I=3/2Nπ scattering and the ∆(1232) resonance on $N_f=2+1$ CLS ensembles using the stochastic LapH method

Andersen, Christian Walther; Bulava, John; Hörz, Ben; Morningstar, Colin

doi:10.22323/1.363.0039

Cited by 5 publications

(4 citation statements)

References 25 publications

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“…With this information we can now construct the relevant states to remove from the amplitude. In both these irreps, the calculation is analogous to a phase-shift analysis for J = 1/2 N π scattering, similar to what has been done in [30,31]. The operator basis is different in the two irreps and includes both N π interpolators with different back-to-back momenta (for G − 1 , this includes an operator with both operators projected to zero spatial momentum, but for G + 1 , at least one unit of back-to-back momentum is required).…”

Section: Jhep04(2023)108mentioning

confidence: 90%

“…The next step is to perform an N π scattering analysis as has been done in refs. [30,31] and as we outline in appendix D. This involves obtaining the finite-volume energies, which via the generalized Lüscher formalism lead to parametrizations of the phase shift δ(E) as well as its derivative. Similarly, a lattice computation of the three-point functions on the right-hand side of eq.…”

Section: Jhep04(2023)108mentioning

confidence: 99%

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Prospects for a lattice calculation of the rare decay Σ+ → pℓ+ℓ−

Erben

Gülpers

Hansen

et al. 2023

J. High Energ. Phys.

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We present a strategy for calculating the rare decay of a Σ+(uus) baryon to a proton (uud) and di-lepton pair using lattice QCD. To determine this observable one needs to numerically evaluate baryonic two-, three-, and four-point correlation functions related to the target process. In particular, the four-point function arises from the insertion of incoming and outgoing baryons, together with a weak Hamiltonian mediating the s → d transition and an electromagnetic current creating the outgoing leptons. As is described in previous work in other contexts, this four-point function has a highly non-trivial relation to the physical observable, due to proton and proton-pion intermediate states. These lead to growing Euclidean time dependence and, in the case of the two-particle intermediate states, to power-like volume effects. We discuss how to treat these issues in the context of the Σ+ → pℓ+ℓ− decay and, in particular, detail the relation between the finite-volume estimator and the physical, complex-valued amplitude. In doing so, we also make connections between various approaches already described in the literature.

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Section: Jhep04(2023)108mentioning

confidence: 90%

Section: Jhep04(2023)108mentioning

confidence: 99%

Prospects for a lattice calculation of the rare decay Σ+ → pℓ+ℓ−

Erben

Gülpers

Hansen

et al. 2023

J. High Energ. Phys.

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show abstract

“…As a first step toward understandings of exotic hadrons including pentaquarks, we focus our attention on decuplet baryons, spin 3/2 baryons symmetric under quark flavor exchanges, since all decuplet baryons except Ω appear as resonances. There are studies on decay properties of the process ∆ → N π by extracting the transfer matrix elements in lattice QCD [8,9], and are also several studies on the N π scatterings for the ∆ baryon in the finitevolume method at the lighter quark masses [10][11][12][13][14], where signals of the ∆ as a resonance are observed.…”

Section: Introductionmentioning

confidence: 99%

Investigations of decuplet baryons from meson-baryon interactions in the HAL QCD method

Murakami¹,

Akahoshi²,

Aoki³

et al. 2022

Proceedings of the 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021)

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We study decuplet baryons from meson-baryon interactions in lattice QCD, in particular, ∆ and Ω baryons from P-wave I = 3/2 N π and I = 0 Ξ K interactions, respectively. Interaction potentials are calculated in the HAL QCD method using 3-quark-type source operators at m π ≈ 410 MeV and m K ≈ 635 MeV, where ∆ as well as Ω baryons are stable. We use the conventional stochastic estimate of all-to-all propagators combined with the all-mode averaging to reduce statistical fluctuations. We have found that the Ξ K system has a weaker attraction than the N π system while the binding energy from the threshold is larger for Ω than ∆. This suggests that an inequalitymainly from a smaller spatial size of a Ξ K bound state due to a larger reduced mass, rather than its interaction. Root-mean-square distances of bound states in both systems are small, indicating that ∆ and Ω are tightly bound states and thus can be regarded qualitatively as composite states of 3 quarks. Results of binding energies agree with those obtained from temporal 2-point functions within large systematic errors, which arise dominantly from the lattice artifact at short distances.

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“…[34]. For the nucleon-pion scattering only a handful of studies have been done in the N π channel [35][36][37][38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

P-wave nucleon-pion scattering amplitude in the $Δ(1232)$ channel from lattice QCD

Silvi,

Paul,

Alexandrou

et al. 2021

Preprint

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We determine the ∆(1232) resonance parameters using lattice QCD and the Lüscher method. The resonance occurs in elastic pion-nucleon scattering with J P = 3/2 + in the isospin I = 3/2, P -wave channel. Our calculation is performed with N f = 2 + 1 flavors of clover fermions on a lattice with L ≈ 2.8 fm. The pion and nucleon masses are mπ = 255.4(1.6) MeV and mN = 1073(5) MeV, respectively, and the strong decay channel ∆ → πN is found to be above the threshold. To thoroughly map out the energy-dependence of the nucleon-pion scattering amplitude, we compute the spectra in all relevant irreducible representations of the lattice symmetry groups for total momenta up to P = 2π L (1, 1, 1), including irreps that mix S and P waves. We perform global fits of the amplitude parameters to up to 21 energy levels, using a Breit-Wigner model for the P -wave phase shift and the effective-range expansion for the S-wave phase shift. From the location of the pole in the P -wave scattering amplitude, we obtain the resonance mass m∆ = 1378(7) MeV and the coupling g∆-πN = 23.8(2.7).

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I=3/2Nπ scattering and the ∆(1232) resonance on $N_f=2+1$ CLS ensembles using the stochastic LapH method

Cited by 5 publications

References 25 publications

Prospects for a lattice calculation of the rare decay Σ+ → pℓ+ℓ−

Prospects for a lattice calculation of the rare decay Σ+ → pℓ+ℓ−

Investigations of decuplet baryons from meson-baryon interactions in the HAL QCD method

P-wave nucleon-pion scattering amplitude in the $Δ(1232)$ channel from lattice QCD

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