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Register a new userSignatures of few-body resonances in finite volume
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We study systems of bosons and fermions in finite periodic boxes and show how the existence and properties of few-body resonances can be extracted from studying the volume dependence of the calculated energy spectra. Using a plane-wave-based discrete variable representation to conveniently implement periodic boundary conditions, we establish that avoided level crossings occur in the spectra of up to four particles and can be linked to the existence of multi-body resonances. To benchmark our method we use two-body calculations, where resonance properties can be determined with other methods, as well as a three-boson model interaction known to generate a three-boson resonance state. Finding good agreement for these cases, we then predict three-body and four-body resonances for models using a shifted Gaussian potential. Our results establish few-body finite-volume calculations as a new tool to study few-body resonances. In particular, the approach can be used to study few-neutron systems, where such states have been conjectured to exist.
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The structures of the hyperon resonance $Lambda (1405)$ and the scalar mesons $sigma$, $f_{0}(980)$, and $a_{0}(980)$ are investigated based on the coupled-channels chiral dynamics with finite volume effect. The finite volume effect is utilized to extract the coupling constant, compositeness, and mean squared distance between two constituents of a Feshbach resonance state as well as a stable bound state. In this framework, the real-valued size of the resonance can be defined from the downward shift of the resonance pole according to the decreasing finite box size $L$ on a given closed channel. As a result, we observe that, when putting the $bar{K}N$ and $Kbar{K}$ channels into a finite box while other channels being unchanged, the poles of the higher $Lambda (1405)$ and $f_{0}(980)$ move to lower energies while other poles do not show downward mass shift, which implies large $bar{K}N$ and $Kbar{K}$ components inside higher $Lambda (1405)$ and $f_{0}(980)$, respectively. Extracting structures of $Lambda (1405)$ and $f_{0}(980)$ in our method, we find that the compositeness of $bar{K}N$ ($Kbar{K}$) inside $Lambda (1405)$ [$f_{0}(980)$] is 0.82-1.03 (0.73-0.97) and the mean distance between two constituents is evaluated as 1.7-1.9 fm (2.6-3.0 fm).
Pionless effective field theory in a finite volume (FVEFT$_{pi!/}$) is investigated as a framework for the analysis of multi-nucleon spectra and matrix elements calculated in lattice QCD (LQCD). By combining FVEFT$_{pi!/}$ with the stochastic variational method, the spectra of nuclei with atomic number $Ain{2,3}$ are matched to existing finite-volume LQCD calculations at heavier-than-physical quark masses corresponding to a pion mass $m_pi=806$ MeV, thereby enabling infinite-volume binding energies to be determined using infinite-volume variational calculations. Based on the variational wavefunctions that are constructed in this approach, the finite-volume matrix elements of various local operators are computed in FVEFT$_{pi!/}$ and matched to LQCD calculations of the corresponding QCD operators in the same volume, thereby determining the relevant one and two-body EFT counterterms and enabling an extrapolation of the LQCD matrix elements to infinite volume. As examples, the scalar, tensor, and axial matrix elements are considered, as well as the magnetic moments and the isovector longitudinal momentum fraction.
We show that the contributions of three-quasiparticle interactions to normal Fermi systems at low energies and temperatures are suppressed by n_q/n compared to two-body interactions, where n_q is the density of excited or added quasiparticles and n is the ground-state density. For finite Fermi systems, three-quasiparticle contributions are suppressed by the corresponding ratio of particle numbers N_q/N. This is illustrated for polarons in strongly interacting spin-polarized Fermi gases and for valence neutrons in neutron-rich calcium isotopes.
Hadronic composite states are introduced as few-body systems in hadron physics. The $Lambda(1405)$ resonance is a good example of the hadronic few-body systems. It has turned out that $Lambda(1405)$ can be described by hadronic dynamics in a modern technology which incorporates coupled channel unitarity framework and chiral dynamics. The idea of the hadronic $bar KN$ composite state of $Lambda(1405)$ is extended to kaonic few-body states. It is concluded that, due to the fact that $K$ and $N$ have similar interaction nature in s-wave $bar K$ couplings, there are few-body quasibound states with kaons systematically just below the break-up thresholds, like $bar KNN$, $bar KKN$ and $bar KKK$, as well as $Lambda(1405)$ as a $bar KN$ quasibound state and $f_{0}(980)$ and $a_{0}(980)$ as $bar KK$.
We resum the ladder diagrams for the calculation of the energy density $cal{E}$ of a spin 1/2 fermion many-body system in terms of arbitrary vacuum two-body scattering amplitudes. The partial-wave decomposition of the in-medium two-body scattering amplitudes is developed, and the expression for calculating $cal{E}$ in a partial-wave amplitude expansion is also given. The case of contact interactions is completely solved and is shown to provide renormalized results, expressed directly in terms of scattering data parameters, within cutoff regularization in a wide class of schemes. $S$- and $P$-wave interactions are considered up to including the first three-terms in the effective-range expansion, paying special attention to the parametric region around the unitary limit.
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