[Paper Review] $ au^- o\pi^-\gamma u_ au$ as a source of background on the Lepton Flavour Violating decay $ au^- o\mu^-\gamma$

Zhi-Hui Guo, Pablo Roig|arXiv (Cornell University)|Oct 14, 2010

Particle physics theoretical and experimental studies37 references1 citations

TL;DR

This paper calculates the radiative decay τ⁻ → π⁻γντ using Resonance Chiral Theory (RχT), incorporating QCD constraints to predict form factors without free parameters. It finds that structure-dependent (SD) contributions dominate at high photon energies—precisely where they mimic the lepton-flavor-violating decay τ⁻ → μ⁻γ—leading to a background underestimation by PHOTOS by a factor of ~5, which could affect current branching ratio limits.

ABSTRACT

We calculate the decay of $ au^- o\pi^-\gamma u_ au$ in the framework of Resonance Chiral Theory ($R\chi T$). By demanding the high energy constraints from QCD on the related form factors, we could predict the various physical observables of $ au^- o\pi^-\gamma u_ au$ without any free parameter. Our results show that for a realistic cut on the photon energy (around $100$ MeV) this mode gives a branching ratio of roughly $0.1%$ that should have already been detected at the heavy-flavour factories. Another interesting subject we have studied based on our calculation of the decay $ au^- o\pi^-\gamma u_ au$ is the experimental background estimation of the lepton flavour violation process $ au^- o \mu^- \gamma$. We point out that although the description of radiation that PHOTOS provides -which has been used by BaBar and Belle collaborations to estimate this source of background- is in excellent agreement with the theoretical expectations in the low energy region in $ au^- o\pi^-\gamma u_ au$ decay, this is not the case in the high energy region, precisely where it is easier that this decay mimics the process $ au^- o\mu^-\gamma$.

Motivation & Objective

• To calculate τ⁻ → π⁻γντ decay amplitudes using Resonance Chiral Theory (RχT) with QCD constraints.
• To assess the impact of structure-dependent (SD) form factors on the photon energy spectrum.
• To evaluate the reliability of PHOTOS in estimating background from τ⁻ → π⁻γντ in searches for lepton-flavor-violating τ⁻ → μ⁻γ.
• To quantify the discrepancy between PHOTOS simulations and theoretical predictions in the high-energy photon region.

Proposed method

• Uses Resonance Chiral Theory (RχT) to model strong interaction effects in τ⁻ → π⁻γντ, incorporating QCD constraints on form factors.
• Derives matrix elements including internal bremsstrahlung (IB) and structure-dependent (SD) contributions via vector (V) and axial-vector (A) form factors.
• Computes the differential decay width dΓ/dx as a function of x = 2pτ·k/Mτ², with x near 1 corresponding to high photon energy.
• Compares theoretical predictions with PHOTOS and MC-TESTER simulations, focusing on the high-energy endpoint region.
• Performs a missing mass reconstruction analysis to isolate events where π and γ reconstruct the τ mass within 9 MeV.
• Estimates the background underestimation by comparing PHOTOS (IB-only) with full theoretical prediction (IB + SD) in the last six bins of the photon spectrum.

Experimental results

Research questions

• RQ1 How do structure-dependent (SD) contributions affect the photon energy spectrum in τ⁻ → π⁻γντ near the endpoint?
• RQ2 To what extent does the PHOTOS event generator underestimate the background from τ⁻ → π⁻γντ in τ⁻ → μ⁻γ searches?
• RQ3 What is the quantitative discrepancy between PHOTOS and theoretical predictions in the high-energy photon region relevant for τ → μ⁻γ?
• RQ4 How does the inclusion of SD form factors alter the branching ratio estimate for τ⁻ → π⁻γντ under realistic experimental cuts?
• RQ5 Can the τ⁻ → π⁻γντ decay serve as a reliable background estimation tool for future lepton-flavor-violating searches?

Key findings

• The branching ratio for τ⁻ → π⁻γντ with photon energy above 100 MeV is predicted to be approximately 0.1%, which should have been detectable at B-factories.
• Structure-dependent (SD) contributions dominate the photon spectrum at high energies (x ≈ 1), contrary to the low-energy dominance of internal bremsstrahlung (IB).
• PHOTOS underestimates the background from τ⁻ → π⁻γντ by a factor of approximately 5 in the high-energy region where it most closely mimics τ⁻ → μ⁻γ.
• The total decay width is only mildly affected by SD contributions (Γ_all / Γ_IB ≈ 1.1), but the spectral shape is significantly altered in the endpoint region.
• The discrepancy arises because PHOTOS only models QED-based IB contributions and neglects SD effects, which are critical near the endpoint.
• The authors recommend updating PHOTOS and TAUOLA with the new RχT-based hadronic currents to improve background estimation accuracy.