Codes and some additional notes related to the author papers on topic Minkowski space solution of QCD and beyond" (papers are available at ArXiV)

QCD and related topics:
  • V. Sauli, Quark spectral functions and the Hadron Vacuum Polarization from application of DSEs in Minkowski space ,
    arXiv:1809.07644


    codes for the quark gap equation:
    ( gold2019.for)
    ( gold2020.for)

  • V. Sauli, Confined gluon from Minkowski space continuation of PT-BFM SDE solution,
    J. Phys. G.: Nucl. Part. Phys. 39 (2012); arXiv:[1102.5765]


    Related nonperturbative studies of quantum field theories . Most of these papers relly on the validity of spectral representation for two point Green's functions and on the Perturbation Theory Integral Representation in more general case.



    In cases bellow the applicability of methods are limited by some critical value of coupling. Numerical calculations were performed bellow this critical coupling and solutions for propagators correspond to free particle propagation plus a continuum. Bound states, if studied were made out of particles , not quarks and gluons.



    • V. Sauli, Implication of analyticity to solution of Schwinger-Dyson equations in Minkowski space,
      submitted to Few Body Systems, arXiv: hep-ph/0412188.


    • V. Sauli, Minkowski solution of Dyson-Schwinger equations in momentum subtraction scheme,
      JHEP 0302 , 001 (2003); arXiv:[hep-ph/0209046]


    • V. Sauli, Running coupling and fermion mass in strong coupling Quantum Electrodynamics,
      J. Phys. G30, 739 (2004); arXiv:[hep-ph/0306081]


    • V. Sauli, J. Adam, Study of relativistic bound states for scalar theories in the Bethe-Salpeter and Dyson-Schwinger formalism,
      Phys. Rev. D67, 085007 (2003);arXiv: [hep-ph/0111433],


    • V. Sauli, Solving the Bethe-Salpeter equation for fermion-antifermion pseudoscalar bound state in Minkowski space,
      submitted to Phys. Rev. D; arXiv: [hep-ph/0404189],


    • V. Sauli, Some aspects of dynamical mass generation,
      oral conference contribution, SMFT Bari 2004, Neutrino Prague 2004; arXiv:[hep-ph/0410167]

    • V. Sauli, Non-perturbative solution of metastable scalar models,
      J. Phys. A36, 8703 (2003); arXiv:[hep-ph/0211221]


    • V. Sauli, Confined gluon from Minkowski space continuation of PT-BFM SDE solution,
      J. Phys. G.: Nucl. Part. Phys. 39 (2012); arXiv:[1102.5765]


    • V. Sauli, Higgsonium in singlet extension of Standard Model
      ; arXiv:[0808.1894]




      Before inventing working methods for QCD The best what I got together with my colaborators Pedro Bicudo and J. Adam in this respect was the solution obtained at the vicinity of critical coupling. Characteristic amount of chiral symmetry breaking known for QCD has not been achieved by the method. See the paper:

    • Dynamical chiral symmetry breaking with Minkowski space integral representations
      V. Sauli, J. Adam, P. Bicudo Phys. Rev. D75; 087701 (2007) ,arXiv:[hep-ph/0607196]

      I made a curious attempt to solve DSE & BSE directly within Minkowski metric, but do not try that:) As one is face the integration along the cut of anayltical functions , the method is not working generaly and it turns this task is not numericaly feasible for the realistic systems. Cases bellow should be regarded as a curiosity. They offer stable results only since some integrations were done analyticaly. (papers are available at ArXiV)

    • V. S., Pions and excited scalars in Minkowski space DSBSE formalism
      arXiv:1411.2568


      The code that calculated the scalars:
      ( superscalar12.for)

      the code that goes in reverse direction .i.e. form higher mass to... whatever (including unphysical tahyonic bound state):
      ( superscalarb12.for)

      Raw sample output for the second case (for C=1/80):
      ( iterscalar12b.dat)

      Raw sample output for the superscalar12.for case (for C=1/80):
      ( iterscalar12.dat) The data are ploted in the Figure at refered paper.

      For C=1/90 (unpublished case):
      ( iterscalar.dat)



      The code, which calculated pions spectra in the paper above is here:
      ( sample data +code)

      The ascii data file includes raw data -three columns output- mass, error, and lambda, then the body of the code follows (superpion2.for in my database). The stability of numerics have been checked many times, e.g. by changin the number of iterations, steps etc. examples of working codes:
      ( superpion0.for) The code for quark gap equation, the first part is just the data:
      ( quargraph138.dat) There are 1200 lines with p2 ,Re M and Im M as a columns, the the code named quark138.for in my database follows, this is the same code which provides S^+ result for the data in the paper "Lattice Inspired..."

      The convergence of the iterations was pretty fast:
      ( iter138.dat)

      Code for the numerical fit of the quark propagator as described in the text:
      ( fit "embecko.for")

    • V. S., Intriguing solutions of the Bethe-Salpeter equation for radially excited pseudoscalar charmonia
      arXiv:1411.2568


      where, appart more standard since Euclidean, the first Minkowski space solution hass been published for charmonium. Added 19.6.2015: Codes related with the paper
      arXiv:1505.03778


      The code which calculates the first(?) excited state of the pion:
      ( pionnew201n.for) with the out-put ( iterpion201n.dat)


    PhD thesis (defended in 19-th September 2005)
    Schwinger-Dyson approach to field models with strong coupling ( ps)
    (Supervisor: J. Adam)

    Abstract of PhD thesis: (pdf, ps)