Volume 171, number 1 PHYSICS LETTERS B 17 April 1986

SQUARK P H O T O P R O D U C T I O N AT HERA

A. DOBADO

Junta de Energia Nuclear, Avenida Complutense 22, 28040 Madria~ Spain and C~ttedra de l~tsica de la ETSII, Universidad Politbcnica, C/Josb Abascal no 2, 28006 Madrid, Spain

and

M.J. HERRERO

Departamento de Ftsica Tebrica, C-XI, Universidad Autbnoma de Madrid, Cantoblanco, 28049 Madrid, Spain

Received 31 October 1985

A detailed calculation of the squark production cross section is presented via the photon-g lu ino fusion mechanism. For light enough gluinos ( - 5 GeV) and heavy squarks ( - 100 GeV) the production rates at HERA are very promising, even after stringent cuts are applied. A realistic study of partial squark decay into a quark and photino leads to a few detectable 2-jet + JPT events clearly characterized by a very high missing transverse momentum.

In the search for supersymmetric particles the most appealing method proposed is that based on their charac- teristic missing momentum (iT) signatures. From the last exhaustive studies motivated by the observation of large missing PT events at the CERN p~ collider, we have learnt that any signal of new physics should be accompanied by the corresponding detailed study of the background that could fake the SUSY signal.

In this context perhaps the machine most appropriate will be the HERA coUider ,1. Apart from having consti- tuent centre-of-mass energies comparable to the SPS ones, HERA (V~ "~ 314 GeV) is unique in that one of the par- ticipating particles in the interaction is observed in the Final state. This makes HERA a precision instrument in the study of unbalanced PT events and in the measurement of the current background. Several SUSY processes of in- terest have been proposed for HERA, all of them based on the pair production of SUSY particles from the con- ventional content of the proton.

In this paper we consider the possibility of producing single squarks at HERA from the gluino content of the proton. As it has been already discussed in the context of p~ and based on the scenario [2-5] with light gluinos (~ 5 GeV) [6] and heavy squarks (~ 100 GeV) [7], the inclusion of processes with a gluino as the initial parton is important because for these masses its contribution could be large.

The dominant process with an initial-state gluino contributing to squark production is the photon-gluino fu- sion one, which would correspond to the SUSY version of the well-known photon-gluon case. Here we present a detailed calculation of the cross section for this process in terms of the gluino, squark masses. The resulting total cross section is found to be large for the mass range considered. We also study the loss through stringent cuts on PT of the direct jet (the q-jet in the subprocesses 3'g -~ ~ and compute the ~T distributions by assuming a squark decay into a quark and photino. We finally show that even after strong cuts on PT and J*T are imposed, and pro- vided the luminosities planned at HERA, a small number of events with a characteristic signal can be detected.

Let us now pass on to describe in detail the calculation of the squark production cross section via the process

,1 For a recent review see ref. [1 ].

118 0370-2693/86/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

Volume 171, number 1 PHYSICS LETTERS B 17 April 1986

e + p ~ g q + q + X . (1)

For this purpose we consider first the dominant subprocess coming from the photon-gluino fusion, with the pho- ton to be real. As it is well known, real photons dominate photoproduction processes in ep collisions because off- shell photons are strongly propagator suppressed.

We have computed the analytical differential cross section in terms of the squark and gluino masses. By assum- ing all the squark masses to be degenerate, and once the quark masses are neglected, we obtain the following re- sult:

db ^ 2rrotOtsZfQf2 m2_g+( /+§)2_(~+[) (3m{+m2)+ 2 2 2m 4 ~-/(s, t ) - ( § - m~)2 ( ' ( m 2 - § - i ) 2 mgm.~+

_ i 2 _ / i + - 2 2 ^ 2 _ 2 2 + 2g(mg ~-(~--~--gT~-mg)+ 3tm~ 2m4+ 2mgmg) , (2)

where g and ~ denote the invariant energies flowing into the photon-gluino subsystem and the first (a), second (b) and third (ab) terms correspond to quark exchange, squark exchange and the interference terms, respectively.

The total cross section will be given as convolution integrals of the hadronic gluino distribution g(x) and the photon spectrum F(V):

1 1 o(ep~+ff+X,?i+q+x)= f g(x) f dyF(y) 6(x,y) , (3)

Xmin Ymin

where

j max d~ . fr(x,y) = ~tt (s, t ) , (4)

tmin

and for F0, ) we have used the well.known Weizs/icker-Williams [8] approximation. As a first estimate of the order of magnitude involved in this process, we have considered the simple case m~- =

0 GeV. The sub cross section was evaluated by analytical integration, giving

tr(x,y) = ba + ~b + ~rab , t = - t > 0 ,

2rr°t~s ~a O 2 ln(tmax/tmin) , ° a - § f

~r b = \ tmi n - s !

4 -2 + tmin(:m4+ 2- tminO+ tmax(--Zm '-s tma,d) l (train - S) ~m--md - ~ ' ) -']

Oab= ~ ^ 2~°~°ts f~Q2 Ira2(§ + 2m 2) ln( tmax\tmin _---s~-)+ 2mq~(§ + m 2) ln(tmax/tmin)+ (tma x - tmin)§]. (5)

Note that the quark exchange term ba and the interference term 6ab become logarithmically divergent at the lower limit t = 0, due to the quark propagator. As it has been argued [9], taking a finite mass for the quark in order to avoid the divergence does not make much sense because the parton model eventually breaks down at small t. In fact, the appropriate value of train is imposed by the experimental constraints near the beam pipe. Although we

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Volume 171, number 1 PHYSICS LETTERS B 17 April 1986

have considered this value in the rest of the paper, we present in the following an estimate that corresponds to an arbitrary value of tmin = 1 GeV 2.

The other integration limits in eqs. (3) and (4) are determined as follows:

tmax = §(1 - m2H)

with § = xys corresponding to the maximum value of t at fixed x a n d y , and

Xmin = m2/s , Ymin = Xmin/x (6)

come from the condition tma x 2 tmin. Finally, for the gluino distribution ~(x) we have taken the following simple form from refs. [2,10]:

~ ( x ) = "~0 - x ) "+ 2/x ,

with v = 4 and ~" fixed by the sum rule

1

f ~ (x )x dx "~ 10%. 0

(7)

The numerical results for o(ep -+ ~ + ~ + X, c.c.) are collected in fig. 1. We have plotted the total cross section

o(pb)

,00

300

200

100

C:~v' I -~-°, °'v t E = 820 GcV

\ - :: :'3°0 ,\

"-.'2"-~ ~'-." 50 60 70 80 90 100

m~ (OIV}

Fig. 1. Total cross sections for the process ep --} q + ~" + X versus the squark mass and for m~" = 0 GeV, Ep = 820 GeV. Solid curves correspond to E e = 40 GeV and dashed lines to E e = 30 GeV. A comparison between the computation of the integrals by (a) tmin = 1 GeV 2, or through (b) the PT q-jet cut ofPT > 10 GeV, is also shown.

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Volume 171, number 1 PHYSICS LETTERS B 17 April 1986

versus the mass of the squarks (50 < m~ ~< 100 GeV) for the energies provided at HERA, Ep = 820 GeV, Ee = 3 0 - 4 0 GeV.

As is clearly indicated by the curves, the production rates are surprisingly large, even for squark masses as large as the order of 100 GeV. This reveals that the procedure proposed here is potentially a rich source of squark par- ticles if gluinos are light enough.

Moreover, due to the characteristic na!ure of squark decays, typicaUy giving h ighP T and t 'T eyents, it suggests us that reliable detection is possible at HERA.

In order to verify this assumption we have made a realistic computation of the cross section,PT distributions and event rates, that include stringent cuts on PT, PT of the direct jet and the gluino mass effect.

In considering the gluino mass we have used the effective gluino distribution from ref. [5], to be evaluated us- ing the Altarelli-Parisi equations, which for definiteness is quoted here:

~(x, Q) = S x al (1 - x) a2 e aa+a4x ,

with

a I = -1 .33139 - 0 .4492S ,

1

f ~ ( x ) x d x ~ - 5 % , m g = 5 G e V , 0

a2 = 6.30712 - 0 .045518S,

(8)

a3 = -0 .55418 - 2 .26574S, a4 = -2 .2188 - 3 .89532S,

= lnIln(Q/A)/In(Qo/A)I, Qo = 2m~, A = QolQ" 2 GeV/Qo125/19 ,

and for Q we have chosen somewhat arbitrarily

Q = [(tmax + tmin)[2] 1/2

This distribution is used above the gluino production threshold given by the condition t > 4m 2. On the other hand, PT cuts are considered through the integration limits in eqs. (3) and (4) as follows:

tma x = [(§ - m2)(g - m~/2g] { 1 + [1 -- 4 ~ T §/(§ - m 2)2] 1/2),

train = max {4m 2, [(§ - m2)(§ - m2)/2s^] { 1 -- [1 -- 4p2T U(g - m2) 2] 112}},

Xmin=(1/s)[m{ + 2p2T + 2PT(P 2 + m ~ l / 2 ] , Ymin=Xmin/X. (9)

Numerical results for the total cross section versus the squark mass (50 < m R < 140 GeV) are shown in fig. 2 for P~r et > 1 0 - 5 0 GeV. We have included for comparison the two cases considered, m.g = 5 GeV (short dashed curves) and rng = 0 GeV (solid lines). The results for mg = 0 GeV and PT > 10 GeV have also been added to fig. 1, in or- der to compare with the simple case determined by tmin = 1 GeV 2.

As mentioned above, the cuts on PT reduce the cross section considerably. For instance by setting PT > 10 GeV against train = 1 GeV 2 with m~. = 0, the reduction factor is about 1/5 for squark masses in the range 5 0 - 1 0 0 GeV. What is interesting to emphasize is that even with the strong cuts applied the cross sections predicted for a large set o f P T and m~ parameters are quite above the limits o f detection. Particularly, if we assume a sensitivity at HERA of over 0.1 pb and by requiring events containing at least one jet with PT > 10 GeV, squark masses up to 140 GeV could be probed.

The difference between the mg = 0 and m~- = 5 GeV results is a direct consequence of the striking difference in the behaviour of the structure functions. For low squark masses (---50 GeV) and Pt cut (PT > 10 GeV) the results differ in a factor o f 2, due essentially to the distinct normalization, but for higher masses ( " 100 GeV) and PT ( > 2 0 GcV) they separate up to a factor of 10 because of the different behaviour in the x -~ 1 limit where these effects are more important. Therefore we would like to remark that a deep knowledge of the gluino distribution is needed if a ref'med analysis is required.

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Volume 171, number 1 PHYSICS LETTERS B 17 April 1986

100

oip~)

0.1

0.0 l I I I 50 60 70

) GeV

; GtV

X \ X It x ~,

x X Xxl ~ • X

I I [ L I L I aO 90 100 HO I:~0 130 140 150

rn-~ ( GeV )

Fig. 2. Squark production cross section in ep collisions at V~'~ 362 GeV versus the squark mass for several choices of the PT q-jet cut: PT > 10, 20, 30, 40, 50 GeV. Solid curves represent m~ = 0 GeV and dashed lines m~" = 5 GeV.

In order to complete our discussion we have studied the most characteristic signature coming from the partial decay of the squark into a quark and photino. This basically consists of 2 jets with high transverse momentum and missing PT.

Fig. 3 shows the missing PT distributions calculated by means o f a Monte Carlo program with 10 000 generated events. These plots correspond to the values my = 0 GeV, mg = 5 GeV and for several choices o f the parameters Pr and nr~ ,2,3.

As it can be seen in this figure, the mechanism proposed by SUSY predicts the familiar strong peaking some- what below ~ rrr~ and gives events with large/ 'T on average. In particular by assuming a HERA luminosity of 200 lab -1 and by requiring ~ T > 30 GeV the estimated number o f 2-jet + i 'T events is between 15 and 2 for several plausible choices: rrr~ = 5 0 - 1 0 0 GeV, PJT et > 10, 20 GeV.

It is worth noting that these rates underestimate the total~T contribution. It is expected that when the domi- nant squark decay into a quark and gluino is included, the rates will increase mainly in the low t 'T range (£ t m~).

Finally, a few comments about background contributions are in order. First, the photoproduction processes (as ours) can be studied at HERA separately from the standard ones.

,2 These distributions will not suffer noticeable changes in the case when taking a small mass for the photino, mainly in the high squatk-mass range.

,3 If for instance the hJggsino H is the LSP, the photino will decay into ?H and the ~I" signal would reduce roughly a factor of the order of two for large-Pr events.

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V o l u m e 171 , n u m b e r 1 PHYSICS LETTERS B 17 April 1986

6

s

e~

- 3

2 " O

1

15

~o

O

~ s

" O

3

cL 2

" O

" O

2

~6T > 10 GeV m~'= 50 GeV ~ 1.5

x

"~ 0.5

I I I l I I I I

10 20 30 40 50 60 70 80 PT (GeV) 5

~ I ~6T > 10 GeV 75 GeV

× 2

; 1 " D

I I I I I I I I t I I I I I I |

1o 20 30 ~o so so 7o eo PT {Gev)

-L] ,PT 1°Gev m~=100GeV 10

~ e

~ 6

f J 7_

I I I I I t 1 I I I I i I I , I 1

10 20 30 40 50 60 70 80 PT (GeV }

"/~T > 20 GeV ~ = 50 GeV

I I I I I I 1 I I i I I 1 I ! J

10 20 30 40 50 60 70 80 PT (GeV)

,46T> 20 GeV ~ = V

!

10 20 30 /,0 50 60 70 80 PT [GeV)

/ r

. . r- %._ | I I I i I I I t I I I J J |

10 20 ,30 40 50 60 70 80 PT ( GeV )

Fig. 3. Missing PT distributions in ep collisions at ~ ~- 362 GeV for m~" = 5 GoV and m~ = 0 GeV. The different plots correspond to several plausible choices of the PT cut and m~ parameters: (a), (b), (e) for PT > 10 GeV and m~ = 50, 7 5 , 1 0 0 GeV, respective- ly, and (d), (e), (f) for PT > 20 GeV and m~ = 50, 7 5 , 1 0 0 GeV, respectively.

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Volume 171, number 1 PHYSICS LETTERS B 17 April 1986

Therefore the background can only come from the photoproduction processes themselves. Second, the only channel in photoproduction processes that could lead to/~T events is the pair production o f

heavy quarks via pho ton-g luon fusion with subsequent quark decay into £vq. However, among these last processes only those where the final lepton is a tau could give 2-jet + 4~T events, like

ours, A rough estimate gives a few background 2-jet + ~T events (O(10)) characterized by a higher multiplicity and

less missing PT than ours. Therefore with the required stringent cuts on ~T and PT the background contribution can be completely sup-

pressed. In summary, if gluinos are light enough, a considerable number of squarks can be produced at the HERA col-

lider by means of the g lu ino-photon fusion mechanism. This procedure allows the detection o f squarks with masses as large as "" 100 GeV.

A realistic study of the signal coming from squark decay into a quark and photino leads to a few detectable 2-jet + ~T events, clearly separated from background.

The importance of requiting a deeper knowledge of the gluino structure function is clearly illustrated.

The authors are grateful to the Mark-J group, the Theory Division, and F. Barreiro and J. Salicio for their hos- pitality at DESY while this work was carried out.

References

[1] E.g., R.J. Cashmore et al., Phys. Rep. 122 (1985) 275. [2] M.J. Herrero, L.E. Ib~ez, C. L6pez and F.J. Yndur~in, Phys. Lett. B 132 (1983) 199; B 145 (1984) 430. [3] V. Barger, K. Hagiwara, W.-Y. Keung and J. Woodside, Phys. Rev. Lett. 53 (1984) 641. [4] M. Barnett, H. Haber and C. Kane, LBL report 18990 (1985);

A. de R6juh and R. Petronzio, preprint CERN-TH-4070/84. [5] V. Barger, J. Jaeobs, J. Woodside and K. Hagiwara, Wisconsin - Madison preprint MAD/PI-I/232 (1985). [6] J. Rohlf, invited talk 1985 Division of Particles and Fields Conf. (Eugene, OR, August 1985).

C. Rubbia, invited talk 1985 Lepton-photon Conf. (Kyoto, Japan, August 1985); A.M. Cooper-Sarkar et al., Phys. Lett. B 160 (1985) 212.

[7] M. Barnett, H. Haber and G. Kane, preprint LBL 20102 (1985). [8] C. yon Weizs~'eker and F.J. Williams, Z. Phys. 88 (1934) 612. [9] C. AltareUi, G. MartineUi, B. Mele and P. Riickl, preprint CERN-TH-4094/85.

[10] M.J. Herrero, C. L6pez and F.J. Yndur~in, Nucl. Phys. B244 (1984) 207.

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