[Paper Review] Measurement of the Energy-Dependent Electromagnetic Form Factors of a Charmed Baryon

BESIII Collaboration, F. De Mori+621 more|arXiv (Cornell University)|Jul 14, 2023

Particle physics theoretical and experimental studiesPhysics and Astronomy3 citations

TL;DR

This study presents the first precise measurement of energy-dependent electromagnetic form factors of the charmed baryon $Λ_c^+$ using $e^+e^-$ collisions at c.m. energies from 4.6119 to 4.9509 GeV. By analyzing $\Lambda_c^+ \to pK^-\pi^+$ decays in large data samples, the BESIII Collaboration determines cross sections and effective form factors with unprecedented precision, revealing a high-frequency oscillation in $|G_E/G_M|$ that suggests non-trivial internal structure in the $\Lambda_c^+$, without evidence for a $Y(4630)$ resonance enhancement.

ABSTRACT

We study the process $e^{+}e^{-} oΛ_{c}^{+}\barΛ_c^{-}$ at twelve center-of-mass energies from $4.6119$ to $4.9509~\mathrm{GeV}$ using data samples collected by the BESIII detector at the BEPCII collider. The Born cross sections and effective form factors ($|G_{\mathrm{eff}}|$) are determined with unprecedented precision after combining the single and double-tag methods based on the decay process $Λ_{c}^{+} o pK^{-}π^{+}$. Flat cross sections around $4.63~\mathrm{GeV}$ are obtained and no indication of the resonant structure $Y(4630)$, as reported by Belle, is found. In addition, no oscillatory behavior is discerned in the $|G_{\mathrm{eff}}|$ energy-dependence of $Λ_{c}^{+}$, in contrast to what is seen for the proton and neutron cases. Analyzing the cross section together with the polar-angle distribution of the $Λ_{c}^{+}$ baryon at each energy point, the moduli of electric and magnetic form factors ($|G_{E}|$ and $|G_{M}|$) are extracted and separated. For the first time, the energy-dependence of the form factor ratio $|G_{E}/G_{M}|$ is observed, which can be well described by an oscillatory function.

Motivation & Objective

• To measure the energy-dependent electromagnetic form factors of the charmed baryon $\Lambda_c^+$ with high precision.
• To investigate the presence or absence of resonance-like enhancements near $Y(4630)$ in the $e^+e^- \to \Lambda_c^+\bar{\Lambda}_c^-$ cross section.
• To determine whether the effective form factor spectrum of $\Lambda_c^+$ exhibits oscillatory behavior similar to that seen in the proton and neutron.
• To probe the internal structure of the $\Lambda_c^+$ baryon through its electromagnetic transition form factors.

Proposed method

• Data collected by the BESIII detector at $e^+e^-$ center-of-mass energies from 4.6119 to 4.9509 GeV are used to study the process $e^+e^- \to \Lambda_c^+\bar{\Lambda}_c^-$.
• The $\Lambda_c^+$ baryon is reconstructed via the decay $\Lambda_c^+ \to pK^-\pi^+$, enabling efficient event selection and background suppression.
• Two independent reconstruction approaches—single-track (ST) and double-track (DT)—are employed to extract cross sections and form factors with reduced systematic uncertainties.
• The Born cross section and polar angle distributions are measured at twelve energy points, with statistical and systematic uncertainties evaluated using data-driven methods.
• The effective electromagnetic form factors $G_E$ and $G_M$ are extracted from the angular distributions of the $\Lambda_c^+$ decay products.
• The ratio $|G_E/G_M|$ is analyzed as a function of energy to search for oscillatory features indicative of internal dynamics.

Experimental results

Research questions

• RQ1 Does the $\Lambda_c^+$ electromagnetic form factor spectrum exhibit oscillatory behavior similar to that of the proton and neutron?
• RQ2 Is there a resonance enhancement near $Y(4630)$ in the $e^+e^- \to \Lambda_c^+\bar{\Lambda}_c^-$ cross section?
• RQ3 What is the energy dependence of the $|G_E/G_M|$ ratio for the $\Lambda_c^+$ baryon, and does it reveal non-trivial internal structure?
• RQ4 How precisely can the electromagnetic form factors of the $\Lambda_c^+$ be measured using $e^+e^-$ annihilation data?

Key findings

• No enhancement is observed around the $Y(4630)$ resonance in the $e^+e^- \to \Lambda_c^+\bar{\Lambda}_c^-$ cross section from threshold up to 4.66 GeV.
• The effective form factor spectrum of $\Lambda_c^+$ does not show oscillatory behavior like that of the proton or neutron.
• The $|G_E/G_M|$ ratio exhibits a high-frequency oscillation with a significantly higher frequency than that of the proton.
• At 4.6819 GeV, the cross section is measured as $188.1 \pm 1.6 \pm 6.3$ pb, with $|G_E/G_M| = 0.88 \pm 0.03 \pm 0.01$.
• At 4.9509 GeV, the cross section is $89.6 \pm 3.6 \pm 3.1$ pb, with $|G_E/G_M| = 0.52 \pm 0.18 \pm 0.01$, indicating a strong energy dependence.
• The measured $|G_E/G_M|$ ratio shows a clear oscillatory trend with energy, suggesting complex internal dynamics in the $\Lambda_c^+$ baryon.