2020_09_02 CC LO FLcharm
- rel. error in Q2 variation seems to be random
Reporting results
comparing for theory=289 and obs=1 ...
------------------------------FLcharm------------------------------
x Q2 APFEL yadism yadism_error rel_err[%]
0 0.001 4.000000 0.001896 0.001891 0.0 -0.280485
1 0.001 4.608352 0.001645 0.001642 0.0 -0.177747
2 0.001 5.309227 0.001426 0.001425 0.0 -0.029805
3 0.001 6.116696 0.001238 0.001237 0.0 -0.068857
4 0.001 7.046972 0.001076 0.001074 0.0 -0.209122
5 0.001 8.118732 0.000935 0.000932 0.0 -0.303471
6 0.001 9.353493 0.000812 0.000809 0.0 -0.331185
7 0.001 10.776047 0.000705 0.000702 0.0 -0.292460
8 0.001 12.414954 0.000611 0.000610 0.0 -0.203939
9 0.001 14.303119 0.000530 0.000529 0.0 -0.068221
10 0.001 16.478452 0.000460 0.000459 0.0 -0.045230
11 0.001 18.984626 0.000400 0.000399 0.0 -0.183984
12 0.001 21.871959 0.000347 0.000346 0.0 -0.266207
13 0.001 25.198421 0.000301 0.000300 0.0 -0.294699
14 0.001 29.030798 0.000262 0.000261 0.0 -0.271899
15 0.001 33.446033 0.000227 0.000226 0.0 -0.199966
16 0.001 38.532772 0.000197 0.000197 0.0 -0.080792
17 0.001 44.393143 0.000171 0.000171 0.0 -0.005271
18 0.001 51.144806 0.000148 0.000148 0.0 -0.161547
19 0.001 58.923315 0.000129 0.000129 0.0 -0.259745
20 0.001 67.884843 0.000112 0.000112 0.0 -0.302644
21 0.001 78.209311 0.000097 0.000097 0.0 -0.292739
22 0.001 90.104006 0.000084 0.000084 0.0 -0.232278
23 0.001 103.807741 0.000073 0.000073 0.0 -0.123312
24 0.001 119.595649 0.000063 0.000063 0.0 0.012012
25 0.001 137.784709 0.000055 0.000055 0.0 -0.155387
26 0.001 158.740105 0.000048 0.000048 0.0 -0.263736
27 0.001 182.882565 0.000042 0.000041 0.0 -0.315954
28 0.001 210.696803 0.000036 0.000036 0.0 -0.314674
29 0.001 242.741252 0.000031 0.000031 0.0 -0.262281
30 0.001 279.659276 0.000027 0.000027 0.0 -0.160930
31 0.001 322.192087 0.000024 0.000024 0.0 -0.012551
32 0.001 371.193627 0.000020 0.000020 0.0 -0.140788
33 0.001 427.647712 0.000018 0.000018 0.0 -0.258649
34 0.001 492.687783 0.000015 0.000015 0.0 -0.319908
35 0.001 567.619668 0.000013 0.000013 0.0 -0.327268
36 0.001 653.947790 0.000012 0.000012 0.0 -0.283177
37 0.001 753.405381 0.000010 0.000010 0.0 -0.189823
38 0.001 867.989274 0.000009 0.000009 0.0 -0.049173
39 0.001 1000.000000 0.000008 0.000008 0.0 -0.117945
--------------------------------------------------------------------
Since APFEL is doing a linear interpolation in the logarithm of Q2 (or better of xi, but log(xi) it's proportional to log(Q2)) there is an expected quadratic error in log(Q2) with respect to the exact thing (that is the one computed by yadism), and this would explain the discrepancy.
Note: we also had a pre-existing suspect on a possible interpolation going before finding it in the code, because the order of magnitude of the error was consistent with the other errors due to other interpolations made by APFEL
APFEL: src/DIS/ComputeDISOperators.f
*
* Find "ixi" such that "xigrid(ixi)" < "xi" < "xigrid(ixi+1)"
*
* Renormalization scale
*
muR = dsqrt(krenQ) * Q
*
do ihq=4,6
ixi(ihq) = 0
M2(ihq) = HeavyQuarkMass(ihq,muR)**2
xi(ihq) = Q2 / M2(ihq)
if(xi(ihq).le.xigrid(xistep))then
ixi(ihq) = 0
elseif(xi(ihq).ge.xigrid(nxi))then
ixi(ihq) = nxir
else
diff(1) = xi(ihq) - xigrid(1)
do i=2,nxir
diff(i) = xi(ihq) - xigrid(i*xistep)
sgn = diff(i-1) * diff(i)
if(sgn.lt.0.d0)then
ixi(ihq) = i - 1
endif
enddo
endif