Three-Body Dynamics of the 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>1260</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>
 Resonance from Lattice QCD

Mai, Maxim; Alexandru, Andrei; Brett, Ruairí; Culver, Chris; Döring, Michael; Lee, Frank; Sadasivan, Daniel

doi:10.1103/physrevlett.127.222001

Cited by 18 publications

(15 citation statements)

References 127 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our methodology can be adopted to resonating systems and processes with non-zero angular momenta. Additionally, the strategies presented here can be used to include the short-distance three-body 𝐾 matrices, determined from the growing body of the three-body LQCD calculations [20,22,[27][28][29][30][31][32][33][34][35][36].…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Infinite volume, three-body scattering formalisms in the presence of bound states

Dawid¹

2021

Preprint

View full text Add to dashboard Cite

Strong interactions produce a rich spectrum of resonances that decay into three or more hadrons. Understanding their phenomenology requires a theoretical framework to extract parameters from experimental data and Lattice QCD simulations of hadron scattering. Two classes of relativistic three-body approaches are currently being pursued: the EFT-based and unitarity-based one. We consider a model of relativistic three-body scattering with an 𝑆-wave bound state in the two-body sub-channel using both formalisms. We present and discuss numerical solutions for the multihadron scattering amplitudes in different kinematical regions, obtained from integral equations of the EFT-based approach. The connection of our work to the ongoing program of computing the three-body spectrum from the lattice is highlighted. Finally, we show how to generalize the unitarity-based framework to include all relevant open channels, discuss the nonphysical singularities near the physical region, and show how to eliminate them in a simple case.

show abstract

Section: Discussionmentioning

confidence: 99%

“…It is the analog of the R matrix of the 𝐵-matrix formalism. In the recent lattice studies [20][21][22], both the R and K df,3 have been determined for the realistic systems of three pions. Finally, the integration in the above equations is defined as,…”

Section: Three-body Integral Equationsmentioning

confidence: 99%

Infinite volume, three-body scattering formalisms in the presence of bound states

Dawid¹

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The three-particle formalism has been derived following three different approaches: 2 (i) generic relativistic effective field theory (RFT) [3-5, 9-11, 15, 16, 18, 22, 24], (ii) nonrelativistic effective field theory (NREFT) [6,7,12,19,23,45], and (iii) (relativistic) finite volume unitarity (FVU) [8,26,29,36]. The equivalence of the RFT and FVU approaches, aside from some technical issues, has been shown in ref.…”

Section: Jhep02(2022)098mentioning

confidence: 99%

“…In the last few years, considerable progress has been made in the development of the formalism needed to connect the three-particle finite-volume spectrum in quantum field theories to infinite-volume scattering amplitudes , and in the implementation of this formalism and its application to the results from lattice QCD (LQCD) simulations [20,[26][27][28][29][30][31][32][33][34][35][36]. For recent reviews see refs.…”

Section: Jhep02(2022)098 1 Introductionmentioning

confidence: 99%

Implementing the three-particle quantization condition for π+π+K+ and related systems

Blanton

Romero-López

Sharpe

2022

J. High Energ. Phys.

View full text Add to dashboard Cite

Recently, the formalism needed to relate the finite-volume spectrum of systems of nondegenerate spinless particles has been derived. In this work we discuss a range of issues that arise when implementing this formalism in practice, provide further theoretical results that can be used to check the implementation, and make available codes for implementing the three-particle quantization condition. Specifically, we discuss the need to modify the upper limit of the cutoff function due to the fact that the left-hand cut in the scattering amplitudes for two nondegenerate particles moves closer to threshold; we describe the decomposition of the three-particle amplitude $$ \mathcal{K} $$ K df,3 into the matrix basis used in the quantization condition, including both s and p waves, with the latter arising in the amplitude for two nondegenerate particles; we derive the threshold expansion for the lightest three-particle state in the rest frame up to $$ \mathcal{O} $$ O (1/L5); and we calculate the leading-order predictions in chiral perturbation theory for $$ \mathcal{K} $$ K df,3 in the π+π+K+ and π+K+K+ systems. We focus mainly on systems with two identical particles plus a third that is different (“2+1” systems). We describe the formalism in full detail, and present numerical explorations in toy models, in particular checking that the results agree with the threshold expansion, and making a prediction for the spectrum of π+π+K+ levels using the two- and three-particle interactions predicted by chiral perturbation theory.

show abstract

“…The three-particle formalism has been derived following three different approaches: 2 (i) generic relativistic effective field theory (RFT) [3-5, 9-11, 15, 16, 18, 22, 24], (ii) nonrelativistic effective field theory (NREFT) [6,7,12,19,23,44], and (iii) (relativistic) finite volume unitarity (FVU) [8,26,29,36]. The equivalence of the RFT and FVU approaches, aside from some technical issues, has been shown in Ref.…”

Section: Introductionmentioning

confidence: 99%

Implementing the three-particle quantization condition for $π^+π^+K^+$ and related systems

Blanton,

Romero-López,

Sharpe

2021

Preprint

View full text Add to dashboard Cite

Recently, the formalism needed to relate the finite-volume spectrum of systems of nondegenerate spinless particles has been derived. In this work we discuss a range of issues that arise when implementing this formalism in practice, provide further theoretical results that can be used to check the implementation, and make available codes for implementing the three-particle quantization condition. Specifically, we discuss the need to modify the upper limit of the cutoff function due to the fact that the left-hand cut in the scattering amplitudes for two nondegenerate particles moves closer to threshold; we describe the decomposition of the three-particle amplitude K df,3 into the matrix basis used in the quantization condition, including both s and p waves, with the latter arising in the amplitude for two nondegenerate particles; we derive the threshold expansion for the lightest three-particle state in the rest frame up to O(1/L 5 ); and we calculate the leading-order predictions in chiral perturbation theory for K df,3 in the π + π + K + and π + K + K + systems. We focus mainly on systems with two identical particles plus a third that is different ("2+1" systems). We describe the formalism in full detail, and present numerical explorations in toy models, in particular checking that the results agree with the threshold expansion, and making a prediction for the spectrum of π + π + K + levels using the two-and three-particle interactions predicted by chiral perturbation theory.

show abstract

Three-Body Dynamics of the a1(1260) Resonance from Lattice QCD

Cited by 18 publications

References 127 publications

Infinite volume, three-body scattering formalisms in the presence of bound states

Infinite volume, three-body scattering formalisms in the presence of bound states

Implementing the three-particle quantization condition for π+π+K+ and related systems

Implementing the three-particle quantization condition for $π^+π^+K^+$ and related systems

Contact Info

Product

Resources

About