[Paper Review] Recent results on fully leptonic and semileptonic charm decays

J. Wiss|ArXiv.org|May 10, 2006

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper presents high-precision measurements of semileptonic and fully leptonic charm decays from CLEO-c, BaBar, and FOCUS, focusing on branching fractions, form factors, and decay constants. It confirms consistency between experimental results and Lattice QCD predictions, particularly for $f_D$ and $f_{D_s}$, and provides first non-parametric form factor measurements, validating LQCD techniques for future B-meson decays.

ABSTRACT

We begin with giving some motivation for the study of charm semileptonic and fully leptonic decays. We turn next to a discussion of semileptonic absolution branching fraction results form CLEO-c. Two exciting high statistics results on fully leptonic decays of the D+ -> mu+ nu and Ds+ -> mu+ nu from CLEO-c and BaBar are reviewed. We turn next to a discussion of recent results on charm meson decay to pseudo-scalar l nu decays from FOCUS, BaBar, and CLEO-c. We conclude with a review of charm meson decay into Vector l nu.

Motivation & Objective

• To measure absolute semileptonic branching fractions of $D^0$ and $D^+$ mesons with high precision using $\psi(3770)$-threshold data.
• To determine the $D^+$ and $D_s^+$ decay constants via fully leptonic decays $D^+ \to \mu^+ \nu$ and $D_s^+ \to \mu^+ \nu$.
• To perform non-parametric measurements of the $q^2$-dependent form factor $f_+(q^2)$ in $D^0 \to K^- \ell^+ \nu$ to test Lattice QCD predictions.
• To investigate the presence of non-resonant $s$-wave contributions and higher partial waves ($d$-, $f$-waves) in $D^+ \to K^- \pi^+ \ell^+ \nu$.
• To assess the validity of spectroscopic pole dominance in vector $\ell^+ \nu$ decays through comparison with non-parametric form factor analyses.

Proposed method

• Utilized $\psi(3770)$-threshold data from CLEO-c to measure absolute semileptonic branching fractions via kinematic reconstruction of missing energy and momentum.
• Applied the $U \equiv E_{\text{miss}} - c|\vec{P}_{\text{miss}}|$ variable to isolate $D \to \pi^- \ell^+ \nu$ signals and suppress $K^- \to \pi^-$ misidentification backgrounds.
• Performed inclusive semileptonic branching fraction measurements by extrapolating electron momentum spectra below 200 MeV/c using ISGW2 form factors and Monte Carlo simulations.
• Conducted non-parametric fits to $f_+(q^2)$ using $D^0 \to K^- \ell^+ \nu$ data, avoiding parametric assumptions about form factor shape.
• Analyzed angular distributions in $D^+ \to K^- \pi^+ \ell^+ \nu$ to search for $s$-wave, $d$-wave, and $f$-wave contributions via interference terms with vector resonances.
• Compared $s$-wave interference patterns with FOCUS data and tested consistency with pole dominance models in vector $\ell^+ \nu$ decays.

Experimental results

Research questions

• RQ1 What are the absolute semileptonic branching fractions of $D^0$ and $D^+$ mesons, and how do they compare to the sum of known exclusive modes?
• RQ2 What is the precision measurement of the $D^+$ and $D_s^+$ decay constants from fully leptonic decays, and how do they compare to Lattice QCD predictions?
• RQ3 How do the $q^2$-dependent form factors in $D^0 \to K^- \ell^+ \nu$ compare to Lattice QCD calculations and parametric models?
• RQ4 Is there evidence for non-resonant $s$-wave contributions in $D^+ \to K^- \pi^+ \ell^+ \nu$, and how does its phase behavior compare to FOCUS data?
• RQ5 Are higher partial waves ($d$-, $f$-waves) present in $D^+ \to K^- \pi^+ \ell^+ \nu$, and can they be distinguished from vector resonance contributions?

Key findings

• The inclusive semileptonic branching fraction for $D^0 \to X e^+ \nu$ is measured as $6.46 \pm 0.17 \pm 0.13\%$, with the sum of known exclusive modes accounting for $6.1 \pm 0.2 \pm 0.2\%$, indicating near saturation.
• The inclusive branching fraction for $D^+ \to X e^+ \nu$ is $16.13 \pm 0.20 \pm 0.33\%$, and the sum of exclusive modes accounts for $15.1 \pm 0.5 \pm 0.5\%$, consistent with expectations.
• The ratio of semileptonic widths $\Gamma_{D^+}^{SL}/\Gamma_{D^0}^{SL} = 0.985 \pm 0.028 \pm 0.015$ is consistent with the expectation of equal widths.
• The $D^+ \to \mu^+ \nu$ branching fraction yields $f_D = 195 \pm 15 \pm 15$ MeV, consistent with Lattice QCD predictions and BaBar's $f_{D_s} = 237 \pm 10 \pm 10$ MeV.
• Non-parametric form factor measurements in $D^0 \to K^- \ell^+ \nu$ show good agreement with Lattice QCD and earlier parametric fits, though one preliminary measurement exhibits a significantly different shape parameter $\alpha$.
• The $s$-wave interference term in $D^+ \to K^- \pi^+ \ell^+ \nu$ is consistent with FOCUS observations, showing strong enhancement below the $\bar{K}^{*0}$ pole and vanishing above it, confirming the existence of a non-resonant $s$-wave contribution.