DIS: FONLL b-PDF contributions

We believe to have found a bug in APFEL:

The FONLL prescription uses 4-flavor PDFs in the range between the charm mass and the bottom mass (using the assumtions threshold = mass)
we do not consider the case of intrinsic charm nor intrinsic bottom here
hence the bottom PDF should not contribute to F2light, since there is no 4-flavor bottom (as said, no intrinsic bottom), but we find it is contributing (see below)
this is present for all FONLL flavors
HOWEVER, this bug is not a problem in the fit, because there the bottom PDF only gets a non-zero value beyond the bottom mass and hence will not trigger this bug,
but, it is a bug for anyone else who uses APFEL to compute structure functions and who uses PDFs that where not obtained using the exact same value for the bottom PDF
the bug is most likely triggered by the fact, that APFEL uses evolution basis, which is always the full basis (and so, e.g., Singlet = u+d+s+c+b+t)

To give an explicit example:

below I attach a computation of F2light/FLlight in FONLL-A
mc = 1.95, mb=1e6 so it should be FONLL all the way

the PDF is bonly which is a dummy PDF containing only the b quark as x(1-x)

yadism + APFEL output

Computing for theory=b7b56b0, ocard=21882ed and pdf=bonly ...
LHAPDF 6.3.0 loading /home/felix/local/share/LHAPDF/bonly/bonly_0000.dat
bonly PDF set, member #0, version 1
[15:52:39] INFO     Inspecting runcards...                                               inspector.py:96
       INFO     Inspection completed: success ✓                                     inspector.py:100
       INFO     Interpolation: number of points = 49, polynomial degree = 4,    interpolation.py:440
                logarithmic = True                                                                  
       INFO     {'MZ2': 8315.178393760001, 'CKM': CKM([[9.49221518e-01      coupling_constants.py:44
                5.07600900e-02 1.20409000e-05] [5.07150400e-02                                      
                9.47604903e-01 1.68100000e-03] [7.43044000e-05                                      
                1.62409000e-03 9.98304719e-01]]), 'sin2theta_weak':                                 
                0.23126, 'MW2': 6463.838403999999}                                                  
       INFO     {'process': 'EM', 'projectilePID': 11, 'polarization': 0,   coupling_constants.py:45
                'propagatorCorrection': 0}                                                          
       INFO     RenScaleVar: False, FactScaleVar: False                       scale_variations.py:56
       INFO     Thresholds: walls = [0, 3.8024999999999998, 1000000000000.0, 1e+16, thresholds.py:79
                inf]                                                                                
       INFO     PTO: 1, process: EM                                                    runner.py:146
       INFO     FNS: FONLL-A, NfFF: 4                                                  runner.py:147
       INFO     Intrinsic: []                                                          runner.py:148
       INFO     projectile: electron, target: {Z: 1, A: 1}                             runner.py:149
       INFO     Thresholds: walls = [0, 0.0, 1000000000000.0, 1e+16, inf]           thresholds.py:79
       INFO     Strong Coupling:                                              strong_coupling.py:151
                a_s(µ_R^2=8317.440000)=0.009390=0.118000/(4π)                                       
                             ┌────────────────────────────────────┐                                 
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                                              Plan                                                  

• F2_light at 40 pts                                                                                   
• FL_light at 40 pts                                                                                   

                                          Calculation                                               
yadism took off! please stay tuned ...
/home/felix/Physik/N3PDF/DIS/yadism/src/yadism/esf/conv.py:152: IntegrationWarning: The algorithm does 
not converge.  Roundoff error is detected
in the extrapolation table.  It is assumed that the requested tolerance
cannot be achieved, and that the returned result (if full_output = 1) is 
the best which can be obtained.
res, err = scipy.integrate.quad(
took 4.96 s
Compute external result

WARNING: FONLL-A is a VFN scheme
      ... setting VFNS PDF evolution
WARNING: FONLL-A is NLO scheme
      ... setting NLO perturbative order

Welcome to 
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_/    _/   _/    _/   _/         _/         _/
_/_/_/_/   _/_/_/_/   _/_/_/     _/_/_/     _/
_/    _/   _/         _/         _/         _/
_/    _/   _/         _/         _/_/_/_/   _/_/_/_/
_____v3.0.5 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: VFNS at N1LO
Solution of the DGLAP equation: 'exactalpha' with maximum 6 active flavours
Solution of the coupling equations: 'exact' with maximum 6 active flavours
Coupling reference value:
- AlphaQCD( 91.2000 GeV) =  0.118000
Pole heavy quark masses:
- Mc =   1.9500 GeV
- Mb = ******** GeV
- Mt = ******** 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   0.536 s

Report of the electroweak parameters:

Mass of the Z = 91.188 GeV
Mass of the W = 80.398 GeV
Mass of the proton = 0.9380 GeV
sin^2(thetaW) = 0.2313
GFermi = 1.16638E-05
   | 0.9743 0.2253 0.0035 |
CKM = | 0.2252 0.9735 0.0410 |
   | 0.0086 0.0403 0.9992 |
Z propagator correction = 0.00000

Report of the DIS parameters:

Computation in the FONLL-A mass scheme
Electromagnetic (EM) process
Scattering electron - proton
muR / Q =  1.0000
muF / Q =  1.0000
(No scale variation in the evolution)
Target Mass corrections disabled
FONLL damping factor disabled for all heavy quarks
Intrinsic charm disabled

Initialization of the DIS module completed in   5.943 s

LHAPDF 6.3.0 loading /home/felix/local/share/LHAPDF/bonly/bonly_0000.dat bonly PDF set, member #0, version 1 LHAPDF 6.3.0 loading /home/felix/local/share/LHAPDF/bonly/bonly_0000.dat bonly PDF set, member #0, version 1 LHAPDF 6.3.0 loading /home/felix/local/share/LHAPDF/bonly/bonly_0000.dat bonly PDF set, member #0, version 1 LHAPDF 6.3.0 loading /home/felix/local/share/LHAPDF/bonly/bonly_0000.dat bonly PDF set, member #0, version 1 LHAPDF 6.3.0 loading /home/felix/local/share/LHAPDF/bonly/bonly_0000.dat bonly PDF set, member #0, version 1 LHAPDF 6.3.0 loading /home/felix/local/share/LHAPDF/bonly/bonly_0000.dat bonly PDF set, member #0, version 1 LHAPDF 6.3.0 loading /home/felix/local/share/LHAPDF/bonly/bonly_0000.dat bonly PDF set, member #0, version 1 LHAPDF 6.3.0 loading /home/felix/local/share/LHAPDF/bonly/bonly_0000.dat bonly PDF set, member #0, version 1 LHAPDF 6.3.0 loading /home/felix/local/share/LHAPDF/bonly/bonly_0000.dat bonly PDF set, member #0, version 1 LHAPDF 6.3.0 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Log added, hash=06dd72d0fd24320c82219a81afe221f795fc915f3a14ca711c8da4e2349f05a4

────────── F2_light
────────── x Q2 yadism yadism_error APFEL percent_error 0 0.000100 20.000000 0.0 0.0 0.000053 -100.0 1 0.000275 20.000000 0.0 0.0 0.000123 -100.0 2 0.000756 20.000000 0.0 0.0 0.000285 -100.0 3 0.002080 20.000000 0.0 0.0 0.000655 -100.0 4 0.005721 20.000000 0.0 0.0 0.001494 -100.0 5 0.015733 20.000000 0.0 0.0 0.003383 -100.0 6 0.043267 20.000000 0.0 0.0 0.007593 -100.0 7 0.118993 20.000000 0.0 0.0 0.016630 -100.0 8 0.327252 20.000000 0.0 0.0 0.032793 -100.0 9 0.900000 20.000000 0.0 0.0 0.021900 -100.0 10 0.000100 4.000000 0.0 0.0 0.000068 -100.0 11 0.000275 4.000000 0.0 0.0 0.000155 -100.0 12 0.000756 4.000000 0.0 0.0 0.000351 -100.0 13 0.002080 4.000000 0.0 0.0 0.000784 -100.0 14 0.005721 4.000000 0.0 0.0 0.001720 -100.0 15 0.015733 4.000000 0.0 0.0 0.003715 -100.0 16 0.043267 4.000000 0.0 0.0 0.007880 -100.0 17 0.118993 4.000000 0.0 0.0 0.016282 -100.0 18 0.327252 4.000000 0.0 0.0 0.031179 -100.0 19 0.900000 4.000000 0.0 0.0 0.024752 -100.0 20 0.100000 4.000000 0.0 0.0 0.014415 -100.0 21 0.100000 5.719877 0.0 0.0 0.014465 -100.0 22 0.100000 8.179247 0.0 0.0 0.014507 -100.0 23 0.100000 11.696071 0.0 0.0 0.014543 -100.0 24 0.100000 16.725021 0.0 0.0 0.014573 -100.0 25 0.100000 23.916263 0.0 0.0 0.014599 -100.0 26 0.100000 34.199519 0.0 0.0 0.014623 -100.0 27 0.100000 48.904257 0.0 0.0 0.014643 -100.0 28 0.100000 69.931579 0.0 0.0 0.014661 -100.0 29 0.100000 100.000000 0.0 0.0 0.014678 -100.0 30 0.001000 4.000000 0.0 0.0 0.000439 -100.0 31 0.001000 5.719877 0.0 0.0 0.000416 -100.0 32 0.001000 8.179247 0.0 0.0 0.000396 -100.0 33 0.001000 11.696071 0.0 0.0 0.000380 -100.0 34 0.001000 16.725021 0.0 0.0 0.000366 -100.0 35 0.001000 23.916263 0.0 0.0 0.000353 -100.0 36 0.001000 34.199519 0.0 0.0 0.000343 -100.0 37 0.001000 48.904257 0.0 0.0 0.000333 -100.0 38 0.001000 69.931579 0.0 0.0 0.000324 -100.0 39 0.001000 100.000000 0.0 0.0 0.000317 -100.0

────────── FL_light
────────── x Q2 yadism yadism_error APFEL percent_error 0 0.000100 20.000000 0.0 0.0 0.000002 -100.0 1 0.000275 20.000000 0.0 0.0 0.000005 -100.0 2 0.000756 20.000000 0.0 0.0 0.000013 -100.0 3 0.002080 20.000000 0.0 0.0 0.000035 -100.0 4 0.005721 20.000000 0.0 0.0 0.000094 -100.0 5 0.015733 20.000000 0.0 0.0 0.000246 -100.0 6 0.043267 20.000000 0.0 0.0 0.000605 -100.0 7 0.118993 20.000000 0.0 0.0 0.001272 -100.0 8 0.327252 20.000000 0.0 0.0 0.001712 -100.0 9 0.900000 20.000000 0.0 0.0 0.000078 -100.0 10 0.000100 4.000000 0.0 0.0 0.000002 -100.0 11 0.000275 4.000000 0.0 0.0 0.000007 -100.0 12 0.000756 4.000000 0.0 0.0 0.000018 -100.0 13 0.002080 4.000000 0.0 0.0 0.000049 -100.0 14 0.005721 4.000000 0.0 0.0 0.000133 -100.0 15 0.015733 4.000000 0.0 0.0 0.000348 -100.0 16 0.043267 4.000000 0.0 0.0 0.000855 -100.0 17 0.118993 4.000000 0.0 0.0 0.001799 -100.0 18 0.327252 4.000000 0.0 0.0 0.002421 -100.0 19 0.900000 4.000000 0.0 0.0 0.000111 -100.0 20 0.100000 4.000000 0.0 0.0 0.001613 -100.0 21 0.100000 5.719877 0.0 0.0 0.001475 -100.0 22 0.100000 8.179247 0.0 0.0 0.001360 -100.0 23 0.100000 11.696071 0.0 0.0 0.001262 -100.0 24 0.100000 16.725021 0.0 0.0 0.001179 -100.0 25 0.100000 23.916263 0.0 0.0 0.001106 -100.0 26 0.100000 34.199519 0.0 0.0 0.001042 -100.0 27 0.100000 48.904257 0.0 0.0 0.000985 -100.0 28 0.100000 69.931579 0.0 0.0 0.000934 -100.0 29 0.100000 100.000000 0.0 0.0 0.000889 -100.0 30 0.001000 4.000000 0.0 0.0 0.000024 -100.0 31 0.001000 5.719877 0.0 0.0 0.000022 -100.0 32 0.001000 8.179247 0.0 0.0 0.000020 -100.0 33 0.001000 11.696071 0.0 0.0 0.000019 -100.0 34 0.001000 16.725021 0.0 0.0 0.000017 -100.0 35 0.001000 23.916263 0.0 0.0 0.000016 -100.0 36 0.001000 34.199519 0.0 0.0 0.000015 -100.0 37 0.001000 48.904257 0.0 0.0 0.000015 -100.0 38 0.001000 69.931579 0.0 0.0 0.000014 -100.0 39 0.001000 100.000000 0.0 0.0 0.000013 -100.0

scarrazza / apfel

DIS: FONLL b-PDF contributions #33