All the channels are treated as two-body (meson-baryon) states and are labeled as follows:
(i) if the state has the same orbital angular momentum ($\ell$) as the partial wave the channel is identified by the names of the meson and the baryon, e.g. $\bar{K}N$ or $\pi \Sigma$;
(ii) if the baryon has spin $3/2$, as it is the case of $\Sigma (1385)$, $\Delta (1232)$ and $\Lambda (1520)$ (in what follows $\Sigma^*$, $\Delta$ and $\Lambda^*$ respectively), the orbital angular momentum of the initial state does not correspond to $\ell$ and a subindex $L$ is added denoting the angular momentum of the initial (final) state. For example, in ${\bar K} N$ system the $S_{01}$ denotes the isoscalar, $l=0$ partial wave with total spin $J=1$. It may couple to $\pi \Sigma^*$ with orbital angular momentum $L=2$ ($D$ wave) which we label as $\left[ \pi \Sigma^*\right]_D$;
(iii) if the state contains a spin one $\bar{K}^*$ and a nucleon, they can couple to spin $1/2$ which we name $\bar{K}_1^*N$ or to spin $3/2$ which we name $\bar{K}_3^*N$. The $\bar{K}_1^*N$ state has the same orbital angular momentum as the $\bar K N$ and the partial wave but the $\bar{K}_3^*N$ does not, hence we add a $L$ subindex to the last. For example, the $S_{01}$ partial wave has as possible states $\bar{K}_1^*N$ and $\left[ \bar{K}_3^*N\right]_D$.

For every partial wave we include an additional meson-hyperon channel that collectively accounts for any any missing inelasticity arising from channels not included explicitly. The kinematical variables for such a dummy channel is chosen arbitrarily as if it was a two-pion $\Lambda$ or $\Sigma$ state labeled as $\pi \pi \Lambda$ for $I=0$ and $\pi \pi \Sigma$ for $I=1$ partial waves. All the channels incorporated in the model have single-energy partial-wave data to fit except for the dummy channels $\pi\pi\Lambda$ and $\pi\pi\Sigma$ and the $\eta \Lambda$ and $\eta \Sigma$ channels in the $S$ waves.

The full list of initial (final) states for each partial wave is:

• $S_{01}$:$\bar{K}N$, $\pi \Sigma$, $\eta \Lambda$, $\bar{K}^*_{1}N$, $\left[ \bar{K}^*_{3}N\right]_D$, $\left[ \pi \Sigma^*\right]_D$, $\pi \pi \Lambda$;
• $P_{01}$: $\bar{K}N$, $\pi \Sigma$, $\bar{K}^*_{1}N$, $\left[ \bar{K}^*_{3}N\right]_P$, $\left[ \pi \Sigma^*\right]_P$, $\pi \pi \Lambda$;
• $P_{03}$: $\bar{K}N$, $\pi \Sigma$, $\bar{K}^*_{1}N$, $\left[ \bar{K}^*_{3}N\right]_P$, $\left[ \bar{K}^*_{3}N\right]_F$, $\left[ \pi \Sigma^*\right]_P$, $\left[ \pi \Sigma^*\right]_F$, $\pi \pi \Lambda$;
• $D_{03}$: $\bar{K}N$, $\pi \Sigma$, $\bar{K}^*_{1}N$, $\left[ \pi \Sigma^*\right]_S$, $\left[ \pi \Sigma^*\right]_D$, $\pi \pi \Lambda$;
• $D_{05}$: $\bar{K}N$, $\pi \Sigma$, $\left[ \pi \Sigma^*\right]_D$, $\left[ \pi \Sigma^*\right]_G$, $\pi \pi \Lambda$;
• $F_{05}$: $\bar{K}N$, $\pi \Sigma$, $\bar{K}^*_{1}N$, $\left[ \bar{K}^*_{3}N\right]_P$, $\left[ \bar{K}^*_{3}N\right]_F$, $\left[ \pi \Sigma^*\right]_P$, $\left[ \pi \Sigma^*\right]_F$, $\pi \pi \Lambda$;
• $F_{07}$: $\bar{K}N$, $\pi \Sigma$, $\bar{K}^*_{1}N$, $\pi \pi \Lambda$;
• $G_{07}$: $\bar{K}N$, $\pi \Sigma$, $\bar{K}^*_{1}N$, $\left[ \bar{K}^*_{3}N\right]_D$, $\left[ \bar{K}^*_{3}N\right]_G$, $\pi \pi \Lambda$;
• $S_{11}$: $\bar{K}N$, $\pi \Sigma$, $\pi \Lambda$, $\eta \Sigma$, $\bar{K}^*_{1}N$, $\left[ \bar{K}^*_{3}N\right]_D$, $\left[ \pi \Sigma^*\right]_D$, $\left[ \pi \Lambda^*\right]_P$, $\left[ \bar{K} \Delta \right]_D$, $\pi \pi \Sigma$;
• $P_{11}$: $\bar{K}N$, $\pi \Sigma$, $\pi \Lambda$, $\bar{K}^*_{1}N$, $\left[ \bar{K}^*_{3}N\right]_P$, $\left[ \pi \Sigma^*\right]_P$, $\left[ \pi \Lambda^*\right]_D$, $\left[ \bar{K} \Delta \right]_P$, $\pi \pi \Sigma$;
• $P_{13}$: $\bar{K}N$, $\pi \Sigma$, $\pi \Lambda$, $\bar{K}^*_{1}N$, $\left[ \bar{K}^*_{3}N\right]_P$, $\left[ \pi \Sigma^*\right]_P$, $\left[ \pi \Lambda^*\right]_D$, $\left[ \pi \Sigma^*\right]_F$, $\left[ \pi \Lambda^*\right]_S$, $\left[ \bar{K} \Delta \right]_P$, $\pi \pi \Sigma$;
• $D_{13}$: $\bar{K}N$, $\pi \Sigma$, $\pi \Lambda$, $\bar{K}^*_{1}N$, $\left[ \bar{K}^*_{3}N\right]_S$, $\left[ \bar{K}^*_{3}N\right]_D$, $\left[ \pi \Sigma^*\right]_S$, $\left[ \pi \Sigma^*\right]_D$, $\left[ \pi \Lambda^*\right]_P$, $\left[ \pi \Lambda^*\right]_F$, $\left[ \bar{K} \Delta \right]_S$, $\left[ \bar{K} \Delta \right]_D$, $\pi \pi \Sigma$;
• $D_{15}$: $\bar{K}N$, $\pi \Sigma$, $\pi \Lambda$, $\bar{K}^*_{1}N$, $\left[ \bar{K}^*_{3}N\right]_D$, $\left[ \pi \Sigma^*\right]_D$, $\left[ \pi \Sigma^*\right]_G$, $\left[ \pi \Lambda^*\right]_P$, $\left[ \pi \Lambda^*\right]_F$, $\left[ \bar{K} \Delta \right]_D$, $\pi \pi \Sigma$;
• $F_{15}$: $\bar{K}N$, $\pi \Sigma$, $\pi \Lambda$, $\bar{K}^*_{1}N$, $\left[ \bar{K}^*_{3}N\right]_P$, $\left[ \bar{K}^*_{3}N\right]_F$, $\left[ \pi \Sigma^*\right]_P$, $\left[ \pi \Sigma^*\right]_F$, $\left[ \pi \Lambda^*\right]_D$, $\left[ \pi \Lambda^*\right]_G$, $\left[ \bar{K} \Delta \right]_P$, $\pi \pi \Sigma$;
• $F_{17}$: $\bar{K}N$, $\pi \Sigma$, $\pi \Lambda$, $\bar{K}^*_{1}N$, $\left[ \bar{K}^*_{3}N\right]_F$, $\left[ \bar{K}^*_{3}N\right]_H$, $\left[ \pi \Sigma^*\right]_F$, $\left[ \pi \Lambda^*\right]_D$, $\left[ \pi \Lambda^*\right]_G$, $\left[ \bar{K} \Delta \right]_F$, $\pi \pi \Sigma$;
• $G_{17}$: $\bar{K}N$, $\pi \Sigma$, $\pi \Lambda$, $\bar{K}^*_{1}N$, $\left[ \bar{K}^*_{3}N\right]_G$, $\left[ \pi \Lambda^*\right]_F$, $\left[ \pi \Lambda^*\right]_H$, $\left[ \bar{K} \Delta \right]_D$, $\left[ \bar{K} \Delta \right]_G$, $\pi \pi \Sigma$.

• Partial Waves Fortran code and input: zip file
• Contact person: Cesar Fernandez-Ramirez
• Last update: September 2015
• Zip File Content:
• README file: README.tex and README.pdf
• Fortran Source File: partialwaves.f
• Parameter files (contain the parameters for each partial wave):
• parameters.s01.inp
• parameters.p01.inp
• parameters.p03.inp
• parameters.d03.inp
• parameters.d05.inp
• parameters.f05.inp
• parameters.f07.inp
• parameters.g07.inp
• parameters.s11.inp
• parameters.p11.inp
• parameters.p13.inp
• parameters.d13.inp
• parameters.d15.inp
• parameters.f15.inp
• parameters.f17.inp
• parameters.g17.inp
• Input File: file.inp
[Show/Hide Details]

Example of input file (file.inp):

            s01

            1 1

            2.5

            4.5

            100

            

• The first line indicates the partial wave, the options are:


• all $\to$ computes all the partial waves for a given channel
• s01 $\to S_{01}$
• p01 $\to P_{01}$
• p03 $\to P_{03}$
• d03 $\to D_{03}$
• d05 $\to D_{05}$
• f05 $\to F_{05}$
• f07 $\to F_{07}$
• g07 $\to G_{07}$
• s11 $\to S_{11}$
• p11 $\to P_{11}$
• p13 $\to P_{13}$
• d13 $\to D_{13}$
• d15 $\to D_{15}$
• f15 $\to F_{15}$
• f17 $\to F_{17}$
• g17 $\to G_{17}$


• The second line indicates the process.
  It is made of two numbers where the first refers to the initial state and the last to the final.
  The options are:


• 1 $\to \bar{K}N$,
• 2 $\to \pi \Sigma$,
• 3 $\to \pi \Lambda$,
• 4 $\to \eta \Lambda$,
• 5 $\to \eta \Sigma$,
• 6 $\to \bar{K}_1 N$,
• 7 $\to \left[ \bar{K}_3 N \right]_-$,
• 8 $\to \left[ \bar{K}_3 N \right]_+$,
• 9 $\to \left[ \pi \Sigma^* \right]_-$,
• 10 $\to \left[ \pi \Sigma^* \right]_+$,
• 11 $\to \left[ \bar{K} \Delta \right]_-$,
• 12 $\to \left[ \bar{K} \Delta \right]_+$,
• 13 $\to \left[ \pi \Lambda(1520) \right]_-$,
• 14 $\to \left[ \pi \Lambda(1520) \right]_+$,
• 15 $\to \pi \pi \Lambda$,
• 16 $\to \pi \pi \Sigma$.


The $+$ and $-$ subindices are short for the angular momentum of the state.
The $+$ stands for the higher angular momentum and $-$ for the lower.
If only one state of angular momentum is possible it corresponds to the $+$ state.

Examples:
• Example 1: For any partial wave, 1 2 computes $\bar{K}N \to \pi \Sigma$.
• Example 2: For partial wave $S_{01}$, 15 10 computes $\pi \pi \Lambda \to \left[ \pi \Sigma(1385)\right]_D$.
• Example 3: For partial wave $F_{05}$, 8 7 computes $\left[ \bar{K}^*_3 N \right]_F \to \left[ \bar{K}^*_3 N \right]_P$.


• The third line indicates the starting value of $s$ in GeV$^2$.


• The fourth line indicates the final value of $s$ in GeV$^2$.


• The fifth line indicates the the amount of points to calculate.
  There is a limit of 1000 points.
  It can be changed modifying variable max_data_points=1000 in module resonancesizes.

The online version of the code is the same as the one available for download except for some built-in functionalities aimed to allow the webpage to produce nicer plots.
The webpage has integrated some restrictions in the inputs through drop-down menus, kinematical ranges and number of points to calculate.
The available range for $s$ is $\left[1.5 , 5.0 \right]$ GeV$^2$ where $s$ is energy squared in the center of mass frame.
There is a limit of 1000 points to calculate.
Any initial and final state can be selected. If that state is not present in the partial wave it will yield a zero result.

The online and the downloadable versions produce an output file (output.txt) which contains six columns:

(i)     $s$ (GeV$^2$),
(ii)   $~E_{lab}$ (GeV),
(iii)  $~p_{lab}$ (GeV),
(iv)   the center of mass incoming momentum squared $q^2$ (GeV$^2$),
(v)    real part of the partial wave (adimensional), and
(vi)   imaginary part of the partial wave (adimensional).

If the process is not kinematically allowed $p_{lab}=0$ in the output file.
The online version also produces a figure of the partial wave vs $s$.
If the selected partial is "all", the partial waves are written in files pw.s01.txt, pw.p01.txt, and so on.
The webpage generates a downloable output.zip file with all the partial waves in it.