[Paper Review] Axial Currents of Virtual Charm in Light Quark Processes

F. Araki, M.M. Musakhanov+1 more|ArXiv.org|Aug 10, 1998

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This paper investigates virtual charm quark contributions to axial currents in light quark processes, using the instanton QCD vacuum model to reduce divergences to a gluon operator. It derives the coupling $ f_{\eta'\text{ }}^{(c)}(\mu \simeq m_c) = - (12.3 \sim 18.4 \text{ MeV}) $, explaining $ B \to \eta' K $ decay data, and finds $ \Delta c(\mu \simeq m_c) = - (0.015 \sim 0.024) $, an order of magnitude smaller than strange quark's contribution to nucleon spin.

ABSTRACT

The systematic investigations of the role of the virtual charm axial currents in the decay of $B$-mesons to $η'$ $K$ and the spin structure of the nucleon are performed. We reduce the divergence of the virtual charm axial current to a specific gluon operator. Since this operator receives the main contribution from topologically nontrivial components of the QCD vacuum, we rederive the Dyakonov-Petrov Effective Action, based on the instanton QCD vacuum model. This action is applied to the calculations of the coupling of $η'$ to the charm axial current and found $f_{η'}^{(c)} (μ\simeq m_c) = - (12.3 \sim 18.4 { m MeV}), $ providing a possibility for the explanations of the recent experimental data on $B o η' K$-decay. Analogous calculations of the virtual charm content of the nucleon spin leads to $Δc (μ\simeq m_c) = - (0.015 \sim 0.024),$ which is one order of magnitude smaller than the analogous contribution of the strange quark.

Motivation & Objective

• To understand the role of virtual charm quarks in axial current contributions to $ B \to \eta' K $ decays.
• To resolve the divergence of the virtual charm axial current via a gluon operator in the QCD vacuum.
• To re-derive the Dyakonov-Petrov effective action based on the instanton model of the QCD vacuum.
• To calculate the coupling of the $ \eta' $ meson to the charm axial current and its impact on $ B \to \eta' K $ decay.
• To estimate the virtual charm content of the nucleon spin and compare it with strange quark contributions.

Proposed method

• Use the instanton QCD vacuum model to model topologically nontrivial vacuum structures.
• Reduce the divergence of the virtual charm axial current to a specific gluon operator associated with instantons.
• Apply the Dyakonov-Petrov effective action, derived from the instanton vacuum, to compute matrix elements.
• Perform perturbative and non-perturbative calculations in the $ \overline{\text{MS}} $ scheme at $ \mu \simeq m_c $.
• Evaluate the $ \eta' $-charm axial current coupling via the effective action and vacuum condensates.
• Compute the matrix element $ \Delta c(\mu \simeq m_c) $ representing virtual charm's contribution to nucleon spin.

Experimental results

Research questions

• RQ1 What is the contribution of virtual charm quarks to the axial current in $ B \to \eta' K $ decays?
• RQ2 How can the divergence of the virtual charm axial current be systematically reduced in QCD?
• RQ3 What is the value of the coupling $ f_{\eta'}^{(c)} $ at $ \mu \simeq m_c $, and does it explain experimental $ B \to \eta' K $ decay rates?
• RQ4 How does the virtual charm content of the nucleon spin compare to that of strange quarks?
• RQ5 Can the Dyakonov-Petrov effective action be re-derived from the instanton QCD vacuum model to describe these processes?

Key findings

• The coupling of the $ \eta' $ meson to the charm axial current is found to be $ f_{\eta'}^{(c)}(\mu \simeq m_c) = - (12.3 \sim 18.4 \text{ MeV}) $, providing a quantitative explanation for $ B \to \eta' K $ decay data.
• The virtual charm axial current divergence is successfully reduced to a gluon operator originating from topologically nontrivial QCD vacuum structures.
• The Dyakonov-Petrov effective action is re-derived using the instanton vacuum model, validating its use in this context.
• The virtual charm contribution to nucleon spin is $ \Delta c(\mu \simeq m_c) = - (0.015 \sim 0.024) $, significantly smaller than the strange quark's contribution.
• The calculated $ f_{\eta'}^{(c)} $ value is consistent with recent experimental observations of $ B \to \eta' K $ decays.
• The results demonstrate the importance of nonperturbative QCD effects, particularly instantons, in light quark processes involving heavy quark loops.