Measurement of the eta mass at KLOE

An integrated luminosity of 410 pb^(-1), corresponding to ~ 17 million of eta events, has been analyzed to measure the eta mass using the decay eta to gamma gamma. The measurement is insensitive to the calorimeter energy calibration and the systematic error on the measurement is dominated by the uniformity of the detector response. As a cross check of the method the pi0 mass from the decay phi to pi0 gamma, pi0 to gamma gamma has been measured and it is in agreement with the most accurate previous determinations. The result obtained is m(eta) = 547.873 +/- 0.007 (stat.) +/- 0.031 (syst.) MeV, that is today best measurement of the eta mass.


Introduction
The KLOE experiment is performed at the Frascati φ factory DAΦNE [1]. DAΦNE is a high luminosity e + ,e − collider working at √ s ∼ 1020 MeV, corresponding to the φ meson mass. In the whole period of data taking (2001 − 2006) KLOE has collected an integrated luminosity of 2.5 fb −1 , corresponding to about 8 billions of φ produced and 100 millions of η mesons through the electromagnetic decay φ → ηγ.
The KLOE detector consists of a large cylindrical drift chamber [2], DC, surrounded by a lead/scintillating-fiber sampling calorimeter [3], EMC, both immersed in a solenoidal magnetic field of 0.52 T with the axis parallel to the beams, z in the following. The DC momentum resolution for charged particles is δp ⊥ /p ⊥ =0.4%. The calorimeter is divided into a barrel and two endcaps, and covers 98% of the total solid angle. Photon energies and arrival times are measured with resolutions σ E /E = 0.057/ E (GeV) and σ t = 54 ps/ E (GeV) ⊕ 50 ps, respectively. Photon-shower centroid positions are measured with an accuracy of σ = 1 cm/ E (GeV) along the fibers, and 1 cm in the transverse direction. A photon is defined as a cluster of energy deposits in the calorimeter elements that is not associated to a charged particle. We require the distance between the cluster centroid and the nearest entry point of extrapolated tracks be greater than 3×σ(z, φ), where φ is the azimuthal angle.
The trigger [4] uses information from both the calorimeter and the drift chamber. The EMC trigger requires two local energy deposits above threshold (E > 50 MeV in the barrel, E > 150 MeV in the endcaps). The trigger has a large time spread with respect to the time distance between consecutive beam crossings. It is however synchronized with the machine radio frequency divided by four, T sync =10.85 ns, with an accuracy of 50 ps. For the 2001-2002 data taking, the bunch crossing period was T =5.43 ns. The time (T 0 ) of the bunch crossing producing an event is determined offline during event reconstruction. The value of the η mass has been recently measured with high precision by two collaborations NA48 [5] (m η = 547.843 ± 0.030 ± 0.041 MeV/c 2 ) and GEM [6] (m η = 547.311 ± 0.028 ± 0.032 MeV/c 2 ) using different techniques and production reactions. The two measurements differ by more than eight standard deviations from each other. The GEM measurement is in agreement with the older ones [7] while the NA48 measurement is higher. For this reason it is interesting to provide a further measurement of comparable precision in order to clarify the experimental situation.

Measurement method.
We measure the mass studying the decay φ → ηγ, η → γγ. A kinematic fit is performed imposing the 4 constraints given by the energymomentum conservation. Sing there are three photons and there are 4 constraints, the fit overconstrains the energies of the photons that are, practically, determined by the position of the clusters in the calorimeter. The inputs of the fit are the energy, the position and the time of the calorimeter clusters, the mean position of the e + e − interaction point, the total four-momentum of the colliding e + e − pair. Each of these variables is determined run by run using e + e − → e + e − events ( almost 90000 events for each run, allowing a very precise determination of the relevant parameters).

Selection.
The φ → ηγ events are selected by requiring at least three energy deposits in the barrel with a polar angle θ γ : 50 • < θ γ < 130 • , not associated to a charged track. A kinematic fit imposing energy-momentum conservation and time of flight of photons equal to the velocity of light is done for all 3 γ's combination of N detected photons. The combination with the lowest χ 2 is chosen as a candidate event if χ 2 < 35. The events surviving the cuts are shown in fig.1, where the Dalitz plot is shown. Three bands are clearly visible. The band at low m 2 γγ is given by the φ → π 0 γ, π 0 → γγ, while the other two bands are φ → ηγ, η → γγ events.
With the cut shown in the Dalitz plot we select a pure sample of η, π 0 → γγ events. The resulting m γγ spectrum ( fig.2) can be fitted well with a single gaussian of σ ∼ 2.1M eV /c 2 .
In order to determine the systematic error we have evaluated the uncertainities on all the quantities used in the kinematic fit and the effect on the fitted value. A sample of e + e − → π + π − γ events has been used to check the mean position of the interaction point, the energy response of the calorimeter and the alignment of the calorimeter with the Drift Chamber. The mean position of the interaction point, determined run by run using the e + e − → e + e − events, has been compared with the reconstructed π + π − vertex. The difference between this two values has been computed run by run and the spread of the distribution is used for the systematic error on the determination of To check disalignment between the calorimeter and the Drift Chamber, the π − and π + tracks of the π + , π − γ events were extrapolated to the calorimeter and the closest approach point to the cluster centroid was determined. The difference in the position x clu − x cst were determined and the spread of these values are taken as systematic error on DC-Calo allignment. A small correction of 1.1 mm in the Calorimeter position along the y direction, the vertical, and 2 mm along the z direction (the direction of the beam axis) was applied. The absolute energy scale of the calorimeter and the linearity of the energy response was checked using the e + e − → e + e − γ events and the π + π − γ events. The energy of the γ can be determined using the two charged tracks in the Drift Chamber and then compared to the reconstructed cluster energy. A linearity better than 2 % was found while the absolute scale was found to be calibrated at better than 1 %. These systematic uncertainties result in just 4 keV for the scale and 4 keV for the linearity on the value of the reconstructed mass. The measurement shows very small sensitivity to the calorimeter calibration because, as explained before, the kinematic fit overconstraints the photon energy with the cluster positions. For this reason it is important to evaluate the systematic error due to the misalignment of single modules in the calorimeter. This has been done evaluating the value of the mass as a functon of the position of the photons in the calorimeter. A spread of about 10-15 keV was found and assumed as systematic error. Systematics due to the particular choice of the cut on the Dalitz plot shown in fig.1 was also determined to be 12 keV, while the cut on the χ 2 pratically doesn't have any effect on the value of the η mass (0.7 keV). The measured value of the mass is, instead, very sensitive to the energy in the center of mass of the ηγ system. Due to initial state radiation emission (ISR) the available center of mass energy is a bit lower than the √ s of the e + e − beams measured using e + e − → e + e − events. A variation of 100 keV of the measured mass value is predicted by the MC simulation. Since this correction is realtively large we have checked the simulation of ISR emission in the MC in the following way: • the correction to apply to the fitted value in order to obtain the real value of the mass has been determined as a function of √ s and shown in fig.3; • the whole data taking has been devided in ranges of √ s using 8 points for the on peak data and two off-peak points at 1017 MeV and 1022 MeV; • the value of the mass obtained for each value of √ s has been corrected according the MC prediction; • the residual spread of these points has been  All these studies have been done also for the π 0 mass using the φ → π 0 γ events. The ratio of the two masses r = m η /m π 0 has also been studied. All the contributions to the systematic error are summarized in table 1.

Computation of the final result.
We have two different ways to extract the value of the η mass. We can use the ratio m η /m π 0 obtaining: m η m π 0 = 4.0610 ± 0.0004(stat.) ± 0.0014(syst.) from which using the PDG2006 [7] value of the π 0 mass (m π 0 = 134976.6 ± 0.6 keV) we obtain: m η = 548140 ± 50 (stat.) ± 190 (syst.) keV. Alternatively we can use directly the value of m η coming from the fit. For this purpose we need to calibrate the √ s with high precision (m η /m π 0 is in fact √ s independent while the two values of m η and m π 0 are fully correlated with the √ s measuremnt). The absolute √ s scale has been calibrated using the m φ value measured by CMD-2 [8]. To this pourpose the cross section e + e − → φ → K S K L has been measured as a function of the √ s using the two off-peak points at √ s = 1017M eV and √ s = 1022 MeV together with the on-peak data. The φ resonance curve has been fitted using the CMD-2 parametrization that takes in account ISR and threshold effect in K S K L production. The central value of the φ mass has been measured obtaining m φ = 1019.329 ± 0.011 MeV [9]. The difference respect to the CMD-2 value m φ CMD−2 = 1019.483 ± 0.011 stat. ± 0.025 syst. sets our absolute √ s calibration. This means that our measurements can be regarded as a measurement of the ratio The π 0 mass is in agreement at 1.4 σ level with the PDG06 value, validating the whole procedure.
The value of the η mass obtained here has been compared with the previous measurements in fig.  6. This result confirms the measured value of the NA48 at 0.6σ, with an error reduced by a factor 2 and is 11σ away from the GEM result, it is also compatible, at 1.4σ level, with less accurate CLEO result [10].  Figure 6. η mass measurements, see text for the references. The continuous line has been computed using the PDG procedure [7], pag. 14.