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Physics Letters B 771 (2017) 242–246

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Spin-dependent μ →e conversion

Vincenzo Cirigliano

, Sacha Davidson

b,∗

, Yoshitaka Kuno

Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

IPNL, CNRS/IN2P3, Université Lyon 1, Univ. Lyon, 69622 Villeurbanne, France

Department of Physics, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan

a r t i c l e i n f o a b s t r a c t

Article history:

Received

16 March 2017

Received

in revised form 6 May 2017

Accepted

19 May 2017

Available

online 22 May 2017

Editor: J.

Hisano

The experimental sensitivity to μ → e conversion on nuclei is expected to improve by four orders

of magnitude in coming years. We consider the impact of μ → e ﬂavour-changing tensor and axial-

vector

four-fermion operators which couple to the spin of nucleons. Such operators, which have not

previously been considered, contribute to μ → e conversion in three ways: in nuclei with spin they

mediate a spin-dependent transition; in all nuclei they contribute to the coherent (A

-enhanced) spin-

independent

conversion via ﬁnite recoil effects and via loop mixing with dipole, scalar, and vector

operators. We estimate the spin-dependent rate in Aluminium (the target of the upcoming COMET and

Mu2e experiments), show that the loop effects give the greatest sensitivity to tensor and axial-vector

operators involving ﬁrst-generation quarks, and discuss the complementarity of the spin-dependent and

independent contributions to μ →e conversion.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

New particles and interactions beyond the Standard Model of

particle physics are required to explain neutrino masses and mix-

ing

angles. The search for traces of this New Physics (NP) is pur-

sued

on many fronts. One possibility is to look directly for the new

particles implicated in neutrino mass generation, for instance at

the LHC [1] or SHiP [2]. A complementary approach seeks new

interactions among known particles, such as neutrinoless double

beta decay [3] or Charged Lepton Flavour Violation (CLFV) [4].

CLFV

transitions of charged leptons are induced by the ob-

served

massive neutrinos, at unobservable rates suppressed by

)

∼10

−48

. A detectable rate would point to the existence

of new heavy particles, as may arise in models that generate neu-

trino

masses, or that address other puzzles of the Standard Model

such as the hierarchy problem. Observations of CLFV are therefore

crucial to identifying the NP of the lepton sector, providing infor-

mation

complementary to direct searches.

From

a theoretical perspective, at energy scales well below the

masses of the new particles, CLFV can be parametrised with effec-

tive

operators (see e.g. [5]), constructed out of the kinematically

accessible Standard Model (SM) ﬁelds, and respecting the relevant

gauge symmetries. In this effective ﬁeld theory (EFT) description,

Corresponding author.

E-mail

address: s.davidson@ipnl.in2p3.fr (S. Davidson).

information about the underlying new dynamics is encoded in the

operator coeﬃcients, calculable in any given model.

The

experimental sensitivity to a wide variety of CLFV pro-

cesses

is systematically improving. Current bounds on branching

ratios of τ ﬂavour changing decays such as τ →μγ , τ →eγ and

τ →3 [6–8] are O(10

−8

), and Belle-II is expected to improve the

sensitivity by an order of magnitude [9]. The bounds on the μ ↔ e

ﬂavour

changing processes are currently of order ∼ 10

−12

[10,11],

with the most restrictive constraint from the MEG collaboration:

BR(μ → eγ ) ≤ 4.2 × 10

−13

[12]. Future experimental sensitivities

should improve by several orders of magnitude, in particular, the

COMET [13] and Mu2e [14] experiments aim to reach a sensitivity

to μ → e conversion on nuclei of ∼ 10

−16

, and the PRISM/PRIME

proposal [15] could reach the unprecedented level of 10

−18

searches for μ → e conversion, a μ

−

from the beam is cap-

tured

by a nucleus in the target, and tumbles down to the 1s

state.

The muon will be closer to the nucleus than an electron

(r ∼ α Z /m ), due to its larger mass. In the presence of a CLFV

interaction with the quarks that compose the nucleus, or with

its electric ﬁeld, the muon can transform into an electron. This

electron, emitted with an energy E

 m

, is the signature of

μ → e conversion.

Initial

analytic estimates of the μ →e conversion rate were ob-

tained

by Feinberg and Weinberg [16], awider range of nuclei

were studied numerically by Shankar [17], and relativistic effects

relevant in heavier nuclei were included in Ref. [18]. State of the

art conversion rates for a broad range of nuclei induced by CLFV

http://dx.doi.org/10.1016/j.physletb.2017.05.053

0370-2693/

SCOAP

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