[Paper Review] On the chiral extrapolation of charmed meson masses

Xiao-Yu Guo, Yonggoo Heo+1 more|arXiv (Cornell University)|Jan 30, 2018

Quantum Chromodynamics and Particle Interactions8 citations

TL;DR

This study develops a chiral extrapolation framework using lattice QCD data from multiple collaborations (PACS-CS, MILC, HPQCD, ETMC, HSC) to determine low-energy constants in a chiral Lagrangian for charmed mesons. It achieves precise fits to light-quark masses below 600 MeV and predicts a narrow exotic sextet state in the ηD channel below the $ar{K}D_s$ threshold, with a D_{s0}(2317) decay width of (45–49) keV.

ABSTRACT

We perform an analysis of QCD lattice data on charmed meson masses. The quark-mass dependence of the data set is used to gain information on the size of counter terms of the chiral Lagrangian formulated with open-charm states with J^P= 0^- and J^P =1^- quantum numbers. Of particular interest are those counter terms that are active in the exotic flavour sextet channel. A chiral expansion scheme where physical masses enter the extrapolation formulae is developed and applied to the lattice data set. Good convergence properties are demonstrated and an accurate reproduction of the lattice data based on ensembles of PACS-CS, MILC, HPQCD, ETMC and HSC with pion and kaon masses smaller than 600 MeV is achieved. It is argued that a unique set of low-energy parameters is obtainable only if additional information from HSC on some scattering observables is included in our global fits. The elastic and inelastic s-wave pi D and eta D scattering as considered by HSC is reproduced faithfully. Based on such low-energy parameters we predict 15 phase shifts and in-elasticities at physical quark masses but also for an additional HSC ensemble at smaller pion mass. In addition we find a clear signal for a member of the exotic flavour sextet states in the eta D channel, below the bar K D_s threshold. For the isospin violating strong decay width of the D_{s0}(2317) we obtain the range (45-49) keV.

Motivation & Objective

• To determine low-energy constants in a chiral Lagrangian for open-charm mesons with J^P = 0^- and 1^- quantum numbers.
• To analyze the quark-mass dependence of lattice QCD data on charmed meson masses across multiple ensembles.
• To assess the role of counter terms, especially those active in the exotic flavour sextet channel.
• To improve convergence and accuracy in chiral extrapolation by incorporating physical masses in the expansion.
• To extract reliable phase shifts and inelasticities for s-wave πD and ηD scattering using global fits including HSC data on scattering observables.

Proposed method

• A chiral expansion scheme is developed where physical masses are used as input in the extrapolation formulae.
• Lattice data from PACS-CS, MILC, HPQCD, ETMC, and HSC with pion and kaon masses < 600 MeV are used.
• Global fits are performed including scattering observables from HSC to constrain low-energy parameters uniquely.
• The method incorporates both elastic and inelastic s-wave πD and ηD scattering amplitudes.
• Counter terms in the chiral Lagrangian are analyzed for their role in the exotic flavour sextet channel.
• The framework is validated by achieving good convergence and accurate reproduction of lattice data.

Experimental results

Research questions

• RQ1 What are the low-energy constants of the chiral Lagrangian for charmed mesons with J^P = 0^- and 1^-?
• RQ2 How do counter terms in the exotic flavour sextet channel affect the description of charmed meson masses and scattering?
• RQ3 Can a unique set of low-energy parameters be determined without additional scattering data from HSC?
• RQ4 What is the predicted phase shift and inelasticity for s-wave πD and ηD scattering at physical quark masses?
• RQ5 Is there evidence for a narrow resonance in the ηD channel below the $ar{K}D_s$ threshold?

Key findings

• A unique determination of low-energy parameters requires inclusion of HSC data on scattering observables, particularly for elastic and inelastic s-wave πD and ηD scattering.
• The chiral extrapolation framework shows good convergence and accurately reproduces lattice data across multiple ensembles with pion masses below 600 MeV.
• Fifteen phase shifts and inelasticities are predicted at physical quark masses and for an additional HSC ensemble with smaller pion mass.
• A clear signal is found for a resonance in the exotic flavour sextet channel within the ηD system, below the $ar{K}D_s$ threshold.
• The isospin-violating strong decay width of the D_{s0}(2317) is predicted to be in the range (45–49) keV.