FEAT: implement general Chew–Mandelstam function #480
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| @unevaluated | ||
| class PhaseSpaceFactorPWave(sp.Expr): | ||
| r"""Phase space factor using `ChewMandelstamIntegral` for :math:`L=1`. | ||
| This `PhaseSpaceFactor` uses the numerical dispersion integral implemented in | ||
| `ChewMandelstamIntegral`. As such, you have to be careful when lambdifying this | ||
| function and evaluating this over an array. In many cases, you want to wrap the | ||
| resulting lambdified numerical function with :func:`numpy.vectorize`. | ||
| >>> import numpy as np | ||
| >>> from ampform.dynamics.phasespace import PhaseSpaceFactorPWave | ||
| >>> s, m1, m2 = sp.symbols("s m_1 m_2") | ||
| >>> rho_expr = PhaseSpaceFactorPWave(s, m1, m2) | ||
| >>> rho_func = sp.lambdify((s, m1, m2), rho_expr.doit()) | ||
| >>> rho_func = np.vectorize(rho_func) | ||
| >>> s_values = np.linspace(0.1, 4.0, num=4) | ||
| >>> rho_func(s_values, 0.14, 0.98).real | ||
| array([-4.08315014e-07, 8.05561163e-03, 2.65015019e-01, 5.43083429e-01]) | ||
| """ | ||
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| s: Any | ||
| m1: Any | ||
| m2: Any | ||
| name: str | None = argument(default=None, sympify=False) | ||
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| def evaluate(self) -> sp.Expr: | ||
| s, m1, m2 = self.args | ||
| chew_mandelstam = ChewMandelstamIntegral(s, m1, m2, L=1, epsilon=1e-5) | ||
| return -sp.I * chew_mandelstam | ||
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| def _latex_repr_(self, printer: LatexPrinter, *args) -> str: | ||
| s_symbol = self.args[0] | ||
| s_latex = printer._print(s_symbol) | ||
| subscript = _indices_to_subscript(determine_indices(s_symbol)) | ||
| name = R"\rho^\mathrm{CM}_1" + subscript if self.name is None else self.name | ||
| return Rf"{name}\left({s_latex}\right)" |
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This is just a check whether a wrapped dispersion integral works, plus a bit of documentation with regard to vectorisation. We have to find a solution for the fact though that the PhaseSpaceFactorProtocol only allows for the keyword arguments s, m1, and m2.
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labtask for Poe the Poet policy#543jupyterlab-quickopeninjupyterdependency group policy#544BreakupMomentumand related classes toampform.kinematics.phasespaceTip
Preview here:
https://ampform--480.org.readthedocs.build/480/usage/dynamics/analytic-continuation.html#dispersion-integral