Pion electromagnetic form factor at spacelike momenta

A novel method is employed to compute the pion electromagnetic form factor, F_\pi(Q^2), on the entire domain of spacelike momentum transfer using the Dyson-Schwinger equation (DSE) framework in quantum chromodynamics (QCD). The DSE architecture unifies this prediction with that of the pion's valence-quark parton distribution amplitude (PDA). Using this PDA, the leading-order, leading-twist perturbative QCD result for Q^2 F_\pi(Q^2) underestimates the full computation by just 15% on Q^2>~8GeV^2, in stark contrast with the result obtained using the asymptotic PDA. The analysis shows that hard contributions to the pion form factor dominate for Q^2>~8GeV^2 but, even so, the magnitude of Q^2 F_\pi(Q^2) reflects the scale of dynamical chiral symmetry breaking, a pivotal emergent phenomenon in the Standard Model.Comment: 5 pages, 2 figures. To appear in Phys. Rev. Let

Pion distribution amplitude from lattice-QCD

A method is explained through which a pointwise accurate approximation to the pion's valence-quark distribution amplitude (PDA) may be obtained from a limited number of moments. In connection with the single nontrivial moment accessible in contemporary simulations of lattice-regularised quantum chromodynamics (QCD), the method yields a PDA that is a broad concave function whose pointwise form agrees with that predicted by Dyson-Schwinger equation analyses of the pion. Under leading-order evolution, the PDA remains broad to energy scales in excess of 100 GeV, a feature which signals persistence of the influence of dynamical chiral symmetry breaking. Consequently, the asymptotic distribution, \phi_\pi^asy(x), is a poor approximation to the pion's PDA at all such scales that are either currently accessible or foreseeable in experiments on pion elastic and transition form factors. Thus, related expectations based on \phi_\pi^asy(x) should be revised.Comment: 5 pages, 2 figure

Transition between nuclear and quark-gluon descriptions of hadrons and light nuclei

We provide a perspective on studies aimed at observing the transition between hadronic and quark-gluonic descriptions of reactions involving light nuclei. We begin by summarizing the results for relatively simple reactions such as the pion form factor and the neutral pion transition form factor as well as that for the nucleon and end with exclusive photoreactions in our simplest nuclei. A particular focus will be on reactions involving the deuteron. It is noted that a firm understanding of these issues is essential for unraveling important structure information from processes such as deeply virtual Compton scattering as well as deeply virtual meson production. The connection to exotic phenomena such as color transparency will be discussed. A number of outstanding challenges will require new experiments at modern facilities on the horizon as well as further theoretical developments.Comment: 37 pages, 17 figures, submitted to Reports on Progress in Physic

State sampling dependence of the Hopfield network inference

The fully connected Hopfield network is inferred based on observed magnetizations and pairwise correlations. We present the system in the glassy phase with low temperature and high memory load. We find that the inference error is very sensitive to the form of state sampling. When a single state is sampled to compute magnetizations and correlations, the inference error is almost indistinguishable irrespective of the sampled state. However, the error can be greatly reduced if the data is collected with state transitions. Our result holds for different disorder samples and accounts for the previously observed large fluctuations of inference error at low temperatures.Comment: 4 pages, 1 figure, further discussions added and relevant references adde

Neutron electric dipole moment: Constituent-dressing and compositeness

Contributions to the neutron's EDM, are calculated using a well-constrained Ansatz for the nucleon's Poincare' covariant Fadde'ev amplitude. The momentum-dependent quark dressing amplifies the contribution from the current-quarks' EDMs; and dressed-quark confinement and binding make distinguishable the effect of the two CP and T violating interactions: i gamma_5 sigma_{mu nu} (p_1-p_2)_nu and gamma_5 (p_1+p_2)_mu, where p_{1,2} are the current-quarks' momenta. The value of |d_n| obtained using the current-quark EDMs generated by a minimal three Higgs doublet model of spontaneous CP violation is close to the current experimental upper bound.Comment: 9 pages, LaTeX2e. Errors in Table 1 corrected; five references added. To appear in Phys. Rev.

Collective perspective on advances in Dyson-Schwinger Equation QCD

We survey contemporary studies of hadrons and strongly interacting quarks using QCD's Dyson-Schwinger equations, addressing: aspects of confinement and dynamical chiral symmetry breaking; the hadron spectrum; hadron elastic and transition form factors, from small- to large-Q^2; parton distribution functions; the physics of hadrons containing one or more heavy quarks; and properties of the quark gluon plasma.Comment: 56 pages. Summary of lectures delivered by the authors at the "Workshop on AdS/CFT and Novel Approaches to Hadron and Heavy Ion Physics," 2010-10-11 to 2010-12-03, hosted by the Kavli Institute for Theoretical Physics, China, at the Chinese Academy of Science

Relation Between Chiral Susceptibility and Solutions of Gap Equation in Nambu--Jona-Lasinio Model

We study the solutions of the gap equation, the thermodynamic potential and the chiral susceptibility in and beyond the chiral limit at finite chemical potential in the Nambu--Jona-Lasinio (NJL) model. We give an explicit relation between the chiral susceptibility and the thermodynamic potential in the NJL model. We find that the chiral susceptibility is a quantity being able to represent the furcation of the solutions of the gap equation and the concavo-convexity of the thermodynamic potential in NJL model. It indicates that the chiral susceptibility can identify the stable state and the possibility of the chiral phase transition in NJL model.Comment: 21 pages, 6 figures, misprints are correcte