I=2 Pion Scattering Length With Improved Actions on Anisotropic Lattices

Du, Xi; Meng, Guangwei; Miao, Chuan; Liu, Chuan

doi:10.1142/s0217751x04019573

Cited by 30 publications

(22 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We begin by reminding the reader that the procedure laid out in the previous two sections is not only useful in the extraction of resonances, scattering amplitudes in which no resonance appears can also be determined. ππ scattering with isospin=2 is the classic example, and this case has been studied in a number of lattice calculations (Aoki et al, 2002;Beane et al, 2006Beane et al, , 2012cBeane et al, , 2008Bulava et al, 2016;Du et al, 2004;Dudek et al, 2011bFeng et al, 2010;Fu, 2013;Fukugita et al, 1995;Gupta et al, 1993;Helmes et al, 2015;Kuramashi et al, 1993;Li et al, 2007;Sasaki et al, 2014;Sharpe et al, 1992;Yagi et al, 2011;Yamazaki et al, 2004). Several recent calculations (Beane et al, 2012c;Bulava et al, 2016;Dudek et al, 2011b determine multiple energy levels and use these to determine the energy-dependence of the elastic phase-shift.…”

Section: Examples Of Resonance Determinationmentioning

confidence: 99%

Scattering processes and resonances from lattice QCD

2018

View full text Add to dashboard Cite

The vast majority of hadrons observed in nature are not stable under the strong interaction, rather they are resonances whose existence is deduced from enhancements in the energy dependence of scattering amplitudes. The study of hadron resonances offers a window into the workings of quantum chromodynamics (QCD) in the low-energy non-perturbative region, and in addition, many probes of the limits of the electroweak sector of the Standard Model consider processes which feature hadron resonances. From a theoretical standpoint, this is a challenging field: the same dynamics that binds quarks and gluons into hadron resonances also controls their decay into lighter hadrons, so a complete approach to QCD is required. Presently, lattice QCD is the only available tool that provides the required non-perturbative evaluation of hadron observables. In this article, we review progress in the study of few-hadron reactions in which resonances and bound-states appear using lattice QCD techniques. We describe the leading approach which takes advantage of the periodic finite spatial volume used in lattice QCD calculations to extract scattering amplitudes from the discrete spectrum of QCD eigenstates in a box. We explain how from explicit lattice QCD calculations, one can rigorously garner information about a variety of resonance properties, including their masses, widths, decay couplings, and form factors. The challenges which currently limit the field are discussed along with the steps being taken to resolve them.

show abstract

Section: Examples Of Resonance Determinationmentioning

confidence: 99%

Scattering processes and resonances from lattice QCD

2018

View full text Add to dashboard Cite

show abstract

“…NPLQCD(2005) [25] −0.0426 ± 0.0006 ± 0.0003 With fully-dynamical domain-wall valence-quark propagators. Du(2004) [23] −0.0467 ± 0.0045 Using anisotropic lattices in an asymmetric box. CP-PACS(2004) [24] −0.0413 ± 0.0029 Compensating the mass dependence of the scattering length.…”

Section: I=2 ππmentioning

confidence: 99%

“…Lattice studies on the ππ scattering have been conducted in quenched QCD by various groups [17][18][19][20][21][22][23]. The full lattice study of the s-wave I = 2 ππ scattering length was first carried out by CP-PACS [24].…”

Section: Introductionmentioning

confidence: 99%

Lattice QCD study of thes-waveππscattering lengths in theI=0and 2 channels

2013

Phys. Rev. D

View full text Add to dashboard Cite

The s-wave pion-pion (ππ) scattering lengths are computed below the inelastic threshold by the Lüscher technique with pion masses ranging from 240 MeV to 463 MeV. In the Asqtad-improved staggered fermion formulation, we calculate the ππ four-point functions for the I = 0 and 2 channels with "moving" wall sources without gauge fixing, and analyze them at the next-to-leading order in the continuum three-flavor chiral perturbation theory. At the physical pion mass, we secure the swave ππ scattering lengths as mπa I=0 ππ = 0.214(4)(7) and mπa I=2 ππ = −0.04430(25)(40) for the I = 0 and 2 channels, respectively, where the first uncertainties are statistical and second ones are our estimates of several systematic effects. Our lattice results for the s-wave ππ scattering lengths are in well accordance with available experimental reports and theoretical forecasts at low momentum. A basic ingredient in our study for the I = 0 case is properly incorporating disconnected diagram. These lattice computations are carried out with the MILC 2 + 1 flavor gauge configurations at two lattice spacings a ≈ 0.15 and 0.12 fm.

show abstract

“…For the study of hadron-hadron interactions at low energies, Lüscher has set up a formalism which relates the twoparticle elastic scattering S-matrix elements with the corresponding two-particle energies in a finite volume [2][3][4][5]. Since the advent of Lüscher's formula, various lattice studies, both quenched [6][7][8][9][10][11][12][13] and unquenched [14][15][16][17][18][19][20][21][22][23], have been performed over the years to investigate the scattering of hadrons.…”

Section: Introductionmentioning

confidence: 99%

Generalized Lüscher’s formula in multichannel baryon-baryon scattering

Liu

2014

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

In this paper, Lüscher's formula is generalized to the case of two spin-1 2 particles in two-channel scattering based on Ref.[1]. This is first done in a non-relativistic quantum mechanics model and then generalized to quantum field theory. We show that Lüscher's formula obtained from these two different methods are equivalent up to terms that are exponentially suppressed in the box size. This formalism can be readily applied to future lattice QCD calculations.

show abstract

I=2 Pion Scattering Length With Improved Actions on Anisotropic Lattices

Cited by 30 publications

References 12 publications

Scattering processes and resonances from lattice QCD

Scattering processes and resonances from lattice QCD

Lattice QCD study of thes-waveππscattering lengths in theI=0and 2 channels

Generalized Lüscher’s formula in multichannel baryon-baryon scattering

Contact Info

Product

Resources

About