Python project to work with 4-vectors and Lorentz boots in high energy physics.
Project description
pylorentz
The python package pylorentz provides classes to facilitate computations with 4-vectors in high-energy physics.
Quickstart
Install the package using pip
$ pip install git+https://gitlab.sauerburger.com/frank/pylorentz.git
or
$ pip install pylorentz
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'
Vectorized Properties
Since version 0.2.0, it is possible to pass numpy arrays to the constructors and operate on multiple vectors at a time.
>>> 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)
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