Search for the dark photon in π0 decays
EPJ Web of Conferences
Search for the dark photon in π0 decays
Roberto Piandani 0
0 for the NA48/2 Collaboration: Cambridge , CERN, Dubna, Chicago, Edinburgh, Ferrara, Firenze, Mainz, Northwestern, Perugia, Pisa, Saclay, Siegen, Torino, Wien
A sample of 1.69 × 107 fully reconstructed π0 → γe+e− in the kinematic range mee > 10MeV/c2 with a negligible background contamination collected by the NA48/2 experiment at CERN in 2003-04 is analysed to search for the dark photon (A ) via the decay chain π0 → γA , A → e+e. No signal is observed, and preliminary exclusion limits on space of dark photon mass mA and mixing parameter 2 are reported. High intensity kaon experiments provide opportunities for precision studies of π0 decay physics due to the fact that kaons represent a source of tagged neutral pion decays, mainly via their K± → π±π0 , K± → e±π0ν and K± → μ±π0ν decays. One of them is the NA48/2 experiment at the CERN SPS, which collected a large sample of charged kaon (K± ) decays in flight in 2003-04 corresponding to ∼ 2 × 1011 K± decays in the fiducial decay volume . This large sample of π0 mesons produced and decaying in vacuum collected by NA48/2 allows for a high sensitivity search for the dark photon (A ), a hypothetical gauge boson appearing in hidden sector new physics models with an extra U(1) gauge symmetry. In these models the interaction of the dark photon with the visible sector proceed through kinetic mixing with the Standard Model (SM) hypercharge . Such scenarios with GeV-scale dark matter provide possible explanations to the observed rise in the cosmic-ray positron fraction with energy and the muon gyromagnetic ratio (g − 2 ) measurement . From the experimental point of view, the dark photon is characterized by two a priori unknown parameters, the mixing parameter and the mass mA . The A production and the subsequent decay can be obtained from the following decay chain:
K± → π±π0, π0 → γA , A
with three charged particles and a photon in the final state. The expected branching fraction of the π0
decay is [
B(π0 → γA ) = 2 2 ⎜⎜⎜⎜⎜⎝⎛ 1 − mm22πA0 ⎟⎟⎟⎠⎟⎟⎞ 3 × B(π0 → γγ)
which is kinematically suppressed as mA approaches mπ0 . In the mass range 2me mA < mπ0
accessible in this analysis, the dark photon is below threshold for all decays into SM fermions except
A → e+e− , while the allowed loop-induced decays (A → 3γ, A → νν¯) are strongly suppressed.
Therefore, assuming that the dark photon decay only in SM particles, B(A → e+e−) 1. The
expected total dark photon decay width is 
→ e+e−) =
mA < mπ0 , the dark photon mean proper lifetime τA satisfies the relation
The NA48/2 analysis is performed assuming that the dark photon decays at the production point
(prompt decay), which is valid for sufficiently large values of the mass (mA > 10MeV/c2) and the
mixing parameter ( 2 > 5 × 10−7). In this condition the dark photon signature is identical to the
Dalitz decay π0 → γe+e− , which therefore represents an irreducible background and determines
the sensitivity. The largest π0D sample is obtained through the reconstruction of K± → π±π0 and
K± → μ±π0ν decays (denoted K2π and Kμ3). In Addition, the K± → π±π0π0 decay (denoted K3π) is
considered as a background in the Kμ3 sample.
2 The NA48/2 experiment
The NA48/2 beam line has been designed to deliver simultaneous narrow momentum band K+ and
K− beams following a common beam axis derived from the primary 400 GeV/c protons extracted
from the CERN SPS. Secondary beams with central momenta of (60 ± 3) GeV/c (r.m.s.) were used.
The beam kaons decayed in a fiducial decay volume contained in a 114 m long cylindrical vacuum
tank. The momenta of charged decay products were measured in a magnetic spectrometer, housed
in a tank filled with helium placed after the decay volume. The spectrometer comprised four drift
chambers (DCHs), two upstream and two downstream of a dipole magnet which provided a
horizontal transverse momentum kick of 120 MeV/c to singly-charged particles. Each DCH was composed of
eight planes of sense wires. A plastic scintillator hodoscope (HOD) producing fast trigger signals and
providing precise time measurements of charged particles was placed after the spectrometer. Further
downstream was a liquid krypton electromagnetic calorimeter (LKr), an almost homogeneous
ionization chamber with an active volume of 7 m3 of liquid krypton, 27X0 deep, segmented transversally
into 13248 projective 2 × 2 cm2 cells and with no longitudinal segmentation. The LKr information
is used for photon measurements and charged particle identification. An iron/scintillator hadronic
calorimeter and muon detectors were located further downstream. A dedicated two-level trigger was
in operation to collect three-track decays with an efficiency of about 98%. A detailed description of
the detector can be found in Ref. .
3 Event selection
The full NA48/2 data sample is used for the analysis. The K2π and Kμ3 with the following π0 →
γe+e− event selection requires a three-track vertex reconstructed in the fiducial decay region formed of
a pion or muon candidate track and two opposite-sign electron (e± ) candidate tracks. Charged particle
identification is based on the ratio of energy deposition in the LKr calorimeter (E) to the momentum
measured by the spectrometer (p). Pions and muons are kinematically constrained to the momentum
range above 5 GeV/c, while the momentum spectra of electrons originating from π0 decays are soft,
peaking at 3 GeV/c. Therefore,p > 5 GeV/c and E/p < 0.85 (E/p < 0.4) are required for the pion
(muon) candidate, while p > 2.75 GeV/c and (E/p)min < E/p < 1.15, where (E/p)min = 0.80 for
p < 5 GeV/c and (E/p)min = 0.85 otherwise, are required for the electron candidates. Furthermore,
a single insolated LKr energy deposition cluster is required and considered as the photon candidate.
The reconstructed invariant mass of the e+e−γ system is required to be compatible with the π0 mass,
|me+e−γ − mπ0 | < 8 Mev/c2 (this interval corresponds to ±5 times the resolution on me+e−γ).
For the K2π selection, the reconstructed invariant mass of the π±e+e−γ (figure 1) system should be
compatible with the K± mass, 474 MeV/c2 < mπe+e−γ < 514 MeV/c2. For the Kμ3 selection, the
squared missing mass m2miss = (PK − Pμ − Pπ0 )2 (figure 1) should be compatible with tne neutrino
mass (|m2miss| < 0.01 GeV2/c4), where Pμ and Pπ0 are the reconstructed μ± and π0 four-momenta, and
PK is the nominal kaon four-momentum.
At the end of the two selections a sample of 1.38 × 107 (0.31 × 107) fully reconstructed π0D decay
candidates comining from K2π (Kμ3) with a negligible background is selected. Correcting the observed
number of candidates for acceptance and trigger efficiency, the total number of K± decays in the 98 m
long fiducial decay region for the analysed data sample is found to be NK = (1.57 ± 0.05) × 107, where
the quoted error is dominated by the external uncertainty on the π0D decay branching fraction. The
reconstructed e+e− invariant mass spectra are displayed in figure 2. In addition to the above individual
K2π and Kμ3 selections, a joint dark photon selection is also considered: an event passes the joint
selection if it passes either the K2π or the Kμ3 selection. The acceptance of the joint selection for any
process is equal to the sum of acceptances of the two mutually exclusive individual selections.
4 The π0 Dalitz simulation
The π0D decay is simulated using the following lowest-order differential decay rate
with x and y, two kinematic variables, defined as
= Γ0 α |F(x)|2 (1 − x)3 1 + y2 +
(q1 + q2)2
= me2e y = 2p(q1 − q2)
m2π0 mπ0 (1 − x)
r = 2me/mπ0 , q1 , q2 and p are the four-momenta of the electrons (e± ) and the neutral pion, Γ0 is the
rate of the π0 → γγ decay, and F(x) is the pion transition form factor (TFF).
Radiative corrections to the differential rate are implemented following the classical approach of
Mikaelian and Smith : the differential decay rate is modified using the following formula
= δ(x, y)
which does not account for the emission of inner bremsstrahlung photons.
The TFF is conventionally parameterized as F(x) = 1 + ax. The transition form factor slope parameter
a is expected from vector meson dominance models to be a 0.03, and detailed theoretical
calculations based on dispersion theory yield a = 0.0307 ± 0.0006 . Experimentally, the PDG average
a = 0.032 ± 0.004 [
] is determined mainly from a e+e− → e+e−π0 rate measurement in the
spacelike region by the CELLO experiment . The precision on the used radiative corrections to the π0
decay is limited: in particular, the missing correction to the measured TFF slope due to two-photon
exchange is estimated to be Δa = +0.005 [
]. Therefore the background description cannot benefit
from the precise inputs on the TFF slope [
], and an “effective” TFF slope obtained from a fit to
the data mee spectrum itself is used to obtain a satisfactory background description (as quantified by
a χ2 test) over the range mee > 8 MeV/c2 used for the dark photon search. The low mee region is
not considered for the search as the acceptance computation is less robust due to the steeply falling
geometrical acceptance at low mee and decreasing electron identification efficiency at low momentum.
5 Search for the dark photon
A scan for a dark photon signal in the mass range 9 MeV/c2 ≤ mA < 120 MeV/c2 is performed. The
lower extent of the considered mass range is determined by the limited precision of MC simulation of
background at low mass, while at the upper limit of the mass range the signal acceptance drops to zero.
The mass step of the scan and the width of the dark photon signal mass window around the assumed
mass are determined by the resolution δmee on the e+e− invariant mass. The resolution on mee as a
function of mee evaluated with MC simulation is parameterized as σm(mee) = 0.067 MeV/c2 + 0.0105 ·
mee, and varies from 0.16 MeV/c2 to 1.33MeV/c2 over the mass range of the scan. The mass step of
the scan is set to be σm/2, while the signal region mass window for each dark photon mass hypothesis
is defined as ±1.5σm around the assumed mass. The mass window width has been optimised with
MC simulations to obtain the highest sensitivity to the dark photon signal, determined by a trade-off
between π0D background fluctuation and signal acceptance.
For each considered dark photon mass value, the number of observed data events Nobs passing the joint
selection is compared to the expected number of background events Nexp. The latter is evaluated from
MC simulations, corrected for the trigger efficiency measured from control data samples passing the
joint selection. The numbers of observed and expected events for each mass value and their estimated
uncertainties δNobs and δNexp are shown in figure 3. The uncertainty δNobs = √Nobs is statistical,
while the uncertainty δNexp has contributions from the limited size of the generated MC samples and
the statistical errors on the trigger efficiencies measured in the dark photon signal region. The local
statistical significance of the dark photon signal for each mass value estimated as
Z = (Nobs − Nexp)/ (δNobs)2 + (δNexp)2
Confidence intervals at 90% CL for the number of A → e+e− decay candidates (NDP ) in each mass
hypothesis are computed from Nobs , Nexp and δNexp using the Rolke–López method  assuming
Poissonian (Gaussian) errors on the numbers of observed (expected) events.
Upper limits at 90% CL on the branching fraction B(π0 → A γ) for each dark photon mass value
with the assumption B(A → e+e−) = 1 (which is a good approximation for mA < 2mμ if A decays to
SM fermions only) are computed using the relation
B(π0 → A γ) =
NK e1e2[B(K2π)ADP(K2π) + B(Kμ3)ADP(Kμ3) + 2B(K3π)ADP(K3π)]
where ADP(K2π), ADP(Kμ3) and ADP(K3π) are the acceptances of the joint dark photon selection for
K2π, Kμ3 and K3π decays, respectively, followed by the prompt π0 → A γ, A → e+e− decay chain. The
trigger efficiencies e1 ane e2 are taken into account neglecting their variations over the mee invariant
mass, variations measured to be at the level of a few permille. Event distributions in the angle between
e+ momentum in the e+e− rest frame and the e+e− momentum in the π0 rest frame are identical for the
decay chain involving the dark photon (π0 → A γ, A → e+e−) and the π0D decay, up to a negligible
effect of the radiative corrections that should not be applied in the former case (found to influence the
acceptance at the level below 1% in relative terms). Therefore dark photon acceptances are evaluated
using the MC samples produced for background description, and no dedicated MC productions are
required. The resulting upper limits on B(π0 → A γ) and signal acceptances are shown in figure 4.
The upper limits are O(10−6) and do not exhibit a strong dependence on the A mass.
Upper limits at 90% CL on the mixing parameter 2 for each dark photon mass value calculated from
the B(π0 → A γ) upper limits using equation 1 are shown in figure 5, together with the constraints
from the SLAC E141 and FNAL E774 , KLOE , WASA , HADES , A1 , APEX
 and BaBar  experiments. Also shown is the band in the (mA , 2) plane where the discrepancy
between the measured and calculated muon (g − 2) values falls into the ±2σ range due to the dark
photon contribution, as well as the region excluded by the electron (g − 2) measurement [
The obtained upper limits on 2 represent an improvement over the existing data in the dark photon
mass range 9 − 70 MeV/c2 , and exclude the whole favoured region by muon g − 2 . The most
stringent limits (2 × 10−7) are achieved at mA ∼ 10 MeV/c2. The sensitivity of the prompt A decay
search is limited by the irreducible π0D background. The achievable upper limit on 2 scales as the
inverse square root of the integrated beam flux, which means that the possible improvements to be
made with this technique using larger future K± samples are modest.
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