Finite-volume energy spectrum of the K − K − K − system

We present a general method for deriving the energy shift of an interacting system of N spinless particles in a finite volume. To this end, we use the nonrelativistic effective field theory (NREFT), and match the pertinent low-energy constants to the scattering amplitudes. Relativistic corrections are explicitly included up to a given order in the 1/L expansion. We apply this method to obtain the ground state of N particles, and the first excited state of two and three particles to order L−6 in terms of the threshold parameters of the two- and three-particle relativistic scattering amplitudes. We use these expressions to analyze the N-particle ground state energy shift in the complex φ4 theory.

Section: Jhep02(2021)060mentioning

confidence: 99%

Section: Jhep02(2021)060mentioning

confidence: 99%

Relativistic N-particle energy shift in finite volume

Romero-López

Rusetsky

Schlage

et al. 2021

“…By contrast, the determination of three-particle scattering quantities has been found to be more challenging -their contribution is suppressed by an additional volume factor. Indeed, while some work finds evidence for a nonzero three-particle interaction [3,6], other studies find no significant signal [7,8,10].…”

Section: Jhep10(2021)023 1 Introductionmentioning

confidence: 99%

“…The era of three-particle spectroscopy in lattice QCD (LQCD) has recently begun, with several studies of three-meson systems at maximal isospin appearing in the literature [1][2][3][4][5][6][7][8][9][10]. These works make use of advances in numerical methods [11,12] for determining the finite-volume spectrum from LQCD, as well as in the theoretical formalism needed to relate the spectrum to infinite-volume scattering amplitudes (the latter reviewed in refs.…”

Section: Jhep10(2021)023 1 Introductionmentioning

confidence: 99%

Interactions of two and three mesons including higher partial waves from lattice QCD

Blanton

Hanlon

Hörz

et al. 2021

We study two- and three-meson systems composed either of pions or kaons at maximal isospin using Monte Carlo simulations of lattice QCD. Utilizing the stochastic LapH method, we are able to determine hundreds of two- and three-particle energy levels, in nine different momentum frames, with high precision. We fit these levels using the relativistic finite-volume formalism based on a generic effective field theory in order to determine the parameters of the two- and three-particle K-matrices. We find that the statistical precision of our spectra is sufficient to probe not only the dominant s-wave interactions, but also those in d waves. In particular, we determine for the first time a term in the three-particle K-matrix that contains two-particle d waves. We use three Nf = 2 + 1 CLS ensembles with pion masses of 200, 280, and 340 MeV. This allows us to study the chiral dependence of the scattering observables, and compare to the expectations of chiral perturbation theory.

“…The theoretical formalism for extracting three-hadron scattering amplitudes using lattice QCD has grown apace in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], and applications to simple systems have been successfully undertaken [21][22][23][24][25][26][27][28][29][30][31]. In all such studies, the basic approach is to extract the spectrum of three-hadron states in a finite spatial volume, and to use this information, by means of general relations, to constrain the infinite-volume scattering amplitudes.…”

Section: Introductionmentioning

confidence: 99%

Decay amplitudes to three hadrons from finite-volume matrix elements

Hansen

Romero-López

Sharpe

2021

We derive relations between finite-volume matrix elements and infinite-volume decay amplitudes, for processes with three spinless, degenerate and either identical or non-identical particles in the final state. This generalizes the Lellouch-Lüscher relation for two-particle decays and provides a strategy for extracting three-hadron decay amplitudes using lattice QCD. Unlike for two particles, even in the simplest approximation, one must solve integral equations to obtain the physical decay amplitude, a consequence of the nontrivial finite-state interactions. We first derive the result in a simplified theory with three identical particles, and then present the generalizations needed to study phenomenologically relevant three-pion decays. The specific processes we discuss are the CP-violating K → 3π weak decay, the isospin-breaking η → 3π QCD transition, and the electromagnetic γ* → 3π amplitudes that enter the calculation of the hadronic vacuum polarization contribution to muonic g − 2.