Lepton flavor violation induced by neutral and doublycharged scalars at future lepton colliders
Abstract
New physics scenarios beyond the Standard Model (SM) for neutrino mass mechanism often necessitate the existence of a neutral scalar and/or doublycharged scalar , which couple to the SM charged leptons in a flavor violating way, while evading all existing constraints. Such scalars could be effectively produced at future lepton colliders like CEPC, ILC, FCCee and CLIC, either onshell or offshell, and induce striking charged lepton flavor violating (LFV) signals. We find that a large parameter space of the scalar masses and the LFV couplings can be probed at lepton colliders, well beyond the current lowenergy constraints in the lepton sector. The neutral scalar explanation of the muon anomaly could also be directly tested.
I Introduction
There are various theoretical models of new physics which lead to charged lepton flavor violation (cLFV) effects at an observable level, which is strongly implied by the observation of flavor violation in the neutral lepton sector, i.e. the solar, atmospheric and reactor neutrino oscillations PDG (). In the minimal extension of Standard Model (SM) with Dirac neutrinos, cLFV rates are highly suppressed due to the tiny neutrino masses. This makes the experimental searches for cLFV all the more interesting, because any observable effect must come from physics beyond the minimally extended SM related to the origin of neutrino mass. LFV often arises from the extension of the Higgs sector, which allows flavorviolating Yukawa couplings of new neutral and/or doublycharged scalars beyond the SM. In this report, we summarize the main results of modelindependent LFV prospects at future lepton colliders, such as the Circular ElectronPositron Collider (CEPC) CEPCSPPCStudyGroup:2015csa (), International Linear Collider (ILC) Baer:2013cma (), Future Circular Collider (FCCee) GomezCeballos:2013zzn () and Compact Linear Collider (CLIC) Battaglia:2004mw (), based on our recent papers Dev:2017ftk (); Dev:2018upe (). This complements previous studies of LFV at lepton colliders that are performed in the framework of effective fourfermion couplings Kabachenko:1997aw (); Cho:2016zqo (); Ferreira:2006dg (); Aranda:2009kz (); Murakami:2014tna () or in the context of flavorviolating SM Higgs decays Banerjee:2016foh (); Chakraborty:2016gff (); Chakraborty:2017tyb (); Qin:2017aju () and tau decays Hays:2017ekz () or with doublycharged scalars Rodejohann:2010bv (); Nomura:2017abh (). Compared to the hadron colliders, the lepton colliders are generally very “clean” and the SM processes therein are well understood, which render them primary facilities to search for new physics via the LFV signals.
If any of the new neutral scalars is hadrophobic (i.e. couples dominantly to leptons), it could remain sufficiently light and contribute sizably to cLFV with the Yukawa couplings ( being the lepton flavor indices), while easily evading the direct searches at hadron colliders, as well as the lowenergy quark flavor constraints, such as the rare flavorchanging decays and oscillations of and mesons. Some wellmotivated examples include supersymmetric models with leptonic parity violation susy (); susy2 (); susy3 (); susy4 (), leftright symmetric models Dev:2016dja (); Dev:2016vle (); Dev:2017dui (); Maiezza:2016ybz (), twoloop models for neutrino masses babu (), mirror models mirror (); mirror2 (); mirror3 (); mirror4 (); mirror5 (), and twoHiggs doublet models 2HDM (); 2HDM2 (), where the cLFV coupling might arise at tree and/or loop level.
The doublycharged scalar and its LFV Yukawa couplings might be closely related to neutrino mass generation, e.g. in the typeII seesaw type2a (); type2b (); type2c (); type2d (); type2e () and its leftright extension LR (); Mohapatra:1974gc (); Senjanovic:1975rk (). The magnitudes of might be sizable and hence accessible at lepton colliders. There are of course constraints on some of these couplings from rare lepton decays like and , but they leave enough room for some of them being of order one. Furthermore, rare lepton decays generally probe products of two different couplings whereas the lepton collider probes them individually Dev:2017ftk (); Dev:2018upe (). We show the interesting ranges of effective Yukawa couplings and that can be measured in the planned lepton colliders such as CEPC and ILC and can provide new ways to test the underlying extended Higgs models. They will in any case provide complementary information to rare lepton decay constraints on the and couplings, which makes such studies interesting from the synergistic viewpoint of energy and intensity frontiers.
This paper is organized as follows: Section II is devoted to the beyond SM neutral scalar , where we consider the LFV from both the onshell and offshell production of at lepton colliders. As two benchmark setups for the future lepton colliders, we show the corresponding prospects at CEPC 240 GeV and ILC 1 TeV, with total integrated luminosity of 5 ab and 1 ab, respectively. In Section III, we focus on the single, pair and offshell production of doublycharged scalar at lepton colliders through the Yukawa couplings and the resultant LFV prospects at ILC and CEPC. We conclude in Section IV. More details can be found in Refs. Dev:2017ftk (); Dev:2018upe ().
Ii LFV induced by new neutral scalar
Without loss of generality, we can write the effective Yukawa couplings of the neutral scalar to the charged leptons as
(1) 
Here for simplicity we assume the couplings are all real and chiralityindependent and thus symmetric. The scalar may or may not be responsible for symmetry breaking and/or mass generation of other particles in realistic models, where it could be part of a singlet, doublet or triplet scalar field. We assume further that is CPeven and its mixing with and coupling to the SM Higgs is small. If the scalar is CPodd, the limits and prospects derived here would not change significantly. Even though there are all varieties of stringent lowenergy cLFV constraints, such as , only a few of them are directly relevant to the LFV prospects discussed below. With an ab level of integrated luminosity at future lepton colliders, a large parameter space of the scalar mass and could be probed, well beyond the current cLFV constraints, and complementary to the projected lowenergy constraints from future experiments at the intensity frontier Calibbi:2017uvl (). In addition, the Lagrangian in Eq. (1) also gives rise to a oneloop contribution to the lepton anomalous magnetic moment. In particular, the scalar field coupling whose induced loop graph helps resolve the longstanding muon discrepancy can be directly tested at lepton colliders.
ii.1 Onshell LFV
If kinematically allowed, the neutral scalar can be directly produced at lepton colliders, in association with a pair of flavorchanging leptons through the couplings in Eq. (1), i.e.
(2) 
mediated by the SM photon or boson,^{2}^{2}2We have also the production channel Dev:2018upe (). However, this process involves only the flavorconserving coupling , and we will not consider it here. and
(3) 
mediated by the SM boson. In future lepton colliders, high luminosity photon beams can also be obtained by Compton backscattering of lowenergy, highintensity laser beam off the highenergy electron beam Ginzburg:1981vm (); Ginzburg:1982yr (); Telnov:1989sd (), and the neutral scalar can also be produced through the processes
(4) 
Let us first consider the coupling , switching off all other (LFV) couplings. It should be emphasized that all the production amplitudes in Eqs. (2) to (4) depend only on the LFV couplings (here ), and thus could be easily made to satisfy the rare lepton decay constraints, such as those from and , which depend on the product . With vanishing or suppressed couplings to the quark sector, the conversion limits are irrelevant. Furthermore, for real Yukawa couplings, we do not either have any limits from electric dipole moment. Only the following constraints are relevant:

Muoniumantimuonium oscillation: This could occur in both and channels, with the oscillation probability , and is constrained by the MACS experiment Willmann:1998gd ().

: The anomalous magnetic moment of electron receives a contribution from the loop, which is strongly constrained from oneelectron quantum cyclotron experiments Hanneke:2008tm ().

: A channel could mediate the scattering , which interferes with the SM diagrams in the channel and is constrained from LEP data Abdallah:2005ph ().
All these constraints on and are shown as the shaded regions in the upper two panels of Fig. 1 (which correspond to two benchmark configurations of future lepton colliders). To explain the longstanding theoretical and experimental discrepancy of the muon , i.e. PDG (), the LFV coupling is required to be larger, as shown by the green band in the upper panels of Fig. 1, which is already excluded by the electron and muonium oscillation constraints.
As for the future lepton collider sensitivity, we specifically consider two benchmark configurations, namely, the CEPC 240 GeV with an integrated luminosity of 5 ab and ILC 1 TeV with a luminosity of 1 ab. The SM background is dominated by particle misidentification, e.g. electron misidentified as muon or vice versa, and is very small (see e.g. Refs. bkg1 (); bkg2 (); bkg3 ()). After being produced, could decay back into the charged lepton pairs or other SM particles. To be concrete, we consider the most optimistic case, i.e. the neutral scalar decays predominantly into a pair of leptons, i.e. (here decays only into pair). We apply nominal cuts GeV, and using CalcHEP Belyaev:2012qa (). The corresponding prospects of and in the channels of Eqs. (2) to (4) at CEPC and ILC are shown respectively in the upper left and upper right panels of Fig. 1, where we have assumed a minimum of 10 signal events at both colliders. It is clear from Fig. 1 that a large region of and can be probed in future lepton colliders, which significantly extends the current limits. Reconstructing the peak from the decay products could further improve the significance of the LFV signals, which however will be rather modeldependent.
Turning now to the coupling , the most stringent limits come from the electron Hanneke:2008tm (), and the LEP data Abdallah:2005ph (). The reconstruction of lepton is more challenging than ,^{3}^{3}3Following Ref. Baer:2013cma (), we have adopted an efficiency factor of for the tau lepton reconstruction. but there is still ample parameter space to probe at both CEPC and ILC, as shown in the middle panels of Fig. 1, where we have assumed is the predominant decay mode.
Regarding the coupling , there are currently no experimental limits, except for the muon discrepancy PDG (). This could be explained in presence of when it couples to muon and tau, as shown by the brown line (for the central value) and the green and yellow bands for the and confidence level (CL), respectively, in the lower panels of Fig. 1, while the shaded region is excluded by the current muon data at the 5 CL. It is clear in Fig. 1 that the anomaly can be directly tested at CEPC (ILC) up to a scalar mass of GeV, in particular in the channel. With a larger luminosity being planned GomezCeballos:2013zzn () at FCCee and a higher energy at CLIC, these prospects could be even better.
ii.2 Offshell LFV
The LFV signals could also be produced from an offshell , i.e. . This could occur in both and channels, whereas in the channel, is onshell if the colliding energy , which corresponds to the resonant production with the subsequent decay of . Different from the onshell case, the offshell production amplitudes have a quadratic dependence on the Yukawa couplings (some of them might be flavor conserving), and thus largely complementary to the onshell LFV searches.
The amplitude is proportional to . This is tightly constrained by the data PDG (), leaving no hope to see any collider LFV signal in this channel. In the tau sector, the LFV decay constraints are comparatively weaker. The limits on from and are almost constants, as in effective field theories with superheavy mediators. As for the onshell case above, the coupling are constrained by electron and the LEP data Abdallah:2005ph (). All the constraints are presented in the top panel of Fig. 2, with the shaded regions excluded. Note that the muon can not be used to set unambiguous limits on the combinations and , although the couplings and could contribute to by themselves.
The dominant SM background is from the process , which is expected to be small, if we require the two charged leptons to be backtoback and their reconstructed energy . Assuming 10 signal events as above, the prospects of the coupling are shown in the left panel of Fig. 2. At the resonance , the production cross section can be greatly enhanced by . To be specific, we have set the width (30) GeV at GeV (1 TeV). For , the production rate diminishes rapidly as becomes heavier. An offshell could however be probed up to a fewTeV range, as shown in Fig. 2, and ILC is expected to be more promising than CEPC in this mass range, as a result of higher .
The process could proceed via both and channels, which depend on different couplings, namely and , and are constrained respectively by the rare decays and . Analogous to the case above, a broad range of and could be probed in the channel, especially in vicinity of the resonance, as shown by the bottom left panel of Fig. 2. In the channel, the cross sections are comparatively smaller, and the detectable regions are much narrower, as shown by the bottom right panel of Fig. 2. One can see that orders of magnitude of the couplings can be probed in the offshell channels at future lepton colliders, i.e. with couplings from up to for a mass range from 100 GeV to few TeV.
Iii LFV induced by doublycharged scalar
In addition to the neutral scalar case, LFV could also be induced by the presence of a doublycharged scalar, with the modelindependent Yukawa couplings
(5) 
with , the flavor indices and superscript denoting charge conjugate. The doublycharged scalar can be either lefthanded or righthanded, i.e. coupling either to the lefthanded or righthanded charged leptons. We take the doublycharged scalar in Eq. (5) to be righthanded, unless otherwise specified. The main results in this section hold also for lefthanded .
At highenergy colliders, the “smokinggun” signal of are samesign charged lepton pairs from the decay , mediated by the interaction in Eq. (5). The current dilepton limits at the Large Hadron Collider (LHC) exclude the righthanded (lefthanded) with mass up to roughly 650 GeV (800 GeV) ATLAS:2017iqw (); CMS:2017pet (), depending on the specific lepton flavors. The final states involving only the and flavors are the most stringent ATLAS:2017iqw () and those with the flavor are much weaker CMS:2017pet (), as a result of the poor reconstruction efficiency of the lepton at hadron colliders.
There are also direct searches of doublycharged scalars at LEP in the single Abbiendi:2003pr () and pair Achard:2003mv () production modes. However, limited by the centerofmass energy, these constraints are very weak. An offshell in the channel could mediate the Bhabha scattering and interfere with the SM diagrams. This alters both the total cross section and the differential distributions Abbiendi:2003pr (); Achard:2003mv (). By Fierz transformation, the doublycharged scalar contributes to the effective fourfermion contact interaction
(6) 
where corresponds to the effective cutoff scale related to the doublycharged scalar mass and the Yukawa couplings, and is constrained by the (with ) data Abdallah:2005ph (). It turns out that the cutoff scale has been excluded up to 7.6 TeV by the LEP data.
For , the effective interaction in Eq. (6) would also induce an additional contribution to the Møller scattering and can be constrained by the upcoming MOLLER experiment Benesch:2014bas (), which could probe the effective scale TeV, slightly stronger than the current limit from LEP data Dev:2018sel (). Other lowenergy LFV constraints on the couplings include the rare decays of charged leptons like and , the anomalous magnetic moments of electron and muon, the LEP data (with ) Abdallah:2005ph (), and muoniumantimuonium oscillation, which are all highly suppressed in the SM. The calculation details can be found in Ref. Dev:2018upe () and references therein.
The doublycharged scalar can be pairproduced at lepton colliders through the DrellYan process via the gauge interactions with the SM photon and boson. DrellYan production is, however, not a useful probe of the Yukawa interactions unless is longlived, because for DrellYan pair production of , both larger and smaller Yukawa couplings give rise to the same lineshape over the background, and thus, we can not determine the absolute values of from the flavordependent branching fractions , as long as the leptonic decays dominate. Only when the Yukawa couplings enter the production of , could we measure these couplings in the (LFV) processes. All the relevant production processes can be categorized into two groups: i) the onshell production including both the pair and single production modes and ii) the offshell production of .
iii.1 Onshell LFV
Besides the DrellYan process,^{4}^{4}4The doublycharged scalar can also be pairproduced from the fusion of laser photons , induced by both the trilinear and quartic gaugescalar interactions Chakrabarti:1998qy (). the doublycharged scalar can be pairproduced at lepton colliders through the Yukawa interactions to the SM charged fermions Kuze:2002vb (),
(7) 
with covering all three flavors , and . Given the Yukawa couplings to the SM charged fermions, the doublycharged scalar can be singly produced from Barenboim:1996pt (); Kuze:2002vb (); Lusignoli:1989tr (); Yue:2007kv (); Dev:2018upe ()
(8) 
and Barenboim:1996pt (); Godfrey:2001xb (); Godfrey:2002wp (); Rizzo:1981xx (); Yue:2007ym ()
(9) 
with the laser photon beam as in the neutral scalar case. With the same cuts as in Section II, we have estimated the prospects of all the LFV couplings at ILC 1 TeV with the integrated luminosity of 1 ab, as functions the doublycharged mass , in all the pair and single production modes in Eqs. (7) to (9), which are collected in Fig. 3. For simplicity, we have assumed that decays predominately back to the samesign charged leptons, and the electron and positron beams are both unpolarized. There is a lower cut of 500 GeV on the single production mode in the and single production processes, as below GeV, the processes are dominated by the pair production with from the decay of an onshell . The limits on the LFV couplings are mainly from the LEP data, as a channel could mediate the processes with the LFV couplings , which exclude the shaded pink regions in Fig. 3. The limits from electron and muon are highly suppressed by the charged lepton masses and are not shown in these plots. One should note that the contributions from doublycharged scalar loops to the magnetic dipole moment are always negative Lindner:2016bgg (), so the muon anomaly can not be explained by the doublycharged scalar . The vertical dashed gray lines indicate the current samesign dilepton limits on the doublycharged scalar mass from LHC ATLAS:2017iqw (); CMS:2017pet (), assuming the dilepton branching of . More details can be found in Ref. Dev:2018upe (). For a smaller dilepton branching ratio, the LHC limits on doublycharged scalar mass will be weaker Dev:2018kpa ().
iii.2 Offshell LFV
With a channel doublycharged scalar , we can have the offshell LFV processes Godfrey:2001xb (); Godfrey:2002wp (); Rizzo:1981xx (); Dev:2018upe ()
(10) 
which depend quadratically on the couplings . As in the neutral scalar case, the limit from is so stringent that it has precluded the doublycharged scalarmediated signal at future lepton colliders. The processes () and () involve the lepton and depend on the coupling (), and their prospects at CEPC 240 GeV and ILC 1 TeV are shown in the left (right) panel of Fig. 4. Suppressed by the threebody phase space, the sensitivities in the processes are comparatively weaker than those from processes. The most important constraints on the couplings and are from the LFV decays , , and the LEP data Abdallah:2005ph (), and these are depicted as the shaded regions in Fig. 4 Dev:2018upe (). It is also possible to probe the LFV couplings
(11) 
in the process, however, as a result of the small production cross section, the probable parameter space is very limited for these couplings at both CEPC and ILC.
One can see in Figs. 3 and 4 that in both onshell and offshell production modes of the doublycharged scalar , a large parameter space of the mass and the LFV couplings can be probed at ILC 1 TeV (and CEPC 240 GeV). With a luminosity of order of ab, the couplings can be probed up to the order of in the onshell mode, and the effective cutoff scale could go up to few 10 TeV in the offshell processes.
Iv Conclusion
We have shown that a neutral scalar and doublycharged scalar , which are both wellmotivated in a large class of new physics scenarios, can be probed at future lepton colliders via their LFV couplings to the SM charged lepton sector. We present a modelindependent analysis of how far the LFV coupling strengths and the scalar masses can be probed beyond the existing limits from the lowenergy sector. In particular, we find that the full mass and coupling range of the neutral scalar, that can explain the muon anomaly, can be tested in the future lepton colliders. This is largely complementary to the searches of LFV in the lowenergy experiments and at hadron colliders.
Acknowledgments
Y.Z. would like to thank the Center for High Energy Physics, Peking University for generous hospitality where the paper was finished. The work of B.D. and Y.Z. is supported by the US Department of Energy under Grant No. DESC0017987. The work of R.N.M was supported by the US National Science Foundation Grant No. PHY1620074.
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