[Paper Review] Study of Dynamics of $D^0 o K^- e^+ u_{e}$ and $D^0 o\pi^- e^+ u_{e}$ Decays

F. De Mori, М. Н. Ачасов+400 more|arXiv (Cornell University)|Aug 30, 2015

Particle physics theoretical and experimental studies4 citations

TL;DR

This study presents the most precise measurements to date of the semileptonic decays $D^0 \to K^- e^+ \bar{\nu}_e$ and $D^0 \to \pi^- e^+ \bar{\nu}_e$ using 2.92 fb$^{-1}$ of data from the BESIII experiment at 3.773 GeV. It determines the products $f_+^K(0)|V_{cs}| = 0.7172 \pm 0.0025 \pm 0.0035$ and $f_+^\pi(0)|V_{cd}| = 0.1435 \pm 0.0018 \pm 0.0009$, enabling extraction of the CKM matrix elements and form factors with improved precision for testing lattice QCD and light-cone sum rules.

ABSTRACT

In an analysis of a 2.92~fb$^{-1}$ data sample taken at 3.773~GeV with the BESIII detector operated at the BEPCII collider, we measure the absolute decay branching fractions to be $\\mathcal B(D^0 \ o K^-e^+\ u_e)=(3.505\\pm 0.014 \\pm 0.033)\\%$ and $\\mathcal B(D^0 \ o \\pi^-e^+\ u_e)=(0.295\\pm 0.004\\pm 0.003)\\%$. From a study of the differential decay rates we obtain the products of hadronic form factor and the magnitude of the CKM matrix element $f_{+}^K(0)|V_{cs}|=0.7172\\pm0.0025\\pm 0.0035$ and $f_{+}^{\\pi}(0)|V_{cd}|=0.1435\\pm0.0018\\pm 0.0009$. Combining these products with the values of $|V_{cs(d)}|$ from the SM constraint fit, we extract the hadronic form factors $f^K_+(0) = 0.7368\\pm0.0026\\pm 0.0036$ and $f^\\pi_+(0) = 0.6372\\pm0.0080\\pm 0.0044$, and their ratio $f_+^{\\pi}(0)/f_+^{K}(0)=0.8649\\pm 0.0112\\pm 0.0073$. These form factors and their ratio are used to test unquenched Lattice QCD calculations of the form factors and a light cone sum rule (LCSR) calculation of their ratio. The measured value of $f_+^{K(\\pi)}(0) |V_{cs(d)}|$ and the lattice QCD value for $f^{K(\\pi)}_+(0)$ are used to extract values of the CKM matrix elements of $|V_{cs}|=0.9601 \\pm 0.0033 \\pm 0.0047 \\pm 0.0239$ and $|V_{cd}|=0.2155 \\pm 0.0027 \\pm 0.0014 \\pm 0.0094$, where the third errors are due to the uncertainties in lattice QCD calculations of the form factors. Using the LCSR value for $f_+^\\pi(0)/f_+^K(0)$, we determine the ratio $|V_{cd}|/|V_{cs}|=0.238\\pm 0.004\\pm 0.002\\pm 0.011$, where the third error is from the uncertainty in the LCSR normalization. In addition, we measure form factor parameters for three different theoretical models that describe the weak hadronic charged currents for these two semileptonic decays. All of these measurements are the most precise to date.

Motivation & Objective

• To measure the absolute branching fractions of $D^0 \to K^-e^+\bar{\nu}_e$ and $D^0 \to \pi^-e^+\bar{\nu}_e$ decays with high precision using a large data sample.
• To determine the products of the hadronic form factors and CKM matrix elements, $f_+^K(0)|V_{cs}|$ and $f_+^\pi(0)|V_{cd}|$, from differential decay rate analyses.
• To extract the absolute values of the CKM matrix elements $|V_{cs}|$ and $|V_{cd}|$ by combining measured form factor products with lattice QCD calculations.
• To test unquenched lattice QCD and light-cone sum rule (LCSR) predictions for form factors and their ratio using the measured data.
• To provide the most precise form factor parameters for theoretical models describing the weak hadronic charged currents in these semileptonic decays.

Proposed method

• Analysis of 2.92 fb$^{-1}$ of data collected at $\sqrt{s} = 3.773$ GeV with the BESIII detector at BEPCII.
• Measurement of absolute branching fractions using fully reconstructed $D^0$ decays into $K^-e^+\bar{\nu}_e$ and $\pi^-e^+\bar{\nu}_e$ final states.
• Differential decay rate fitting to extract $f_+^K(0)|V_{cs}|$ and $f_+^\pi(0)|V_{cd}|$ with constraints from the measured branching fractions.
• Combination of measured form factor products with lattice QCD results to extract $f_+^K(0)$ and $f_+^\pi(0)$, and to determine $|V_{cs}|$ and $|V_{cd}|$.
• Use of light-cone sum rule (LCSR) predictions for the ratio $f_+^\pi(0)/f_+^K(0)$ to extract $|V_{cd}|/|V_{cs}|$ with uncertainty propagation.
• Fitting of form factor parameters to three theoretical models describing the weak hadronic current in semileptonic $D^0$ decays.

Experimental results

Research questions

• RQ1 What is the most precise measurement of the absolute branching fraction for $D^0 \to K^-e^+\bar{\nu}_e$?
• RQ2 What is the most precise determination of $f_+^K(0)|V_{cs}|$ from the differential decay rate analysis?
• RQ3 How do the measured values of $f_+^K(0)$ and $f_+^\pi(0)$ compare with unquenched lattice QCD calculations?
• RQ4 What is the extracted value of $|V_{cs}|$ when combining the measured $f_+^K(0)|V_{cs}|$ with lattice QCD form factor predictions?
• RQ5 What is the precision of the $|V_{cd}|/|V_{cs}|$ ratio derived using the LCSR prediction for the form factor ratio?

Key findings

• The absolute branching fraction for $D^0 \to K^-e^+\bar{\nu}_e$ is measured as $\mathcal{B} = (3.505 \pm 0.014 \pm 0.033)\%$.
• The absolute branching fraction for $D^0 \to \pi^-e^+\bar{\nu}_e$ is measured as $\mathcal{B} = (0.295 \pm 0.004 \pm 0.003)\%$.
• The product $f_+^K(0)|V_{cs}|$ is determined to be $0.7172 \pm 0.0025 \pm 0.0035$.
• The product $f_+^\pi(0)|V_{cd}|$ is determined to be $0.1435 \pm 0.0018 \pm 0.0009$.
• The hadronic form factor $f_+^K(0)$ is extracted as $0.7368 \pm 0.0026 \pm 0.0036$ using lattice QCD inputs.
• The hadronic form factor $f_+^\pi(0)$ is extracted as $0.6372 \pm 0.0080 \pm 0.0044$ using lattice QCD inputs.