IC/95/317 INTERNAL REPORT 1 Introduction (Limited Distribution) The theories beyond the Standard Model (SM) such as composite models[l], grand uni- International Atomic Energy Agency fied theories[2], and £o superstring-inspired models[3] predict the existence of lepto- and quarks carrying baryon and lepfon numbers simultaneously and having the electric charges United Nations Educational Scientific and Cultural Organization ±5/3; ±4/3; ±2/3 and ±1/3 [4]. INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS The production and possibility of the detection of leptoquarks have been analysed in detail for, for instance, ep [5-7], hadronic [8], and e+e~ colliders [4,9]. It is well known that high mergy ep colliders can be converted into a high energy 7p collider with the help SINGLE LEPTOQUARK PRODUCTION AT TeV ENERGY yp COLLIDERS of backscattered laser beams [10]. The single and double leptoquark production in 771 colliders are also analysed in the literature [11,12] without taking the hadronic structure of photon into account. Namely they neglected the resolved photon contribution. Fur- T.M. Aliev1 thermore in these works the distribution of quarks and gluons in the proton are described International Centre of Theoretical Physics, Trieste, Italy by a Q2 independent parametrisation which may be misleading since the cm. energy for each subprocess supporting jp —> Lc is not identical. In this work we shall analyse D.A. Demir, E. Utan and N.K. Pak the production of vector (L = V) and scalar leptoquarks (L = 5) in fp colliders by Physics Department, Middle East Technical University, Ankara, Turkey. considering the resolved photon contribution as well. The article is organized as follows: Section 2 describes the theoretical basis and Section ABSTRACT 3 is devoted to the numerical analysis and discussions.

The resolved and direct photon contributions to the single leptoquark (L) production 2 Total Cross Section for 'yp —> Le Scattering process yp —» Le are analysed for both scalar (S) and vector (V) leptoquarks in detail. It is shown that resolved photon contribution dominates for ML < 300GeV. For My > The production of leptoquarks in ~/p collisions can occur cither by direct or resolved pho- ITeV and Ms > 0.5TeV cross section is completely determined by the direct photon ton processes. In the latter case photon interacts with the proton through its hadronic contribution. The vector leptoquarks are discussed for both gauge- and non-gauge cases components.lt is clear that the following processes are responsible for the yp -+ Le scat- separately. tering:

79 Le 19 (1) Le MIRAMARE - TRIESTE December 1995 7,9 Le (2)

where processes in (1) defines the direct photon scattering and those in (2) defines resolved photon scattering.

'Permanent address: Physics Department, Middle East Technical University, Ankara, The complete 5f(3)c x SU(2)L x U (l)y invariant Lagrangian in the low energy range Turkey. (Mi as UWJ.conserving baryon (B) and lepton (L) numbers, is given by [-1] gauge bosons of an extended gauge group, then the trilinear vertices are completely and unambiguously fixed by the gauge invariance. When they are not gauge bosons, then L=4 + 4 +Lsra""- + Ll-'or (3) =2 =0 the vector leptoquark lagrangian can be regarded as an effective theory. It is clear that where F =\ 3B + L \. The first two terms in the lagrangian are given by the following in this effective theory there are many free parameters. In order to restrict the number expressions of these parameters, in addition to SU{3)C x SU(2)L x U{1)Y invariance and B and L conservations, we impose the CP invariance in the effective lagrangian. Moreover we restrict ourselves to operators of dimensionality 4 or less. There is only one operator 4=9 = <7l ignV^V^V complying with these conditions and it describes the anomalous magnetic moment contribution to the trilinear vertex. Thus the effective gauge boson- vector leptoquark lagrangian £"tc'or conserving CP and containing operators of dimension 4 or less is given by (see, for example, [17])

(7) 4=0 = h2(qiiT2eR + uRlt,)R2 ~ i E

where i runs over all vector leptoquarks, V)M = D^VV — DJV^. is the leptoquark field

strength and G]iiu is the field strength tensor of photon (j — 7) or gluon (j — g). In what

h.c. (5) follows we shall take anomalous couplings of photon and gluon identical; K^ = ng = K. One can readily obtain the Feynman rules for trilinear vertices immediately from WcclOT In 4=o and 4=2 tnere exist various kinds of leptoquarks interacting with leptons and c r quarks. Here qL and li are SU[2)i left handed quark and lepton doublets, V = Cpsi 9 is the charge conjugated fermion field. Among vector leptoquarks, U^,U\ are 5f/(2)/, (8) singlets, V2, % are left handed SU(2)[, doublets, and U3 is SU(2)i triplet. Among scalar leptoquarks, SuSi are SU(2)L singlets, R2,R2 are left handed SU(2)L doublets, and S3 where all momenta are incoming. Here k\, k2 and £3 are the 4- momenta of photon (gluon) is SU(2)i triplet. Note that there are certain cons, raints on the leptoquark masses and and leptoquarks respectively. We will next turn our attention to the calculation of the coupling constants from low energy experiments, which follows, for instance, from the cross section for jp —> Le scattering. absence of FCNC at the tree level, and from D° - D° and J5° - B° mixings [13-16]. The total cross section for 7p —> Le scattering has the form

jacaiar m j-ne Lagrangian describes the interaction of scalar leptoquarks with the neu- Le) (9) tral gauge bosons, and is given by

where o&lT and aTe3 represent the contributions of the direct and resolved photons respec- tively. The total cross section for the leptoquark production by direct photon interaction where 5' is the i-th scalar leptoquark field and D^ = d^ — ieA^ — igsY^t 's tne covariant can be obtained by folding the cross section for the elementary process (1) with the the derivative. photon distribution in electron and quark distribution in the proton: Unlike the scalar leptoquark case, VV7 and VVg vertices involve an ambiguity de- •0.83 /•! Le) = ) alq{xys) (10) pending on the nature of vector leptoquarks. For example, if the vector leptoquarks are dx J^ dy fl/e(x) fq/p{y, In the same manner, the total cross section for leptoquark production by resolved photon where superscripts V and S refer to the vector and scalar lcptoquark productions respec-

contribution can be obtained by folding the cross section of the elementary process (2) tively. In (4) and (5) a = M£/s, b =• m^/s, qx = q, q2 = 1, q3 = q + 1 (q quark charge), with quark (gluon) distribution in the photon, gluon (quark) distribution in the proton and K is the anomalous coupling of leptoquarks to photon and gluon [IT]. The factor A-, and photon distribution in the electron: is given by

X na (14) Le) = dx f dyf dzfl/c{x)\fgh(y, -f )/,,„(->, ^ IT x The cross sections a gq and a^q could be obtained from (4) and (5) with the following (11) replacements: 2 2 In (10) and (11) fa/b(x,Q ) is the Q dependent distribution function of the parton a in 2 A,) (15) the hadron 6 (f-,/e(x) is an exception). In all these functions we have set Q = •• where s = 1. ti = 0,93 = 1, is the invariant mass flow to the subprocess under concern, y/s is the cm. energy of the where 2 collider and A = (ML + mq) /s, where ML and mq are the leptoquark and quark masses respectively. (16) 12s Let us now discuss the construction of the formulae (10) and (11) in the case of and Q3 is given by ygq —» Le, as an example. Here s is the cm. energy squared of ep collider. Only fraction 12?r x of s enters the jp system, so syp = xsep, 0 < x < 1. Now hadronic components of 2 2 (17) «»v<« ; (33-2/}In

lna[4q3gi(K + 6K + - q2))

in the limit s » M2-. We see that for K ^ 1 the cross section grows logarithmically. This 8a2{q qi - 8q (q + 9i) + 2q2} + a{q\ - 2 3 3 is due to the t- channel contribution. As we noted before, if V is a non- gauge particle (1/4)9|K(/C + 2) + (33/4)q| -

~{q\ + 9293(K - 3) + 2q2qi + (l/4)g3V + 26« + 9) a more fundamental theory at a higher energy scale. So, according to the effective theory 2 9391 {* - 3) + q\) - 2q\ + Aq2q3 - Aq2qx - (l/2)qj(K + 14« + 5) description, the behaviour of the cross section is acceptable as long as energy is sufficiently low. At high energies, the effective theory is superseded by a more fundamental theory, where the increase of the cross section with s is stopped and unitarity is preserved. If V and has the gauge nature (where K = 1), the cross section reaches the constant value

(13) 2 2 v Aira (q +1) 2 2 (19) Iaa[2aq3{q3 + a(9i + 92)}] + a {(l/2)g - 29,92 Ml

2?1?3 - 2q\} + a{~q\ + 'lqtq2 + 2qlQ3 which is similar to the single W boson production in the reaction -yp —• WX [17] in the 2 (l/2)g -2gl92} standard model. After giving the expression for subprocess cross sections we now turn to the explicit where the coefficients C, are functions of expressions for the distribution functions in (10) and (11). 2 /. = (27) The function f-,/e(x,Q ) is the energy spectrum of the backseattored laser photons [10] and are tabulated in [19]. Ax Ax2 The quark distributioii (sea plus valence) in the photon is parametrised by (20) /,„(*, Q2) = AMx, Q?) + Djq.{x, Q2) (28) where where the coefficients Aj and Bj [19] change as the number of flavours / changes ( in 4 8. .1 8 1 1 2 2 (21) connection with the momentum scale Q ) and the functions qv(x,Q ) and qa(x, Q' ) (r/J-A. and S"* respectively, in the notation of [19]) are given by with £ = 4.82. The maximum value of x is found as xmax = ^ = 0.83 which is the upper limit of the i integral in (2) and (3). In describing the quark and gluon distributions in the proton we shall use the results of where j = v,s, and the coefficients D, (i = 1..5, j = v,s) arc given in [19]. [18] where a Q2 dependent parametrisation is given. We shall not reproduce all the details } of the parametrisations here, instead we summarize the general form of the functions and 2 3 Numerical Analysis refer the reader to the references for details. fq/p(x,Q ) parametrizes the quark (sen plus valence) distributions in the proton We will now analyze the total cross section a(ip —> Le) defined in (9) for vector and scalar leptoquarks. We based our analysis only to the first generation so that the quark (22) entering the scattering process is either u or d, producing in the final state leptoquarks of 2 A ,(l + A5x + A6x ){l - x) * (23) electromagnetic charge 5/3 or 2/3 [4] respectively. Although there are many accelerators [11,12] deserving analysis under such a work, for our purpose it is sufficient to analyze a where B(x,y) is the Euler's Beta function, N equals 2 for u quark and 1 for d quark. The single accelerator which we choose to be LHC + TESLA with y/s = 5.5TeV. coefficients A, (i=l,..,9) are tabulated in [18] and they are explicit functions of Fig.2 and Fig.2 show the total cross section in (9), at -y/s = 5.5TeV, for V5/3 (gauge (24) particle) and S5/3 respectively. We give Fig.l and Fig.2 to demonstrate the relative magnitude of the direct and resolved photon contributions as the leptoquark mass changes. where Qjj = AGeV2 and A = OAGeV. These two are typical examples applicable to all other cases. From Fig. 1 and Fig. 2 we The gluon distribution in the proton is parametrised by f / having the expression [18] g p see that for ML < SQQGeV the total cross section in (9) is strongly dominated by resolved

2 photon contribution in (11). Moreover, Fig. 1 and Fig. 2 show, respectively, that for xfg/p(x,Q ) = (25) My > ITeV and Ms > 0.5TeV the total cross section in (9) is completely determined and again the coefficients Bi are functions of s and are tabulated in [18]. by the direct photon contribution in (10). We see that the leptoquark mass range where For the gluon and quark distributions in the photon we shall use the Q2 dependent the resolved photon contribution is non negligible is within the mass bounds given in parametrisation given in [19]. The quark distribution in the photon is parametrised by [17]; thus, the effects of the hadronic component of photon in 7p colliders are directly fg/iix, Q2) which is given by observable in future experiments. Fig. 3 shows the dependence of the total cross section in (12) on My for different (26) values of K. From this figure we see that for non- gauge V, the cross section in (12)

8 is considerably enhanced (suppressed) as « grows (falls) to higher (lower) values from Refers** cos unity. Especially the K > 1 case is interesting, because enhancement in the cross section [1] L. AiJiK-tt and B.Farhi, Phys. Lett. 3101(1981)69; Nucl.Phys. B189(1981)547. is large for low values of Mv where the resolved photon contribution dominates. Lastly,

we observe from this figure that the cross section for Vi/3 is always larger than that for [2] P. Langacker, Phys. Rep. 72(1981)193.

V2/3. [3] J. L. Hewett and T. Rizzo, Phys. Rep. 183(1989)193. Finally, in Fig.4 we show the variation of the total cross section in (13) with A/s-. We conclude from this figure that the total cross section for S5/3 is always larger than that [4] J. Blumlein and R. Ruckl, Phys. Lett. 0304(1993)337. for S2/3 ( see also [11,12]). In conclusion, wo have discussed the single leptoquark production in y// colliders for [5] J. Wudka, Phys. Lett. B 167(1986)337. scalar and vector leptoquarks. We have analysed the contribution of the hadronie com- [6] J.F. Gunion and E. Ma, Phys. Lett. B195(1987)257. ponent of the photon to the total cross section. Moreover, gauge- and non-gauge-vector leptoquarks are discussed separately in terms of their contribution to the total cross .sec- [7] W. Buchmuller et. al. Phys. Lett. B191(1987)442. tion. [8] O.J.P. Eboli and A.V. Olinto, Phys. Rev. D38(1988)3461.

[9] J. L. Hewett and S. Pakvasa, Phys. Lett. 3227(1989)178. Acknowledgments. One of the authors (T.M.A.) thanks the International Centre for O.J.P. Eboli et. al., Phys. Lett. 3311(1993)147. Theoretical Physics, Trieste, for hospitality, where part of this work is done. [10] I. F. Ginzburg et.al., Nucl. Ins. Methods, 5(1984)219.

[11] S. Atag et.al., Phys. Lett. B326(1994)185.

[12] S. Atag et.al., J. Phys. G: Nucl. Part. Phys 21(1995)1189.

[13] W. Buchmuller et. al., Phys. Lett. B177(1987)377.

[14] O. Shanker, Nucl. Phys. B20C(1982)49.

[15] M. Leurer, Phys. Rev. D50(1994)536.

[16] S. Davidson et. al., Z. Phys. 061(1994)613.

[17] J. Blunilein and E. Boos, Prep. DESY 94-144 (1994).

[18] M. Gluck, E. Hoffmann and E. Reya, Z.Physik 013(1982)119.

[19] M. Drees and K. Grassie, Z.Physik 028(1985)451.

10 Figure Captions

CD Figure 1: For V5/3 (gauge particle) at y/s = 5.5TeV, contributions of resolved photon o (dashed) and direct photon (short- dashed) to the total crossection (solid). o

Figure 2: The same as in Fig. 1 but for Ss/3.

Figure 3: Variation of the total crossection for vector leptoquarks as a function of lep- toquark mass for different values of anomalous coupling. Here circle, square and o triangle corresponds to K = 0.5, K = 1.0 and K = 2.0 respectively. .o o Figure 4: Variation of the total crossection for scalar leptoquarks as a function of lopto- quark mass.

o _o o CM o

. O O

i—{nun 11—limn 11 m—|iiiin i i II i |i

o o o o o o o

12 11 10 =

1 -

2 \ 10" - \ \ \ \ 3 \ io - - \ \ \ Ms(GeV) i i i i i i i i i i i i i I-I i i i i i i i i i 0 500 1000 1500 2000 FIG 2

10 S

SOLID: V5/3 3 10 i DASHED: V2/3

.Q

102"E

10 •=

Mv(GeV) o 1000 1500 2000 FIG. 3 10 d S0LID:S5/3 DASHED:S2/3

\ 1 d

10 "'d

' Ms(GeV) -2 10 • ' i i ' i i i i i ii i iii iii i i i i i i i i i I 0 500 1000 1500 2000 FIG. 4