TauSpinner: τ-Lepton Reweighting Tool

• TauSpinner is a specialized Monte Carlo reweighting tool that reconstructs τ-lepton spin effects from event records for precise collider studies.
• It rapidly computes per-event weights by modeling spin correlations and polarization, facilitating studies of both Standard Model and New Physics effects.
• Its modular design integrates kinematic reconstruction, CP-mixing, and electroweak corrections, making it valuable for precision τ-related analyses.

TauSpinner is a specialized Monte Carlo reweighting algorithm designed for emulating, modifying, or removing τ-lepton spin effects and production matrix elements in already generated event samples, critically important for precision studies at the Large Hadron Collider (LHC) and analogous experiments. The architecture depends only on the four-momenta of τ leptons and their decay products, reconstructs all necessary production and decay kinematics from event records, and produces per-event weights encoding full spin-correlation and polarization subtleties. TauSpinner's rapid event-by-event reweighting allows analyses to incorporate Standard Model (SM) and New Physics (NP) effects, including τ polarization, spin correlations, CP-mixing, anomalous dipole interactions, and improved electroweak corrections, without necessitating re-generation or re-simulation of events (Czyczula et al., 2011, Przedzinski et al., 2018, Richter-Was et al., 2020).

1. Physics Motivation and Overview

TauSpinner is motivated by the critical role of tau spin observables—τ polarization and τ–τ spin correlations—in searches for new particles (e.g., Higgs boson, heavy resonances), precision SM parameter measurements (weak mixing angles, CP-properties), and background estimation in τ-embedded analyses (Czyczula et al., 2011, Przedzinski et al., 2014). The program enables modification of MC samples for Z/γ*, W, H^0, H^± production, accommodating both longitudinal and transverse spin effects at leading-order (LO) accuracy. The importance of proper τ spin treatment spans from acceptance modeling and detector efficiency to observable sensitivity in measuring CP violation and systematic uncertainties (Kaczmarska et al., 2014, Bahmani et al., 2017).

2. Mathematical and Algorithmic Foundations

TauSpinner employs exact factorization of production and decay amplitudes, modeling all spin effects via spin-correlation weights. For hard 2→2 or 1→2 production, the spin weight is constructed from the production density matrix ρ and τ helicity amplitudes Mλ: $$W_\text{spin} = \frac{\sum_{\lambda,\lambda'} \rho_{\lambda,\lambda'} M_\lambda M^*_{\lambda'}}{\sum_\lambda |M_\lambda|^2}$$ (Czyczula et al., 2011). For τ^+τ^− pairs, the spin weight contracts the production correlation matrix R_{ij} and mode-dependent polarimetric vectors h^i: $$w_\text{spin} = \sum_{i,j=t,x,y,z} R_{ij} \, h^i_{\tau^+} \, h^j_{\tau^-}$$ (Przedzinski et al., 2018, Przedzinski et al., 2014). The density matrix is determined analytically or numerically, depending on process topology (DY, VBF, H→ττ) (Kalinowski et al., 2016, Bahmani et al., 2017). TauSpinner computes per-event weights for production (w_prod) and spin (w_spin), and combines: $W = w_\text{prod} \cdot w_\text{spin}$ Transverse spin correlations are handled using pre-tabulated density-matrix look-up tables or user-supplied Born amplitudes, including external NP effects (e.g., spin-2, anomalous dipoles) (Banerjee et al., 2012, Korchin et al., 18 Jun 2025, Korchin et al., 28 Dec 2025).

3. Event Processing Workflow and Software Interfaces

TauSpinner is implemented as a C++/Fortran library with integrations for HepMC/LHE event records, Tauola++ τ-decay routines, LHAPDF for parton distribution functions, and API points for user-supplied Born or NP matrix elements (Czyczula et al., 2011, Przedzinski et al., 2018). The typical workflow consists of:

1. Initialization: Load Tauola, LHAPDF, configure process type, polarization mode, collision energy (via initialize_spinner), select physics and electroweak schemes (vbfinit, ExtraEWparamsSet) (Czyczula et al., 2011, Richter-Was et al., 2020).
2. Event Loop: Extract boson/parent, τ pair, and τ decay product four-momenta (from HepMC/LHE/user format).
3. Kinematic Reconstruction: Infer incoming parton momentum fractions (x₁, x₂), reconstruct ττ rest frame and scattering angle, attribute initial-state flavors via PDFs (Przedzinski et al., 2018).
4. Polarimetric Vectors: Boost τ daughters to the τ rest frame; compute h^i with Tauola routines (Kaczmarska et al., 2014).
5. Weight Calculation: For each event, compute w_spin and, if applicable, w_prod for alternative production hypotheses or NP insertions (J=0,1,2, anomalous couplings). Combine for final event weight.
6. Histogramming/Output: Use weights to fill user-defined histograms (e.g., polarization, acoplanarity, invariant mass distributions).

This modular workflow accommodates analysis-level manipulation of spin effects for arbitrary samples, including τ-embedded and real-data driven backgrounds (Czyczula et al., 2011, Kaczmarska et al., 2014, Richter-Was et al., 2020).

4. Coverage of Production Mechanisms and Decay Channels

TauSpinner fully supports longitudinal spin effects for Z/γ→ττ, W→τν, H→ττ across leptonic and hadronic τ decay channels, leveraging the near-complete coverage of Tauola++ for all major modes (>97.5%) (Kaczmarska et al., 2014, Przedzinski et al., 2018). For Z/γ, the program reconstructs the initial-state quark configuration with stochastic flavor sampling using PDFs, solving: $$x_1 x_2\, s = \hat{s}, \quad (x_1 - x_2) E_{\text{cm}} = p_z(\text{boson})$$ (Czyczula et al., 2011). The density matrix assembly accommodates both effective Born and improved EW-corrected amplitudes, with SANC/DIZET form-factor integration for precision studies (Richter-Was et al., 2018, Richter-Was et al., 2020). Extension to VBF production utilizes full 2→4 matrix elements generated by MadGraph5, with explicit helicity treatment, supporting user-defined coupling scenarios (including spin-2 and alternative Higgs sector couplings) (Kalinowski et al., 2016, Bahmani et al., 2017). For photonic initial states (γγ→ττ), TauSpinner supports anomalous electric/magnetic dipole moments via form-factor manipulations at the vertex level (Korchin et al., 18 Jun 2025).

5. Extensions, New Physics, and CP Applications

TauSpinner provides flexible hooks for the insertion of NP effects, including but not limited to:

• Spin-2 Exchange (e.g., new resonance X): Implements dimension-5 couplings, full Born amplitude supplementation, and event-wise reweighting from SM to NP cross sections (Banerjee et al., 2012, Bahmani et al., 2017).
• Anomalous Dipole Moments: Incorporates modified γττ and Zττ vertices with form-factors F₂(q²), F₃(q²), X(s), Y(s) in density-matrix formalism, enabling charge-parity violation studies (Korchin et al., 18 Jun 2025, Korchin et al., 28 Dec 2025).
• Higgs CP Tests: Accommodates scalar/pseudoscalar mixing by direct manipulation of transverse spin-correlation matrices, selection of R_{xx}, R_{yy}, R_{xy}, R_{yx} per hypothesis (Przedzinski et al., 2014).
• Electroweak Corrections: Supports Effective Born and Improved Born schemes (with one-loop form-factors from DIZET), permitting per-event upgrades for precision measurements of sin²θW^eff, A_FB, Pτ (Richter-Was et al., 2020, Richter-Was et al., 2018).

Users may supply external routine pointers to custom Born amplitudes or matrix elements for arbitrary NP scenarios, provided the matrix element extensions adhere to the factorized SM-like structure, including arbitrary chiral couplings or phase shifts (Przedzinski et al., 2014, Bahmani et al., 2017).

6. Validation, Numerical Benchmarks, Systematics

Extensive validation has demonstrated high fidelity for reweighting spin effects and production hypotheses. For Z/γ*, W, and H^0 channels, TauSpinner-reweighted samples agree with Tauola-generated distributions in τ polarization and spin-correlation observables within statistical uncertainties (Czyczula et al., 2011, Kaczmarska et al., 2014). Comparison of 2→2 (Born) and 2→4 (jets included) implementations show sub-percent differences in τ polarization for inclusive and VBF-like selections, with ~10% effects possible in restricted phase space (Kalinowski et al., 2016, Bahmani et al., 2017). Sensitivity to the choice of electroweak scheme (e.g., sin²θ_W vs. sin²θ_W^eff) can induce shifts in τ polarization and forward-backward asymmetry at the percent level (Kalinowski et al., 2016, Richter-Was et al., 2020). For NP tests, the program yields per-mille level accuracy for polarization over a wide range of kinematics and demonstrates clear discrimination power for spin-0 vs. spin-2 hypotheses (Banerjee et al., 2012).

7. Practical Considerations and Limitations

TauSpinner operation depends only on reconstructed four-momenta and decay-chain identification—no explicit partonic history is necessary, although PDF uncertainty enters inferred flavor assignment and normalization. The algorithm assumes complete phase-space coverage and moderate weight ranges—extreme couplings or poorly covered regions can result in unstable weights or zero-density artifacts (Kaczmarska et al., 2014, Bahmani et al., 2017). By design, TauSpinner omits higher-order QCD corrections, relying on the generator’s event sequence; transverse spin effects require special treatment or lookup table supplementation. Integration into analysis workflows is direct, with plug-and-play C++/Python APIs and, for electroweak upgrades, table-driven form-factor imports (Richter-Was et al., 2018, Richter-Was et al., 2020). Memory and CPU overheads are minimal; processing rates of >10^5 events/sec are typical on modern hardware.

Table: Core API Functions (from documentation and code summaries)

Function	Purpose	Key Parameters/Inputs
initialize_spinner	Set up process, polarization, energy	Ipp, Ipol, CMSene, nonSM2, nonSMN
calculateWeightFromParticlesH	Compute w_spin (Z/γ*, H^0)	Boson, τ₁, τ₂, daughters
calculateWeightFromParticlesWorHpn	Compute w_spin (W, H^±)	Entities as above (W/H^± parentage)
calculateWeightFromParticlesVBF	Reweight for VBF (2→4)	jets, τ's, daughters
set_nonSM_born, set_vbfdistrModif	Insert user-supplied NP matrix elements	Function pointer
getWtNonSM	Return w_prod (production weight)	None (current event context)

TauSpinner’s structure and modular interfaces make it suitable for advanced analyses requiring flexible, precision-level control of spin effects and event weights in τ-lepton physics at hadron colliders and e+e− experiments. The program’s rigorous mathematical basis and validated algorithms support studies involving SM precision observables, CP-mixing characterization, and NP hypothesis testing, enabling systematic uncertainty evaluation and robust physics extraction from existing datasets.