*Last modified 29/04/2008 by N.Molokanova*

**Dalitz plot linear slope asymmetry in
decays**

**Published final 2003 result**

(full 2003 data sample of
1.67x10^9 events selected for analysis):

**Ag = (1.7 ± 2.1stat ± 1.4stat.trig ± 1.4syst) * 10 ^{-4} =
(1.7 ± 2.9) * 10^{-4} **

in ** Physics
Letters B 634 (2006) 474-482**.

**Final combined 2003+2004 result **

(adding the full 2004 data sample for a total of 3.8x10^9 events selected
for analysis):

Ag = (-1.5 ± 1.5(stat) ± 0.9(stat-trig) ± 1.3 (syst)) * 10^{-4}= (-1.5 ± 2.2) * 10^{-4}

first presented by S. Balev at ** La
Thuile 2007**,

later updated and published in

**Published final 2003 result**

(full 2003 data sample of 47x10^6 events selected for analysis):

Ag = (1.8 ± 2.2 (stat) ± 1.0 (stat-trig) ± 0.8 (syst) ± 0.2 (ext.)) * 10^{-4}= (1.8 ± 2.6) * 10^{-4}

in *Physics
Letters B 638 (2006) 22-29.*

**Public preliminary combined 2003+2004
result **
(adding the full 2004 data sample for a total of 91x10^6 events selected for
analysis):

Ag = (1.8 ± 1.7(stat) ± 0.6(syst)) * 10^{-4}= (1.8 ± 1.8) * 10^{-4}

first presented by S. Balevat,La Thuile 2007

later updated and published ine-Print: arXiv:0707.0697.Eur.Phys.J.C52:875-891,2007;

For the purpose of allowing comparisons with earlier results, these slopes are measured deliberately ignoring the fact that the traditional PDG parameterization of the Dalitz plot distribution is inadequate (see Pion-pion scattering) and only including anaiveCoulomb correction term.

The result (on about 30% of the total available data set) is:

g = (-21.134 ± 0.017)%h = (1.848 ± 0.040)%k = (-0.463 ± 0.014)%first presented by E. Goudzovski at

More relevant values for the weak transition slope parameters require a full analysis including strong rescattering effects and electro-magnetic corrections, for which complete and adequate theoretical models are needed.and later updated; the corresponding paper isCrimea 2006and available in hep-ex/0702045.Physics Letters B 649 (2007) 349-358

## Pion-pion scattering

Published 2003 result:

based on the improved Cabibbo-Isidori theoretical framework (JHEP 0503 (2005) 021), obtained from a uni-dimensional fit to the squared pi0-pi0 invariant mass in which the quadratic Dalitz plot slope parameter k is set to 0 (as suggested by PDG 2005), the scattering length difference is(a0-a2) m(pi+) = 0.268 ± 0.010 (stat) ± 0.004 (syst) ± 0.013 (ext)a2 m(pi+) = -0.041 ± 0.022 (stat) ± 0.014 (syst)or

(a0-a2) m(pi+) = 0.264 ± 0.006 (stat) ± 0.004 (syst) ± 0.013 (ext)if the correlation between a0 and a2 predicted by Chiral Perturbation Theory is taken into account.

From the same fit the following slope parameters are extracted:

g0 = 0.645 ± 0.004 (stat) ± 0.009 (syst)h' = -0.047 ± 0.012 (stat) ± 0.011 (syst)corresponding to the functional form M0 = 1 + (½) g0 u + (½) h' u^2 for the matrix element.

These results appear in.Physics Letters B 633 (2006) 173-182

Update to 2003 result:

The above result was obtained assuming no quadratic term in v (k=0) for the unperturbed matrix element, consistently with PDG data. The analysis shows evidence for a non-zero quadratic v term: using for the unperturbed matrix element the functional form M0 = 1 + (½) g0 u + (½) h' u^2 + (½) k' v^2:k' = 0.0097 ± 0.0003 (stat) ± 0.0008 (syst)The corresponding changes in the g0 and h' parameters are of order 2% and 25% respectively, while the scattering length parameters do not change in a significant way with respect to the k=0 case.

Work is going on on fitting 2004 data with the above model and with the Bern-Bonn model (Phys. Lett. B638 (2006) 187and subsequent improvements).

## Leptonics and semileptonics

Ke3:

BR(K+/- -> pi0 e+/- nu) = 0.05168 ± 0.00019(stat) ± 0.00008(syst) ± 0.00030(norm)

Kmu3:

BR(K+/- -> pi0 mu+/- nu) = 0.03425 ± 0.00013(stat) ± 0.00006(syst) ± 0.00020(norm)

Ke3/K2pi:

Gamma(pi0 e+ nu)/Gamma(pi pi0) = 0.2470 ± 0.0009(stat) ± 0.0004(syst)

Kmu3/Ke3:

Gamma(pi0 mu+/- nu)/Gamma(pi0 e+/- nu) = 0.663 ± 0.003 (stat) ± 0.001 (syst)

Kmu3/K2pi:

Gamma(pi0 mu+ nu)/Gamma(pi pi0) = 0.1637 ± 0.0006(stat) ± 0.0003(syst)

Results fromEur.Phys.J.C50:329-340,2007, Erratum-ibid.C52:1021-1023,2007.

K+/- -> pi+/-e+e-gamma:

BR(K->pieeg, m(eeg) > 260 MeV/c^{2}) = (1.19 ± 0.12(stat) ± 0.04(syst))*10^{-8}

; e-Print: arXiv:0711.4313.Phys.Lett.B659:493-499,2008

A preliminary result is available from 2003 test run data:

Ke2/Kmu2:

Gamma(e+/- nu)/Gamma(mu+/- nu) = (2.416 ± 0.043 (stat) ± 0.024 (syst))*10^{-5}The control of the trigger systematics is limiting the above result.

Work is ongoing to extract a measurement from the 2004 data set, with comparable statistics but improved control systematics.