Add DY positivity using vrap

[scarlehoff]

Add positivity on top of #139

[scarlehoff]

@enocera a few questions regarding positivity:

• Can I just run vrap at LO? (since we are just worried about the luminosity, right?)
• In principle the infamous jacobian or factors like 54.4 should not matter but where is the actual formula for the positivity fktable? (so that at least the dimensions are comparable). In the 3.0 paper there's only "proportional to"
• Same for the ECM that was used for the computation? I cannot find it in the 3.0 paper nor in the previous one.

I think that's all I will need in order to compare them with the old ones.

[enocera]

• Can I just run vrap at LO? (since we are just worried about the luminosity, right?)

I don't think so. Look for example at Eq. (6.2) in https://arxiv.org/pdf/hep-ph/0312266.pdf. What we call, e.g., POSDYU the following quantity: $$\frac{d^2\sigma_{u\bar u}^{\gamma, Z}}{dMdy}=\frac{4\pi\alpha^2}{9M^3} \int dx_1 dx2 N^{\gamma, Z} \frac{d\sigma{u\bar u}^{\gamma,Z}}{dy} \mathcal{L}_{u\bar u}$$.

I'd say that $$\frac{d\sigma_{u\bar u}^{\gamma,Z}}{dy}=1+\mathcal{O}(\alpha_s)$$ depends on the perturbative order. Wouldn't you say the same?

• In principle the infamous jacobian or factors like 54.4 should not matter but where is the actual formula for the positivity fktable? (so that at least the dimensions are comparable). In the 3.0 paper there's only "proportional to"

Somewhere in APFEL... Let me check.

• Same for the ECM that was used for the computation? I cannot find it in the 3.0 paper nor in the previous one.

From POS.cc in buildmaster/filters I read: $\sqrt{s}=q2pos/\tau$ with $q2pos=5$ GeV $\tau=x{\rm min}\cdot x{\rm max}$ where $x{min}=0.01$ and $x{max}=0.9$

[enocera]

• In principle the infamous jacobian or factors like 54.4 should not matter but where is the actual formula for the positivity fktable? (so that at least the dimensions are comparable). In the 3.0 paper there's only "proportional to"

Somewhere in APFEL... Let me check.

So it seems that for the positivity constraints no overall kinematic factors/normalisations are imposed in APFEL, so for example POSDYU=$\int dx_1 dx2 N^{\gamma, Z} \frac{d\sigma{u\bar u}^{\gamma,Z}}{dy} \mathcal{L}_{u\bar u}$.

[scarlehoff]

depends on the perturbative order. Wouldn't you say the same?

I have a question, should I include the gluon? The positivity that we currently have in NNPDF does include the gluon (fair enough, a gluon-quark channel is opened at NLO) however I was under the impression that we are interested only on the uub contribution (so those channels should be turned off also at NLO).

Edit: also, good news, when including the gluon -like in APFEL- the vrap-generated luminosity is equal to that generated with APFEL with only a factor of 0.7 of difference which is perfectly ok for luminosity observables.

[scarlehoff]

Can we merge this. Also, can you fix the conflicts that are coming from the rebase on the branch @AleCandido ?

[alecandido]

Can we merge this. Also, can you fix the conflicts that are coming from the rebase on the branch @AleCandido ?

I can solve for poetry.lock (trivial -> rerun poetry update) and for yad.py (just one import). But for vrap.py it would be better if you do it yourself @scarlehoff

[scarlehoff]

Ok, fix those two and I'll fix the other.

[alecandido]

Ok, fix those two and I'll fix the other.

How can I rebase preserving a conflict?

[scarlehoff]

You can always say the conflict was solved even if it wasn't. I'll have a look at vrap.py afterwards.

[alecandido]

Actually, rebase was straight, I just had to run poetry update for the lockfile (that took 2026.9s, but it was working on its own).

Please check that everything is alright @scarlehoff

[scarlehoff]

Numerical results seems to be unchanged. I would say we merge.