From f0092bd2355241a31ea6b3da39c7d6e54c1c9ebf Mon Sep 17 00:00:00 2001 From: "pre-commit-ci[bot]" <66853113+pre-commit-ci[bot]@users.noreply.github.com> Date: Mon, 27 May 2024 21:27:27 +0000 Subject: [PATCH] [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --- docs/description.md | 11 +++++------ 1 file changed, 5 insertions(+), 6 deletions(-) diff --git a/docs/description.md b/docs/description.md index dc4bc56..b8b3489 100644 --- a/docs/description.md +++ b/docs/description.md @@ -135,7 +135,7 @@ It species the main properties such as spin, and masses of all particles. ## Topology and Reference Topology -Purpose of the `reference_topology` is two folded. First, it defines how kinematics of the decay is parametrized, i.e. which combination of masses and angles is used to describe the phase space. Second, the `reference_topology` plays crucial role in defining how helicity amplitudes are computed. The reference topology is used to fix the quantization axes for particle helicities. Since helicity is the projection of a particle's spin along its direction of motion, its precise definition depends upon the frame of reference in which it is evaluated. +Purpose of the `reference_topology` is two folded. First, it defines how kinematics of the decay is parametrized, i.e. which combination of masses and angles is used to describe the phase space. Second, the `reference_topology` plays crucial role in defining how helicity amplitudes are computed. The reference topology is used to fix the quantization axes for particle helicities. Since helicity is the projection of a particle's spin along its direction of motion, its precise definition depends upon the frame of reference in which it is evaluated. As the `reference_topology` unambiguously defines the path to traverse the decay graph from initial to the final states, it sets a frame for each helicity, where it is defined. The helicity values employed in the indices of Wigner rotations `D_{λ1, λ2}` and couplings `H_{λ1, λ2}` are thus indicative of this frame. ### An example of four-body decay @@ -149,16 +149,16 @@ The decay amplitude reads as a series of Wigner $D$-functions, each corresp $$ \begin{align} A &= n_{j_0} D_{m_0, \tau-\lambda_2}^{j_0}(\text{angles}_{[[3,1],4]}) \,\, H_{\tau,\lambda_2} \\ -% +% &\quad \cdot n_{j_{[[3,1],4]}} D_{\tau, \nu-\lambda_4}^{j_{[[3,1],4]}}(\text{angles}_{[3,1]}) \\ -% +% &\quad \cdot n_{j_{[3,1]}} D_{\nu, \lambda_3-\lambda_1}^{j_{[3,1]}}(\text{angles}_3) \,\, H_{\lambda_3,\lambda_1} \end{align} $$ - $D_{m_0, \tau - \lambda_2}^{j_0}(\text{angles}_{[[3,1],4]})$ describes the decay of particle 0 into a system `[3,1,4]`, and a particle `2` with helicities $\nu$, and $\lambda_2$, respectively. The decay is considered in the overall rest frame of the system (comprising particles `3`, `1`, `4`, and `2`). -Here is the first appearence of the $\lambda_2$, hence the helicity state of particle `2` is defined from its rest frame by boost-z and rotation to the total center of momentum. -The index $m_0$ is the spin projection of the decaying particle (0). It's a canontical state as the particle is at rest. + Here is the first appearence of the $\lambda_2$, hence the helicity state of particle `2` is defined from its rest frame by boost-z and rotation to the total center of momentum. + The index $m_0$ is the spin projection of the decaying particle (0). It's a canontical state as the particle is at rest. - $D_{\tau,\nu-\lambda_4}^{j_{[[3,1],4]}}(\text{angles}_{[3,1]})$: For particle `4`, its helicity, $\lambda_4$, is defined within the rest frame of the `[3,1,4]` system. This frame is obtained from the overall rest frame by applying a rotation and boost, signifying the progression of the decay sequence. @@ -201,7 +201,6 @@ Vertices define the nodes in the decay graphs, where one particle transits into \end{multline} $$ - ### Propagators - **`type`:** The `type` field within each propagator specifies the mathematical or physical model used to describe the propagation of a particle between interactions. This type is directly linked to the `lineshapes` section, where the detailed characteristics of each propagator type (e.g., resonance models like Breit-Wigner or Flatté) are defined. The `type` essentially dictates how the propagator influences the chain's overall amplitude, based on its lineshape parameters.