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Shung-Ichi Ando

Publications and source records attributed to Shung-Ichi Ando.

27 records · Page 2Linked to original sources
arXiv2017

A renormalization method for three-boson system with a triboson field

A renormalization method that introduces an auxiliary field to represent a three-body bound state is studied in a three-boson system with a triboson field. A cutoff dependence in the three-boson system emerges as a limit cycle, and the cyclic singularity is renormalized by employing two methods: a standard method and the auxiliary field method. For each method, different sets of diagrams are involved for renormalization, and thus we numerically study three quantities: counter term for renormalization, scattering length of $s$-wave boson-diboson scattering, and normalized wavefunction. We confirm that the two methods would lead to the same result.

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arXiv2016

Elastic $α$-$^{12}$C scattering at low energies in cluster effective field theory

The elastic $α$-$^{12}$C scattering at low energies is studied employing an effective field theory in which the $α$ and $^{12}$C states are treated as elementary-like fields. We discuss scales of the theory at stellar energy region that the ${}^{12}$C($α$, $γ$)$^{16}$O process occurs, and then obtain an expression of the elastic scattering amplitudes in terms of effective range parameters. Using experimental data of the phase shifts for $l=0,1,2$ channels at low energies, for which the resonance regions are avoided, we fix values of the parameters and find that the phase shifts at the low energies are well reproduced by using three effective range parameters for each channel. Furthermore, we discuss problems and uncertainties of the present approach when the amplitudes are extrapolated to the stellar energy region.

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arXiv2016

Hypernuclei in Halo/Cluster Effective Field Theory

The light double $Λ$ hypernuclei, ${}_{ΛΛ}^{\ \ 4}$H and ${}_{ΛΛ}^{\ \ 6}$He, are studied as three-body $ΛΛd$ and $ΛΛα$ cluster systems in halo/cluster effective field theory at leading order. We find that the $ΛΛd$ system in spin-0 channel does not exhibit a limit cycle whereas the $ΛΛd$ system in spin-1 channel and the $ΛΛα$ system in spin-0 channel do. The limit cycle is associated with the formation of bound states, known as Efimov states, in the unitary limit. For the $ΛΛd$ system in the spin-0 channel we estimate the scattering length $a_0$ for $S$-wave $Λ$ hyperon-hypertriton scattering as $a_0=16.0\pm 3.0$ fm. We also discuss that studying the cutoff dependences in the $ΛΛd$ and $ΛΛα$ systems, the bound state of ${}_{ΛΛ}^{\ \ 4}$H is not an Efimov state but formed due to a high energy mechanism whereas that of ${}_{ΛΛ}^{\ \ 6}$He may be regarded as an Efimov state.

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arXiv2015

Investigation of the $nnΛ$ bound state in pionless effective theory

The possibility of an $nnΛ$ bound state is investigated in the framework of pionless effective field theory at leading order. A system of coupled integral equations are constructed in the spin-isospin basis, of which numerical solutions are investigated. In particular, we make use of the limit cycle behavior, i.e., cyclic singularities of coupled integral equations of the system, which would be associated with the formation of a three-body bound state, so-called the Efimov state, in the unitary limit. Furthermore, we find that, when the sharp momentum cutoff introduced in the integral equations is taken significantly larger than the hard scale of the effective theory, the coupling of a three-body contact interaction becomes cyclically singular indicating the onset of Efimov-like bound state formation. However, the paucity of empirical information to determine the parameters of the theory precludes a definitive conclusion on the existence of such a bound state. As a simple test of the feasibility of the $nnΛ$ bound system in nature, we explore the cutoff dependence of the theory, and uncertainties of the present study are discussed as well.

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arXiv2014

${}^{\ \ \ 6}_{ΛΛ} He$ in cluster effective field theory

The hypernucleus $\nuclide[6][ΛΛ]{He}$ is studied as a three-body ($ΛΛα$) cluster system in cluster effective field theory at leading order. We find that the three-body contact interaction exhibits the limit cycle when the cutoff in the integral equations is sent to the asymptotic limit, and thus it should be promoted to leading order. We also derive a determination equation of the limit cycle which reproduces the numerically obtained limit cycle. We then study the correlations between the double $Λ$ separation energy $B_{ΛΛ}^{}$ of $\nuclide[6][ΛΛ]{He}$ and the scattering length $a_{ΛΛ}^{}$ of the $S$-wave $ΛΛ$ scattering. The role of the scale in this approach is also discussed.

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arXiv2014

The Born series for $S$-wave quartet $nd$ scattering at small cutoff values

Perturbative expansions, the Born series, of the scattering length and the amplitude of $S$-wave neutron-deuteron scattering for spin quartet channel below deuteron breakup threshold are studied in pionless effective field theory at small cutoff values. A three-body contact interaction is introduced when the integral equation is solved using the small cutoffs. After renormalizing the three-body interaction by using the scattering length, we expand the integral equation as the ordinary and inverted Born series. We find that the scattering length and the phase shift are considerably well reproduced with a few terms of the inverted Born series at relatively large cutoff values, $Λ\simeq 100$ MeV.

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arXiv2014

${}_{ΛΛ}^{4}$H in halo effective field theory

The ${}_{ΛΛ}^{\ \ 4}$H bound state and the $S$-wave hypertriton(${}_Λ^{ \, 3}$H)-$Λ$ scattering in spin singlet and triplet channels below the hypertriton breakup momentum scale are studied in halo/cluster effective field theory at leading order by treating the ${}_{ΛΛ}^{\ \ 4}$H system as a three-cluster ($Λ$-$Λ$-deuteron) system. In the spin singlet channel, the amplitude is insensitive to the cutoff parameter $Λ_c$ introduced in the integral equation, and we find that there is no bound state. In this case, the scattering length of the hypertriton-$Λ$ scattering is found to be $a_0^{} = 16.0\pm 3.0$ fm. In the spin triplet channel, however, the amplitude obtained by the coupled integral equations is sensitive to $Λ_c$, and we introduce the three-body contact interaction $g_1^{} (Λ_c)$. After phenomenologically fixing $g_1^{} (Λ_c)$, we find that the correlation between the two-$Λ$ separation energy $B_{ΛΛ}$ from the $_{ΛΛ}^{\ \ 4}$H bound state and the scattering length $a_{ΛΛ}^{}$ of the $S$-wave $Λ$-$Λ$ scattering is significantly sensitive to the value of $Λ_c$.

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arXiv2012

Effective range corrections from effective field theory with di-baryon fields and perturbative pions

Contributions of perturbative pions around a non-trivial fixed point are studied by utilizing di-baryon fields. We calculate ${}^1S_0$ and ${}^3S_1$ phase shifts for the $np$ scattering at low energies up to one-pion-exchange contributions. We also calculate effective range parameters, $v_2$, $v_3$ and $v_4$ in the higher order of the effective range expansion, and obtain corrections of the effective range to the expressions previously reported by Cohen and Hansen. After the scattering length and the effective range are renormalized, we study the role of renormailzation scale parameter $μ$ and discuss the range of validity of the theory.

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