The Lippmann–Schwinger Formula and One Dimensional Models with Dirac Delta Interactions

We show how a proper use of the Lippmann–Schwinger equation simplifies the calculations to obtain scattering states for one dimensional systems perturbed by N Dirac delta equations. Here, we consider two situations. In the former, attractive Dirac deltas perturbed the free one dimensional Schrödinger Hamiltonian. We obtain explicit expressions for scattering and Gamow states. For completeness, we show that the method to obtain bound states use comparable formulas, although not based on the Lippmann–Schwinger equation. Then, the attractive N deltas perturbed the one dimensional Salpeter equation. We also obtain explicit expressions for the scattering wave functions. Here, we need regularisation techniques that we implement via heat kernel regularisation

Comparison of Newtonian and Special-Relativistic Trajectories with the General-Relativistic Trajectory for a Low-Speed Weak-Gravity System

We show, contrary to expectation, that the trajectory predicted by general-relativistic mechanics for a low-speed weak-gravity system is not always well-approximated by the trajectories predicted by special-relativistic and Newtonian mechanics for the same parameters and initial conditions. If the system is dissipative, the breakdown of agreement occurs for chaotic trajectories only. If the system is non-dissipative, the breakdown of agreement occurs for chaotic trajectories and non-chaotic trajectories. The agreement breaks down slowly for non-chaotic trajectories but rapidly for chaotic trajectories. When the predictions are different, general-relativistic mechanics must therefore be used, instead of special-relativistic mechanics (Newtonian mechanics), to correctly study the dynamics of a weak-gravity system (a low-speed weak-gravity system)

3-cocycles, non-associative star-products and the magnetic paradigm of R-flux string vacua

We consider the geometric and non-geometric faces of closed string vacua arising by T-duality from principal torus bundles with constant H-flux and pay attention to their double phase space description encompassing all toroidal coordinates, momenta and their dual on equal footing. We construct a star-product algebra on functions in phase space that is manifestly duality invariant and substitutes for canonical quantization. The 3-cocycles of the Abelian group of translations in double phase space are seen to account for non-associativity of the star-product. We also provide alternative cohomological descriptions of non-associativity and draw analogies with the quantization of point-particles in the field of a Dirac monopole or other distributions of magnetic charge. The magnetic field analogue of the R-flux string model is provided by a constant uniform distribution of magnetic charge in space and non-associativity manifests as breaking of angular symmetry. The Poincare vector comes to rescue angular symmetry as well as associativity and also allow for quantization in terms of operators and Hilbert space only in the case of charged particles moving in the field of a single magnetic monopole

First measurement of the |t|-dependence of coherent J/ψ photonuclear production

The first measurement of the cross section for coherent J/ψ photoproduction as a function of |t|, the square of the momentum transferred between the incoming and outgoing target nucleus, is presented. The data were measured with the ALICE detector in ultra-peripheral Pb–Pb collisions at a centre-of-mass energy per nucleon pair sNN=5.02TeV with the J/ψ produced in the central rapidity region |y|<0.8, which corresponds to the small Bjorken-x range (0.3−1.4)×10−3. The measured |t|-dependence is not described by computations based only on the Pb nuclear form factor, while the photonuclear cross section is better reproduced by models including shadowing according to the leading-twist approximation, or gluon-saturation effects from the impact-parameter dependent Balitsky–Kovchegov equation. These new results are therefore a valid tool to constrain the relevant model parameters and to investigate the transverse gluonic structure at very low Bjorken-x.publishedVersio

First measurement of coherent ρ0 photoproduction in ultra-peripheral Xe–Xe collisions at √sNN = 5.44 TeV

The first measurement of the coherent photoproduction of ρ0 vector mesons in ultra-peripheral Xe–Xe collisions at sNN=5.44 TeV is presented. This result, together with previous HERA γp data and γ–Pb measurements from ALICE, describes the atomic number (A) dependence of this process, which is particularly sensitive to nuclear shadowing effects and to the approach to the black-disc limit of QCD at a semi-hard scale. The cross section of the Xe+Xe→ρ0+Xe+Xe process, measured at midrapidity through the decay channel ρ0→π+π−, is found to be dσ/dy=131.5±5.6(stat.)−16.9+17.5(syst.) mb. The ratio of the continuum to resonant contributions for the production of pion pairs is also measured. In addition, the fraction of events accompanied by electromagnetic dissociation of either one or both colliding nuclei is reported. The dependence on A of cross section for the coherent ρ0 photoproduction at a centre-of-mass energy per nucleon of the γA system of WγA,n=65 GeV is found to be consistent with a power-law behaviour σ(γA→ρ0A)∝Aα with a slope α=0.96±0.02(syst.). This slope signals important shadowing effects, but it is still far from the behaviour expected in the black-disc limit.publishedVersio

Resolving the strange behavior of extraterrestrial potassium in the upper atmosphere

It has been known since the 1960s that the layers of Na and K atoms, which occur between 80 and 105 km in the Earth's atmosphere as a result of meteoric ablation, exhibit completely different seasonal behavior. In the extratropics Na varies annually, with a pronounced wintertime maximum and summertime minimum. However, K varies semiannually with a small summertime maximum and minima at the equinoxes. This contrasting behavior has never been satisfactorily explained. Here we use a combination of electronic structure and chemical kinetic rate theory to determine two key differences in the chemistries of K and Na. First, the neutralization of K+ ions is only favored at low temperatures during summer. Second, cycling between K and its major neutral reservoir KHCO3 is essentially temperature independent. A whole atmosphere model incorporating this new chemistry, together with a meteor input function, now correctly predicts the seasonal behavior of the K layer

Flow Dominance and Factorization of Transverse Momentum Correlations in Pb-Pb Collisions at the LHC

We present the first measurement of the two-particle transverse momentum differential correlation function, P2≡ ΔpTΔpT/ pT2, in Pb-Pb collisions at sNN=2.76 TeV. Results for P2 are reported as a function of the relative pseudorapidity (Δη) and azimuthal angle (Δφ) between two particles for different collision centralities. The Δφ dependence is found to be largely independent of Δη for |Δη|≥0.9. In the 5% most central Pb-Pb collisions, the two-particle transverse momentum correlation function exhibits a clear double-hump structure around Δφ=π (i.e., on the away side), which is not observed in number correlations in the same centrality range, and thus provides an indication of the dominance of triangular flow in this collision centrality. Fourier decompositions of P2, studied as a function of the collision centrality, show that correlations at |Δη|≥0.9 can be well reproduced by a flow ansatz based on the notion that measured transverse momentum correlations are strictly determined by the collective motion of the system

K*(892)(0) and phi(1020)meson production at high transverse momentum in pp and Pb-Pb collisions at root sNN=2.76 TeV

The production of K∗(892)0 and φ(1020) mesons in proton-proton (pp) and lead-lead (Pb-Pb) collisions at √sNN = 2.76 TeV has been analyzed using a high luminosity data sample accumulated in 2011 with the ALICE detector at the Large Hadron Collider (LHC). Transverse momentum (pT) spectra have been measured for K∗(892)0 and φ(1020) mesons via their hadronic decay channels for pT up to 20 GeV/c. The measurements in pp collisions have been compared to model calculations and used to determine the nuclear modification factor and particle ratios. The K∗(892)0/K ratio exhibits significant reduction from pp to central Pb-Pb collisions, consistent with the suppression of the K∗(892)0 yield at low pT due to rescattering of its decay products in the hadronic phase. In central Pb-Pb collisions the pT dependent φ(1020)/π and K∗(892)0/π ratios show an enhancement over pp collisions for pT ≈ 3 GeV/c, consistent with previous observations of strong radial flow. At high pT, particle ratios in Pb-Pb collisions are similar to those measured in pp collisions. In central Pb-Pb collisions, the production of K∗(892)0 and φ(1020) mesons is suppressed for pT &gt; 8 GeV/c. This suppression is similar to that of charged pions, kaons, and protons, indicating that the suppression does not depend on particle mass or flavor in the light quark sector