[Paper Review] Vector and scalar form factors for K- and D-meson semileptonic decays from twisted mass fermions with Nf = 2

Stefano Di Vita, Benjamin Haas+4 more|arXiv (Cornell University)|Oct 26, 2009

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This lattice QCD study computes vector and scalar form factors for K→πℓν and D→πℓν semileptonic decays using Nf=2 twisted-mass fermions at pion masses as light as 260 MeV. It achieves high-precision results, with f₊(0) = 0.9560(57)stat(62)syst for K→π decay, leading to |Vus| = 0.2267(5)exp(20)fs(0), consistent with CKM unitarity, and f₊(0) = 0.64(5) for D→π decay, in good agreement with experiment after extrapolation via Heavy Meson Chiral Perturbation Theory.

ABSTRACT

We present lattice results for the form factors relevant in the K -> pion and D -> pion semileptonic decays, obtained from simulations with two flavors of dynamical twisted-mass fermions and pion masses as light as 260 MeV. For K -> pion decays we discuss the estimates of the main sources of systematic uncertainties, including the quenching of the strange quark, leading to our final result f+(0) = 0.9560 (57) (62). Combined with the latest experimental data, our value of f+(0) implies for the CKM matrix element |Vus| the value 0.2267 (5) (20) consistent with the first-row CKM unitarity. For D -> pion decays the application of Heavy Meson Chiral Perturbation Theory allows to extrapolate our results for both the scalar and the vector form factors at the physical point with quite good accuracy, obtaining a nice agreement with the experimental data. In particular at zero-momentum transfer we obtain f+(0) = 0.64 (5).

Motivation & Objective

• To compute vector and scalar form factors for K→πℓν and D→πℓν semileptonic decays using lattice QCD with Nf=2 dynamical twisted-mass fermions.
• To determine f₊(0) for K→πℓν with high precision, including systematic uncertainties, to extract |Vus| and test CKM unitarity.
• To apply Heavy Meson Chiral Perturbation Theory to extrapolate lattice results for D→πℓν to the physical point and compare with experiment.
• To assess discretization effects and systematic errors, including finite-size effects, chiral extrapolation, and strange quark quenching.
• To provide a reliable lattice determination of form factors at light pion masses (down to 260 MeV) and at a single lattice spacing.

Proposed method

• Simulate Nf=2 dynamical twisted-mass fermions on lattices with spatial sizes up to 32³×64 and a ≈ 0.088 fm, achieving pion masses from 260 to 575 MeV.
• Compute matrix elements ⟨π|Vμ|K⟩ and ⟨π|Vμ|D⟩ via three-point correlation functions to extract form factors f₊(q²) and f₀(q²).
• Use SU(2) and SU(3) Chiral Perturbation Theory to perform chiral extrapolations of f₊(0) and assess systematic uncertainties.
• Apply Heavy Meson Chiral Perturbation Theory (HMChPT) to extrapolate D→πℓν form factors to the physical point, using energy and pion mass dependence of low-energy constants.
• Perform a simultaneous fit of energy and pion mass dependence of form factors using HMChPT parameterizations with polynomial forms for LECs.
• Estimate discretization effects by computing form factors at three lattice spacings (a ≈ 0.069, 0.088, 0.103 fm) for Mπ ≈ 470 MeV and compare results.

Experimental results

Research questions

• RQ1 What is the precise value of the vector form factor f₊(0) for K→πℓν decays at the physical point, including all systematic uncertainties?
• RQ2 How do the lattice results for D→πℓν form factors compare with experimental data after extrapolation to the physical point using Heavy Meson Chiral Perturbation Theory?
• RQ3 What are the dominant sources of systematic error in the determination of f₊(0) for K→πℓν, and how are they quantified?
• RQ4 To what extent do discretization effects influence the form factors in D→πℓν decays, particularly at large q²?
• RQ5 How well do the lattice results for f₊(q²) and f₀(q²) in D→πℓν agree with the latest CLEO experimental data?

Key findings

• The vector form factor for K→πℓν at zero momentum transfer is determined as f₊(0) = 0.9560(57)stat(62)syst, with a total uncertainty of 0.0084.
• Combined with the latest experimental data, this yields |Vus| = 0.2267(5)exp(20)fs(0), which is consistent with first-row CKM unitarity.
• The chiral extrapolation for K→πℓν is validated using both SU(2) and SU(3) ChPT, yielding consistent results with a systematic uncertainty of 0.0035.
• For D→πℓν decays, the application of Heavy Meson Chiral Perturbation Theory enables accurate extrapolation to the physical point, with f₊(0) = 0.64(5) at q² = 0.
• The lattice results for D→πℓν form factors show good agreement with CLEO experimental data across the q² range, except slightly below at q² ≈ q²max.
• Discretization effects are small at q² ≈ 0 (on the order of 1%) but increase toward q²max, particularly for f₊(q²), though still at the few percent level for f₀(q²).