Total Cross Sections Sigma Research Articles

Measurement of the total cross section and rho -parameter from elastic scattering in pp collisions at sqrt{s}=13 TeV with the ATLAS detector

In a special run of the LHC with beta ^{star } = 2.5 km, proton–proton elastic-scattering events were recorded at sqrt{s} = 13 TeV with an integrated luminosity of 340~upmu {text {b}}^{-1} using the ALFA subdetector of ATLAS in 2016. The elastic cross section was measured differentially in the Mandelstam t variable in the range from -t = 2.5 cdot 10^{-4} GeV^{2} to -t = 0.46 GeV^{2} using 6.9 million elastic-scattering candidates. This paper presents measurements of the total cross section sigma _{text {tot}}, parameters of the nuclear slope, and the rho -parameter defined as the ratio of the real part to the imaginary part of the elastic-scattering amplitude in the limit t rightarrow 0. These parameters are determined from a fit to the differential elastic cross section using the optical theorem and different parameterizations of the t-dependence. The results for sigma _{text {tot}} and rho are σtot(pp→X)=104.7±1.1mb,ρ=0.098±0.011.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\sigma _{\ ext {tot}}(pp\\rightarrow X) = 104.7 \\pm 1.1 \\; \ ext{ mb },\\quad \\rho = 0.098 \\pm 0.011 . \\end{aligned}$$\\end{document}The uncertainty in sigma _{text {tot}} is dominated by the luminosity measurement, and in rho by imperfect knowledge of the detector alignment and by modelling of the nuclear amplitude.

Production of double heavy quarkonia at super Z factory

Within the color singlet model, we calculate the exclusive production of double charmonia, double bottomonia, and double B_c mesons at future super Z factory. The two heavy quarkonia or B_c’s are either two S-wave Fock states (^1S_0, ~^3S_1), or one S-wave and one P-wave states (^1P_1,~^3P_J~(J=0,1,2)). The top three Z^0 propagated channels in cross sections for double charmonia are sigma {(J/psi +h_c)}_{Z^0}=(454.0^{+39.1}_{-59.2})times 10^{-5} fb, sigma {(eta _c+chi _{c2})}_{Z^0}=(284.2^{+22.2}_{-35.3})times 10^{-5} fb, and sigma {(eta _c+chi _{c0})}_{Z^0}=(137.0^{+9.9}_{-16.4})times 10^{-5} fb. For double bottomonia, they are sigma {(eta _b+Upsilon )}_{Z^0}=(428.6^{+67.9}_{-60.9})times 10^{-4} fb, sigma {(Upsilon +chi _{b2})}_{Z^0}=(230.6^{+23.6}_{-22.2})times 10^{-4} fb, and sigma {(Upsilon +Upsilon )}_{Z^0}=(119.9^{+18.4}_{-16.6})times 10^{-4} fb. For double B_c mesons, they are sigma {(B_c^{*+}+B_c^{*-})}_{Z^0}=(1150^{+87}_{-84})times 10^{-3} fb, sigma {(B_c^{*+}+chi _{bc2}^-)}_{Z^0}=(1133^{-16}_{+22})times 10^{-3} fb, and sigma {(eta _{bc}^++B_c^{*-})}_{Z^0}=(634.6^{+47.8}_{-45.8})times 10^{-3} fb. Here the uncertainties come from the varying masses of constituent heavy quarks, which bring up to 20% corrections. The cross sections of double B_c mesons are roughly one order of magnitude larger than those of the double bottomonia, and two orders of magnitude larger than those of the double charmonia. To make it helpful for experimental study, we present the total cross sections sigma as functions of CM energy sqrt{s}, sigma as functions of the renormalization scale mu , the angle distributions dsigma /dcostheta , and the p_T distributions dsigma /dp_{t}. We also find that the initial state radiation can bring about 30–40% suppresions when 1%m_Z energy is losing, and cross sections can increase by about 2–3 times or decrease by an order of magnitude when adopting different potential models which becomes the major source of uncertainty. The numerical results show that it might be not optimistic for the experimental observation, but it is still far from excluded at the FCC-ee and also the CEPC running in the Z factory mode.

Adequacy of Effective Born for electroweak effects and TauSpinner algorithms for high energy physics simulated samples

Matching and comparing the measurements of past and future experiments call for consistency checks of electroweak (EW) calculations used for their interpretation. On the other hand, new calculation schemes of the field theory can be beneficial for precision, even if they may obscure comparisons with earlier results. Over the years, concepts of Improved Born, Effective Born, as well as of effective couplings, in particular of sin ^2theta _W^{{textit{eff}}} mixing angle for EW interactions, have evolved. In our discussion, we use four versions of DIZET EW library for phenomenology of practically all HEP accelerator experiments over the last 30 years. We rely on the codes published and archived with the KKMC Monte Carlo program for e^+e^- rightarrow f {bar{f}} n(gamma ) and available for the TauSpinner as well. TauSpinner re-weighs generated events for introduction of EW effects. To this end, DIZET is first invoked, and its results are stored in data file and later used. Documentation of TauSpinner upgrade, to version 2.1.0, and that of its new arrangement for semi-automated benchmark plots are provided. In our paper, focus is placed on the numerical results, on the different approximations introduced in Improved Born to obtain Effective Born, which is simpler for applications of strong or QED processes in pp or e^+e^- colliders. The tau lepton polarization P_{tau }, forward–backward asymmetry A_{{textit{FB}}} and parton-level total cross section sigma ^{{textit{tot}}} are used to monitor the size of EW effects and effective sin ^2theta _W^{{textit{eff}}} picture limitations for precision physics. Collected results include: (i) Effective Born approximations and sin ^2theta _W^{{textit{eff}}}, (ii) differences between versions of EW libraries and (iii) parametric uncertainties due to, for example, m_t or Delta alpha _h^{(5)}(s). These results can be considered as benchmarks and also allow to evaluate the adequacy of Effective Born with respect to Improved Born. Definitions are addressed too.

α scattering and α -induced reaction cross sections of Zn64 at low energies

Background: alpha-nucleus potentials play an essential role for the calculation of alpha-induced reaction cross sections at low energies in the statistical model... Purpose: The present work studies the total reaction cross section sigma_reac of alpha-induced reactions at low energies which can be determined from the elastic scattering angular distribution or from the sum over the cross sections of all open non-elastic channels. Method: Elastic and inelastic 64Zn(a,a)64Zn angular distributions were measured at two energies around the Coulomb barrier at 12.1 MeV and 16.1 MeV. Reaction cross sections of the (a,g), (a,n), and (a,p) reactions were measured at the same energies using the activation technique. The contributions of missing non-elastic channels were estimated from statistical model calculations. Results: The total reaction cross sections from elastic scattering and from the sum of the cross sections over all open non-elastic channels agree well within the uncertainties. This finding confirms the consistency of the experimental data. At the higher energy of 16.1 MeV, the predicted significant contribution of compound-inelastic scattering to the total reaction cross section is confirmed experimentally. As a by-product it is found that most recent global alpha-nucleus potentials are able to describe the reaction cross sections for 64Zn around the Coulomb barrier. Conclusions: Total reaction cross sections of alpha-induced reactions can be well determined from elastic scattering angular distributions. The present study proves experimentally that the total cross section from elastic scattering is identical to the sum of non-elastic reaction cross sections. Thus, the statistical model can reliably be used to distribute the total reaction cross section among the different open channels.

Ultrahigh-Energy Neutrino-Nucleon Deep-Inelastic Scattering and the Froissart Bound

We present a simple formula for the total cross section σ(νN) of neutral- and charged-current deep-inelastic scattering of ultrahigh-energy neutrinos on isoscalar nuclear targets, which is proportional to the structure function F(2)(νN)(M(V)(2)/s,M(V)(2)), where M(V) is the intermediate-boson mass and s is the square of the center-of-mass energy. The coefficient in front of F(2)(νN)(x,Q(2)) depends on the asymptotic low-x behavior of F(2)(νN). It contains an additional lns term if F(2)(νN) scales with a power of ln(1/x). Hence, an asymptotic low-x behavior F(2)(νN)∝ln(2)(1/x), which is frequently assumed in the literature, already leads to a violation of the Froissart bound on σ(νN).

Search for anomalous top–gluon couplings at LHC revisited

Through top-quark pair productions at LHC, we study possible effects of nonstandard top-gluon couplings yielded by SU(3)xSU(2)xU(1) invariant dimension-6 effective operators. We calculate the total cross section and also some distributions for p p -> t tbar X as functions of two anomalous-coupling parameters, i.e., the chromoelectric and chromomagnetic moments of the top, which are constrained by the total cross section sigma(p pbar -> t tbar X) measured at Tevatron. We find that LHC might give us some chances to observe sizable effects induced by those new couplings.

Soft Open Charm Production in Heavy-Ion Collisions

The effects of strong longitudinal color electric fields on the open charm production in nucleus-nucleus (A+A) collisions at 200A GeV are investigated within the framework of the HIJING/BB[over ] v2.0 model. A threefold increase of the effective string tension due to in-medium effects in A+A collisions results in a sizable ( approximately 60%-70%) enhancement of the total charm production cross sections (sigma (cc)(NN)). The nuclear modification factor shows a suppression at moderate transverse momentum (p(T)) consistent with BNL Relativistic Heavy Ion Collider data. At Large Hadron Collider energies the model predicts an increase of sigma (cc)(NN) by approximately an order of magnitude.

Calculation of low-Z impurity pellet induced fluxes of charge exchange neutral particles escaping from magnetically confined toroidal plasmas

Measurements of energy- and time-resolved neutral hydrogen and helium fluxes from an impurity pellet ablation cloud, referred to as pellet charge exchange or PCX experiments, can be used to study local fast ion energy distributions in fusion plasmas. The estimation of the local distribution function f(i)(E) of fast ions entering the cloud requires knowledge of both the fraction F(0)(E) of incident ions exiting the cloud as neutral atoms and the attenuation factor A(E,rho) describing the loss of fast atoms in the plasma. Determination of A(E,rho), in turn, requires the total stopping cross section sigma(loss) of neutral atoms in the plasma and the Jacobian reflecting the measurement geometry and the magnetic surface shape. The obtained functions F(0)(E) and A(E,rho) enter multiplicatively into the probability density for escaping neutral particle kinetic energy. A general calculation scheme has been developed and realized as a FORTRAN code, which is to be applied for the calculation of f(i)(E) from PCX experimental results obtained with low-Z impurity pellets.

Optical nonlinearities in silicon for pulse durations of the order of nanoseconds at 1.06 µm

We study free-carrier nonlinearities in crystalline silicon at 1.064 microm using the Z-scan technique, with special emphasis on the dependence of their nonlinearities on the width of incident pulses. In the Z-scan experiment, the pulse duration was changed from 11.5 ns to 1.6 ns by the pulse compression using stimulated Brillouin scattering in a liquid. At this excitation wavelength, linear absorption is dominant for the creation of electron-hole pairs and the photoexcited carriers can modify the refractive index and absorption coefficient just as a third-order nonlinear effect. The effective nonlinear refractive index n(2eff) and nonlinear absorption coefficient beta(eff) are proportional to the pulse duration and optical intensity, i.e. the fluence when the pulse duration is shorter than the carrier recombination lifetime. We can determine the variation of refractive index per unit of photoexcited carrier density sigma(r) and the total carrier absorption cross section sigma(ab) from the dependence of n(2eff) and beta(eff) on the pulse width, respectively. In this work we had sigma(r) =-1.0 x 10(-21) cm(3) and sigma(ab)=8.4 x 10(-18) cm(2), which agree well with previous data. We also observed the decrease in the magnitude of n(2eff) and beta(eff) at high incident fluence, which is presumably attributed to band filling. This new measurement approach has an advantage of being able to separate an ultrafast Kerr nonlinearity and a cumulative nonlinearity such as the free-carrier nonlinearity treated in this paper and can be utilized to evaluate the optical nonlinearities of other materials.

Measurement of the cross section forW-boson production in association with jets inpp¯collisions ats=1.96 TeV

We present a measurement of the cross section for W-boson production in association with jets in pbar-p collisions at sqrt(s)=1.96 TeV. The analysis uses a data sample corresponding to an integrated luminosity of 320 pb^-1 collected with the CDF II detector. W bosons are identified in their electron decay channel and jets are reconstructed using a cone algorithm. For each W+>= n-jet sample (n= 1 - 4) we measure dsigma(ppbar =>W+>=n-jet)/dE_T^(nth-jet) x BR(W => e nu) with respect to the transverse energy E_T of the n^th-highest E_T jet above 20 GeV, and the total cross section sigma(ppbar =>W+>=n-jet; E_T^(nth-jet)>25 GeV) x BR(W => e nu), for a restricted W => e nu decay phase space. The cross sections, corrected for all detector effects, can be directly compared to particle level W+ jet(s) predictions. We present here comparisons to leading order and next-to-leading order predictions.

On the Discrepancy of pp, Formulap Total Cross Sections at s = 1.8 TeV between E710, E811 and CDF

Based on the previous approach, we have investigated a possibility to resolve the discrepancy between the E710, E811 and CDF at sqrt s =1.8TeV, using the experimental data of the pp, pbar p total cross sections sigma tot(+) and rho(+)$ ratio up to the SPS experiments (sqrt s = 0.9TeV) as inputs. We predict sigma tot(pbar p) and rho(pbar p) at the Tevatron energy(sqrt s=1.8TeV) as sigma tot(pbar p)=75.9+- 1.0mb, rho(pbar p)=0.136+- 0.005. It turns out that only the data of E710 is consistent with the prediction in the one standard deviation. So we can conclude that E710 is preferable but we can exclude neither CDF nor E811 results.

Total cross section in γγ collisions at LEP

The reaction e+e- -> e+e- gamma* gamma* -> e+e- hadrons for quasi-real photons is studied using data from root(s) = 183 GeV up to 202 GeV. Results on the total cross sections sigma(e+e- -> e+e- hadrons) and sigma(+e- gamma* gamma* -> e+e- hadrons) are given for the two-photon centre-of-mass energies 5 GeV < Wgammagamma < 185 GeV. The total cross section of two real photons is described by a Regge parametrisation. We observe a steeper rise with the two-photon centre-of-mass energy as compared to the hadron-hadron and the photon-proton cross sections. The data are also compared to the expectations of different theoretical models.

Neutron cross sections for 56Fe and 238U, from 0.2 to 22 MeV energy

Neutron total and differential elastic cross sections for 56Fe and 238U nuclei were calculated from different global spherical optical potential (SOP) sets. The total cross sections sigma t for these nuclei for different neutron energies were calculated. The results were compared with those of the experimental data obtained from the EXFOR data file to select the best-fit potential parameters. In addition, the angular distributions of elastically scattered neutrons at different neutron energies were also studied. It was observed that the best overall fit to the experimental values of the total cross sections and angular distributions are obtained from SOP parameter set 2 of Wilmore and Hodgson for 56Fe and set 12 of Bersillon and Cindro for 238U.

Ionisation in He+-He+collisions

Total cross sections sigma 2+ for He2+ formation from the combined processes of charge transfer ( sigma c) and ionisation ( sigma i) in He+-He+ collisions have been measured using an intersecting beam techniques for CM energies in the range 11-113 keV. Cross sections for ionisation sigma i= sigma 2+- sigma c are derived by subtracting the authors' recently measured sigma c values from the sigma 2+ data. The results are compared with data extracted from previous experimental measurements of Peart et al (1983) in the range 14-58 keV and with theoretical predictions.

Charge transfer of 0.2-5.0 keV protons and hydrogen atoms in sodium-, potassium- and rubidium-vapour targets

Total cross sections sigma +0 and sigma +- for single- and double-electron capture by protons, and total cross sections sigma 0- and sigma 0+ for single-electron capture and single-electron loss by neutral hydrogen atoms in single collisions with atoms of sodium, potassium and rubidium have been measured in the energy range 0.2-5.0 keV. All electron capture cross sections show a maximum at an energy which depends on the energy defects of the reaction. The electron loss cross sections increase monotonically with increasing collision energy. The results are discussed and compared with previous measurements and theoretical calculations. Some of the cross sections show considerable discrepancies with previous measurements.

Ionisation in H+-He+collisions using an improved beam-pulsing technique for measuring the formation of He2+

An improved beam-pulsing technique has been developed for an experiment with two intersecting charged-particle beams. The total cross sections sigma 2+ for He2+ formation from the combined processes H+He+ to H0+He2+ (charge transfer, cross section sigma c) and H++He+ to H++He2++e (ionisation, cross section sigma i) have been measured in the centre-of-mass energy range 17-100 keV. The cross sections sigma i for ionisation are determined by subtracting the authors' recently measured sigma c values from the cross sections sigma 2+. The data are compared with previous experimental and theoretical results.

Positron-monosilane (SiH4) collisions at low, intermediate and high energies using a spherical complex optical potential approach

The author reports the first calculations on the total (elastic plus inelastic) cross sections ( sigma t) of positron-SiH4 scattering in a wide energy range (1-400 eV). A spherical complex optical potential (SCOP) is generated between the target and the projectile and treated exactly in a partial-wave analysis to extract complex phaseshifts. The real part of the optical potential consists of an accurate repulsive static term calculated from one-centre near-Hartree-Fock silane wavefunctions plus a polarisation potential of the correct asymptotic form (- alpha 0/2r4, where alpha 0 is the dipole polarisability of the molecule) smoothly joined with the target correlation energy at short distances. For the imaginary part of the SCOP, he employs a recently semi-empirically derived form, which is based on the electron absorption potential. The final sigma t results compare fairly well with the only available measurements of Sueoka and Mori. In particular, the present model reproduces the sharp rise of sigma t near the positronium formation threshold and a bell-shaped feature around 20 eV. Below the positronium threshold, his elastic cross sections agree to within 2-3% with the more rigorous close-coupling results of Jain et al. (1986).

Redetermination of cross sections for charge transfer and ionisation in H+-He+collisions

The cross sections sigma c for charge transfer in H+-He+ collisions previously measured in this laboratory have been found to be subject to an arithmetical error of 25%. The error has now been confirmed by remeasurements of sigma c in the CM energy range 49-141 keV. The revised values of sigma c and the cross sections for ionisation sigma i= sigma (He2+)- sigma c derived from the previous measurements (Angel et al., 1978) of the total cross sections sigma (He2+) for He2+ formation are in good accord with other measurements. The experimental data now permit a useful assessment of the range of validity of a number of theoretical predictions.

Subshell-selective electron capture in collisions of C4+, N5+, O6+with H, H2and He

By means of optical spectroscopy the authors have determined absolute subshell-selective single electron capture cross sections sigma nl for collisions of C4+, N5+ and O6+ with atomic and molecular hydrogen and helium at impact velocities between 0.1 and 0.5 au. The absolute sensitivity calibration of the monochromators is discussed briefly. In addition they have measured the total single electron capture cross section sigma t by means of charge state analysis, for atomic and molecular hydrogen as targets. In all cases it is found that one or two n shells are dominantly populated and that the total cross section is only weakly dependent on the impact velocity, in contrast to the subshell-selective cross sections sigma nl. The main features of the results obtained are qualitatively explained by means of simple diabatic potential diagrams and the classical overbarrier transition model. For several systems a detailed comparison can be made with recent theoretical calculations, showing satisfactory agreement.

Neutrino reactions in 13C and the behavior of the axial current form factor.

The total and differential cross sections sigma(..nu../sub ..mu../+ /sup 13/C..-->../sup 13/N g.s.+..mu../sup -/) and dsigma/d..cap omega..(..nu../sub ..mu../+/sup 13/C..-->../sup 13/N g.s.+..mu../sup -/) are calculated from threshold to E/sub ..nu../ = 260 MeV. The dependence of the cross section on the axial current form factor F/sub A/(q/sup 2/) is obtained for a range of assumptions. The dependence of the cross section on the pseudoscalar form factor is found to be negligible.