[Paper Review] Resonance Parameters for the rho-meson from Lattice QCD

Dehua Guo, Andrei Alexandru|arXiv (Cornell University)|Nov 19, 2015

Quantum Chromodynamics and Particle Interactions4 references3 citations

TL;DR

This lattice QCD study computes the rho-meson resonance parameters using asymmetric boxes to access scattering phase shifts in the $π$-$\pi$ system at $m_\pi \approx 315$ MeV and $m_\pi \approx 227$ MeV. By employing variational methods with $q\bar{q}$ and $\pi\pi$ interpolators and LapH smearing for all-to-all propagators, the authors extract a resonance mass of $m_\rho = 716(6)$ MeV at the physical pion mass, consistent with other $N_f=2$ studies, though lower than experiment due to missing $K\bar{K}$ channel effects.

ABSTRACT

We present a calculation of the phase-shift for $π$-$π$ scattering in isospin-1, spin-1 channel in the elastic region. The mass and width of the rho resonance is extracted by fitting these phaseshifts. To vary the scattering momentum we employ asymmetric boxes. We use $N_f = 2$ nHYP-smeared clover fermions and generate two sets of ensembles with pion masses about 315MeV and 227MeV. To determine the phase shifts we compute the energy spectrum both for states at rest and boosted. We employ a variational analysis with interpolating fields including several $q$-$\bar{q}$ and $π$-$π$ interpolating fields with different scattering momenta.

Motivation & Objective

• To compute the $\pi$-$\pi$ scattering phase shift in the isospin-1, spin-1 channel using lattice QCD.
• To extract the rho-meson resonance mass and width from phase-shift data in the elastic region.
• To investigate the impact of finite volume effects and the need for modified Breit-Wigner forms in fitting phase shifts.
• To extrapolate the resonance mass to the physical pion mass using $m_\pi^2$-dependent fits.
• To assess the role of the $K\bar{K}$ channel in resolving the discrepancy between lattice results and experiment.

Proposed method

• Utilizes Lüscher’s method with asymmetric boxes of geometry $L \times L \times \eta L$ to vary scattering momentum via $\eta$.
• Employs $N_f=2$ nHYP-smeared clover fermions on two ensembles with $m_\pi \approx 315$ MeV and $m_\pi \approx 227$ MeV.
• Applies a variational method with interpolating fields including $q\bar{q}$ and $\pi\pi$ states to extract multiple energy levels.
• Uses LapH smearing to efficiently compute all-to-all quark propagators for correlation matrices.
• Applies the $A_2$ irrep of $D_{4h}$ symmetry to isolate $l=1$ partial waves and extract phase shifts via Lüscher’s formula.
• Fits phase shifts with both standard and modified Breit-Wigner forms, including a centrifugal barrier term with interaction radius $R$.

Experimental results

Research questions

• RQ1 How do phase shifts for $\pi$-$\pi$ scattering in the $I=1$, $J=1$ channel evolve with center-of-mass energy in the resonance region?
• RQ2 Can the standard Breit-Wigner parameterization accurately describe the phase shift data across the full energy range?
• RQ3 What is the effect of including a centrifugal barrier term in the resonance width parameterization on fitting quality?
• RQ4 How do the extracted resonance parameters depend on pion mass, and what is the extrapolated value at the physical pion mass?
• RQ5 Why is the lattice result for $m_\rho$ lower than the physical value, and what role does the $K\bar{K}$ channel play?

Key findings

• The standard Breit-Wigner form fails to describe the phase shift data well in the high-energy region, especially at $m_\pi \approx 315$ MeV.
• Including a centrifugal barrier term with interaction radius $R = 0.376(65)$ fm significantly improves the fit quality in the high-energy region.
• For $m_\pi \approx 227$ MeV, excluding the lowest three phase shift points yields a good fit, but the model still misses the threshold region by a few sigmas.
• The extrapolated rho-meson mass at the physical pion mass is $m_\rho = 716(6)$ MeV, consistent with other $N_f=2$ lattice studies.
• The discrepancy of about 60 MeV between the extrapolated $m_\rho$ and the physical value is attributed to the absence of $K\bar{K}$ channel contributions.
• Finite volume effects are found to be negligible, as the extrapolation curve passes through results from a smaller-volume ensemble.