Eur. Phys. J. C (2016) 76:434
DOI 10.1140/epjc/s10052-016-4271-x
Regular Article - Experimental Physics
Search for the lepton flavour violating decay µ
+
→ e
+
γ
with the full dataset of the MEG experiment
MEG Collaboration
A. M. Baldini
4a
,Y.Bao
1
, E. Baracchini
3,16
, C. Bemporad
4a,4b
,F.Berg
1,2
,M.Biasotti
8a,8b
, G. Boca
6a,6b
,
M. Cascella
13a,13b,17
, P. W. Cattaneo
6a
,G.Cavoto
7a
,F.Cei
4a,4b
, C. Cerri
4a
, G. Chiarello
13a,13b
, C. Chiri
13a,13b
,
A. Corvaglia
13a,13b
, A. de Bari
6a,6b
, M. De Gerone
8a
,T.Doke
9
, A. D’Onofrio
4a,4b
, S. Dussoni
4a
, J. Egger
1
,Y.Fujii
3
,
L. Galli
4a
, F. Gatti
8a,8b
, F. Grancagnolo
13a
, M. Grassi
4a
, A. Graziosi
7a,7b
, D. N. Grigoriev
10,14,15
, T. Haruyama
11
,
M. Hildebrandt
1
, Z. Hodge
1,2
, K. Ieki
3
, F. Ignatov
10,15
,T.Iwamoto
3
, D. Kaneko
3
, T. I. Kang
5
, P.-R. Kettle
1
,
B. I. Khazin
10,15
, N. Khomutov
12
, A. Korenchenko
12
, N. Kravchuk
12
,G.M.A.Lim
5
, A. Maki
11
, S. Mihara
11
,
W. Molzon
5
, Toshinori Mori
3
, F. Morsani
4a
, A. Mtchedilishvili
1
, D. Mzavia
12
, S. Nakaura
3
, R. Nardò
6a,6b
,
D. Nicolò
4a,4b
, H. Nishiguchi
11
, M. Nishimura
3
, S. Ogawa
3
, W. Ootani
3
,S.Orito
3
, M. Panareo
13a,13b
, A. Papa
1
,
R. Pazzi
4
, A. Pepino
13a,13b
, G. Piredda
7a
, G. Pizzigoni
8a,8b
, A. Popov
10,15
, F. Raffaelli
4a
, F. Renga
1,7a,7b
,
E. Ripiccini
7a,7b
,S.Ritt
1
, M. Rossella
6a
, G. Rutar
1,2
, R. Sawada
3
, F. Sergiampietri
4a
, G. Signorelli
4a
,
M. Simonetta
6a,6b
,G.F.Tassielli
13a
, F. Tenchini
4a,4b
, Y. Uchiyama
3
, M. Venturini
4a,4c
, C. Voena
7a
, A. Yamamoto
11
,
K. Yoshida
3
,Z.You
5
, Yu. V. Yudin
10,15
, D. Zanello
7
1
Paul Scherrer Institut PSI, 5232 Villigen, Switzerland
2
Swiss Federal Institute of Technology ETH, CH-8093 Zurich, Switzerland
3
ICEPP, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
4 (a)
INFN Sezione di Pisa, dell’Università, Largo B. Pontecorvo 3, 56127 Pisa, Italy;
(b)
Dipartimento di Fisica, dell’Università, Largo B. Pontecorvo 3, 56127 Pisa, Italy;
(c)
Scuola Normale Superiore, Piazza dei Cavalieri, 56127 Pisa, Italy
5
University of California, Irvine, CA 92697, USA
6 (a)
INFN Sezione di Pavia, dell’Università, Via Bassi 6, 27100 Pavia, Italy;
(b)
Dipartimento di Fisica, dell’Università, Via Bassi 6, 27100 Pavia, Italy
7 (a)
INFN Sezione di Roma, dell’Università “Sapienza”, Piazzale A. Moro, 00185 Rome, Italy;
(b)
Dipartimento di Fisica, dell’Università “Sapienza”, Piazzale A. Moro, 00185 Rome, Italy
8 (a)
INFN Sezione di Genova, dell’Università, Via Dodecaneso 33, 16146 Genoa, Italy;
(b)
Dipartimento di Fisica, dell’Università, Via Dodecaneso 33, 16146 Genoa, Italy
9
Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
10
Budker Institute of Nuclear Physics of Siberian Branch of Russian Academy of Sciences, 630090 Novosibirsk, Russia
11
KEK, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan
12
Joint Institute for Nuclear Research, 141980 Dubna, Russia
13 (a)
INFN Sezione di Lecce, dell’Università del Salento, Via per Arnesano, 73100 Lecce, Italy;
(b)
Dipartimento di Matematica e Fisica, dell’Università del Salento, Via per Arnesano, 73100 Lecce, Italy
14
Novosibirsk State Technical University, 630092 Novosibirsk, Russia
15
Novosibirsk State University, 630090 Novosibirsk, Russia
16
Present address: INFN, Laboratori Nazionali di Frascati, Via E. Fermi, 40-00044 Frascati, Rome, Italy
17
Present address: Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
Received: 1 June 2016 / Accepted: 11 July 2016 / Published online: 3 August 2016
© The Author(s) 2016. This article is published with open access at Springerlink.com
Abstract The final results of the search for the lepton
flavour violating decay μ
+
→ e
+
γ based on the full dataset
collected by the MEG experiment at the Paul Scherrer Insti-
T. Doke, B. I. Khazin, A. Korenchenko, D. Mzavia, S. Orito,
G. Piredda, deceased.
a
e-mail:
fabrizio.cei@pi.infn.it
tut in the period 2009–2013 and totalling 7.5× 10
14
stopped
muons on target are presented. No significant excess of events
is observed in the dataset with respect to the expected back-
ground and a new upper limit on the branching ratio of this
decay of B(μ
+
→ e
+
γ) < 4.2 × 10
−13
(90 % confidence
level) is established, which represents the most stringent limit
on the existence of this decay to date.
123
434 Page 2 of 30 Eur. Phys. J. C (2016) 76 :434
Contents
1 Introduction ..................... 2
2 MEG detector .................... 3
3 Reconstruction .................... 8
4 Analysis ....................... 19
5 Conclusions ..................... 28
References ........................ 29
1 Introduction
The standard model (SM) of particle physics allows
charged lepton flavour violating (CLFV) processes with
only extremely small branching ratios (≪10
−50
) even when
accounting for measured neutrino mass differences and mix-
ing angles. Therefore, such decays are free from SM physics
backgrounds associated with processes involving, either
directly or indirectly, hadronic states and are ideal labora-
tories for searching for new physics beyond the SM. A pos-
itive signal would be an unambiguous evidence for physics
beyond the SM.
The existence of such decays at measurable rates not far
below current upper limits is suggested by many SM exten-
sions, such as supersymmetry [
1]. An extensive review of
the theoretical expectations for CLFV is provided in [
2].
CLFV searches with improved sensitivity probe new regions
of the parameter spaces of SM extensions, and CLFV decay
μ
+
→ e
+
γ is particularly sensitive to new physics. The
MEG collaboration has searched for μ
+
→ e
+
γ decay at
the Paul Scherrer Institut (PSI) in Switzerland in the period
2008–2013. A detailed report of the experiment motivation,
design criteria, and goals is available in reference [
3,4] and
references therein. We have previously reported [
5–7] results
Fig. 1 A schematic view of the MEG detector showing a simulated event
of partial datasets including a limit on the branching ratio for
this decay B < 5.7 × 10
−13
at 90 % C.L.
The signal consists of a positron and a photon back-to-
back, each with energy of 52.83 MeV (half of the muon
mass), and with a common origin in space and time. Figure 1
shows cut schematic views of the MEG apparatus. Positive
muons are stopped in a thin plastic target at the centre of
a spectrometer based on a superconducting solenoid. The
decay positron’s trajectory is measured in a magnetic field
by a set of low-mass drift chambers and a scintillation counter
array is used to measure its time. The photon momentum vec-
tor, interaction point and timing are measured by a homoge-
neous liquid xenon calorimeter located outside the magnet
and covering the angular region opposite to the acceptance
of the spectrometer. The total geometrical acceptance of the
detector for the signal is ≈11 %.
The signal can be mimicked by various processes, with the
positron and photon originating either from a single radiative
muon decay (RMD) (μ
+
→ e
+
γν¯ν) or from the acciden-
tal coincidence of a positron and a photon from different
processes. In the latter case, the photon can be produced
by radiative muon decay or by Bremsstrahlung or positron
annihilation-in-flight (AIF) (e
+
e
−
→ γγ). Accidental coin-
cidences between a positron and a photon from different pro-
cesses, each close in energy to their kinematic limit and with
origin, direction and timing coincident within the detector
resolutions are the dominant source of background.
Since the rate of accidental coincidences is proportional
to the square of the μ
+
decay rate, the signal to background
ratio and data collection efficiency are optimised by using
a direct-current rather than pulsed beam. Hence, the high
intensity continuous surface μ
+
beam (see Sect.
2.1) at PSI
is the ideal facility for such a search.
123
Eur. Phys. J. C (2016) 76 :434 Page 3 of 30 434
The remainder of this paper is organised as follows. After
a brief introduction to the detector and to the data acqui-
sition system (Sect.
2), the reconstruction algorithms are
presented in detail (Sect.
3), followed by an in-depth dis-
cussion of the analysis of the full MEG dataset and of the
results (Sect.
4). Finally, in the conclusions, some prospects
for future improvements are outlined (Sect.
5).
2 MEG detector
The MEG detector is briefly presented in the following,
emphasising the aspects relevant to the analysis; a detailed
description is available in [
8]. Briefly, it consists of the μ
+
beam, a thin stopping target, a thin-walled, superconducting
magnet, a drift chamber array (DCH), scintillating timing
counters (TC), and a liquid xenon calorimeter (LXe detec-
tor).
In this paper we adopt a cylindrical coordinate system
(r,φ,z) with origin at the centre of the magnet (see Fig.
1).
The z-axis is parallel to the magnet axis and directed along the
μ
+
beam. The axis defining φ = 90
◦
(the y-axis of the corre-
sponding Cartesian coordinate system) is directed upwards
and, as a consequence, the x-axis is directed opposite to the
centre of the LXe detector. Positrons move along trajecto-
ries with decreasing φ-coordinate. When required, the polar
angle θ with respect to the z-axis is also used. The region
with z < 0 is referred to as upstream, that with z > 0as
downstream.
2.1 Muon beam
The requirement to stop a large number of μ
+
in a thin target
of small transverse size drives the beam requirements: high
flux, small transverse size, small momentum spread and small
contamination, e.g. from positrons. These goals are met by
the 2.2 mA PSI proton cyclotron and π E5 channel in com-
bination with the MEG beam line, which produces one of
the world’s most intense continuous μ
+
beams. It is a sur-
face muon beam produced by π
+
decay near the surface of
the production target. It can deliver more than 10
8
μ
+
/s at
28 MeV/c in a momentum bite of 5–7 %. To maximise the
experiment’s sensitivity, the beam is tuned to a μ
+
stopping
rate of 3×10
7
, limited by the rate capabilities of the track-
ing system and the rate of accidental backgrounds, given the
MEG detector resolutions. The ratio of e
+
to μ
+
flux in
the beam is ≈8, and the positrons are efficiently removed
by a combination of a Wien filter and collimator system.
The muon momentum distribution at the target is optimised
by a degrader system comprised of a 300 µm thick mylar
®
foil and the He-air atmosphere inside the spectrometer in
front of the target. The round, Gaussian beam-spot profile
has σ
x,y
≈10 mm.
Fig. 2 The thin muon stopping target mounted in a Rohacell frame
The muons at the production target are produced fully
polarized (P
μ
+
=−1) and they reach the stopping targetwith
a residual polarization P
μ
+
=−0.86 ± 0.02 (stat)
+0.05
−0.06
(syst)
consistent with the expectations [
9].
Other beam tunes are used for calibration purposes,
including a π
−
tune at 70.5 MeV/c used to produce
monochromatic photons via pion charge exchange and a
53 MeV/c positron beam tune to produce Mott-scattered
positrons close to the energy of a signal positron (Sect.
2.7).
2.2 Muon stopping target
Positive muons are stopped in a thin target at the centre of
the spectrometer, where they decay at rest. The target is opti-
mised to satisfy conflicting goals of maximising stopping
efficiency (≈80 %) while minimising multiple scattering,
Bremsstrahlung and AIF of positrons from muon decays.
The target is composed of a 205 µm thick layer of polyethy-
lene and polyester (density 0.895 g/cm
3
) with an elliptical
shape with semi-major and semi-minor axes of 10 cm and
4 cm. The target foil is equipped with seven cross marks
and eight holes of radius 0.5 cm, used for optical survey and
for software alignment purposes. The foil is mounted in a
Rohacell
®
frame, which is attached to the tracking system
support frame and positioned with the target normal vector
in the horizontal plane and at an angle θ ≈70
◦
. The target
before installation in the detector is shown in Fig.
2.
2.3 COBRA magnet
The COBRA (constant bending radius) magnet [
10] is a thin-
walled, superconducting magnet with an axially graded mag-
netic field, ranging from 1.27 T at the centre to 0.49 T at
either end of the magnet cryostat. The graded field has the
advantage with respect to a uniform solenoidal field that par-
ticles produced with small longitudinal momentum have a
much shorter latency time in the spectrometer, allowing sta-
ble operation in a high-rate environment. Additionally, the
graded magnetic field is designed so that positrons emitted
from the target follow a trajectory with almost constant pro-
jected bending radius, only weakly dependent on the emis-
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434 Page 4 of 30 Eur. Phys. J. C (2016) 76 :434
sion polar angle θ
e
+
(see Fig.
3a), even for positrons emitted
with substantial longitudinal momentum.
The central part of the coil and cryostat accounts for
0.197 X
0
, thereby maintaining high transmission of signal
photons to the LXe detector outside the COBRA cryostat.
The COBRA magnet is also equipped with a pair of com-
pensation coils to reduce the stray field to the level neces-
sary to operate the photomultiplier tubes (PMTs) in the LXe
detector.
The COBRA magnetic field was measured with a com-
mercial Hall probe mounted on a wagon moving along z,
r and φ in the ranges |z| < 110 cm, 0
◦
<φ<360
◦
and
0 < r < 29 cm, covering most of the positron tracking vol-
ume. The probe contained three Hall sensors orthogonally
aligned to measure B
z
, B
r
and B
φ
individually. Because the
main (axial) field component is much larger than the others,
even small angular misalignments of the other probes could
cause large errors in B
r
and B
φ
. Therefore, only the mea-
sured values of B
z
are used in the analysis and the secondary
components B
r
and B
φ
are reconstructed from the measured
B
z
using Maxwell’s equations as
B
φ
(z, r,φ) = B
φ
(z
B
, r,φ)+
1
r
z
z
B
∂ B
z
(z
′
, r,φ)
∂φ
dz
′
B
r
(z, r,φ) = B
r
(z
B
, r,φ)+
z
z
B
∂ B
z
(z
′
, r,φ)
∂r
dz
′
.
The measured values of B
r
and B
φ
are required only at
z
B
= 1 mm near the symmetry plane of the magnet where
the measured value of B
r
is minimised (|B
r
(z
B
, r,φ)| <
2 × 10
−3
T) as expected. The effect of the misalignment
of the B
φ
-measuring sensor on B
φ
(z
B
, r,φ)is estimated by
checking the consistency of the reconstructed B
r
and B
φ
with
Maxwell’s equations.
The continuous magnetic field map used in the analysis is
obtained by interpolating the reconstructed magnetic field at
the measurement grid points by a B-spline fit [
11].
2.4 Drift chamber system
The DCH system [
12] is designed to ensure precise mea-
surement of the trajectory and momentum of positrons from
μ
+
→ e
+
γ decays. It is designed to satisfy several require-
ments: operate at high rates, primarily from positrons from
μ
+
decays in the target; have low mass to improve kinematic
resolution (dominated by scattering) and to minimise pro-
duction of photons by positron AIF; and provide excellent
resolution in the measurement of the radial and longitudinal
coordinates.
The DCH system consists of 16 identical, independent
modules placed inside COBRA, aligned in a semi-circle with
10.5
◦
spacing, and covering the azimuthal region between
191.25
◦
and 348.75
◦
and the radial region between 19.3 and
(a)
(b)
Fig. 3 Concept of the gradient magnetic field of COBRA. The
positrons follow trajectories at constant bending radius weakly depen-
dent on the emission angle θ
e
+
(a) and those emitted from the target
with small longitudinal momentum (θ
e
+
≈90
◦
) are quickly swept away
from the central region (b)
Fig. 4 View of the DCH system from the downstream side of the MEG
detector. The muon stopping target is placed in the centre and the 16
DCH modules are mounted in a semi-circular array
27.9 cm (see Fig.
4). Each module has a trapezoidal shape
with base lengths of 40 and 104 cm, without supporting struc-
ture on the long (inner) side to reduce the amount of material
intercepted by signal positrons. A module consists of two
independent detector planes, each consisting of two cath-
ode foils (12.5 µm-thick aluminised polyamide) separated
by 7 mm and filled with a 50:50 mixture of He:C
2
H
6
. A plane
of alternating axial anode and potential wires is situated mid-
123
Eur. Phys. J. C (2016) 76 :434 Page 5 of 30 434
Fig. 5 Schematic view of the cell structure of a DCH plane
Fig. 6 Schematic view of the Vernier pad method showing the pad
shape and offsets. Only one of the two cathode pads in each cell is
shown
way between the cathode foils with a pitch of 4.5 mm. The
two planes of cells are separated by 3 mm and the two wire
arrays in the same module are staggered by half a drift cell
to help resolve left-right position ambiguities (see Fig.
5). A
double wedge pad structure is etched on both cathodes with
a Vernier pattern of cycle λ = 5 cm as shown in Fig.
6.The
pad geometry is designed to allow a precise measurement
of the axial coordinate of the hit by comparing the signals
induced on the four pads in each cell. The average amount of
material intercepted by a positron track in a DCH module is
2.6 × 10
−4
X
0
, with the total material along a typical signal
positron track of 2.0 × 10
−3
X
0
.
2.5 Timing counter
The TC [
13,14] is designed to measure precisely the impact
time and position of signal positrons and to infer the muon
decay time by correcting for the track length from the target
to the TC obtained from the DCH information.
The main requirements of the TC are:
– provide full acceptance for signal positrons in the DCH
acceptance matching the tight mechanical constraints
dictated by the DCH system and COBRA;
– ability to operate at high rate in a high and non-uniform
magnetic field;
– fast and approximate (≈5 cm resolution) determination
of the positron impact point for the online trigger;
– good (≈1 cm) positron impact point position resolution
in the offline event analysis;
– excellent (≈50 ps) time resolution of the positron impact
point.
The system consists of an upstream and a downstream
sector, as shown in Fig.
1.
Fig. 7 Schematic picture of a TC sector. Scintillator bars are read out
by a PMT at each end
Each sector (see Fig.
7) is barrel shaped with full angular
coverage for signal positrons within the photon and positron
acceptance of the LXe detector and DCH. It consists of an
array of 15 scintillating bars with a 10.5
◦
pitch between adja-
cent bars. Each bar has an approximate square cross-section
of size 4.0 × 4.0 × 79.6cm
3
and is read out by a fine-mesh,
magnetic field tolerant, 2” PMT at each end. The inner radius
of a sector is 29.5 cm, such that only positrons with a momen-
tum close to that of signal positrons hit the TC.
2.6 Liquid xenon detector
The LXe photon detector [
15,16] requires excellent posi-
tion, time and energy resolutions to minimise the number
of accidental coincidences between photons and positrons
from different muon decays, which comprise the dominant
background process (see Sect.
4.4.1).
It is a homogeneous calorimeter able to contain fully the
shower induced by a 52.83 MeV photon and measure the
photon interaction vertex, interaction time and energy with
high efficiency. The photon direction is not directly measured
in the LXe detector, rather it is inferred by the direction of a
line between the photon interaction vertexin the LXe detector
and the intercept of the positron trajectory at the stopping
target.
Liquid xenon, with its high density and short radiation
length, is an efficient detection medium for photons; optimal
resolution is achieved, at least at low energies, if both the
ionisation and scintillation signals are detected. In the high
rate MEG environment, only the scintillation light with its
very fast signal, is detected.
A schematic view of the LXe detector is shown in Fig.
8.It
has a C-shaped structure fitting the outer radius of COBRA.
The fiducial volume is ≈800 ℓ, covering 11 % of the solid
angle viewed from the centre of the stopping target. Scin-
tillation light is detected in 846 PMTs submerged directly
123