Unintuitive behavior of `Math::PxPyPzMVector` in calculations

[Zehvogel]

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Description

Depending on the mixture of 4-vector types and the order of operations the result can change, e.g. lv1 - lv2 != -lv2 + lv1 See reproducer for all combinations.

Reproducer

import ROOT

lv1 = ROOT.Math.PxPyPzEVector(0, 0, 1, 1)
lv2 = ROOT.Math.PxPyPzMVector(lv1)

print(lv1 - lv2)
# (0,0,0,0)
print(lv2 - lv1)
# (0,0,0,0)
print(-lv1 + lv2)
# (0,0,0,0)
print(-lv2 + lv1)
# (0,0,0,2)

but I am relatively sure that it will also happen in c++

ROOT version

ROOT Version: 6.33.01
Built for linuxx8664gcc on Jun 12 2024, 23:54:24
From heads/master@v6-31-01-2329-g4fe33d2d91

Installation method

LCG dev3

Operating system

Alma9

Additional context

No response

[m-fila]

Hi, I think this is a known limitation of the design

The issue here is not a mixture of vector classes but a negation of a vector from a coordinate system using mass (so just the PxPyPzMVector part):

root [0] auto v = ROOT::Math::PxPyPzMVector(0,0,1,0)
(ROOT::Math::LorentzVector<ROOT::Math::PxPyPzM4D<double> > &) (0,0,1,0)
root [1] v-v
(ROOT::Math::LorentzVector) (0,0,0,0)
root [2] v+(-v)
(ROOT::Math::LorentzVector) (0,0,0,2)

For coordinate systems represented with mass an unary operator- doesn't model a '4-vector negation' operation, because it returns a vector with negated momentum and negated mass instead of returning a properly negated 4-vector. A negated 4-vector should have negated momentum and negated energy but the same mass, and that can't be achieved with a representation containing only momentum and mass. It could be done by introducing another member (sign of energy), but that would be intrusive into design