A promising direction to find physics beyond the standard model is to look
for violation of $L_{e,\mu,\tau}$ conservation. In particular the process $e^-
e^- \to \mu^- \mu^-$ with the exchange of a gauge bilepton has a striking
signal without background and is predicted in the most economical model to have
a cross-section an order of magnitude higher than previous estimates.Comment: 4 pages LaTeX and 5 postscript figure

Andrija Rašin

Aulakh

Barber

Frampton

Paul H. Frampton

Pisano

Tully

Physics Letters B

English

arXiv

Crossref

Seeking gauge bileptons in linear colliders

A promising direction to find physics beyond the standard model is to look for violation of $L_{e,\mu,\tau}$ conservation. In particular the process $e^- e^- \to \mu^- \mu^-$ with the exchange of a gauge bilepton has a striking signal without background and is predicted in the most economical model to have a cross-section an order of magnitude higher than previous estimates

Frampton, Paul H.

Rašin, Andrija

Carolina Digital Repository

arXiv:hep-ph/0002135v1  14 Feb 2000IFP-781-UNC, hep-ph/0002135Seeking Gauge Bileptons in Linear CollidersPaul H. Frampton and Andrija RašinDepartment of Physics and AstronomyUniversity of North Carolina, Chapel Hill, NC 27599-3255October 31, 2018A promising direction to find physics beyond the standard model is to look for violation of Le,µ,τconservation. In particular the process e−e− → µ−µ− with the exchange of a gauge bilepton has astriking signal without background and is predicted in the most economical model to have a cross-section an order of magnitude higher than previous estimates.October 31, 2018I. INTRODUCTIONConservation laws, and their relation to symmetries,are fundamental to the theoretical physics of nuclei, con-densed matter as well as high energy physics. This hasalready led to great advances and further progress willcertainly come when the correct symmetries are betterprobed and identified.It is expected that clear deviations from the StandardModel (SM) of particle physics should soon show up inexperiment. Already the non-zero neutrino mass is oneexample of this - in the minimal SM neutrinos have nomass. Beyond that the best hope is to observe rare pro-cesses, especially those absolutely forbidden in the min-imal SM. The best suited are processes which violateglobal conservation laws, since there is no reason to be-lieve in their exactness. For example, baryon number (B)might be violated as in the proton decay predicted by e.g.grand unification. Even more amenable to test may bethe processes which violate the separate lepton numbersLe,µ,τ since, even if L = Le + Lµ + Lτ is good, thereis little reason to believe in Le,µ,τ . Neutrino oscillationsexemplify this.One outstanding question of the SM is the occur-rence of replicas of the quark-lepton families and one ap-proach to that issue is the cancellation of chiral anoma-lies between asymmetric non-sequential families of the331 model [1,2] (based on the gauge group SU(3)c ×SU(3)L×U(1)). Recall that anomaly cancellation is cru-cial in many situations of model building beyond stan-dard model, e.g. chiral color [3] and in string theory [4].The 331 model simultaneously predicts that while L is agood quantum number perturbatively, processes do occurwith |∆Li| = 2 (i = e, µ, τ). There is no SM background,and so a process like e−e− → µ−µ− shown in Figure 1provides a way to test [5] whether bileptonic Y −− gaugebosons are present, as they are if SU(2)L ⊂ SU(3)L forthe gauge group. Another model studied in this con-text is the SU(15) theory, where there are double chargedgauge bileptons too, however with a smaller coupling (seeeeYµµ------λλFIG. 1. Contribution of the gauge bilepton to thee−e− → µ−µ− scattering.next Section). Among other theories which have doublycharged particles with L = 2 are the left-right modelsbased on the group SU(2)L × SU(2)R × U(1)B−L [6].However, the couplings of these states to the SM fermionsare of Yukawa type and are not fixed. On the other hand,even though MR, the scale of SU(2)R symmetry break-ing, may be high, there are light double charged scalarsand fermions [7,8], which may lie close to the weak scale.The situation also holds in the supersymmetric grandunified versions of left-right models, where complete dou-ble charged Higgs multiplets may be much lighter thanthe scales of left-right and grand unified symmetries [9].The same experiments that will search for gauge bilep-tons will set important limits for these states as well [10].In old work on the subject of gauge bileptons in theearly 90’s, the Le,µ violating processes were calculated inthe context of an SU(15) theory [11,12]. Here we pointout that in the more economic and attractive 331 model,the cross-section σ(e−e− → µ−µ−) is larger by an orderof magnitude than in SU(15). This result holds true inany model that embeds the gauge group SU(2)L in asingle SU(3)L.The lower limit on M(Y −−) is currently claimed to beat 850 GeV [13] (however see discussion below, also see[14,15]), and with that value ofM(Y −−) the cross-sectionfor σ(e−e− → µ−µ−) is already ∼ 5 fb at √s = 100 GeVand climbs very fast with s to several hundred fb at√s =1500 GeV. This implies a readily detectable event rate foran Le,µ violating process in a collider with integratedluminosity of 10(fb)−1 or higher, e.g. 1033/cm2s for afew months or 1034/cm2s for a week.Some of the leading candidates presently discussed forthe next generation of particle colliders (beyond LEP,Tevatron and LHC) are the Next Linear Collider (NLC),the (circular) Muon Collider (MC) and the Very LargeHadron Collider (VLHC). Of these the most advancedin design and preparation is the NLC. This is most of-ten assumed to be an e+e− positron-electron colliderwith center of mass energy in the range above LEP:200GeV <√s < 2000GeV, although also being discussedis the desirability to operate e+e− at√s = MZ with highluminosity.The motivation for such an NLC is to investigatephysics in a presently-unexplored energy domain, al-though by the time of its start-up initial discoveries canbe expected to have been made by LHC whereupon theNLC provides an excellent tool for detailed studies.It is these machines that are ideally suited for findingthe bilepton even for√s < 200 GeV (see Figure 2), butwith luminosity higher than LEP. These machines couldtherefore initially run in both charge modes at such anenergy.II. CROSS SECTIONThe interaction Lagrangian between the bilepton Yand leptons is given byLY = λY++µ eTCγµP−e++λ†Y −−µ eγµP−CeT (1)where λ is the 3 × 3 coupling matrix. For simplicity, inthe following we will assume λij ∼ λ1.In the 331 model the group SU(2)L is completely em-bedded in the SU(3)L so that the gauge bilepton couplingis equal to the coupling of SU(2)Lλ =g√2≈ 2.08e√2(2)This coupling is larger than the coupling arising fromthe SU(15) models where λ ≈ 1.19e/√2 simply becausethe SU(2)L in that case is not residing entirely in a sin-gle SU(3)L but also partially in the SU(6)L subgroup ofSU(15) [16].The differential cross section (see also [11,17]) for thegauge bilepton exchange in the process e−e− → µ−µ− isgiven bydσd cos θ=λ432π(1 + cos2 θ)s(s−m2Y )2 +m2Y Γ2Y(3)700 900 1100130015001700mY in GeV100101102103cross sec in fb100GeV250GeV500GeVFIG. 2. Total cross section in the 331 model for thee−e− → µ−µ− process as a function of bilepton mass at√s = 100, 250, 500 GeV.where θ goes from 0 to π/2 reflecting the identical par-ticles in the final states. Here mY and ΓY are the massand decay width of the bilepton and s is the square ofthe center of mass energy. This leads to the total crosssectionσ =λ424πs(s−m2Y )2 +m2Y Γ2Y(4)When the flavor and mass eigenbasis of leptons do notmatch, the results above must be corrected by λ2 →λ2VejV∗jeVµjV∗jµ.The total cross section as a function of the bileptonmasses is plotted in Figure 2 for various values of√s(We estimated the decay width of the bilepton as [17]ΓY = λ2mY /8π.)We see that already at√s = 100 GeV we get a crosssection of about σ ∼ 5 fb for a bilepton mass mY = 850GeV, and for the same mY becomes 250 fb at√s = 500GeV. This is about an order of magnitude higher than inthe case of SU(15) model.Such a large cross section makes such a process highlyvisible. The situation is especially good for NLC-turned-into-e−e−-machine, even if it would run only at√s = 100GeV, but with the desired luminosity of 1033/cm2s.This motivates a first run of future linear colliders(electron or muon) machines as same charge lepton col-lider. There are another two reasons for considering do-ing this: a) the additional cost to switch a machine frome+e− to e−e− is relatively negligible ; b) the highest en-ergy that previously probed e−e− collisions was in 1971at√s = 1.12 GeV [18], so this would present an oppor-tunity to improve bounds on the bilepton mass consider-ably.2The spin 1 of the state Y can be checked by the angulardistribution of Eq. (3). For spin 0 the distribution isisotropic.The inverse process µ+µ+ → e+e+ (µ+ is easier to“cool” than µ−) has the same cross section and could beprobed at muon colliders, which are recently discussed asthe next colliders in addition to e+e− machines.III. BACKGROUNDSSince the scattering violates Le and Lµ it does not haveany background in the standard model. However, a non-zero neutrino mass violates lepton number and one caneasily find processes which involve neutrino mass thatproduce e−e− → µ−µ−, as for example shown in Fig-ure 3. Recently, first indications of neutrino mass havebeen found, and one can ask the question how serious abackground the neutrino exchange can be to the bilep-ton exchange, given the mass ranges quoted in the at-mospheric and solar neutrino data. In fact such calcu-lations have been done recently [19] which find that thecross section is very small. The strongest bound for Fig-ure 3a) comes from the neutrinoless double beta decaywhere it was found that the cross section for the processe−e− → WW is smaller than 2.5× 10−7 fb for √s = 100GeV and is thus quite negligible compared to the vectorbilepton exchange. Bounds on contributions in Figure3b) are found in [19] to be of a similar order, either be-cause of a small light neutrino mass or a small mixingwith the heavy Majorana neutrino masses. On the otherhand, using fine tuning, very light right-handed neutri-nos, or contributions from extra doubly charged scalarstates, it is possible [19] to make the cross sections some-what larger (typically 10−6− 10−5 fb), but these are stillmuch smaller than the bilepton signal. Also, we note thata cut would have to be applied for back-to-back muonsin the final state, and therefore the signal to backgroundratio would be even higher.In any case, non-back-to-back µ−µ− in the final stateare more likely to be from e−e− → Y −− → τ−τ− →µ−µ− + neutrinos, which has the same cross-section asin Eq.(4), giving another positive signal for the Y −−.A diagram not discussed in previous papers that con-tributes to the e−e− scattering and involves a pair ofback-to-back scattered muons in the final states is shownin Figure 4. This process is not related directly to theneutrinoless double beta decay data. However, it isbound to be still smaller than the processes in Figure3, because of the small neutrino masses. We estimateTFig.4 ∼116π2|Vei|2|Vµj |2mνimνjM4W(5)where Vli are the Kobayashi-Maskawa like mixing anglesin the lepton sector. Even if we take typical neutrinoeeWWµννννµa)eeWWµµννννb)FIG. 3. Contributions from non-zero neutrino mass tobackground of e−e− → µ−µ−.eeWWµννµννFIG. 4. Another contribution to background ofe−e− → µ−µ−.masses to be ∼ 1eV this process is completely negligible(down by over ten orders of magnitude) compared to thebilepton diagram (with mY in the TeV region) which hasT ∼ VeiV ∗µj/m2Y .IV. DISCUSSIONIn this letter we have shown that the next generationof linear colliders, when run in the same charge mode,are especially suitable for search of doubly charged gaugebosons, that naturally appear in theories where SU(2)L iscompletely embedded in a new SU(3)L gauge group. Ofspecial interest is the process e−e− → µ−µ− which hasno background in the standard model. Even if neutrinomasses are taken to be non-zero, with the current limits,the background to the bilepton exchange is completelynegligible for√s ≤ 1 TeV. This, in our opinion, strongly3motivates renewed interest in running the future collidersfirst as e−e− or µ−µ− machines.One aspect of the NLC, not usually mentioned in aphysics paper but relevant to the real world and to ourdiscussion, is its cost and the concomitant likelihood ofbeing funded and constructed. For simplicity take thecost of an NLC to be linear in energy and assume it as onepenny per eV. This estimate is very approximate, but, inany case, the minimization of E will clearly minimize thestart-up cost of a machine which could then be extendedto achieve higher E. The cost of running e−e− is perhapsslightly less than for e+e−, but both are needed for theirphysics interests. The e+e− mode at√s = 100 GeVprovides useful machine physics and exploration of theZ pole at a higher luminosity than that of LEP (5 ×1031/cm2s).Finally, we comment on the current experimental lim-its on the bilepton mass. One of the strongest limitscomes from the fermion pair production and lepton-flavorviolating charged lepton decays [20] and is about 750GeV. We see from Figure 2, that even for√s = 100 GeVwe get huge signals for masses above the current limitand up to 1 TeV and well beyond. On the other hand aneven stronger limit is claimed to come from the muonium-antimuonium conversion [13] which currently set the limitat about 850 GeV for the SU(15) like coupling. Since thediagram contributing to that process is exactly the sameas the one contributing to the e−e− → µ−µ− scatter-ing, one would at first sight think that the same limitapplies, and so for a 331 coupling (which is larger thanthe SU(15)) the above limit would translate to an evenstronger bound. However, there are several reasons whythe bound from the muonium-antimuonium conversiondoes not have to apply in the same way. First, it wasnoted by Pleitez [14] that the limit of 850 GeV may bemuch less severe if there are additional diagrams with, forexample, scalars contributing to the same process, thatmay cancel each other. In fact such extra scalars do ap-pear in the minimal 331 model [1]. Second, the muonium-antimuonium conversion happens at energies which aremuch smaller than mY , typically less than 1 GeV. Then,however, for the e−e− → µ−µ− process which is happen-ing at much higher energies (and with a nonnegligiblecenter of energy s) the cancellation of diagrams may dis-appear and the process will be enhanced relatively to themuonium- antimuonium conversion.Nevertheless, as we have shown, even for gauge bilep-ton masses in the TeV region, the signatures in e−e− →µ−µ− scattering would be significant at attainable de-sign luminosities. In our opinion this warrants a seriousexamination of the possibility of including this mode inthe designs of the future generation of linear colliders. Itwould provide a potentially very exciting experiment inthe early stages of operation of such machines.AcknowledgmentsWe thank David Burke for answering experimentalqueries and Ryan Rohm for a very useful discussion. Thiswork was supported in part by the US Department of En-ergy under the Grant No. DE-FG02-97ER-41036.[1] P.H. Frampton, Phys. Rev. Lett. 69, 2889 (1992).[2] F. Pisano and V. Pleitez, Phys. Rev. D46, 410 (1992).[3] P.H. Frampton and S.L. Glashow, Phys. Lett. B190, 157(1987); Phys. Rev. Lett. 58, 2168 (1987).[4] P.H. Frampton and T.W. Kephart, Phys. Rev. Lett. 50,1343 (1983); ibid, 50, 1347 (1983).[5] See for example Proceedings to the 1st and 2nd Work-shops (3rd to be published) on Electron-Electron Inter-actions on TeV Energies, ed. C.A. Heusch, Int. J. Mod.Phys. A11, 1523 (1996); ibid A13, 2217 (1998); See alsohttp://www.hep.psi.ch/e-e-.html[6] J. Pati and A. Salam, Phys. Rev. D10, 275 (1974); R.Mohapatra and J. Pati, Phys. Rev. D11, 2558 (1975);G. Senjanović and R. Mohapatra, Phys. Rev. D12, 1502(1975); G. Senjanović, Nucl. Phys. B153, 334 (1979).[7] C.S. Aulakh, A. Melfo and G. Senjanović, Phys. Rev.D57, 4174 (1998), hep-ph/9707256.[8] See also Z. Chacko and R.N. Mohapatra, Phys. Rev.D58, 015001 (1998), hep-ph/9712359; C.S. Aulakh,A. Melfo, A. Rašin and G. Senjanović, Phys. Rev.D58, 115007 (1998), hep-ph/9712551; For a modelwith low MR scale and broken R-parity see K. Huituand J. Maalampi, Phys. Lett. B344, 217 (1995), hep-ph/9410342;[9] C.S. Aulakh, B. Bajc, A. Melfo, A. Rašin and G. Sen-janović, Phys. Lett. B460, 325 (1999), hep-ph/9904352.[10] See, for example, J.F. Gunion, Int. J. Mod. Phys. A13,2277 (1998), hep-ph/9803222; K. Huitu it et al, hep-ph/9912405.[11] P.H. Frampton and D. Ng, Phys. Rev. D45, 4240 (1992).[12] P.H. Frampton, Mod. Phys. Lett. A7, 2017 (1992).[13] L. Willmann et al., Phys. Rev. Lett. 82, 49 (1999); B. Niet al., Phys. Rev. D48, 1976 (1993).[14] V. Pleitez, hep-ph/9905406.[15] P. Das and P. Jain, hep-ph/9903432.[16] P.H.Frampton and B.-H. Lee, Phys. Rev. Lett. 64, 619(1990).[17] See also F. Cuypers and M. Raidal, Nucl. Phys. B501,3 (1997), hep-ph/9704224. F. Cuypers and S. Davidson,Eur. Phys. J. C2, 503 (1998), hep-ph/9609487.[18] W.C. Barber et al, Phys. Rev. D3, 2796 (1971).[19] G. Belanger et al, Phys. Rev. D53, 6292 (1996), hep-ph/9508317. For various ways of somewhat relaxing theselimits see P. Duka, J. Gluza and M. Zra lek, Phys. Rev.D58, 053009 (1998), hep-ph/9804372. Also for an earlierattempt see C.A. Heusch and P. Minkowski, Nucl. Phys.B416, 3 (1994).[20] M.B. Tully and G.C. Joshi, Phys. Lett. B466, 333(1999), hep-ph/9905552.4

Seeking Gauge Bileptons in Linear Colliders

Seeking Gauge Bileptons in Linear Colliders

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