vrap grids at NNLO

[scarlehoff]

Addresses #13

For the central scale seems to work (pineappl and vrap produce the same result). It would be good to have a third code to properly check the results of course... (beyond the fact that they haven't changed since the initial version).

[scarlehoff]

The numbers are not absolutely crazy for the scale variations (which means that if I missed something at least it does not multiply a divergence).

In order to test the scale variations I can also generate a grid for r_muR=2, r_muF=0.5 for instance. @cschwan how do I get the results for that? What would --scales 3 or --scales 7 produce?

[cschwan]

@scarlehoff I suppose you can leave the scale variation set to its default (7-point scale variation), but give convolute the extra switch -a (short for --absolute), which will explicitly show you all seven scale-varied results.

[cschwan]

In order to test the scale variations I can also generate a grid for r_muR=2, r_muF=0.5 for instance.

However, for this particular scale variation you'll need the 9-point one.

[scarlehoff]

Ok -s 9 -a is what I need. Thanks!

[cschwan]

One last comment:

b                   etal                   dsig/detal     (1,1)       (2,2)     (0.5,0.5)     (2,1)       (1,2)      (0.5,1)     (1,0.5)  
                     []                       [pb]        [pb]        [pb]        [pb]        [pb]        [pb]        [pb]        [pb]    
--+-------------------+-------------------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------
 0                   0 0.21000000000000002 5.8160276e2 5.8160276e2 5.9586544e2 5.7033788e2 5.8173849e2 5.9153986e2 5.8143363e2 5.6518854e2
 1 0.21000000000000002 0.42000000000000004 5.8305367e2 5.8305367e2 5.9740188e2 5.7166953e2 5.8318310e2 5.9309082e2 5.8289238e2 5.6652444e2
 2 0.42000000000000004                0.63 5.8507036e2 5.8507036e2 5.9952938e2 5.7351192e2 5.8522952e2 5.9520110e2 5.8487204e2 5.6842278e2
 3                0.63  0.8400000000000001 5.8978094e2 5.8978094e2 6.0445348e2 5.7789617e2 5.8985141e2 6.0024712e2 5.8969313e2 5.7274408e2
 4  0.8400000000000001                1.05 5.9404180e2 5.9404180e2 6.0883674e2 5.8190653e2 5.9407032e2 6.0470514e2 5.9400625e2 5.7675040e2
 5                1.05                1.37 6.0055591e2 6.0055591e2 6.1572014e2 5.8782319e2 6.0043869e2 6.1183196e2 6.0070196e2 5.8261226e2
 6                1.37                1.52 6.0807392e2 6.0807392e2 6.2360037e2 5.9472526e2 6.0764516e2 6.2016255e2 6.0860817e2 5.8930040e2
 7                1.52                1.74 6.0948805e2 6.0948805e2 6.2532209e2 5.9560835e2 6.0896514e2 6.2213068e2 6.1013961e2 5.9024710e2
 8                1.74                1.95 6.1029012e2 6.1029012e2 6.2631099e2 5.9590317e2 6.0925596e2 6.2391246e2 6.1157873e2 5.9024184e2
 9                1.95                2.18 6.0109307e2 6.0109307e2 6.1710921e2 5.8635416e2 5.9964338e2 6.1550267e2 6.0289943e2 5.8061802e2
10                2.18                 2.5 5.7361389e2 5.7361389e2 5.8869057e2 5.5929736e2 5.7108844e2 5.8881951e2 5.7676068e2 5.5301373e2

will show you the results as tuples of the form (xi_R, xi_F).

[scarlehoff]

Great, it works :)

Results computed "by hand":

(1,1) --- (0.5, 0.5) --- (2,1)  --- (1,2) --- (2,2) --- (0.5, 2)  ---  (2, 0.5)
440.5  ---     471.8  ---  421.0   ---  435.6 --- 411.4 ---  468.2   --- 441.4

results produced by pineappl

Pineappl results:
bin       x0           x1        diff        (1,1)       (2,2)     (0.5,0.5)     (2,1)       (1,2)      (0.5,1)     (1,0.5)     (2,0.5)     (0.5,2)  
---+-------+-------+----+----+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------
  0 7.10428 7.10428 -0.2 -0.2 4.4126323e2 4.4126323e2 4.1193325e2 4.7313431e2 4.2144816e2 4.3644362e2 4.6793163e2 4.5582043e2 4.4179080e2 4.7050294e2

[cschwan]

Results computed "by hand":

Do you have these results with more digits? For some of them the accuracy is a bit worse maybe - are they computed using separate MC runs? If so, what are the MC uncertainties for them?

[scarlehoff]

I added one extra digit (the mc error is around 0.1 for everyone).

The only one that worries me is (0.5, 2.0) but since (0.5, 2.0) is ok I'm less worried.

[cschwan]

This is what I find (differences are given in per mille):

      scale      diff
1     (1,1) 1.7326447
2     (2,2) 1.2961838
3 (0.5,0.5) 2.8281263
4     (2,1) 1.0645131
5     (1,2) 1.9366850
6   (2,0.5) 0.8853647
7   (0.5,2) 4.9187100

and the differences in multiples of the MC uncertainty (0.1):

      scale   sigma
1     (1,1)  7.6323
2     (2,2)  5.3325
3 (0.5,0.5) 13.3431
4     (2,1)  4.4816
5     (1,2)  8.4362
6   (2,0.5)  3.9080
7   (0.5,2) 23.0294

[scarlehoff]

yeah, as I said, 0.5-2 is the only one that worries me. I wonder whether vrap implements its own alpha_s since the other bigger difference is 0.5,0.5.

[scarlehoff]

At NLO we have the same kind of differences.

If you want we can do a proper check etc to know where the differences are coming from and all that, but I think most of it is due to the interpolation itself (already almost a 2 per-mille difference for (1,1)) which makes sense since we are subtracting numerical divergences inside the pineappl grid. Then these differences increase a bit more when the values grow (as alpha_s grow).

I would consider these numbers as ok x)