We study the processes $\gamma \gamma \to K^0_S K^{\pm}\pi^{\mp}$ and $\gamma \gamma \to K^+ K^- \pi^0$ using a data sample of 519~$fb^{-1}$ recorded with the BaBar detector operating at the SLAC PEP-II asymmetric-energy $e^+ e^-$ collider at center-of-mass energies at and near the $\Upsilon(nS)$ ($n = 2,3,4$) resonances. We observe $\eta_c$ decays to both final states and perform Dalitz plot analyses using a model-independent partial wave analysis technique. This allows a model-independent measurement of the mass-dependence of the $I=1/2$ $K \pi$ $\mathcal{S}$-wave amplitude and phase. A comparison between the present measurement and those from previous experiments indicates similar behaviour for the phase up to a mass of 1.5 $GeV/c^2$. In contrast, the amplitudes show very marked differences. The data require the presence of a new $a_0(1950)$ resonance with parameters $m=1931 \pm 14 \pm 22 \ MeV/c^2$ and $\Gamma=271 \pm 22 \pm 29 \ MeV$.
Measured amplitude and phase values for the $I=1/2$ $K \pi$ $\mathcal{S}$-wave as functions of mass obtained from the Model Independent Partial Wave Analysis (MIPWA) of $\eta_c \to K^0_{\scriptscriptstyle S} K^{\pm}\pi^{\mp}$. The amplitudes and phases in the mass interval 14 are fixed to constant values.
Measured amplitude and phase values for the $I=1/2$ $K \pi$ $\mathcal{S}$-wave as functions of mass obtained from the Model Independent Partial Wave Analysis (MIPWA) of $\eta_c \to K^+ K^- \pi^0$. The amplitudes and phases in the mass interval 14 are fixed to constant values.
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The energy dependence of the modulus and phase of the K L 0 -K S 0 regeneration amplitude on hydrogen in the range of 14–50 GeV has been investigated at the Serpukhov 70 GeV accelerator. It has been established that the modulus of the modified regeneration amplitude decreases with increasing momentum as 2|ƒ 21 0 (p)|/k = (0.84 ± 0.42) · p −0.50±0.15 mb . The amplitude phase is energy-independent and its mean value is ϕ 21 0 = −132° ± 5°. The results obtained are compared with other experiments and with predictions of different theoretical models.
TABLE ALSO CALCULATES FORWARD DIFFERENTIAL CROSS SECTION AND SIG(AK0 P) - SIG(K0 P) TOTAL CROSS SECTION DIFFERENCES.
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The measurements of the transmission regeneration amplitude on hydrogen in the momentum region of 14–42 GeV/ c indicate that in accordance with the Pomeranchuk theorem its magnitude |ƒ° − ƒ °|/k decreases as energy increases and its phase is approximately constant and equal to arg (ƒ° − ƒ °) = (−118 ± 13)° .
THE REGENERATION AMPLITUDE DECREASES OVER THIS ENERGY RANGE.