[Paper Review] The kaon semileptonic form factor in Nf=2+1 domain wall lattice QCD with physical light quark masses

Peter A. Boyle, Norman H. Christ+9 more|arXiv (Cornell University)|Apr 7, 2015

Particle physics theoretical and experimental studies26 references15 citations

TL;DR

This paper presents the first lattice QCD calculation of the kaon semileptonic form factor $f_{+}^{K\pi}(0)$ with physical valence and sea quark masses in the continuum limit using $N_f=2+1$ domain wall fermions. The result, $f_{+}^{K\pi}(0) = 0.9685(34)(14)$, enables a precise determination of the CKM matrix element $|V_{us}| = 0.2233(5)(9)$, improving the precision of the unitarity test of the CKM matrix.

ABSTRACT

We present the first calculation of the kaon semileptonic form factor with sea and valence quark masses tuned to their physical values in the continuum limit of 2+1 flavour domain wall lattice QCD. We analyse a comprehensive set of simulations at the phenomenologically convenient point of zero momentum transfer in large physical volumes and for two different values of the lattice spacing. Our prediction for the form factor is f+(0)=0.9685(34)(14) where the first error is statistical and the second error systematic. This result can be combined with experimental measurements of K->pi decays for a determination of the CKM-matrix element for which we predict |Vus|=0.2233(5)(9) where the first error is from experiment and the second error from the lattice computation.

Motivation & Objective

• To compute the kaon semileptonic form factor $f_{+}^{K\pi}(0)$ with physical light quark masses and in the continuum limit using domain wall fermions.
• To eliminate the dominant systematic uncertainty from chiral extrapolation by simulating directly at physical pion masses.
• To provide a first-principles lattice QCD prediction for $|V_{us}|$ by combining with experimental data on $K\to\pi$ decays.
• To assess and quantify finite-volume effects as the dominant remaining systematic uncertainty.
• To support a stringent test of CKM matrix unitarity and constraints on new physics.

Proposed method

• Use of $N_f=2+1$ flavor domain wall lattice QCD with physical valence and sea quark masses to simulate QCD in large physical volumes.
• Computation of the vector form factor $f_{+}^{K\pi}(0)$ via two- and three-point correlation functions of vector and scalar currents in Euclidean spacetime.
• Application of the vector Ward-Takahashi identity to relate the scalar current matrix element to $f_{+}^{K\pi}(0)$ at zero momentum transfer, eliminating renormalization constants.
• Interpolation to the physical point using a fit ansatz that weights the physical-point data most heavily, minimizing model dependence.
• Extrapolation to the continuum limit using simulations at two different lattice spacings.
• Estimation of finite-volume effects using chiral perturbation theory, with a systematic error assigned to this component.

Experimental results

Research questions

• RQ1 What is the value of the kaon semileptonic form factor $f_{+}^{K\pi}(0)$ when computed with physical light quark masses and in the continuum limit?
• RQ2 How does the inclusion of physical quark masses and the continuum limit affect the precision and systematic uncertainty of the lattice QCD prediction?
• RQ3 What is the resulting value of the CKM matrix element $|V_{us}|$ when combining this lattice result with experimental data on $K\to\pi$ decays?
• RQ4 What is the dominant remaining systematic uncertainty in the current calculation, and how is it estimated?
• RQ5 How does this result impact the unitarity test of the first row of the CKM matrix?

Key findings

• The kaon semileptonic form factor at zero momentum transfer is determined to be $f_{+}^{K\pi}(0) = 0.9685(34)(14)$, with statistical and systematic errors.
• The CKM matrix element is predicted as $|V_{us}| = 0.2233(5)(9)$, where the first error is from experiment and the second from the lattice computation.
• The finite-volume systematic error is estimated using effective field theory and contributes 14 to the total systematic uncertainty.
• The calculation achieves a significant reduction in systematic uncertainty by eliminating the need for chiral extrapolation through the use of physical sea and valence quark masses.
• The unitarity test for the first row of the CKM matrix yields $1 - |V_{ud}|^2 - |V_{us}|^2 = 0.0010(6)$, consistent with the Standard Model.
• The result provides a stringent constraint on new physics through the precision test of CKM unitarity.