Phase shifts and inelasticities in pseudoscalar scatterings $0^- 0^- \to 0^- 0^-$.
- Isoscalar $s$-wave: $L = 0$ $I = 0$
- Isospinor $s$-wave: $L = 0$ $I = 1/2$
- Isovector $s$-wave: $L = 0$ $I = 1$
- Isotensor $s$-wave: $L = 0$ $I = 2$
- Isoscalar $p$-wave: $L = 1$ $I = 0$
- Isovector $p$-wave: $L = 1$ $I = 1$
Phase shifts $\delta_\ell$ and inelasticities $\eta_\ell$ are defined by
\begin{align}
S_\ell = \eta_\ell e^{2i \delta_\ell} = 1 + 2i \sqrt{p_i}\ T_\ell\ \sqrt{p_f}.
\end{align}
The relation to the differential cross section is
\begin{align}
\frac{d \sigma}{d\Omega} & = \frac{\kappa_i \kappa_f}{4 p_i^2} \sum_{\ell \ell'}
\left[ (2\ell+1) (\eta_\ell e^{2i \delta_\ell}-1) P_\ell(z) \right]
\left[ (2\ell'+1) (\eta_{\ell'} e^{-2i \delta_{\ell'}}-1) P_{\ell'}(z) \right]
\end{align}
where $p_i$ ($p_f$) is the initial (final) momentum in the center-of-mass and
$\kappa_{i,f}$ are the symmetry factor of the initial and final states. $\kappa_{1,2} = 1$ (2) for two different (identical) particles.
Isoscalar $s$-wave $L = 0$ $I = 0$
Isospinor $s$-wave $L = 0$ $I = 1/2$
Publication: J. Pelaez and A. Rodas Phys. Rev. D93 (2016) 074025 , $\pi K \to \pi K$
- Files:
allfiles.zip,
ModS12c.dat, ModP12c.dat, ModD12c.dat, ModF12c.dat, PhaseS12c.dat, PhaseP12c.dat, PhaseD12c.dat, PhaseF12c.dat - Format:
The $I=3/2$ from the same publication are also provided in the section $L = 0$ $I = 3/2$ Below the $\pi \eta$ thresold, the partial waves are considered elastic and hence the phase is the phase shift. - Format:
Both the modulus and the phase of the I=1/2 partial waves are provided.
For the file with the modulus, the format is $\sqrt{s}$ in GeV, $\sqrt(2\ell+1)|t_\ell|$, error up and error down.
For the file with the phase, the format is $\sqrt{s}$ in GeV, $\phi(t_\ell)$, error up and error down.
Isovector $s$-wave $L = 0$ $I = 1$
Publication: M. Albaladejo and B. Moussallam Eur. Phys. J. C45 (2015) 488 , $\pi\eta \to \pi\eta, K\bar K$
- Files: fort.125, fort.130, fort.135, fort.140, fort.145, fort.150, fort.155, fort.160, fort.165, fort.170, fort.175, allfiles.zip
- Comments:
There are several files fort.X, where X ranges from 125 to 175.
That number is the phase $\delta_1 + \delta_2$ at $\sqrt{s} = m_{a_0(1450)}$, which is used to characterize the global behaviour of the amplitudes.
The parameters are chosen so as to reproduce the $a_0$'s poles positions and this number.
$\eta\pi$ is channel 1 ; $K \bar K$ is channel 2. - Format:
In each file, column 1 is $\sqrt{s}$ in MeV, columns 2-7 are Re and Im of $T(11,12,22)$,
columns 8-13 are Re and Im of $S(11,12,22)$, columns 14-17 are $\delta_1$, $\delta_2$, $\delta_1+\delta_2$, $\eta$,
and column 18 is $\delta_1$ again (but without making it continuous with $\pi$ jumps). - Figures: fig1.pdf , fig2.pdf , fig3.pdf
Publication: Z.-H. Guo et al. Phys. Rev. D95 (2015) 054004 , $\pi\eta \to \pi\eta$
- Files: pieta-phaseLO-err.txt, pieta-phaseNLO-low-err.txt, pieta-phaseNLO-up-err.txt
- Format: The LO results are given in the file pieta-phaseLO-err.txt.
The columns are: $\sqrt{s}$, phase shift central value, lower-error band, upper-error band, inelasticity, lower- and upper-error band.
The file pieta-phase-NLO-low-err.txt provides the lower NLO solution in Fig 13, with the same meaning for each column,
whereas pieta-phase-NLO-up-err ($\sqrt{s}$, lower error band, upper error band), provides the upper solution.
Publication: Z.-H. Guo, J.A. Oller and J. Ruiz de Elvira, Phys.Lett. B712 (2012) 407, Phys. Rev. D86 (2012) 054006, $\pi\eta \to \pi\eta$
- Files: delta10err.dat , eta10err.dat
- Format: delta10err.dat (eta10err.dat) contains the phase-shift (inelasticity).
In each file, the three different columns stand for $\sqrt{s}$, central value and error. - Comments:
These results are based on U(3) ChPT up to NNLO in $\delta=\{p,1/N_c\}$,
where the order $p^4$ parameters are extracted from resonance saturation.
In addition the solutions are constrained to satisfy Weinberg spectral functions and semi-local duality.