High-energy colliders as a probe of neutrino properties

The mediators of neutrino mass generation can provide a probe of neutrino properties at the next round of high-energy hadron (FCC-hh) and lepton colliders (FCC-ee/ILC/CEPC/CLIC). We show how the decays of the Higgs triplet scalars mediating the simplest seesaw mechanism can shed light on the neutrino mass scale and mass-ordering, as well as the atmospheric octant. Four-lepton signatures at the high-energy frontier may provide the discovery-site for charged lepton flavour non-conservation in nature, rather than low-energy intensity frontier experiments.


I. INTRODUCTION
Solar and atmospheric neutrino studies provided the discovery site for neutrino oscillations [1,2]. These experiments were followed by reactor [3] and acceleratorbased [4] studies that have confirmed the oscillation phenomenon and also substantially improved parameter determination. The discovery of neutrino oscillations has brought neutrino physics to the center of particle physics, giving the first clear evidence for new physics. Their existence also suggests the possibility of charged lepton flavour violating effects including rare processes, such as µ → eγ decays [5].
Although current neutrino data are well-described by the three-neutrino paradigm, there are still loose ends to sort out, such as the neutrino mass-ordering, the atmospheric octant and the precise value of the CP phase [6,7]. Back in the LEP days it was suggested that the mediators of neutrino mass generation could be produced at collider experiments [8] in such a way that * smandal@kias.re.kr † omr@fis.cinvestav.mx ‡ gsanchez@fis.cinvestav.mx § valle@ific.uv.es ¶ xuxj@ihep.ac.cn high-energy studies could be used to probe neutrino oscillation parameters, such as the atmospheric angle. This is a characteristic feature, e.g., of models where supersymmetry is the origin of neutrino mass [9][10][11][12], which allow for such independent probes of neutrino mixing [13][14][15].
In this letter we propose the use of high-energy frontier hadron (FCC-hh [16]) and lepton colliders (FCCee [17]/ILC [18]/ CLIC [19], CEPC [20]), as an inde- so that only one complex symmetric Yukawa matrix Y ∆αβ describes the full flavour structure of the lepton sector [21,22] through the Yukawa Lagrangian term where L α are the lepton doublets, C is the charge conjugation operator. The scalar potential V (Φ, ∆) is given as, where Φ is the SM Higgs doublet. Its minimization generates a non-zero vacuum expectation value (VEV) for the neutral component of the triplet. Within the simplest ap- where v Φ is the SM Higgs VEV. Eq. (4) shows how the smallness of v ∆ requires either by a small µ, or a large value forM ∆ characterizing the triplet scalar mass [23].
Note that in a more complete setup the parameter µ can be given a full dynamical interpretation [22,24]. Following t'Hooft's naturalness argument, the small µ parameter sources lepton number violation, so that in the limit µ → 0, lepton number symmetry is recovered. After electroweak symmetry breaking one obtains small neutrino For the simplest CP-conserving case the neutrino oscillation parameters will be determined by six elements of the real symmetric Yukawa matrix Y ∆αβ . Four of these are well measured [6,7], the remaining ones being the absolute neutrino mass and the atmospheric octant.
There are seven physical Higgs fields with definite masses namely, a doubly-charged (H ±± ) and a singlycharged (H ± ) scalar boson, plus two massive CPeven (h, H) and one massive CP-odd Higgs (A). The new scalars present in such simplest seesaw scheme may hold the key to electroweak vacuum stability and perturbative unitarity [24,25]. The associated theoretical consistency restrictions, as well as the constraints from electroweak precision data and other experiments are discussed extensively in [23].
A key feature of the simplest seesaw mechanism is the presence of a doubly charged Higgs scalar H ±± which can be produced via the Drell-Yan process Once produced, the neutrino mass mediator H ±± can decay to two same-sign charged leptons (l ± l ± ). The H ±± decay branching ratio to charged leptons depends on the  The decay widths are given by where U is the lepton mixing matrix measured in oscillation experiments. The patterns of various leptonic channels will follow the profile of Y ij ∆ . Current measurements of neutrino oscillation parameters [6,7] restrict the diagonal and off-diagonal entries of the Yukawa coupling matrix  This provides a way to probe the neutrino mass-ordering through the four-lepton final states coming from doublycharged Higgs H ±± H ∓∓ pair-production.

IV. LEPTON FLAVOUR VIOLATION
The oscillation discovery has brought neutrino physics to the center of particle physics, giving the first clear evidence for new physics namely, lepton flavour nonconservation in neutrino propagation. This suggests also the possibility of charged lepton flavour violating effects including rare decays such as µ → eγ, so far never observed [5]. It is straightforward to determine the corresponding expressions for the µ → eγ branching ratio [37,38]: In Fig. 5 we display some BR(µ → eγ) contours in the m H ±± −v ∆ plane, obtained for normal ordered light neu- trino spectrum and best-fit values for the neutrino oscillation parameters. One sees that the µ → eγ branching ratio can easily exceed current senstivities [5] for small values of the triplet VEV v ∆ .
The idea that charged lepton flavour (and CP) violation could be first seen at high energies was first put forward in [39,40] and revived in [41]. Here we demostrate that the type II seesaw provides the simplest realization of this idea.
. We again sees that the flavour-violating four-lepton final state cross-section can be sizeable even for tiny values of BR(τ → µγ).
Notice that in Fig. 4 we have scanned over the full 3σ range of the oscillation parameters and found that the cross sections distinguish the mass orderings for most neutrino mass values. Likewise, in Fig. 6 the predicted ranges differ, except for tiny cLFV branching fractions. and BR(τ → µγ). Red bands correspond to IO, while blue denote NO. The lightest neutrino mass is taken to be zero.

The gray bands are excluded by the MEG [5] (top panel) and
BaBar limits [42] (bottom panel).

V. SUMMARY AND OUTLOOK
In the simplest seesaw mechanism one can probe neutrino oscillation physics at collider energies through the pattern of triplet Higgs boson decays. These can probe not only the lightest neutrino mass and the ordering of the neutrino masses, but also the flavour structure of the neutrino sector, paving the way to the reconstruction of neutrino oscillation parameters at collider experiments.
For example, Fig. 3 illustrates how the decay pattern of the triplet Higgs that mediates neutrino mass generation may probe the octant of the atmospheric mixing angle. This can be tested at a high energy hadron colliders such as the FCC, as well as future e + e − colliders such as ILC, CLIC or CEPC in China.
Likewise, Fig. 4 shows how the rates for fourlepton final-state events coming from pair-producing the doubly-charged Higgs may be used as a probe of the light neutrino mass ordering, illustrating how high-energy signatures clearly complement neutrino oscillation studies.
Last, but not least, Fig. 6 clearly suggests that charged lepton flavour violation could be observed first as a high-energy phenomenon, since the corresponding signal cross section can be sizeable even when low-energy rare processes, such as µ → eγ, have negligible rates.
In short, high-energy probes clearly complement lowenergy searches for charged lepton flavour violation at high-intensity facilities.
The results found here illustrate the complementarity and interplay of the high-energy and high-intensity frontiers in particle physics, providing encouragement for dedicated simulation studies to evaluate the potential of these proposed facilities in probing the neutrino sector.