Study of the η → π + π − π 0 Dalitz plot with the KLOE detector

In this article we present the status of an ongoing analysis of the η→ π+π−π0 Dalitz plot based on data taken with the KLOE detector at the DAFNE φ factory. 1 Theoretical Motivation The study of the η → π+π−π0 Dalitz plot has two main reasons. Firstly, the experimental decay width (Γexp = 296 ± 16 eV) is not well described by leading or next to leading order χPT (ΓLO ∼ 70 eV, ΓNLO = 160 ± 50 eV). Secondly, this Dalitz plot can be used to extract Q, defined as: Q2 = ms − m̂2 md − mu (1) with m̂ = 1 2 (md + mu) (2) which provides the elliptic constraint seen in figure1 for the light quark mass ratios. a e-mail: li.caldeira balkestahl@physics.uu.se Fig. 1. Constraints on the light quark mass ratios, the ellipse is calculated with Q = 22.3 ± 0.8 [1]. EPJ Web of Conferences DOI: 10.1051/ C © Owned by the authors, published by EDP Sciences, 2012 , epjconf 20123 / 09002 (2012) 37 709002 This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20123709002 EPJ Web of Conferences (ns) π t_ ∆ -10 -8 -6 -4 -2 0 2 4 6 8 10 t _e ( n s) ∆ -10 -8 -6 -4 -2 0 2 4 6 8 10 Data (ns) π t_ ∆ -10 -8 -6 -4 -2 0 2 4 6 8 10 t _e ( n s) ∆ -10 -8 -6 -4 -2 0 2 4 6 8 10 Signal (ns) π t_ ∆ -10 -8 -6 -4 -2 0 2 4 6 8 10 t_ e (n s) ∆ -10 -8 -6 -4 -2 0 2 4 6 8 10 Bhabha background Fig. 2. ∆te vs ∆tπ for data (left), MC signal (middle) and MC Bhabha background (right). Q is calculated from: Γ = ( QD Q )4 Γ̄ (3) where Γ is the experimental decay width, Γ̄ is the theoretical decay width in the Dashen limit[2] and QD is Q in the Dashen limit. To evaluate Γ̄ one can use χPT or dispersive analysis [3]. In the first case, comparison to the experimental Dalitz plot serves to validate the result, in the second case the Dalitz plot can also be used as input for the calculations. 2 KLOE data analysis The KLOE detector is located at the DAFNE electron positron collider, in Frascati, Italy. It consists of a large drift chamber and an electromagnetic calorimeter, both inserted inside a superconducting coil providing an axial magnetic field of ∼ 0.5 T. In 2008, the KLOE collaboration has presented a Dalitz plot analysis of η → π+π−π0, based on ∼ 450 pb−1 of data collected in 2001-2002 [4]. The new analysis in progress is done on a different and larger data set (∼ 2.0 fb−1 from 2004-2005 run) with the aim to reduce systematic errors, by using a different analysis scheme, improved MC description, and a better understanding of the event classification procedure. Until now, the analysis is performed on only 560 pb−1 from 2005. The decay chain studied is e+e− → φ → ηγrec → πππγrec → ππγγγrec. Events selected have at least 3 prompt neutral clusters in the calorimeter and at least a positive and a negative track in the drift chamber. The most energetic photon is assumed to be the recoil photon γrec and its energy is calculated from the 2-body φ decay kinematics (this gives a better resolution than using the EMC information alone). The π0 four-momentum is calculated from η decay kinematics and the photons from the π0 decay are selected by transverse opening angle in the π0 rest frame. To improve the signal bo background ratio, several selection cuts are made. A time of flight cut permits the rejection of electrons, especially from Bhabha scattering. The time of flight variable is calculated as ∆t = ttrack − tcluster for π+/− and e+/− hypothesis. For each track, the event is discarded if ∆te > −∆tπ or ∆te > −0.7 ns (black and red line, respectively, in figure 2). To reject more of these events, an angle cut is made. As seen in figure 3, the minimum angle between the positive track and the π0 decay photons is plotted against the minimum angle for the negative track. The boxes in the corners are cut away. A cut on the invariant mass M(φ − π− − π − γrec) around the π0 mass, as shown in figure 4 on the left, is made to reject background. On the right of figure 4 another cut is shown. This plot is the transverse angle between the two photons from the π0 decay, in the π0 rest frame (the photons go back to back). These figures also show the good agreement between data and MC. After all these cuts there are 1.7275 · 106 MC signal events left and the background is ∼ 1%. The final result of this analysis will be the Dalitz plot parameters when the Dalitz density is fitted by |A(X,Y)|2 ' 1 + aY + bY2 + cX + dX2 + eXY + f Y3 + . . . (4) where X = √ 3 T+ − T− Qη Y = 3 T0 Qη − 1 Qη = T0 + T− + T+ (5) 09002-p.2 MESON2012 12th International Workshop on Meson Production, Properties and Interaction ) (rad) γ (track-, min ∠ 0 0.5 1 1.5 2 2.5 3 ) (r ad ) γ (t ra ck +,

which provides the elliptic constraint seen in figure1 for the light quark mass ratios.
a e-mail: li.caldeira balkestahl@physics.uu.seFig. 1.Constraints on the light quark mass ratios, the ellipse is calculated with Q = 22.3 ± 0.8 [1].Q is calculated from: where Γ is the experimental decay width, Γ is the theoretical decay width in the Dashen limit [2] and Q D is Q in the Dashen limit.To evaluate Γ one can use χPT or dispersive analysis [3].In the first case, comparison to the experimental Dalitz plot serves to validate the result, in the second case the Dalitz plot can also be used as input for the calculations.

KLOE data analysis
The KLOE detector is located at the DAFNE electron positron collider, in Frascati, Italy.It consists of a large drift chamber and an electromagnetic calorimeter, both inserted inside a superconducting coil providing an axial magnetic field of ∼ 0.5 T.
In 2008, the KLOE collaboration has presented a Dalitz plot analysis of η → π + π − π 0 , based on ∼ 450 pb −1 of data collected in 2001-2002 [4].The new analysis in progress is done on a different and larger data set (∼ 2.0 fb −1 from 2004-2005 run) with the aim to reduce systematic errors, by using a different analysis scheme, improved MC description, and a better understanding of the event classification procedure.Until now, the analysis is performed on only 560 pb −1 from 2005.
The decay chain studied is e + e − → φ → ηγ rec → π + π − π 0 γ rec → π + π − γγγ rec .Events selected have at least 3 prompt neutral clusters in the calorimeter and at least a positive and a negative track in the drift chamber.The most energetic photon is assumed to be the recoil photon γ rec and its energy is calculated from the 2-body φ decay kinematics (this gives a better resolution than using the EMC information alone).The π 0 four-momentum is calculated from η decay kinematics and the photons from the π 0 decay are selected by transverse opening angle in the π 0 rest frame.
To improve the signal bo background ratio, several selection cuts are made.A time of flight cut permits the rejection of electrons, especially from Bhabha scattering.The time of flight variable is calculated as ∆t = t track − t cluster for π +/− and e +/− hypothesis.For each track, the event is discarded if ∆t e > −∆t π or ∆t e > −0.7 ns (black and red line, respectively, in figure 2).To reject more of these events, an angle cut is made.As seen in figure 3, the minimum angle between the positive track and the π 0 decay photons is plotted against the minimum angle for the negative track.The boxes in the corners are cut away.
A cut on the invariant mass M(φ − π − − π + − γ rec ) around the π 0 mass, as shown in figure 4 on the left, is made to reject background.On the right of figure 4 another cut is shown.This plot is the transverse angle between the two photons from the π 0 decay, in the π 0 rest frame (the photons go back to back).These figures also show the good agreement between data and MC.After all these cuts there are 1.7275 • 10 6 MC signal events left and the background is ∼ 1%.
The final result of this analysis will be the Dalitz plot parameters when the Dalitz density is fitted by where  and T 0 , T − and T + are the kinetic energies of the pions in the η rest frame.
To extract the parameters (a, b,. . . ) a fit to the data will be done, minimizing: where Nb is the number of bins of the Dalitz plot, N i is the number of data events in bin i, j is the efficency for bin j, S i j the smearing matrix from bin j to bin i, N j theory the theoretical number of events in bin j calculated with equation 4 and σ i the error in bin i.The fit procedure is at the moment being checked with MC, and so far there is good agreement between the results of the fit and the MC input.
At KLOE-2 [5] with an improved reconstruction of charged tracks coming from the interaction region, thanks to the new inner tracker detector, and more integrated luminosity, further significant improvements in this analysis are expected.

Fig. 4 .
Fig.4.On the left the invariant mass of π 0 , on the right the tranverse angle between π 0 decay photons, in π 0 rest frame.Black triangles are data, blue line the MC signal+background, black line MC signal, and red line MC background.