[Paper Review] Spectroscopy of heavy baryons with breaking of heavy-quark symmetry

Shigehiro Yasui|arXiv (Cornell University)|Aug 16, 2014

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper develops a heavy-baryon effective field theory framework to compute one-pion transition decay widths for excited heavy baryons (charmed and bottom) up to O(1/M) corrections, incorporating heavy-quark symmetry and its breaking via spin operators and velocity-rearrangement invariance. The key result is a set of model-independent selection rules and constraints on decay widths that are valid for arbitrary brown-muck spin, enabling direct comparison with experimental data on excited heavy baryons beyond the leading-order heavy-quark symmetry limit.

ABSTRACT

Transition decay widths by one-pion emissions for excited heavy-baryons with a single heavy (charm and bottom) quark are investigated by following the heavy-quark symmetry and its breaking effects at ${\cal O}(1/M)$ for a heavy-baryon mass $M$. Based on the heavy-baryon effective theory, interaction Lagrangian for the heavy baryons with axial-vector current induced by a pion is constructed. It is presented that the transition decay widths up to ${\cal O}(1/M)$ in several channels are constrained. The results will be useful in experimental study of excited heavy-baryons.

Motivation & Objective

• To extend heavy-quark symmetry-based predictions for excited heavy baryons beyond the leading order in 1/M.
• To systematically incorporate O(1/M) corrections due to heavy-quark symmetry breaking in transition decay widths.
• To derive general selection rules and constraints on one-pion decay widths for excited heavy baryons with arbitrary brown-muck spin.
• To provide a framework applicable to experimental studies of charmed and bottom baryons with higher spin excitations.
• To bridge the gap between effective field theory and quark model calculations by including symmetry-breaking effects explicitly.

Proposed method

• Constructs effective tensor-spinor fields for heavy baryons with arbitrary brown-muck spin j using the heavy-quark limit and projection operators.
• Derives the leading-order effective Lagrangian invariant under heavy-quark symmetry and velocity-rearrangement (VR) symmetry.
• Introduces O(1/M) corrections via spin-operators acting on the heavy quark, breaking heavy-quark symmetry explicitly.
• Derives the interaction Lagrangian between heavy baryons and pions via axial-vector current coupling, focusing on p-wave transitions.
• Applies the formalism to two classes of transitions: (i) between different HQS doublets/singlets (j → j+1), and (ii) within the same j (j → j).
• Uses 3j and 6j symbols to compute decay width amplitudes, ensuring angular momentum conservation and parity selection rules.

Experimental results

Research questions

• RQ1 How do O(1/M) corrections from heavy-quark symmetry breaking affect one-pion transition decay widths in excited heavy baryons?
• RQ2 What selection rules govern the decay widths of excited heavy baryons with arbitrary brown-muck spin j?
• RQ3 How do the decay widths differ between transitions involving different j (j → j+1) versus same j (j → j)?
• RQ4 Can the formalism predict which decay channels are kinematically allowed and which are suppressed due to symmetry constraints?
• RQ5 How do the derived constraints compare with existing quark model predictions that neglect symmetry-breaking effects?

Key findings

• The transition decay width for one-pion emission is constrained by a formula involving 3j and 6j symbols, with the amplitude proportional to the square of a 3j symbol coupling angular momenta j, j', and 1/2.
• For transitions between different HQS doublets (j → j+1), the decay width is non-zero only when the total spin J and J' satisfy specific angular momentum coupling rules, with selection rules depending on j and j′.
• For transitions within the same brown-muck spin (j → j), the decay width is non-zero only for specific combinations of J and J′, and the amplitude vanishes unless the angular momentum coupling is allowed.
• The formalism predicts that s-wave transitions (opposite parity) are enhanced compared to p-wave transitions (same parity), but the latter are still kinematically accessible and constrained by symmetry.
• The derived constraints are valid up to O(1/M) and hold without assuming specific quark-model structures, making them robust for experimental comparison.
• The results provide a model-independent framework to test experimental data on excited heavy baryons, especially for states with high spin or exotic quantum numbers.