K → π ν ν
KL→π0νν
K+ → π+ ν ν



Since the experimental uncertainties are under control and improvement is expected on the experimental side, the measurement of BR(K → π ν ν ) will play a major role in the UT fit in the next future. The BR value can be related to ρ and η parameters through the relation

η )2+ (ρ - ρ0 )2 = σ BR(K+ → π+ ν ν )

κ+|Vcb|4 X2(xt )
which is represented by an ellipse centered in (ρ0 ;0 ).

Several theoretical quantities enter the formula:

The values for X(xt), κ+ and P0(X) are taken from G. D'Ambrosio and G. Isidori, hep-ph/0112135, while for the experimental determination we use BR(K → π ν ν ) = (1.47 +1.30, - 0.89) • 10-10 from A.V. Artamonov, et al. [E949 Collab.], hep-ex/0403036.

The constraint is represented by an ellipse (an elliptical crown once the uncertainties are taken into account). The error on the actual measurement is still too large to allow an improvement of the determination of ρ and η.


Experimental likelihood for
                                   BR(K → π ν νbar)
(EPS) [JPG]

Likelihood BR(K → π ν ν) (from the derivative of experimental CL)


present bound from K → π ν ν bar
(EPS) [JPG]

bound from K → π ν ν from present experimental
measurement, compared to the standard UTfit result

We studied the bound one can get from 100 observed events, the error coming from Poissonian fluctuations (i.e. assuming an optimistic scenario of complete rejection of background), to quantify the impact of the next generation of experiments (such as NA48 3). We repeated this exercise with the SM central value (0.83x10-10) and the present experimental result, using the present theoretical error on the long distance charm contribution or assuming a factor two in the reduction of it.


bound from k to π ν ν bar assuming
                                    100 events, the present central value and 
                                    present theoretical error
(EPS) [JPG]

bound from K → π ν ν assuming 100 events, the present central value and present theoretical error


bound from k to π ν ν bar assuming
                                    100 events, the present central value and 
                                    1/2 theoretical error
(EPS) [JPG]

bound from K → π ν ν assuming 100 events, the present central value and 1/2 theoretical error


bound from k to π ν ν bar assuming
                                    100 events, the SM central value and 
                                    present theoretical error
(EPS) [JPG]

bound from K → π ν ν assuming 100 events, the SM central value and present theoretical error

bound from k to π ν ν bar assuming
                                    100 events, the SM central value and 
                                    present theoretical error
(EPS) [JPG]

bound from K → π ν ν assuming 100 events, the SM central value and 1/2 theoretical error



KL → π0 ν ν

The knowledge of BR(KL → π0 ν ν) provides a measurement of η2, through the relation

BR(KL → π0 ν ν) = κL Im(λt)2X2(xt)

λ10

where κL is a theoretical correction similar to κ+ (introduced for the case of K → π ν ν decay) and related to it through the relation

κL= κ+ rKL

rK+
τ(KL)

τ(K+)

where τ(KL) and τ(K+) are kaon lifetimes and rKL = 0.944 ± 0.028 represents the isospin breaking correction. This constraint is sensitive to new physics in a complimentary way respect to the bounds currently used in the UTfit. Waiting for an experimental measurement of BR(KL → π0 ν ν), we can compare the present bounf from UTfit with a hypothetical 10% precise measurement.


Prediction on  BR(K_L to π0 ν ν bar)
                                    from UTfit
(EPS) [JPG]

UTfit Prediction
BR(KL → π0 ν ν) = (0.25 ± 0.03)10-10


bound from K_L to π0 ν ν bar assuming
                                    10% precision on BR and agreement to
                                    the SM
(EPS) [JPG]

bound from KL → π0 ν ν assuming 10% precision
on the BR and agreeement
with respect to the Standard Model



Combining the hypothetical 10% precise measurements on BR(K → π ν ν) and BR(KL → π0 ν ν) to the present knowledge on εK, one can illustrate the impact of Kaon physics on the UTfit at the end of the next generation of K-physics experiements. To do that, we assumed two different scenarios, in agreement (left) or disagreement (right) to the Standard Model expectations


bound from Kaon physics in the
                               case of agreement with the SM
(EPS) [JPG]

impact of Kaon physics to the UTfit, assuming agreement between rare kaon decays and the SM


bound from Kaon physics in the
                               case of disagreement with the SM
(EPS) [JPG]

impact of Kaon physics to the UTfit, assuming disagreement between rare kaon decays and the SM


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