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Register a new userVirtual Photon Correction to the $K^+topi^+pi^0pi^0$ Decay
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A. Nehme
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We consider electromagnetic corrections to the non-leptonic kaon decay, $K^+topi^+pi^0pi^0$, due to explicit virtual photons only. The decay amplitude is calculated at one-loop level in the framework of Chiral Perturbation Theory. The interest in this process is twofold: It is actually measured by the NA48 collaboration from one side, and, the value of the amplitude at the $pipi$ threshold gives access to $pipi$ scattering lengths from the other side. We found that the present correction is about 5 to 6% the value of the Born amplitude squared. Combined with another piece published recently, this fixes the size of isospin breaking correction to the amplitude squared to 7% its one-loop level value in the absence of isospin breaking and at the center of Dalitz plot.
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The $g$, $h$, and $k$ Dalitz plot parameters, which are coefficients in a series expansion of the squared module of the matrix element $|M(u,v)|^{2} propto 1 + gu + hu^{2} + kv^{2}$ ($u$, $v$ are invariant variables), have been measured for $K^{pm}to pi^{pm} pi^{0} pi^{0}$ decays using $35 GeV/c$ hadron beams at the IHEP (Protvino) accelerator. Dependences of parameters and fit quality on the $pi^0pi^0$ mass cut were investigated. The results point to the important role of $pi^+pi^- to pi^0pi^0$ charge exchange scattering near the $pi^0pi^0$ mass threshold. The comparison of our data with previous measurements is presented.
In the SND experiment at VEPP-2M $e^+e^-$ collider the $phi(1020)topi^0pi^0gamma$ decay was studied and its branching ratio was measured: $B(phitopi^0pi^0gamma)=(1.221pm 0.098pm0.061)cdot10^{-4}$. It was shown, that $f_0(980)gamma$ intermediate state dominates in this decay and the $f_0(980)$-meson parameters were obtained.
We present the results of a Dalitz plot analysis of D^0 to K^0_S pi^0 pi^0 using the CLEO-c data set of 818 inverse pico-barns of e^+ e^- collisions accumulated at sqrt{s} = 3.77 GeV. This corresponds to three million D^0 D^0-bar pairs from which we select 1,259 tagged candidates with a background of 7.5 +- 0.9 percent. Several models have been explored, all of which include the K^*(892), K^*_2(1430), K^*(1680), the f_0(980), and the sigma(500). We find that the combined pi^0 pi^0 S-wave contribution to our preferred fit is (28.9 +- 6.3 +- 3.1)% of the total decay rate while D^0 to K^*(892)^0 pi^0 contributes (65.6 +- 5.3 +- 2.5)%. Using three tag modes and correcting for quantum correlations we measure the D^0 to K^0_S pi^0 pi^0 branching fraction to be (1.059 +- 0.038 +- 0.061)%.
The KTeV E799 experiment has conducted a search for the rare decay $K_{L}topi^{0}pi^{0}gamma$ via the topology $K_{L}topi^{0}pi^{0}_Dgamma$ (where $pi^0_Dtogamma e^+e^-$). Due to Bose statistics of the $pi^0$ pair and the real nature of the photon, the $K_{L}topi^{0}pi^{0}gamma$ decay is restricted to proceed at lowest order by the CP conserving direct emission (DE) of an E2 electric quadrupole photon. The rate of this decay is interesting theoretically since chiral perturbation theory predicts that this process vanishes at level $O(p^4)$. Therefore, this mode probes chiral perturbation theory at $O(p^6)$. In this paper we report a determination of an upper limit of $2.43times 10^{-7}$ (90% CL) for $K_{L}topi^{0}pi^{0}gamma$. This is approximately a factor of 20 lower than previous results.
We present a measurement of $B(pi^0 rightarrow e^+e^- gamma)/B(pi^0 rightarrow gammagamma)$, the Dalitz branching ratio, using data taken in 1999 by the E832 KTeV experiment at Fermi National Accelerator Laboratory. We use neutral pions from fully reconstructed $K_L$ decays in flight; the measurement is based on about 60 thousand $K_L rightarrow pi^0pi^0pi^0 rightarrow gammagamma~gammagamma~e^+e^-gamma$ decays. We normalize to $K_L rightarrow pi^0pi^0pi^0 rightarrow 6gamma$ decays. We find $B(pi^0 rightarrow e^+e^- gamma)/B(pi^0 rightarrow gammagamma)$ $(m_{e^+e^-}$ > 15 MeV/$c^2)$ = $[3.920 pm 0.016(stat) pm 0.036 (syst)] times 10^{-3}$. Using the Mikaelian and Smith prediction for the $e^+e^-$ mass spectrum, we correct the result to the full $e^+e^-$ mass range. The corrected result is $B(pi^0 rightarrow e^+e^- gamma)/B(pi^0 rightarrow gammagamma) = [1.1559 pm 0.0047(stat) pm 0.0106 (syst)]$%. This result is consistent with previous measurements and the uncertainty is a factor of three smaller than any previous measurement.
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