Some Relations for Quark Confinement and Chiral Symmetry Breaking in QCD

We analytically study the relation between quark confinement and spontaneous chiral-symmetry breaking in QCD. In terms of the Dirac eigenmodes, we derive some formulae for the Polyakov loop, its fluctuations, and the string tension from the Wilson loop. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clover and the domain wall fermion kernels, respectively. For the confinement quantities, the low-lying Dirac/fermion eigenmodes are found to give negligible contribution, while they are essential for chiral symmetry breaking. These relations indicate no direct one-to-one correspondence between confinement and chiral symmetry breaking in QCD, which seems to be natural because confinement is realized independently of the quark mass

Dirac spectrum representation of Polyakov loop fluctuations in lattice QCD

Dirac spectrum representations of the Polyakov loop fluctuations are derived on the temporally odd-number lattice, where the temporal length is odd with the periodic boundary condition. We investigate the Polyakov loop fluctuations based on these analytical relations. It is semianalytically and numerically found that the low-lying Dirac eigenmodes have little contribution to the Polyakov loop fluctuations, which are sensitive probe for the quark deconfinement. Our results suggest no direct one-to-one corresponding between quark confinement and chiral symmetry breaking in QCD.Comment: 7 pages and 1 figure. Proceeding of the 33rd International Symposium on Lattice Field Theory (Lattice 2015), 14-18 July 2015, Kobe International Conference Center, Kobe, Japan. Also regarded as the Proceeding of the 4th International Conference on new Frontiers in Physics (ICNFP 2015), 23-30 August 2015, Conference Center of the Orthodox Academy of Crete, Crete, Greec

Relating Quark Confinement and Chiral Symmetry Breaking in QCD

We study the relation between quark confinement and chiral symmetry breaking in QCD. Using lattice QCD formalism, we analytically express the various "confinement indicators", such as the Polyakov loop, its fluctuations, the Wilson loop, the inter-quark potential and the string tension, in terms of the Dirac eigenmodes. In the Dirac spectral representation, there appears a power of the Dirac eigenvalue $\lambda_n$ such as $\lambda_n^{N_t-1}$, which behaves as a reduction factor for small $\lambda_n$. Consequently, since this reduction factor cannot be cancelled, the low-lying Dirac eigenmodes give negligibly small contribution to the confinement quantities,while they are essential for chiral symmetry breaking. These relations indicate no direct, one-to-one correspondence between confinement and chiral symmetry breaking in QCD. In other words, there is some independence of quark confinement from chiral symmetry breaking, which can generally lead to different transition temperatures/densities for deconfinement and chiral restoration. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clover and the domain-wall fermion kernels, respectively, and find the similar results. The independence of quark confinement from chiral symmetry breaking seems to be natural, because confinement is realized independently of quark masses and heavy quarks are also confined even without the chiral symmetry.Comment: 20 pages, 10 figures. arXiv admin note: text overlap with arXiv:1611.0874

Neutrino Scattering on Glass: NuSOnG

These proceedings describe the physics goals and initial design for a new experiment: NuSOnG -- Neutrino Scattering On Glass. The design will yield about two orders of magnitude higher statistics than previous high energy neutrino experiments, observed in a detector optimized for low hadronic energy and electromagnetic events. As a result, the purely weak processes $\nu_{\mu}+e^- \to \nu_{\mu}+ e^-$ and $\nu_{\mu}+ e^- \to \nu_e + \mu^-$ (inverse muon decay) can be measured with high accuracy for the first time. This allows important precision electroweak tests and well as direct searches for new physics. The high statistics also will yield the world's largest sample of Deep Inelastic (DIS) events for precision parton distribution studies.Comment: Proceedings of NuFact0

MANX: A 6D Ionization-Cooling Experiment

Six-dimensional ionization cooling of muons is essential for muon colliders and possibly beneficial for neutrino factories. An experiment to demonstrate six-dimensional ionization cooling using practical apparatus is presented. It exploits recent innovative ideas that may lead to six-dimensional muon-cooling channels with emittance reduction approaching that needed for high-luminosity muon colliders.Comment: 3 pages, 4 figures, to appear in Proceedings of the 9th International Workshop on Neutrino Factories, Superbeams, and Betabeams (NuFact07), August 6-11, 2007, Okayama University, Japa

Nuclear effects in Neutrino Nuclear Cross-sections

Nuclear effects in the quasielastic and inelastic scattering of neutrinos(antineutrinos) from nuclear targets have been studied. The calculations are done in the local density approximation which take into account the effect of nucleon motion as well as renormalisation of weak transition strengths in the nuclear medium. The inelastic reaction leading to production of pions is calculated in a $\Delta$ dominance model taking into account the renormalization of $\Delta$ properties in the nuclear medium.Comment: 4 pages,3 figures, Ninth International Workshop on Neutrino Factories, Superbeams and Betabeams (NuFact07), August 6-11, 2007, Okayama University, Okayama, Japa

Chiral Symmetry and Neutrino Pion Production off the Nucleon

The neutrino pion production off the nucleon is traditionally described in the literature by means of the weak excitation of the Delta(1232) resonance and its subsequent decay into N pi. Here, we present results from a model that includes also some background terms required by chiral symmetry. We show that the contribution of these terms is sizeable and leads to significant effects in total and partially integrated pion production cross sections at intermediate energies of interest for neutrino oscillation experiments. Finally, we discuss parity-violating contributions to the pion angular differential cross section induced by the interference of these non-resonant terms with the Delta piece.Comment: To appear in the proceedings of 9th International Workshop On Neutrino Factories, Superbeams and Betabeams (NuFact07) August 6-11, 2007, Okayama University, Japa

Global NLO Analysis of Nuclear Parton Distribution Functions

Nuclear parton distribution functions (NPDFs) are determined by a global analysis of experimental measurements on structure-function ratios F_2^A/F_2^{A'} and Drell-Yan cross section ratios \sigma_{DY}^A/\sigma_{DY}^{A'}, and their uncertainties are estimated by the Hessian method. The NPDFs are obtained in both leading order (LO) and next-to-leading order (NLO) of \alpha_s. As a result, valence-quark distributions are relatively well determined, whereas antiquark distributions at x>0.2 and gluon distributions in the whole x region have large uncertainties. The NLO uncertainties are slightly smaller than the LO ones; however, such a NLO improvement is not as significant as the nucleonic case.Comment: 3 pages, LaTeX, 4 eps files, to be published in the AIP proceedings of the 9th International Workshop on Neutrino Factories, Superbeams and Betabeams (NuFact07), Okayama, Japan, August 6 - 11, 2007. A code for calculating our nuclear parton distribution functions and their uncertainties can be obtained from http://research.kek.jp/people/kumanos/nuclp.htm

Vector-axialvector mixing from a chiral effective field theory at finite temperature

We study the vector-axialvector mixing in a hot medium and its evolution toward the chiral phase transition using different symmetry restoration scenarios based on the generalized hidden local symmetry framework. We show that the presence of the $a_1$ meson reduces the vector spectral function around $\rho$ meson mass and enhances it around $a_1$ meson mass. The coupling strength of $a_1$ to $\rho$ and $\pi$ vanishes at the critical temperature due to the degenerate $\rho$-$a_1$ masses. This feature holds rigorously in the chiral limit and still stays intact to good approximation for the physical pion mass.Comment: v2:11 pages, 6 figures, reorganized and expanded the text, new plots and references added, main result and conclusions unchange

Paramagnetic‐Resonance Absorption of Ions with Spin 5/2: Mn++ in Calcite

The theory of the paramagnetic‐resonance absorption of ions with S = S=52 in crystalline fields of trigonal symmetry is presented. The case of manganous ions in calcite (CaCO3) is taken as an example. It is shown that the splitting of the fine‐structure satellites into doublets first reported by Hurd, Sachs, and Hershberger [Phys. Rev. 93, 373 (1954)] can be accounted for by assuming that the manganous ions can occupy the two nonequivalent Ca++ sites at random. The maximum splitting was measured at X band and K band and found to be 19.3±0.5 gauss. The value computed from the theory, assuming an ionic model, is 23.8 gauss. In addition, five pairs of weak lines were found, each pair occurring midway between adjacent hyperfine groups. The origin of these lines is uncertain. The applicability of the present theory to Al2O3:Fe, a zero‐field maser material, and to the photosensitive Fe+++ center in CdS is pointed out.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71145/2/JCPSA6-33-2-601-1.pd