Recent results on Kaon Physics at KLOE-2

KLOE-2 extends the physics program of the forerunner KLOE experiment, especially in the field of discrete symmetries tests with neutral kaons. KLOE and KLOE-2 have collected together the largest sample of electronpositron collisions at an energy equal to the φ-meson mass, corresponding to about 2.4×1010 produced φ mesons. The latest results on neutral kaon physics at KLOE will be reviewed, together with the status and prospects of the analyses of KLOE-2 data. A new measurement of the charge asymmetry in KS semileptonic decays with 1.7 fb−1 of KLOE data, which improves the sensitivity of previous measurements of about a factor two, will be presented. Furthermore, the status of the analysis devoted to directly test T and CPT symmetries in neutral kaons transitions, as well as the search of the pure CP-violating KS → 3π0 decay using part of the recently acquired KLOE-2 dataset, will be presented.


Introduction
Flavoured neutral mesons are a powerful tool for testing fundamental discrete symmetries and their combinations such as CP and CPT . Among them, neutral kaons are extensively used to search for manifestations of symmetry violations as they are easily translated to constraints on the properties of the mesons [1].
The KLOE experiment has contributed to determine most of the properties of neutral kaons as well as a number of tests of CP and CPT symmetries [2]. The KLOE dataset is still being analysed with the aim of obtaining more precise results on the charge asymmetry in semileptonic K S decays and preforming a first direct CPT test in transitions of neutral kaons. Furthermore, the KLOE-2 experiment has ended its data taking on March 2018, collecting about 5 fb −1 of data, which will allow to enhance the upper limit set on the branching fraction of the pure CP-violating decay K S → 3π 0 by KLOE. volume is filled with Helium (90%) and Isobutane (10%), surrounded by a lead/scintillatingfiber sampling calorimeter (EMC), whose coverage is about 98% of the solid angle [7]. KLOE-2 additionally featured a cylindrical triple-GEM inner tracker [8] -installed close to the e + e − interaction point to improve vertex reconstruction for quantum interferometry studies [9] -and a system of calorimeters, devoted to enlarge the solid angle coverage of the EMC for detecting photons from K S,L decays and electrons/positrons from γ-γ processes.
KLOE and KLOE-2 datasets provide the largest sample of e + e − → φ events, corresponding to about 24 billions of produced φ mesons.

CPT symmetry test with K S semileptonic decays
A test of CPT symmetry can be performed by comparing the value of the lepton charge asymmetry, A S ,L , for short-and long-lived neutral kaons: where ( ) and (δ) are related to T and CPT violation in the K 0 -K 0 mixing, respectively, while (y) and (x − ) parametrize the CPT violation in ∆S = ∆Q and ∆S ∆Q decay amplitudes, respectively [10]. If CPT symmetry is not violated, then the aforementioned asymmetries are expected to be identical: The charge asymmetry for K L was precisely determined from the KTeV experiment at Fermilab: A L = (3.322±0.058 stat ±0.047 syst )×10 −3 [11], while the most precise measurement of A S was performed by the KLOE collaboration using 410 pb −1 of integrated luminosity collected in 2001-2002: A S = (1.5 ± 9.6 stat ± 2.9 syst ) × 10 −3 [12].
The KLOE-2 Collaboration has recently published a new measurement based on a larger data sample, corresponding to an integrated luminosity of 1.63 fb −1 collected in 2004-2005 [13]: A S = (−4.9 ± 5.7 stat ± 2.6 syst ) × 10 −3 , which improves the statistical accuracy of previous determination by almost a factor of two. Taking into account the correlation between both measurements, the combination of KLOE and KLOE-2 results is: which represent the most precise measurement of A S to date. This value, combined with KTeV result on A L and providing also (δ) [14] and ( ) [15] as external inputs, allows to extract the CPT -violating parameters [13]: which are consistent with CPT invariance and improve by almost a factor of two the previous results [12]. The rare K S decays are currently being studied using the full KLOE-2 dataset: with some 5 fb −1 total integrated luminosity a pure data sample of about 5 × 10 9 tagged K S decays will be available.

Direct test of T and CPT in transitions of neutral kaons
The comparison of the rates of neutral mesons transitions between their flavour and CP eigenstates allows for a model independent test of T and CPT symmetries [16,17]. Such a test -up to date performed only in the case of neutral B mesons, where it delivered the first direct evidence of T violation [18] -is pursued with the K 0 -K 0 system at KLOE-2. To this extent, quantum entangled meson pairs are used to identify the initial state of a particle transition by the decay of its entangled partner, while the final state is tagged by semileptonic and hadronic decays into two and three pions.
Two T violating observables are determined as ratios between the rates of two classes of processes: K S K L → π ± e ∓ ν, 3π 0 and K S K L → π + π − , π ± e ∓ ν: where I( f 1 , f 2 ;∆t) denotes the number of recorded events characterized by a time-ordered pair of kaon decays f 1 and f 2 separate by an interval of proper kaon decay times ∆t [16]. Any deviations of the asymptotic level of these ratios from unity for large transition times would be a manifestation of T violation. The novel concept of such test can be generalized to test CPT symmetry through the determination of the asymptotic level of the following double ratio: where the δ and x − are the parameters already presented in Equation 1. This double ratio constitutes a robust CPT -violation-sensitive observable [17], which has never been measured. The analysis tools required to determine both the T -violation-sensitive ratios and the CPT -violation-sensitive double ratio are being tested using the full KLOE dataset, corresponding to an integrated luminosity of about 1.7 fb −1 . A preliminary distribution of the ratio defined in Equation 6 is presented in Figure 1. Although the uncertainty on the asymptotic level of these observables available with KLOE data is only at the percent level, the analysis of the full KLOE-2 dataset will allow to perform statistically significant tests of T and CPT at the 10 −3 level of precision.

Search for the pure CP-violating K S → 3π 0 decay
Another class of CP-violating phenomena in the neutral kaon system is represented by the decays of K S into a CP-asymmetric state with three pions. While the K S → π + π − π 0 process contains both CP-violating and conserving amplitudes, the observation of the K S → 3π 0 decay would be a clear signature of CPviolation. The present best upper limit has been set by KLOE at BR(K S → 3π 0 ) < 2.6 × 10 −8 [19], still almost an order of magnitude lower than the precision of the Standard Model prediction (1.9 × 10 −9 ). Therefore, the search for K S → 3π 0 is already performed using the recently collected ∼5 fb −1 of KLOE-2 data. With a larger data sample and an optimized analysis to properly treat KLOE-2 data, the sensitivity on this decay measurement is expected to be beyond the level of 10 −8 .

Summary
The measurements of the KLOE detector have recently delivered the most precise result on the charge asymmetry in the semileptonic decays of the short-lived neutral K meson, consistent with CPT conservation within the total uncertainty of 5.6×10 −3 . The larger dataset collected by the upgraded KLOE-2 detector is expected to further improve the precision of this measurement to the level of 3 × 10 −3 . The full datasets of KLOE is being used to perform a first direct tests of T and CPT symmetries in transitions of neutral kaons. Profiting also of KLOE-2 data, the precision on this novel tests is expected to reach the level of 10 −3 . Finally, the search for the pure CP-violating decay K S → 3π 0 is being performed with the full KLOE-2 dataset: The expected sensitivity to this process should allow KLOE-2 Collaboration to approach the level of the present Standard Model predicion for BR(K S → 3π 0 ).