On the three-particle analog of the Lellouch-Lüscher formula

Müller, Fabian; Rusetsky, Akaki

doi:10.1007/jhep03(2021)152

Cited by 30 publications

(33 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is expected that this is equivalent to the three-particle decay formalism derived in the NREFT approach in Ref. [175], when the nonrelativistic limit of our result is taken.…”

Section: 61)mentioning

confidence: 52%

See 1 more Smart Citation

Implementing the three-particle quantization condition including higher partial waves

Blanton

Romero-López

Sharpe

2019

J. High Energ. Phys.

102

193

View full text Add to dashboard Cite

We present an implementation of the relativistic three-particle quantization condition including both sand d-wave two-particle channels. For this, we develop a systematic expansion of the three-particle K matrix, K df,3 , about threshold, which is the generalization of the effective range expansion of the two-particle K matrix, K 2 . Relativistic invariance plays an important role in this expansion. We find that d-wave two-particle channels enter first at quadratic order. We explain how to implement the resulting multichannel quantization condition, and present several examples of its application. We derive the leading dependence of the threshold three-particle state on the two-particle d-wave scattering amplitude, and use this to test our implementation. We show how strong twoparticle d-wave interactions can lead to significant effects on the finite-volume three-particle spectrum, including the possibility of a generalized three-particle Efimov-like bound state. We also explore the application to the 3π + system, which is accessible to lattice QCD simulations, where we study the sensitivity of the spectrum to the components of K df,3 . Finally, we investigate the circumstances under which the quantization condition has unphysical solutions.F Properties of the isotropic approximation 50 G Failure of Eq. (4.34) for quadratic and cubic terms in the threshold expansion 53There is also an induced three-particle interaction due to the exchange of a virtual particle between a pair of two-particle interactions. This is included in all approaches.2 The p wave is absent due to Bose symmetry. 3 It is expected, however, that there is no barrier to extending to higher waves.-3 -Z 2 symmetry that forbids 2 ↔ 3 transitions. Another important feature of this approach is that it can be made relativistic [5], which turns out to simplify the expansion about threshold. Although we use the RFT approach, we expect that many of the technical considerations and general conclusions will apply to all three approaches to the quantization condition.The formalism of Ref.[1] is restricted to two-particle interactions that do not lead to poles in K 2 , the two-particle K matrix. If there are such poles, then one should use the generalized, and more complicated, formalism derived in Ref. [7]. For simplicity, we consider here only examples in which there are no K-matrix poles.Since our main goal is to show how the formalism works when including higher waves, our numerical examples are mainly chosen for illustrative purposes and do not represent physical systems. However, there is one case in nature for which our simplified setting applies, namely the 3π + system. Thus, in one of our examples, we set the two-particle scattering parameters to those measured experimentally for two charged pions, and illustrate the dependence of the resulting three-pion spectrum on the three-particle scattering parameters. This is similar to the study made in Ref.[15] using the FVU approach, except here we include d-wave dimers.All three-particle quantization condi...

show abstract

“…It is expected that this is equivalent to the three-particle decay formalism derived in the NREFT approach in Ref. [175], when the nonrelativistic limit of our result is taken.…”

Section: 61)mentioning

confidence: 52%

“…Moreover, both the RFT and FVU formalisms have been confronted with lattice QCD 7 data [3,10,168,[171][172][173][174]. Finally, a three-particle generalization of the Lellouch-Lüscher formalism exists in two of the approaches: NREFT [175] and RFT [6].…”

Section: Three-particle Scattering In Finite Volumementioning

confidence: 99%

Implementing the three-particle quantization condition including higher partial waves

Blanton

Romero-López

Sharpe

2019

J. High Energ. Phys.

102

193

View full text Add to dashboard Cite

show abstract

“…Furthermore, in quite a few recent papers, the theoretical approaches mentioned above have been successfully used to analyze data from lattice calculations [38,53,[55][56][57][58][59][60][61][62][63][64][65]. Last but not least, a three-body analog of the Lellouch-Lüscher formula for the finite-volume matrix elements [66] has been recently derived in two different settings [67,68]. These developments are extensively covered in the latest reviews on the subject, to which the reader is referred for further details [69,70].…”

Section: Introductionmentioning

confidence: 99%

Relativistic-invariant formulation of the NREFT three-particle quantization condition

Müller¹,

Pang

Rusetsky

et al. 2022

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

A three-particle quantization condition on the lattice is written down in a manifestly relativistic-invariant form by using a generalization of the non-relativistic effective field theory (NREFT) approach. Inclusion of the higher partial waves is explicitly addressed. A partial diagonalization of the quantization condition into the various irreducible representations of the (little groups of the) octahedral group has been carried out both in the center-of-mass frame and in moving frames. Furthermore, producing synthetic data in a toy model, the relativistic invariance is explicitly demonstrated for the three-body bound state spectrum.

show abstract

“…This will be discussed in Sec. 5, where we reflect on the latest developments related to the derivation of a three-body analog of the Lellouch-Lüscher formula that enables one to measure three-body decay amplitudes on the lattice [139,140].…”

Section: Introductionmentioning

confidence: 99%

Multi-particle systems on the lattice and chiral extrapolations: a brief review

Mai,

Döring,

Rusetsky

2021

Preprint

Self Cite

View full text Add to dashboard Cite

The extraction of two-and three-body hadronic scattering amplitudes and the properties of the low-lying hadronic resonances from the finite-volume energy levels in lattice QCD represents a rapidly developing field of research. The use of various modifications of the Lüscher finite-volume method has opened a path to calculate infinitevolume scattering amplitudes on the lattice. Many new results have been obtained recently for different two-and three-body scattering processes, including the extraction of resonance poles and their properties from lattice data. Such studies, however, require robust parametrizations of the infinite-volume scattering amplitudes, which rely on basic properties of S-matrix theory and -preferably -encompass systems with quark masses at and away from the physical point. Parametrizations of this kind, provided by unitarized Chiral Perturbation Theory, are discussed in this review. Special attention is paid to three-body systems on the lattice, owing to the rapidly growing interest in the field. Here, we briefly survey the formalism, chiral extrapolation, as well as finite-volume analyses of lattice data.

show abstract

On the three-particle analog of the Lellouch-Lüscher formula

Cited by 30 publications

References 44 publications

Implementing the three-particle quantization condition including higher partial waves

Implementing the three-particle quantization condition including higher partial waves

Relativistic-invariant formulation of the NREFT three-particle quantization condition

Multi-particle systems on the lattice and chiral extrapolations: a brief review

Contact Info

Product

Resources

About