Properties

The package defines three types of 4-vectors: general purpose vectors, 4-positions and 4-momenta. The working horse of the package are 4-momenta.

>>> from pylorentz import Momentum4
>>> muon = Momentum4.m_eta_phi_pt(0.1057, 4.5, 1.5, 35)
>>> muon.eta
4.5
>>> muon.phi
1.5
>>> muon.p_t
35.0
>>> "%.2f" % muon.p
'1575.49'
>>> "%.2f" % muon.e
'1575.49'

>>> from pylorentz import Momentum4
>>> import numpy as np
>>> masses = np.array([0.0005, 0.1057, 1.7769])
>>> etas = np.array([1, 2, 3])
>>> phis = np.array([0, 0, 0])
>>> pts = np.array([10, 10, 10])
>>> muon = Momentum4.m_eta_phi_pt(masses, etas, phis, pts)
>>> ["%.2f" % m for m in muon.e]
['15.43', '37.62', '100.69']

Arithmetics

4-vectors support a variety of arithmetic operations. The most important one is the addition of two vectors.

>>> from pylorentz import Momentum4
>>> tau_1 = Momentum4.m_eta_phi_pt(1.777, 4.5, 1.5, 35)
>>> tau_2 = Momentum4.m_eta_phi_pt(1.777, -4.5, 1.5, 35)

We can add the momenta of the two tau leptons and access the properties of the parent particle.

>>> parent = tau_1 + tau_2
>>> "%.2f" % parent.m
'3150.21'
>>> "%.2f" % parent.eta
'0.00'
>>> "%.2f" % parent.phi
'1.50'

Lorentz Boosts

The package also provides methods to perform Lorentz boosts. For example, consider the decay of a Higgs boson to a pair of tau leptons in the rest frame of the Higgs boson. The tau leptons are back-to-back in the y-z-plane.

>>> import math
>>> from pylorentz import Momentum4
>>> m = 125.0
>>> tau_1 = Momentum4.e_m_eta_phi(m / 2, 1.777, 1.5, math.pi / 2)
>>> tau_2 = Momentum4.e_m_eta_phi(m / 2, 1.777, -1.5, -math.pi / 2)

Now let’s assume the Higgs boson itself is not at rest. We can define its momentum and then boost the two tau leptons.

>>> higgs = Momentum4.m_eta_phi_pt(m, 2, 0, 250)
>>> tau_1.boost_particle(higgs)
Momentum4(884.599, 220.498, 26.5578, 856.264)
>>> tau_2.boost_particle(higgs)
Momentum4(64.2195, 29.5021, -26.5578, 50.451)