# PhaseSpace¶

Python implementation of the Raubold and Lynch method for n-body events using TensorFlow as a backend.

The code is based on the GENBOD function (W515 from CERNLIB), documented in [1] and tries to follow it as closely as possible.

If you use phasespace in a scientific publication we would appreciate citations to the zenodo publication:

@article{phasespace-2019,
title={phasespace: n-body phase space generation in Python},
DOI={10.5281/zenodo.2926058},
publisher={Zenodo},
author={Albert Puig and Jonas Eschle},
year={2019},
month={Mar}}


Free software: BSD-3-Clause.

[1] F. James, Monte Carlo Phase Space, CERN 68-15 (1968)

## Why?¶

Lately, data analysis in High Energy Physics (HEP), traditionally performed within the ROOT ecosystem, has been moving more and more towards Python. The possibility of carrying out purely Python-based analyses has become real thanks to the development of many open source Python packages, which have allowed to replace most ROOT functionality with Python-based packages.

One of the aspects where this is still not possible is in the random generation of n-body phase space events, which are widely used in the field, for example to study kinematics of the particle decays of interest, or to perform importance sampling in the case of complex amplitude models. This has been traditionally done with the TGenPhaseSpace class, which is based of the GENBOD function of the CERNLIB FORTRAN libraries and which requires a full working ROOT installation.

This package aims to address this issue by providing a TensorFlow-based implementation of such a function to generate n-body decays without requiring a ROOT installation. Additionally, an oft-needed functionality to generate complex decay chains, not included in TGenPhaseSpace, is also offered, leaving room for decaying resonances (which don’t have a fixed mass, but can be seen as a broad peak).

## Installing¶

phasespace is available on conda-forge and pip.

To install phasespace with conda, run:

$conda install phasespace -c conda-forge  To install with pip: $ pip install phasespace


This is the preferred method to install phasespace, as it will always install the most recent stable release.

For the newest development version, which may be unstable, you can install the version from git with

\$ pip install git+https://github.com/zfit/phasespace


## How to use¶

The generation of simple n-body decays can be done using the nbody_decay shortcut to create a decay chain with a very simple interface: one needs to pass the mass of the top particle and the masses of the children particle as a list, optionally giving the names of the particles. Then, the generate method can be used to produce the desired sample. For example, to generate $$B^0\to K\pi$$, we would do:

import phasespace

B0_MASS = 5279.58
PION_MASS = 139.57018
KAON_MASS = 493.677

weights, particles = phasespace.nbody_decay(B0_MASS,
[PION_MASS, KAON_MASS]).generate(n_events=1000)


This returns a numpy array of 1000 elements in the case of weights and a list of n particles (2) arrays of (1000, 4) shape, where each of the 4-dimensions corresponds to one of the components of the generated Lorentz 4-vector. All particles are generated in the rest frame of the top particle; boosting to a certain momentum (or list of momenta) can be achieved by passing the momenta to the boost_to argument.

Behind the scenes, this function runs the TensorFlow graph, but no caching of the graph or reusing the session is performed. If we want to get the graph to avoid an immediate execution, we can use the generate_tensor method. Then, to produce the equivalent result to the previous example, we simply do:

import tensorflow as tf

with tf.Session() as sess:
weights, particles = phasespace.nbody_decay(B0_MASS,
[PION_MASS, KAON_MASS]).generate_tensor(n_events=1000)
weights, particles = sess.run([weights, particles])


Sequential decays can be handled with the GenParticle class (used internally by generate) and its set_children method. As an example, to build the $$B^{0}\to K^{*}\gamma$$ decay in which $$K^*\to K\pi$$, we would write:

from phasespace import GenParticle

B0_MASS = 5279.58
KSTARZ_MASS = 895.81
PION_MASS = 139.57018
KAON_MASS = 493.677

pion = GenParticle('pi+', PION_MASS)
kaon = GenParticle('K+', KAON_MASS)
kstar = GenParticle('K*', KSTARZ_MASS).set_children(pion, kaon)
gamma = GenParticle('gamma', 0)
bz = GenParticle('B0', B0_MASS).set_children(kstar, gamma)

weights, particles = bz.generate(n_events=1000)


Where we have used the fact that set_children returns the parent particle. In this case, particles is a dict with the particle names as keys:

>>> particles
{'K*': array([[ 1732.79325872, -1632.88873127,   950.85807735,  2715.78804872],
[-1633.95329448,   239.88921123, -1961.0402768 ,  2715.78804872],
[  407.15613764, -2236.6569286 , -1185.16616251,  2715.78804872],
...,
[ 1091.64603395, -1301.78721269,  1920.07503991,  2715.78804872],
[ -517.3125083 ,  1901.39296899,  1640.15905194,  2715.78804872],
[  656.56413668,  -804.76922982,  2343.99214816,  2715.78804872]]),
'K+': array([[  750.08077976,  -547.22569019,   224.6920906 ,  1075.30490935],
[-1499.90049089,   289.19714633, -1935.27960292,  2514.43047106],
[   97.64746732, -1236.68112923,  -381.09526192,  1388.47607911],
...,
[  508.66157459,  -917.93523639,  1474.7064148 ,  1876.11771642],
[ -212.28646168,   540.26381432,   610.86656669,   976.63988936],
[  177.16656666,  -535.98777569,   946.12636904,  1207.28744488]]),
'gamma': array([[-1732.79325872,  1632.88873127,  -950.85807735,  2563.79195128],
[ 1633.95329448,  -239.88921123,  1961.0402768 ,  2563.79195128],
[ -407.15613764,  2236.6569286 ,  1185.16616251,  2563.79195128],
...,
[-1091.64603395,  1301.78721269, -1920.07503991,  2563.79195128],
[  517.3125083 , -1901.39296899, -1640.15905194,  2563.79195128],
[ -656.56413668,   804.76922982, -2343.99214816,  2563.79195128]]),
'pi+': array([[  982.71247896, -1085.66304109,   726.16598675,  1640.48313937],
[ -134.0528036 ,   -49.3079351 ,   -25.76067389,   201.35757766],
[  309.50867032,  -999.97579937,  -804.0709006 ,  1327.31196961],
...,
[  582.98445936,  -383.85197629,   445.36862511,   839.6703323 ],
[ -305.02604662,  1361.12915468,  1029.29248526,  1739.14815935],
[  479.39757002,  -268.78145413,  1397.86577911,  1508.50060384]])}


The GenParticle class is able to cache the graphs so it is possible to generate in a loop without overhead:

for i in range(10):
weights, particles = bz.generate(n_events=1000)
...
(do something with weights and particles)
...


This way of generating is recommended in the case of large samples, as it allows to benefit from parallelisation while at the same time keep the memory usage low.

If we want to operate with the TensorFlow graph instead, we can use the generate_tensor method of GenParticle, which has the same signature as generate.

More examples can be found in the tests folder and in the documentation.

## Physics validation¶

Physics validation is performed continuously in the included tests (tests/test_physics.py), run through Travis CI. This validation is performed at two levels:

• In simple n-body decays, the results of phasespace are checked against TGenPhaseSpace.
• For sequential decays, the results of phasespace are checked against RapidSim, a “fast Monte Carlo generator for simulation of heavy-quark hadron decays”. In the case of resonances, differences are expected because our tests don’t include proper modelling of their mass shape, as it would require the introduction of further dependencies. However, the results of the comparison can be expected visually.

The results of all physics validation performed by the tests_physics.py test are written in tests/plots.

## Contributing¶

Contributions are always welcome, please have a look at the Contributing guide.