[Paper Review] Eta and eta' meson masses from Nf=2+1+1 twisted mass lattice QCD

Konstantin Ottnad, Carsten Urbach+2 more|arXiv (Cornell University)|Nov 15, 2011

Quantum Chromodynamics and Particle Interactions12 references3 citations

TL;DR

This study computes the masses and flavor content of the η and η′ mesons using Nf=2+1+1 twisted mass lattice QCD with two lattice spacings (a ≈ 0.08 fm and a ≈ 0.09 fm) and pion masses from 270 to 500 MeV. The results show high-precision determination of the η meson mass, with the η′ mass requiring larger correlation matrices for reliable extraction; the η is dominated by strange quark content, while the η′ is primarily light-quark driven, with a preliminary mixing angle of ~60°.

ABSTRACT

We determine mass and flavour content of eta and eta' states using Nf=2+1+1 Wilson twisted mass lattice QCD. We describe how those flavour singlet states need to be treated in this lattice formulation. Results are presented for two values of the lattice spacing, a~0.08 fm and a~0.09 fm, with a range of light quark masses corresponding to values of the pion mass from 270 to 500 MeV and fixed bare strange and charm quark mass values.

Motivation & Objective

• To determine the masses and flavor decomposition of the η and η′ mesons in Nf=2+1+1 twisted mass lattice QCD.
• To address the challenges of flavor singlet states in twisted mass fermions, particularly mixing between strange and charm quarks due to explicit flavor symmetry breaking.
• To investigate the dependence of η and η′ masses on light quark mass and charm quark contributions.
• To assess the impact of bare strange and charm quark mass tuning on meson mass values.
• To lay the groundwork for future mixed-action approaches to improve precision and reduce unitarity-breaking effects.

Proposed method

• Utilizes gauge configurations from the European Twisted Mass Collaboration with Nf=2+1+1 dynamical quarks and Iwasaki gauge action.
• Employs the twisted mass Dirac operator with automatic O(a) improvement at maximal twist, using bare twisted masses μℓ, μσ, and μδ for light, strange, and charm quarks.
• Constructs interpolating operators for pseudo-scalar and scalar currents in the twisted basis, transforming to the physical basis via axial rotations.
• Computes three-point correlation functions using a 3×3 matrix of interpolating fields including light, strange, and charm contributions to extract the η and η′ states.
• Applies the generalized eigenvalue problem (GEVP) to extract effective masses and suppress excited-state contamination.
• Uses renormalization factors ZS/ZP to relate twisted-basis operators to physical states, with ZS/ZP estimated from non-perturbative or perturbative matching.

Experimental results

Research questions

• RQ1 How do the masses of the η and η′ mesons depend on the light quark mass in Nf=2+1+1 twisted mass lattice QCD?
• RQ2 What is the flavor content (strange, charm, light) of the η and η′ mesons, and how does it vary with quark mass?
• RQ3 How does the choice of bare strange and charm quark masses affect the η and η′ masses, and what is the impact of improved tuning?
• RQ4 Can the η′ meson mass be reliably extracted from a 3×3 correlation matrix, or is a larger matrix required?
• RQ5 What is the mixing angle between the physical η and η′ states and the flavor eigenstates, and how stable is it across ensembles?

Key findings

• The η meson mass is determined with high precision across the pion mass range from 270 to 500 MeV, showing weak dependence on light quark mass.
• The η′ meson mass is significantly noisier in a 3×3 matrix and requires larger correlation matrices for reliable extraction, though preliminary results are consistent with the physical value.
• The η meson has a dominant strange quark content, with a non-zero but small charm quark contribution, while the η′ is dominated by light quark content.
• A preliminary mixing angle of approximately 60° is obtained between the physical states and the flavor eigenstates, indicating a strong mixing between η8 and η0 components.
• The choice of bare strange and charm quark masses has a measurable effect on the η mass, while the η′ mass remains relatively insensitive within current errors.
• The results suggest that improved tuning of the bare strange and charm masses (e.g., in ensemble A80.24s) leads to better agreement with physical kaon and D-meson masses, indicating tuning sensitivity in the light sector.