Fitting two nucleons inside a box: Exponentially suppressed corrections to Lüscher’s formula

Sato, Ikuro; Bedaque, Paulo F.

doi:10.1103/physrevd.76.034502

Cited by 41 publications

(31 citation statements)

References 13 publications

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“…(3) to the infinite-volume limit to determine the binding energy of the bound state, B ∞ = γ 2 /m. The range of nuclear interactions is set by the pion mass, and therefore the use of Lüscher's method requires that m π L 1 in order to strongly suppress the contributions that depend upon the volume as e −mπL [27].…”

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confidence: 99%

Evidence for a BoundHDibaryon from Lattice QCD

et al. 2011

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We present evidence for the existence of a bound H-dibaryon, an I = 0, J = 0, s = −2 state with valence quark structure uuddss, at a pion mass of mπ ∼ 389 MeV. Using the results of Lattice QCD calculations performed on four ensembles of anisotropic clover gauge-field configurations, with spatial extents of L ∼ 2.0, 2.5, 3.0 and 3.9 fm at a spatial lattice spacing of bs ∼ 0.123 fm, we find an H-dibaryon bound by B H ∞ = 16.6 ± 2.1 ± 4.6 MeV at a pion mass of mπ ∼ 389 MeV.It is now well established that quantum chromodynamics (QCD), the theory describing the dynamics of quarks and gluons, and the electroweak interactions, underlie all of nuclear physics, from the hadronic mass spectrum to the synthesis of heavy elements in stars. To date, there have been few quantitative connections between nuclear physics and QCD, but fortunately, Lattice QCD is entering an era in which precise predictions for hadronic quantities with quantifiable errors are being made. This development is particularly important for processes which are difficult to explore in the laboratory, such as hyperon-hyperon and hyperon-nucleon interactions for which knowledge is scarce, primarily due to the short lifetimes of the hyperons, but which may impact the late-stages of supernovae evolution. In this letter we report strong evidence for a bound H-dibaryon, a six-quark hadron with valence structure uuddss, from n f = 2 + 1 Lattice QCD calculations at light-quark masses that give the pion a mass of m π ∼ 389 MeV.The prediction of a relatively deeply bound system with the quantum numbers of ΛΛ (called the H-dibaryon) by Jaffe [1] in the late 1970s, based upon a bag-model calculation, started a vigorous search for such a system, both experimentally and also with alternate theoretical tools. Experimental constraints on, and phenomenological models of, the H-dibaryon can be found in Refs. [2,3,4]. While experimental studies of doublystrange hypernuclei restrict the H-dibaryon to be unbound or to have a small binding energy, the most recent constraints on the existence of the H-dibaryon come from heavy-ion collisions at RHIC, from which it is concluded that the H-dibaryon does not exist in the mass region 2.136 < M H < 2.231 GeV [5], effectively eliminating the possibility of a loosely-bound H-dibaryon at the physical light-quark masses. Recent experiments at KEK suggest there is a resonance near threshold in the H-dibaryon channel [6].The first study of baryon-baryon interactions with Lattice QCD was performed more than a decade ago [7,8]. This calculation was quenched and with m π > ∼ 550 MeV. The NPLQCD collaboration performed the first n f = 2+ 1 QCD calculations of baryon-baryon interactions [9,10] at low-energies but at unphysical pion masses. Quenched and dynamical calculations were subsequently performed by the HALQCD collaboration [11,12]. A number of quenched Lattice QCD calculations [13,14,15,16,17,18] have searched for the H-dibaryon, but to date no definitive results have been reported. Earlier work concluded that the H-dibaryon does not exi...

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confidence: 99%

Evidence for a BoundHDibaryon from Lattice QCD

et al. 2011

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“…In the end, this effect reflects the necessity of the inclusion of pions in the effective theory for the correct description of processes where momenta are of the order of the pion mass. However, we find that the size of the corrections is smaller than naively expected: for the smallest box size with m π L = 3.5 the leading effect should scale as c 1 e −mπL = 18% [34], where c 1 = 6 denotes the multiplicity of nearest neighbors, but the actually observed deviation merely amounts to about 3%. This finding could be related to the observation in [34] that for a realistic NN potential the effective scale in the exponent can exceed the pion mass, leading to a stronger suppression than expected from the one-pion exchange alone.…”

Section: Chiral Eft Interactionsmentioning

confidence: 53%

“…In Ref. [34], the size of these corrections in the two-nucleon system was estimated for EFT-inspired potentials with pion exchange and contact interactions.…”

Section: Lüscher Formulamentioning

confidence: 99%

Quantum Monte Carlo calculations of two neutrons in finite volume

Klos¹,

Lynn²,

Tews³

et al. 2016

Phys. Rev. C

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Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finite-volume effects, whose understanding is crucial for determining observables from the calculated energies. Using the Lüscher formula, we extract the low-energy S-wave scattering parameters from ground-and excited-state energies for different box sizes.

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“…We will neglect any terms in the correlation function that are exponentially suppressed with the mass of any particle in any coupled channel since O(e −m i L ) ≤ O(e −mπL ). These corrections have been previously determine for ππ [229] and N N systems [230] in an S-wave, as well as the ππ system in a P-wave in Ref. [231,232].…”

Section: Two-point Correlation Functionsmentioning

confidence: 99%

Multi-Hadron Observables from Lattice Quantum Chromodynamics

Hansen¹

2014

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Multi-Hadron Observables from Lattice Quantum Chromodynamics Maxwell T. HansenChair of the Supervisory Committee:Professor Stephen R. Sharpe Department of PhysicsWe describe formal work that relates the finite-volume spectrum in a quantum field theory to scattering and decay amplitudes. This is of particular relevance to numerical calculations performed using Lattice Quantum Chromodynamics (LQCD). Correlators calculated using LQCD can only be determined on the Euclidean time axis. For this reason the standard method of determining scattering amplitudes via the Lehmann-Symanzik-Zimmermann reduction formula cannot be employed. By contrast, the finite-volume spectrum is directly accessible in LQCD calculations. Formalism for relating the spectrum to physical scattering observables is thus highly desirable.In this thesis we develop tools for extracting physical information from LQCD for four types of observables. First we analyze systems with multiple, strongly-coupled two-scalar channels. Here we accommodate both identical and nonidentical scalars, and in the latter case allow for degenerate as well as nondegenerate particle masses. Using relativistic field theory, and summing to all orders in perturbation theory, we derive a result relating the finite-volume spectrum to the two-to-two scattering amplitudes of the coupled-channel theory. This generalizes the formalism of Martin Lüscher for the case of single-channel scattering. Second we consider the weak decay of a single particle into multiple, coupled two-scalar channels. We show how the finite-volume matrix element extracted in LQCD is related to matrix elements of asymptotic two-particle states, and thus to decay amplitudes. This generalizes work by Laurent Lellouch and Martin Lüscher. Third we extend the method for extracting matrix elements by considering currents which insert energy, momentum and angular momentum. This allows one to extract transition matrix elements and form factors from LQCD. Finally we look beyond two-particle systems to those with three-particles in asymptotic states. Working again to all orders in relativistic field theory, we derive a relation between the spectrum and an infinite-volume three-to-three scattering quantity. This final analysis is the most complicated of the four, because the all-orders summation is more difficult for this system, and also because a number of new technical issues arise in analyzing the contributing diagrams.

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Fitting two nucleons inside a box: Exponentially suppressed corrections to Lüscher’s formula

Cited by 41 publications

References 13 publications

Evidence for a BoundHDibaryon from Lattice QCD

Evidence for a BoundHDibaryon from Lattice QCD

Quantum Monte Carlo calculations of two neutrons in finite volume

Multi-Hadron Observables from Lattice Quantum Chromodynamics

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