B2DxDK

Julia implementation of the amplitude model for the three-body decay

$$B^+ \to D^- D^{*+} K^+$$

from the LHCb publication Observation of New Charmonium or Charmoniumlike States (InspireHEP:2794793).

The model is built with CascadeDecays.jl and aligned with the TF-PWA reference implementation. It lives in scripts/model.jl; the scripts in scripts/ and the regression checks load it with include. The serialized model (amplitude-serialization JSON) is in data/b2dxdk_amplitude_model_{Cminus,Cplus}.json.

Setup

using Pkg
Pkg.activate(".")
Pkg.instantiate()

Usage

A. Build the model

include("scripts/model.jl")

cascade = build_all_resonance_cascade()
# optional: build_resonance_cascade("Psi(4040)") for a single resonance

Couplings are loaded from data/final_params_full.json when the model is included.

B. Execute the model on four-vectors

Final-state four-momenta are passed in the order

$$(p_{D^0},\ p_{\pi^+},\ p_{D^-},\ p_{K^+})$$

The $D^{+}$ is reconstructed as $D^0,\pi^+$ (cascade kinematics with $D^{+}$ at nominal mass).

include("scripts/model.jl")

cascade = build_all_resonance_cascade()

pD0     = FourVector(px_D0,  py_D0,  pz_D0;  E=E_D0)
piplus  = FourVector(px_pip, py_pip, pz_pip; E=E_pip)
pDminus = FourVector(px_Dm,  py_Dm,  pz_Dm;  E=E_Dm)
pKplus  = FourVector(px_Kp,  py_Kp,  pz_Kp;  E=E_Kp)

point = KinematicPoint(kinematic_task, (pD0, piplus, pDminus, pKplus))

# amplitude for one resonance (sum over its sub-chains)
amp_psi4040 = only(amplitude(cascade[resonance_chain_names("Psi(4040)")], point))

# coherent sum over all chains (all resonances)
amp_total = only(amplitude(cascade, point))

If four-momenta are stored in a table row (as in data/crosscheck.arrow), use event_point(row) instead.

Regression checks

julia --project=. test/runtests.jl

Analysis references

• Internal documentation: TWiki
• Internal code: GitLab@CERN, GitLab@EP1
• Full TF2 code: fork by Alexander Kazatsky

Archive

Earlier notebooks, investigation material, and convention notes are under archive/.

Acknowledgements

This model was developed in the context of the LHCb collaboration analysis of

$$B^+ \to D^- D^{*+} K^+$$

The amplitude structure follows the TF-PWA framework used in that analysis. We especially thank Yi Juang for the TF-PWA reference implementation and for extensive cross-checks while building this Julia port.