Elastic differential cross-section measurement at $$\sqrt{s}=13$$ TeV by TOTEM

The TOTEM collaboration has measured the elastic proton-proton differential cross section $$\mathrm{d}\sigma /\mathrm{d}t$$dσ/dt at $$\sqrt{s}=13$$s=13 TeV LHC energy using dedicated $$\beta ^{*}=90$$β∗=90 m beam optics. The Roman Pot detectors were inserted to 10$$\sigma $$σ distance from the LHC beam, which allowed the measurement of the range [0.04 GeV$$^{2}$$2; 4 GeV$$^{2}$$2$$]$$] in four-momentum transfer squared |t|. The efficient data acquisition allowed to collect about 10$$^{9}$$9 elastic events to precisely measure the differential cross-section including the diffractive minimum (dip), the subsequent maximum (bump) and the large-|t| tail. The average nuclear slope has been found to be $$B=(20.40 \pm 0.002^{\mathrm{stat}} \pm 0.01^{\mathrm{syst}})~$$B=(20.40±0.002stat±0.01syst)GeV$$^{-2}$$-2 in the |t|-range 0.04–0.2 GeV$$^{2}$$2. The dip position is $$|t_{\mathrm{dip}}|=(0.47 \pm 0.004^{\mathrm{stat}} \pm 0.01^{\mathrm{syst}})~$$|tdip|=(0.47±0.004stat±0.01syst)GeV$$^{2}$$2. The differential cross section ratio at the bump vs. at the dip $$R=1.77\pm 0.01^{\mathrm{stat}}$$R=1.77±0.01stat has been measured with high precision. The series of TOTEM elastic pp measurements show that the dip is a permanent feature of the pp differential cross-section at the TeV scale.

Differential cross sections in a thick brane world scenario

The elastic differential cross section is calculated at low energies for the elements 3He, 20Ne, 40Ar, 14N, 12C, and for 208Pb using an effective 4D electromagnetic potential coming from the contribution of the massive Kaluza–Klein modes of the 5D vector field in a thick brane scenario. The length scale is adjusted in the potential to compare with known experimental data and to set bounds for the parameter of the model.

Fine structure of the diffraction cone: From the ISR to the LHC

Following earlier findings, we argue that the low-[Formula: see text] structure in the elastic diffractive cone, recently reported by the TOTEM Collaboration at [Formula: see text] TeV, is a consequence of the threshold singularity required by [Formula: see text]channel unitarity, such as revealed earlier at the ISR. By using simple Regge-pole models, we analyze the available data on the [Formula: see text] elastic differential cross section in a wide range of c.m. energies, namely those from ISR to LHC8, obtaining good fits of all datasets. This study hints at the fact that the non-exponential behavior observed at LHC8 is a recurrence of the low-[Formula: see text] “break” phenomenon, observed in the seventies at ISR, being induced by the presence of a two-pion loop singularity in the Pomeron trajectory.

Quantum diffraction grating: A possible new description of nuclear elastic scattering

The problem of discontinuous functions and their representations in the form of Legendre polynomial series in quantum nuclear scattering theory is presented briefly. The problem is quite old yet not adequately explained in numerous Quantum Theory textbooks and sometimes not correctly understood by physicists. Introduction of the generalized functions into the quantum scattering theory clarifies the problem and allows to propose new interpretations of nuclear elastic scattering phenomenon. The derived new forms of the full elastic scattering amplitudes and possibility of splitting them suggest existence of dynamical quantum diffraction grating around the nuclei. Particularly important fact is that this grating existing in the space around the nucleus makes considerable contribution to the experimental elastic differential cross-section. All these might be quite important in analyses of nuclear elastic scattering data and so require to be stated in a more detailed and clear way.

Elastic and inelastic scattering for the elements 12C, 6Li, and 40Ca using the reaction KN

The study of the nuclear structure for the elements 12C, 40Ca, and 6Li has been performed in the momentum range from 0 to 0.8 GeV/c by using K+N phase shifts. An optical potential is used to calculate the elastic differential cross section and total cross section for K+ scattering from 12C, 40Ca, and 6Li. Comparison with previous experiments shows better results for the elements 6Li and 40Ca and fair agreement for the element 12C.