Disagreement with sector decomposition

[lgoetzfried]

I recently computed some triangle and box integrals with QCDLoop and compared them to sector decomposition results from pysecdec. This was actually intended to compute some subtopologies of a pentagon, thus the variables are adapted to that. At a certain point in phase-space, I find disagreement for several triangles and boxes.
For example, if I run the following C++ program:

#include <iostream>
#include <iomanip>
#include <complex>
#include <qcdloop/qcdloop.h>
#include <qcdloop/cache.h>

using namespace std::numbers;
using std::vector;
using std::complex;
using std::cout;
using std::endl;
using std::setprecision;
using std::scientific;
using std::rand;

int main()
{  
  double mu2 = ql::Pow(1.0,2.0);
  
  complex<double> m12 = complex<double>(1.0,-0.1); // internal mass square
  double m22 = 5./2.; // off-shellness of one of the five particles
  double s12 = 7.; // five-particle Mandelstam invariants
  double s23 = -(7./2.);
  double s34 = 23./2.;
  double s45 = -(5./2.);
  double s15 = 6.;
  
  vector<complex<double>> res(3);
  
  // pysecdec results
  complex<double> pysecValue0 = 0;
  complex<double> pysecValue1 = 0;
  complex<double> pysecValue2 = complex<double>(0.3313048590525264,-0.33478605007189316);
  
  // QCDloop results
  
  /**
   * Triangle
   */
  vector<complex<double>> m = {m12, 0.0, 0.0};
  vector<double> p = {s12, s34, 0.0};
  cout << ql::red << "\n====== Triangle 6 ======" << ql::def << endl;
  ql::Triangle<complex<double>,complex<double>,double> tr;
  tr.integral(res, mu2, m, p);
  cout << "QCDLoop - pysecdec:" << endl;
  // pysecdec (as I set it up) uses a different normalization than QCDLoop. Hence the "-pow(pi,2)/12. * res[2]".
  cout << "eps^(" << 0 << ")\t\t" << (res[0]-pow(pi,2)/12. * res[2] - pysecValue2) << endl;
  cout << "eps^(" << -1 << ")\t" << (res[1] - pysecValue1) << endl;
  cout << "eps^(" << -2 << ")\t" << (res[2] - pysecValue0) << endl; 
  cout << "pysecdec:" << endl;
  cout << "\teps^(" << 0 << ")\t\t" << (pysecValue2) << endl;
  cout << "\teps^(" << -1 << ")\t" << (pysecValue1) << endl;
  cout << "\teps^(" << -2 << ")\t" << (pysecValue0) << endl; 

  return 0;
}

I obtain a deviation of 2.37609 + 0.859857*I - which appears quite huge for me. Moreover, this is just an example, for other diagrams I obtain similar deviations.

My PySecDec setup is

#!/usr/bin/env python3
import pySecDec as psd

if __name__ == "__main__":

    li = psd.LoopIntegralFromGraph(
        internal_lines = [['m1',[5,1]], ['m1',[1,2]], ['0',[2,3]], ['0',[3,4]], ['0',[4,5]]],
        external_lines = [['p1',1], ['p2',2], ['p3',3], ['p4',4], ['p5',5]],
        replacement_rules = [
            ('p1', '-p2-p3-p4-p5'),
            ('p2*p2', '0'),
            ('p3*p3', '0'),
            ('p4*p4', '0'),
            ('p5*p5', '0'),
            ('p2*p3', 's23/2'),
            ('p2*p4', 's15/2-s23/2-s34/2'),
            ('p2*p5', 'm22/2-s12/2-s15/2+s34/2'),
            ('p3*p4', 's34/2'),
            ('p3*p5', 's12/2-s34/2-s45/2'),
            ('p4*p5', 's45/2'),
            ('m1**2', 'm12')
        ],
        powerlist = [1, 0, 1, 0, 1]
    )

    Mandelstam_symbols = ['m22','s12','s23','s34','s45','s15']
    mass_symbols = ['m12']

    psd.loop_package(
        name = 'triangle6',

        loop_integral = li,

        real_parameters = Mandelstam_symbols,
        complex_parameters = mass_symbols,

        requested_orders = [2],
        additional_prefactor = 'exp(eps*EulerGamma)'
    )

(and an integration script which I did not want to attach here because it bloats up the post). To the best of my knowledge, this should define the same diagram. Indeed, if I instead run the very same test with the imaginary part of m12 set to zero, I find agreement.

I have tested also for my relevant configuration several other triangles and boxes. For some of them, I found agreement, for some not; I can share the list with you if you want. Moreover, I have myself written a library to compute these diagrams analytically, which agrees with pysecdec but disagrees with QCDLoop in these cases.

If there is anything more on information that I can provide you, please let me know.

Best regards,
Linus Götzfried