Session FH: Nuclear Theory

The Sp(3,$R$) model and rotational phenomena in light nuclei

The symplectic model, based on Sp(3,$R$)--the smallest algebra containing both the shell model Hamiltonian and the rotor algebra--has a close physical connection both to the microscopic shell model and the collective deformation and rotational degrees of freedom. Symplectic model calculations of light $p$-shell nuclei will be presented and discussed in the context of emerging rotational phenomena in no-core shell model (NCSM) calculations.   

Uncertainty Quantification for Nuclear Currents: A Bayesian $\chi$-EFT view of the Triton and $\beta^-$ Decay

Chiral Effective Field Theory ($\chi$-EFT) provides a framework for the generation and systematic improvement of model independent inter-nucleon interaction Hamiltonians and nuclear current operators. Within $\chi$-EFT, short and mid distance physics is encoded through a gradient expansion and multiple pion exchange parameterized by a set of low energy constants (LECs). The LECs are often constrained via non-linear least squares using nuclear bound state and scattering observables. This has produced reasonable low-energy descriptions in the past, but has been plagued by LECs that are unnaturally large. Additional issues manifest in medium mass nuclei where the $\chi$-EFT Hamiltonians fail to adequately describe saturation properties. It has been suggested that Bayesian approaches may remedy the unnaturally large LECs using carefully selected priors. Other analyses have suggested that the inclusion and feedback of nuclear currents into the constraints of the LECs may improve saturation properties. We combine these approaches using Markov chain Monte Carlo (MCMC) to study and quantify uncertainties in the Triton and the $\chi$-EFT axial-vector current, with the aim of providing a foundation for quantifying $\chi$-EFT uncertainties for weak processes in nuclei.   

The vacuum in light-front quantum field theory

Light-front formulations of quantum field theory have many advantages over canonical formulations of the theory, but they have properties that are difficult to reconcile with the canonical formulation. Two of these properties are the presence of ``zero modes'' and the triviality of the light-front vacuum. We discuss how both of these features can be reconciled with covariant formulations of the theory by considering the relation between the Wightman functions of the theory and the algebra of free fields restricted to a light front.   

The Extraction of Neutrino Flux from Inclusive Neutrino-Nucleus Reaction

Precise determination of neutrino flux, especially its energy dependence is crucial to advance physics of neutrino mixing parameters. Conventionally, quasi-elastic (QE) events are used to reconstruct the neutrino flux, since neutrino energy can be uniquely determined from observed muon energy and scattering angle. However, pure QE mechanism is main but part of the reaction mechanisms of neutrino reaction. Other mechanisms, such as rescattering, Fermi motion contribute. Moreover those mechanisms interfere with the QE amplitude. There will be limitation of the accuracy of neutrino flux extracted by using QE kinematics. In this report, we propose a method for extraction of neutrino flux from inclusive neutrino-nucleus cross section by using the Maximum Entropy Method (MEM). We demonstrate that one can extract the neutrino flux without assuming QE kinematics.   

Noise, Statistics and Sign Problems

Sign problems typically plague lattice field theory computations for many-body systems, or thermodynamic systems at finite density. Sign problems are closely associated with noise problems in the measurements of correlators. I discuss how the statistics of this noise conveys information about the underlying physics, and how it often shows curiously universal behavior which can be exploited to better extract physics from the measurement. This investigation gives a picture for how a solution to the sign problem might look.   

Inhomogeneous Polyakov loop induced by inhomogeneous chiral condensates

Inhomogeneous chiral condensates have been actively studied at finite temperatures and densities using chiral effective models. We study inhomogeneous Polyakov loop induced by such inhomogeneous chiral condensates in quenched lattice QCD simulation. For this purpose, we construct an effective model of gluons on the background fields of inhomogeneous chiral condensates. We show that the Polyakov loop exhibits a spatial oscillation parallel to that of chiral condensates, which indicates a possible coexistence of inhomogeneous Polyakov loop and chiral condensates. We also study the anisotropic heavy quark potential obtained from the inhomogeneous Polyakov loop correlation function.   

Nuclear parity violation from Lattice QCD

The steady advancement of computing technology and algorithms now allows for the computation of basic low-energy hadronic and nuclear observables directly from the fundamental theory of strong interactions, using the numerical technique of lattice QCD. We are beginning to compute specific matrix elements which are necessary to interpret the results from significant experimental efforts designed to probe the limits of the Standard Model. In this talk, I will present preliminary results of the first lattice QCD calculation of parity violation in the di-proton system, as well as the P-wave scattering phase shift necessary to determine the former. Ultimately, this calculation will determine low-energy coefficients in the parity-violating two-nucleon Lagrangian as well as the Desplanques, Donoghue, and Holstein (DDH) model, which can be used to compare with the experimental results.   

Can we perturbatively expand the $\hat Q$-box in the Bloch-Horowitz Hamiltonian?

In nuclear many-body problems, it is impossible to diagonalize the Hamiltonian directly because of the huge Hilbert space. We introduce, therefore, the concept of the effective interaction. We first partition the whole Hilbert space into the model space of tractable size and its complement, and then look for the effective Hamiltonian defined in the model space that reproduces exact eigenenergies and model space projections of the corresponding eigenstates. Effective Hamiltonians are categorized into energy-independent and energy-dependent groups. The energy-independent effective Hamiltonian has been calculated by iterative methods, and has been used widely for a long time. The energy-dependent effective Hamiltonian is known as the Bloch-Horowitz (BH) Hamiltonian. Though it requires a self-consistent solution, it can, in principle, give all the eigenenergies of the Hamiltonian, if provided with the exact BH Hamiltonian. In actual calculations, however, we can calculate the $\hat Q$-box only up to a finite order of perturbation expansion. In this work, we clarify its convergence condition and examine what we can obtain with the approximate BH Hamiltonian, and what we cannot.   

Magnetic property of quark matter in inhomogeneous chiral phase

Recently, a new phase where chiral symmetry is broken with the periodically modulating chiral condensate is found in mean field approximation of the NJL model [1]. Here we consider formation of static dual scalar and pseudoscalar density wave condensates on the chiral circle called ``dual chiral density wave (DCDW).'' By the analysis of the thermodynamic potential, it has been found that the DCDW phase is more favored in an external magnetic field [2]. We study the response of quark matter to a weak external magnetic field to show the spontaneous magnetization in the DCDW phase. In an external magnetic field, the energy spectrum of the lowest Landau level becomes asymmetric about zero and chiral anomaly manifests through [3]. This spectral asymmetry contributes to the thermodynamic potential by the term propotional to a magnetic field, which is the origin of the spontaneous magnetization in the DCDW phase. We also discuss the magnetic transition around the Lifshitz point by examining the magnetic susceptibility.\\[4pt] [1] E. Nakano, T. Tatsumi, Phys. Rev. D 71 (2005) 114006.\\[0pt] [2] I. E. Frolov, V. Ch. Zhukovsky, K.G. Klimenko, Phys. Rev. D 82 (2010) 076002.\\[0pt] [3] T. Tatsumi, K. Nishiyama, S. Karasawa, arXiv:1405.2155.   

Vacuum instability in AdS/CFT: Schwinger effect and Euler-Heisenberg Lagrangian of Supersymmetric QCD

To reveal the Schwinger effect for quarks, i.e., pair creation process of quarks and antiquarks, we derive the vacuum decay rate in strong external fields. Magnetic fields, in addition to the electric fields, are considered [1]. This is done through the gravity dual, where we obtain the full Euler-Heisenberg Lagrangian of N$=$2 supersymmetric QCD. First, in zero magnetic fields, we find that the decay rate given by the imaginary part of the effective Lagrangian becomes nonzero above a critical electric field set by the confining force between quarks. Second, in finite magnetic fields, we find that the creation rate becomes substantially large. This indicates the relevance of magnetic instability in the QGP formation at RHIC/LHC. Then, the time-dependent response of the system in a strong electric field is solved non-perturbatively, and we observe a universal thermalization at a shortest timescale ``Planckian thermalization time.'' Stronger electric fields accelerate the thermalization, and for a realistic value of the electric field in RHIC experiment, we obtain 1 [fm/c], which is consistent with the believed timescale. \\[4pt] [1] K. Hashimoto, T. Oka, JHEP 10, 116 (2013), K. Hashimoto, A. Sonoda, T. Oka, to be published in JHEP.   

Quantized Expression of electrostatic Force of Hydrogen Atom

The force of each state of the hydrogen atom is determined by the value of the Quantum number (n). $F_n=\frac{F_0}{n^4}$ where the $F_0=\frac{e^2}{4\pi\epsilon_0a_0^2}$ and $a_0$ is bohr radius. as n increases, the force level separation decreases rapidly. since n can take all integral values, the force spectrum of the hydrogen atom contains an infinite number of discrete force levels.   

The long range order in QCD: Applications to heavy ions and cosmology

We argue that the local violation of P invariance in heavy ion collisions is a consequence of the long range topological order which is inherent feature of strongly coupled QCD. The phenomenon is similar to many well-known topologically ordered condensed matter systems with a gap. Our arguments are based on an analysis of the so-called ``deformed QCD" model which is a weakly coupled gauge theory, but nevertheless preserves all the crucial elements of strongly interacting QCD, including confinement, nontrivial theta dependence, degeneracy of the topological sectors, etc. We also discuss possible cosmological applications of this long range order in QCD. Talk is based on three recent papers: \\[4pt] [1] ``QCD as a topologically ordered system,'' Annals Phys. 336, 462 (2013).\\[0pt] [2] ``Local P Violation Effects and Thermalization in QCD: Views from Quantum Field Theory and Holography,'' Nucl. Phys. A 886, 17 (2012).\\[0pt] [3] ``Inflaton as an auxiliary topological field in a QCD-like system,'' Phys. Rev. D 89, 063529 (2014).   

Nuclear Barrier Heights As Potential Waves With Varying Heights

Because the nucleus is often vibrating the potential associated with it is a wave with varying amplitudes. If the vibrating nucleus is out of target position for much of the time as the incoming charged particle approaches it and then strikes the nucleus, the barrier height can be lower than if static thereby allowing low energy nuclear reactions to take place. Since the nucleus is in varying positions due to its vibrations the barrier height waves are variable to the incoming charged particles.