Title: Isospin 0 and 2 two-pion scattering at physical pion mass using all-to-all propagators with periodic boundary conditions in lattice QCD

Journal Article · · Physical Review. D.
ORCiD logo [1];  [2]; ORCiD logo [3]; ORCiD logo [4];  [2]; ORCiD logo [1]; ORCiD logo [2];  [2];  [5]; ORCiD logo [6];  [2]; ORCiD logo [7]
  1. University of Connecticut, Storrs, CT (United States); Brookhaven National Laboratory (BNL), Upton, NY (United States)
  2. Brookhaven National Laboratory (BNL), Upton, NY (United States)
  3. Universitá di Milano-Bicocca (Italy); INFN, Sezione di Milano-Bicocca, Milano (Italy)
  4. University of Bern (Switzerland)
  5. Universität Regensburg (Germany)
  6. University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
  7. University of Connecticut, Storrs, CT (United States)
+ Show Author Affiliations

A study of two-pion scattering for the isospin channels, 𝐼 = 0 and 𝐼 = 2, using lattice QCD is presented. Möbius domain-wall fermions, on top of the Iwasaki-DSDR gauge action for gluons with periodic boundary conditions, are used for the lattice computations, which are carried out on two ensembles of gauge field configurations generated by the RBC and UKQCD Collaborations with physical masses, inverse lattice spacings of 1.023 and 1.378 GeV, and spatial extents of 𝐿 = 4.63 and 4.58 fm, respectively. The all-to-all propagator method is employed to compute a matrix of correlation functions of two-pion operators. The generalized eigenvalue problem (GEVP) is solved for a matrix of correlation functions to extract phase shifts with multiple states—two pions with a nonzero relative momentum, as well as two pions at rest. Our results for phase shifts for both the 𝐼 = 0 and 𝐼 = 2 channels are consistent with the Roy equation and chiral perturbation theory, though at this preliminary stage our errors for 𝐼 = 0 are large. An important outcome of this work is that we are successful in extracting two-pion excited states, which are useful for studying 𝐾 → 𝜋⁢𝜋 decay, on physical-mass ensembles using the GEVP.

Research Organization:
Brookhaven National Laboratory (BNL), Upton, NY (United States); University of California, Berkeley, CA (United States)
Sponsoring Organization:
Swiss National Science Foundation (SNSF); USDOE; USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), High Energy Physics (HEP); e Swiss National Science Foundation (SNSF)
Contributing Organization:
RBC Collaboration; RBC and UKQCD Collaborations; UKQCD Collaboration
Grant/Contract Number:
FG02-92ER40716; SC0004658; SC0010339; SC0012704
OSTI ID:
1974837
Report Number(s):
BNL-225457-2024-JAAM
Journal Information:
Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 9 Vol. 107; ISSN 2470-0010; ISSN 2470-0029
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (52)

Isospin-violating contributions to ∈′/∈ journal February 2020
The strategy for computing the hadronic mass spectrum journal January 1984
Exact integral equation for pion-pion scattering involving only physical region partial waves journal September 1971
Final state interactions from euclidean correlation functions journal August 1990
Elastic ππ scattering to two loops journal May 1996
How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation journal July 1990
Two-particle states on a torus and their relation to the scattering matrix journal May 1991
Resonance scattering phase shifts on a non-rest-frame lattice journal September 1995
Roy equation analysis of ππ scattering journal November 2001
The ππ S-wave scattering lengths journal September 2000
ππ scattering journal June 2001
Pion-pion scattering at low energy journal December 1997
Erratum journal April 1998
Practical all-to-all propagators for lattice QCD journal November 2005
I = 1 and I = 2 π – π scattering phase shifts from N f = 2 + 1 lattice QCD journal September 2016
Search for CP Violation in the Decay τ−→π−KS0(≥0π0)ντ at BaBar journal August 2014
The π+π+ scattering length from maximally twisted mass lattice QCD journal February 2010
Multi-Grid Lanczos journal January 2018
On the generalized eigenvalue method for energies and matrix elements in lattice field theory journal April 2009
Pion scattering in the isospin I = 2 channel from elongated lattices journal August 2019
Lattice simulations with G -parity boundary conditions journal January 2020
Direct C P violation and the Δ I = 1 / 2 rule in K → π π decay from the standard model journal September 2020
Lattice determination of I=0 and 2 ππ scattering phase shifts with a physical pion mass journal December 2021
I = 2 π π scattering phase shift with two flavors of O a improved dynamical quarks journal October 2004
I = 2 pion scattering length from two-pion wave functions journal May 2005
Angular momentum on the lattice: The case of nonzero linear momentum journal January 2006
I = 2 π π scattering from fully-dynamical mixed-action lattice QCD journal March 2006
Erratum: Angular momentum on the lattice: The case of nonzero linear momentum [Phys. Rev. D 73 , 014504 (2006)] journal October 2006
Precise determination of the I = 2 π π scattering length from mixed-action lattice QCD journal January 2008
Novel quark-field creation operator construction for hadronic physics in lattice QCD journal September 2009
Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV journal April 2011
I = 2 π π S -wave scattering phase shift from lattice QCD journal February 2012
S - and D -wave phase shifts in isospin-2 π π scattering from lattice QCD journal August 2012
Lattice QCD study of the s -wave π π scattering lengths in the I = 0 and 2 channels journal April 2013
New class of variance-reduction techniques using lattice symmetries journal November 2013
K → π π Δ I = 3 / 2 decay amplitude in the continuum limit journal April 2015
Covariant approximation averaging journal June 2015
Domain wall QCD with physical quark masses journal April 2016
Lattice calculation of electric dipole moments and form factors of the nucleon journal July 2017
Isospin-0 π π s-wave scattering length from twisted mass lattice QCD journal September 2017
I = 0 π π s -wave scattering length from lattice QCD journal July 2018
Precise Determination of the f 0 ( 600 ) and f 0 ( 980 ) Pole Parameters from a Dispersive Data Analysis journal August 2011
Standard Model Prediction for Direct C P Violation in K → π π Decay journal November 2015
Isoscalar π π Scattering and the σ Meson Resonance from QCD journal January 2017
Calculation of the Hadronic Vacuum Polarization Contribution to the Muon Anomalous Magnetic Moment journal July 2018
Observation of C P Violation in Charm Decays journal May 2019
Lattice QCD calculation of full pion scattering lengths journal October 1993
Scattering of two and three physical pions at maximal isospin from lattice QCD: Extended Twisted Mass Collaboration journal May 2021
FLAG Review 2021 journal October 2022
Reducing Chiral Symmetry Breaking in Domain Wall Fermions at fixed $L_s$
  • Blum, Tom; Christ, Norman H.; Mawhinney, Robert
  • Proceedings of The XXVI International Symposium on Lattice Field Theory — PoS(LATTICE 2008) https://doi.org/10.22323/1.066.0048
conference June 2009
Exclusive Channel Study of the Muon HVP conference January 2020
$K \to \pi\pi$ decay matrix elements at the physical point with periodic boundary conditions
  • Tomii, Masaaki; Blum, Thomas; Hoying, Daniel
  • Proceedings of The 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021) https://doi.org/10.22323/1.396.0394
conference May 2022

Similar Records

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Hadron-hadron interactions
Lattice QCD
Pions
Scattering amplitudes