[Paper Review] Mass and magnetic dipole moment of negative parity heavy baryons with spin--3/2

K. Azizi, H. Sundu|arXiv (Cornell University)|Jun 28, 2015

Particle physics theoretical and experimental studies4 references4 citations

TL;DR

This study calculates the masses, residues, and magnetic dipole moments of negative parity spin-3/2 heavy baryons (with charm or bottom quarks) using QCD sum rules and light-cone sum rules. It derives transition form factors via photon distribution amplitudes and computes magnetic moments, finding significant deviations from naive mass-scaling expectations for certain charmed baryons due to interference effects from mixed parity contributions.

ABSTRACT

We calculate the mass and residue of the heavy spin--3/2 negative parity baryons with single heavy bottom or charm quark by the help of a two-point correlation function. We use the obtained results to investigate the diagonal radiative transitions among the baryons under consideration. In particular, we compute corresponding transition form factors via light cone QCD sum rules which are then used to obtain the magnetic dipole moments of the heavy spin--3/2 negative parity baryons. We remove the pollutions coming from the positive parity spin--3/2 and positive/negative parity spin--1/2 baryons by constructing sum rules for different Lorentz structures. We compare the results obtained with the existing theoretical predictions.

Motivation & Objective

• To calculate the masses and pole residues of negative parity spin-3/2 heavy baryons with single charm or bottom quarks using QCD sum rules.
• To compute the electromagnetic transition form factors for diagonal radiative transitions among these baryons using light-cone QCD sum rules.
• To extract the magnetic dipole moments of the negative parity spin-3/2 baryons by employing photon distribution amplitudes in the light-cone sum rule framework.
• To suppress contaminating contributions from positive parity spin-3/2 and spin-1/2 baryons by using distinct Lorentz structures and Dirac matrix ordering.
• To compare the results with existing theoretical predictions and assess the validity of naive mass-scaling relations between positive and negative parity baryons.

Proposed method

• Constructs a two-point correlation function using interpolating currents that couple to both positive and negative parity spin-3/2 baryons.
• Evaluates the correlation function in the hadronic representation via a complete set of intermediate states, including higher resonances and continuum contributions.
• Performs operator product expansion (OPE) in the QCD side of the correlation function to express it in terms of QCD parameters and condensates.
• Imposes Borel transformation and continuum subtraction to derive sum rules for masses and residues, using the Borel parameter and continuum threshold as input parameters.
• Derives light-cone sum rules for electromagnetic form factors by coupling the baryon current to a photon via the electromagnetic current, using photon distribution amplitudes.
• Extracts the magnetic dipole moment by relating the form factor at zero momentum transfer to the OPE side of the sum rule, leading to a closed-form expression involving residues, masses, and form factor integrals.

Experimental results

Research questions

• RQ1 What are the masses and residues of negative parity spin-3/2 heavy baryons with single charm or bottom quarks?
• RQ2 How do the electromagnetic transition form factors for diagonal radiative decays of these baryons behave in the light-cone QCD sum rule framework?
• RQ3 What are the magnetic dipole moments of these negative parity spin-3/2 baryons, and how do they compare to those of their positive parity counterparts?
• RQ4 To what extent do contributions from positive parity and spin-1/2 baryons contaminate the sum rules, and how are they suppressed?
• RQ5 Does the naive mass-scaling relation μ⁻ ≈ (m⁺/m⁻)μ⁺ hold for negative parity baryons, or are there significant deviations due to dynamics of mixed parity transitions?

Key findings

• The magnetic dipole moment of the Ωb*⁻ is predicted to be −1.37 ± 0.41 μN, consistent with other b-baryons but differing from positive parity counterparts.
• The Ωc*⁰ has a large negative magnetic moment of −3.46 ± 1.04 μN, indicating a significant deviation from the naive mass-scaling relation.
• The Σc*⁺⁺ has a large positive magnetic moment of 7.73 ± 2.31 μN, suggesting strong sensitivity to interference effects in the sum rule formalism.
• The magnetic moments of b-baryons generally follow the naive scaling relation μ⁻ ≈ (m⁺/m⁻)μ⁺, but this fails for several charmed baryons due to enhanced contributions from mixed-parity transitions.
• Uncertainties in the results are dominated by variations in the continuum threshold (47%), followed by Borel parameter (14%) and photon distribution amplitudes (39%).
• The sign of the magnetic dipole moment is the same for both positive and negative parity baryons, indicating a consistent behavior in the spin-3/2 sector.