DIS: F2charm is non-zero at low Q2 in FFNS4 for uonly PDF

[felixhekhorn]

• We find F2charm beeing non-zero when using the uonly PDF (which does what it name says uonly.tar.gz)
• We believe this to be wrong

F2charm with theory=99 using uonly
      x        Q2     APFEL  yadism  yadism_error  rel_err[%]
0  0.01  2.000000  0.000260     0.0           0.0      -100.0
1  0.01  2.444444  0.000304     0.0           0.0      -100.0
2  0.01  2.888889  0.000336     0.0           0.0      -100.0
3  0.01  3.333333  0.000356     0.0           0.0      -100.0
4  0.01  3.777778  0.000366     0.0           0.0      -100.0
5  0.01  4.222222  0.000000     0.0           0.0         NaN
6  0.01  4.666667  0.000000     0.0           0.0         NaN
7  0.01  5.111111  0.000000     0.0           0.0         NaN
8  0.01  5.555556  0.000000     0.0           0.0         NaN
9  0.01  6.000000  0.000000     0.0           0.0         NaN

theory 99

{'ID': 22,
 'PTO': 0,
 'FNS': 'FFNS',
 'DAMP': 0,
 'IC': 0,
 'ModEv': 'EXA',
 'XIR': 1.0,
 'XIF': 1.0,
 'NfFF': 4,
 'MaxNfAs': 6,
 'MaxNfPdf': 6,
 'Q0': 1,
 'alphas': 0.11800000000000001,
 'Qref': 91.2,
 'QED': 0,
 'alphaqed': 0.007496251999999999,
 'Qedref': 1.777,
 'SxRes': 0,
 'SxOrd': 'LL',
 'HQ': 'POLE',
 'mc': 2,
 'Qmc': 2,
 'kcThr': 1.0,
 'mb': 4,
 'Qmb': 4,
 'kbThr': 1.0,
 'mt': 173.07,
 'Qmt': 173.07,
 'ktThr': 1.0,
 'CKM': '0.97428 0.22530 0.003470 0.22520 0.97345 0.041000 0.00862 0.04030 0.999152',
 'MZ': 91.1876,
 'MW': 80.398,
 'GF': 1.1663787e-05,
 'SIN2TW': 0.23126,
 'TMC': 0,
 'MP': 0.938,
 'Comments': 'LO baseline for small-x res',
 'global_nx': 0,
 'EScaleVar': 1,
 '_modify_time': '2020-05-28 16:55:02.164765'}

might be related to #22

[juanrojochacon]

what is the uonly PDFs? Only up quark to all scales?
You use mc = 2 GeV, so mc2 = 4 GeV2 right? So F2c = 0 above the charm threshold, as it should be. The funny thing is that it is also different from zero below, but F2c should not be used there?

[vbertone]

Dear @felixhekhorn, I also found your result worrisome.
Therefore, using a simple modification of the code that @juanrojochacon posted here #22 :

#include "APFEL/APFEL.h"
#include <utility>
#include <vector>
#include <math.h>
int main()
{
  APFEL::SetPerturbativeOrder(0);
  APFEL::SetPDFSet("uonly");
  APFEL::InitializeAPFEL_DIS();
  const std::vector<std::pair<double, double>> kin{
   {0.01, 2.000000}, {0.01, 2.444444}, {0.01, 2.888889}, {0.01, 3.333333}, {0.01, 3.777778},
   {0.01, 4.222222}, {0.01, 4.666667}, {0.01, 5.111111}, {0.01, 5.555556}, {0.01, 6.000000}};
  for (auto k : kin)
    {
      APFEL::ComputeStructureFunctionsAPFEL(sqrt(k.second), sqrt(k.second));
      std::cout << std::scientific << k.first << "\t" << k.second << "\t"
		<< APFEL::F2charm(k.first) << "\t"
		<< std::endl;
    }
  return 0;
}

and using the "uonly" PDF set, I find:

     x               Q2             F2c
1.000000e-02	2.000000e+00	0.000000e+00	
1.000000e-02	2.444444e+00	0.000000e+00	
1.000000e-02	2.888889e+00	0.000000e+00	
1.000000e-02	3.333333e+00	0.000000e+00	
1.000000e-02	3.777778e+00	0.000000e+00	
1.000000e-02	4.222222e+00	0.000000e+00	
1.000000e-02	4.666667e+00	0.000000e+00	
1.000000e-02	5.111111e+00    0.000000e+00	
1.000000e-02	5.555556e+00	0.000000e+00	
1.000000e-02	6.000000e+00	0.000000e+00

that seems to be consistent with the expectation.
Are you able to reproduce these results?

[alecandido]

The differences with the last comment snippet and what we used in the original post are:

• the snippet is using the default mass scheme, i.e. ZM-VFNS, while we are using explicitly (see the name of the issue) FFNS4
• the snippet is not setting the pole masses, so the Q2 chosen happen to be all on the same side of the threshold mc2 (that in the snippet is 2, while for us it was mc = 2 and so the threshold it was 4)

here there is the updated snippet, to make the correct comparison:

#include "APFEL/APFEL.h"
#include <utility>
#include <vector>
#include <math.h>
int main()
{
  APFEL::SetPerturbativeOrder(0);
  APFEL::SetPDFSet("uonly");

  APFEL::SetPoleMasses(2, 4, 175);
  APFEL::SetMassScheme("FFNS4");
  APFEL::SetFFNS(4); // this statement is ignored by APFEL

  APFEL::InitializeAPFEL_DIS();
  const std::vector<std::pair<double, double>> kin{
   {0.01, 2.000000}, {0.01, 2.444444}, {0.01, 2.888889}, {0.01, 3.333333}, {0.01, 3.777778},
   {0.01, 4.222222}, {0.01, 4.666667}, {0.01, 5.111111}, {0.01, 5.555556}, {0.01, 6.000000}};
  for (auto k : kin)
    {
      APFEL::ComputeStructureFunctionsAPFEL(sqrt(k.second), sqrt(k.second));
      std::cout << std::scientific << k.first << "\t" << k.second << "\t"
        << APFEL::F2charm(k.first) << "\t"
        << std::endl;
    }
  return 0;
}

and the results:

     x               Q2              F2c
1.000000e-02    2.000000e+00    2.603139e-04
1.000000e-02    2.444444e+00    3.037474e-04
1.000000e-02    2.888889e+00    3.357870e-04
1.000000e-02    3.333333e+00    3.562243e-04
1.000000e-02    3.777778e+00    3.656866e-04
1.000000e-02    4.222222e+00    0.000000e+00
1.000000e-02    4.666667e+00    0.000000e+00
1.000000e-02    5.111111e+00    0.000000e+00
1.000000e-02    5.555556e+00    0.000000e+00
1.000000e-02    6.000000e+00    0.000000e+00

APFEL parameters' report

 WARNING: FFNS is a FFN scheme
          ... setting NF = 4 FFNS PDF evolution
Welcome to

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_____v3.0.4 A PDF Evolution Library, arXiv:1310.1394

Authors: V. Bertone, S. Carrazza, J. Rojo
Report of the evolution parameters:
QCD evolution

Space-like evolution (PDFs)

Unpolarized evolution

Evolution scheme: FFNS with 4 active flavours at N0LO

Solution of the DGLAP equation: 'exactalpha'

Solution of the coupling equations: 'exact'

Coupling reference value:

AlphaQCD(  1.4142 GeV) =  0.350000

Pole heavy quark masses:
Mc =   2.0000 GeV
Mb =   4.0000 GeV
Mt = 175.0000 GeV

The matching thresholds coincide with the physical masses

muR / muF =  1.0000

Allowed evolution range [   1.0000 :  10000.0000 ] GeV

The internal subgrids will be locked

Fast evolution enabled
Initialization of the evolution completed in   0.053 s
Report of the electroweak parameters:
Mass of the Z = 91.188 GeV

Mass of the W = 80.385 GeV

Mass of the proton = 0.9383 GeV

sin^2(thetaW) = 0.2313

GFermi = 1.16638E-05

| 0.9743 0.2254 0.0036 |

CKM = | 0.2252 0.9734 0.0414 |

| 0.0089 0.0405 0.9991 |

Z propagator correction = 0.00000
Report of the DIS parameters:
Computation in the FFNS4 mass scheme

Electromagnetic (EM) process

Scattering electron - proton

muR / Q =  1.0000

muF / Q =  1.0000

Target Mass corrections disabled

Intrinsic charm disabled
Initialization of the DIS module completed in   0.034 s