Synergy and complementarity between neutrino physics and low-energy intensity frontiers
aa r X i v : . [ h e p - ph ] D ec Synergy and complementarity between neutrinophysics and low-energy intensity frontiers
Ana M. Teixeira ∗ Laboratoire de Physique de Clermont, CNRS/IN2P3 – UMR 6533,Campus des Cézeaux, 4 Av. Blaise Pascal, F-63178 Aubière Cedex, FranceE-mail: [email protected]
Massive neutrinos and leptonic mixings have provided the first evidence of flavour violation in thelepton sector, opening a unique gateway to many new phenomena. Among the latter, one findsprocesses violating lepton number, charged lepton flavours, or even the universality of leptonflavours. These very rare transitions can be studied in high-intensity facilities, and if observed,constitute a clear sign of New Physics. After a brief review of the experimental status of dedi-cated searches, we comment on the prospects of several well-motivated models of neutrino massgeneration to several of the above mentioned observables, also discussing how the interplay ofhigh-intensity observables and neutrino data can shed light on the underlying New Physics model.
The 19th International Workshop on Neutrinos from Accelerators-NUFACT201725-30 September, 2017Uppsala University, Uppsala, Sweden ∗ Speaker. c (cid:13) Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/ eutrino physics and the low-energy intensity frontiers
Ana M. Teixeira
1. Introduction
Neutrino oscillations provided the first confirmation that the Standard Model (SM) should beextended; eversince, the quest for the new physics (NP) model accounting for neutrino masses andmixings has become one of the most active quests in particle physics. There is a vast array of well-motivated SM extensions, relying on additional fields, extended gauge groups, or even completeNP frameworks - all capable of successfully accommodating neutrino oscillation data. Fortunately,massive neutrinos and leptonic mixings offer a true gateway to many experimental signals that areeither forbidden or extremely suppressed in the SM; these include charged lepton flavour violation(cLFV), lepton number violation (LNV), contributions to lepton dipole moments, among manyothers. The interplay of oscillation data with the results of the searches for these rare processes,which are being actively looked for at numerous high-intensity facilities, may then allow to shedlight on, and hopefully identify, the underlying model of neutrino masses and mixings.In the original formulation of the SM, neutrinos are strictly massless and lepton number(s) areconserved; leptonic electric dipole moments (EDMs) are generated at 4-loop level, and their valueis tiny ( d CKM e ≤ − e cm). Minimal SM extensions in which Dirac ν masses are put by hand, andthe leptonic mixing matrix U PMNS accounts for ν oscillation data, still preserve total lepton number;cLFV transitions can theoretically occur, but the smallness of neutrino masses strongly suppressesthe branching fractions, rendering them unobservable. Likewise, and despite being generated at the2-loop level, EDMs still remain beyond experimental sensitivity.Reviews of the experimental status of numerous (rare) leptonic processes were conducted inthe dedicated NUFACT2017 sessions, as well as in plenary presentations [1]; a full summary ofcurrent bounds, including electric and magnetic (anomalous) lepton moments can be found in [2].A detailed discussion of the model-independent approach to constrain NP models based onthe searches for the above mentioned observables has been done in [3]; in what follows, we focusthe discussion on specific NP realisations - from simple, minimal SM extensions, to completeframeworks.
2. SM extensions via sterile neutrinos
Sterile fermions are an integral part of several well-motivated mechanisms of neutrino massgeneration; before addressing the contributions of the latter constructions to different high-intensityobservables (and discuss how the interplay of distinct signals can favour or exclude them), a firstphenomenological - and convenient - approach consists in considering simple “toy models”, inwhich the SM is extended by a single massive sterile state (possibly encoding the effects of a largernumber of sterile states).
Without any assumption on the mechanism of neutrino mass generation, this simple construc-tion relies in extending the SM content via one massive heavy sterile state; the interaction andphysical basis are related via a 4 × U (whose upper 3 × eutrino physics and the low-energy intensity frontiers Ana M. Teixeira handed leptonic mixings). The non-negligible active-sterile mixings are at the source of modifiedcharged and neutral lepton currents, and hence of new contributions to many observables .For example, concerning EDMs, the new Majorana and Dirac phases induce non-vanishingcontributions; in the presence of two non-degenerate sterile states (with masses between 100 GeVand 100 TeV), one can have | d e | / e ≥ − cm, within future ACME sensitivity [4], as displayedon the left panel of Fig. 1. Since the Majorana contribution is dominant, the interpretation of anEDM observation in such a minimal framework would suggest CP violating Majorana neutrinos,with potential implications for leptogenesis. ▲(cid:0)✁✂✄☎✆✄ ✝✞✆✆✟ ✝✶ ✥☎✠✡⑤☛ ❜❜⑤☞✌✍✎ ✾✏✑ ✒✓▲✓ ✔✕✕✖✗ ▲✘✙✘✚✛✜✲✹ ✛✜✲✸ ✛✜✲✷ ✛✜✲✢ ✛✛✜✲✹✛✜✲✸✛✜✲✷✛✜✲✢✛ ◆✣✤♠✦✧ ★♥ ✩✤✪✫✤✐✬✭ ✮ ★s★♥★✯✰ Figure 1:
On the left, contributions to | d e | / e as a function of the sterile neutrino masses; from [4]. On theright, effective Majorana mass m ββ as a function of the lightest (active) neutrino mass (normal ordering ofthe light ν spectrum); from [5]. Other than strongly impacting the prediction for 0 ν β decays (due to the augmented ranges forthe effective mass in both normal and inverted ordering schemes, a future observation can no longerbe straightforwardly associated with an inverted ordering [5], as visible on the right panel of Fig. 1),the sterile states can also be at the origin of LNV semileptonic tau and meson decays. If producedon-shell, sterile neutrinos can lead to a resonant enhancement of the LNV decay amplitudes, someprocesses already within experimental reach, as is the case of τ − → µ + π − π − , or K + → ℓ + α ℓ + β π − (see left panel of Fig. 2). A comprehensive study of such decays allows to infer bounds on allentries of a generalised definition of the effective Majorana mass matrix: with the exception ofthe m ττν entry (whose bounds . − GeV strongly improve existing ones), all other entries areconstrained to lie below . − GeV [6]. An example for m µµν is displayed on Fig. 2.Such a minimal construction also leads to important contributions to cLFV observables: inthe e − µ sector, neutrinoless conversion in Nuclei (e.g. Aluminium) is one of the most sensitiveobservables (although for heavier nuclei, the Coulomb-enhanced decay of a muonic atom mightbe also competitive [7], see Fig. 3). For sterile states heavier than the electroweak scale, three-body decays receive the dominant contributions from Z -penguins, leading to a strong correlationbetween the corresponding cLFV decays. In turn, this not only allows to probe µ − τ flavour In many of the subsequent numerical results, the additional physical parameters of the model were randomlysampled from the following intervals: m ∈ [ . − ] GeV, 0 . θ α . π (and likewise for the CP violating phases). eutrino physics and the low-energy intensity frontiers Ana M. Teixeira | U µ | m (GeV) -12 -10 -8 -6 -4 -2 -1 -10-9-8-7-6-5-4 SHIP FCC-eeOTHER BOUNDSBBN
DUN E MESON DECAYS N A Figure 2:
On the left, lines (surfaces) denoting the maximal (allowed) BR( τ − → µ + P − P − ) vs. the heavyneutrino mass, m . On the right, predictions for the effective mass, log m αβν , in the ( | U µ | , m ) plane, asderived from LNV B-meson decays. Coloured surfaces and grey points denote excluded regimes. From [6]. violation beyond the reach of Belle II, but also to explore this minimal SM extension at severalfrontiers [8], as displayed in Fig. 3. -25 -20 -15 -10 -5 -1 -25 -20 -15 -10 -5 B R ( µ - e - → e - e - , A l ) CR ( µ - e , A l ) m (GeV) CR( µ - e, Al)BR ( µ - e - → e - e - , Al) -25 -20 -15 -10 -5 -20 -18 -16 -14 -12 -10 -8 B R ( Z → µ τ ) BR( τ → µ µ µ ) Figure 3:
BR( µ − e − → e − e − , Al) (cyan, left axis) and CR( µ − e , Al) (dark blue, right axis) as a functionof m . Grey points correspond to the violation of at least one experimental bound; dashed horizontal linesdenote the future sensitivity of COMET; from [7]. On the right, BR( Z → τµ ) vs. BR( τ → µ ); blue (grey)points denote allowed (excluded) regimes, and yellow points are associated with 0 ν β decays within futuresensitivity; the upper (lower) horizontal line corresponds to the expected sensitivity for a Linear Collider(FCC-ee), while vertical lines denote current and future τ → µ sensitivities; from [8]. In its different realisations, the seesaw mechanism is perhaps one the most appealing mecha-nisms of neutrino mass generation. Whether or not a given seesaw realisation can be at the originof a high-intensity observable depends on the size of the Yukawa-like couplings, and most im-portantly, on the scale of the new (heavy) mediators. The low-scale seesaw (and its variants) is anexample of a type I seesaw, whose mediators have non-negligible mixings with the active neutrinos,and do not decouple. Not only can they give rise to contributions to numerous cLFV observables3 eutrino physics and the low-energy intensity frontiers
Ana M. Teixeira (within future sensitivity reach), but the high-intensity searches for the latter allow to explore andconstrain regions of the parameter space which would be otherwise inaccessible [9] (see left panelof Fig. 4). -25 -20 -15 -10 -5 -20 -18 -16 -14 -12 -10 -8 -6 B R ( Z → µ τ ) BR( τ → µ µ µ ) Figure 4:
On the left, maximal allowed cLFV rates compatible with current searches in a low-scale see-saw; horizontal full (dashed) lines denote present (future) experimental sensitivity; from [9]. On the right,BR( Z → τµ ) vs. BR( τ → µ ) in a (3,3) ISS realisation; coloured (grey) points denote allowed (excluded)regimes; the upper (lower) horizontal line corresponds to the expected sensitivity for a Linear Collider (FCC-ee), while vertical lines denote current and future τ → µ sensitivities; from [8]. Another phenomenologically and theoretically appealing low-scale model of neutrino massgeneration is the Inverse Seesaw (ISS). In its (3,3) realisation, three sets of right-handed neutrinosand extra sterile fermions are added to the SM content ; the new states do not decouple, leading tomodified leptonic currents and extensive contributions to many observables. For example, this isthe case of cLFV muonic channels. However, and although Z → τµ decays are still within FCC-ee reach, τ → µ lies clearly beyond the reach of Belle II (cf. right panel of Fig. 4). Althoughthe ISS encompasses several Dirac and Majorana CPV phases, having the heavy states formingpseudo-Dirac pairs precludes significant contributions to lepton EDMs [10].Due to the triplet nature of the mediators, both type II and type III seesaws lead to very distinc-tive cLFV signatures. While in all type I-like realisations, cLFV are higher order (loop) processes,in the type II seesaw 3-body decays occur at tree-level; in the type III, both 3-body decays and co-herent conversion in Nuclei are tree-level processes (only radiative decays occur at loop level). Byconstructing ratios of observables, one can aim at disentangling the different realisations: for exam-ple, BR( µ → e γ ) / BR( µ → e ) ∼ − ( & ) for type III (I); likewise CR( µ − e , Ti) / BR( µ → e γ ) ∼ ( ∈ [ . − ]) for type III (II) [11].
3. Embedding the seesaw in complete NP frameworks
Aiming at addressing other observational (and theoretical) problems of the SM, the seesaw Since in the ISS the light neutrino masses receive an extra suppression factor from the parameter which is at theorigin of all LNV in the model ( µ X ), one can accommodate oscillation data with sizeable Yukawa couplings and acomparatively light NP scale by taking small values of µ x . The model remains theoretically natural, as in the limit µ x → eutrino physics and the low-energy intensity frontiers Ana M. Teixeira can be embedded in larger, complete NP frameworks, as is the case of supersymmetry (SUSY) orgrand unified theories (GUTs).
The SUSY seesaw consists in the embedding of a (for example type I) seesaw in the frame-work of otherwise flavour conserving SUSY models. Having a unique source of LFV (the neutrinoYukawa couplings) implies that all observables exhibit a strong degree of correlation. This is mani-fest at low-energies in the strong synergy between µ → e γ and τ → µγ decays, which remain tightlycorrelated regardless of the typical SUSY spectrum or of the seesaw scale [12] - see left panel ofFig. 5. One can further explore the synergy between low- and high-energy cLFV observables (forinstance new edges in dilepton mass distributions, or relative mass differences between left-handedselectrons and smuons [13]) to probe the SUSY seesaw hypothesis. Isolated cLFV manifestationswould disfavour the latter, while compatible ones - as for example ∆ m ˜ ℓ / m ˜ ℓ ( ˜ e L , ˜ µ L ) & .
5% and anobservation of µ → e γ at MEG - would not only strengthen it, but further hint on the seesaw scale( M R ∼ O ( GeV ) ) [14], as visible on the right panel of Fig. 5. MEG 2013 B R ( µ → e γ ) CR ( µ - e , T i ) ∆ m l~ / m l~ (e~ L , µ ~ L )10 -18 -17 -16 -15 -14 -13 -12 -5 -4 -3 -2 -1 -20 -19 -18 -17 -16 -15 Figure 5:
Type I SUSY seesaw: on the left, correlation between BR( µ → e γ ) and BR( τ → µγ ) for differentseesaw scales, M R ; from [12]. On the right, BR( µ → e γ ) and CR( µ − e , Ti) vs. ∆ ˜ ℓ / m ˜ ℓ ( ˜ e L , ˜ µ L ) , also fordifferent seesaw scales, M R ; from [14]. Increasing the degree of symmetry (be it in the form of extended gauge symmetries, flavourones, or gauge unification) reduces the arbitrariness of the couplings, rendering the model more pre-dictive, and hence easier to test (and falsify). GUTs are particularly appealing and well-motivatedtheoretical constructions: in addition to offering a common scheme for Yukawa couplings, theycan even relate observables in the lepton and quark sectors. In the simple case of a SU(5) type ISUSY seesaw, there is a strong correlation between flavour violating observables - as well as CPviolating observables - in leptons and hadrons (see, for example [15, 16]). A second example ofGUT-induced correlation of high-intensity observables can be found in a leptogenesis motivatedSO(10) type II SUSY seesaw, which could be easily falsified by any future observation of twolow-energy cLFV processes.
Massive vector-like fermions are present in many well-motivated SM extensions (as is the case5 eutrino physics and the low-energy intensity frontiers
Ana M. Teixeira of composite Higgs, warped extra dimensions, ...). The prospects for cLFV (at high-intensities andin Higgs decays) were addressed in [17], for a generic set-up - inspired by composite Higgs mod-els - in which 3 generations of vector-like left-handed ( L Vi ) and right-handed ( E Vi ) charged leptonswere included. Neutrino masses can be obtained from additional right-handed states, and the corre-sponding vector-like partners. The contributions to cLFV observables (and lepton dipole moments)turn out to be parametrised by a small set of couplings, leading to correlated observables. For ex-ample one has BR( h → ℓ i ℓ j ) / BR( ℓ i → ℓ j γ ) ≈ π / α BR( h → ℓ i ℓ i ) | SM / BR( ℓ i → ℓ j ν i ¯ ν j ). Otherthan the latter synergy, a strong correlation between EDMs and the muon anomalous magnetic mo-ment ( δ a µ ) was also found. Interestingly, attempts to explain the current tension between theoryand observation in ( g − ) µ implies excessive contributions to the electron EDM, almost leading tothe exclusion of the model - as can be seen from Fig. 6 (left panel). Figure 6:
On the left, correlation of δ a µ with the electron EDM for a model of vector-like leptons; greypoints are ruled out by LHC, and dashed lines show the 2 σ experimental region for δ a µ , and the 90% C.L.upper bound on | d e | ; from [17]. On the right, effective Majorana mass m ee as a function of the lightestneutrino mass, for flavour groups ∆ ( n ) and specific classes of CP transformations; from [19]. The flavour puzzle remains one of the most important open questions in particle phyics. A pos-sible way to address it, starting from first principles, it to relate the flavour patterns (for example, thetexture of the Yukawa couplings) to the breaking of a flavour symmetry G f , continuous or discrete.This avenue has been extensively explored in recent years, relying on very distinct approaches. Theonly phenomenological caveat of certain constructions lies on the difficulty of testing them - how-ever, many realisations have well-defined, peculiar signatures. We have discussed two illustrativeexamples: (i) continuous flavour symmetry - minimal Abelian case, with G f = U(1) L e + L µ × U(1) L τ -leading to predictions of the BR( µ → e γ ) correlated with the ordering scheme of the light neutrinospectrum (for an example see [18]); (ii) a discrete group based approach, with G f of the ∆ ( n ) type, which predicts both lepton mixings as well as low- and high-scale CPV phases [19] (seeFig. 6). Other than constraining predictions for neutrinoless double beta decays, the latter con-struction further leads to the interplay of low-energy CP phases and a successful explanation of thebaryon asymmetry of the Universe from leptogenesis.6 eutrino physics and the low-energy intensity frontiers Ana M. Teixeira
4. Overview