LNF 12/12/06 1 F.Ambrosino-T. Capussela-F.Perfetto Update on        Dalitz plot slope Where we started from A big surprise Systematic checks Conclusions and outlook

LNF 12/12/06 2 The dynamics of the       decay can be studied analysing the Dalitz plot distribution. The Dalitz plot density ( |A| 2 ) is specified by a single parameter: |A| 2   z with: E i = Energy of the i-th pion in the  rest frame.  = Distance to the center of Dalitz plot.  max = Maximun value of . Z  [ 0, 1 ]   Dalitz plot expansion

LNF 12/12/06 3   Dalitz plot expansion

LNF 12/12/06 4 Cutting on: Minimum  2 value  2 between “best” and “second” combination One can obtain samples with different purity-efficiency Purity= Fraction of events with all photons correctly matched to p 0 ‘s Combination selection Pur  85 % Eff  22 % Pur  92 % Eff  14 % Pur  98 % Eff  4.5 %

LNF 12/12/06 5 Folding procedure Let us free of the binning: For each MC event (generated according to phase space) Evaluate its z true and its z rec (if any!) Enter an histogram with the value of z rec Weight the entry with a z true Then iterate procedure to find a maximizing log likelihood

LNF 12/12/06 6 Preliminary result We have analyzed 415 pb -1 of data and we find the preliminary result: This result differs by roughly 3 standard deviations from the published Crystal Ball result:  =  ± The systematic is obtained considering the maximum variation wrt the fitting region for the chosen sample.  =  ± stat  syst

LNF 12/12/06 7 More checks More checks on range dependance Two more samples (75% and 95% purity respectively) Low energy photons correction Resolution/BKG correction

LNF 12/12/06 8 A big surprise… Trying some more systematics checks on the fitting range we got in BIG trouble… Range85% Pur.92% Pur.98% Pur ± ± ± ± ± ±0.006

LNF 12/12/06 9 A big surprise…(2) Idea: check linearity of DATA/MCreco using for MC pure phase space… Nothing really high purity…

LNF 12/12/06 10 A big surprise…(3) Idea: check linearity of DATA/MCreco using for MC pure phase space… low purity = High statistics…

LNF 12/12/06 11 Explanation (1) The edge of the flat part of the phase space depends in the value of the eta mass. What if its value on data is larger than the nominal one ?

LNF 12/12/06 12 Explanation (2) To understand the effect used a toy MC to generate events with different eta mass: Sample 1 : M = MeV Sample 2 : M = MeV If one uses the nominal value to build the z variable for the sample 2 obtaines a big deviation from the phase space reconstructed with the right mass value. If one uses the shifted value to reconstruct the sample 2, no deviation is present.

LNF 12/12/06 13 Explanation (3) To understand the effect used a toy MC to generate events with different eta mass: Sample 1 : M = MeV Sample 2 : M = MeV If one uses the nominal value to build the z variable for the sample 2 obtaines a big deviation from the phase space reconstructed with the right mass value. If one uses the shifted value to reconstruct the sample 2, no deviation is present.

LNF 12/12/06 14 Linearity If the effect is given by the eta mass, correcting for it now all sample should exhibit good linearity for the ratio DATA/MCrec (phase space)

LNF 12/12/06 15 Linearity (2) If the effect is given by the eta mass, correcting for it now all sample should exhibit good linearity for the ratio DATA/MCrec (phase space)

LNF 12/12/06 16 Range stability Let us look at what happens now…With two more samples Range75% Pur.85% Pur.92% Pur.95% Pur.98% Pur ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±0.008

LNF 12/12/06 17 Resolution (I) Different samples have different resolutions:

LNF 12/12/06 18 Resolution (I) Different samples have different resolutions:

LNF 12/12/06 19 Resolution (I) Different samples have different resolutions:

LNF 12/12/06 20 Resolution (I) Different samples have different resolutions:

LNF 12/12/06 21 Resolution (I) Different samples have different resolutions:

LNF 12/12/06 22 The center of Dalitz plot corresponds to 3 pions with the same energy (E i = M  /3 = MeV). A good check of the MC performance in evaluating the energy resolution of  0 comes from the distribution of E  0 - E i for z = 0 Resolution (II)

LNF 12/12/06 23 The center of Dalitz plot corresponds to 3 pions with the same energy (E i = M  /3 = MeV). A good check of the MC performance in evaluating the energy resolution of  0 comes from the distribution of E  0 - E i for z = 0 Resolution (II)

LNF 12/12/06 24 E* g 1 - E* g 2 Vs. E p Resolution (III) A further check can be done comparing the energies of the two photons in the pion rest frame as function of pion energy

LNF 12/12/06 25 Resolution (IV) A further check can be done comparing the energies of the two photons in the pion rest frame as function of pion energy We have inserted a correction for the ratio of these RMS inside the fit. The correction is flat and about 1% thus we fit filling a histo with: Z’rec = Zgen+0.99(Zrec –Zgen)

LNF 12/12/06 26 Background Background composition is fitted directly on data using the z obtained from the second best pairing Some correction found wrt expected values. Inserted in the fit to obtain systematics

LNF 12/12/06 27 Low energy photons Correcting for low energy photons DATA/MC efficiency introduces a very small correction to the slope alpha:

LNF 12/12/06 28 Systematics summary We take as milestone, for each sample, the fit in the range (0,1) Effect75% Pur.85% Pur.92% Pur.95% Pur.98% Pur Range / Resol BKG Low E g M eta± /+0.003±0.002 TOTAL-0.007/ / / /+0.004±0.004

LNF 12/12/06 29 High statistics or High purity ? We believe that the best sample is not the one with highest purity. In fact this sample has the largest slope for the efficiency (26%, cfr 2alpha= 6%) while the lowest purity sample has only 8% slope. Anyhow we use the maximum spread observed as function of the purity as a systematic error.

LNF 12/12/06 30 Conclusions Very big and unexpected effect of the wrong value of the eta mass used on data found. The preliminary result was WRONG  New result is purity): a = ( ± (stat.) / (syst.)) This is in complete agreement with Crystal Ball

LNF 12/12/06 31 SPARE SLIDES

LNF 12/12/06 32 Kinematic fit with no mass constrains