Finite-volume energy shift of the three-pion ground state

Müller, Fabian; Yu, Tiansu; Rusetsky, Akaki

doi:10.1103/physrevd.103.054506

Cited by 33 publications

(22 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[132,133], where results for a 0 at heavier-than-physical pion masses were combined with a chiral extrapolation to reach the physical point. It must also be mentioned that perturbative expansions in 1/L have been extended to three and more particles, as well as excited states [11,[134][135][136][137][138].…”

Section: The Lüscher Formalismmentioning

confidence: 99%

Implementing the three-particle quantization condition including higher partial waves

Blanton

Romero-López

Sharpe

2019

J. High Energ. Phys.

100

195

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

Section: The Lüscher Formalismmentioning

confidence: 99%

Implementing the three-particle quantization condition including higher partial waves

Blanton

Romero-López

Sharpe

2019

J. High Energ. Phys.

100

195

View full text Add to dashboard Cite

show abstract

“…This highly intuitive result has been derived for the ground state in the 𝑷 = 0 case in Refs. [42][43][44][45][46], but the result for all excited states and all moving frames is new to this work. A comparison of this generic expression to specific excited state results derived using a different formalism [47,48], together with the full proof, is given in a manuscript in preparation [41].…”

Section: Three-particle Resultsmentioning

confidence: 99%

Analytic expansions of two- and three-particle excited-state energies

Grabowska¹,

Hansen²

2021

Preprint

View full text Add to dashboard Cite

The last years have seen significant developments in methods relating two-and three-particle finite-volume energies to scattering observables. These relations hold for both weakly and strongly interacting systems, and studying their predictions in limiting cases can provide important cross checks as well as giving useful insights into the general formulae. In these proceedings, we present analytic results for finite-volume excited states, recovered by expanding the general relations in powers of the interaction strength. We highlight elegant patterns that emerge, especially for excited three-particle energies, and discuss various applications of the results. The two-particle results summarized here are described in more detail in Ref. [1], and the three-particle results are detailed in a manuscript to appear.

show abstract

“…The threshold expansion has been derived previously for systems of identical particles [12,21,[56][57][58], for three-pion systems with I = 1 [23], and for the nπ + + mK + system [59]. The fully nondegenerate three-particle system has not been previously considered.…”

Section: B Threshold Expansion In the Nondegenerate Casementioning

confidence: 99%

“…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

Finite-volume energy shift of the three-pion ground state

Cited by 33 publications

References 52 publications

Implementing the three-particle quantization condition including higher partial waves

Implementing the three-particle quantization condition including higher partial waves

Analytic expansions of two- and three-particle excited-state energies

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

Contact Info

Product

Resources

About