Muon-proton Colliders: Leptoquarks, Contact Interactions and Extra Dimensions 1 Kingman Cheung 0 0 0 Department of Physics, University of California at Davis, Davis, CA 95616 2 n a J Abstract. We discussthe physicspotentialof the µp collider;especially, leptoquarks, 6 leptogluons, R-parity violating squarks, contact interactions, and large extra dimen- 2 sions. Wecalculatethesensitivityreachforthesenewphysicsatµpcollidersofvarious 1 energies and luminosities. v 5 7 2 INTRODUCTION 1 0 The R&D [1,2] of the muon collider is well underway. The First Muon Collider 0 0 (FMC) will have a 200 GeV muon beam on a 200 GeV anti-muon beam, which / h could possibly be at the Fermilab [2]. With the existing Tevatron proton beam p the muon-proton collision becomes a possible option. It would be a 200 GeV 1 - ⊗ p TeV µp collider. The existing lepton-proton collider is the ep collider at HERA. e Lepton-proton colliders have been proved to be successful by the physics results h : from HERA. In this work, we shall discuss the physics potential of the µp colliders v i at various energies and luminosities. Other µp colliders that we consider in this X study are summarized in Table 1. The nominal yearly luminosity of the 200 GeV ar 1 TeV µp collider is about 13 fb−1. 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 Q2 and small x in µp colliders of higher energies. At the 200 GeV 1 TeV µp collider the ⊗ 1) Invited talk at the 5th InternationalConference on the Physics Potentialand Development of µ+µ− Colliders, San Francisco CA, December 1999. Work supported by DOE. TABLE 1. The center-of-mass energies √s and luminosities for various designs of L muon-proton colliders. √s(GeV) (fb−1) L 30GeV 820GeV 314 0.1 ⊗ 50GeV 1TeV 447 2 ⊗ 200GeV 1TeV 894 13 ⊗ 1TeV 1TeV 2000 110 ⊗ 2TeV 3TeV 4899 280 ⊗ Q2 can be measured up to 106 GeV2. In addition, QCD studies, search for super- symmetry and other exotic particles can also be carried out. Here we concentrate on leptoquarks, leptogluons, R-parity violating squarks, µ-q contact interactions, and the large extra dimensions. The goal here is to estimate the sensitivity reach for these new physics at various energies and luminosities. Leptoquarks and Leptogluons 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, µ c(s) L (L ). It is conventional to as- µc µs → sumenointer-generationalmixinginordertopreventthedangerousflavor-changing neutral currents. The production cross section of the leptoquark in µp collisions is πλ2 2 σ = q(x,Q ) (J +1) , (1) 2s × where λ is the coupling constant and J is the spin of the leptoquark. Onthe other hand, a leptogluonhasa spin ofeither 1/2or3/2, a leptonquantum number (in this case it is the muon), and a color quantum number (the same as gluon.) The interaction for a spin 1/2 leptogluon is given by M = g LµgLa σµνµGb δ +h.c. , (2) L s2Λ2 µg µν ab µg where Λ is the scale that determines the strength of the interaction. The lep- µg togluon can also be produced in the s-channel and the production cross section is 4π2α M2 2 σ = s Lµg g(x,Q2) , (3) s Λ2µg ! where g(x,Q2) is the gluon luminosity. The R-parity violating squarks can be considered special scalar leptoquarks that are the SUSY partners of quarks. The cross section for µ+p t˜ is given by L → σt˜L = π|λ4′2s31|2 d ms2t˜L,Q2 = m2t˜L! , (4) where d is the down-quark luminosity. The above formula can be easily modified to ′ the production of other squarks with the corresponding subscripts in λ and parton functions. If kinematically allowed the leptoquarks, leptogluons, and the R-parity violat- ing squarks are produced in the s-channel and thus give rise to a spectacular en- hancement in a single bin of the invariant mass M distribution or the x = M2/s distribution. Contact Interactions The effective four-fermion contact interactions can arise from fermion compos- ′ iteness or exchanges of heavy particles like heavy Z , heavy leptoquarks, or other exoticparticles. TheconventionalLagrangianforllqq (l = e,µ)contactinteractions has the form [3] L = η l γ l (q γµq )+η l γ l (q γµq ) NC LL L µ L L L RR R µ R R R q Xh (cid:16) (cid:17) (cid:16) (cid:17) +η l γ l (q γµq )+η l γ l (q γµq ) , (5) LR L µ L R R RL R µ R L L (cid:16) (cid:17) (cid:16) (cid:17) i 2 where ηlq = ǫ4π/Λlq . We introduce the reduced amplitudes Mµq, where the αβ αβ αβ subscripts label the chiralities of the initial lepton (α) and quark (β). The SM tree-level reduced amplitudes for µq µq are → e2Q e2 gµgq Mµq(tˆ) = q + α β , α,β = L,R . (6) αβ − tˆ sin2θ cos2θ tˆ m2 w w − Z µq The new physics contributions to M from the µµqq contact interactions are αβ ∆Mµq = ηµq. The differential cross sections are given by [3] αβ αβ dσ(µ+p) sx = u(x,Q2) Mµu 2 + Mµu 2 +(1 y)2 Mµu 2 + Mµu 2 dxdy 16π | LR| | RL| − | LL| | RR| n h (cid:16) (cid:17)i 2 2 2 2 2 µd µd 2 µd µd +d(x,Q ) M + M +(1 y) M + M (7) LR RL − LL RR − (cid:20)(cid:12) (cid:12) (cid:12) (cid:12) (cid:18)(cid:12) (cid:12) (cid:12) (cid:12) (cid:19)(cid:21)(cid:27) dσ(µ p) sx (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) = u(x,Q2) (cid:12)Mµu(cid:12)2 +(cid:12)Mµu(cid:12)2 +(1 y)2 (cid:12)Mµu(cid:12)2 +(cid:12)Mµu(cid:12)2 dxdy 16π | LL| | RR| − | LR| | RL| n h (cid:16) (cid:17)i 2 2 2 2 2 µd µd 2 µd µd +d(x,Q ) M + M +(1 y) M + M . (8) LL RR − LR RL (cid:20)(cid:12) (cid:12) (cid:12) (cid:12) (cid:18)(cid:12) (cid:12) (cid:12) (cid:12) (cid:19)(cid:21)(cid:27) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) Model of extra dimensions Arkani-Hamed, Dimopoulos and Dvali [4] proposed that in the extra dimensions gravity is free to propagate while the SM particles are restricted to a 3-D-brane. The size of the extra dimensions is postulated to be as large as mm to solve the hierarchyproblembybringingtheeffectivePlanckscaleM downtoTeV.Itimplies S a new gravity interaction for the graviton in the bulk. In our 3 + 1 dimensional pointofview, thegravitonbehaves asatower ofclosely-spaced Kaluza-Kleinstates. Each state still couples to the SM particles with a normal gravitational strength of order of 1/M but, however, there are a huge number of such states. Collectively, Pl the overall coupling strength becomes of order of 1/M . In the presence of the new S interaction the double differential cross section is given by [5]. d2σ(µ+p) sx 2 2 2 2 2 = f (x) (1 y) ( M + M )+ M + M q LL RR LR RL dxdy 16π q ( − | | | | | | | | X π2 2 2 2 3 4 + (sx) F (32 64y +42y 10y +y ) 2 MS4! − − (2 y)3 2 +2πe Q Q F − e q MS4! y 2πe2 1 + F (sx) gegq(6y 6y2+y3) sin2θwcos2θw MS4! −Q2 −MZ2 (cid:20) a a − +gegq(y 2)3 v v − (cid:21)) 2 π 3 2 + f (x)(sx) F (1 y)(y 2y +2) . (9) 2 g MS4! − − Unlike the leptoquarks, the contact interactions and the extra dimensions do not enhance the cross section in a single invariant mass bin, instead, they enhance the cross section at large Q2. SENSITIVITY REACH The 95% sensitivity reach on the contact interactions and extra dimensions are calculated as follows. We use the the 2-dimensional x-y distribution to calculate the sensitivity to these new interactions, so as to maximize the sensitivity [6]. We divide the x-y plane (0.05 < x < 0.95 and 0.05 < y < 0.95) into a grid. We calculate the number of events predicted by the standard model in each bin with an efficiency of 0.8. We then follow the Monte Carlo approach in Ref. [6]. Thesensitivity reachonthecontact interactionscales Λµq istabulatedinTable2. αβ ThemaximumreachofΛateachcenter-of-massenergyroughlyscalesasΛ 40√s. ∼ The effect of luminosity on Λ is rather small: Λ only scales as the 1/4th power of TABLE 2. The 95% sensitivity reach on Λµq, (α,β = L,R; q = u,d) at various µ+(µ−)p αβ colliders. µ+p 30GeV 820GeV 50GeV 1TeV 200GeV 1TeV 1TeV 1TeV 2TeV 3TeV ⊗ ⊗ ⊗ ⊗ ⊗ √s(GeV) 314 447 894 2000 4899 (fb−1) 0.1 2 13 110 280 L + + + + + Λµu 3.4 3−.4 9.6 9−.1 22.8 2−1.5 57.4 5−6.3 112.7 10−9.7 LL Λµu 4.7 4.2 11.4 10.7 24.0 23.1 58.9 55.8 115.2 105.6 LR Λµu 4.4 3.4 9.7 8.8 19.2 16.8 43.8 38.1 86.0 64.9 RL Λµu 3.2 3.0 9.0 7.9 20.1 18.8 48.6 49.3 98.7 92.3 RR Λµd 7.0 7.0 17.3 18.0 45.0 48.3 88.9 96.1 LL Λµd 1.9 2.9 5.1 6.5 11.1 13.5 26.8 31.9 46.7 63.4 LR Λµd 2.1 2.2 4.7 3.8 11.4 6.9 30.4 22.8 64.0 45.5 RL Λµd 1.4 2.3 5.0 5.7 12.0 13.1 31.4 32.1 58.2 65.5 RR Λ 6.5 6.1 16.6 15.5 35.2 34.0 85.4 84.9 166.8 161.9 VV Λ 2.8 5.0 10.6 11.8 22.6 25.8 58.6 62.3 109.4 125.0 AA − µ p + + + + + Λµu 5.2 5−.0 13.2 1−2.9 29.6 2−9.6 76.9 7−2.9 147.6 14−4.8 LL Λµu 3.1 2.7 7.1 6.9 14.3 13.9 34.4 31.2 64.9 58.9 LR Λµu 3.0 2.5 6.7 6.1 12.3 11.6 26.9 22.5 50.6 39.7 RL Λµu 4.8 4.5 12.0 11.3 26.0 25.5 65.5 63.2 128.5 121.7 RR Λµd 2.9 3.4 8.2 8.5 19.3 20.5 50.0 53.3 101.1 102.4 LL Λµd 1.6 2.2 4.2 4.7 8.8 9.6 19.4 22.9 38.6 44.6 LR Λµd 1.6 1.9 3.8 3.3 7.1 4.9 20.5 14.3 45.7 37.7 RL Λµd 2.1 2.8 6.0 6.6 13.4 14.6 33.3 37.0 64.3 71.7 RR Λ 6.5 6.4 16.4 15.6 35.7 34.4 87.7 85.9 173.7 162.9 VV Λ 5.4 1.8 13.2 12.3 29.2 27.6 73.5 69.7 142.9 135.7 AA the luminosity. The sensitivity reach on the effective Planck scale M for the model S of large extra dimensions is tabulated in Table 3. To estimate the sensitivity reach for R-parity violating squarks, leptoquarks and leptogluons with a mass m, we assume the enhancement in cross section is in the mass bin of (0.9m, 1.1m). We calculate the number of events predicted by the standard model in this bin with an efficiency of 0.8, call it nsm. Then we use the poisson statistics to estimate the nth that nsm can fluctuate to at the 95% CL. Once the nth is obtained the coupling constant λ or the leptogluon scale Λ can µg be determined. These results are tabulated in Tables 4 to 6. REFERENCES 1. Proceedings of the Symposium on Physics Potential and Development of µ+µ− Collid- ers,SanFrancisco, CADecember1995; µ+µ− Colliders: A Feasible Study, Snowmass, TABLE 3. The 95% sensitivity reach on η = /M4 and the corresponding F S M for n=3 6 at various µ+(µ−)p colliders. S − µ+p 30GeV 50GeV 200GeV 1TeV 2TeV ⊗ ⊗ ⊗ ⊗ ⊗ 820GeV 1TeV 1TeV 1TeV 3TeV √s(GeV) 314 447 894 2000 4899 (fb−1) 0.1 2 13 110 280 L η (TeV−4) 2.24 1.69 10−1 9.35 10−3 3.01 10−4 1.38 10−5 · · · · M (TeV) S n=3 0.97 1.86 3.82 9.03 19.5 n=4 0.82 1.56 3.22 7.59 16.4 n=5 0.74 1.41 2.91 6.86 14.8 n=6 0.69 1.31 2.70 6.38 13.8 − µ p η (TeV−4) 2.14 1.72 10−1 8.95 10−3 2.99 10−4 1.38 10−5 · · · · M (TeV) S n=3 0.98 1.85 3.87 9.05 19.5 n=4 0.83 1.55 3.25 7.61 16.4 n=5 0.75 1.40 2.94 6.87 14.8 n=6 0.70 1.31 2.73 6.40 13.8 TABLE 4. 95% sensitivity reach on λ′ (λ′ ) for a few choices of m (m ) at various µ+p 231 213 t˜L ˜bR (µ−p) colliders. The subprocess is µ+d t˜ (µ−u ˜b ). L R → → 30GeV 50GeV 200GeV 1TeV 2TeV ⊗ ⊗ ⊗ ⊗ ⊗ 820GeV 1TeV 1TeV 1TeV 3TeV √s(GeV) 314 447 894 2000 4899 (fb−1) 0.1 2 13 110 280 L m (GeV) t˜L,˜bR 200 0.014 (0.0097) 0.0043 (0.0036) 0.0025 (0.0023) 0.0015 (0.0014) 0.0010 (0.0010) 300 (0.23) 0.0091 (0.0062) 0.0031 (0.0028) 0.0019 (0.0018) 0.0014 (0.0014) ∞ 400 - 0.062 (0.029) 0.0039 (0.0034) 0.0021 (0.0020) 0.0017 (0.0016) 500 - - 0.0054 (0.0042) 0.0024 (0.0022) 0.0019 (0.0019) 600 - - 0.0083 (0.0057) 0.0026 (0.0024) 0.0021 (0.0020) 700 - - 0.016 (0.0095) 0.0029 (0.0026) 0.0023 (0.0022) 800 - - 0.067 (0.027) 0.0032 (0.0028) 0.0025 (0.0023) 900 - - - 0.0036 (0.0031) 0.0026 (0.0024) 1000 - - - 0.0041 (0.0034) 0.0027 (0.0026) 1500 - - - 0.012 (0.0071) 0.0033 (0.0030) 2000 - - - - 0.0041 (0.0036) 2500 - - - - 0.0053 (0.0043) 3000 - - - - 0.0075 (0.0055) 3500 - - - - 0.012 (0.0078) 4000 - - - - 0.027 (0.014) 4500 - - - - 0.12 (0.052) TABLE 5. 95% sensitivity reach on λ0 λ1 for a few choices of mL0,L1 at various µ−p colliders. The subprocess is µ−(c,s) L0,1. → 30GeV 50GeV 200GeV 1TeV 2TeV ⊗ ⊗ ⊗ ⊗ ⊗ 820GeV 1TeV 1TeV 1TeV 3TeV √s(GeV) 314 447 894 2000 4899 (fb−1) 0.1 2 13 110 280 L µ−c(s) L0 → mL0 (GeV) 200 0.097 (0.072) 0.017 (0.012) 0.0040 (0.0033) 0.0014 (0.0013) 0.0008 (0.0008) 300 2.3 (2.3) 0.071 (0.054) 0.0081 (0.0062) 0.0022 (0.0020) 0.0012 (0.0011) 400 - 0.43 (0.43) 0.016 (0.012) 0.0031 (0.0026) 0.0015 (0.0014) 500 - - 0.031 (0.023) 0.0043 (0.0035) 0.0018 (0.0017) 600 - - 0.065 (0.050) 0.0059 (0.0047) 0.0022 (0.0020) 700 - - 0.15 (0.14) 0.0079 (0.0061) 0.0026 (0.0023) 800 - - 0.38 (0.38) 0.011 (0.0081) 0.0030 (0.0027) 900 - - - 0.014 (0.011) 0.0035 (0.0030) 1000 - - - 0.019 (0.014) 0.0040 (0.0034) 1500 - - - 0.10 (0.090) 0.0076 (0.0061) 2000 - - - - 0.014 (0.011) 2500 - - - - 0.026 (0.019) 3000 - - - - 0.049 (0.038) 3500 - - - - 0.10 (0.084) 4000 - - - - 0.22 (0.22) 4500 - - - - 0.57 (0.57) µ−c(s) L1 → mL1 (GeV) 200 0.068 (0.051) 0.012 (0.0087) 0.0029 (0.0024) 0.0010 (0.0009) 0.0006 (0.0005) 300 1.6 (1.6) 0.050 (0.038) 0.0057 (0.0044) 0.0016 (0.0014) 0.0008 (0.0008) 400 - 0.30 (0.30) 0.011 (0.0082) 0.0022 (0.0019) 0.0011 (0.0010) 500 - - 0.022 (0.016) 0.0031 (0.0025) 0.0013 (0.0012) 600 - - 0.046 (0.035) 0.0042 (0.0033) 0.0016 (0.0014) 700 - - 0.11 (0.098) 0.0056 (0.0043) 0.0018 (0.0016) 800 - - 0.27 (0.27) 0.0075 (0.0057) 0.0021 (0.0019) 900 - - - 0.010 (0.0076) 0.0025 (0.0021) 1000 - - - 0.014 (0.010) 0.0029 (0.0024) 1500 - - - 0.074 (0.063) 0.0054 (0.0043) 2000 - - - - 0.0099 (0.0075) 2500 - - - - 0.018 (0.014) 3000 - - - - 0.035 (0.027) 3500 - - - - 0.072 (0.059) 4000 - - - - 0.16 (0.15) 4500 - - - - 0.40 (0.40) CO, July 1996; Proceedings of the Symposium on Physics Potential and Development of µ+µ− Colliders, San Francisco, CA December 1997. 2. Workshop on Physics at the First Muon Collider and at the Front End of a Muon Collider, Fermilab, Batavia IL, December 1997. TABLE 6. 95% sensitivity reach on Λ for a few choices of m at various µ−p colliders. µg Lµg − The subprocess is µ g L . µg → 30GeV 820GeV 50GeV 1TeV 200GeV 1TeV 1TeV 1TeV 2TeV 3TeV ⊗ ⊗ ⊗ ⊗ ⊗ √s(GeV) 314 447 894 2000 4899 (fb−1) 0.1 2 13 110 280 L − µ g L (Λ ) in TeV µg µg → mL0 (GeV) 200 1.9 4.3 8.5 14.4 19.5 300 0.2 3.3 9.0 17.0 23.9 400 - 1.2 8.6 18.6 27.4 500 - - 7.8 19.6 30.4 600 - - 6.5 20.1 32.8 700 - - 4.7 20.2 35.0 800 - - 2.3 20.0 36.7 900 - - - 19.5 38.2 1000 - - - 18.7 39.4 1500 - - - 11.9 42.4 2000 - - - - 41.8 2500 - - - - 38.8 3000 - - - - 34.0 3500 - - - - 27.2 4000 - - - - 18.3 4500 - - - - 7.7 3. For a recent review, see V. Barger et al. Phys. Rev. D57, 391 (1998). 4. N. Arkani-Hamed, S. Dimopoulos and G. Dvali, Phys. Lett. B429, 263 (1998). 5. K. Cheung, Phys. Lett. B460, 383 (1999). 6. K. Cheung and G. Landsberg, hep-ph/9909218 .