arXiv:0911.1232v1 [hep-ex] 6 Nov 2009
Search for Lepton Flavor Violation Process e+e−→ eµ in the
Energy Region√s = 984 – 1060 MeV and φ → eµ decay
M. N. Achasov,∗K. I. Beloborodov, A. V. Bergyugin, A. G. Bogdanchikov,
A. D. Bukin , D. A. Bukin, T. V. Dimova, V. P. Druzhinin, V. B. Golubev,
I. A. Koop, A. A. Korol, S. V. Koshuba, A. P. Lysenko, E. V. Pakhtusova,
S. I. Serednyakov, Yu. M. Shatunov, Z. K. Silagadze, A. N. Skrinsky, and A. V. Vasiljev
Budker Institute of Nuclear Physics,
Siberian Branch of the Russian Academy of Sciences
11 Lavrentyev,Novosibirsk,630090, Russia and
Novosibirsk State University, 630090, Novosibirsk, Russia
(Dated: November 6, 2009)
The search for lepton-flavor-violation process e+e−→ eµ in the energy region√s = 984 – 1060
MeV with SND detector at VEPP-2M e+e−collider is reported. The model independent 90% CL
upper limits on the e+e−→ eµ cross section, σeµ< 11 pb, as well as on the corresponding φ → eµ
branching fraction, B(φ → eµ) < 2×10−6, for the final particles polar angles 55◦< θ < 125◦, were
For the most of fundamental fermions (quarks and neutrinos) the processes with flavor
violation, quarks decays and neutrinos oscillation, are known. At the same time the LFV
processes with charged leptons has never been observed. Theoretically the processes of this
kind are not strictly forbidden and can occur in many extensions of the Standard Model.
For the LFV hunting, the decays of µ and τ leptons, as well as of the Z-boson and
of various quark-antiquark mesons (K,B,D,η,J/ψ,Υ), along with a conversion process
µN → eN are used [1, 2]. The annihilation processes e+e−→ eµ, eτ, µτ are also suitable
for this purpose. Theoretically these processes and related gauge boson and vector meson
decays were studied, for example, in . On the experimental side, the searches for the
decays J/ψ → eµ,eτ,µτ , Υ → µτ , Z → eµ,eτ,µτ , as well as for the annihilation
processes e+e−→ eτ, µτ in the Υ(4S) energy domain , and for the processes e+e−→ eµ,
eτ, µτ in the energy region√s = 189 – 209 GeV  were performed. However, in the
energy region below the J/ψ production threshold such studies were not done yet. In the
φ(1020)-meson energy domain, it is possible to search for the LFV process e+e−→ eµ and
the corresponding decay φ → eµ (Fig.1).
FIG. 1: The diagrams of the e+e−→ eµ process.
Existing stringent bounds on LFV µ → 3e decay can be transformed to a severe constraint
on the two-body φ → eµ branching fraction: B(φ → eµ) ≤ 4 × 10−17unless some magic
cancellations take place in the µ → 3e decay amplitude . At first sight, such a strong
constraint makes doubtful any experimental effort to search this decay. However, the magic
cancellations mentioned above, although unlikely, cannot be absolutely excluded.
This work reports the results of studies of the process e+e−→ eµ in the energy region
√s ∼ 1 GeV with SND detector at e+e−collider VEPP-2M.
The SND detector  operated from 1995 to 2000 at the VEPP-2M  collider in
the energy range√s from 360 to 1400 MeV. The detector contains several subsystems.
The tracking system includes two cylindrical drift chambers. The three-layer spherical
electromagnetic calorimeter is based on NaI(Tl) crystals. The muon system consists of
plastic scintillation counters and two layers of streamer tubes.The calorimeter energy
and angular resolutions depend on the photon energy as σE/E(%) = 4.2%/
σφ,θ= 0.82◦/?E(GeV) ⊕ 0.63◦. The tracking system angular resolution is about 0.5◦and
2◦for azimuthal and polar angles respectively.
This work is based on the data collected in the scans of the φ-meson energy region. The
total integrated luminosity used is IL = 8.5 pb−1. The luminosity was measured using the
process e+e−→ e+e−with the accuracy of about 2%.
In the reaction e+e−→ eµ the final particles are detected by the tracking system and
have substantively different energy depositions in the calorimeter. The muon system detects
muons with a probability of greater than 90%, while electrons are detected by this system
with the probability of less than 0.2%. To search for e+e−→ eµ process, the so called
collinear events containing two charged particles were used. We assume that the charged
particle with higher energy deposition in the calorimeter (particle number one) is an electron,
while the particle with lower energy deposition (particle number two) is a muon. The events
were selected using the following criteria (subscripts 1 and 2 denote the particle number):
1. Ncha = 2, where Ncha is the number of the charged particles originated from the
interaction point: |z1,2| < 10 cm and r1,2 < 1 cm. Here z is the coordinate of the
charged particle production point along the beam axis (the longitudinal size of the
interaction region σz about 2.5 cm), r is the distance between the charged particle
track and the beam axis in the r − φ plane;
2. |∆θ| = |180◦− (θ1+ θ2)| < 20◦, where θ is the particle polar angle;
3. |∆φ| = |180◦− |φ1− φ2|| < 5◦, where φ is the particle azimuthal angle;
4. 55◦< θ1,2< 125◦;
5. the angular region 240◦< φ1,2< 300◦not covered with the muon system was excluded;
6. the muon system was hited by the second particle and was not hited by the first one;
7. 20 < EI
2< 50 MeV, 40 < EII
2 < 80 MeV and 50 < EIII
< 90 MeV, where Ej
the energy depositions in the calorimeter layers, i denotes the particle number and
j = I,II,III is the layer number;
1> 70 MeV, EII
1> 130 MeV and 20 < EIII
< 100 MeV.
As a result 146 events were selected. The visible cross section (the events number divided
by the integrated luminosity) varies weakly with beam energy. No contribution from the φ-
meson decays φ → K+K−, KSKL, π+π−π0is seen. This agrees with the expectations from
the Monte-Carlo (MC) simulation. The events from the background process e+e−→ π+π−
can pass the selection if one of the pions looses its energy due to the ionization, while the
other pion – due to nuclear interactions.
* / Ee
FIG. 2: The first particle E∗
e/Eefor selected events (dots with errors). Solid curve – fit by a sum
of the distribution for electrons (histogram) and Gaussian. Dashed curve – fit by a sum of the
distribution for electrons (histogram) and third-order polynomial.
In order to obtain the cross section of the process e+e−→ eµ in the whole energy region
√s = 984 – 1060 MeV, the E∗
e/Eedistribution (Fig.2) was analyzed. Here E∗
the electron energies measured by the calorimeter and expected from the process kinematics
respectively. To obtain the number of e+e−→ eµ events (Neµ), the E∗
by a sum of distributions for electrons and background. The distribution for electrons was
e/Eespectrum was fit
obtained using experimental data. The background was approximated either by Gaussian
function or by a third-order polynomial. The coefficients of the background function and
Neµwere free parameters of the fit. When the background was approximated with Gaussian,
it was found that
Neµ= 12 ±14
This corresponds to the upper limit
Neµ< 30 CL=90%.
In the case of the third-order polynomial it was obtained
Neµ= 7 ±11
The corresponding upper limit is
Neµ< 21 CL=90%.
The higher limit Neµ< 30 was used for the further considerations.
Tracking system detection efficiency for the e+e−→ eµ events, εtrack(cuts 1 – 5), was
obtained from MC simulation [10, 12]. The MC events were generated with 1 + cos2θ
distribution.The detection efficiency obtained for the angular region 55◦< θ < 125◦
actually does not depend on the model of the θ-distribution. It’s equal to εtrack= 0.59. The
experimental and simulated θ, ∆θ and ∆φ distributions for the processes e+e−→ e+e−,
e+e−→ π+π−, e+e−→ µ+µ−are in a good agreement [12, 13]. The systematic uncertainty
associated with εtrackdetermination is estimated to be less than 3 %.
The efficiencies of muon and electron detection by the muon system were obtained using
e+e−→ µ+µ−and e+e−→ e+e−data events. The e+e−→ µ+µ−events were selected
according to the criteria 1–5 described above. The additional cut r1,2< 0.1 cm was used
for suppression of the cosmic ray background. The cut 7 was imposed on both particles.
One particle was required to hit the muon system, while the other particle was used to
determine the detection efficiency. The residual cosmic background was subtracted using the
distribution of the z-coordinate of the particles production point . Detection efficiency
muondepends on the muon energy. Its value varies from 0.90 to 0.95 with the average value
muonbeing equal to 0.94. The e+e−→ e+e−events were selected by the cuts 1– 5 and
the condition E1,2/E0> 0.7. It was found that 1 − εe
Probabilities for muons and electrons to pass condition on the energy deposition in the
calorimeter were obtained in a similar way. The e+e−→ µ+µ−events were selected using
cuts 1 – 5 and additional requirements r1,2< 0.2 cm, E1,2/E0< 0.6. It was required that
the muon system was hit by the both particles. The cosmic background was suppressed by
the restriction |τ1− τ2| < 5 ns, where τ1,2are time intervals between the signals from the
scintillation counters and the beam collision moment. The probability for muons to pass
cut 7 was found to be εµ
cal= 0.86. The e+e−→ e+e−events were selected using criteria 1
– 5 and requiring that the muon system was not fired by any particle and that the energy
deposition of a randomly chosen particle was greater than 0.85 × E0. Other particle was
used to obtain probability to satisfy the criterion 8, εe
cal= 0.70. The values of εµ
do not depend on the beam energy.
N / IL, pb
FIG. 3: The visible cross section obtained after additional cut 0.9 < E∗
e/Ee< 1.1. The solid curve
is expected resonance line shape corresponding to the upper limit on B(φ → eµ), dashed curve is
The detection efficiency of the e+e−→ eµ process was calculated as follows
εeµ= εtrack× εµ
muon× (1 − εe
muon) × εµ
and the e+e−→ eµ cross section as
where Neµ< 30, εeµ= 0.31 (the average value εµ
muon= 0.94 was used), IL = 8.5 pb−1. The
following upper limit for the angular region 55◦< θ < 125◦was obtained
σeµ< 11 pb CL=90%.
The upper limit on the φ → eµ decay was obtained assuming absence of any non-resonance
contribution and by using the additional cut 0.9 < E∗
e/E0< 1.1 (then εe
cal= 0.64). The
energy dependence of the visible cross section is shown in Fig.3. It was fit by the function:
σ = εeµ× (1 + δrad) ×4πα2
B(φ → e+e−)B(φ → eµ)
φ− s − i√sΓφ(s)
where (1 + δrad) is the radiative correction factor , P2(s) is a second-order polynomial
describing the background, mφ, Γφare the φ-meson mass and total width, respectively. The
branching ratio and the coefficients of the P2(s) were free fit parameters. For the angular
region 55◦< θ < 125◦, it was obtained
B(φ → eµ) = (0.0 ± 1.5) × 10−6,
which corresponds to the upper limit
B(φ → eµ) < 2 × 10−6CL=90%.
The presented upper limits do not depend on the angular distribution of the process e+e−→
The work is supported in part by RF Presidential Grant for Sc. Sch. NSh-5655.2008.2,
and by RFBR grants 08-02-00328-a, 08-02-00634-a, 08-02-00660-a.
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