[Paper Review] Measurement of Ds+ to mu+ nu and the Decay constant f_Ds

M. Artuso, Collaboration, CLEO|ArXiv.org|Jul 26, 2006

Particle physics theoretical and experimental studies6 references3 citations

TL;DR

This paper presents the most precise measurement to date of the $D_s^+$ decay constant $f_{D_s^+}$ using $D_s^+ \to \mu^+ \nu$ and $D_s^+ \to \tau^+ \nu$ decays at $\sqrt{s} = 4.17$ GeV with the CLEO-c detector. The measured $f_{D_s^+} = 282 \pm 16 \pm 7$ MeV and the ratio $f_{D_s^+}/f_{D^+} = 1.27 \pm 0.12 \pm 0.03$ are consistent with lattice QCD predictions and improve precision over prior results by eliminating normalization dependence on $\mathcal{B}(D_s^+ \to \phi\pi^+)$.

ABSTRACT

We examine e+e- to Ds- Ds*+ or Ds-* Ds+ collisions at 4170 MeV using the CLEO-c detector in order to measure the decay constant f_Ds+. We use the Ds+ to ell+ nu channel, where the ell+ designates either a mu+ or a tau+. Analyzing both modes simultaneously, we determine B(D_s^+ to mu+ nu)= (0.657 +- 0.090 +- 0.028)%, B(D_s^+ to tau+ nu)= (7.1 +- 1.4 +- 0.3)%, and extract f_Ds+ = 282 +- 16 +- 7 MeV. Combining with our previous determination of B(D+ to mu+ nu), we find that the ratio f_Ds+/f_D+ = 1.27 +- 0.12 +- 0.03. (All new results here are preliminary.) We compare with current theoretical estimates.

Motivation & Objective

• To measure the $D_s^+$ leptonic decay branching fractions $\mathcal{B}(D_s^+ \to \mu^+\nu)$ and $\mathcal{B}(D_s^+ \to \tau^+\nu)$ with high precision.
• To extract the decay constant $f_{D_s^+}$ without relying on the normalization mode $\mathcal{B}(D_s^+ \to \phi\pi^+)$, which previously introduced large systematic uncertainties.
• To determine the ratio $f_{D_s^+}/f_{D^+}$ to test theoretical predictions of the Cabibbo-Kobayashi-Maskawa matrix element ratio $|V_{cd}/V_{cs}|$.
• To compare the measured $f_{D_s^+}$ and $f_{D_s^+}/f_{D^+}$ with current lattice QCD and other theoretical models.

Proposed method

• The analysis uses $e^+e^-$ collisions at $\sqrt{s} = 4.17$ GeV, producing $D_s^+D_s^{*+}$ or $D_s^{*-}D_s^+$ final states via $e^+e^- \to D_s^-D_s^{*+}$.
• Charged leptons ($\mu^+$, $\tau^+$) are reconstructed in $D_s^+ \to \ell^+ \nu$ decays, with $\tau^+ \to \pi^+ \bar{\nu}$ used for $\tau$ identification.
• The decay rate formula $\Gamma(D_s^+ \to \ell^+ \nu) = \frac{G_F^2}{8\pi} f_{D_s^+}^2 m_\ell^2 M_{D_s^+} \left(1 - \frac{m_\ell^2}{M_{D_s^+}^2}\right)^2 |V_{cs}|^2$ is used to extract $f_{D_s^+}$ from measured branching fractions.
• Systematic uncertainties are minimized by simultaneously analyzing $\mu^+\nu$ and $\tau^+\nu$ modes, reducing dependence on external normalization modes.
• The $f_{D_s^+}/f_{D^+}$ ratio is extracted by combining with the CLEO-c’s prior measurement of $f_{D^+}$, canceling a portion of the systematic error.

Experimental results

Research questions

• RQ1 What is the precise value of the $D_s^+$ decay constant $f_{D_s^+}$, and how does it compare to lattice QCD predictions?
• RQ2 What is the ratio $f_{D_s^+}/f_{D^+}$, and does it agree with theoretical expectations for the CKM matrix element ratio $|V_{cd}/V_{cs}|$?
• RQ3 Can the $D_s^+ \to \mu^+\nu$ and $D_s^+ \to \tau^+\nu$ branching fractions be measured with reduced systematic error by avoiding normalization to $\mathcal{B}(D_s^+ \to \phi\pi^+)$?
• RQ4 How do the measured branching fractions and $f_{D_s^+}$ compare with previous experimental results and theoretical models?

Key findings

• The measured branching fraction for $D_s^+ \to \mu^+\nu$ is $\mathcal{B}(D_s^+ \to \mu^+\nu) = (0.657 \pm 0.090 \pm 0.028)\%$, with a combined uncertainty of $\pm 0.095\%$.
• The branching fraction for $D_s^+ \to \tau^+\nu$ is $\mathcal{B}(D_s^+ \to \tau^+\nu) = (7.1 \pm 1.4 \pm 0.3)\%$, consistent with the expected ratio of $\Gamma(\tau^+\nu)/\Gamma(\mu^+\nu) \approx 9.72$.
• The $D_s^+$ decay constant is determined to be $f_{D_s^+} = 282 \pm 16 \pm 7$ MeV, representing the most precise measurement to date.
• The ratio $f_{D_s^+}/f_{D^+} = 1.27 \pm 0.12 \pm 0.03$ is extracted, with a significant reduction in systematic uncertainty due to cancellation between the $D_s^+$ and $D^+$ measurements.
• The result is consistent with lattice QCD predictions, particularly the $n_f = 2+1$ flavor calculation from MILC ($f_{D_s^+}/f_{D^+} = 1.24 \pm 0.01 \pm 0.07$), and lies above most other theoretical estimates.
• Using the lattice QCD prediction $f_{D_s^+}/f_{D^+} = 1.24 \pm 0.01 \pm 0.07$, the ratio $|V_{cd}/V_{cs}|$ is derived as $0.22 \pm 0.03$, consistent with the Standard Model.