TUM-HEP 142222 IFT-UAMCSIC-22-124 Indirect upper limits on ijfromij

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TUM-HEP 1422/22

IFT-UAM/CSIC-22-124

Indirect upper limits on `i→`jγγ from `i→`jγ

Fabiola Fortuna,1Alejandro Ibarra,2Xabier Marcano,3Marcela Mar´ın,1and Pablo Roig1

1Departamento de F´ısica, Centro de Investigaci´on y de Estudios Avanzados del Instituto Polit´ecnico Nacional,

Apdo. Postal 14-740, 07000 Ciudad de M´exico, M´exico.

2Physik-Department, Technische Universit¨at M¨unchen, James-Franck-Straße, 85748 Garching, Germany

3Departamento de F´ısica Te´orica and Instituto de F´ısica Te´orica UAM/CSIC,

Universidad Aut´onoma de Madrid, Cantoblanco, 28049 Madrid, Spain

We perform an eﬀective ﬁeld theory analysis to correlate the charged lepton ﬂavor violating

processes `i→`jγγ and `i→`jγ. Using the current upper bounds on the rate for `i→`jγ, we

derive model-independent upper limits on the rates for `i→`jγγ. Our indirect limits are about

three orders of magnitude stronger than the direct bounds from current searches for µ→eγγ, and

four orders of magnitude better than current bounds for τ→`γγ. We also stress the relevance of

Belle II or a Super Tau Charm Facility to discover the rare decay τ→`γγ.

I. INTRODUCTION

The experimental observation of charged lepton ﬂa-

vor violation (cLFV) would undoubtedly imply the ex-

istence of new physics beyond neutrino oscillations [1].

This has motivated a strong experimental program over

the last 75 years searching for diﬀerent cLFV processes,

see Fig. 1, each observable providing complementary in-

formation about possible beyond the Standard Model

(BSM) scenarios.

Here we consider the cLFV decays of leptons to two

photons, `i→`jγγ [2–4], which have been explored in

less detail than other cLFV processes such as the single

photon process, `i→`jγ, specially for the case of τ→

`γγ [5–9].

Experimentally, µ→eγγ was searched for by several

experiments aiming also for µ→eγ. The latest of these

experiments was the Crystal Box detector, whose result

still provides the strongest bound for µ→eγγ [10].

This limit is however two orders of magnitude weaker

than present µ→eγ bounds, see Table I, since the

MEG experiment was optimized for back-to-back topolo-

gies and no new dedicated experiment for µ→eγγ has

been carried out since Crystal Box. On the other hand,

τ→`γγ has rarely been searched for. To the best

of our knowledge, the only existing direct experimental

search was performed by ATLAS, setting an upper limit

of BR(τ→µγγ)<1.5×10−4after the LHC run-I [11].

No direct experimental search exists for τ→eγγ.

An alternative for exploring the `i→`jγγ channels is

to recast the searches for `i→`jγ, as some of the events

of the former would fall into the signal region deﬁned

for the latter [3]. This idea has been recently applied to

recast the BABAR search for τ→`γ [12], ﬁnding that at

90%CL BR(τ→µγγ)<5.8×10−4and BR(τ→eγγ)<

2.5×10−4[9]. These limits are however several orders

of magnitude weaker than the associated ones on τ→`γ

due to the low acceptance of these searches for τ→`γγ

events.

In this letter, we consider the theoretical correlation

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▼μ → �γ

▲μ → �γγ

●τ → μ μ μ

▼τ → μ γ

▲τ → μ γγ

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10-16

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FIG. 1. Historical evolution for the 90%CL upper lim-

its on several cLFV leptonic decays. Solid markers corre-

spond to published direct experimental searches, while empty

ones indicate future expected sensitivities at MEG II [13],

Mu3e [14] and Belle II [15] (arbitrary year). Lighter mark-

ers for `i→`jγγ were obtained by recasting the available

searches for `i→`jγ[3,9] or µe →γγ [2]. The evolution for

τ→esector is similar to the τ→µone, with the exception

that no direct search for τ→eγγ exists.

between the `i→`jγγ and the `i→`jγdecays.

Clearly, any scenario generating `i→`jγwould auto-

matically generate a (model-independent) contribution

to `i→`jγγ, from the radiation of an additional pho-

ton in the ﬁnal state. Further, any scenario generating

`i→`jγγ will generate a (model-dependent) contribu-

tion to `i→`jγat the quantum level. Barring cancella-

arXiv:2210.05703v1 [hep-ph] 11 Oct 2022

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TUM-HEP1422/22IFT-UAM/CSIC-22-124Indirectupperlimitson`i!`jfrom`i!`jFabiolaFortuna,1AlejandroIbarra,2XabierMarcano,3MarcelaMarn,1andPabloRoig11DepartamentodeFsica,CentrodeInvestigacionydeEstudiosAvanzadosdelInstitutoPolitecnicoNacional,Apdo.Postal14-740,07000CiudaddeMexico,Mexico.2Physik-Dep...

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