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Kinematic coverage for dijet measurements

Created by: gstagnit

Hi all, I'm producing some plots for my thesis @stefanoforte . In particular kinematic coverage plots for jet measurements. I'm using the plot_xq2 function of validphys. While I think things are working fine for single jet measurements, dijet data points in the (x,Q^2) plane are completely off.

I don't know if you are aware of this already, I'm opening this issue to share my thoughts with you, with the hope this will be useful (I guess that at some point you would like to produce kinematic plots for NNPDF4.0, which will include jet measurements).

At the moment, given the three kinematic variables [k1,k2,k3] associated to each data point, the JETXQ2MapMixin function (implemented here: https://github.com/NNPDF/nnpdf/blob/330a53c463d2a3d46f2944dfa809ccde88790347/validphys2/src/validphys/plotoptions/kintransforms.py#L103) returns:

 (**) x = k2/k3 * (exp(k1) + exp(-k1)), Q2 = k2^2

This function is used for any jet measurement. Studying the LO kinematics, I came up with the following conclusions:

  • INCLUSIVE JETS: [k1, k2, k3] = [|y|, pt, sqrt(s)] with pt= jet transverse momentum and y= jet rapidity. Given pt and |y|, the minimum and maximum momentum fractions read:
x_min = 2 pt/sqrt(s) exp(-|y|), x_max = 2 pt/sqrt(s) exp(+|y|)

Thus (**) returns (x_min + x_max)/2, and this should be fine.

  • DIJETS (CMS_2JET_7TEV): [(k1, k2, k3] = [|ymax|=max(|y1|,|y2|), m12, sqrt(s)] with m12 invariant mass of the dijet system. Given that, at LO, the following relation holds:
x1 = m12/sqrt(s) exp(+|yb|), x2 = m12/sqrt(s) exp(-|yb|)

with |yb|=|y1+y2|/2 (as in DY), I would say that the min and max x are given by the previous relations with |yb|=|ymax| i.e.

x_min = m12/sqrt(s) exp(-|ymax|), x_max = m12/sqrt(s) exp(+|ymax|)

Thus the average value should be given by (**)/2.

  • DIJETS (ATLAS_2JET_7TEV): [(k1, k2, k3] = [|y*|=|y1-y2|/2, m12, sqrt(s)]. Here I think that the situation is similar to eq.(7.33) of pinkbook, with tanh(y*) = cos(theta*). You see that parton luminosities factorize from matrix elements, and x1*x2*s = m12^2. Then I think that max and min x are simply given by:
x_min = m12^2/sqrt(s), x_max = 1

In this case (**) is completely off, and the mean would be something like

x = 1/2 * (1 + m12^2/sqrt(s))
  • DIJETS 3D (CMS_2JET_3D_8TEV): [(k1, k2, k3] = [|y*|=|y1-y2|/2, ptavg=(pt1+pt2)/2, |yb|=|y1+y2|/2]. In this case we know exactly the two momentum fractions:
x1 = 2 pt/sqrt(s) * cosh(|y*|) * exp(+|yb|), x2 = 2 pt/sqrt(s) * cosh(|y*|) * exp(-|yb|)

However, we need also sqrt(s), not present among the kinematic variables. So for now, I don't know how to represent these points on the (x,Q^2) plane.