ar X iv : h ep - p h / 98 02 21 9 v 1 2 F eb 1 99 8 Muon - proton Colliders : Leptoquarks and Contact Interactions 1

The muon-proton (μp) collider is an interesting option of the muon collider. Here we discuss the physics potential of the μp collider; especially, leptoquarks and contact interactions. We calculate the sensitivity reach for the second generation leptoquarks and leptogluons, R-parity violating squarks, and μq contact interactions for the μp colliders of various energies and luminosities. INTRODUCTION Recently, the muon collider has received a lot of attentions [1]. The muon collider of a few hundred GeV center-of-mass energy is considered a Higgs factory [2], where interactions and branching ratios of the Higgs boson can be studied in detail. It is also an excellent place to study the top-quark near the threshold region [3]. Other physics opportunities include precision studies of gauge bosons [3], search for supersymmetry and lepton-number violation, and other new physics. Muon colliders in TeV range should be feasible for studying strong electroweak symmetry breaking [4], lepton-number violation, and search for heavy exotic particles. The R&D [1,5] of the muon collider is underway. The First Muon Collier (FMC) will have a 200 GeV muon beam on a 200 GeV anti-muon beam, which could possibly be at the Fermilab [5]. With the existing Tevatron proton beam the muon-proton collision becomes a possible option. It would be a 200 GeV ⊗ 1 TeV μp collider, where the first energy is the energy of the muon beam and the second energy is the proton beam energy. The existing lepton-proton collider is the ep collider at HERA. Lepton-proton colliders have been proved to be successful by the physics results from HERA. In this work, we shall discuss the physics potential of the μp colliders at various energies and luminosities. Other μp colliders that we are considering are 50 GeV ⊗ 1 TeV, 1 TeV ⊗ 1 TeV, and 2 TeV ⊗ 3 TeV. The center-of-mass energies and luminosities of these various designs are summarized in Table 1. The nominal yearly luminosity of the 200 GeV ⊗ 1 TeV μp collider is 1) Invited talk present at the Fourth International Conference on the Physics Potential and Development of μμ Colliders, San Francisco CA, Decmember 1997. about 13 fb. Luminosities for other designs are roughly scaled by one quarter power of the muon beam energy and given in Table 1. PHYSICS POTENTIAL The physics opportunities of μp colliders are similar to those of ep colliders, but the sensitivity reach might be very different, which depends on how precise the particles can be identified and measured in ep and μp environments. Similar to ep colliders the proton structure functions can be measured to very large Q and small x in μp colliders of higher energies. At HERA, the Q has been measured up to Q ≃ 10 GeV and x down to x ∼ 3 × 10. At the 200 GeV ⊗ 1 TeV μp collider the Q can be measured up to 10 GeV. In addition, QCD studies, search for supersymmetry and other exotic particles can be carried out at the μp colliders. Here we are particularly interested in the leptoquarks, leptogluons, Rparity violating squarks, and the contact interactions that are specific to the muon. The goal here is to estimate the sensitivity reach for these new physics at various energies and luminosities. Leptoquarks The second generation leptoquarks made up of a muon and a charm or strange quark are particularly interesting at the μp collider because they can be directly produced in the s-channel processes, e.g., μc → L0μc . (1) It is conventional to assume no inter-generational mixing in order to prevent the dangerous flavor-changing neutral currents. The s-channel production will give spectacular enhancement in the invariant mass M of the muon and the hadronic final state, or the x = s/M distribution. The Lagrangian of the second generation leptoquark with the muon and charm and strange quarks is given by L = λ0μq q̄μL0μq + λ1μq q̄γρμL μq + h.c. , (2) TABLE 1. The center-of-mass energies √ s and luminosities L of various designs of muon-proton colliders. √ s(GeV) L (fb) 30GeV⊗ 820GeV 314 0.1 50GeV⊗ 1TeV 447 2 200GeV⊗ 1TeV 894 13 1TeV⊗ 1TeV 2000 110 2TeV⊗ 3TeV 4899 280 where q = c, s and the superscripts (0, 1) on the leptoquark field denote the scalar and the vector leptoquarks, respectively. The production cross section of the leptoquark at the μp collider is given by σ = πλ 4s q(x,Q)× (J + 1) , (3) where J is the spin of the leptoquark and q(x,Q) is the parton luminosity. Leptogluons A leptogluon has a spin of either 1/2 or 3/2, a lepton quantum number (in this case it is the muon), and a color quantum number (the same as gluon.) The interaction Lagrangian for a spin 1/2 leptogluon is given by L = gs MLμg 2Λ Lμgσ μνμGbμν δab + h.c. , (4) where Λ is the scale that determines the strength of the interaction. The decay width of the leptogluon into a muon and a gluon is given by Γ(Lμg → μg) = αsM 5 Lμg 2Λ . (5) The leptogluon can be produced in s-channel in a μp collider and the production cross section is given by σ = 4παs s ( M Lμg Λ 2 g(x,Q) , (6) where g(x,Q) is the gluon luminosity. R-parity Violating Squarks R-parity is in general assumed in supersymmetry, but there is no theoretical reasons why R-parity should conserve. R-parity violation is included by introducing additional terms in the superpotential: W6R = λijkLiLjEk + λ′ijkLiQjDk + λ ′′ ijkUi Dj Dk + μiLiHu , (7) where L,E,Q, U,D,Hu are superfields. The relevant term in the superpotential for the direct production of the R-parity violating squark at the μp collider is λijkLiQjDk. The corresponding Lagrangian is