0000000000216795
AUTHOR
G. Lamanna
The data acquisition system for the ANTARES neutrino telescope
The ANTARES neutrino telescope is being constructed in the Mediterranean Sea. It consists of a large three-dimensional array of photo-multiplier tubes. The data acquisition system of the detector takes care of the digitisation of the photo-multiplier tube signals, data transport, data filtering, and data storage. The detector is operated using a control program interfaced with all elements. The design and the implementation of the data acquisition system are described.
Precision measurement of the ratio BR(KS→π+π−e+e−)/BR(KL→π+π−πD0)
Abstract The K S → π + π − e + e − decay mode was investigated using the data collected in 2002 by the NA48/1 Collaboration. With about 23 k K S → π + π − e + e − events and 59 k K L → π + π − π D 0 normalization decays, the K S → π + π − e + e − branching ratio relative to the K L → π + π − π D 0 one was determined to be BR ( K S → π + π − e + e − ) / BR ( K L → π + π − π D 0 ) = ( 3.28 ± 0.06 stat ± 0.04 syst ) × 10 − 2 . This result was used to set the upper limit | g E1 / g BR | 3.0 at 90% CL on the presence, in the decay amplitude, of an E1 direct emission ( g E1 ) term relative to the dominant inner bremsstrahlung ( g BR ) term. The CP-violating asymmetry A ϕ in the sin ϕ cos ϕ distri…
Search for heavy neutrinos at the NA48/2 and NA62 experiments at CERN
© The Authors, published by EDP Sciences. The NA48/2 experiment at CERN has collected large samples of charged kaons decaying into a pion and two muons for the search of heavy nuetrinos. In addition, its successor NA62 has set new limits on the rate of charged kaon decay into a heavy neutral lepton (HNL) and a lepton, with = e, µ, using the data collected in 2007 and 2015. New limits on heavy neutrinos from kaon decays into pions, muons and positrons are presented in this report.
Empirical parameterization of the K±→π±π0π0 decay Dalitz plot
As first observed by the NA48/2 experiment at the CERN SPS, the π0π0 invariant mass (M00) distribution from K±→π±π0π0 decay shows a cusp-like anomaly at M00=2m+, where m+ is the charged pion mass. An analysis to extract the ππ scattering lengths in the isospin I=0 and I=2 states, a0 and a2, respectively, has been recently reported. In the present work the Dalitz plot of this decay is fitted to a new empirical parameterization suitable for practical purposes, such as Monte Carlo simulations of K±→π±π0π0 decays.
A new measurement of the K±→π±γγ decay at the NA48/2 experiment
Abstract The NA48/2 experiment at CERN collected two data samples with minimum bias trigger conditions in 2003 and 2004. A measurement of the rate and dynamic properties of the rare decay K ± → π ± γ γ from these data sets based on 149 decay candidates with an estimated background of 15.5 ± 0.7 events is reported. The model-independent branching ratio in the kinematic range z = ( m γ γ / m K ) 2 > 0.2 is measured to be B MI ( z > 0.2 ) = ( 0.877 ± 0.089 ) × 10 − 6 , and the branching ratio in the full kinematic range assuming a particular Chiral Perturbation Theory description to be B ( K π γ γ ) = ( 0.910 ± 0.075 ) × 10 − 6 .
The ANTARES Optical Beacon System
ANTARES is a neutrino telescope being deployed in the Mediterranean Sea. It consists of a three dimensional array of photomultiplier tubes that can detect the Cherenkov light induced by charged particles produced in the interactions of neutrinos with the surrounding medium. High angular resolution can be achieved, in particular when a muon is produced, provided that the Cherenkov photons are detected with sufficient timing precision. Considerations of the intrinsic time uncertainties stemming from the transit time spread in the photomultiplier tubes and the mechanism of transmission of light in sea water lead to the conclusion that a relative time accuracy of the order of 0.5 ns is desirabl…
Measurement of the branching ratios of the decays Ξ0→Σ+e−ν¯e and Ξ0¯→Σ+¯e+νe
Abstract From 56 days of data taking in 2002, the NA48/1 experiment observed 6316 Ξ 0 → Σ + e − ν ¯ e candidates (with the subsequent Σ + → p π 0 decay) and 555 Ξ 0 ¯ → Σ + ¯ e + ν e candidates with background contamination of 215 ± 44 and 136 ± 8 events, respectively. From these samples, the branching ratios BR ( Ξ 0 → Σ + e − ν ¯ e ) = ( 2.51 ± 0.03 stat ± 0.09 syst ) × 10 −4 and BR ( Ξ 0 ¯ → Σ + ¯ e + ν e ) = ( 2.55 ± 0.14 stat ± 0.10 syst ) × 10 −4 were measured allowing the determination of the CKM matrix element | V us | = 0.209 −0.028 +0.023 . Using the Particle Data Group average for | V us | obtained in semileptonic kaon decays, we measured the ratio g 1 / f 1 = 1.20 ± 0.05 of the …
Observation of the rare decay K-S -> pi(0)e(+)e(-)
A search for the decay Ks->pi0e+e- has been made by the NA48/1 experiment at the CERN SPS accelerator. Using data collected during 89 days in 2002 with a high-intensity Ks beam, 7 events were found with a background of 0.15 events. The branching fraction BR(Ks->pi0e+e-, m(ee) > 0.165 GeV/c^2) = (3.0^{+1.5}_{-1.2}(stat) +/-0.2 (syst)) x 10^{-9} has been measured. Using a vector matrix element and a form factor equal to one, the measurement gives BR(Ks->pi0e+e-) = (5.8^{+2.9}_{-2.4}) x 10^{-9}.
Searches for lepton number violating $K^+$ decays
The NA62 experiment at CERN reports a search for the lepton number violating decays K+ -> pi(-)e(+)e(+) and K+ -> pi(-)mu(+)mu(+) using a data sample collected in 2017. No signals are observed, and upper limits on the branching fractions of these decays of 2.2 x 10(-10) and 4.2 x 10(-11) are obtained, respectively, at 90% confidence level. These upper limits improve on previously reported measurements by factors of 3 and 2, respectively.
Search for heavy neutrinos in K + → μ + ν μ decays
The NA62 experiment recorded a large sample of K+→μ+νμ decays in 2007. A peak search has been performed in the reconstructed missing mass spectrum. In the absence of a signal, limits in the range 2×10−6 to 10−5 have been set on the squared mixing matrix element |Uμ4|2 between muon and heavy neutrino states, for heavy neutrino masses in the range 300–375 MeV/ c2 . The result extends the range of masses for which upper limits have been set on the value of |Uμ4|2 in previous production search experiments.
First results of the Instrumentation Line for the deep-sea ANTARES neutrino telescope
In 2005, the ANTARES Collaboration deployed and operated at a depth of 2500 m a so-called Mini Instrumentation Line equipped with Optical Modules (MILOM) at the ANTARES site. The various data acquired during the continuous operation from April to December 2005 of the MILOM confirm the satisfactory performance of the Optical Modules, their front-end electronics and readout system, as well as the calibration devices of the detector. The in-situ measurement of the Optical Module time response yields a resolution better than 0.5 ns. The performance of the acoustic positioning system, which enables the spatial reconstruction of the ANTARES detector with a precision of about 10 cm, is verified. T…
Search for direct CP violation in the decays K-+/- -> 3 pi(+/-)
Abstract We report a measurement of the direct CP violation asymmetry parameter A g in charged kaon decays K ± → π ± π + π − by the NA48/2 experiment at the CERN SPS. The experiment has been designed not to be limited by systematics in the asymmetry measurement. Using 1.67 × 10 9 such decays collected during the 2003 run, the charge asymmetry in the Dalitz plot linear slope parameter g has been measured to be A g = ( 1.7 ± 2.9 ) × 10 −4 . The precision of the result is limited by the statistics used.
Measurement of the KL→e+e−e+e− decay rate
Abstract The decay rate of the long-lived neutral K meson into the e + e − e + e − final state has been measured with the NA48 detector at the CERN SPS. Using data collected in 1998 and 1999, a total of 200 events has been observed with negligible background. This observation corresponds to a branching ratio of Br ( K L → e + e − e + e − ) = ( 3.30 ± 0.24 stat ± 0.23 syst ± 0.10 norm ) × 10 −8 .
Search for heavy neutral lepton production in K+ decays to positrons
A search for heavy neutral lepton ($N$) production in $K^+\to e^+N$ decays using the data sample collected by the NA62 experiment at CERN in 2017--2018 is reported. Upper limits of the extended neutrino mixing matrix element $|U_{e4}|^2$ are established at the level of $10^{-9}$ over most of the accessible heavy neutral lepton mass range 144--462 MeV/$c^2$, with the assumption that the lifetime exceeds 50 ns. These limits improve significantly upon those of previous production and decay searches. The $|U_{e4}|^2$ range favoured by Big Bang Nucleosynthesis is excluded up to a mass of about 340 MeV/$c^2$.
A measurement of the CP-conserving component of the decay KS0→π+π−π0
Abstract The NA48 Collaboration has measured the amplitude of the CP-conserving component of the decay K S 0 → π + π − π 0 relative to K L 0 → π + π − π 0 . For the characteristic parameter λ , the values Re λ = 0.038 ± 0.010 and Im λ = − 0.013 ± 0.007 have been extracted. These values agree with earlier measurements and with theoretical predictions from chiral perturbation theory.
First observation and branching fraction and decay parameter measurements of the weak radiative decay Xi0 -> Lambda e+ e-
The weak radiative decay Xi0 --> Lambda e+e- has been detected for the first time. We find 412 candidates in the signal region, with an estimated background of 15 +/- 5 events. We determine the branching fraction B(Xi0 --> Lambda e+e-) = [7.6 +/- 0.4(stat) +/- 0.4(syst) +/- 0.2(norm)] x 10^{-6}, consistent with an internal bremsstrahlung process, and the decay asymmetry parameter alpha_{XiLambdaee} = -0.8 +/- 0.2, consistent with that of Xi0 --> Lambda gamma. The charge conjugate reaction Xi0_bar --> Lambda_bar e+e- has also been observed.
Measurement of the branching ratio of the decay Ξ0→Σ+μ−ν¯μ
Abstract From the 2002 data taking with a neutral kaon beam extracted from the CERN-SPS, the NA48/1 experiment observed 97 Ξ 0 → Σ + μ − ν ¯ μ candidates with a background contamination of 30.8 ± 4.2 events. From this sample, the BR ( Ξ 0 → Σ + μ − ν ¯ μ ) is measured to be ( 2.17 ± 0.32 stat ± 0.17 syst ) × 10 − 6 .
First observation and measurement of the decay K±→π±e+e−γ
Abstract Using the full data set of the NA48/2 experiment, the decay K ± → π ± e + e − γ is observed for the first time, selecting 120 candidates with 7.3 ± 1.7 estimated background events. With K ± → π ± π D 0 as normalisation channel, the branching ratio is determined in a model-independent way to be Br ( K ± → π ± e + e − γ , m e e γ > 260 MeV / c 2 ) = ( 1.19 ± 0.12 stat ± 0.04 syst ) × 10 −8 . This measured value and the spectrum of the e + e − γ invariant mass allow a comparison with predictions of chiral perturbation theory.
First observation and study of the K± → π±π0e+e− decay
The NA48/2 experiment at CERN reports the first observation of the K-+/- -> pi(+/-)pi(0)e(+)e(-) decay from an exposure of 1.7 x 10(11) charged kaon decays recorded in 2003-2004. A sample of 4919 candidates with 4.9% background contamination allows the determination of the branching ratio in the full kinematic region, BR(K-+/- -> pi(+/-)pi(0)e(+)e(-)) = (4.24 +/- 0.14) x 10(-6). The study of the kinematic space shows evidence for a structure dependent contribution in agreement with predictions based on chiral perturbation theory. Several P- and CP-violating asymmetries are also evaluated.
Search for K+→ π+νν¯ at NA62
Flavour physics is one of the most powerful fields for the search of new physics beyond the Standard Model. The kaon sector with the rare decay K+ → π+νν̅ provides one of the cleanest and most promising channels. NA62, a fixed target experiment at the CERN SPS, aims to measure BR (K+ → π+νν̅) with 10% precision to test the Standard Model validity up to an energy scale of hundreds of TeV. NA62 had dedicated data taking for the K+ → π+νν̅ measurement in 2016 and 2017 and will continue in 2018. Here preliminary results on a fraction of 2016 dataset are presented. The analysis of the complete 2016 data sample is expected to achieve the SM sensitivity.
NA48/62 latest results
The NA62 experiment at the CERN SPS recorded in 2007 a large sample of K+ ? µ+?µ decays. A peak search in the missing mass spectrum of this decay is performed. In the absence of observed signal, the limits obtained on B(K+ ? µ+?h) and on the mixing matrix element |Uµ 4| are reported. The upgraded NA62 experiment started data taking in 2015. About 5×1011K+ decays have been recorded so far to measure the branching ratio of the K+ ? ?+?? decay. Preliminary results from the K+ ? ?+?? analysis based on about 5% of the 2016 statistics are reported.
Sensitivity of the Cherenkov Telescope Array for probing cosmology and fundamental physics with gamma-ray propagation
Full list of authors: Abdalla, H.; Abe, H.; Acero, F.; Acharyya, A.; Adam, R.; Agudo, I; Aguirre-Santaella, A.; Alfaro, R.; Alfaro, J.; Alispach, C.; Aloisio, R.; Batista, R. Alves; Amati, L.; Amato, E.; Ambrosi, G.; Anguner, E. O.; Araudo, A.; Armstrong, T.; Arqueros, F.; Arrabito, L.; Asano, K.; Ascasibar, Y.; Ashley, M.; Backes, M.; Balazs, C.; Balbo, M.; Balmaverde, B.; Baquero Larriva, A.; Martins, V. Barbosa; Barkov, M.; Baroncelli, L.; de Almeida, U. Barres; Barrio, J. A.; Batista, P-, I; Becerra Gonzalez, J.; Becherini, Y.; Beck, G.; Tjus, J. Becker; Belmont, R.; Benbow, W.; Bernardini, E.; Berti, A.; Berton, M.; Bertucci, B.; Beshley, V; Bi, B.; Biasuzzi, B.; Biland, A.; Bissaldi, …
Design of the online PC farm for the high level trigger of the NA62 experiment at CERN
We present a highly efficient data processing framework optimized for software based triggers of fixed-target HEP experiments with continuous data collection during burst time alternating with longer out-of-burst periods.
Search for the dark photon in π0 decays
A sample of $1.69\times 10^7$ fully reconstructed $\pi^0\to\gamma e^+e^-$ decay candidates collected by the NA48/2 experiment at CERN in 2003--2004 is analysed to search for the dark photon ($A'$) production in the $\pi^0\to\gamma A'$ decay followed by the prompt $A'\to e^+e^-$ decay. No signal is observed, and an exclusion region in the plane of the dark photon mass $m_{A'}$ and mixing parameter $\varepsilon^2$ is established. The obtained upper limits on $\varepsilon^2$ are more stringent than the previous limits in the mass range $9~{\rm MeV}/c^2<m_{A'}<70~{\rm MeV}/c^2$. The NA48/2 sensitivity to the dark photon production in the $K^\pm\to\pi^\pm A'$ decay is also evaluated.
New measurement of the K±→π±μ+μ− decay
Abstract A sample of 3120 K ± → π ± μ + μ − decay candidates with ( 3.3 ± 0.7 ) % background contamination has been collected by the NA48/2 experiment at the CERN SPS, allowing a detailed study of the decay properties. The branching ratio was measured to be BR = ( 9.62 ± 0.25 ) × 10 − 8 . The form factor W ( z ) , where z = ( M μ μ / M K ) 2 , was parameterized according to several models. In particular, the slope of the linear form factor W ( z ) = W 0 ( 1 + δ z ) was measured to be δ = 3.11 ± 0.57 . Upper limits of 2.9 × 10 − 2 and 2.3 × 10 − 2 on possible charge asymmetry and forward–backward asymmetry were established at 90% CL. An upper limit BR ( K ± → π ∓ μ ± μ ± ) 1.1 × 10 − 9 was e…
Measurement of the polarization of the Ξ0 (Ξ0¯) hyperon beam by the NA48/1 experiment
Abstract A total of 368 415 Ξ 0 → Λ π 0 and 31 171 Ξ 0 ¯ → Λ ¯ π 0 were selected from data recorded in the NA48/1 experiment during 2002 data taking. From this sample, the polarization of Ξ 0 and Ξ 0 ¯ hyperons was measured to be P Ξ 0 = − 0.102 ± 0.012 (stat) ± 0.008 (syst) and P Ξ 0 ¯ = − 0.01 ± 0.04 (stat) ± 0.008 (syst) . The dependence of P Ξ 0 on the Ξ 0 transverse momentum with respect to the primary proton beam is also presented. With the same data sample, the ratio of Ξ 0 ¯ and Ξ 0 fluxes in proton collisions at 400 GeV / c on a beryllium target was measured.
New precise measurements of the and decay asymmetries
Abstract The decay asymmetries of the weak radiative hyperon decays Ξ 0 → Λ γ and Ξ 0 → Σ 0 γ have been measured with high precision using data of the NA48/1 experiment at CERN. From about 52 000 Ξ 0 → Λ γ and 15 000 Ξ 0 → Σ 0 γ decays, we obtain for the decay asymmetries α Ξ 0 → Λ γ = − 0.704 ± 0.019 stat ± 0.064 syst and α Ξ 0 → Σ 0 γ = − 0.729 ± 0.030 stat ± 0.076 syst , respectively. These results are in good agreement with previous experiments, but more precise.
Search for heavy neutral lepton production in K+ decays
A search for heavy neutral lepton production in $K^+$ decays using a data sample collected with a minimum bias trigger by the NA62 experiment at CERN in 2015 is reported. Upper limits at the $10^{-7}$ to $10^{-6}$ level are established on the elements of the extended neutrino mixing matrix $|U_{\ell 4}|^2$ ($\ell=e,\mu$) for heavy neutral lepton mass in the range $170-448~{\rm MeV}/c^2$. This improves on the results from previous production searches in $K^+$ decays, setting more stringent limits and extending the mass range.
Sensitivity of the Cherenkov Telescope Array to a dark matter signal from the Galactic centre
Full list of authors: Acharyya, A.; Adam, R.; Adams, C.; Agudo, I.; Aguirre-Santaella, A.; Alfaro, R.; Alfaro, J.; Alispach, C.; Aloisio, R.; Alves Batista, R.; Amati, L.; Ambrosi, G.; Angüner, E. O.; Antonelli, L. A.; Aramo, C.; Araudo, A.; Armstrong, T.; Arqueros, F.; Asano, K.; Ascasíbar, Y. Ashley, M.; Balazs, C.; Ballester, O.; Baquero Larriva, A.; Barbosa Martins, V.; Barkov, M.; Barres de Almeida, U.; Barrio, J. A.; Bastieri, D.; Becerra, J.; Beck, G.; Becker Tjus, J.; Benbow, W.; Benito, M.; Berge, D.; Bernardini, E.; Bernlöhr, K.; Berti, A.; Bertucci, B.; Beshley, V.; Biasuzzi, B.; Biland, A.; Bissaldi, E.; Biteau, J.; Blanch, O.; Blazek, J.; Bocchino, F.; Boisson, C.; Bonneau Arbe…
Search for direct CP-violation in K±→π±π0π0 decays
Abstract A search for direct CP-violation in K ± → π ± π 0 π 0 decay based on 47.14 million events has been performed by the NA48/2 experiment at the CERN SPS. The asymmetry in the Dalitz plot linear slopes A g = ( g + − g − ) / ( g + + g − ) is measured to be A g = ( 1.8 ± 2.6 ) × 10 −4 . The design of the experiment and the method of analysis provide good control of instrumental charge asymmetries in this measurement. The precision of the result is limited by statistics and is almost one order of magnitude better than that of previous measurements by other experiments.
Search for Lepton Number and Flavor Violation in K+ and π0 Decays
Searches for the lepton number violating $K^{+} \rightarrow \pi^{-} \mu^{+} e^{+}$ decay and the lepton flavour violating $K^{+} \rightarrow \pi^{+} \mu^{-} e^{+}$ and $\pi^{0} \rightarrow \mu^{-} e^{+}$ decays are reported using data collected by the NA62 experiment at CERN in $2017$-$2018$. No evidence for these decays is found and upper limits of the branching ratios are obtained at 90% confidence level: $\mathcal{B}(K^{+}\rightarrow\pi^{-}\mu^{+}e^{+})<4.2\times 10^{-11}$, $\mathcal{B}(K^{+}\rightarrow\pi^{+}\mu^{-}e^{+})<6.6\times10^{-11}$ and $\mathcal{B}(\pi^{0}\rightarrow\mu^{-}e^{+})<3.2\times 10^{-10}$. These results improve by one order of magnitude over previous results for thes…
Study of the K±→π±γγ decay by the NA62 experiment
Abstract A study of the dynamics of the rare decay K ± → π ± γ γ has been performed on a sample of 232 decay candidates, with an estimated background of 17.4 ± 1.1 events, collected by the NA62 experiment at CERN in 2007. The results are combined with those from a measurement conducted by the NA48/2 Collaboration at CERN. The combined model-independent branching ratio in the kinematic range z = ( m γ γ / m K ) 2 > 0.2 is B MI ( z > 0.2 ) = ( 0.965 ± 0.063 ) × 10 − 6 , and the combined branching ratio in the full kinematic range assuming a Chiral Perturbation Theory description is B ( K π γ γ ) = ( 1.003 ± 0.056 ) × 10 − 6 . A detailed comparison of the results with the previous measurements…
Test of lepton flavour universality in K+→ℓ+ν decays
Abstract A precision test of lepton flavour universality has been performed by measuring the ratio R K of kaon leptonic decay rates K + → e + ν and K + → μ + ν in a sample of 59 813 reconstructed K + → e + ν candidates with ( 8.71 ± 0.24 ) % background contamination. The result R K = ( 2.487 ± 0.013 ) × 10 − 5 is in agreement with the Standard Model expectation.
Broadband Multi-wavelength Properties of M87 during the 2017 Event Horizon Telescope Campaign
Full list of authors: EHT MWL Science Working Group; Algaba, J. C.; Anczarski, J.; Asada, K.; Baloković, M.; Chandra, S.; Cui, Y. -Z.; Falcone, A. D.; Giroletti, M.; Goddi, C.; Hada, K.; Haggard, D.; Jorstad, S.; Kaur, A.; Kawashima, T.; Keating, G.; Kim, J. -Y.; Kino, M.; Komossa, S.; Kravchenko, E. V.; Krichbaum, T. P.; Lee, S. -S.; Lu, R. -S.; Lucchini, M.; Markoff, S.; Neilsen, J.; Nowak, M. A.; Park, J.; Principe, G.; Ramakrishnan, V.; Reynolds, M. T.; Sasada, M.; Savchenko, S. S.; Williamson, K. E.; Event Horizon Telescope Collaboration; Akiyama, Kazunori; Alberdi, Antxon; Alef, Walter; Anantua, Richard; Azulay, Rebecca; Baczko, Anne-Kathrin; Ball, David; Barrett, John; Bintley, Dan; …
Precise measurement of the K±→π±e+e− decay
Abstract A sample of 7253 K ± → π ± e + e − ( γ ) decay candidates with 1.0% background contamination has been collected by the NA48/2 experiment at the CERN SPS, which allowed a precise measurement of the decay properties. The branching ratio in the full kinematic range was measured to be BR = ( 3.11 ± 0.12 ) × 10 − 7 , where the uncertainty includes also the model dependence. The shape of the form factor W ( z ) , where z = ( M e e / M K ) 2 , was parameterized according to several models, and, in particular, the slope δ of the linear form factor W ( z ) = W 0 ( 1 + δ z ) was determined to be δ = 2.32 ± 0.18 . A possible CP violating asymmetry of K + and K − decay widths was investigated,…
Precision measurement of the ratio of the charged kaon leptonic decay rates
A precision measurement of the ratio RK of the rates of kaon leptonic decays K+- --> e nu and K+- --> mu nu with the full data sample collected by the NA62 experiment at CERN in 2007-2008 is reported. The result, obtained by analysing ~150000 reconstructed K+- --> e nu candidates with 11% background contamination, is RK = (2.488+-0.010)*10^{-5}, in agreement with the Standard Model expectation.
Measurement of the Dalitz plot slope parameters of the K±→π±π+π− decay
Abstract The distribution of the K ± → π ± π + π − decays in the Dalitz plot has been measured by the NA48/2 experiment at the CERN SPS with a sample of 4.71 × 10 8 fully reconstructed events. With the standard Particle Data Group parameterization the following values of the slope parameters were obtained: g = ( − 21.134 ± 0.017 ) % , h = ( 1.848 ± 0.040 ) % , k = ( − 0.463 ± 0.014 ) % . The quality and statistical accuracy of the data have allowed an improvement in precision by more than an order of magnitude, and are such as to warrant a more elaborate theoretical treatment, including pion–pion rescattering, which is in preparation.