Search

The MEG II experiment, based at the Paul Scherrer Institut in Switzerland, reports the result of a search for the decay $\mu^+\to e^+\gamma$ from data taken in the first physics run in 2021. No excess of events over the expected background is observed, yielding an upper limit on the branching ratio of B($\mu^+\to e^+\gamma$) < $7.5 \times 10^{-13}$ (90% C.L.). The combination of this result and the limit obtained by MEG gives B($\mu^+\to e^+\gamma$) < $3.1 \times 10^{-13}$ (90% C.L.), which is the most stringent limit to date. A ten-fold larger sample of data is being collected during the years 2022-2023, and data-taking will continue in the coming years., Comment: 10 pages, 6 figures. To be published in EPJC

The MEG II experiment, located at the Paul Scherrer Institut (PSI) in Switzerland, is the successor to the MEG experiment, which completed data taking in 2013. MEG II started fully operational data taking in 2021, with the goal of improving the sensitivity of the mu+ -> e+ gamma decay down to 6e-14 almost an order of magnitude better than the current limit. In this paper, we describe the operation and performance of the experiment and give a new estimate of its sensitivity versus data acquisition time., Comment: 42 pages, 55 figures. Submitted to EPJC

The HOLMES experiment will perform a precise calorimetric measurement of the end point of the Electron Capture (EC) decay spectrum of 163Ho in order to extract information on neutrino mass with a sensitivity below 2 eV. In its final configuration, HOLMES will deploy 1000 detectors of low-temperature microcalorimeters with implanted 163Ho nuclei. The baseline sensors for HOLMES are Mo/Cu TESs (Transition Edge Sensors) on SiNx membrane with gold absorbers. Considering the large number of pixels and an event rate of about 300 Hz/pixel, a large multiplexing factor and a large bandwidth are needed. To fulfill this requirement, HOLMES will exploit recent advances in microwave multiplexing. In this contribution, we present the status of the activities in development, the performances of the developed microwave-multiplexed readout system, and the results obtained with the detectors specifically designed for HOLMES in terms of noise, time, and energy resolutions

We present a novel technique, called DSVP (Discrimination through Singular Vectors Projections), to discriminate spurious events within a dataset. The purpose of this paper is to lay down a general procedure which can be tailored for a broad variety of applications. After describing the general concept, we apply the algorithm to the problem of identifying nearly coincident events in low temperature microcalorimeters in order to push the time resolution close to its intrinsic limit. In fact, from simulated datasets it was possible to achieve an effective time resolution even shorter than the sampling time of the system considered. The obtained results are contextualized in the framework of the HOLMES experiment, which aims at directly measuring the neutrino mass with the calorimetric approach, allowing to significally improve its statistical sensitivity.

This paper discusses the effects of radiation damage to SiPMs on the performances of plastic scintillator counters with series-connected SiPM readout, focusing on timing measurements. The performances of a counter composed of a $120 \times 40 \times5~\mathrm{mm}^3$ scintillator tile read out by two sets of six SiPMs from AdvanSiD connected in series attached on the short sides are presented, for different combinations of SiPMs at various levels of irradiation. Firstly, six SiPMs were equally irradiated with electrons from $^{90}$Sr sources up to a fluence of $\Phi_\mathrm{e^-}\approx 3 \times 10^{12}~\mathrm{cm}^{-2}$. The timing resolution of the counter gradually deteriorated by the increase in dark current. The dark current and the deterioration were reduced when the counter was cooled from 30$^\circ$C to 10$^\circ$C. Secondly, 33 SiPMs were irradiated with reactor neutrons. The characteristics of counters read out by series-connected SiPMs with non-uniform damage levels, were investigated. The signal pulse height, the time response, and the timing resolution depend on the hit position in the counter, when SiPMs' irradiation is not uniform., Comment: 13 pages, 27 figures, Major revision based on the reviewers' comments

We present the first direct search for lepton flavour violating muon decay mediated by a new light particle X, $\mu^+ \to \mathrm{e}^+\mathrm{X}, \mathrm{X} \to \gamma\gamma$. This search uses a dataset resulting from $7.5\times 10^{14}$ stopped muons collected by the MEG experiment at the Paul Scherrer Institut in the period 2009--2013. No significant excess is found in the mass region 20--45 MeV/c$^2$ for lifetimes below 40 ps, and we set the most stringent branching ratio upper limits in the mass region of 20--40 MeV/c$^2$, down to $\mathcal{O}(10^{-11})$ at 90\% confidence level.

The determination of the neutrino mass is an open issue in modern particle physics and astrophysics. The direct mass measurement is the only theory-unrelated experimental tool capable to probe such quantity. The HOLMES experiment aims to measure the end-point energy of the electron capture (EC) decay of $^{163}$Ho with a statistical sensitivity on the neutrino mass as low as $\sim 1$ eV/c$^2$. In order to acquire the large needed statistics, by keeping the pile-up contribution as low as possible, 1024 transition edge sensors (TESs) with high energy and time resolutions will be employed. Microcalorimeter and bolometer arrays based on transition edge sensor with thousands of pixels are under development for several space-based and ground-based applications, including astrophysics, nuclear and particle physics, and materials science. The common necessary challenge is to develop pratical multiplexing techniques in order to simplify the cryogenics and readout systems. Despite the various multiplexing variants which are being developed have been successful, new approaches are needed to enable scaling to larger pixel counts and faster sensors, as requested for HOLMES, reducing also the cost and complexity of readout. A very novel technique that meets all of these requirements is based on superconducting microwave resonators coupled to radio-frequency Superconducting Quantum Interference Devices, in which the the changes in the TES input current is tranduced to a change in phase of a microwave signal. In this work we introduce the basics of this technique, the design and development of the first two-channel read out system and its performances with the first TES detectors specifically designed for HOLMES. In the last part we explain how to extend this approach scaling to 1024 pixels., Comment: accepted on JINST

We have developed a new laser-based time calibration system for highly segmented scintillator counters like the MEG II pixelated Timing Counter (pTC), consisting of 512-centimeter scale scintillator counters read out by silicon photomultipliers (SiPMs). It is difficult to apply previous laser-based calibration methods for conventional meter-scale Time-Of-Flight detectors to the MEG II pTC from the implementation and the accuracy points of view. This paper presents a new laser-based time calibration system which can overcome such difficulties. A laser pulse is split into each scintillator counter via several optical components so that we can directly measure the time offset of each counter relative to the laser-emitted time. We carefully tested all the components and procedures prior to the actual operation. The laser system was installed into the pTC and thoroughly tested under the real experimental condition. The system showed good stability and being sensitive to any change of timing larger than ~10 ps. Moreover, it showed an uncertainty of 48 ps in the determination of the time offsets, which meets our requirements. The new method provides an example of the implementation of a precise timing alignment for the new type of detectors enabled by the advance of SiPM technology., Comment: 11 pages, 17 figures

We have developed a new laser-based time calibration system for the MEG II timing counter dedicated to timing measurement of positrons. The detector requires precise timing alignment between $\sim\,$500 scintillation counters. In this study, we present the calibration system which can directly measure the time offset of each counter relative to the laser-synchronized pulse. We thoroughly tested all the optical components and the uncertainty of this method is estimated to be 24 ps. In 2017, we installed the full system into the MEG II environment and performed a commissioning run. This method shows excellent stability and consistency with another method. The proposed system provides a precise timing alignment for SiPM-based timing detectors. It also has potential in areas such as TOF-PET., Comment: 3 pages, 3 figures, proceedings of the 2018 IEEE Nuclear Science Symposium and Medical Imaging Conference

The MEG II experiment at Paul Scherrer Institut in Switzerland will search for the lepton flavour violating muon decay, $\mu^+\to e^+\gamma$, with a sensitivity of $4\times10^{-14}$ improving the existing limit of an order of magnitude. In 2016, we finished the construction of the MEG II Timing Counter, the subdetector dedicated to the measurement of the positron emission time. The first one-fourth of it was installed in the experimental area and we performed a pilot run with the MEG~II beam of $7\times10^{7}\mu^+/$s. The timing resolution reached the design value improving by a factor of two compared to MEG., Comment: 4 pages, 2 figures

The assessment of neutrino absolute mass scale is still a crucial challenge in today particle physics and cosmology. Beta or electron capture spectrum end-point study is currently the only experimental method which can provide a model independent measurement of the absolute scale of neutrino mass. HOLMES is an experiment funded by the European Research Council to directly measure the neutrino mass. HOLMES will perform a calorimetric measurement of the energy released in the electron capture decay of the artificial isotope $^{163}$Ho. In a calorimetric measurement the energy released in the decay process is entirely contained into the detector, except for the fraction taken away by the neutrino. This approach eliminates both the issues related to the use of an external source and the systematic uncertainties arising from decays on excited final states. The most suitable detectors for this type of measurement are low temperature thermal detectors, where all the energy released into an absorber is converted into a temperature increase that can be measured by a sensitive thermometer directly coupled with the absorber. This measurement was originally proposed in 1982 by A. De Rujula and M. Lusignoli, but only in the last decade the technological progress in detectors development has allowed to design a sensitive experiment. HOLMES plans to deploy a large array of low temperature microcalorimeters with implanted $^{163}$Ho nuclei. In this contribution we outline the HOLMES project with its physics reach and technical challenges, along with its status and perspectives., Comment: This is a pre-print of an article published in Journal of Low Temperature Physics. The final authenticated version is available online at: https://doi.org/10.1007/s10909-018-2025-x

The MEG experiment, designed to search for the mu+->e+ gamma decay at a 10^-13 sensitivity level, completed data taking in 2013. In order to increase the sensitivity reach of the experiment by an order of magnitude to the level of 6 x 10-14 for the branching ratio, a total upgrade, involving substantial changes to the experiment, has been undertaken, known as MEG II. We present both the motivation for the upgrade and a detailed overview of the design of the experiment and of the expected detector performance., Comment: 61 pages and 97 figures

HOLMES is a new experiment aiming at directly measuring the neutrino mass with a sensitivity below 2 eV. HOLMES will perform a calorimetric measurement of the energy released in the decay of $^{163}$Ho. The calorimetric measurement eliminates systematic uncertainties arising from the use of external beta sources, as in experiments with spectrometers. This measurement was proposed in 1982 by A. De Rujula and M. Lusignoli, but only recently the detector technological progress has allowed to design a sensitive experiment. HOLMES will deploy a large array of low temperature microcalorimeters with implanted $^{163}$Ho nuclei. HOLMES, besides being an important step forward in the direct neutrino mass measurement with a calorimetric approach, will also establish the potential of this approach to extend the sensitivity down to 0.1 eV and lower. In its final configuration HOLMES will collect about $3\cdot 10^{13}$ decays with 1000 detectors characterized by an instrumental energy resolution of the order of few eV and a time resolution of few microseconds. To embed the $^{163}$Ho into the gold absorbers a custom mass separator ion implanter is being developed. The detectors used for the HOLMES experiment will be Mo/Cu bilayers TESs (Transition Edge Sensors) on SiN$_x$ membrane with gold absorbers. Microwave multiplexed rf-SQUIDs are the best available technique to read out large array of such detectors. An extensive R&D activity is in progress in order to maximize the multiplexing factor while preserving the performances of the individual detectors. The current activities are focused on the the single detector performances optimization and on the $^{163}$Ho isotope production and embedding. A preliminary measurement of a sub-array of $4\times 16$ detectors is planned late in 2017. In this contribution we present the HOLMES project with its technical challenges, its status and perspectives.

A new timing detector measuring ~50 MeV/c positrons is under development for the MEG II experiment, aiming at a time resolution $\sigma_t \sim 30~\mathrm{ps}$. The resolution is expected to be achieved by measuring each positron time with multiple counters made of plastic scintillator readout by silicon photomultipliers (SiPMs). The purpose of this work is to demonstrate the time resolution for ~50 MeV/c positrons using prototype counters. Counters with dimensions of $90\times 40\times 5~\mathrm{mm}^3$ readout by six SiPMs (three on each $40\times 5~\mathrm{mm}^2$ plane) were built with SiPMs from Hamamatsu Photonics and AdvanSiD and tested in a positron beam at the DA$\Phi$NE Beam Test Facility. The time resolution was found to improve nearly as the square root of the number of counter hits. A time resolution $\sigma_t=26.2\pm1.3~\mathrm{ps}$ was obtained with eight counters with Hamamatsu SiPMs. These results suggest that the design resolution is achievable in the MEG II experiment., Comment: 12 pages, 18 figures. Published in NIM A

The MEG experiment makes use of one of the world's most intense low energy muon beams, in order to search for the lepton flavour violating process $\mu^{+} \rightarrow {\rm e}^{+} \gamma$. We determined the residual beam polarization at the thin stopping target, by measuring the asymmetry of the angular distribution of Michel decay positrons as a function of energy. The initial muon beam polarization at the production is predicted to be $P_{\mu} = -1$ by the Standard Model (SM) with massless neutrinos. We estimated our residual muon polarization to be $P_{\mu} = -0.85 \pm 0.03 ~ {\rm (stat)} ~ { }^{+ 0.04}_{-0.05} ~ {\rm (syst)}$ at the stopping target, which is consistent with the SM predictions when the depolarizing effects occurring during the muon production, propagation and moderation in the target are taken into account. The knowledge of beam polarization is of fundamental importance in order to model the background of our ${\megsign}$ search induced by the muon radiative decay: $\mu^{+} \rightarrow {\rm e}^{+} \bar{\nu}_{\mu} \nu_{\rm e} \gamma$.

The European Research Council has recently funded HOLMES, a new experiment to directly measure the neutrino mass. HOLMES will perform a calorimetric measurement of the energy released in the decay of 163Ho. The calorimetric measurement eliminates systematic uncertainties arising from the use of external beta sources, as in experiments with beta spectrometers. This measurement was proposed in 1982 by A. De Rujula and M. Lusignoli, but only recently the detector technological progress allowed to design a sensitive experiment. HOLMES will deploy a large array of low temperature microcalorimeters with implanted 163Ho nuclei. The resulting mass sensitivity will be as low as 0.4 eV. HOLMES will be an important step forward in the direct neutrino mass measurement with a calorimetric approach as an alternative to spectrometry. It will also establish the potential of this approach to extend the sensitivity down to 0.1 eV. We outline here the project with its technical challenges and perspectives., Comment: 11 pages, 9 figures

We studied the radiative muon decay $\mu^+ \to e^+\nu\bar{\nu}\gamma$ by using for the first time an almost fully polarized muon source. We identified a large sample (~13000) of these decays in a total sample of 1.8x10^14 positive muon decays collected in the MEG experiment in the years 2009--2010 and measured the branching ratio B($\mu^+ \to e^+\nu\bar{\nu}\gamma$) = (6.03+-0.14(stat.)+-0.53(sys.))x10^-8 for E_e > 45 MeV and E_{\gamma} > 40 MeV, consistent with the Standard Model prediction. The precise measurement of this decay mode provides a basic tool for the timing calibration, a normalization channel, and a strong quality check of the complete MEG experiment in the search for $\mu^+ \to e^+\gamma$ process., Comment: 8 pages, 7 figures. Added an introduction to NLO calculation which was recently calculated. Published version

The design and tests of Timing Counter elements for the upgrade of the MEG experiment, MEG II,is presented. The detector is based on several small plates of scintillator with a Silicon PhotoMultipliers dual-side readout. The optimisation of the single counter elements (SiPMs, scintillators, geometry) is described. Moreover, the results obtained with a first prototype tested at the Beam Test Facility (BTF) of the INFN Laboratori Nazionali di Frascati (LNF) are presented., Comment: 10 pages, 7 figures. Presented at the 13th Topical Seminar on Innovative Particle and Radiation Detectors (IPRD13) 7-10 October 2013 Siena, Italy

The Athena+ mission concept is designed to implement the Hot and Energetic Universe science theme submitted to the European Space Agency in response to the call for White Papers for the definition of the L2 and L3 missions of its science program. The Athena+ science payload consists of a large aperture high angular resolution X-ray optics and twelve meters away, two interchangeable focal plane instruments: the X-ray Integral Field Unit (X-IFU) and the Wide Field Imager (WFI). The X-IFU is a cryogenic X-ray spectrometer, based on a large array of Transition Edge Sensors (TES), offering 2.5 eV spectral resolution, with ~5" pixels, over a field of view of 5 arc minutes in diameter. In this paper, we briefly describe the Athena+ mission concept and the X-IFU performance requirements. We then present the X-IFU detector and readout electronics principles, the current design of the focal plane assembly, the cooling chain and review the global architecture design. Finally, we describe the current performance estimates, in terms of effective area, particle background rejection, count rate capability and velocity measurements. Finally, we emphasize on the latest technology developments concerning TES array fabrication, spectral resolution and readout performance achieved to show that significant progresses are being accomplished towards the demanding X-IFU requirements., Comment: Supporting paper for the science theme "The Hot and Energetic Universe" to be implemented by the Athena+ X-ray observatory (http://www.the-athena-x-ray-observatory.eu). 17 pages, 19 figures

The MEG (Mu to Electron Gamma) experiment has been running at the Paul Scherrer Institut (PSI), Switzerland since 2008 to search for the decay \meg\ by using one of the most intense continuous $\mu^+$ beams in the world. This paper presents the MEG components: the positron spectrometer, including a thin target, a superconducting magnet, a set of drift chambers for measuring the muon decay vertex and the positron momentum, a timing counter for measuring the positron time, and a liquid xenon detector for measuring the photon energy, position and time. The trigger system, the read-out electronics and the data acquisition system are also presented in detail. The paper is completed with a description of the equipment and techniques developed for the calibration in time and energy and the simulation of the whole apparatus., Comment: 59 pages, 90 figures

The analysis of a combined data set, totaling 3.6 \times 10^14 stopped muons on target, in the search for the lepton flavour violating decay mu^+ -> e^+ gamma is presented. The data collected by the MEG experiment at the Paul Scherrer Institut show no excess of events compared to background expectations and yield a new upper limit on the branching ratio of this decay of 5.7 \times 10^-13 (90% confidence level). This represents a four times more stringent limit than the previous world best limit set by MEG., Comment: 5 pages, 3 figures, a version accepted in Phys. Rev. Lett

We propose the continuation of the MEG experiment to search for the charged lepton flavour violating decay (cLFV) \mu \to e \gamma, based on an upgrade of the experiment, which aims for a sensitivity enhancement of one order of magnitude compared to the final MEG result, down to the $6 \times 10^{-14}$ level. The key features of this new MEG upgrade are an increased rate capability of all detectors to enable running at the intensity frontier and improved energy, angular and timing resolutions, for both the positron and photon arms of the detector. On the positron-side a new low-mass, single volume, high granularity tracker is envisaged, in combination with a new highly segmented, fast timing counter array, to track positron from a thinner stopping target. The photon-arm, with the largest liquid xenon (LXe) detector in the world, totalling 900 l, will also be improved by increasing the granularity at the incident face, by replacing the current photomultiplier tubes (PMTs) with a larger number of smaller photosensors and optimizing the photosensor layout also on the lateral faces. A new DAQ scheme involving the implementation of a new combined readout board capable of integrating the diverse functions of digitization, trigger capability and splitter functionality into one condensed unit, is also under development. We describe here the status of the MEG experiment, the scientific merits of the upgrade and the experimental methods we plan to use., Comment: A. M. Baldini and T. Mori Spokespersons. Research proposal submitted to the Paul Scherrer Institute Research Committee for Particle Physics at the Ring Cyclotron. 131 Pages

A new experiment with an intense ~2 GeV neutrino beam at CERN SPS is proposed in order to definitely clarify the possible existence of additional neutrino states, as pointed out by neutrino calibration source experiments, reactor and accelerator experiments and measure the corresponding oscillation parameters. The experiment is based on two identical LAr-TPCs complemented by magnetized spectrometers detecting electron and muon neutrino events at Far and Near positions, 1600 m and 300 m from the proton target, respectively. The ICARUS T600 detector, the largest LAr-TPC ever built with a size of about 600 ton of imaging mass, now running in the LNGS underground laboratory, will be moved at the CERN Far position. An additional 1/4 of the T600 detector (T150) will be constructed and located in the Near position. Two large area spectrometers will be placed downstream of the two LAr-TPC detectors to perform charge identification and muon momentum measurements from sub-GeV to several GeV energy range, greatly complementing the physics capabilities. This experiment will offer remarkable discovery potentialities, collecting a very large number of unbiased events both in the neutrino and antineutrino channels, largely adequate to definitely settle the origin of the observed neutrino-related anomalies., Comment: Contribution to the European Strategy for Particle Physics - Open Symposium Preparatory Group, Kracow 10-12 September 2012

This proposal describes an experimental search for sterile neutrinos beyond the Standard Model with a new CERN-SPS neutrino beam. The experiment is based on two identical LAr-TPC's followed by magnetized spectrometers, observing the electron and muon neutrino events at 1600 and 300 m from the proton target. This project will exploit the ICARUS T600, moved from LNGS to the CERN "Far" position. An additional 1/4 of the T600 detector will be constructed and located in the "Near" position. Two spectrometers will be placed downstream of the two LAr-TPC detectors to greatly complement the physics capabilities. Spectrometers will exploit a classical dipole magnetic field with iron slabs, and a new concept air-magnet, to perform charge identification and muon momentum measurements in a wide energy range over a large transverse area. In the two positions, the radial and energy spectra of the nu_e beam are practically identical. Comparing the two detectors, in absence of oscillations, all cross sections and experimental biases cancel out, and the two experimentally observed event distributions must be identical. Any difference of the event distributions at the locations of the two detectors might be attributed to the possible existence of {\nu}-oscillations, presumably due to additional neutrinos with a mixing angle sin^2(2theta_new) and a larger mass difference Delta_m^2_new. The superior quality of the LAr imaging TPC, in particular its unique electron-pi_zero discrimination allows full rejection of backgrounds and offers a lossless nu_e detection capability. The determination of the muon charge with the spectrometers allows the full separation of nu_mu from anti-nu_mu and therefore controlling systematics from muon mis-identification largely at high momenta., Comment: Experiment proposal

The Timing Counter of the MEG (Mu to Electron Gamma) experiment is designed to deliver trigger information and to accurately measure the timing of the $e^+$ in searching for the decay $\mu^+ \rightarrow e^+\gamma$. It is part of a magnetic spectrometer with the $\mu^+$ decay target in the center. It consists of two sectors upstream and downstream the target, each one with two layers: the inner one made with scintillating fibers read out by APDs for trigger and track reconstruction, the outer one consisting in scintillating bars read out by PMTs for trigger and time measurement. The design criteria, the obtained performances and the commissioning of the detector are presented herein., Comment: 10 pages, 20 figures. Presented at the IEEE Nuclear Science Symposium 2010, Knoxville, TN, USA. Accepted by IEEE Transaction on Nuclear Science

I report on the research status and the perspectives of the Lepton Flavor Violating decays {\mu}{\to}e{\gamma} and {\mu}{\to}eee. In particular, I will concentrate on the {\mu}{\to}e{\gamma} decay and the preliminary results obtained from the analysis of the 2009 data collected by the MEG experiment., Comment: Presented at The Ninth International Conference on Flavor Physics and CP Violation FPCP2011

We present a new result based on an analysis of the data collected by the MEG detector at the Paul Scherrer Institut in 2009 and 2010, in search of the lepton flavour violating decay mu->e gamma. The likelihood analysis of the combined data sample, which corresponds to a total of 1.8 x 10**14 muon decays, gives a 90% C.L. upper limit of 2.4 x 10**-12 on the branching ratio of the mu->e gamma decay, constituting the most stringent limit on the existence of this decay to date., Comment: 5 pages, 2 figures, accepted for publication at Phys. Rev. Lett

The MEG detector is designed to test Lepton Flavor Violation in the $\mu^+\rightarrow e^+\gamma$ decay down to a Branching Ratio of a few $10^{-13}$. The decay topology consists in the coincident emission of a monochromatic photon in direction opposite to a monochromatic positron. A precise measurement of the relative time $t_{e^+\gamma}$ is crucial to suppress the background. The Timing Counter (TC) is designed to precisely measure the time of arrival of the $e^+$ and to provide information to the trigger system. It consists of two sectors up and down stream the decay target, each consisting of two layers. The outer one made of scintillating bars and the inner one of scintillating fibers. Their design criteria and performances are described., Comment: Presented at the 12th Topical Seminar on Innovative Particle and Radiation Detectors (IPRD10) 7 - 10 June 2010, Siena. Accepted by Nuclear Physics B (Proceedings Supplements) (2011)taly

A search for the decay mu -> e gamma, performed at PSI and based on data from the initial three months of operation of the MEG experiment, yields an upper limit on the branching ratio of BR(mu -> e gamma) < 2.8 x 10**-11 (90% C.L.). This corresponds to the measurement of positrons and photons from ~ 10**14 stopped mu-decays by means of a superconducting positron spectrometer and a 900 litre liquid xenon photon detector., Comment: 13 pages, 9 figures. v2: improved estimate of photon reconstruction efficiency