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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)
┌────────────────────────────────────┐
│ │
│ __ __ _ _ │
│ \ \ / / | (_) │
│ \ \_/ /_ _ __| |_ ___ _ __ ___ │
│ \ / _` |/ _` | / __| '_ ` _ \ │
│ | | (_| | (_| | \__ \ | | | | | │
│ |_|\__,_|\__,_|_|___/_| |_| |_| │
│ │
└────────────────────────────────────┘
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 /// //// //// ///_/ _/
_/ / / / / / / //// //// /// /// _/
_/ _/ _/ _/ _/ _/ / / / / //// ////
_____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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We believe to have found a bug in APFEL:
F2light, since there is no 4-flavor bottom (as said, no intrinsic bottom), but we find it is contributing (see below)To give an explicit example:
mc = 1.95, mb=1e6so it should be FONLL all the waybonlywhich 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) ┌────────────────────────────────────┐ │ │ │ __ __ _ _ │ │ \ \ / / | (_) │ │ \ \_/ /_ _ __| |_ ___ _ __ ___ │ │ \ / _` |/ _` | / __| '_ ` _ \ │ │ | | (_| | (_| | \__ \ | | | | | │ │ |_|\__,_|\__,_|_|___/_| |_| |_| │ │ │ └────────────────────────────────────┘• F2_light at 40 pts
• FL_light at 40 pts
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
/// //// //// ///_/ _/
_/ / / / / / /
//// //// /// /// _/
_/ _/ _/ _/ _/ _/
/ / / / //// ////
_____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:
Pole heavy quark masses:
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
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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
The text was updated successfully, but these errors were encountered: