I=1/2 S -wave and P -wave Kπ scattering and the κ and K* resonances from lattice QCD

Rendon, Gumaro; Leskovec, Luka; Meinel, Stefan; Negele, John; Paul, Srijit; Petschlies, Marcus; Pochinsky, Andrew; Silvi, Giorgio; Syritsyn, Sergey

doi:10.1103/physrevd.102.114520

Title: I=1/2 S -wave and P -wave Kπ scattering and the κ and K* resonances from lattice QCD

Abstract

We present a lattice-QCD determination of the elastic isospin-$1/2$ $$S$$-wave and $$P$$-wave $$K\pi$$ scattering amplitudes as a function of the center-of-mass energy using Lüscher's method. We perform global fits of $$K$$-matrix parametrizations to the finite-volume energy spectra for all irreducible representations with total momenta up to $$\sqrt{3}\frac{2\pi}{L}$$; this includes irreps that mix the $$S$$- and $$P$$-waves. Several different parametrizations for the energy dependence of the $$K$$-matrix are considered. We also determine the positions of the nearest poles in the scattering amplitudes, which correspond to the broad $$\kappa$$ resonance in the $$S$$-wave and the narrow $K^*(892)$ resonance in the $$P$$-wave. Our calculations are performed with $2+1$ dynamical clover fermions for two different pion masses of 317.2(2.2) and 175.9(1.8) MeV. Our preferred $$S$$-wave parametrization is based on a conformal map and includes an Adler zero; for the $$P$$-wave we use a standard pole parametrization including Blatt-Weisskopf barrier factors. The $$S$$-wave $$\kappa$$-resonance pole positions are found to be $$\left[0.86(12)- 0.309(50)\,i\right]\:{\rm GeV}$$ at the heavier pion mass and $$\left[0.499(55)- 0.379(66)\,i\right]\:{\rm GeV}$$ at the lighter pion mass. The $$P$$-wave $K^*$-resonance pole positions are found to be $$\left[0.8951(64)- 0.00250(21)\,i\right]\:{\rm GeV}$$ at the heavier pion mass and $$\left[0.8718(82)- 0.0130(11)\,i\right]\:{\rm GeV}$$ at the lighter pion mass, which corresponds to couplings of $$g_{K^* K\pi}=5.02(26)$$ and $$g_{K^* K\pi}=4.99(22)$$, respectively.

Authors:

;

; Negele, John; Paul, Srijit; Petschlies, Marcus;

; Silvi, Giorgio; Syritsyn, Sergey

Publication Date:: Mon Dec 28 00:00:00 EST 2020

Research Org.:: Brookhaven National Laboratory (BNL), Upton, NY (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)

OSTI Identifier:: 1749966

Alternate Identifier(s):: OSTI ID: 1633866; OSTI ID: 1755331; OSTI ID: 1785107; OSTI ID: 1824810

Report Number(s):: BNL-216066-2020-JAAM; JLAB-THY-20-3213; DOE/OR/23177-4990; arXiv:2006.14035; BNL-221547-2021-JAAM
Journal ID: ISSN 2470-0010; 114520

Grant/Contract Number:: AC02-05CH1123; AC05-00OR22725; AC05-06OR23177; SC0009913; SC0011090; SC0018121; SC0012704; SC0019229; ACI-1548562; PHY-1847893

Resource Type:: Published Article

Journal Name:: Physical Review. D.

Additional Journal Information:: Journal Name: Physical Review. D. Journal Volume: 102 Journal Issue: 11; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; hadron-hadron interactions; lattice QCD; particle interactions; scattering amplitudes

Citation Formats


                    Rendon, Gumaro, Leskovec, Luka, Meinel, Stefan, Negele, John, Paul, Srijit, Petschlies, Marcus, Pochinsky, Andrew, Silvi, Giorgio, and Syritsyn, Sergey. I=1/2 S -wave and P -wave Kπ scattering and the κ and K* resonances from lattice QCD.  United States: N. p., 2020. 
Web.  doi:10.1103/physrevd.102.114520.

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                    Rendon, Gumaro, Leskovec, Luka, Meinel, Stefan, Negele, John, Paul, Srijit, Petschlies, Marcus, Pochinsky, Andrew, Silvi, Giorgio, & Syritsyn, Sergey. I=1/2 S -wave and P -wave Kπ scattering and the κ and K* resonances from lattice QCD.  United States.  https://doi.org/10.1103/physrevd.102.114520

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                    Rendon, Gumaro, Leskovec, Luka, Meinel, Stefan, Negele, John, Paul, Srijit, Petschlies, Marcus, Pochinsky, Andrew, Silvi, Giorgio, and Syritsyn, Sergey. Mon .  
"I=1/2 S -wave and P -wave Kπ scattering and the κ and K* resonances from lattice QCD".  United States.  https://doi.org/10.1103/physrevd.102.114520.

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@article{osti_1749966,

  title        = {I=1/2 S -wave and P -wave Kπ scattering and the κ and K* resonances from lattice QCD},

  author       = {Rendon, Gumaro and Leskovec, Luka and Meinel, Stefan and Negele, John and Paul, Srijit and Petschlies, Marcus and Pochinsky, Andrew and Silvi, Giorgio and Syritsyn, Sergey},

  abstractNote = {We present a lattice-QCD determination of the elastic isospin-$1/2$ $S$-wave and $P$-wave $K\pi$ scattering amplitudes as a function of the center-of-mass energy using Lüscher's method. We perform global fits of $K$-matrix parametrizations to the finite-volume energy spectra for all irreducible representations with total momenta up to $\sqrt{3}\frac{2\pi}{L}$; this includes irreps that mix the $S$- and $P$-waves. Several different parametrizations for the energy dependence of the $K$-matrix are considered. We also determine the positions of the nearest poles in the scattering amplitudes, which correspond to the broad $\kappa$ resonance in the $S$-wave and the narrow $K^*(892)$ resonance in the $P$-wave. Our calculations are performed with $2+1$ dynamical clover fermions for two different pion masses of 317.2(2.2) and 175.9(1.8) MeV. Our preferred $S$-wave parametrization is based on a conformal map and includes an Adler zero; for the $P$-wave we use a standard pole parametrization including Blatt-Weisskopf barrier factors. The $S$-wave $\kappa$-resonance pole positions are found to be $\left[0.86(12)- 0.309(50)\,i\right]\:{\rm GeV}$ at the heavier pion mass and $\left[0.499(55)- 0.379(66)\,i\right]\:{\rm GeV}$ at the lighter pion mass. The $P$-wave $K^*$-resonance pole positions are found to be $\left[0.8951(64)- 0.00250(21)\,i\right]\:{\rm GeV}$ at the heavier pion mass and $\left[0.8718(82)- 0.0130(11)\,i\right]\:{\rm GeV}$ at the lighter pion mass, which corresponds to couplings of $g_{K^* K\pi}=5.02(26)$ and $g_{K^* K\pi}=4.99(22)$, respectively.},

  doi          = {10.1103/physrevd.102.114520},

  journal      = {Physical Review. D.},

  number       = 11,

  volume       = 102,

  place        = {United States},

  year         = {Mon Dec 28 00:00:00 EST 2020},

  month        = {Mon Dec 28 00:00:00 EST 2020}

}

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Lattice study on $π K$ scattering with moving wall source
journal, April 2012

$K_{0}^{⁎} (800)$ as a companion pole of $K_{0}^{⁎} (1430)$
journal, August 2016

Two-particle multichannel systems in a finite volume with arbitrary spin
journal, April 2014

How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation
journal, July 1990

Meson-meson scattering within one-loop chiral perturbation theory and its unitarization
journal, January 2002

Studying κ Meson with a milc fine Lattice
journal, June 2013

Multichannel $1 \to 2$ transition amplitudes in a finite volume
journal, February 2015

Nonperturbative Approach to Effective Chiral Lagrangians and Meson Interactions
journal, April 1998

S-wave scattering in chiral perturbation theory with resonances
journal, October 2000

Continuum limit and improved action in lattice theories
journal, September 1983

Analytic smearing of $SU (3)$ link variables in lattice QCD
journal, March 2004

A new analysis of $\pi K$ scattering from Roy and Steiner type equations
journal, March 2004

Meson-meson interactions in a nonperturbative chiral approach
journal, February 1999

Confinement of quarks
journal, October 1974

B-decay discrepancies after Moriond 2019
journal, March 2020

$K π$ scattering and the $K^{*}$ decay width from lattice QCD
journal, September 2013

Resonances in Coupled $π K − η K$ Scattering from Quantum Chromodynamics
journal, October 2014

Scalar mesons moving in a finite volume and the role of partial wave mixing
journal, August 2012

Resonances in coupled $π K, η K$ scattering from lattice QCD
journal, March 2015

Scattering processes and resonances from lattice QCD
journal, April 2018

$N / D$ description of two meson amplitudes and chiral symmetry
journal, September 1999

A low lying scalar meson nonet in a unitarized meson model
journal, December 1986

$K π$ interaction in finite volume and the $K^{*}$ resonance
journal, May 2015

Inverse amplitude method in chiral perturbation theory
journal, September 1997

The K* 0(800) scalar resonance from Roy–Steiner representations of πK scattering
journal, November 2006

Two-particle states on a torus and their relation to the scattering matrix
journal, May 1991

Measurement of $C P$ -Averaged Observables in the $B^{0} \to K^{* 0} μ^{+} μ^{-}$ Decay
journal, July 2020

Determination of s- and p-wave I = 1/2 Kπ scattering amplitudes in Nf = 2 + 1 lattice QCD
journal, July 2018

Resonances from meson-meson scattering in $U (3)$ $χ PT$
journal, August 2011

Pion-kaon scattering amplitude constrained with forward dispersion relations up to 1.6 GeV
journal, April 2016

Tetraquarks, hadronic molecules, meson-meson scattering, and disconnected contributions in lattice QCD
journal, October 2013

Differential branching fraction and angular analysis of the decay B 0 → K ∗0 μ + μ −
journal, August 2013

Non-singlet axial vector couplings of the baryon octet in lattice QCD
journal, August 1989

Centrifugal-Barrier Effects in Resonance Partial Decay Widths, Shapes, and Production Amplitudes
journal, February 1972

Study of Kπ scattering using the reactions
journal, February 1978

Test of lepton universality with B 0 → K *0 ℓ + ℓ − decays
journal, August 2017

Scalar mesons in a finite volume
journal, January 2011

Continuum limit and improved action in lattice theories
journal, September 1983

Erratum: Lattice study of $K π$ scattering in $I = 3 / 2$ and 1/2 channels [Phys. Rev. C 80 , 045203 (2009)]
journal, July 2011

Rummukainen-Gottlieb formula on a two-particle system with different masses
journal, January 2012

Erratum: Meson-meson interactions in a nonperturbative chiral approach [Phys. Rev. D 59, 074001 (1999)]
journal, October 1999

Coupled-channel scattering on a torus
journal, July 2013

Multiple-channel generalization of Lellouch-Lüscher formula
journal, July 2012

The kappa in E791 data for D→Kππ
journal, January 2006

Decay width of light quark hybrid meson from the lattice
journal, April 2006

Measurement of Form-Factor-Independent Observables in the Decay $B^{0} \to K^{* 0} μ^{+} μ^{-}$
journal, November 2013

Pion-kaon scattering near the threshold in chiral SU(2) perturbation theory
journal, August 1999

Bottomonium spectrum at order $v^{6}$ from domain-wall lattice QCD: Precise results for hyperfine splittings
journal, December 2010

Necessary and sufficient conditions for the Adler zero
journal, May 1974

Improving the volume dependence of two-body binding energies calculated with lattice QCD
journal, December 2011

Chiral perturbation theory: Expansions in the mass of the strange quark
journal, January 1985

Evidence for a scalar κ(900) resonance in $π K$ scattering
journal, August 1998

πK scattering in chiral perturbation theory to one loop
journal, June 1991

Chiral dynamics and S-wave contributions in semileptonic B decays
journal, October 2013

Resonance scattering phase shifts on a non-rest-frame lattice
journal, September 1995

$P$ -wave $π π$ scattering and the $ρ$ resonance from lattice QCD
journal, August 2017

Consistency Conditions on the Strong Interactions Implied by a Partially Conserved Axial-Vector Current. II
journal, September 1965