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1 Introduction 2 Total Cross Section 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<? /A photon mediate some fraction y of s-,p, so sgp = ys-,p, 0 < y < 1. Similarly, quark coming off the proton takes away some fraction z of sgp so sm — zsgp, 0 < : < 1. up to one-loop accuracy. The total cross section of the elementary subprocess (1) is given by Now, let us consider the large s behaviour of the cross section for the subprocess in (1) for the arbitrary values of K. Prom (12) one can easily obtain (12) 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| - <MI(-5K + 3) - 3??} (K ^ 1) this logarithmic dependence can be considered as the low energy manifestation of ~{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.
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