Modern Physics Letters A

New and recent results on QCD measurements from the H1 and ZEUS experiments at the HERA ep collider are reviewed. The final results on the combined deep-inelastic neutral and charged current cross-sections are presented and their role in the extractions of parton distribution functions (PDFs) is studied. The PDF fits give insight into the compatibility of QCD evolution and heavy flavor schemes with the data as a function of kinematic variables such as the scale Q². Measurements of jet production cross-sections in ep collisions provide direct proves of QCD and extractions of the strong coupling constants are performed. Charm and beauty cross-section measurements are used for the determination of the heavy quark masses. Their role in PDF fits is investigated. In the regime of diffractive DIS and photoproduction, dijet and prompt photon production cross-sections provide insights into the process of factorization and the nature of the diffractive exchange.

There exist four pion nucleon coupling constants, $f_{{\pi }^{0}pp}$, $-f_{{\pi }^{0}nn}$, $f_{{\pi }^{+}pn}/\sqrt{2}$ and $f_{{\pi }^{-}np}/\sqrt{2}$ which coincide when up and down quark masses are identical and the electron charge is zero. While there is no reason why the pion–nucleon–nucleon coupling constants should be identical in the real world, one expects that the small differences might be pinned down from a sufficiently large number of independent and mutually consistent data. Our discussion provides a rationale for our recent determination

The second (unphysical) critical charge in the three-body quantum Coulomb system of a nucleus of positive charge $Z$ and mass $m_p$, and two electrons, predicted by Stillinger has been calculated to be equal to $Z_B^{\infty }=0.904854$ and $Z_B^{m_p}=0.905138$ for infinite and finite (proton) mass $m_p$, respectively. It is shown that in both cases, the ground state energy $E(Z)$ (analytically continued beyond the first critical charge $Z_c$, for which the ionization energy vanishes, to $\mathrm{\text{Re}}Z$$<$$Z_c$) has a square-root branch point with exponent 3/2 at $Z=Z_B$ in the complex $Z$-plane. Based on analytic continuation, the second, excited, spin-singlet bound state of negative hydrogen ion H${}^{-}$ is predicted to be at −0.51554 a.u. (−0.51531 a.u. for the finite proton mass $m_p$). The first critical charge $Z_c$ is found accurately for a finite proton mass $m_p$ in the Lagrange mesh method, $Z_c^{m_p}=0.911069724655$.

The q-theory approach to the cosmological constant problem is reconsidered. The new observation is that the effective classical q-theory gets modified due to the back-reaction of quantum-mechanical particle production by spacetime curvature. Furthermore, a Planck-scale cosmological constant is added to the potential term of the action density, in order to represent the effects from zero-point energies and phase transitions. The resulting dynamical equations of a spatially-flat Friedmann–Robertson–Walker universe are then found to give a steady approach to the Minkowski vacuum, with attractor behavior for a finite domain of initial boundary conditions on the fields. The approach to the Minkowski vacuum is slow and gives rise to an inflation-type increase of the particle horizon.

The isotopic structure of the well-established s-wave resonances in the presence of a hypnotized narrow resonance N(1670)1/2${}^{+}$ in the $\gamma n\to \eta n$ amplitude is discussed. Two sets of results coming out of fitting two different sets of the data are discussed.

A new empirical formula is proposed for mass excess of heavy and superheavy nuclei in the region Z = 96–129. The parameters of the formula are obtained by making a polynomial fit to the available theoretical and experimental data. The calculated mass excess values are compared with the experimental values and other results of the earlier proposed models such as finite range droplet model (FRDM) and Hartree–Fock–Bogoliubov (HFB) method. Standard deviation of calculated mass excess values for each atomic number is tabulated. The good agreement of present formula with the experiment and other models suggests that the present formula could be used to evaluate the mass excess values of heavy and superheavy nuclei in the region 96$\le$Z$\ge$129. This formula is a model-independent formula and is first of its kind that produces a mass excess values with the only simple inputs of only Z and A.

The large-scale magnetic fields we observe today in galaxies and galaxy clusters could be the result of a pure quantum effect taking place during inflation, to wit, the creation of particles (photons) out from the vacuum in a curved spacetime. We show that, whenever the conformal invariance of electromagnetism is broken during inflation, the actual magnetic field spectrum, in the classical limit, is given by $B_k\simeq k^2\sqrt{n_k}$, where $n_k\gg 1$ is the number of created photons with wave number $k$. In particular, a scale-invariant magnetic field of order of 10${}^{12}$ G can emerge in the simplest model of cosmic magnetogenesis, the one where the inflaton is kinetically coupled to the photon. Moreover, and contrarily to the general belief, we show that such a model is free from the so-called strong-coupling and backreaction problems. This conclusion follows, indirectly, from the observation that post-inflationary electric currents, which in the literature are incorrectly supposed to freeze superhorizon magnetic fields after inflation, are indeed vanishing on superhorizon scales due to causality.