MultiParticlePtCorrelations

class MultiParticlePtCorrelations.MultiParticlePtCorrelations(max_order: int)

Compute multi-particle transverse momentum correlations and cumulants up to the 8th order. This class is based on the following paper:

• [1] Eur. Phys. J. A 60 (2024) 2, 38 [2312.00492 [nucl-th]]

For the computation of transverse momentum correlations and cumulants, the implementation closely follows the equations and methods described in Ref. [1].

Parameters:

max_orderint

Maximum order of correlations and cumulants to compute (must be between 1 and 8).

Examples

A demonstration of how to use the MultiParticlePtCorrelations class to calculate transverse momentum correlations and cumulants.

>>> from sparkx import *
>>>
>>> # Maximum order for correlations and cumulants
>>> max_order = 8
>>> # Create a MultiParticlePtCorrelations object
>>> corr_obj = MultiParticlePtCorrelations(max_order=max_order)
>>>
>>> # List of events, where each event is a list of particle objects
>>> particle_list = Jetscape("./particles.dat").particle_object_list()
>>>
>>> # Compute mean transverse momentum correlations
>>> mean_pT_correlations = corr_obj.mean_pT_correlations(particle_list_all_events)
>>> print(mean_pT_correlations)
>>>
>>> # Compute mean transverse momentum cumulants
>>> mean_pT_cumulants = corr_obj.mean_pT_cumulants(particle_list_all_events)
>>> print(mean_pT_cumulants)

Attributes:

mean_pT_correlationnp.ndarray, optional

Mean transverse momentum correlations for each order up to max_order.

mean_pT_correlation_errornp.ndarray, optional

Error estimates (if computed) for mean transverse momentum correlations.

kappanp.ndarray, optional

Mean transverse momentum cumulants for each order up to max_order.

kappa_errornp.ndarray, optional

Error estimates (if computed) for mean transverse momentum cumulants.

N_eventslist

List to store numerators (N) of correlations for each event.

D_eventslist

List to store denominators (D) of correlations for each event.

Methods

mean_pT_correlations:	Computes the mean transverse momentum correlations for each order k across all events.
mean_pT_cumulants:	Computes the mean transverse momentum cumulants for each order k from the correlations.

MultiParticlePtCorrelations.mean_pT_correlations(particle_list_all_events: List[List[Particle]], compute_error: bool = True, delete_fraction: float = 0.4, number_samples: int = 100, seed: int = 42) → ndarray | Tuple[ndarray, ndarray]

Computes mean transverse momentum correlations for each order up to max_order using Eq. [14] in Ref. [1]. The weight is chosen to be \(W^{\prime}_{m} = D\langle m\rangle_{p_{\mathrm{T}}}\).

Parameters:

particle_list_all_eventslist

List of events, where each event is a list of particle objects.

compute_errorbool, optional

Whether to compute error estimates (default is True).

delete_fractionfloat, optional

Fraction of data to delete for Jackknife method (default is 0.4).

number_samplesint, optional

Number of Jackknife samples (default is 100).

seedint, optional

Random seed for reproducibility (default is 42).

Returns:

np.ndarray or tuple

Mean transverse momentum correlations for each order. If compute_error is True, returns a tuple (mean_pT_correlation, mean_pT_correlation_error).

Raises:

TypeError

If delete_fraction is not a float. If number_samples is not an integer. If seed is not an integer. If compute_error is not a boolean.

ValueError

If delete_fraction is not between 0 and 1. If number_samples is not greater than 0.

MultiParticlePtCorrelations.mean_pT_cumulants(particle_list_all_events: List[List[Particle]], compute_error: bool = True, delete_fraction: float = 0.4, number_samples: int = 100, seed: int = 42) → ndarray | Tuple[ndarray, ndarray]

Computes the mean transverse momentum cumulants for each order k from Eqs. B9-B16 in Ref. [1].

Parameters:

particle_list_all_eventslist

List of events, where each event is a list of particle objects.

compute_errorbool, optional

Whether to compute error estimates (default is True).

delete_fractionfloat, optional

Fraction of data to delete for Jackknife method (default is 0.4).

number_samplesint, optional

Number of Jackknife samples (default is 100).

seedint, optional

Random seed for reproducibility (default is 42).

Returns:

np.ndarray or tuple

Mean transverse momentum cumulants for each order. If compute_error is True, returns a tuple (kappa, kappa_error).

Raises:

TypeError

If delete_fraction is not a float. If number_samples is not an integer. If seed is not an integer. If compute_error is not a boolean.

ValueError

If delete_fraction is not between 0 and 1. If number_samples is not greater than 0.