Pion $\beta$ decay and $\tau \to \pi \pi {\nu }_{\tau }$ beyond leading logarithms

Abstract

The consistent matching of short-distance contributions and hadronic matrix elements is crucial for precise predictions of weak processes involving hadrons. In this Letter, we address this point for charged-current processes involving two pions -- pion $\beta$ decay ${\pi }^{\pm }\to {\pi }^0{e}^{\pm }{\nu }_e$ and hadronic $\tau$ decays ${\tau }^{\pm }\to {\pi }^{\pm }{\pi }^0{\nu }_{\tau }$ -- whose decay rates depend on the so-called $\gamma W$ box correction. Using recent results from lattice QCD, we show how to formulate the matching beyond leading-logarithmic accuracy, in particular, how to cancel the dependence on the scheme choice for evanescent operators. As main results, we obtain a prediction for the decay rate of pion $\beta$ decay with theory uncertainties improved by a factor of three, which renders theory uncertainties negligible for future determinations of $V_{ud}$ even beyond the reach of the PIONEER experiment, and an evaluation of isospin-breaking corrections to $\tau \to \pi \pi {\nu }_{\tau }$ with negligible uncertainty from the short-distance matching, as necessary for a future $\tau$-based determination of the hadronic-vacuum-polarization contribution to the anomalous magnetic moment of the muon.

arXiv comment13 pages, 2 figures; journal version

References in corpus (87)

• The anomalous magnetic moment of the muon in the Standard Model
• Measurement of the fine-structure constant as a test of the Standard Model
• RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses
• The $g-2$ of charged leptons, $\alpha (M_Z^2)$ and the hyperfine splitting of muonium
• A new evaluation of the hadronic vacuum polarisation contributions to the muon anomalous magnetic moment and to $\mathbf{\alpha }({\mathbf{m}}_{\mathbf{Z}}^2)$
• High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
• Three-Loop Polarization Function and $\mathcal{O}({\alpha }_s^2)$ Corrections to the Production of Heavy Quarks
• Reduced hadronic uncertainty in the determination of $V_{ud}$
• Improved Calculation of Electroweak Radiative Corrections and the Value of V_ud
• Version 3 of {\tt RunDec} and {\tt CRunDec}
• Measurement of the Electron Magnetic Moment
• Virtual Photons in Chiral Perturbation Theory
• Confronting Spectral Functions from e+e- Annihilation and tau Decays: Consequences for the Muon Magnetic Moment
• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• Radiative Corrections to Neutron and Nuclear Beta Decays Revisited
• Dispersive Evaluation of the Inner Radiative Correction in Neutron and Nuclear $\beta$-decay
• High-precision quark masses and QCD coupling from $n_f=4$ lattice QCD
• Low-energy effective field theory below the electroweak scale: matching at one loop
• Precision Measurements and CKM Unitarity
• The Discrepancy Between tau and e+e- Spectral Functions Revisited and the Consequences for the Muon Magnetic Anomaly
• A sum rule approach to the violation of Dashen's theorem
• Pion and Kaon Electromagnetic Form Factors
• The CKM unitarity problem: A trace of new physics at the TeV scale?
• The anomalous magnetic moment of the muon in the Standard Model: an update
• Joint lattice QCD - dispersion theory analysis confirms the quark-mixing top-row unitarity deficit
• Electroweak Corrections to the Charm Quark Contribution to K+ -> pi+ nu nu-bar
• Precise Measurement of the Pi+ -> Pi0 e+ nu Branching Ratio
• Isospin Violation and the Magnetic Moment of the Muon
• Radiative tau decay and the magnetic moment of the muon
• The strong coupling from a nonperturbative determination of the $\Lambda$ parameter in three-flavor QCD
• Incorporation of QCD Effects in Basic Corrections of the Electroweak Theory
• Global Fit to Modified Neutrino Couplings and the Cabibbo-Angle Anomaly
• Beta decays as sensitive probes of lepton flavor universality
• Detailed Report of the MuLan Measurement of the Positive Muon Lifetime and Determination of the Fermi Constant
• Chiral Perturbation Theory with Virtual Photons and Leptons
• Improved measurement of the $π\rightarrow \mbox{e} ν$ branching ratio
• Standard Model $\mathcal{O}(\alpha )$ renormalization of $g_A$ and its impact on new physics searches
• Global Electroweak Fit and Vector-Like Leptons in Light of the Cabibbo Angle Anomaly
• $\gamma W$-box Inside-Out: Nuclear Polarizabilities Distort the Beta Decay Spectrum
• Electroweak axial structure functions and improved extraction of the $V_{ud}$ CKM matrix element
• FLAG Review 2024
• Scrutinizing CKM unitarity with a new measurement of the $K_{\mu 3}/K_{\mu 2}$ branching fraction
• First-principles calculation of electroweak box diagrams from lattice QCD
• Precise determination of the strong coupling constant in Nf=2+1 lattice QCD with the Schrödinger functional scheme
• The Fermi constant from muon decay versus electroweak fits and CKM unitarity
• Cabibbo anomaly versus electroweak precision tests: An exploration of extensions of the Standard Model
• Explaining $b\to s{\ell }^{+}{\ell }^{-}$ and the Cabibbo Angle Anomaly with a Vector Triplet
• Long-distance radiative corrections to the di-pion tau lepton decay
• Radiative corrections in weak semi-leptoni processes at low energy: a two-step matching determination
• The Realistic Lattice Determination of alpha_s(M_Z) Revisited
• Searching for Lepton Flavour (Universality) Violation and Collider Signals from a Singly-Charged Scalar Singlet
• Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization
• Determination of the QCD coupling from the static energy and the free energy
• New $\tau$-based evaluation of the hadronic contribution to the vacuum polarization piece of the muon anomalous magnetic moment
• The hadronic running of the electromagnetic coupling and the electroweak mixing angle from lattice QCD
• First-Generation New Physics in Simplified Models: From Low-Energy Parity Violation to the LHC
• A Minimal Explanation of Flavour Anomalies: B-Meson Decays, Muon Magnetic Moment, and the Cabibbo Angle
• Leptonic contributions to the effective electromagnetic coupling at four-loop order in QED
• Pion-induced radiative corrections to neutron beta-decay
• Effective field theory for radiative corrections to charged-current processes I: Vector coupling
• Combined Explanation of the $Z\to b\bar{b}$ Forward-Backward Asymmetry, the Cabibbo Angle Anomaly, $\tau \to \mu \nu \nu$ and $b\to s{\ell }^{+}{\ell }^{-}$ Data
• The pionic beta decay in chiral perturbation theory
• Improved Determination of the Hadronic Contribution to the Muon (g-2) and to alpha(M_Z**2) Using new Data from Hadronic Tau Decays
• Tensions in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}(\gamma )$ measurements: the new landscape of data-driven hadronic vacuum polarization predictions for the muon $g-2$
• Mounting Evidence for the Violation of Lepton Flavor Universality
• Lattice QCD calculation of the electroweak box diagrams for the kaon semileptonic decays
• On the effective theory of neutrino-electron and neutrino-quark interactions
• A phenomenological estimate of isospin breaking in hadronic vacuum polarization
• Electroweak Radiative Corrections to Semileptonic Tau Decays
• Vector-like Quark Interpretation for the CKM Unitarity Violation, Excess in Higgs Signal Strength, and Bottom Quark Forward-Backward Asymmetry
• W-propagator corrections to muon and tau leptonic decays
• Contributions of the W-boson propagator to muon and tau leptonic decay rates
• Beta-decay implications for the W-boson mass anomaly
• Ab-initio electroweak corrections to superallowed $\beta$ decays and their impact on $V_{ud}$
• Dispersive formalism for the nuclear structure correction ${\delta }_{\mathrm{NS}}$ to the $\beta$ decay rate
• Running coupling constant from position-space current-current correlation functions in three-flavor lattice QCD
• An $\text{ab initio}$ strategy for taming nuclear-structure dependence of $V_{ud}$ extractions: the ${}^{10}\mathrm{C}\to {}^{10}\mathrm{B}$ superallowed transition
• Radiative corrections to superallowed $\beta$ decays in effective field theory
• Strong coupling constant from moments of quarkonium correlators revisited
• Determination of ${\alpha }_s(m_Z)$ by the non-perturbative decoupling method
• Field Theory of the Fermi Function
• Towards $ab$-$initio$ nuclear theory calculations of ${\delta }_{\mathrm{C}}$
• Isospin breaking corrections in $2\pi$ production in tau decays and $e^{+}{e}^{-}$ annihilation: consequences for the muon $g-2$ and CVC tests
• Observations on the radiative corrections to pion beta-decay
• Renormalization of beta decay at three loops and beyond
• Radiative corrections to $\tau \to \pi \pi {\nu }_{\tau }$
• Improved calculation of radiative corrections to $\tau \to \pi \pi {\nu }_{\tau }$ decays