

 20 Apr 1994

DESY 94-072

April 1994

Leptoquark Pair Production at ep Colliders

Johannes Bl"umlein1, Edward Boos1;2, and Alexander Pukhov2

1DESY - Institut f"ur Hochenergiephysik Zeuthen,

Platanenallee 6, D-15735 Zeuthen, Germany 2Institute of Nuclear Physics, Moscow State University,

RU-119899 Moscow, Russia

Abstract The pair production cross section for scalar and vector leptoquarks at ep colliders is calculated for the case of photon-gluon fusion. In a model independent analysis we consider the most general C and P conserving couplings of gluons and photons to both scalar and vector leptoquarks described by an effective low-energy Lagangian which obeys U (1)em \Theta SU (3)c invariance. Numerical predictions are given for the kinematical regime at HERA and LEP \Omega LHC.

1 Introduction Many theories beyond the Standard Model try to unify the observed quark and lepton degrees of freedom on a more fundamental level [1]. As a consequence, new bosons, the leptoquarks, are contained in these models. For a long time ep colliders have been considered as ideal facilities to search for leptoquarks through e\Sigma q(q) fusion [2, 3], since their signal emerges as a narrow peak in the deep inelastic differential e\Sigma p scattering cross sections d2oee

\Sigma p=dxdQ2. Searching for

these peaks, the first experimental limits from collider experiments on the mass and the l\Sigma q(q) couplings, *lq, of leptoquarks to the fermions of the first generation have been given by ZEUS and H1 (cf. [4]) at HERA recently. The couplings *lq are not predicted by theory and it is not excluded that *lq=e o/ 1. In fact, a recent re-analysis of different measurements with respect to leptoquark contributions [5] constrains *lq=e !, 0:07:::0:27, depending on the type of scalar and vector leptoquarks. For *lq=e o/ 1 both the production cross sections for e\Sigma q(q) fusion and e\Sigma g fusion [6] are rather small.

Leptoquark pair production via photon-gluon fusion depends on the gauge boson couplings to leptoquarks only. Thus, a dedicated search for leptoquarks is possible also in the range of small fermion couplings. In the case of scalar leptoquarks all couplings are known completely 1. For vector leptoquarks the situation is more complex and depends on the specific nature of the low-energy leptoquark states emerging after symmetry breaking in a unified theory or in some scenario of compositeness. To keep the analysis as model independent as possible we assume the most general Lorentz structure for photon and gluon-leptoquark couplings which respect C and P conservation [8]. The cases of a minimal vector boson coupling (cf. [9]) and a Yang- Mills type coupling are contained in this description as well as the 'anomalous' couplings ^A;G and *A;G. These parameters determine the production cross sections in addition to the known electromagnetic and color couplings.

In this letter we derive the pair production cross sections for vector leptoquarks based on photon-gluon fusion (section 2). The expectations to produce the different types of scalar and vector leptoquarks at HERA and possible future experiments at LEP \Theta LHC are discussed in section 3. An appendix summarizes the functions which describe the differential and integrated cross section of vector leptoquark pair production.

2 Production Cross Sections We will calculate the contributions to leptoquark pair production due to photon-gluon fusion and consider the direct terms only. The resolved photon contributions are dealt with in a separate paper [10] 2. The Feynman diagrams which determine both the scalar and vector leptoquark pair production cross sections are shown in figure 1. Note, that contrary to the case of e+e\Gamma annihilation [9] Yukawa-type fermion couplings do not contribute. The interaction of the different leptoquarks species with photons and gluons is described by the effective Lagrangian in equ. (1) which is constructed to be invariant under U (1)em \Theta SU (3)c gauge transformations.

L = Ls + Lv (1) 1The structure of the scattering cross section for this case has been known from scalar electrodynamics for a very long time [7]. We include a brief discussion of scalars only for the purpose of a systematic comparison with respect to the classification of leptoquark states [3] and as a numerical update.

2At high virtualities, Q2, of the intermediate boson terms due to fl-Z interference and Z-exchange also

become relevant. Furthermore, pairs of different type leptoquarks (cf. [9]) can be produced via W \Sigma g fusion in this kinematical range.

2

with L

s = X

scalars h

(D_\Phi )y (D_\Phi ) \Gamma M 2s \Phi y\Phi i (2)

and 3

Lv = X

vectors ae\Gamma

1 2 G

y _* G

_* + M 2

v \Phi

y _\Phi

_ \Gamma ie "(1 \Gamma ^A)\Phi y

_\Phi * F

_* + *A

M 2v G

y oe_G

_ * F

*oe#

\Gamma igs "(1 \Gamma ^G)\Phi y_ *

a

2 \Phi * G

_*a + *G

M 2v G

yoe_ *a

2 G

_* G*oea #) : (3)

Here e and gs denote the electromagnetic and strong coupling constant, and ^A;G and *A;G are the anomalous couplings. The field strength tensors of the photon-, gluon-, and vector leptoquark fields are

F_* = @_A* \Gamma @*A_;G

a_* = @_Aa* \Gamma @*Aa_ + if abcA_bA*c;

G_* = D_\Phi * \Gamma D* \Phi _ (4)

with the covariant derivative given as

D_ = @_ \Gamma ieQflA_ \Gamma igs *

a

2 A

a_: (5)

The parameters ^A;G and *A;G are assumed to be real. They are related to the anomalous 'magnetic' moment _\Phi and 'electric' quadrupole moment q\Phi of the leptoquarks in the electromagnetic and color fields

_\Phi ;ff = ga2M

\Phi (2 \Gamma ^

ff + *ff)

q\Phi ;ff = \Gamma gffM 2

\Phi (1 \Gamma ^

ff \Gamma *ff) (6)

where gff = e or gs and ff = A or G 4.

In particular we assume that these quantities are all independent since we wish to keep the analysis as model independent as possible.

We consider the leptoquarks which have been classified in [3, 9]. They are color triplets or anti-triplets, and the magnitude of their electric charges jQ\Phi j can take the values 5/3, 4/3, 2/3, or 1/3. The cross sections are calculated using the (improved) Weizs"acker-Williams approximation (WWA) [12].

The integrated pair production cross sections read

oes;v(S; M 2\Phi ) = Z

ymax

ymin dy Z

xmax xmin dx Z

1 \Gamma 1 d cos ` OEfl=e(y)Gg=p(x; _

2) d^oes;v

d cos ` `(^s \Gamma 4M

2\Phi ): (7)

Here d^oes;v=d cos ` denotes the differential cross section in the photon-gluon center-of-momentum system (cms), Gg=p(x; _2) is the gluon distribution at the factorization mass _, S = 4EeEp,

3In compositeness scenarios one might wish to relate the quantities ^A;G and *A;G to the compositeness scale \Lambda . This can be achieved e.g. rescaling these quantities by factor M 2v =\Lambda 2.

4Note that the convention for the ^A and *A used here translates into that of [11] by substituting ^A = 1\Gamma ^fl ,

*A = *fl.

3

^s = xyS, x is the longitudinal momentum fraction of the proton carried by the gluon, and M\Phi denotes the mass of the leptoquarks. The photon distribution is described in WWA by

OEfl=e(y) = ff2ss "2m2ey 1Q2

max \Gamma

1 Q2min ! +

1 + (1 \Gamma y)2

y log

Q2max

Q2min # : (8)

The kinematical boundaries in (7) and (8) are:

Q2min = m

2ey2

1 \Gamma y Q

2 max = yS \Gamma 4M 2\Phi \Gamma 4M\Phi mp

xmin = 4M

2\Phi

yS xmax = 1

ymin;max = S + fW

2 \Sigma q(S \Gamma fW 2)2 \Gamma 4m2e fW 2

2(S + m2e) (9) where fW 2 = (2M\Phi + mp)2 \Gamma m2p, me and mp are the electron and proton mass, respectively, y = P:q=P:le, with q = le \Gamma l0e, and P; le; l0e the four momenta of the proton, the incoming and outgoing electron.

2.1 Scalar Leptoquarks The differential and integrated production cross sections in the fl-g cms are5

d^oes d cos ` =

ssffffs(_2)

2^s Q

2\Phi fi (1 \Gamma 2(1 \Gamma fi2)

1 \Gamma fi2 cos2 ` +

2(1 \Gamma fi2)2 (1 \Gamma fi2 cos2 `)2 ) (10)

and

^oes(^s; fi) = ssffffs(_

2)

2^s Q

2\Phi (2(2 \Gamma fi2)fi \Gamma (1 \Gamma fi4) log fififififi 1 + fi

1 \Gamma fi fififififi) : (11)

Here, fi = q1 \Gamma 4M 2\Phi =^s and ffs denotes the strong coupling constant. The production cross section varies / Q2\Phi . For the leptoquark states classified in [3] one obtains e.g. oes(R5=32 ) = 25 oes(S1=33 ), etc. 6.

2.2 Vector Leptoquarks The corresponding cross sections for vector leptoquarks can be represented in terms of the individual A $ G symmetric combinations of ^A;G and *A;G at tree level. The differential cross section in the fl-g cms is

d^oev d cos ` =

ssffffs(_2)

2^s Q

2\Phi 20X

j=0

O/j(^A;G; *A;G) Fj(^s; fi; cos `)(1 \Gamma fi2 cos2 `)2 (12)

5The form of the cross section (10,11) has been derived in [7] and was used mutually in the literature for various processes [13] with different couplings and group theoretical factors.

6In the case of leptoquark pair production through flfl fusion [14], the ratio of the production cross sections

varies even by factors up to 625.

4

with P

20j=0 O/j(^A;G; *A;G)Fj = F0 + (^A + ^G)F1

+ (^2A + ^2G)F2 + ^A^GF3 + ^A^G(^A + ^G)F4 + ^2A^2GF5 + (*A + *G)F6 + (*2A + *2G)F7 + *A*GF8 + *A*G(*A + *G)F9 + *2A*2GF10 + (^A*A + ^G*G)F11 + (^A*G + ^G*A)F12 + *A*G(^A + ^G)F13 + (^A*2G + ^G*2A)F14 + *A*G(^A*G + ^G*A)F15 + (^2A*G + ^2G*A)F16 + (^2A*2G + ^2G*2A)F17 + ^A^G(*A + *G)F18 + ^A^G*A*GF19 + ^A^G(^A*G + ^G*A)F20

and the integrated cross section reads

^oev = ssffffs(_

2)

M 2v Q

2\Phi 20X

j=0

O/j(^A;G; *A;G) eFj(^s; fi) (13)

where e

Fj = M

2v

^s Z

fi 0 d,

Fj (, = fi cos `)

(1 \Gamma ,2)2 : (14)

The functions Fj(^s; fi; cos `) and eFj(^s; fi) are obtained in a lengthly but straightforward calculation which has been performed using the package CompHEP [15]. They are given in eqs. (17,18) in the appendix.

For the case ^A = ^G and *A = *G the equations (17) agree with results obtained in [11] for the case of W -boson pair production in fl-fl fusion. Other more specific results derived earlier for particular choices of ^ and * [16] are described by (12). In our notation the case ^A;G = *A;G j 0 corresponds to Yang-Mills type couplings of photons and gluons to vector leptoquarks, while ^A;G = 1; *A;G = 0 describes the case of 'minimal' vector boson couplings [17]. Most of the above terms contain contributions / (^s=M 2\Phi )n which are of O(1) in the threshold range. These unitarity-violating terms (for ^s AE M 2v ) are absent in some of the functions eFj, particularly for the contributions which are at most linear in ^A;G and *A;G.

One may ask whether apart from the Yang-Mills case another combination of these couplings exists which preserves tree-level unitarity. Since only in eF10 a term / (^s=M 2\Phi )3 appears either *A or *G must vanish to preserve unitarity. Furthermore, the terms / (^s=M 2\Phi )2 cancel only for

*2A(G) h1 + (1 \Gamma ^2G(A))2i = 0 (15) Both *A and *G have to vanish to obtain real solutions. The terms / (^s=M 2\Phi ) cancel if ^A and ^G obey the relation

(^A + ^G \Gamma ^A^G)2 + 23 ^2A^2G = 0: (16)

Thus, for any non vanishing values of ^A; ^G; *A; *G tree-level unitarity is not preserved by oev. At high energies (i.e. ^s AE 4M 2v ) the effective low energy Lagrangian (1) is no longer valid since terms which decouple at low energies become relevant. Instead one has to consider the full gauge theory from which (1) was obtained.

5

3 Numerical Results In the subsequent numerical calculations we used the CTEQ2 (LO) parametrization to describe the gluon distribution [18]. Other recent parametrizations [19] yield similar numerical results. The factorization mass _ and the scale of ffs were choosen to be p^s. The uncertainty of the cross section calculation due to the use of the improved Weizs"acker-Williams approximation [12] was estimated to be of O(6%) both for the case of HERA and LEP \Theta LHC due to the choice of the kinematical bounds (9a).

In figure 2a the integrated cross section for ep scattering at HERA is shown for scalar leptoquarks with jQ\Phi j = 1=3 and 5=3, respectively. Production cross sections oetots ?, 0:1pb - corresponding to 10 events at an integrated luminosity of L = 100pb\Gamma 1 - are obtained for the states with jQ\Phi j = 2=3 to jQ\Phi j = 5=3 for M\Phi ! 55 to 65 GeV. For jQ\Phi j = 1=3 the production cross section is too small for M\Phi ?, 45 GeV, a bound set previously by the LEP experiments [20]. At LEP \Theta LHC the search limits on a rate of 10 events extend from M\Phi = 140 GeV for jQ\Phi j = 1=3 to M\Phi = 220 GeV for jQ\Phi j = 5=3 assuming L = 1f b\Gamma 1 as shown in figure 2b.

Limits on the allowed mass range of scalar leptoquarks have been derived by different experiments. Bounds which are independent of the leptoquark-fermion couplings were given by the LEP experiments as M\Phi ? 44:4 GeV at 95 % CL [20, 21]7 for almost all scalars classified in [3] and all three generations. Other limits have been found by the UA2 [23], CDF and D0 [24] experiments for the 1st generation scalar leptoquarks, excluding the mass ranges between 44 and 132 GeV depending on the branching ratios Br(\Phi s ! eq). Independently of the yet unknown

fermion couplings *L;R, the states eS1; S4=33 ; R5=32 and eR2=32 are excluded for masses M\Phi ! 132 GeV and the state S1 for M\Phi ! 86 GeV. For general values of the fermion couplings, the states S\Gamma 2=33 ; eR\Gamma 1=32 ; R2=32 and S1=33 are constrained by the LEP bound only. Unlike these partial results a systematic search for scalar leptoquarks of all generations above the LEP limit is still needed in the kinematically accessible range at HERA, M\Phi !, 63 GeV. Among the different states [3] the

search for S\Gamma 2=33 and eR2=32 (with *R = 0) (cf. [9]) is particularly difficult, since these leptoquarks decay only into a neutrino-quark pair, a signature with a large QCD background.

Figure 3a shows the integrated cross section for vector leptoquark pair production at HERA for different choices of ^A;G and *A;G. In a model independent analysis the complete dependences on these four parameters must be explored. From the examples shown in figure 3a it is evident, that severe constraints on the parameter space of the anomalous couplings can be obtained at HERA. Complementary to searches at pp colliders the photon couplings ^A and *A can be probed besides of ^G and *G at ep colliders. Due to accidental cancellations between the different contributions, eFj, for specific values of ^A;G; *A;G even smaller cross sections than that of the minimal vector coupling (M.C.) can be obtained. The cross section oetotM:C: for the case of HERA amounts to 0.2 pb only at the LEP bound8. For minimal vector coupling, the search limits at a rate of 10 events extend to 52 GeV (jQ\Phi j = 1=3) and to 74 GeV (jQ\Phi j = 5=3). Figure 3b shows the mass dependence of the integrated cross sections for vector leptoquark pair production at LEP \Theta LHC with jQ\Phi j = 1=3. The search limits on a rate of 10 events for leptoquarks coupling to both photons and gluons with a minimal vector coupling extend from M\Phi = 185 GeV to

7In [21] also limits on 1st and 2nd generation scalar leptoquarks are derived from a search in e+e\Gamma ! SS\Lambda ,! lq [22]. However, these bounds depend on assumptions made on *lq .

8Neither the LEP experiments nor searches at proton colliders have investigated vector leptoquarks so far

allowing for general vector boson-gauge boson couplings (3). Since there is a symmetry in the decay pattern of scalar and vector leptoquarks (cf. [9], table 3), one finds from the cross sections calculated in [9] that the exclusion limit found for scalars at LEP holds for vectors as well.

6

270 GeV for jQ\Phi j = 1=3 to jQ\Phi j = 5=3 vector leptoquarks.

Note that the above bounds have been calculated on the basis of the direct contributions due to photon-gluon fusion only. The resolved photon contributions [10] will allow to extend the mass ranges correspondingly.

In summary we have shown that in a search for both scalar and vector leptoquark pair production at ep colliders yet open mass ranges can be explored independently of the size of the leptoquark-fermion couplings and fermion generation to which the leptoquarks are associated. For vector leptoquarks constraints on both the anomalous ^A; *A and ^G; *G can be derived.

Acknowledgement. We are grateful to Slava Ilyin and Sergey Shichanin for discussions. We would like to thank G"unter Wolf and Peter Zerwas for conversations, and James Botts for reading the manuscript. E.B. would like to thank DESY-Zeuthen for the warm hospitality extended to him.

4 Appendix The functions Fi(^s; fi; cos `) of (12) are:

F0 = 19 \Gamma 6fi2 + 6fi4 + (16 \Gamma 6fi2)fi2 cos2 ` + 3fi4 cos4 ` F1 = \Gamma 22 \Gamma 10fi2 cos2 `

F2 = 4 + ^sM 2

\Phi

1 \Gamma fi4 cos4 `

2 +

^s2 M 4\Phi

(1 \Gamma fi2 cos2 `)2

16

F3 = 28 + 4fi2 cos2 ` + ^sM 2

\Phi fi

2 cos2 `(1 \Gamma fi2 cos2 `) + ^s2

M 4\Phi

(1 \Gamma fi2 cos2 `)2

8

F4 = \Gamma 5 + fi2 cos2 ` + ^sM 2

\Phi \Gamma

3 + fi2 cos2 ` + 2fi4 cos4 `

4 \Gamma

^s2 M 4\Phi

(1 \Gamma fi2 cos2 `)2

8

F5 = 3 \Gamma fi

2 cos2 `

4 +

^s M 2\Phi

5 \Gamma 4fi2 cos2 ` \Gamma fi4 cos4 `

16

+ ^s

2

M 4\Phi

13 \Gamma 25fi2 cos2 ` + 11fi4 cos4 ` + fi6 cos6 `

128 F6 = \Gamma 4 + 4fi2 cos2 `

F7 = 4 + ^sM 2

\Phi \Gamma

7 + 8fi2 cos2 ` \Gamma fi4 cos4 `

2 +

^s2 M 4\Phi

(1 \Gamma fi2 cos2 `)2

2

+ ^s

3

M 6\Phi

(1 \Gamma fi2 cos2 `)3

16

F8 = \Gamma ^sM 2

\Phi (1 \Gamma fi

2 cos2 `) + ^s2

M 4\Phi

11 \Gamma 13fi2 cos2 ` + fi4 cos4 ` + fi6 cos6 `

8

\Gamma ^s

2

M 4\Phi

(1 \Gamma fi2 cos2 `)3

8

F9 = 1 \Gamma fi2 cos2 ` + ^sM 2

\Phi \Gamma

3 + 4fi2 cos2 ` \Gamma fi4 cos4 `

2 +

^s2 M 4\Phi (1 \Gamma fi

2 cos2 `)2

+ ^s

3

M 6\Phi \Gamma

3 + 7fi2 cos2 ` \Gamma 5fi4 cos4 ` + fi6 cos6 `

16

7

F10 = 3 \Gamma fi

2 cos2 `

4 +

^s M 2\Phi \Gamma

19 + 20fi2 cos2 ` \Gamma fi4 cos4 `

16

+ ^s

2

M 4\Phi

141 \Gamma 249fi2 cos2 ` + 107fi4 cos4 ` + fi6 cos6 `

128

+ ^s

3

M 6\Phi \Gamma

53 + 119fi2 cos2 ` \Gamma 79fi4 cos4 ` + 13fi6 cos6 `

128

+ ^s

4

M 8\Phi

27 \Gamma 68fi2 cos2 ` + 58fi4 cos4 ` \Gamma 20fi6 cos6 ` + 3fi8 cos8 `

512

F11 = \Gamma 8 + ^sM 2

\Phi (3 \Gamma 4fi

2 cos2 ` + fi4 cos4 `)

F12 = ^sM 2

\Phi (2 \Gamma 3fi

2 cos2 ` + 4fi4 cos4 `)

F13 = \Gamma 2(1 \Gamma fi2 cos2 `) + ^sM 2

\Phi

9 \Gamma 13fi2 cos2 ` + 4fi4 cos4 `

4

\Gamma ^s

2

M 4\Phi

2 \Gamma 3fi2 cos2 ` + fi4 cos4 `

2 +

^s3 M 6\Phi

(1 \Gamma fi2 cos2 `)3

16

F14 = \Gamma 5 + fi2 cos2 ` + ^sM 2

\Phi

7 \Gamma 8fi2 cos2 ` + fi4 cos4 `

2 \Gamma 3

^s2 M 4\Phi

(1 \Gamma fi2 cos2 `)2

8

\Gamma (1 \Gamma fi

2 cos2 `)3

16 F15 = \Gamma 3 \Gamma fi

2 cos2 `

2 +

^s M 2\Phi

13 \Gamma 14fi2 cos2 ` + fi4 cos4 `

8

\Gamma ^s

2

M 4\Phi

41 \Gamma 81fi2 cos2 ` + 39fi4 cos4 ` + fi6 cos6 `

64

+ ^s

3

M 6\Phi

11 \Gamma 25fi2 cos2 ` + 17fi4 cos4 ` \Gamma 3fi6 cos6 `

128

F16 = 1 \Gamma fi2 cos2 ` \Gamma ^sM 2

\Phi

3 \Gamma 5fi2 cos2 ` + 2fi4 cos4 `

4

F17 = 3 \Gamma fi

2 cos2 `

4 \Gamma

^s M 2\Phi

7 \Gamma 8fi2 cos2 ` + fi4 cos4 `

16

\Gamma ^s

2

M 4\Phi

3 \Gamma 7fi2 cos2 ` + 5fi4 cos4 ` \Gamma fi6 cos6 `

128 +

^s3 M 6\Phi

(1 \Gamma fi2 cos2 `)3

32

F18 = 2(5 \Gamma fi2 cos2 `) \Gamma ^sM 2

\Phi

11 \Gamma 15fi2 cos2 ` + 4fi4 cos4 `

4

\Gamma ^s

2

M 4\Phi

(1 \Gamma fi2 cos2 `)2

4

F19 = 3 \Gamma fi2 cos2 ` \Gamma ^sM 2

\Phi

7 \Gamma 8fi2 cos2 ` + fi4 cos4 `

4

+ ^s

2

M 4\Phi

11 \Gamma 13fi2 cos2 ` + fi4 cos4 ` + fi6 cos6 `

32

+ ^s

3

M 6\Phi

5 \Gamma 7fi2 cos2 ` \Gamma fi4 cos4 ` + 3fi6 cos6 `

128

8

F20 = \Gamma 3 \Gamma fi

2 cos2 `

2 +

^s M 2\Phi

(1 \Gamma fi2 cos2 `)2

8

+ ^s

2

M 4\Phi

11 \Gamma 23fi2 cos2 ` + 13fi4 cos4 ` \Gamma fi6 cos6 `

64 (17)

The functions eFi(^s; fi), which describe the different contributions to the integrated cross section (13), are:e

F0 = fi ` 112 \Gamma 94 fi2 + 34 fi4' \Gamma 38 i1 \Gamma fi2 \Gamma fi4 + fi6j ln fififififi 1 + fi1 \Gamma fi fififififie F1 = \Gamma 4fi \Gamma 34 i1 \Gamma fi2j log fififififi 1 + fi1 \Gamma fi fififififie F2 = 116 fi ^sM 2

\Phi +

3 \Gamma fi2

4 log fififififi

1 + fi 1 \Gamma fi fififififie

F3 = 3fi + 18 fi ^sM 2

\Phi + `2 \Gamma

3 2 fi

2' log fififififi 1 + fi

1 \Gamma fi fififififie

F4 = \Gamma 18 fi ^sM 2

\Phi + `\Gamma 1 +

3 8 fi

2' log fififififi 1 + fi

1 \Gamma fi fififififie

F5 = \Gamma 196 fi + 548 fi ^sM 2

\Phi +

4 \Gamma fi2

16 log fififififi

1 + fi 1 \Gamma fi fififififie

F6 = \Gamma 12 i1 \Gamma fi2j log fififififi 1 + fi1 \Gamma fi fififififie

F7 = 712 fi ^sM 2

\Phi +

1 24 fi

^s2 M 4\Phi \Gamma

5 + fi2

4 log fififififi

1 + fi 1 \Gamma fi fififififie

F8 = \Gamma 16 fi + 14 fi ^sM 2

\Phi \Gamma

1 12 fi

^s2 M 4\Phi + \Gamma

1 2 +

1 2

^s M 2\Phi ! log fififififi

1 + fi 1 \Gamma fi fififififie

F9 = \Gamma 12 fi + 1112 fi ^sM 2

\Phi \Gamma

1 6 fi

^s2 M 4\Phi \Gamma

3 + fi2

8 log fififififi

1 + fi 1 \Gamma fi fififififie

F10 = \Gamma 196 fi + 5980 fi ^sM 2

\Phi \Gamma

113 320 fi

^s2 M 4\Phi +

43 960 fi

^s3 M 6\Phi + \Gamma

1 2 \Gamma

1 16 fi

2 + 1

8

^s M 2\Phi ! log fififififi

1 + fi 1 \Gamma fi fififififie

F11 = 12 i1 + fi2j log fififififi 1 + fi1 \Gamma fi fififififie

F12 = fi + 12 log fififififi 1 + fi1 \Gamma fi fififififie F13 = fi \Gamma 512 fi ^sM 2

\Phi +

1 24 fi

^s2 M 4\Phi + "\Gamma

1 4

^s M 2\Phi + `

3 8 +

1 4 fi

2'# log fififififi 1 + fi

1 \Gamma fi fififififie

F14 = \Gamma 1124 fi ^sM 2

\Phi \Gamma

1 24 fi

^s2 M 4\Phi +

9 + 3fi2

8 log fififififi

1 + fi 1 \Gamma fi fififififie

F15 = 148 fi \Gamma 5996 fi ^sM 2

\Phi +

5 64 fi

^s2 M 4\Phi +

5 + fi2

8 log fififififi

1 + fi 1 \Gamma fi fififififie

F16 = \Gamma 12 fi \Gamma 18 fi2 log fififififi 1 + fi1 \Gamma fi fififififi

9

eF17 = \Gamma 1

96 fi +

1 48 fi

^s M 2\Phi +

1 48 fi

^s2 M 4\Phi \Gamma

2 + fi2

16 log fififififi

1 + fi 1 \Gamma fi fififififie

F18 = \Gamma 14 fi ^sM 2

\Phi \Gamma

1 \Gamma 6fi2

8 log fififififi

1 + fi 1 \Gamma fi fififififie

F19 = \Gamma 124 fi + 796 fi ^sM 2

\Phi +

3 64 fi

^s2 M 4\Phi + "

1 8

^s M 2\Phi \Gamma

2 + fi2

4 # log fififififi

1 + fi 1 \Gamma fi fififififie

F20 = 148 fi + 16 fi ^sM 2

\Phi \Gamma

1 8 i1 \Gamma fi

2j log fififififi 1 + fi

1 \Gamma fi fififififi (18)

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Figure 1: Diagrams describing leptoquark pair production via fl-g fusion

11

10-2 10-1

1 10

40 45 50 55 60 65 70

MLQ / GeV

stot / pb

10 #

Figure 2a: Integrated cross sections for scalar leptoquark pair production, pS = 314 GeV.

12

10-2 10-1

1 10

100 120 140 160 180 200 220

MLQ / GeV

stot / pb

10 # Figure 2b: Integrated cross sections for scalar leptoquark pair production, pS = 1260 GeV.

13

10-1

1 10 10 2

40 45 50 55 60 65 70 75 80 85 90

MLQ / GeV

stot / pb

10 # Figure 3a: Integrated cross sections for vector leptoquark pair production for pS = 314 GeV and different values of ^A;G and *A;G. Full lines: mimimal coupling (M.C.) ^A;G = 1, *A;G = 0, and Yang- Mills coupling (Y-M) ^A;G = *A;G = 0. Upper dashed line: ^A;G = *A;G = \Gamma 1, lower dashed line: ^A;G = *A;G = 1; upper dotted line: ^A;G = \Gamma 1; *A;G = 1; lower dotted line: ^A;G = 1; *A;G = \Gamma 1; dash-dotted line: ^A = 1; ^G = \Gamma 1; *A = 1; *G = \Gamma 1.

14

10-2 10-1

1 10 10 2

100 120 140 160 180 200 220 240 260 280 300

MLQ / GeV

stot / pb

10 # Figure 3b: Integrated cross sections for vector leptoquark pair production for pS = 1260 GeV. The other parameters are the same as in figure 3a.

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