[Paper Review] Rare Decays of D Mesons

Svjetlana Fajfer|ArXiv.org|Aug 22, 2002

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper investigates rare charm decays in the D meson sector to probe new physics beyond the Standard Model, focusing on radiative and dilepton decays such as $D \to V\gamma$, $D \to Pl^+l^-$, and $D \to \gamma\gamma$. Using heavy quark chiral Lagrangian and factorization approximations, it predicts branching ratios in the $10^{-5}$ to $10^{-8}$ range, with $D^0 \to \gamma\gamma$ at $(1.0 \pm 0.5) \times 10^{-8}$, and highlights the role of light vector mesons in nonresonant $K\pi\gamma$ decays.

ABSTRACT

The flavor changing transitions in the c->u gamma, c->u gamma gamma and c->u l+ l- offer the possibility to search for new physics in the charm sector. We investigate dominant decay mechanisms in the radiative decays D->V gamma, D->P(V) l+ l-, D->gamma gamma and we discuss chances to see physics beyond the standard model in these decays. In addition, we analyze Cabibbo allowed D->K pi gamma decays with nonresonant K pi, and we probe the role of light vector mesons in these decays.

Motivation & Objective

• To investigate flavor-changing neutral currents (FCNC) in the charm sector via rare $D$ decays, which are sensitive to new physics beyond the Standard Model.
• To assess the feasibility of detecting rare radiative and dilepton decays of $D$ mesons, given current experimental upper bounds near $10^{-4}$ to $10^{-5}$.
• To study the role of light vector mesons in nonresonant $D \to K\pi\gamma$ decays, analogous to $K \to \pi\pi\gamma$ decays, to probe hadronic dynamics.
• To quantify short-distance contributions in $c \to u\gamma$ and $c \to ul^+l^-$ transitions, especially in the context of MSSM enhancements.
• To provide theoretical predictions for branching ratios of $D \to \gamma\gamma$, $D \to V\gamma$, and $D \to K\pi\gamma$ decays to guide future experimental searches at BELLE, BABAR, and Tevatron.

Proposed method

• Uses an effective Lagrangian approach with $c \to u\gamma$ transition via QCD-corrected Wilson coefficient $C_{7\gamma}^{\text{eff}} = (-0.7 + 2i) \times 10^{-2}$ to compute short-distance contributions.
• Applies heavy quark chiral Lagrangian and factorization approximation to compute weak transition matrix elements for nonleptonic decays.
• Derives the decay amplitude for $D \to K\pi\gamma$ using a model-dependent form with $F_0$ from experiment and $F_1$, $F_2$ as form factors, including bremsstrahlung and direct transitions.
• Incorporates intermediate vector meson resonances via the Breit-Wigner propagator when on-shell, to model $K\pi$ nonresonant states.
• Calculates branching ratios by combining experimental $D \to K\pi$ amplitudes with theoretical form factors, applying a photon energy cut $E_c \geq 100$ MeV.
• Compares predictions in the Standard Model and MSSM, particularly for $c \to ul^+l^-$, to assess potential new physics enhancements.

Experimental results

Research questions

• RQ1 What are the predicted branching ratios for $D \to V\gamma$ decays, and how do they compare to current experimental upper bounds?
• RQ2 To what extent can the $c \to u\gamma$ transition be probed in $D^0 \to \rho^0\gamma$ and $D^0 \to \omega\gamma$ decays, given the cancellation of long-distance contributions?
• RQ3 How do light vector mesons influence the $D \to K\pi\gamma$ decay amplitudes, and what role do they play in direct and bremsstrahlung contributions?
• RQ4 Can the $D \to \gamma\gamma$ decay be observed at rates significantly higher than the SM prediction, and what would such a signal imply?
• RQ5 What is the expected size of the direct parity-violating and parity-conserving electromagnetic transitions in $D \to K\pi\gamma$ decays, and how do they depend on vector meson contributions?

Key findings

• The branching ratio for $D^0 \to \gamma\gamma$ is predicted to be $(1.0 \pm 0.5) \times 10^{-8}$, with any observation at a rate an order of magnitude larger suggesting new physics.
• The $D^+ \to \bar{K}^{0}\pi^{+}\gamma$ decay has a predicted branching ratio of $(2.3 - 2.5) \times 10^{-4}$, dominated by bremsstrahlung from the $D \to K\pi$ amplitude.
• The $D^0 \to K^{-}\pi^{+}\gamma$ decay is predicted to have a branching ratio of $(4.3 - 6.0) \times 10^{-4}$, with significant contributions from both bremsstrahlung and direct transitions.
• The direct parity-violating transition in $D^0 \to K^{-}\pi^{+}\gamma$ contributes $1.64 \times 10^{-4}$, while the parity-conserving magnetic transition contributes $1.4 \times 10^{-4}$, indicating comparable strengths.
• Excluding light vector meson contributions reduces the parity-conserving direct rate by two orders of magnitude in $D^0 \to K^{-}\pi^{+}\gamma$, highlighting their critical role.
• The ratio $R = \frac{\text{BR}(D^0 \to \rho^0\gamma) - \text{BR}(D^0 \to \omega\gamma)}{\text{BR}(D^0 \to \omega\gamma)}$ is predicted to be $6 \pm 15\%$ in the SM but can reach $\mathcal{O}(1)$ in MSSM, offering a sensitive probe for new physics.