-Norbert's … BUBBLEGUM v.2 CODE for two-channel resonance scattering -

Disclaimer: this code has no "background terms" as the author does not believe in abstract and incoherent background, which is normally added to improve the resonance fit. This problem is under investigation. The present code focuses on unitarity, analyticity, and form factors.

The FORTRAN code BUBBLEGUM.f calculates the unitary, analytic T-matrix for a two-channel problem with an arbitrary number of resonances. It also gives the approximate results from the K-matrix method, the Breit-Wigner approximation, or the perturbative method for the same problem.
The FORTRAN code EPLOT.f generates a standard eps figure "plot.eps" from the data files generated by BUBBLEGUM.f. It allows one to include and exclude certain data files.
The Coherent Bubble Sum Approximation (hence the name "bubblegum") which is used to determine the exact T-matrix is explained in the paper bubblegum.ps (bubblegum.pdf).
Three key features of bubblegum, which are absent in most coupled channel codes:
  • ANALYTICITY AND UNITARITY
  • MASS SHIFTS DIRECTLY CORRELATED WITH THE HADRONIC FORM FACTORS
  • EXPANSION FOR THE FORM FACTORS; ALLOWS ONE TO FIT THE FORM FACTORS FROM THE DATA
    •  Version 2 attempts global mass shifts for the resonances, such that the T-matrix results and the approximate results compare better. However, for large values of the coupling constants, i.e., greater than 0.3, such a global mass shift might not exists. The program signals such failure, and will use unshifted values in that case.


    An example input file "in.dat" with two resonances. The general layout of the input file with an arbitary number of resonances and an arbitrary expansion is given in "template.in.dat"

    The example is taken from the S11 channel.




    The first comment lines of the BUBBLEGUM.f.




    The output of EPLOT.f: "plot.eps", plotting "11100" which means T-matrix and K-matrix results. The green vertical lines indicate the position of the bare resonances. The light-blue lines at the bottom are the normalized Gamma, or W, functions of each channel. The numbers in the corner are the maximum and minimum value in each channel (single channel unitarity restricts the real part from -0.5 to 0.5, and the imaginary part from 0.0 to 1.0 (the Argand circle)). The horizontal black line is the zero axis. The Breit-Wigner and the perturbative results are not plotted here, but can be plotted with "11111". The program has no other options on purpose. For more elaborate plotting use your own favorite plotting program. The output files: t11.dat, t12.dat, t21.dat, t22.dat, k11.dat, k12.dat, k21.dat, k22.dat, b11.dat, b12.dat, b21.dat, b22.dat, p11.dat, p12.dat, p21.dat, p22.dat, gamma1.dat, and gamma2.dat contain all the BUBBLEGUM.f output information, which is required for EPLOT.f, together with the BUBBLEGUM.f input file in.dat.


    Below a little shell window, with all the commands required to generate some output:

    Some of the main formulas of the bubblegum approximation:




    Any problems compiling: (I used GNU Fortran 0.5.26 20000731 (Red Hat Linux 7.1 2.96-85)), please send me the log file. Any problems running, please send me the input file, and the error message.