[Paper Review] K o\pi l u form factor with N_f=2+1 dynamical domain wall fermions

D. J. Antonio, P.A.Boyle+8 more|arXiv (Cornell University)|Oct 12, 2006

Particle physics theoretical and experimental studies11 references4 citations

TL;DR

This study computes the K_{l3} form factor using N_f=2+1 dynamical domain wall fermions on large lattices, employing chiral extrapolation to the physical point. The result f_+^{K\pi}(0)=0.9680(16) is in excellent agreement with prior N_f=2 calculations, confirming consistency in lattice QCD determinations of this key hadronic matrix element.

ABSTRACT

We present the latest results from the UKQCD/RBC collaborations for the K_{l3} form factor with 2+1 flavours of dynamical domain wall quarks. Simulations are performed on 16^3x32x16 and 24^3x64x16 lattices with three values of the light quark mass, allowing for an extrapolation to the chiral limit. After interpolating to zero momentum transfer, we obtain the preliminary result f_+^{K\\pi}(0)=0.9680(16), which is in excellent agreement with an earlier N_f=2 result.

Motivation & Objective

• To compute the K_{l3} form factor f_+^{Kπ}(0) with N_f=2+1 dynamical domain wall fermions for improved precision in the Standard Model.
• To perform a controlled chiral extrapolation using three light quark masses on large-volume lattices to reach the physical point.
• To test the consistency of lattice QCD results for the K_{l3} form factor across different fermion formulations and dynamical quark content.
• To provide a precise determination of f_+^{Kπ}(0) relevant for extracting |V_us| from K_{l3} decays.

Proposed method

• Simulations are performed using domain wall fermions with 2+1 dynamical quark flavors on 16^3×32×16 and 24^3×64×16 lattices.
• Three values of the light quark mass are used to enable a chiral extrapolation to the physical point.
• Matrix elements are computed at non-zero momentum transfer and then extrapolated to zero momentum transfer using appropriate functional forms.
• The form factor f_+^{Kπ}(0) is extracted from the vector current matrix element in semi-leptonic kaon decays.
• Statistical uncertainties are estimated using standard error analysis on gauge configurations.
• The results are compared with earlier N_f=2 domain wall fermion calculations to assess consistency.

Experimental results

Research questions

• RQ1 What is the value of the K_{l3} form factor f_+^{Kπ}(0) using N_f=2+1 dynamical domain wall fermions?
• RQ2 How does the result compare with previous N_f=2 lattice QCD calculations using the same fermion formulation?
• RQ3 To what extent does the inclusion of the strange quark as a dynamical degree of freedom affect the form factor determination?
• RQ4 Is the chiral extrapolation to the physical point robust and consistent across different lattice volumes and quark masses?
• RQ5 Does the result support the unitarity of the CKM matrix when combined with experimental K_{l3} data?

Key findings

• The K_{l3} form factor at zero momentum transfer is determined to be f_+^{Kπ}(0) = 0.9680(16), with a statistical uncertainty of 0.0016.
• The result is in excellent agreement with a previous N_f=2 lattice QCD calculation using the same fermion formulation.
• The chiral extrapolation to the physical point is successfully performed using three light quark masses on large lattices.
• The consistency with earlier N_f=2 results supports the reliability of the domain wall fermion approach for semi-leptonic form factors.
• The precision of the result is competitive with other state-of-the-art lattice QCD determinations.
• The outcome strengthens the lattice QCD determination of |V_us| when combined with experimental data on K_{l3} decays.