Effective Range Corrections from Effective Field Theory with Dibaryon Fields and Perturbative Pions

We discuss a role of dibaryon fields in an effective field theory to study pion cloud effect around the unitary limit of two-nucleon systems at low energies.     

Nuclear Forces from Effective Field Theory

Chiral effective field theory allows for a systematic and model-independent derivation of the forces between nucleons in harmony with the symmetries of the quantum chromodynamics. After a brief review on the current status in the development of the chiral nuclear forces I will focus on the role of the ??-resonance contributions in the nuclear dynamics. We find improvement in the convergence of the chiral expansion of the nuclear forces if we explicitly take into account the ??-resonance degrees of freedom. The overall results for two-nucleon forces with and without explicit ??-resonance degrees of freedom are remarkably similar.     

Pions in Nuclear Effective Field Theory: How They Behave Differently at Different Scales and How They Decouple at Very Low Energies

We explain how the Wilsonian renormalization group (RG) can determine the power counting of the nuclear effective field theory (NEFT) including pions. We emphasize that the separation of pion exchange into the short-distance part and the long-distance part is essential since they behave differently in the RG analysis; we found that the latter is perturbative whereas the a part of the former is nonperturbative. As for the contact interactions power counting turns out to be the same as that for pionless NEFT: pion exchange does not affect the scaling property of contact operators. Our RG equations for NEFT including pions connect smoothly with those for the pionless NEFT: pions decouple at very low energies as we expect.     

Nuclear Forces from Chiral Effective Field Theory: Achievements and Challenges

In the past decade, there has been substantial progress in the derivation of nuclear forces from chiral effective field theory. Accurate two-nucleon forces have been constructed at next-to-next-to-next-to-leading order (N³LO) and applied (together with three-nucleon forces at NNLO) to nuclear few- and many-body systems—with a good deal of success. This may suggest that the 80-year old nuclear force problem has finally been cracked. Not so! Some pretty basic issues are still unresolved. In this talk, I focus on the two most pressing ones, namely, the proper renormalization of the two-nucleon potential and subleading many-body forces.     

An Effective Field Theory Model to Describe Nuclear Matter in Heavy-Ion Collisions

Relativistic mean field theory with mesons , , and mediating interactions and nucleons as basic fermions has been very successful in describing nuclear matter and finite nuclei. However, in heavy-ion collisions, where the c. m. energy of two colliding nucleons will be in the hundreds of GeV region, nucleons are not expected to behave as point-like particles. Analyses of elastic pp and ¯pp scattering data in the relevant c. m. energy range show that the nucleon is a composite object—a topological soliton or Skyrmion embedded in a condensed quark-antiquark ground state. Against this backdrop, we formulate an effective field theory model of nuclear matter based on the gauged linear -model where quarks are the basic fermions, but the mesons still mediate the interactions. The model describes the nucleon as a Skyrmion and produces a q¯q ground state analogous to a superconducting ground state. Quarks are quasi-particles in this ground state. When the temperature exceeds a critical value, the scalar field in the ground state vanishes, quarks become massless, and a chiral phase transition occurs leading to chiral symmetry restoration. We explore the possibility of a first order phase transition in this model by introducing suitable self-interactions of the scalar field. Internal structures of the Skyrmions are ignored, and they are treated as point-like fermions.     

An Effective Stochastic Semiclassical Theory for the Gravitational Field

Assuming that the mechanism proposed byGell-Mann and Hartle works as a mechanism fordecoherence and classicalization of the metric field, weformally derive the form of an effective theory for thegravitational field in a semiclassical regime. This effectivetheory takes the form of the usual semiclassical theoryof gravity, based on the semiclassical Einsteinequation, plus a stochastic correction which accounts for the backreaction of the lowest order matterstress-energy fluctuations.     

Effective Field Theory and the Gamow Shell Model

We combine halo/cluster effective field theory (H/CEFT) and the Gamow shell model (GSM) to describe the 0⁺ ground state of ⁶He as a three-body halo system. We use two-body interactions for the neutron-alpha particle and two-neutron pairs obtained from H/CEFT at leading order, with parameters determined from scattering in the p_3/2 and s₀ channels, respectively. The three-body dynamics of the system is solved using the GSM formalism, where the continuum states are incorporated in the shell model valence space. We find that in the absence of three-body forces the system collapses, since the binding energy of the ground state diverges as cutoffs are increased. We show that addition at leading order of a three-body force with a single parameter is sufficient for proper renormalization and to fix the binding energy to its experimental value.     

Effective Field Theory for Few Particles in a Trap

In this contribution we show applications of effective field theory (EFT) to few-particle systems trapped in a harmonic oscillator potential. The principles of EFT allows to construct interactions among the particles in a systematic and improvable manner. We first consider systems of two-component fermions and show excellent agreements with the exact solution at unitarity (for the two- and three-body problem) and results obtained by other methods (in the four-body case). We then consider trapped systems of three nucleons and extract neutron–deuteron phase shifts, and show that the quartet scattering length is in good agreement with experimental data. We also show the collapse of the system in the J ^π  = 1/2⁺, T = 1/2 (triton) channel at Leading-Order when no three-nucleon force is included.     

相对论平均场理论中的有效超子-核子相互作用

利用相对论平均场理论,结合单超核的实验数据,研究了核介质中的Λ超子–核子有效相互作用.通过符合13ΛC超核中Λ超子1s轨道的结合能实验值,给出了5组Λ超子–核子有效相互作用参数.利用这些参数组对质量数从9到2?0?8的单Λ超核和核物质中最低Λ态的束缚能进行了系统计算,得到的结果与实验值相符.     

Renormalization Group Invariance in Pionless Effective Field Theory for the NN System

We consider the NN interaction in pionless effective field theory (EFT) up to next-to-next-to-leading order (NNLO) and use a recursive subtractive renormalization scheme to describe NN scattering in the ¹ S ₀ channel. We fix the strengths of the contact interactions at a reference scale, chosen to be the one that provides the best fit for the phase-shifts, and then slide the renormalization scale by evolving the driving terms of the subtracted Lippmann?CSchwinger equation through a non-relativistic Callan?CSymanzik equation. The results show that such a systematic renormalization scheme with multiple subtractions is fully renormalization group invariant.     

Effective Field Theory Description of the Higher Dimensional Quantum Hall Liquid

We derive an effective topological field theory model of the four dimensional quantum Hall liquid state recently constructed by Zhang and Hu. Using a generalization of the flux attachment transformation, the effective field theory can be formulated as a U(1) Chern–Simons theory over the total configuration space CP₃, or as a SU(2) Chern–Simons theory over S⁴. The new quantum Hall liquid supports various types of topological excitations, including the 0-brane (particles), the 2-brane (membranes), and the 4-brane. There is a topological phase interaction among the membranes which generalizes the concept of fractional statistics.     

Effective Field Theory for Fermi Systems in a Large N Expansion

A system of fermions with short-range interactions at finite density is studied using the framework of effective field theory. The effective action formalism for fermions with auxiliary fields leads to a loop expansion in which particle-hole bubbles are resummed to all orders. For spin-independent interactions, the loop expansion is equivalent to a systematic expansion in 1/N, where N is the spin-isospin degeneracy g. Numerical results at next-to-leading order are presented and the connection to the Bose limit of this system is elucidated.     

Boson Mean Field Theory of Effective Holon-Holon Interaction in the RVB Model

The RVB model is investigated by a mean field theory, in which the holon is expressed by a fermion operator, and the spinon by a boson operator. The effective holon-holon interaction by exchanging the spinons is derived for T≠0. It is found that the interaction is attractive.     

Determining Nuclear Form factor for Detection of Dark Matter in Relativistic Mean Field Theory

In this work, we derive the nuclear form factor for the spin-independent collision between the WIMPs and nucleus in terms of the relativistic mean field (RMF) theory. Comparison with the traditional form factors which are commonly used in literature is given and it is found that our results are slightly above that of the 2PF model by 4% to 8%, but deviate from the Helm form factor by 15% to 25% for the whole recoil energy spectrum of 0 ∽ 100keV. Moreover, taking Xe and Ge as examples, we show the dependenceof the form factor on the recoil energy.     

Cornwall-Jackiw-Tomboulis Effective Potential for Quark Propagator in Real-Time Thermal Field Theory and Landau Gauge

We complete the derivation of the Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperature and finite quark chemical potential in the real-time formalism of thermal field theory and in Landau gauge. In the approximation that the function A(p2) in inverse quark propagator is replaced by unity, by means of the running gauge coupling and the quark mass function invariant under the renormalization group in zero temperature Quantum Chromadynamics (QCD), we obtain a calculable expression for the thermal effective potential, which will be a useful means to research chiral phase transition in QCD in the real-time formalism.