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Improved dispersion relations for gammagammato pi^0pi^0

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 Added by Jose Antonio Oller
 Publication date 2007
  fields
and research's language is English




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We perform a dispersive theoretical study of the reaction gammagammato pi^0pi^0 emphasizing the low energy region. The large source of theoretical uncertainty to calculate the gammagammatopi^0pi^0 total cross section for sqrt{s}gtrsim 0.5 GeV within the dispersive approach is removed. This is accomplished by taking one more subtraction in the dispersion relations, where the extra subtraction constant is fixed by considering new low energy constraints, one of them further refined by taking into consideration the f_0(980) region. This allows us to make sharper predictions for the cross section for sqrt{s}lesssim 0.8 GeV, below the onset of D-wave contributions. In this way, were new more precise data on gammagammatopi^0pi^0 available one might then distinguish between different parameterizations of the pipi isoscalar S-wave. We also elaborate on the width of the sigma resonance to gammagamma and provide new values.



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Based on a sample of $1.31 times 10^9$ $J/psi$ events collected with the BESIII detector, an amplitude analysis of the isospin-violating decays $eta^prime rightarrow pi^+pi^-pi^0$ and $eta^prime rightarrow pi^0pi^0pi^0$ is performed. A significant $P$-wave contribution from $eta^prime rightarrow rho^{pm} pi^{mp}$ is observed for the first time in $eta^prime rightarrow pi^+pi^-pi^0$. The branching fraction is determined to be ${mathcal B}(eta^prime rightarrow rho^{pm}pi^{mp})=(7.44pm0.60pm1.26pm1.84)times 10^{-4}$, where the first uncertainty is statistical, the second systematic, and the third model dependent. In addition to the nonresonant $S$-wave component, there is a significant $sigma$ meson component. The branching fractions of the combined $S$-wave components are determined to be ${mathcal B}(eta^prime rightarrow pi^+pi^-pi^0)_S=(37.63pm0.77pm2.22pm4.48)times 10^{-4}$ and ${mathcal B}(eta^prime rightarrow pi^0pi^0pi^0)=(35.22pm0.82pm2.54)times 10^{-4}$, respectively. The latter one is consistent with previous BESIII measurements.
Using $2.92$ fb$^{-1}$ of electron-positron annihilation data collected at $sqrt{s} = 3.773$~GeV with the BESIII detector, we report the results of a search for the flavor-changing neutral current process $D^0togammagamma$ using a double-tag technique. We find no signal and set an upper limit at $90%$ confidence level for the branching fraction of $B(D^0togammagamma) < 3.8times10^{-6}$. We also investigate $D^0$-meson decay into two neutral pions, obtaining a branching fraction of $B(D^0topi^0pi^0) = (8.24pm0.21(text{stat.})pm0.30(text{syst.}))times10^{-4}$, the most precise measurement to date and consistent with the current world average
Based on a sample of $1.31 times 10^9$ $J/psi$ events collected with the BESIII detector at the BEPCII collider, Dalitz plot analyses of selected 79,625 $etarightarrowpi^{+}pi^{-}pi^0$ events, 33,908 $etarightarrowpi^0pi^0pi^0$ events and 1,888 $eta^{prime}rightarrowpi^0pi^0pi^0$ events are performed. The measured matrix elements of $etarightarrowpi^+pi^-pi^0$ are in reasonable agreement with previous measurements. The Dalitz plot slope parameters of $etarightarrowpi^0pi^0pi^0$ and $eta^{prime}rightarrowpi^0pi^0pi^0$ are determined to be $-0.055 pm 0.014 pm 0.004$ and $-0.640 pm 0.046 pm 0.047$, respectively, where the first uncertainties are statistical and the second systematic. Both values are consistent with previous measurements, while the precision of the latter one is improved by a factor of three. Final state interactions are found to have an important role in those decays.
We revisit the coupled channel $Kbar{K}$ interactions and dynamically generate the resonances $f_0(980)$ and $a_0(980)$ within both the isospin and the physical bases. The $f_0(980)-a_0(980)$ mixing effects are generated in the scattering amplitudes of the coupled channels with the physical basis, which exploits the important role of the $Kbar{K}$ channel in the dynamical nature of these resonances. With the scattering amplitudes obtained, we investigate the $f_0(980)$ and $a_0(980)$ contributions to the $J/psito gammaetapi^0$, $J/psito gammapi^+pi^-$ and $J/psito gammapi^0pi^0$ radiative decays through the final-state interactions. We obtain the corresponding branching fractions $Br(J/psito gamma a_0(980) to gammaetapi^0) = (0.47pm0.05) times 10^{-7}$, $Br(J/psito gamma f_0(980) to gammapi^+pi^-) = 0.37 times 10^{-7} - 1.98 times 10^{-6}$, $Br(J/psito gamma f_0(980) to gammapi^0pi^0) = 0.18 times 10^{-7} - 9.92 times 10^{-7}$, and predict $Br(J/psito gamma a_0(980)) = 1.72 times 10^{-8} - 3.07times 10^{-7}$ and $Br(J/psito gamma f_0(980)) = 1.86 times 10^{-8} - 1.89times 10^{-5}$. These fractions are within the upper limits of the experimental measurements.
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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