Bug fix in VRAP

[mariaubiali]

Hi all,

As we mentioned at the PC on Wednesday Lance Dixon has not updated the public version of VRAP, but I got hold of the files that Marco Bonvini edited to fix the bug that currently is in VRAP that has to do with the intergration of teh plus prescription and causes numerical instabilities at large-x, small-Q2.
Here's the list

• integration.h that fixes the integration range bug
• Vlumifns_LHApdf.C where we have modified the luminosities to account for s!=sbar, c!=cbar and b!=bbar
• dilog.C and dilog.h, where we have just changed the name of the function "abs" to "dabs", to avoid conflicts with the builtin C abs function (my compiler was giving an error about it).

I have compressed the fixed files and attched them here. Would it be difficult to check if this makes a difference in the observables?
bug-fix-bonvini.zip

[cschwan]

I believe we've already fixed points 2 and 3 and saw that this didn't make a big difference, certainly at the level of the cross sections for the FTDY datasets that we consider, but also in the fit (right, @scarlehoff?). But especially for point 2 these source are a good double-check for #25 and #26.

[scarlehoff]

Vlumifns_LHApdf.C where we have modified the luminosities to account for s!=sbar, c!=cbar and b!=bbar
dilog.C and dilog.h,

Yes, as @cschwan said these two points should be fixed in this repository.

Regarding the actual bug:

integration.h that fixes the integration range bug

If I'm looking at it correctly the only change with respect to the version we started with seems to be:

-  if ((tau * exp(2.*y) >= 1.) || (tau * exp(-2.*y) >= 1.)
-                                 || (z <= tau)){ return 0.; } 
+  if ((tau * exp(2.*y) >= 1.) || (tau * exp(-2.*y) >= 1.)){ return 0.; }

in the NNLO cross section. A quick check for a few points doesn't seem to produce any changes so we might be free from the bug.

And since for now we are still using NLO fktables we should be fine (I don't know if maybe the NNLO MHOU are already using the NNLO grids for vrap? @andreab1997 ?)

In any case, I've added the fix in #28, recomputing the grids should be fairly quick so we can check explicitly.

[mariaubiali]

Thanks a lot @scarlehoff and @cschwan

[andreab1997]

And since for now we are still using NLO fktables we should be fine (I don't know if maybe the NNLO MHOU are already using the NNLO grids for vrap? @andreab1997 ?)

No, all the grids I am using are still NLO, with the kfactor included.

[scarlehoff]

Perfect, then we should be safe.

[scarlehoff]

I've recomputed the NNLO grids. For E605 the difference is below per-mille:

E605

NNPDF31_nnlo_as_0118 PDF set, member #0, version 1; LHAPDF ID = 303600
 b        x1           x2                     diff                 
---+-------+-------+----+----+-------------+-------------+---------
  0 7.10428 7.10428 -0.2 -0.2   4.4168053e2   4.4094677e2  1.664e-3
  1 7.30604 7.30604 -0.2 -0.2   3.7837893e2   3.7779209e2  1.553e-3
  2  7.5078  7.5078 -0.2 -0.2   3.2450954e2   3.2401430e2  1.528e-3
  3 7.70568 7.70568 -0.2 -0.2   2.7938109e2   2.7897179e2  1.467e-3
  4 7.90744 7.90744 -0.2 -0.2   2.4002454e2   2.3971822e2  1.278e-3
  5 8.10532 8.10532 -0.2 -0.2   2.0699663e2   2.0671613e2  1.357e-3
  6 8.30708 8.30708 -0.2 -0.2   1.7810675e2   1.7788477e2  1.248e-3
  7 8.50496 8.50496 -0.2 -0.2   1.5378135e2   1.5358856e2  1.255e-3
  8 8.70672 8.70672 -0.2 -0.2   1.3237081e2   1.3220102e2  1.284e-3
  9 8.90848 8.90848 -0.2 -0.2   1.1396367e2   1.1383165e2  1.160e-3
 10  10.507  10.507 -0.2 -0.2   3.5358445e1   3.5324436e1  9.628e-4
 11 10.7088 10.7088 -0.2 -0.2   3.0623947e1   3.0595764e1  9.211e-4
 12 10.9106 10.9106 -0.2 -0.2   2.6541533e1   2.6519982e1  8.126e-4
 13 11.3102 11.3102 -0.2 -0.2   2.0043746e1   2.0030057e1  6.834e-4
 14 12.1095 12.1095 -0.2 -0.2   1.1612623e1   1.1603315e1  8.022e-4
 15 13.3123 13.3123 -0.2 -0.2   5.3003149e0   5.2975005e0  5.313e-4
 16 14.9108 14.9108 -0.2 -0.2   1.8491329e0   1.8485686e0  3.053e-4
 17 7.10428 7.10428 -0.1 -0.1   4.5992028e2   4.5910934e2  1.766e-3
 18 7.30604 7.30604 -0.1 -0.1   3.9474947e2   3.9408512e2  1.686e-3
 19  7.5078  7.5078 -0.1 -0.1   3.3919683e2   3.3865197e2  1.609e-3
 20 7.70568 7.70568 -0.1 -0.1   2.9259577e2   2.9214504e2  1.543e-3
 21 7.90744 7.90744 -0.1 -0.1   2.5186086e2   2.5150448e2  1.417e-3
 22 8.10532 8.10532 -0.1 -0.1   2.1760874e2   2.1729844e2  1.428e-3
 23 8.30708 8.30708 -0.1 -0.1   1.8757987e2   1.8732844e2  1.342e-3
 24 8.50496 8.50496 -0.1 -0.1   1.6224891e2   1.6203674e2  1.309e-3
 25 8.70672 8.70672 -0.1 -0.1   1.4001287e2   1.3985299e2  1.143e-3
 26 8.90848 8.90848 -0.1 -0.1   1.2087248e2   1.2073769e2  1.116e-3
 27  10.507  10.507 -0.1 -0.1   3.7739355e1   3.7701835e1  9.952e-4
 28 10.7088 10.7088 -0.1 -0.1   3.2562368e1   3.2533186e1  8.970e-4
 29 10.9106 10.9106 -0.1 -0.1   2.8088758e1   2.8063977e1  8.830e-4
 30 11.3102 11.3102 -0.1 -0.1   2.1015229e1   2.0997435e1  8.475e-4
 31 12.1095 12.1095 -0.1 -0.1   1.1835935e1   1.1826749e1  7.767e-4
 32 13.3123 13.3123 -0.1 -0.1   5.0870230e0   5.0837367e0  6.464e-4
 33 14.9108 14.9108 -0.1 -0.1   1.8081608e0   1.8072876e0  4.831e-4
 34 16.9129 16.9129 -0.1 -0.1  5.0960540e-1  5.0966184e-1 -1.107e-4
 35 7.10428 7.10428    0    0   4.7619403e2   4.7528271e2  1.917e-3
 36 7.30604 7.30604    0    0   4.0940217e2   4.0867938e2  1.769e-3
 37  7.5078  7.5078    0    0   3.5238579e2   3.5178651e2  1.704e-3
 38 7.70568 7.70568    0    0   3.0447589e2   3.0398013e2  1.631e-3
 39 7.90744 7.90744    0    0   2.6255769e2   2.6216692e2  1.491e-3
 40 8.10532 8.10532    0    0   2.2725965e2   2.2692068e2  1.494e-3
 41 8.30708 8.30708    0    0   1.9625950e2   1.9599449e2  1.352e-3
 42 8.50496 8.50496    0    0   1.7007461e2   1.6984913e2  1.328e-3
 43 8.70672 8.70672    0    0   1.4706798e2   1.4689600e2  1.171e-3
 44 8.90848 8.90848    0    0   1.2723787e2   1.2709340e2  1.137e-3
 45  10.507  10.507    0    0   4.0513495e1   4.0478913e1  8.543e-4
 46 10.7088 10.7088    0    0   3.4982930e1   3.4949401e1  9.594e-4
 47 10.9106 10.9106    0    0   3.0187715e1   3.0158528e1  9.678e-4
 48 11.3102 11.3102    0    0   2.2503635e1   2.2483900e1  8.777e-4
 49 12.1095 12.1095    0    0   1.2408975e1   1.2399510e1  7.634e-4
 50 13.3123 13.3123    0    0   5.1400587e0   5.1364391e0  7.047e-4
 51 14.9108 14.9108    0    0   1.7096195e0   1.7086163e0  5.871e-4
 52 16.9129 16.9129    0    0  5.2398712e-1  5.2374721e-1  4.581e-4
 53 7.10428 7.10428  0.1  0.1   4.8953417e2   4.8856117e2  1.992e-3
 54 7.30604 7.30604  0.1  0.1   4.2151824e2   4.2076096e2  1.800e-3
 55  7.5078  7.5078  0.1  0.1   3.6340994e2   3.6277525e2  1.750e-3
 56 7.70568 7.70568  0.1  0.1   3.1448695e2   3.1396664e2  1.657e-3
 57 7.90744 7.90744  0.1  0.1   2.7167563e2   2.7128220e2  1.450e-3
 58 8.10532 8.10532  0.1  0.1   2.3557353e2   2.3521969e2  1.504e-3
 59 8.30708 8.30708  0.1  0.1   2.0382339e2   2.0354386e2  1.373e-3
 60 8.50496 8.50496  0.1  0.1   1.7695811e2   1.7671749e2  1.362e-3
 61 8.70672 8.70672  0.1  0.1   1.5330413e2   1.5309962e2  1.336e-3
 62 8.90848 8.90848  0.1  0.1   1.3285193e2   1.3268975e2  1.222e-3
 63  10.507  10.507  0.1  0.1   4.2789700e1   4.2752353e1  8.736e-4
 64 10.7088 10.7088  0.1  0.1   3.7057973e1   3.7024610e1  9.011e-4
 65 10.9106 10.9106  0.1  0.1   3.2081807e1   3.2053168e1  8.935e-4
 66 11.3102 11.3102  0.1  0.1   2.4107063e1   2.4088768e1  7.595e-4
 67 12.1095 12.1095  0.1  0.1   1.3494012e1   1.3485180e1  6.550e-4
 68 13.3123 13.3123  0.1  0.1   5.5622545e0   5.5589874e0  5.877e-4
 69 14.9108 14.9108  0.1  0.1   1.7952419e0   1.7943463e0  4.991e-4
 70 16.9129 16.9129  0.1  0.1  4.6300380e-1  4.6274491e-1  5.595e-4
 71 7.10428 7.10428  0.2  0.2   4.9889118e2   4.9791059e2  1.969e-3
 72 7.30604 7.30604  0.2  0.2   4.3015607e2   4.2938820e2  1.788e-3
 73  7.5078  7.5078  0.2  0.2   3.7133333e2   3.7070287e2  1.701e-3
 74 7.70568 7.70568  0.2  0.2   3.2178774e2   3.2126660e2  1.622e-3
 75 7.90744 7.90744  0.2  0.2   2.7833739e2   2.7792767e2  1.474e-3
 76 8.10532 8.10532  0.2  0.2   2.4163327e2   2.4127811e2  1.472e-3
 77 8.30708 8.30708  0.2  0.2   2.0931849e2   2.0903774e2  1.343e-3
 78 8.50496 8.50496  0.2  0.2   1.8194595e2   1.8171705e2  1.260e-3
 79 8.70672 8.70672  0.2  0.2   1.5773134e2   1.5752617e2  1.302e-3
 80 8.90848 8.90848  0.2  0.2   1.3677347e2   1.3661561e2  1.156e-3
 81  10.507  10.507  0.2  0.2   4.4562780e1   4.4528919e1  7.604e-4
 82 10.7088 10.7088  0.2  0.2   3.8700161e1   3.8666820e1  8.622e-4
 83 10.9106 10.9106  0.2  0.2   3.3605195e1   3.3576263e1  8.617e-4
 84 11.3102 11.3102  0.2  0.2   2.5396405e1   2.5375055e1  8.414e-4
 85 12.1095 12.1095  0.2  0.2   1.4528503e1   1.4518858e1  6.643e-4
 86 13.3123 13.3123  0.2  0.2   6.2506064e0   6.2481862e0  3.873e-4
 87 14.9108 14.9108  0.2  0.2   1.9347504e0   1.9337621e0  5.111e-4
 88 16.9129 16.9129  0.2  0.2  2.0861552e-1  2.0852059e-1  4.553e-4
 89 7.10428 7.10428  0.3  0.3   5.0243911e2   5.0148123e2  1.910e-3
 90 7.30604 7.30604  0.3  0.3   4.3370462e2   4.3294200e2  1.761e-3
 91  7.5078  7.5078  0.3  0.3   3.7478394e2   3.7413224e2  1.742e-3
 92 7.70568 7.70568  0.3  0.3   3.2486471e2   3.2436528e2  1.540e-3
 93 7.90744 7.90744  0.3  0.3   2.8097686e2   2.8058987e2  1.379e-3
 94 8.10532 8.10532  0.3  0.3   2.4389345e2   2.4354794e2  1.419e-3
 95 8.30708 8.30708  0.3  0.3   2.1123125e2   2.1097177e2  1.230e-3
 96 8.50496 8.50496  0.3  0.3   1.8357664e2   1.8338189e2  1.062e-3
 97 8.70672 8.70672  0.3  0.3   1.5920295e2   1.5901505e2  1.182e-3
 98 8.90848 8.90848  0.3  0.3   1.3810830e2   1.3795244e2  1.130e-3
 99  10.507  10.507  0.3  0.3   4.5376541e1   4.5345114e1  6.931e-4
100 10.7088 10.7088  0.3  0.3   3.9496395e1   3.9464135e1  8.175e-4
101 10.9106 10.9106  0.3  0.3   3.4403906e1   3.4377717e1  7.618e-4
102 11.3102 11.3102  0.3  0.3   2.6185003e1   2.6169230e1  6.027e-4
103 12.1095 12.1095  0.3  0.3   1.5132952e1   1.5125903e1  4.661e-4
104 13.3123 13.3123  0.3  0.3   6.5508347e0   6.5488724e0  2.996e-4
105 14.9108 14.9108  0.3  0.3   1.6797837e0   1.6787760e0  6.002e-4
106 16.9129 16.9129  0.3  0.3  1.2781372e-1  1.2768174e-1  1.034e-3
107 8.30708 8.30708  0.4  0.4   2.0875941e2   2.0851517e2  1.171e-3
108 8.50496 8.50496  0.4  0.4   1.8137848e2   1.8119962e2  9.871e-4
109 8.70672 8.70672  0.4  0.4   1.5726567e2   1.5708791e2  1.132e-3
110 8.90848 8.90848  0.4  0.4   1.3640631e2   1.3626584e2  1.031e-3
111  10.507  10.507  0.4  0.4   4.4935987e1   4.4903895e1  7.147e-4
112 10.7088 10.7088  0.4  0.4   3.9099077e1   3.9074368e1  6.323e-4
113 10.9106 10.9106  0.4  0.4   3.4002504e1   3.3981042e1  6.316e-4
114 11.3102 11.3102  0.4  0.4   2.5807078e1   2.5793742e1  5.170e-4
115 12.1095 12.1095  0.4  0.4   1.4755179e1   1.4748672e1  4.412e-4
116 13.3123 13.3123  0.4  0.4   5.7446015e0   5.7422002e0  4.182e-4
117 14.9108 14.9108  0.4  0.4   1.3204562e0   1.3199108e0  4.132e-4
118 16.9129 16.9129  0.4  0.4 -2.4551158e-2 -2.4688223e-2 -5.552e-3

and similarly for all the others (which also might mean that I didn't apply the patch correctly if greater differences were expected).

[cschwan]

That's good, OTOH we know that small differences at the level of the cross sections may result in not so small differences of the chi^2.