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- W2003933254 startingPage "1434" @default.
- W2003933254 abstract "A model is proposed, within the framework of single-channel Frye-Warnock formalism, in which it is assumed that at high energies low partial waves become purely imagninary. A Pomeranchuk-type theorem then implies that the Frye-Warnock Born term must vanish asymptotically. Thus no cutoffs are needed in the integral equations. For the $P$-wave $ensuremath{pi}ensuremath{pi}$ amplitude we assume that only the nearby part of the left cut (i.e., the part up to a finite negative value ---${s}_{A}$) is given by the discontinuity due to elementary $ensuremath{rho}$ exchange. The rest of the left cut is assumed to be given by the asymptotic right-hand discontinuity which, because of unitarity, is positive and ensuremath{le}textonehalf{}, and is smaller than the abnormally large discontinuity ($ensuremath{simeq}3$) given, in the earlier models, by the elementary $ensuremath{rho}$ exchange. For the right cut of the Frye-Warnock Born term, two cases have been considered: (a) The absorption parameter $ensuremath{eta}(s)$ is assumed constant beyond $s=100{{m}_{ensuremath{pi}}}^{2}$. (b) The $ensuremath{eta}(s)$ is assumed constant ($={ensuremath{eta}}_{d}$) between $100{{m}_{ensuremath{pi}}}^{2}$ and $300{{m}_{ensuremath{pi}}}^{2}$, and beyond $300{{m}_{ensuremath{pi}}}^{2}$ it is assumed to be $ensuremath{simeq}0.5$ as given by Regge fits with a flat Pomeranchuk trajectory. Unlike earlier models, the width of the $ensuremath{rho}$ can be controlled. Its value is very sensitive to $ensuremath{eta}$. For case (a) with $ensuremath{eta}=0.2ifmmodetimeselsetexttimesfi{}{10}^{ensuremath{-}1}$ and ${s}_{A}=225{{m}_{ensuremath{pi}}}^{2}$, and for case (b) with ${ensuremath{eta}}_{d}=0.2ifmmodetimeselsetexttimesfi{}{10}^{ensuremath{-}3}$ and ${s}_{A}=380{{m}_{ensuremath{pi}}}^{2}$, we obtain ${m}_{ensuremath{rho}}=760$ MeV and the $ensuremath{rho}$ width ${ensuremath{Gamma}}_{ensuremath{rho}}$ as small as 100 MeV." @default.
- W2003933254 created "2016-06-24" @default.
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- W2003933254 date "1968-09-25" @default.
- W2003933254 modified "2023-10-16" @default.
- W2003933254 title "Pomeranchuk Theorem for Partial Waves and Narrowing of Resonance Widths: TheϱMeson" @default.
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- W2003933254 doi "https://doi.org/10.1103/physrev.173.1434" @default.
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