pyhs3.distributions.CrystalBallDist

class pyhs3.distributions.CrystalBallDist(**data)

Single-sided Crystal Ball distribution implementation.

Implements the ROOT RooCrystalBall lineshape with a single power-law tail. This is the standard Crystal Ball distribution with shared parameters for both sides of the Gaussian core, but only one tail (usually on the left).

Mathematical Form:

\[\begin{split}f(m; m_0, \sigma, \alpha, n) = \begin{cases} A \cdot \left(B - \frac{m - m_0}{\sigma}\right)^{-n}, & \text{for } \frac{m - m_0}{\sigma} < -\alpha \\ \exp\left(-\frac{1}{2} \cdot \left[\frac{m - m_0}{\sigma}\right]^2\right), & \text{otherwise} \end{cases}\end{split}\]

where:

\[\begin{split}\begin{align} A &= \left(\frac{n}{\alpha}\right)^{n} \cdot \exp\left(-\frac{\alpha^2}{2}\right) \\ B &= \frac{n}{\alpha} - \alpha \end{align}\end{split}\]

Parameters:

• m – Observable variable

• m0 – Peak position (mean)

• sigma – Width parameter (must be > 0)

• alpha – Transition point (must be > 0)

• n – Power law exponent (must be > 0)

Note

All parameters except m and m0 must be positive. This is the standard single-sided Crystal Ball used widely in high-energy physics.

Parameters:

data (Any)

__init__(**data)

Create a new model by parsing and validating input data from keyword arguments.

Raises [ValidationError][pydantic_core.ValidationError] if the input data cannot be validated to form a valid model.

self is explicitly positional-only to allow self as a field name.

Parameters:

data (Any)

Methods

__init__(**data)	Create a new model by parsing and validating input data from keyword arguments.
construct([_fields_set])
copy(*[, include, exclude, update, deep])	Returns a copy of the model.
dict(*[, include, exclude, by_alias, ...])
expression(context)	Evaluate the single-sided Crystal Ball distribution.
from_orm(obj)
get_parameter_list(context, param_key)	Reconstruct a parameter list from flattened indexed keys.
json(*[, include, exclude, by_alias, ...])
model_construct([_fields_set])	Creates a new instance of the Model class with validated data.
model_copy(*[, update, deep])	!!! abstract "Usage Documentation"
model_dump(*[, mode, include, exclude, ...])	!!! abstract "Usage Documentation"
model_dump_json(*[, indent, include, ...])	!!! abstract "Usage Documentation"
model_json_schema([by_alias, ref_template, ...])	Generates a JSON schema for a model class.
model_parametrized_name(params)	Compute the class name for parametrizations of generic classes.
model_post_init(context, /)	This function is meant to behave like a BaseModel method to initialise private attributes.
model_rebuild(*[, force, raise_errors, ...])	Try to rebuild the pydantic-core schema for the model.
model_validate(obj, *[, strict, ...])	Validate a pydantic model instance.
model_validate_json(json_data, *[, strict, ...])	!!! abstract "Usage Documentation"
model_validate_strings(obj, *[, strict, ...])	Validate the given object with string data against the Pydantic model.
parse_file(path, *[, content_type, ...])
parse_obj(obj)
parse_raw(b, *[, content_type, encoding, ...])
process_parameter(param_key)	Process a single parameter that can be either a string reference or numeric value.
process_parameter_list(param_key)	Process a list parameter containing mixed string references and numeric values.
schema([by_alias, ref_template])
schema_json(*[, by_alias, ref_template])
update_forward_refs(**localns)
validate(value)

Attributes

constants	Dictionary of PyTensor constants generated from numeric field values.
model_computed_fields
model_config	Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].
model_extra	Get extra fields set during validation.
model_fields
model_fields_set	Returns the set of fields that have been explicitly set on this model instance.
parameters	Set of parameter names this component depends on.
type
alpha
m
m0
n
sigma
name