Dynamical Twisted Mass Fermions with Light Quarks: Simulation and Analysis Details (0803.0224v2)

Abstract: In a paper [hep-lat/0701012] we presented precise lattice QCD results of our European Twisted Mass Collaboration (ETMC). They were obtained by employing two mass-degenerate flavours of twisted mass fermions at maximal twist. In the present paper we give details on our simulations and the computation of physical observables. In particular, we discuss the problem of tuning to maximal twist, the techniques we have used to compute correlators and error estimates. In addition, we provide more information on the algorithm used, the autocorrelation times and scale determination, the evaluation of disconnected contributions and the description of our data by means of chiral perturbation theory formulae.

• The paper meticulously details maximal twist tuning in lattice QCD to achieve automatic O(a) improvement and reduce discretization errors.
• It explains efficient computation of charged and neutral meson correlators using stochastic methods and variance reduction techniques.
• Simulation algorithms with mass preconditioning and robust error analysis ensure reliable extraction of physical observables in meson studies.

Overview of "Dynamical Twisted Mass Fermions with Light Quarks: Simulation and Analysis Details"

This paper presents an in-depth examination of simulations performed using two mass-degenerate flavors of twisted mass fermions, specifically tuned to maximal twist, as developed by the European Twisted Mass Collaboration (ETMC). The approach is fundamental for the paper of lattice Quantum Chromodynamics (QCD) with improved precision in the measurement of mesonic quantities, particularly for masses as low as 300 MeV. The intricate details of the simulations and the analysis provided herein serve to complement prior publications and address omitted computational specifics.

Technical Highlights

The paper systematically explores several aspects critical to the simulation of twisted mass fermions:

1. Maximal Twist Tuning:
   • Achieving maximal twist is pivotal in ensuring automatic O(a) improvement, thus minimizing lattice discretization errors to O(a²). This is done by setting the PCAC mass to zero through the stringent evaluation of correlators, ensuring the pion ground state is dominant.
   • The authors address the practical determination of the critical untwisted quark mass, articulating a method that allows balancing computational expense with sufficient accuracy.
2. Correlators and Error Estimation:
   • Techniques for calculating charged and neutral meson correlators are detailed. For charged mesons, only propagators for one flavor are necessary, making use of the twisted basis where computational efficiency is greatly improved.
   • Neutral mesons require both connected and disconnected contributions for evaluation. Stochastic source methods and variance reduction techniques are employed for effective computation.
3. Simulation Algorithms:
   • HMC algorithms with mass preconditioning and multiple time scale integration are employed, as detailed with exhaustive parameter settings specific to each simulation instance. These are crucial for efficient trajectory generation and autocorrelation management.
   • The analysis of statistical errors employs the Gamma and data-blocking methods, ensuring precise measurement of observables while managing autocorrelation.
4. Static Potential and Scale Setting:
   • A robust method for setting the scale via the static potential using the hadronic scale r₀ is presented. The paper gives detailed procedures for spatial and temporal smearing to optimize measurements and minimize errors inherent in Wilson loops.
5. Implementation of Physical Observables and Finite Size Effects:
   • Masses and decay constants of charged and neutral pseudoscalar mesons are extracted. Due to significant lattice artifacts at maximal twist, the neutral pseudoscalar meson mass requires careful treatment to isolate O(a²) discrepancies from physical effects.
   • Finite size effects are treated using chiral perturbation theory expressions to accurate account for corrections in small volumes.

Implications and Future Directions

• Theoretical Impact: The procedures refined in this paper bolster the capability of lattice QCD simulations to accurately reflect low-meson mass realms, allowing robust extrapolation and analysis within the chiral regime.
• Practical Developments: Continued refinement of the tuning and correlator computation approaches promise enhanced precision in lattice calculations, foundational for future exploration of QCD phenomena and beyond.
• Speculative Future Work: The meticulous attention to error management and computational efficiency opens pathways for deploying cutting-edge hybrid computational methods and exploring larger parameter spaces with minimized error margins.

In conclusion, this paper offers a comprehensive paper, solidifying the understanding and methodical execution of maximal twist tuning and twisted mass fermion simulations in lattice QCD, providing ample groundwork for improved accuracy and expanded theoretical inquiries into mesonic systems.