.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/04_sunset_dispersion.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_04_sunset_dispersion.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_04_sunset_dispersion.py:


Two-loop sunset: imaginary part and dispersion relation
=======================================================

The imaginary part of the massive sunset from its phase-space representation, and
the twice-subtracted dispersion relation :math:`S(s) - S(0) - s S'(0)`. Both are
precision-checked numerical integrations, validated against Feynman-parameter integrals
and a closed form. Each subtracted value takes 10-20 s.

.. GENERATED FROM PYTHON SOURCE LINES 10-19




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    threshold (m1+m2+m3)^2 = 17.1915082254503
    s =   10:  Im S =              0.0   S(s) - S(0) - s S'(0) = (-0.914137148613 + 0.0j)
    s =   20:  Im S =  -0.375849653338   S(s) - S(0) - s S'(0) = (-5.11009352005 - 0.375849653338j)
    s =   50:  Im S =   -24.9914650397   S(s) - S(0) - s S'(0) = (-20.0295703709 - 24.9914650397j)
    s =  100:  Im S =   -88.1849955516   S(s) - S(0) - s S'(0) = (-19.9854890522 - 88.1849955516j)






|

.. code-block:: Python

    import mpmath as mp

    from ramanujan_qft import sunset_im, sunset_subtracted, sunset_threshold

    m = (1, 2, 3)
    print("threshold (m1+m2+m3)^2 =", sunset_threshold(*m))
    for s in (10, 20, 50, 100):
        print(f"s = {s:>4}:  Im S = {mp.nstr(sunset_im(s, *m), 12):>16}   "
              f"S(s) - S(0) - s S'(0) = {mp.nstr(sunset_subtracted(s, *m), 12)}")


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (1 minutes 36.433 seconds)


.. _sphx_glr_download_auto_examples_04_sunset_dispersion.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: 04_sunset_dispersion.ipynb <04_sunset_dispersion.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: 04_sunset_dispersion.py <04_sunset_dispersion.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: 04_sunset_dispersion.zip <04_sunset_dispersion.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_