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Register a new userA chiral effective field theory study of hadronic parity violation in few-nucleon systems
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We reconsider the derivation of the nucleon-nucleon parity-violating (PV) potential within a chiral effective field theory framework. We construct the potential up to next-to-next-to-leading order by including one-pion-exchange, two-pion-exchange, contact, and 1/M (M being the nucleon mass) terms, and use dimensional regularization to renormalize the pion-loop corrections. A detailed analysis of the number of independent low-energy constants (LECs) entering the potential is carried out. We find that it depends on six LECs: the pion-nucleon PV coupling constant $h^1_pi$ and five parameters multiplying contact interactions. We investigate PV effects induced by this potential on several few-nucleon observables, including the $vec{p}$-$p$ longitudinal asymmetry, the neutron spin rotation in $vec{n}$-$p$ and $vec{n}$-$d$ scattering, and the longitudinal asymmetry in the $^3$He$(vec{n},p)^3$H charge-exchange reaction. An estimate for the range of values of the various LECs is provided by using available experimental data.
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A systematic description of low-energy observables in light nuclei is presented. The effective field theory formalism without pions is extended to: i) predictions with next-to-leading-order (non-perturbatively) accuracy for the 4-helium binding energy B({alpha}), the triton charge radius, and the 3-helium-neutron scattering length; ii) phase shifts for neutron-deuteron scattering and {alpha}-neutron low-energy scattering at leading order; iii) the ground states of the 5-helium (with and without Coulomb interaction) and 6-helium isotopes up to next-to-leading order; The convergence from leading- to next-to-leading order of the theory is demonstrated for correlations between: i) the triton binding energy B(t) and the triton charge radius; ii) B(t) and the 4-helium binding energy B({alpha}); Furthermore, a correlation between B(t) and the scattering length in the singlet S-wave channel of neutron-helium-3 scattering is discovered, and a model-independent estimate for the trinucleon binding energy splitting is provided. The results provide evidence for the usefulness of the applied power-counting scheme, treating next-to-leading-order interactions nonperturbatively and four-nucleon interactions as, at least, one order higher. The 5- and 6-helium ground states are analyzed with a power-counting scheme which includes the momentum-dependent next-to-leading order vertices perturbatively. All calculations include a full treatment of the Coulomb interaction. The assessment of numerical uncertainties associated with the solution of the few-body equation of motion through the Resonating Group Method parallels the report of the results for light nuclei in order to establish this method as practical for the analysis of systems with up to six particles interacting via short-range interactions.
The history and phenomenology of hadronic parity nonconservation (PNC) is reviewed. We discuss the current status of the experimental tests and theory. We describe a re-analysis of the asymmetry for polarized proton-proton scattering that, when combined with other experimental constraints and with a recent lattice QCD calculation of the weak pion-nucleon coupling, reveals a much more consistent pattern of PNC couplings. In particular, isoscalar coupling strengths are similar to but somewhat larger than the best value estimate of Donoghue, Desplanques, and Holstein, while both lattice QCD and experiment indicate a suppressed parity-nonconserving pion-nucleon coupling. We discuss the relationship between meson-exchange models of hadronic PNC and formulations based on effective theory, stressing their general compatibility as well as the challenge presented to theory by experiment, as several of the most precise measurements involve significant momentum scales. Future directions are proposed.
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.
The $Lambda N$ and $Sigma N$ interactions are considered at next-to-leading order in SU(3) chiral effective field theory. Different options for the low-energy constants that determine the strength of the contact interactions are explored. Two variants are analysed in detail which yield equivalent results for $Lambda N$ and $Sigma N$ scattering observables but differ in the strength of the $Lambda N to Sigma N$ transition potential. The influence of this difference on predictions for light hypernuclei and on the properties of the $Lambda$ and $Sigma$ hyperons in nuclear matter is investigated and discussed. The effect of the variation in the potential strength of the $Lambda N$-$Sigma N$ coupling (also called $Lambda -Sigma$ conversion) is found to be moderate for the considered $^3_Lambda rm H$ and $^4_Lambda rm He$ hypernuclei but sizable in case of the matter properties. Further, the size of three-body forces and their relation to different approaches to hypernuclear interactions is discussed.
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 $bar KK$.
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