The diffraction slope parameter is investigated for elastic proton-proton and proton-antiproton scattering based on the all available experimental data at low momentum transfer values. Energy dependence of the elastic diffraction slopes is approximated by various analytic functions. The expanded "standard" logarithmic approximations allow to describe experimental slopes in all available energy range reasonably. Various approximations differ from each other both in the low energy and very high energy domains. Predictions for diffraction slope parameter are obtained for elastic proton-proton scattering at RHIC and LHC energies, for proton-antiproton elastic reaction in FAIR energy domain for various approximation functions.
The diffraction slope parameter is investigated for elastic proton-proton and proton-antiproton scattering based on the all available experimental data at intermediate square of momentum transfer in the main. Energy dependence of the elastic diffraction slope is approximated by various analytic functions in a model-independent fashion. The expanded standard logarithmic approximations allow to describe experimental slopes in all available energy range at qualitative level reasonably. Various fitting functions differ from each other both in low energy and very high energy domains. Predictions fo…
Studying antiproton scattering by nuclei (atoms) in the range of low energies, we found out that the increase in the antiproton-nucleus scattering amplitude through Coulomb interaction provides the possibility to investigate spin-dependent processes accompanying the interaction of antiprotons with nuclei (polarized or unpolarized) by means of mirror reflection of antiprotons from the vacuum-matter boundary, diffraction and channeling (surface diffraction and channeling) of antiprotons in crystals.
The diffraction slope parameter is investigated for elastic proton-proton and proton-antiproton scattering based on the all available experimental data at low and intermediate momentum transfer values. Energy dependence of the elastic diffraction slopes is approximated by various analytic functions. The expanded "standard" logarithmic approximations with minimum number of free parameters allow to describe experimental slopes in all available energy range reasonably. The estimations of asymptotic shrinkage parameter $α'_{\cal{P}}$ were obtained for various $|t|$ domains based on the all availab…
We show that the cross section of the diffractive production of $b \bar b$ can be described as the sum of two contributions: the first is proportional to the probability of finding a small size $b \bar b$ color dipole in the fast hadron wave function before the interaction with a target, while the second is the $b \bar b$-production after or during the interaction with the target. The formulae are presented as well as the discussion of the interralation between these two contributions and the Ingelman- Schlein and coherent diffraction mechanisms. The main precdition is that the coherent diffra…
We present the first evaluation of the color dipole diffraction slope from the data on diffractive photo- and electroproduction of vector mesons. The energy and dipole size dependence of the found dipole diffraction slope are consistent with the color dipole gBFKL dynamics.
The study of slope parameter is presented for elastic proton-proton and antiproton-proton scattering with taking into account the resent experimental data at high energies. The expanded logarithmic approximations allow the description of the experimental slopes in all available energy range reasonably. Accounting for the LHC results leads to the dramatic change of behavior of the quadratic in logarithm approximation at high energies and to the closer trends for all fitting functions under study in comparison with the analysis at collision energies up to the 200 GeV. The estimations of the asym…
The Chou-Yang model based on multiple diffraction theory has already been used by us to predict the characteristics of antiproton-proton elastic scattering at very high energies. But the recent precise data on proton elastic form factor obtained at JLab essentially deviates from the dipole approximation. We have parametrized the data for the form factor. The computations have been made by using the new expression for the form factor. The implications of the new form factor on the characteristics of antiproton-proton elastic scattering at very high energy have been studied.
We consider a multi-channel correction accounting for intermediate transitions inside an equivalence class of diffractive states. Our formalism of 'diffractive limit' provides an excellent description of elastic and inclusive inelastic scattering of high energy (53 - 546 GeV) protons and antiprotons.
The scaling of the diffraction peak in antiproton--proton scattering has been investigated from near threshold up to $3\,\,\, GeV/c$ laboratory momenta.It was shown that the scaling of the differential cross sections are evidentiated with a surprising accuracy not only at high energies,but also at very low ones(e.q. $p_{LAB}=0.1--0.5\,\,\, GeV/c$),beyond the resonance and exotic resonance regions.This precociuos scaling strongly suggests that the s -- channel helicity conservation (SCHC) can be a peculiar property that should be tested in antiproton -proton interaction not only at high energie…
In the color dipole gBFKL dynamics we predict a strikingly different Q^2 and energy dependence of the diffraction slope for the elastic production of ground state V(1S) and radially excited V'(2S) light vector mesons. The color dipole model predictions for the diffraction slope for ρ^0 and ϕ^0 production are in a good agreement with the data from the fixed target and collider HERA experiments. We present how a different form of anomalous energy and Q^2 dependence of the diffraction slope for V'(2S) production leads to a different position of the node in radial wave function and discuss a possi…
New scaling structure for the shadow corrections in elastic scattering from deuteron at high energies has been presented and discussed. It is shown that this structure corresponds to the experimental data on proton(antiproton)-deuteron total cross sections. The effect of weakening for the inelastic screening at superhigh energies has been theoretically predicted.
We develop the color dipole gBFKL phenomenology of a diffraction cone for photo- and electroproduction $γ^{*}N \to VN$ of heavy vector mesons (charmonium & bottonium) at HERA and in fixed target experiments. We predict a substantial shrinkage of the diffraction cone from the CERN/FNAL to the HERA range of c.m.s. energy $W$. The $Q^{2}$-controlled selectivity to the color dipole size (scanning phenomenon) is shown to lead to a decrease of the diffraction slope with $Q^{2}$ (which is supported by the available experimental data). We predict an approximate flavor independence of the diffraction s…
The analysis of data on hyperon transverse momentum distributions, dN/dPt, that were gathered from various experiments (ISR, STAR, UA1, UA5 and CDF) reveals an important difference in the dynamics of multiparticle production in proton-proton vs. antiproton-proton collisions in the region of transverse momenta 0.3 GeV/c < Pt < 3 GeV/c. Hyperons produced with proton beams display the sharp exponential slope at low Pt, while spectra prodused with antiproton beam don't. Since LHC experiments have proton projectiles, the spectra of baryon production should seem "softer" in comparison to expectation…
We present a formalism for high energy soft processes, mediated by Pomerons, which embodies pion-loop insertions in the Pomeron trajectory, rescattering effects via a two-channel eikonal and high-mass diffractive dissociation. It describes all the main features of the data throughout the ISR to Tevatron energy interval. We give predictions for soft diffractive phenomena at the LHC energy, and we calculate the different survival probabilities of rapidity gaps which occur in various diffractive processes.
In color dipole gBFKL dynamics, we describe the emerging gBFKL phenomenology of a subasymptotic energy dependence of the diffraction slope and discuss possibilities of testing the gBFKL predictions in exclusive photo- and electroproduction of vector mesons $V$ at HERA. A substantial shrinkage of the diffraction cone $γ^{*}p\rightarrow Vp$ processes from the CERN/FNAL to HERA range of energy $W$ is predicted. This subasymptotic shrinkage is faster than expected from the small slope of pomeron's Regge trajectory $α_{\Pom}'$. We point out that the diffraction slope is a scaling function of $(m_{V…
We present a study of $\bar pp$ collisions with a leading antiptoton and a rapidity gap in addition to that associated with the antiproton. The second gap is either within the region available to the proton dissociation products, $\bar p+p\to (\bar p+gap)+X+gap+Y$, or adjacent to the outgoing proton $\bar p+p\to (\bar p+gap)+X+(gap+p)$. Results are reported for two-gap to one-gap event ratios and compared with one-gap to no-gap ratios and with theoretical expectations.
We re-examine the extraction of ρ(s,t), the ratio of the real part to the imaginary part of the scattering amplitude, and of the spin-flip amplitude, from the existing experimental data in the Coulomb-hadron interference region. We show that it is not possible to find reasonable assumptions about the structure of the scattering amplitude of proton-proton and proton-antiproton elastic scattering at high energy that would lead, in proton-antiproton scattering for 3.8 < p_L <6 GeV/c, to an agreement between data and an analysis based on dispersion relations.
The logarithmic slope of the diffractive structure function is a potential observable scanning the hard and soft contributions in diffraction, allowing to disentangle the QCD dynamics. We report our calculations concerning this quantity, in particular the estimates emerging from the saturation model applied to diffraction dissociation.
Old models of the scattering of composite systems based on the Glauber model of multiple diffraction are applied to hadron-nucleus scattering. We obtain an excellent fit with only two free parameters to the highest energy hadron-nucleus data available. Because of the quality of the fit and the simplicity of the model it is argued that it should continue to be reliable up to the highest cosmic ray energies. Logarithmic extrapolations of proton-proton and proton-antiproton data are used to calculate the proton-air cross sections at very high energy. Finally, it is observed that if the exponentia…
The color dipole gBFKL phenomenology of a diffraction cone for photo- and electroproduction $γ^{*}N \to VN$ of heavy vector mesons (charmonium & bottonium) at HERA and in fixed target experiments is presented. A substantial shrinkage of the diffraction cone from the CERN/FNAL to the HERA range of c.m.s. energy $W$ is predicted. The $Q^{2}$-controlled selectivity to the color dipole size (scanning phenomenon) is shown to lead to a decrease of the diffraction slope with $Q^{2}$ (which is supported by the available experimental data). An approximate flavor independence of the diffraction slope in…
We investigate the energy behavior of the diffraction cone in the exclusive vector meson production in diffractive DIS within the k_t-factorization approach. In our calculations, we make full use of fits to the unintegrated gluon structure functions extracted recently from experimental data on F_2p. Confirming early predictions, we observe that shrinkage of the diffraction cone due to the slope of the Pomeron trajectory is significantly compensated by the anti-shrinkage behavior of the gamma -> V transition. In order to match recent ZEUS data on the energy behavior of the diffraction slope, al…
In this paper the optimal unitarity lower bound on logarithmic slope of the diffraction peak is investigated. It is shown that the unitarity lower bound is just the optimal logarithmic slopes predicted by the principle of least distance in space of states. A systematic tendency towards the saturation of the most forward-peaked limit is observed from all the available experimental data of all principal hadron-hadron (e.g., antiproton-proton, proton-proton, kaon-proton, pion-proton) scatterings practically at all laboratory momenta.
We present and discuss two different topics where Tevatron and HERA data can be compared directly. A method allowing for a direct comparison of data with theoretical predictions is proposed for forward jet production at HERA. An application to the determination of the effective Pomeron intercept in the BFKL-LO parametrization from $dσ/dx$ data at HERA leads to a good fit with a significantly high effective intercept, $α_P= 1.43 \pm 0.025 (stat.) \pm 0.025 (syst.)$. It is less than the value of the pomeron intercept using dijets with large rapidity intervals obtained at Tevatron. In a second pa…
The multiperipheral ladder structure of the Pomeron leads to the quite natural conclusion that the elastic slope Bel is not simple linear function of the colliding particles energy logarithm. The existing experimental data on the diffraction cone shrinkage points to such "complicated" dependence indeed. The shrinkage diffraction cone speed up with the beam energy is directly connected with an extreme rise of total cross-section (Froissart limit).
Exclusive diffractive photoproduction of heavy vector mesons (V=phi, J/psi and Upsilon) at HERA is studied in a model employing a dipole Pomeron exchange (P) with an inelastic gamma-P-V vertex. The model is fitted to the data on dsigma/dt, B and elastic sigma for Q^2=0 and beyond the threshold region. The elastic cross sections for both phi and J/psi photoproduction show a moderate increase within the HERA energy region. The flattening of the slope B(s) (little or no shrinkage) for J/psi is not correlated with the slope of the Pomeron trajectory. Estimates for Upsilon photoproduction at HERA a…
We demonstrate that the diffraction slope of the generalized BFKL pomeron amplitude has the conventional Regge growth $B(s) = B(0) + 2α_{\Pom}'\log(s)$. This proves that the generalized BFKL pomeron is described by the moving $j$-plane singularity. We give an estimate for the slope $α_{\Pom}'$ in terms of the correlation radius for the perturbative gluons.
The predictions of an impact-picture model for proton-antiproton elastic scattering are compared with the new UA4 experimental data in the Coulomb interference region at the center-of-mass energy of $541 GeV$. The predicted differential cross section, the parameter $ρ$ and the forward slope are in very good agreement with the data.
The relationships between the fundamental dynamics and diffraction phenomena in scattering from two-body composite system are discussed. A new simple formula for the shadow corrections to the total cross-section in scattering from deuteron has been derived and new scaling characteristics with a clear physical interpretation have been established. The effect of weakening the inelastic screening at super-high energies is theoretically discovered. A comparison with the experimental data on proton(antiproton)-deuteron total cross-sections has been performed. It is shown that there is quite a remar…
We perform Glauber model calculations of the antiproton-nucleus elastic and quasielastic scattering and absorption in the beam momentum range $\sim 0.5\div10$ GeV/c. A good agreement of our calculations with available LEAR data and with earlier Glauber model studies of the $\bar p A$ elastic scattering allows us to make predictions at the beam momenta of $\sim 10$ GeV/c, i.e. at the regime of the PANDA experiment at FAIR. The comparison with the proton-nucleus elastic scattering cross sections shows that the diffractive minima are much deeper in the $\bar p A$ case due to smaller absolute valu…
In this work we consider the QCD parton saturation models to describe soft interactions at the high energy limit. The total and elastic cross sections as well as the elastic slope parameter are obtained for proton-proton and pion-proton collisions and compared to recent experimental results. The analyses are done within the color dipole formalism taking into account saturation models which have been tested against DIS data. The main point is that the match between soft and hard interaction occurs in the saturation region which can be described by high density QCD approaches. Discussion is perf…
Within the color dipole gBFKL dynamics applied to the diffraction slope we predict an anomalous t dependence of the differential cross section as a function of energy and Q^2 for production of radially excited V'(2S) light vector mesons in contradiction with a well known standard monotonous t- behaviour for V(1S) mesons. The origin of this phenomenon is based on the interplay of the nodal structure of V'(2S) radial wave function with the energy and dipole size dependence of the color dipole cross section and of the diffraction slope. We present how a different position of the node in V'(2S) wa…
Currently available estimates of the gluon-fusion effect in ultra-high energy neutrino-nucleon interactions as well as in DIS on protons suffer from uncertainty in defining the scattering profile function $Γ(b)$. Indeed, the area, $S$, in the impact parameter space populated with interacting gluons varies by a factor of $4 - 5$ from one analysis to another. To get rid of uncertainties we specify the dipole-nucleon partial-wave amplitude $Γ(b)$ which meets the restrictions imposed by both the total dipole-nucleon cross section and the small angle elastic scattering amplitude. The area $S$ becom…
Using a model based on two elements: the Good-Walker mechanism for low mass diffraction and multi-pomeron interactions for high mass diffraction, we obtain an excellent description of all aspects of soft scattering at high energy. The parameters of the model are determined by a fit to experimental data, giving the slope of pomeron to be $α'_{IP} \approx 0.01 GeV^{-2}$. We calculate the survival probability of diffractive Higgs production, and obtained a value for this observable, which is smaller than 1% for the LHC energy range.
Analysis of directed flow ($v_1$) of protons, antiprotons and pions in heavy-ion collisions is performed in the range of incident energies $\sqrt{s_{NN}}$ = 2.7--27 GeV. Simulations have been done within a three-fluid model employing a purely hadronic equation of state (EoS) and two versions of the EoS involving deconfinement transitions: a first-order phase transition and a smooth crossover transition. High sensitivity of the directed flow, especially the proton one, to the EoS is found. The crossover EoS is favored by the most part of considered experimental data. A strong wiggle in the exci…
We report our calculations on the logarithmic slope of the diffractive structure function F_2^D considering distinct approaches coming from both the pQCD and the Regge descriptions of diffractive DIS. Such a quantity is a potential observable to discriminate between pQCD and Regge domains and allows to disentangle the underlying dynamics.
We demonstrate that the entirety of the data on proton--proton and antiproton--proton forward scattering between 6 GeV and 57 TeV center-of-mass energy is sufficient to show that $σ_{\rm elas}/σ_{\rm tot} \rightarrow 1/2$, and that $8πB/σ_{\rm tot}\rightarrow 1$ at very high energies, where $B$ the forward slope parameter for the differential elastic scattering cross sections. The relations demonstrate convincingly that the asymptotic $pp$ and $\bar{p}p$ scattering amplitudes approach those of scattering from a black disk. This result obviously has implications for any new physics that modifie…
The Froissart bound on the total cross section is subjected to test against very high energy data. We have found no clear evidence for its violation. The scaling property of differential cross section in the diffraction region is investigated. It exhibits scaling in the ISR, SPS, Tevatron and LHC energy domain which had hitherto remained unexplored. The slope of the diffraction peak is fitted and the data are tested against the rigorous bounds.
Soft diffraction phenomena in elastic nucleon scattering are considered from the viewpoint of the spin dependence of the interaction potential. Spin-dependent pomeron effects are analyzed for elastic $pp$ scattering, spin-dependent differential cross sections and spin correlation parameters are calculated. The spin correlation parameter $A_N$ is examined on the basis of experimental data from $\sqrt{s} = 4.9 \ GeV$ up to $23.4 \ $GeV in the framework of the extended High Energy Generalized Structure (HEGS) model. It is shown that the existing experimental data of proton-proton and proton-antip…
The high energy part of the hadron spin flip amplitude is examined in the framework of the new high energy general structure (HEGS) model of the elastic hadron scattering at high energies. The different forms of the hadron spin flip amplitude are compared in the impact parameters representation. It is shown that the existing experimental data of the proton-proton and proton-antiproton elastic scattering at high energy in the region of the diffraction minimum and at large momentum transfer give support in the presence of the energy-independent part of the hadron spin flip amplitude with the mom…
Multi Pomeron interactions are the main source of high mass diffraction. Their role in high energy dynamics greatly influences the predictions for high energy cross sections and survival probabilities of hard diffraction channels, notably, diffractive Higgs production at the LHC. Our approach, is motivated by the fact that we obtain a very small value for the fitted slope of the Pomeron trajectory, which justifies the use of perturbative QCD for soft scattering. Our suggested model differs from the proposal of the Durham KMR group which is based on a parton model interpretation of the Reggeon …
We make a detailed eikonal fit to current data on the total and elastic scattering cross sections, the ratios $ρ$ of the real to the imaginary parts of the forward elastic scattering amplitudes, and the logarithmic slopes $B$ of the differential cross sections $dσ/dt$ at $t=0$, for proton-proton and antiproton-proton scattering at center-of-mass energies $W$ from 5 GeV to 57 TeV. The fit allows us to investigate the structure of the eikonal amplitudes in detail, including the impact-parameter structure of the energy-independent edge in the scattering amplitude shown to exist by Block {\em et a…
We re-examine V. Gribov's theorem of 1960 according to which the total cross-section cannot approach a finite non-zero limit with, at the same time, a diffraction peak having a finite slope. We are very close to proving by an explicit counter-example that elastic unitarity in the elastic region is an essential ingredient of the proof. By analogy, we raise the question of the saturation of the Froissart-Martin bound, for which no examples incorporating elastic unitarity exist at the present time.
In this paper we compare the prediction for high energy soft interactions in the model of N=4 SYM, with the experimental data. It is shown that this model is able to describe the total, elastic and inelastic cross sections and the elastic slope with only three free parameters. However, the model failed to obtain the cross sections for diffractive production, which was close to the experimental data, giving small values for them. We believe that the theory of N=4 SYM, of the order of $1/λ$ is needed to find the origin of large mass diffraction.
Cosmic ray (CR) physics has entered a precision-driven era. With the latest AMS-02 nuclei data (boron-to-carbon ratio, proton flux, helium flux and antiproton-to-proton ratio), we perform a global fitting and constrain the primary source and propagation parameters of cosmic rays in the Milky Way by considering 3 schemes with different data sets (with and without $\bar{\mathrm{p}}/\mathrm{p}$ data) and different propagation models (diffusion-reacceleration and diffusion-reacceleration-convection models). We find that the data set with $\bar{\mathrm{p}}/\mathrm{p}$ data can remove the degeneracy…
Some time ago, an accurate phenomenological approach, the BSW model, was developed for proton-proton and antiproton-proton elastic scattering cross sections at center-of-mass energies above 10 GeV. This model has been used to give successful theoretical predictions for these processes, at successive collider energies. The BSW model involves a combination of integrals that, while computable numerically at fairly high energies, require some mathematical analysis to reveal the high-energy asymptotic behavior. In this paper we present a high-energy asymptotic representation of the scattering ampli…
We analyze the recently discovered phenomena in elastic proton-proton scattering at the LHC, challenging the standard Regge-pole theory: the low-$|t|$ "break" (departure from the exponential behavior of the diffraction cone), the accelerating rise with energy of the forward slope $B(s,t=0)$, the absence of secondary dips and bumps on the cone and the role of the odderon in the forward phase of the amplitude, $ρ(13~TeV)=0.1\pm0.01$, and especially its contribution at the dip region, measured recently by TOTEM. Relative contributions from different components to the scattering amplitude are eval…
It is shown that the darkness of the interaction region of protons is governed by the ratio of the slope of the diffraction cone to the total cross section. At LHC energies, it becomes completely absorptive at small impact parameters. The lower limit of the ratio is determined. That imposes some restrictions on its energy behavior. It is argued that the black disk terminology should be replaced by the black torus.
The long standing mystery of smallness of diffractive dissociation of hadrons to large effective masses (the Pomeron-proton cross section is only 2 mb) witnesses that the gluonic clouds of valence quarks are so small (r_0=0.3fm) that soft interaction hardly resolves those gluons (diffraction is \propto r_0^4). A color-dipole light-cone (LC) approach is developed which incorporates a strong nonperturbative interaction of the LC gluons. The energy dependent part of the total hadronic cross section is calculated in a parameter-free way employing the nonperturbative LC wave functions of the quark-…
The rise of the total, elastic and inelastic hadronic cross sections at high energies is investigated by means of an analytical parametrization, with the exponent of the leading logarithm contribution as a free fit parameter. Using derivative dispersion relations with one subtraction, two different fits to proton-proton and antiproton-proton total cross section and rho parameter data are developed, reproducing well the experimental information in the energy region 5 GeV - 7 TeV. The parametrization for the total cross sections is then extended to fit the elastic (integrated) cross section data…
We present a bound on the imaginary part of the single helicity-flip amplitude for spin 1/2-spin 1/2 scattering at small momentum transfer. The variational method of Lagrange multipliers is employed to optimize the single-flip amplitude using the values of the total cross section, the elastic cross section and diffraction slope as equality constraints in addition to the inequality constraints resulting from unitarity. Such bounds provide important information related to the determination of polarization of a proton beam. In the case of elastic proton collisions the analyzing power at small sca…
High energy proton-proton and antiproton-proton elastic scattering are studied first in a model where the nucleon has an outer cloud and an inner core. Elastic scattering is viewed as due to two processes: a) diffraction scattering originating from cloud-cloud interaction; b) a hard or large |t| scattering originating from one nucleon core scattering off the other via vector meson omega exchange, while their outer clouds interact independently. The omega-exchange amplitude shows that omega behaves like an elementary vector meson at high energy, contrary to a regge pole behavior. This behavior,…
We review the evolution of the studies of diffractive processes in the strong interaction over the last 60 years. First, we briefly outline the early developments of the theory based on analyticity and unitarity of the S-matrix, including the derivation and exploration of the Regge trajectories and related moving cuts. Special attention is paid to the concept of the Pomeron trajectory introduced for description of total, elastic and diffractive cross sections at high energies and to the emergence of the dynamics of multi-Pomeron interactions.The role of large longitudinal distances and color c…
The following effects in the nearly forward ("soft") region of the LHC are proposed to be investigated: 1) At small |t| the fine structure of the cone (Pomeron) shouldbe scrutinized: a) a break of the cone near $t\approx - 0.1 ~ GeV$^2, due to the two-pion threshold, and required by t-channel unitarity, is expected, and b) possible small-period oscillations between $t=0$ and the dip region. 2) In measuring the elastic $pp$ scattering and total $pp$ cross section at the LHC, the experimentalists are urged to treat the total cross section $σ_t,$ the ratio $ρ$, the forward slope $B$ and the lumin…
The elastic hadronic amplitude is calculated using the nonperturbative light-cone dipole representation for gluon bremsstrahlung. The data for large mass diffraction demand a two-scale structure of light hadrons: the gluon clouds of the valence quarks with a size of 0.3fm and the hadronic size 1fm. The presence of the two scales unavoidably leads to a specific form for the total hadronic cross section which consists of a steeply rising \propto s^Δ (Δ=0.17 +/- 0.01) term related to gluon radiation, and a large constant term originating from soft interactions which does not induce any gluon emis…
In the absence of a global description of the experimental data on elastic and soft diffractive scattering from the first principles of QCD, model-independent analyses may provide useful phenomenological insights for the development of the theory in the soft sector. With that in mind, we present an empirical study on the energy dependence of the ratio $X$ between the elastic and total cross sections; a quantity related to the evolution of the hadronic central opacity. The dataset comprises all the experimental information available on proton-proton and antiproton-proton scattering in the c.m. …
