Lattice QCD studies on baryon resonances and pentaquarks from meson-baryon scatterings

概要

therefore are evaluated approximately. The first attempt at the study of resonances in the HAL
QCD method is the investigation of the ρ resonance from P-wave I = 1 ππ scatterings using the
LapH method [20], which has found that the technique is not applicable because it worsens the
truncation approximation of the derivative expansion of the non-local potential. There is also
work for the same scattering system which employs the hybrid method [21], concluding that this
is not useful in the HAL QCD method due to its large fluctuation coming from the noise vectors.
Recently, Akahoshi et al. proposed an improved calculation technique for all-to-all propagators
to avoid these difficulties as much as possible, in which they use the one-end trick combined
with the covariant-approximation averaging (CAA). The authors also applied it to the P-wave
I = 1 ππ scatterings [22], and then extracted the signal of the ρ resonance successfully. This
work plays a role in opening a new frontier of the studies on meson resonances and tetraquarks
using the HAL QCD method, which, together with the studies in the finite-volume method, will
develop the understanding of their properties.
In our studies, towards the researches of baryon resonances and pentaquarks, we try to
analyze meson-baryon scatterings having quark pair creation and annihilation using a similar
technique to Ref. [22]. Since the HAL QCD method is advantageous compared with the finitevolume method in that it can avoid the problem due to the existence of a baryon, it is worth
analyzing such scattering systems from the approach of the HAL QCD method. As a first step,
we investigate the S = +1 S-wave nucleon-kaon (N K) scatterings, which allow no quark pair
creation and annihilation. This study has the aspect of a test of the efficiency of the technique
for the meson-baryon systems. We employ all-to-all propagators together with the one-end trick
and the CAA as a calculation technique for the propagators. Thanks to the all-to-all propagators,
we can use the hadron operators with zero momenta at both source and sink together with the
smeared quark operators at the source in this study.
The next study in this thesis is the analysis of P-wave I = 3/2 nucleon-pion (N π) and I = 0
¯ ) scatterings, which couple to ∆ and Ω baryons, respectively. This is
Ξ baryon-antikaon (ΞK
the first study on meson-baryon scatterings having the quark pair creation and annihilation in
the HAL QCD method. In order to reduce computational costs, we employ the heavy quark
masses, where u, d quark masses are close to the s quark mass. In this case, ∆ baryon exists as
a stable particle as well as Ω, which is more or less far from the situation in nature. We use a
3-quark-type source operator with zero momentum, which requires an all-to-all propagator, and
then employ the conventional stochastic technique together with CAA.
Furthermore, in this thesis, we show the preliminary study on Λ(1405), one of the exotic
¯ scatterings,
hadrons, in the flavor SU(3) limit. As is the case of the analysis of the N π and ΞK
we introduce an all-to-all propagator to use a 3-quark-type source operator with zero momentum,
and then we employ the conventional stochastic technique together with CAA.
This thesis is organized as follows. In Chapter 2, we define the lattice QCD theory and
review how to calculate the correlation functions in lattice QCD. Then in Chapter 3, we derive an
asymptotic behavior of the Nambu-Bethe-Salpeter wave function and introduce the HAL QCD
method. In Chapter 4, we express the all-to-all propagator techniques that we use in our studies:
the stochastic estimation and the one-end trick, and then explain the covariant approximation
averaging, which is an efficient method to increase statistics. We show our studies of S-wave
¯ scatterings in Chapter 6. In Chapter 7,
N K scatterings in Chapter 5, and P-wave N π and ΞK
we present our preliminary study on meson-baryon scatterings to study Λ(1405) in flavor SU(3)
limit. Chatper 8 is devoted to the summary and discussion. ...

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