. 2 Also at Institut de Physique Nucl6aire, Lyon, France.

weak gauge bosons (gauginos). We also give est imates

o f the total cross sections for the fol lowing processes:

e + + e -+se + G ° + e + , e + + e - + s v + G - + e + . ( 2 )

We show that s e - , sv, ~0 and G - can be produced at

H E R A or at LEP with a detectable number o f events

per day (if "super-par t ic les" are not too heavy), pro-

vided the planned luminosit ies can be achieved [5].

The most general parametr iza t ion of the f e r m i o n -

gaug ino - s f e rmion vertex can be wri t ten as

- i e (c~ - 13")'5) , (3)

where e is the electron charge, a and 13 are constants depending on the low energy supersymmetr ic model .

As we calculate total cross sections, the factor o~ 2 +/32 is factorized in their expressions and appears as the only quant i ty which is model dependent , apart

f rom the masses o f the "super-part ic les" . The value o f a2 +/~2 is generally unknown and thus, we have calcu-

lated for each react ion the " reduced cross sect ion":

o R = o / ( a 2 + /32) . (4)

As an example, we consider two classes o f SU(2)

0 0 3 1 - 9 1 6 3 / 8 3 / 0 0 0 0 - 0 0 0 0 / $ 03.00 © 1983 Nor th-Hol land 397

Volume 122B, number 5,6 PHYSICS LETTERS 17 March 1983

Table 1 a and/3 parameters of the electron-G°-selectron vertex in two classes of SU(2) X U(1) invariant low energy supersym- metric models. In the first class, ~o and ~ are mass eigenstates whereas, in the secon d class, if3 and B are mass eigenstates.

Neutral gaugino a ~3 a 2 +/J 2

mass eigenstate proton

~'o 1 - 4 sin20w 1 0.37 2 sin 20 W 2 sin 20 W

1 1 - - + _ - -

e- ,~3 1 1 0.57 " 4 sin 0 w 4 sin 0 w

g 3 1 080 4 cos 0 W 4 cos 0 w

X U(1) invariant low energy supersymmetric models, previously c.oonsidered by Ellis et al. [6]. Let us denote by W + and W the charged gaugino mass eigenstates. As for the neutral gauginos, the mass eigenstates can be of two kinds:

either Z ' 0 a n d ~ or ~3 and B'.

In table 1, we present the resulting expressions for the e lec t ron-G0-selec t ron vertex and their numerical val- ues are collected for the two types of model. In the numerical evaluation, we have taken sin20 w = 0.22. It appears that for the previous models, a 2 +/32 is of the order of 1 and in that respect some conclusions can be drawn from the curves o R versus the mass of the super-particles.

For the processes (1), we assume that the domi- nant diagrams are those shown in fig. 1. Instead of calculating the cross section o, we compute the "reduced cross section" o R .

We repeat that the (a 2 + ~32) term comes from the reduction of the traces which appear in the evaluation of the squared amplitude of the process. As we sum over the final spin states and average over the initial ones, this term is factorized. It follows from above that o R gives the correct order of magnitude for o and is sufficient to draw a few conclusions at the pres- ent time. For the evaluation of the total cross section, we use the method which we have followed in another paper [7] for the calculation of the total cross section

e- ID

se- (sv) P2 ~~ go (~-) P3

l_

proton

~se- (g- se- (g-)

-y

Fig. 1. Relevant Feynman diagrams for the 2 processes: e- + p ~ se- + ff, o + X and e- + p ~ sv + if,- + X.

of the Z 0 production in e - p collisions. We only repeat the main steps of the procedure.

(i) We start from the calculation of elastic scatter- ing (X = p). The averaged squared amplitude is a con- traction of 2 Lorentz tensors:

1 (5) 4 spins

Huv refers to the hadronic vertex for which we use a dipole form factor. LUV refers to the leptonic vertex and as Huv is symmetric in #u, one only has to con- sider the symmetrical part of L uv in/av. We have written LUV in the form

L U V = ~ ] C i / , u .. Pi P/ + Cg g" v, (6) t]

where i a n d j are indices running over 1,2 and 3 (see fig. 1) and the coefficients C are functions of the vari- ous four-momenta Pi which appear in the leptonic part of the Feynman diagrams. The numerical computation of the phase space integration uses the GSET routine of the CERN CDC library. We have plotted the "reduced" elastic cross section for the two processes (1) under consideration, versus the mass of the sfer-

398

Volume 122B, number 5,6 PHYSICS LETTERS 17 March 1983

10-37 F I 1 I

10-38- I I

~10-39 ~-

10-~0

10-/.1

(Q)

\

\

P 2O

e-p~se-÷p.~ °

~'s=3OOGeV . . . . ¢" s=150GeV

i ", ~ ~ "~G':6OGeV"

Xkx \\\ ~

MG°:"°O~V \ \ --"" "~.go ~ooG,v 40 60 80 100

Hse- (geV)

10 -37 ,

10-38 a-

10-39 t

10-~1 0

( b )

e_p_ se.~O(X#p)

x N N N L _ _ 4"s=300GeV ,,,,, \ \ . . . . ~~:~soG~v

\ \ \ \ i "q,,.'q,\ \ \ J

',, \ \ \ ~ -,~go:2oG~v, , ?, \ \ ~ ! ', "< \ \ ",g.:~oG~vi

MG':,0G,#% " , ~H~':I00GeV 1 I I \ I ', I

20 &O 60 80 100 Hse-(geV)

Fig. 2. "Reduced cross section" o R for e- + p ~ se- + if0 + X processes in the case of elastic scattering (a) (X = p), and in the case of an inelastic one (b) (X 4: p). cr R is plotted versus the mass of the selectron for different values of the mass of the outgoing if0, and for different values of the energy in the center of mass frame of the reaction. Continued lines correspond to ,,/7 = 300 GeV and dotted lines to ,,/s= 150 GeV.

mion (msf) and for fixed values of the gaugino mass ( m ~ ) and of the total energy (x/s) in the center o f mass frame of the reaction. Having in mind that groups at PETRA have been able to set a selectron mass limit of 16.8 GeV [8], we consider the following ranges of masses:

2 0 < m ~ < 100 GeV, 20 ~<msf ~< 100 GeV,

x/S- = 150 and 300 GeV.

The results are collected in fig. 2a ( e - + p ~ se- + ~0 + p) and fig. 3a ( e - + p ~ su + G - + p).

(ii) Then, starting from the elastic cross section and setting the p ro ton form factor equal to 1 to obta in the scattering of an electron upon a point-l ike particle (namely a quark-pat ton) , we compute the inelastic cross section of processes (1) (X @ p) which has the following form:

l do o e2 C Oinela.ic = J • ~ j F / ( x , taveraged) , (7 )

/ 0

x is the fraction of the pro ton fou r -momen tum car- ried by the quark-par ton on which the electron scat- ters. a/and f j are, respectively, the fractional electric charge and the dis t r ibut ion funct ion of the par ton of flavour j ( / r u n s over up, down, strange...), da/dx is the e lementary elastic scattering cross section (whose averaged momentum- t rans fe r squared is denoted taveraged ) of an electron upon a point-like particle with the electric charge e. When we use the structure funct ion F 2 [7] (7) gives:

1 F " . d o dx

°inelastic = f 2 ix ' taveraged) ~ d t ' (8) 0

We have imposed a cut-off on the square t of the momentum- t rans fe r carried by the virtual pho ton

t ~> 1 GeV2/c 2 . (9)

The scattering is inelastic when the virtual pho ton interacts incoherent ly on quark-partons. For low val- ues of t; the virtual pho ton interacts coherent ly and the scattering is elastic. Taking 2 GeV2/c 2 instead of

399

Volume 122B, number 5,6 PHYSICS LETTERS 17 March 1983

~

e-p-- sv*p~-G"

-HG-=2OGe

g

(a) I I I ~ I

10-~' 20 ~.O 60 80 100 MsvIGeV)

e'p--sv.G-qx=p)

1047 ~ ¢'s:3OOGeV -~ . ~ . . . . ~ ~ : % O G e V |

MG-4OG~v\ ~ I

,

/ u xx x.x. !

.g',SOG,

(b) - ""', " " ~ , .~- ~oo~.~ Hfi'=t, OGeV \~ ,, = I

20 ~10 60 8~0 100 v

H~,, (GeV) Fig. 3. "Reduced cross section" a R for e- + p --, su + G- + X processes in the case of elastic scattering (a) (X = p), and in the case of an inelastic one (b) (X :~ p). a R is plotted versus the mass of the sneutrino for different values of the mass of the outgoing U_,-, and for different values of the energy in the center of mass frame of the reaction. Continued lines correspond to ~ = 300 GeV and dotted lines correspond to ,q/s= 150 GeV.

~*(sv) 5°(sv)

. ~ ~ - s e- (~'=) I "( se'(n-)

e" e ° e" e ° a) b)

G°lsv)

e

~- s~-(~-) e- s~(~l c) d)

se-(~') " --

e o

e: ~T'(sv) e" G°(sv)

e) f)

. ,. ~ ~ _ se-(?~,

- ~ ?,°(sv) g) h)

1 G e V 2 / c 2 for the cu t -o f f does no t m o d i f y the results.

The resul ts for the " r e d u c e d inelast ic cross s ec t i on"

are s h o w n in fig. 2b (e~ + p ~ s e - + ~ 0 + X) and in

fig. 3b ( e - + p ~ sv + G - + X). No te t h a t the elastic

cross sec t ion is o f the same order t h a n the inelast ic

one. We n o w pass on to the discussion o f the numer -

ical results for the process e - + p ~ s e - + ~ 0 + X. I f

the ou tgo ing neu t ra l gaugino has a mass larger t han

0 ( 4 0 ) GeV, it will p r o b a b l y be very diff icul t , even at

H E R A , to de tec t the se lec t ron and o b t a i n evidence

for the occur rence o f reac t ion (1) . On the o t h e r hand ,

if t he mass of the neu t ra l gaugino is less t h a n 30 GeV,

reac t ion (1) b e c o m e s visible at H E R A (v~-~-- 300 GeV; l u m i n o s i t y ~ 6 × 1031 cm - 2 s - l ) , w i th O(1) event

per day ( for m~,0 = 20 GeV and mse - = 20 GeV). In a cer ta in class o f mode ls [ 1 ] , the p h o t i n o is ex-

pec t ed to be very l ight ( m y < 1 MeV). We can rough- ly ex t r apo la t e f rom our curves t h a t the to ta l cross sec-

Fig. 4. Feynman diagrams for e + + e- ~ se- + ~j0 + e + and e + + e- - sv + U~- + e + reactions.

400

Volume 122B, number 5,6 PHYSICS LETTERS 17 March 1983

t ion for the process: e - + p ~ s e - + ~ + X is o f the

order o f 4 × 10 -36 cm 2 (for mse- = 20 GeV) to 10 37

cm 2 (for rose- = 60 GeV). This would lead to a total number o f p roduced light phot inos and selectrons per

day at H E R A of 0 (0 .5 ) to 0 (20) . F N A L or SPS/LEP

exper iments (x/}-respectively equal to 200 and 240

GeV and luminos i ty equal to 1031 cm - 2 s - 1 ) will

probably be unable to detect selectrons and neutral

gauginos. Numerica l results for e - + p ~ su + G - + X

lead to similar conclusions concerning the relat ion

be tween the expec ted number o f events per day and

the masses o f the "super-par t ic les" involved.

We now est imate the total cross section of the pro- ce~es (2): e - + e + ~ se - + ~ 0 + e + and e - + e + -+ su

+ G + e +. The relevant diagrams are shown in fig. 4.

Outgoing positrons, which are scattered forward at

small angles near the beam axis are not detected, so

we have imposed in our est imate the condi t ion that

the angle be tween the outgoing posi t ron and the beam

axis had to be larger than 4 ° . The dominan t diagrams

are a and b. Diagrams c, d, e and f are suppressed by

propagator effects which are due to the exchange of

massive "super-par t ic les" , and diagrams c and d are

also suppressed by a factor 1/S. In the most favorable

case ( low masses and high energy in the center o f

mass), mse- = m~o = 20 GeV and ~/s-= 260 GeV, we find that diagrams c, d, e, f, g, h at most cont r ibute , respectively, only 17%, 10%, 4%, 4%, 1% and 0.3% of

the total. Thus, we have only considered diagrams a

and b, and calculated the " reduced total cross sec t ion"

a R. The numerical results are col lected in fig. 5a (e +

+ e - -+ se - + G 0 + e +) and in fig. 5b (e + + e - -+ su +

G - + e+). We have p lo t ted the " reduced cross sect ion"

versus the mass o f the sfermion involved in each reac-

t ion (20 ~< msf ~< 100 GeV), for f ixed gaugino mass

(20 ~< m g ~< 100 GeV) and for f ixed energy in the

10-36

10-37

10-38

E

10-39

10-~o

(a)

~

e 'e - - - e*se-G ° - - ¢'s:260 GeV . . . . ~s: 1/~0 6eV

x

*',, xx x • • x xx

',, _ ' ~ ~Mgo:zoG~v " \ " " ' ~ i "M~°:60fieV

,-, ]-16°=800eV

XMfjo:2oGev

10 -36 r

i l

80 M ~ (GeV)

I0-~o

~

e*e---CsvC-

I ~ ~Nff':60Ge~

i I I I 1010 210 I 20 &0 60 0 ~.0 6'0 0 100

Msv(GeV)

Fig. 5. Estimated "reduced cross section" o R for reactions e ÷ + e- ~ se- + ~0 + e ÷ (a) and e ÷ + e- -~ sv + G- + e ÷ (b). o R is plotted versus the mass of the sfermion, for different values of the mass of the outgoing gaugino, and for different values of the energy in the center of mass frame of the reaction. Continued lines correspond to x/s = 260 GeV and dotted lines to x/S -= 140 GeV.

401

Volume 122B, number 5,6 PHYSICS LETTERS 17 March 1983

center o f mass frame ( ~ = 140 and 260 GeV). With

the expected parameters o f LEP (x/s -= 140 and then 260 GeV; luminosi ty = 1032 cm - 2 s - 1 ) it will be pos-

sible to produce a few selectrons and phot inos per day,

provided that mse- is less than 0 ( 4 0 ) GeV with V~ -= 260 GeV. Under these condi t ions, it is wor th not icing

that one o f the predict ions of the Fayet mode l [ 1 ]

concerning the mass o f the selectron,

1 0 ( 4 0 ) G e V , (10) mse- ~< ~m w --~

will be testable at LEP. The si tuation seems to be a li t t le more satisfactory

for

e + + e - ~ s p + G - + e + , (11)

fig. 5b shows that it would be very diff icult to produce t

a detectable number o f charged gauginos if their mass

is larger than 40 GeV. Finally, as far as de tec t ion is concerned, the selec-

t ron is generally expec ted to decay into a gaugino and

an electron. Faye t ' s mode l predicts the decay

se ~ e + ~ .

The pho t ino is not direct ly detectable and experimen-

talists should look for the energy loss in the events. At

the present time, we cannot say anymore .

We are very grateful to J. Ellis for having suggested

to us the idea o f this paper and to G. Girardi and P.

Sorba for numerous discussions and helpful comments .

References

[1] P. Fayet, XVI Rencontre de Moriond (1981), first session; G. Farrar, Supersymmetry in nature, Erice Subnuclear Physics (1978) p. 59.

[2] S. Weinberg, HUTP-81/A047 (1981); M. Dine and W. Fischler, Phys. Lett. 110B (1982) 227, L. Alvarez-Gaume, M. Claudson and M.B. Wise, HUTP- 81/A063 (1981); L. Ibfifiez and G. Ross, Phys. Lett. l l0B (1982) 215; C. Nappi and B. Ovrut, LAS preprint (1982); L. Hall and I. Hinchliffe, Phys. Lett. l12B (1982) 351; R. Barbieri, S. Ferrara and D.V. Nanopoulos, Z. Phys. C13 (1982); J. Ellis, L. Ib~fiez and G.C. Ross, Phys. Lett. l13B (1982) 283.

[3] M. Suzuki, UCB-PTH-82/8 (1982); J. Ellis and D.V. Nanopoulos, Phys. Lett. 110B (1982) 44.

[4] H. Pagels and J.R. Primack, Phys. Rev. Lett. 48 (1982) 223; S. Weinberg, Phys. Rev. Lett. 48 (1982) 303; N. Cabibbo, G. Farrar and L. Maiani, Phys. Lett. 105B (1981) 155.

[5] Physics with ep colliders, Discussion meeting in view of HERA jointly organized by: DESY, ECFA and University of Wuppertal (Wuppertal, Germany, October 1981), DESY HERA 81/18 (October 1981);CERN/ISR-LEP/ 78-17 (August 1978), Design study of a 15 to 100 GeV e+e - colliding beam machine (LEP).

[6] J. Ellis and G.C. Ross, Phys. Lett. l17B (1982) 397; J. Ellis, J. Hagelin and D.V. Nanopoulos, Phys. Lett. 116B (1982) 283.

[7] P. Salati and J.C. Wallet, LAPP - TH 64 preprint (1982). [8] Cello Collab., H.T. Behrend et al., Contrib. 1981 Bonn

Conf.; Cello Collab., H.T. Behrend et al., DESY 85-021 (1982).

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