DIS: FONLL b-PDF contributions #33
Description
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=1e6so it should be FONLL all the way- the PDF is
bonlywhich is a dummy PDF containing only the b quark asx(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
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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