[Paper Review] The D to K and D to pi semileptonic decay form factors from Lattice QCD

the HPQCD Collaboration, J. Koponen+6 more|arXiv (Cornell University)|Nov 1, 2011

Particle physics theoretical and experimental studies4 citations

TL;DR

This lattice QCD study computes D to K and D to π semileptonic decay form factors with high statistical precision using MILC Nf=2+1 lattices and the Highly Improved Staggered Quark (HISQ) action. The key finding is that form factors are nearly insensitive to the spectator quark, with D→K and Ds→ηs form factors being essentially identical, implying similar behavior in B/Bs systems and supporting the use of spectator-independent form factors in B-meson decays.

ABSTRACT

We present a new and very high statistics study of D and D_s semileptonic decay form factors on the lattice. We work with MILC N_f=2+1 lattices and use the Highly Improved Staggered Action (HISQ) for both the charm and the light valence quarks. We use both scalar and vector currents to determine the form factors f_0(q^2) and f_+(q^2) for a range of D and D_s form factors including those for D to pi and D to K semileptonic decays. By using a phased boundary condition we are able to tune accurately to q^2=0. We also compare the shape in q^2 to that from experiment. We show that the form factors are very insensitive to the spectator quark: D to K and D_s to eta_s form factors are essentially the same, and the same is true for D to pi and D_s to K. This has important implications when considering the corresponding B/B_s processes.

Motivation & Objective

• To compute D→K and D→π semileptonic decay form factors with high statistical precision using lattice QCD.
• To investigate the dependence of form factors on the spectator quark in D and Ds decays.
• To test the validity of the z-expansion and continuum extrapolation for form factor fitting.
• To compare lattice results with experimental data and previous lattice studies.
• To assess the implications for B and Bs semileptonic decays, particularly the spectator quark independence of form factors.

Proposed method

• Uses MILC Nf=2+1 lattice ensembles with the Highly Improved Staggered Quark (HISQ) action for both charm and light valence quarks.
• Employs twisted boundary conditions to tune q² to zero and access multiple q² values in a single calculation.
• Extracts form factors f₀(q²) and f₊(q²) from scalar and vector 3-point correlators using simultaneous fits to 2- and 3-point functions.
• Applies the z-expansion to remove poles and perform continuum extrapolation via power series in z up to z⁴.
• Uses the symmetric vector current and scalar current to determine renormalization factors Z, ensuring consistency across different meson systems.
• Performs tests including speed-of-light checks, momentum dependence, and symmetric scalar current consistency to validate the method.

Experimental results

Research questions

• RQ1 How do the D→K and D→π semileptonic form factors depend on the spectator quark?
• RQ2 To what extent do lattice results for f₀(q²) and f₊(q²) agree with experimental data from CLEO?
• RQ3 Can the z-expansion accurately describe the q² dependence of the form factors and enable reliable continuum extrapolation?
• RQ4 How sensitive are the form factors to the choice of valence quark masses and lattice spacing?
• RQ5 What are the implications of spectator independence for B and Bs semileptonic decays?

Key findings

• The form factors f₀ and f₊ for D→K and Ds→ηs decays are indistinguishable within uncertainties, indicating spectator quark independence.
• Similarly, D→π and Ds→K form factors show identical shapes, confirming the same insensitivity to spectator quark.
• The lattice results for f₀(0) and the q² shape of f₊(q²) agree well with CLEO experimental data, validating the lattice approach.
• The z-expansion fits show small lattice spacing dependence, and the continuum extrapolation is stable and well-behaved.
• The renormalization factor Z for the 1-link vector current is consistent across different mesons and momenta, confirming reliability of the current renormalization.
• The symmetric scalar current test confirms the correct chiral behavior, with ⟨H|S|H⟩(q²=0) matching the expected derivative of mass squared with respect to quark mass.