Three-body unitarity versus finite-volume π+π+π+ spectrum from lattice QCD
TL;DR: In this article, a formalism for three-body systems in moving frames was developed and applied numerically to obtain the three-S$-matrix principle of unitarity.
Abstract: Strong three-body interactions above threshold govern the dynamics of many exotics and conventional excited mesons and baryons. Three-body finite-volume energies calculated from lattice QCD promise an ab initio understanding of these systems. We calculate the three-${\ensuremath{\pi}}^{+}$ spectrum unraveling the three-body dynamics that is tightly intertwined with the $S$-matrix principle of three-body unitarity and compare it with recent lattice QCD results. For this purpose, we develop a formalism for three-body systems in moving frames and apply it numerically.
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TL;DR: In this article, the authors show that lattice QCD calculations have reached a stage where these three-body states can be accurately resolved, using three positively charged pions, with different lattice geometries and quark masses, and find all states below inelastic threshold agree with predictions from a state-of-theart phenomenological formalism.
Abstract: Three-body states are critical to the dynamics of many hadronic resonances. We show that lattice QCD calculations have reached a stage where these states can be accurately resolved. We perform a calculation over a wide range of parameters and find all states below inelastic threshold agree with predictions from a state-of-the-art phenomenological formalism. This also illustrates the reliability of the formalism used to connect lattice QCD results to infinite volume physics. Our calculation is performed using three positively charged pions, with different lattice geometries and quark masses.
69 citations
TL;DR: In this article, a generalization of the relativistic, finite-volume, three-particle quantization condition for non-identical pions in isosymmetric QCD is presented.
Abstract: We present a generalization of the relativistic, finite-volume, three-particle quantization condition for non-identical pions in isosymmetric QCD. The resulting formalism allows one to use discrete finite-volume energies, determined using lattice QCD, to constrain scattering amplitudes for all possible values of two- and three-pion isospin. As for the case of identical pions considered previously, the result splits into two steps: The first defines a non-perturbative function with roots equal to the allowed energies, $E_n(L)$, in a given cubic volume with side-length $L$. This function depends on an intermediate three-body quantity, denoted $\mathcal{K}_{\mathrm{df},3}$, which can thus be constrained from lattice QCD input. The second step is a set of integral equations relating $\mathcal{K}_{\mathrm{df},3}$ to the physical scattering amplitude, $\mathcal M_3$. Both of the key relations, $E_n(L) \leftrightarrow \mathcal{K}_{\mathrm{df},3}$ and $\mathcal{K}_{\mathrm{df},3}\leftrightarrow \mathcal M_3$, are shown to be block-diagonal in the basis of definite three-pion isospin, $I_{\pi \pi \pi}$, so that one in fact recovers four independent relations, corresponding to $I_{\pi \pi \pi}=0,1,2,3$. We also provide the generalized threshold expansion of $\mathcal{K}_{\mathrm{df},3}$ for all channels, as well as parameterizations for all three-pion resonances present for $I_{\pi\pi\pi}=0$ and $I_{\pi\pi\pi}=1$. As an example of the utility of the generalized formalism, we present a toy implementation of the quantization condition for $I_{\pi\pi\pi}=0$, focusing on the quantum numbers of the $\omega$ and $h_1$ resonances.
68 citations
Cites methods from "Three-body unitarity versus finite-..."
...In particular, a three-particle quantization condition for identical (pseudo)scalars has been derived following three different approaches:1 (i) generic relativistic effective field theory (RFT) [17–24], (ii) nonrelativistic effective field theory (NREFT) [25–28], and (iii) (relativistic) finite volume unitarity (FVU) [29–31]....
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TL;DR: In this article, the progress of lattice QCD studies of nuclear matrix elements of electroweak currents and beyond-Standard-Model operators is summarized, and connections with effective field theories and nuclear models are outlined.
55 citations
TL;DR: In this paper, the relativistic three-body quantization condition was extended to the strangeness sector, and the excited level finite-volume spectrum of three-kaon systems at maximal isospin was predicted.
Abstract: The dynamics of multikaon systems are of relevance for several areas of nuclear physics. However, even the simplest systems, two and three kaons, are hard to prepare and study experimentally. Here we show how to extract this information using first-principle lattice QCD results. We (i) extend the relativistic three-body quantization condition to the strangeness sector, predicting for the first time the excited level finite-volume spectrum of three-kaon systems at maximal isospin and (ii) present a first lattice QCD calculation of the excited levels of this system in a finite box. We compare our predictions with the lattice results reported here and with previous ground state calculations and find very good agreement.
43 citations
TL;DR: In this paper, a simplified derivation of the relativistic three-particle quantization condition for identical, spinless particles described by a generic field theory satisfying a 2-symmetric symmetry was presented.
Abstract: We present a simplified derivation of the relativistic three-particle quantization condition for identical, spinless particles described by a generic relativistic field theory satisfying a ${\mathbb{Z}}_{2}$ symmetry. The simplification is afforded by using a three-particle quasilocal K matrix that is not fully symmetrized, ${\stackrel{\texttildelow{}}{\mathcal{K}}}_{\mathrm{df},3}^{(u,u)}$, and makes extensive use of time-ordered perturbation theory (TOPT). We obtain a new form of the quantization condition. This new form can then be related algebraically to the standard quantization condition, which depends on a fully symmetric three-particle K matrix, ${\mathcal{K}}_{\mathrm{df},3}$. The new derivation is fully explicit, allowing, for example, a closed-form expression for ${\mathcal{K}}_{\mathrm{df},3}$ to be given in terms of TOPT amplitudes. The new form of the quantization condition is similar in structure to that obtained in the ``finite-volume unitarity'' approach, and in a companion paper we make this connection concrete. Our simplified approach should also allow a more straightforward generalization of the quantization condition to nondegenerate particles, and perhaps also to more than three particles.
42 citations
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TL;DR: In this article, the low energy representation of several Green's functions and form factors and of the na scattering amplitude are calculated in terms of a few constants, which may be identified with the coupling constants of a unique effective low energy Lagrangian.
3,277 citations
TL;DR: The low-lying energy values associated to energy eigenstates describing two stable particles enclosed in a (space-like) box of sizeL are shown to be expandable in an asymptotic power series of 1/L as mentioned in this paper.
Abstract: The low-lying energy values associated to energy eigenstates describing two stable particles enclosed in a (space-like) box of sizeL are shown to be expandable in an asymptotic power series of 1/L The coefficients in these expansions are related to the appropriate elastic scattering amplitude in a simple and apparently universal manner At low energies, the scattering amplitude can thus be determined, if an accurate calculation of two-particle energy values is possible (by numerical simulation, for example)
1,060 citations
TL;DR: In this paper, the energy spectrum of a system of two particles enclosed in a box with periodic boundary conditions is determined by the scattering phases at these energies, and exact exact formulae are derived which can be used to compute the energy levels given the scattering phase.
968 citations
TL;DR: In this article, the authors describe the structure of neutron stars constructed from the unified equations of states with crossover, and present the current equations of state-called "QHC18" for quark-hadron crossover-in a parametrized form practical for neutron star modeling.
Abstract: In recent years our understanding of neutron stars has advanced remarkably, thanks to research converging from many directions. The importance of understanding neutron star behavior and structure has been underlined by the recent direct detection of gravitational radiation from merging neutron stars. The clean identification of several heavy neutron stars, of order two solar masses, challenges our current understanding of how dense matter can be sufficiently stiff to support such a mass against gravitational collapse. Programs underway to determine simultaneously the mass and radius of neutron stars will continue to constrain and inform theories of neutron star interiors. At the same time, an emerging understanding in quantum chromodynamics (QCD) of how nuclear matter can evolve into deconfined quark matter at high baryon densities is leading to advances in understanding the equation of state of the matter under the extreme conditions in neutron star interiors. We review here the equation of state of matter in neutron stars from the solid crust through the liquid nuclear matter interior to the quark regime at higher densities. We focus in detail on the question of how quark matter appears in neutron stars, and how it affects the equation of state. After discussing the crust and liquid nuclear matter in the core we briefly review aspects of microscopic quark physics relevant to neutron stars, and quark models of dense matter based on the Nambu-Jona-Lasinio framework, in which gluonic processes are replaced by effective quark interactions. We turn then to describing equations of state useful for interpretation of both electromagnetic and gravitational observations, reviewing the emerging picture of hadron-quark continuity in which hadronic matter turns relatively smoothly, with at most only a weak first order transition, into quark matter with increasing density. We review construction of unified equations of state that interpolate between the reasonably well understood nuclear matter regime at low densities and the quark matter regime at higher densities. The utility of such interpolations is driven by the present inability to calculate the dense matter equation of state in QCD from first principles. As we review, the parameters of effective quark models-which have direct relevance to the more general structure of the QCD phase diagram of dense and hot matter-are constrained by neutron star mass and radii measurements, in particular favoring large repulsive density-density and attractive diquark pairing interactions. We describe the structure of neutron stars constructed from the unified equations of states with crossover. Lastly we present the current equations of state-called 'QHC18' for quark-hadron crossover-in a parametrized form practical for neutron star modeling.
440 citations
TL;DR: In this article, a coupled-channel formalism was employed to simultaneously fit elastic scattering and charge-exchange data to 0.8 GeV and 2.6 GeV in the lab pion kinetic energy.
Abstract: We present results from a comprehensive partial-wave analysis of ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$ elastic scattering and charge-exchange data, covering the region from threshold to 2.6 GeV in the lab pion kinetic energy, employing a coupled-channel formalism to simultaneously fit ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}\ensuremath{\eta}n$ data to 0.8 GeV. Our main result, solution SP06, utilizes a complete set of forward and fixed-$t$ dispersion relation constraints applied to the $\ensuremath{\pi}N$ elastic amplitude. The results of these analyses are compared with previous solutions in terms of their resonance spectra and preferred values for couplings and low-energy parameters.
361 citations