We propose to describe the process $ p ~ \bar{p} \rightarrow π^+ ~ π^-$ in a perturbative, QCD motivated framework in which a hard $ud \, \bar{u} \bar{d} \rightarrow d \, \bar{d} $ annihilation factorizes from soft transition distribution amplitudes. We advocate that the scale allowing for this factorization is the large transverse momentum transfer. In our simplified model, in which the proton is considered as a (scalar)diqark-quark system, a transition distribution amplitude describes the non-perturbative transition of the proton to the meson by emission of a scalar, isoscalar $ ud $-diquark and absorption of an antiquark (analogously for $ \bar{p} \rightarrow π^- $). We model the transition distribution amplitudes as an overlap of light-cone wave functions and present first results for the differential cross section. This process will be measured by the $ \bar{\mbox{P}}$ANDA experiment at GSI-FAIR.
We report on the handbag contribution to two-photon annihilation into pion and kaon pairs at large energy and momentum transfer. The underlying physics of the mechanism is outlined and characteristic features and predictions are presented.
We propose to describe the process $ p \bar{p} \,\to\, \bar{D^0} D^0$ in a perturbative QCD motivated framework where a double-handbag hard process $ u d \bar u \bar d \to \bar{c} c$ factorizes from transition distribution amplitudes, which are quasi forward hadronic matrix elements of $Ψ_q Ψ_q Ψ_c $ operators, where q denotes light quarks and c denotes the heavy quark. We advocate that the charm-quark mass acts as the large scale allowing this factorization. We calculate this process in the simplified framework of the scalar diquark model and present the expected cross sections for the PANDA …
We investigate the soft handbag contribution to two-photon annihilation into pion or kaon pairs at large energy and momentum transfer. The amplitude is expressed as a hard gamma gamma -> q qbar subprocess times a form factor describing the soft transition from q qbar to the meson pair. We find the calculated angular dependence of the cross section in good agreement with data, and extract annihilation form factors of plausible size. A key prediction of the handbag mechanism is that the differential cross section is the same for charged and neutral pion pairs, in striking contrast with what is f…
We study the handbag contribution to two-photon annihilation into baryon-antibaryon pairs at large energy and momentum transfer. We derive factorization of the process amplitude into a hard gamma gamma -> q qbar subprocess and form factors describing the soft q qbar -> B Bbar transition, assuming that the process is dominated by configurations where the (anti)quark approximately carries the full momentum of the (anti)baryon. The form factors represent moments of time-like generalized parton distributions, so-called B Bbar distribution amplitudes. A characteristic feature of the handbag mechani…
The annihilation of antiprotons on deuterons at rest are investigated for the case when pion-nucleon and pion-delta-isobar pairs are produced. The two-step mechanism is investigated by analysing these processes when either neutral particles and charged ones are produced. Some predictions for the branching ratios are presented.
The annihilation of proton and antiproton to electron-positron pair, including radiative corrections due to the emission of virtual and real photons is considered. The results are generalized to leading and next-to leading approximations. The relevant distributions are derived and numerical applications are given in the kinematical range accessible to the PANDA experiment at the FAIR facility.
The pentaquark component is included in the proton wave functions to study phi meson production proton-antiproton annihilation reactions. With all possible configurations of the uuds subsystem proposed for describing the strangeness spin and magnetic moment of the proton, we estimate the branching ratios of the annihilation reactions at rest proton-antiproton to phi + X (X=pi, eta, rho, omega) from atomic proton-antiproton S- and P-wave states by using effective quark line diagrams incorporating the 3P0 model. The best agreement of theoretical prediction with the experimental data is found whe…
The associated production of a $J/ψ$ and a $π$-meson in antiproton-nucleon annihilation is studied in the framework of QCD collinear factorization. In this approach, a hard subprocess responsible for the production of the heavy quark-antiquark pair factorizes from soft hadronic matrix elements, such as the antiproton (nucleon) distribution amplitude and the nucleon-to-pion (antiproton-to-pion) transition distribution amplitude. This reaction mechanism should dominate the forward and backward kinematical regions, where the cross sections are expected to be measurable in the set-up of the PANDA …
The process p-pbar -> Lambda_c-Antilambda_c is investigated within the handbag approach. It is shown that the dominant dynamical mechanism, characterized by the partonic subprocess u-ubar -> c-cbar factorizes in the sense that only the subprocess contains highly virtual partons, a gluon to lowest order of perturbative QCD, while the hadronic matrix elements embody only soft scales and can be parameterized in terms of helicity flip and non-flip generalized parton distributions. Modelling these parton distributions by overlaps of light-cone wave functions for the involved baryons we are able to …
Exclusive proton-antiproton annihilation into two photons can be viewed as the Compton process in the crossed channel. At large s (~10 GeV^2) and |t|,|u| s this process can be described by a generalized partonic picture, analogous to the 'soft mechanism' in wide-angle real Compton scattering. The two photons are emitted in the annihilation of a single fast quark and antiquark ('handbag graph'). The transition of the p-pbar system to a q-qbar pair through soft interactions is described by double distributions, which can be related to the timelike proton elastic form factors as well as, by cross…
Antiproton--proton annihilation into light neutral mesons in the few GeV energy domain is investigated in view of a global description of the existing data and predictions for future experiments at PANDA, FAIR. An effective meson model earlier developed, with mesonic and baryonic degrees of freedom in $s$, $t$, and $u$ channels, is applied here to $π^0π^0$ production. Form factors with logarithmic $s$ and $t(u)$ dependencies are applied. A fair agreement with the existing angular distributions is obtained. Applying SU(3) symmetry, it is straightforward to recover the angular distributions for …
We study the pair-production of heavy mesons in proton-antiproton annihilations within a perturbative QCD-motivated framework. In particular we investigate $p \bar{p} \rightarrow \overline{D^0} D^0$ within a double handbag approach, where a hard subprocess factorizes from soft hadronic matrix elements. The soft matrix elements can be parametrized by transition distribution amplitudes, which are off-diagonal in flavor space. The transition distribution amplitudes are modelled as overlaps of light-cone wave functions. We obtain rather robust model results for $p \bar{p} \rightarrow \overline{D^0…
We study the production of charmed mesons (D, D_s) in antiproton-proton annihilation close to the reaction thresholds. The elementary charm production process is described by baryon exchange and in the constituent quark model, respectively. Effects of the interactions in the initial and final states are taken into account rigorously. The calculations are performed in close analogy to our earlier study on pbarp to KbarK by connecting the processes via SU(4) flavor symmetry. Our predictions for the DDbar production cross section are in the order of 10^{-2} -- 10^{-1} mu b. They turned out to be …
The pion multiplicity distribution is widely believed to reflect the statistical aspects of $\bar{p}p$ annihilation at rest. We try to reproduce it in a grand canonical picture with explicit conservation of electric charge, isospin, total angular momentum, and the parity quantum numbers $P$, $C$, and $G$ via the projection operator formalism. Bose statistics is found to be non-negligible, particularly in fixing the interaction volume. The calculated pion multiplicity distribution for $\left\langle n_π \right\rangle = 5$ turns out to depend strongly on the conservation of the angular momentum a…
Apparent channel-dependent violations of the OZI rule in nucleon-antinucleon annihilation reactions are discussed in the presence of an intrinsic strangeness component in the nucleon. Admixture of strange-antistrange quark pairs in the nucleon wave function enables the direct coupling to the phi-meson in the annihilation channel without violating the OZI rule. Three forms are considered in this work for the strangeness content of the proton wave function, namely, the uud cluster with a strange-antistrange sea quark component, kaon-hyperon clusters based on a simple chiral quark model, and the …
We estimate the flux of cosmic-ray antiprotons expected from the annihilation of neutralinos in the galactic halo. The antiproton signal may offer an important alternative detection scheme in the case that neutralino annihilation proceeds mainly to the two-gluon final state.
We study in this paper the scenario where the dark matter is constituted by Majorana particles which couple to a light Standard Model fermion and an extra scalar via a Yukawa coupling. In this scenario, the annihilation rate into the light fermions with the mediation of the scalar particle is strongly suppressed by the mass of the fermion. Nevertheless, the helicity suppression is lifted by the associated emission of a gauge boson, yielding annihilation rates which could be large enough to allow the indirect detection of the dark matter particles. We perform a general analysis of this scenario…
In this talk the handbag approach to hard exclusive wide-angle processes is reviewed and applications, as for instance two-photon annihilations into pairs of mesons, are discussed.
We use classical or large Nc QCD to describe the mesons (pion, rho, omega) coming from proton-antiproton annihilation at rest as classical fields, which we then quantize as coherent states. This treatment gives a nearly parameter free account of the pion branching ratios in annihilation.
We show that in the scenario where dark matter (DM) particles annihilate through light mediators, the energy spectra of the final state cosmic-ray particles depend strongly on the mediator mass. For final state antiprotons, a spectrum with relatively narrow peak occurs when the mediator mass is comparable to the $\pbar p$ production threshold. Of interest, the latest AMS-02 data on the $\pbar/p$ flux ratio hint at a bump-like excess over the expected background in the energy range $\sim100-450$ GeV. We show that such a light mediator scenario is favoured by the latest AMS-02 data over the scen…
AMS-02 provided the unprecedented statistics in the measurement of the positron fraction from cosmic rays. That may offer a unique opportunity to distinguish the positron spectrum coming from various dark matter (DM) annihilation channels, if DM is the source of this positron excess. Therefore, we consider the scenario that the DM can annihilate into leptonic, quark, and massive gauge boson channels simultaneously with floating branching ratios to test this hypothesis. We also study the impacts from MAX, MED, MIN, and DC diffusion models as well as from isothermal, NFW, and Einasto DM density …
Annihilation process of proton and antiproton to guark antiquark pair accompanied by emission of two additional gluon jets with intermediate state of vector meson is considered.Strong azimuthal correlation is revealed of two gluonic jets,effectively created in the same plane.Some applications to cosmic ray events and to LHC experiments are discussed.
The handbag mechanism for wide-angle exlusive scattering reactions is discussed and compared with other theoretical approaches. Its application to Compton scattering, meson photoproduction and two-photon annihilations into pairs of hadrons is reviewed.
The lightest neutralino is a viable dark matter (DM) candidate. In this paper we study indirect detection of the wino-like neutralino DM using positrons and antiprotons from the annihilation in the galactic halo. When the mass is around 2 TeV, which is favored from the thermal relic abundance, the non-perturbation effect significantly enhances the annihilation cross sections into positrons and antiprotons. We find that the positron and antiproton fluxes with energies larger than 100 GeV may become larger than the expected backgrounds. Since the positron flux is less sensitive to the astrophysi…
We study the production of charmed mesons (D) and baryons (Lambda_c) in antiproton-proton (app) annihilation close to their respective production thresholds. The elementary charm production process is described by either baryon/meson exchange or by quark/gluon dynamics. Effects of the interactions in the initial and final states are taken into account rigorously. The calculations are performed in close analogy to our earlier study on app -> antiLambda-Lambda and app -> antiK-K by connecting the processes via SU(4) flavor symmetry. Our predictions for the antiLambda_c-Lambda_c production cross …
Antiproton proton annihilation reactions allow unique access to the moduli and phases of nucleon electromagnetic form factors in the time like region. We present the helicity amplitudes for the unequal mass single photon reaction $p \bar{p}\to l^+ l^-$ in the s channel including the lepton mass. The relative signs of these amplitudes are determined using simple invariance properties. Helicity amplitudes for the annihilation reaction $p \bar{p} \to N \bar{N}$ are also given, where $N$ is any spinor particle with structure. Crossing relations between the $e p \to e p$ scattering and the $p \bar{…
We study the cosmic ray antiprotons with updated constraints on the propagation, proton injection, and solar modulation parameters based on the newest AMS-02 data near the Earth and Voyager data in the local interstellar space, and on the cross section of antiproton production due to proton-proton collisions based on new collider data. We use a Bayesian approach to properly consider the uncertainties of the model predictions of both the background and the dark matter (DM) annihilation components of antiprotons. We find that including an extra component of antiprotons from the annihilation of D…
A possible interpretation of the near-threshold enhancement in the $(p\bar{p})$-mass spectrum in $J/ψ{\to}γp{\bar p}$ is the of existence of a narrow baryonium resonance X(1860). Mesonic decays of the $(p\bar{p})$-bound state X(1860) due to the nucleon-antinucleon annihilation are investigated in this paper. Mesonic coherent states with fixed $G$-parity and $P$-parity have been constructed . The Amado-Cannata-Dedoder-Locher-Shao formulation(Phys Rev Lett. {\bf 72}, 970 (1994)) is extended to the decays of the X(1860). By this method, the branch-fraction ratios of $Br(X\to η4π)$, $Br(X\to η2π)$…
Antiproton--proton annihilation into light mesons is revisited in the few GeV energy domain, in view of a global description of the existing data. An effective meson model is developed, with mesonic and baryonic degrees od freedom in $s$, $t$, and $u$ channels. Regge factors are added to reproduce the proper energy behavior and the forward and backward peaked behavior. A comparison with existing data and predictions for angular distributions and energy dependence are done for charged and neutral pion pair production.
We report the main results of a paper where recent data of low-energy cosmic-ray $\bar p$ spectrum have been analyzed in terms of newly calculated fluxes for secondary antiprotons and for a possible contribution of an exotic signal due to neutralino annihilation in the galactic halo. We also present the results of a paper in which we have proved that a sizeable fraction of the supersymmetric neutralino configurations, singled out by the DAMA/NaI data on a possible annual modulation effect in WIMP direct search, may provide detectable cosmic-ray antiproton signals.
We analyze the data of low-energy cosmic-ray antiproton spectrum, recently published by the BESS Collaboration, in terms of newly calculated fluxes for secondary antiprotons and for a possible contribution of an exotic signal due to neutralino annihilation in the galactic halo. We single out the relevant supersymmetric configurations and discuss their explorability with experiments of direct search for particle dark matter and at accelerators. We discuss how future measurements with the Alpha Magnetic Spectrometer (AMS) on the Shuttle flight may disentangle the possible neutralino-induced cont…
In this talk, we discuss the physics modeling of antiproton spectra arising from dark matter (DM) annihilation or decay in a model-independent manner. The modeling of antiproton spectra contains some intrinsic uncertainties related to QCD parton showers and hadronisation of baryons. We briefly assess the sources of these uncertainties and their impact on antiproton energy spectra for a few selected DM scenarios. The results are provided in tabulated form for future analyses.
Lattice QCD and other theoretical models predict that the 0(-+), 2(++) and 2(-+) glueballs have masses in the range of 2.0 to 2.4 GeV. For resonances in such an energy range, three-body decay modes are expected to be large. The strategy for looking for these glueballs and the newest results from studying Crystal Barrel data on the three-body annihilation of proton-antiproton in flight are presented.
Decays into two charged pions of the f0(1370) are the main source of an isolated structure localized between 1.2 and 1.5 GeV in the two charged pions mass spectrum measured in pp Central Exclusive Production (CEP) at 200 GeV at very low four momentum transfer ltl by the STAR experiment. These data confirm in the two charged pions decay channel the existence of the f0(1370) as an isolated well identified structure previously observed in K+K-, KsKs, 4 charged pions, two charged and two neutral pions and 4 neutral pions decays measured in antiproton annihilations at rest. The ensemble of these da…
Previous analytical formulas in the Glauber model for high-energy nucleus-nucleus collisions developed by Wong are utilized and extended to study antiproton-nucleus annihilations for both high and low energies, after taking into account the effects of Coulomb and nuclear interactions, and the change of the antiproton momentum inside a nucleus. The extended analytical formulas capture the main features of the experimental antiproton-nucleus annihilation cross sections for all energies and mass numbers. At high antiproton energies, they exhibit the granular property for the lightest nuclei and t…
The $Δ$-excitation in $\overline{p}d$ annihilation at rest was studied. The annihilation amplitude from the statistical model and the $πN$ amplitude from the resonance model were adopted in our calculations. We analyze the invariant mass of the $π^+p$ and $π^-p$ systems selecting the protons with momenta above 400 MeV/c and with respect to the different final reaction channels. Our model reproduces reasonably the experimental data.
The existence of antimatter domains in baryon asymmetrical Universe can appear as the cosmological consequence of particle theory in inflationary models with non-homogeneous baryosynthesis. Such a domain can survive in the early Universe and form globular cluster of antimatter stars in our Galaxy. The model of antimatter pollution of Galaxy and annihilation with matter gas is developed. The proton-antiproton annihilation gamma flux is shown to reproduce the observed galactic gamma background measured by EGRET. From comparison with observational data the estimation on the maximally allowed amou…
Two new observations have strengthened the case for the supersymmetric nature of the Cold Dark Matter component in our universe: First, it was shown that new data on the nuclear abundance, B/C - and 10Be/9Be ratios constrain the diffusion parameters in Galactic Models so strongly, that they lead to a clear deficiency in the production of diffuse hard gamma rays, antiprotons and hard positrons, if no anomalous sources or anomalous energy dependence of the diffusion coefficients are postulated. Second, from the precise relic density measurement by WMAP the WIMP annihilation cross section can be …
We present a geometric interpretation of the so-called annihilation range in reactions of the type $\bar pp \to$ {\em two light mesons} based upon Lorentz effects in the highly relativistic final states ($γ=E_{\mathrm{cm}}/2mc^2\simeq 6.8-8.0$). Lorentz-boosted meson wave functions, within the framework of the constituent quark model, result in a richer angular dependence of the annihilation amplitudes and thus in higher partial wave contributions ($J>1$) than usually obtained. This approach sheds some light on what could be a "{\em short}" annihilation range and how it is influenced by the an…
We extend previous calculations of polarization observables for the annihilation reaction $\bar p +p\to \ell^{-}+\ell^{+}$ to the case of heavy leptons, such as the $τ$-lepton. We consider the case when the beam and/or the target are polarized, as well as the polarization of the outgoing leptons. We give the dependence of the unpolarized cross section, angular asymmetry, and various polarization observables on the relevant kinematical variables in the center of mass and in the laboratory system, with particular attention to the effect of the mass induced terms.
Quark model intrinsic wave functions of highly energetic pions in the reaction \bar pp->π^-π^+ are subjected to a relativistic treatment. The annihilation is described in a constituent quark model with A2 and R2 flavor-flux topology and the annihilated quark-antiquark pairs are in 3P_0 and 3S_1 states. We study the effects of pure Lorentz transformations on the antiquark and quark spatial wave functions and their respective spinors in the pion. The modified quark geometry of the pion has considerable impact on the angular dependence of the annihilation mechanisms.
Exclusive proton-antiproton annihilation into two photons at large s (~10 GeV^2) and |t|,|u| ~ s can be described by a generalized parton picture analogous to the 'soft mechanism' in wide-angle real Compton scattering. The two photons are emitted in the annihilation of a single fast quark and antiquark. The matrix element describing the transition of the p-pbar system to a q-qbar pair can be related to the timelike proton elastic form factors as well as to the quark/antiquark distributions measured in inclusive deep-inelastic scattering. The reaction could be studied with the proposed 1.5-15 G…
A possible hint of dark matter annihilation has been found in Cuoco, Korsmeier and Krämer (2017) from an analysis of recent cosmic-ray antiproton data from AMS-02 and taking into account cosmic-ray propagation uncertainties by fitting at the same time dark matter and propagation parameters. Here, we extend this analysis to a wider class of annihilation channels. We find consistent hints of a dark matter signal with an annihilation cross-section close to the thermal value and with masses in range between 40 and 130 GeV depending on the annihilation channel. Furthermore, we investigate in how fa…
In the reaction of the antiproton-deuteron electromagnetic annihilation pbar + d --> e+e-n the value of the invariant mass M of the (e+e-) pair can be near or below the (pbar p) mass even for enough high momentum of incident antiproton. This allows to access the proton electromagnetic form factors in the time-like region of q^2 near the (pbar p) threshold. We estimate the cross section dsigma(pbar + d --> e+e-n)/dM for an antiproton beam momentum of 1.5 GeV/c. We find that near the (pbar p) threshold this cross section is about 1 pb/MeV. The case of heavy nuclei target is also discussed. Eleme…
We evaluate the antiproton--to--proton flux ratio which can be generated by neutralino--neutralino annihilation in the galactic halo, considering the most general compositions for the relic neutralinos and modelling the neutralino local density according to its relic abundance. We find that in the case of mixed neutralino compositions this $\bar p/p$ ratio is higher than for pure higgsinos or gauginos. It is shown how the expected improvements in sensitivity for the new measurements of the $\bar p/p$ may provide very useful information, complementary to the one obtainable with other experiment…
Contrary to the reaction pbar + p --> e+ e- with a high momentum incident antiproton on a free target proton at rest, in which the invariant mass M of the (e+ e-) pair is necessarily much larger than the (pbar p) mass, in the reaction pbar + d --> n e+ e- the value of M can take values near or below the (pbar p) mass. In the antiproton-deuteron electromagnetic annihilation, this allows to access the proton electromagnetic form factors in the time-like region of q^2 near the (pbar p) threshold. We estimate the cross section dsigma(pbar +d --> e+ e- n)/dM for an antiproton beam momentum of 1.5 G…
The all-sky survey in high-energy gamma rays (E > 30 MeV) carried out by the Energetic Gamma Ray Experiment Telescope (EGRET) aboard the Compton Gamma-Ray Observatory provides a unique opportunity to examine in detail the diffuse gamma-ray emission. The observed diffuse emission has a Galactic component arising from cosmic-ray interactions with the local interstellar gas and radiation as well an almost uniformly distributed component that is generally believed to originate outside the Galaxy. The results of the observations have been interpreted as the extragalactic high-energy gamma-ray emiss…
Radiative corrections to the annihilation of proton--antiproton into electron--positron are revisited, including virtual and real (soft and hard) photon emission. This issue is relevant for the time-like form factors measurements planned at the PANDA experiment at the FAIR facility, in next future. The relevant formulas are given. A stand-alone Monte-Carlo integrator is developed on the basis of the calculated radiative cross section and its application to the PANDA experiment is illustrated.
The large set of accurate data on differential cross section and analyzing power from the CERN LEAR experiment on $\bar pp \to π^+π^-$ in the range from 360 to 1550 MeV/c is well reproduced within a distorted wave approximation approach. The initial $\bar pp$ scattering wave functions originate from a recent $\bar N N$ model. The transition operator is obtained from a combination of the $^3P_0$ and $^3S_1$ quark-antiquark annihilation mechanisms. A good fit to the data, in particular the reproduction of the double dip structure observed in the analyzing powers, requires quark wave functions fo…
The cross sections for the production of $B_s$ and $B_s^*$ mesons through the fragmentation process in $\bar{p}p$ collisions were calculated. The input parameters were determined from the measured $B_s$ and $B_s^*$ production rates in $e^+e^-$ annihilation. The transverse momentum distributions $dσ/dp_{T}$ are given for $\sqrt{s}=1.8$ TeV, the Fermilab Tevatron energy.
Using an effective interaction approach to describe the interactions between the dark matter particle and the light degrees of freedom of the standard model, we calculate the antiproton flux due to the annihilation of the dark matter in the Galactic Halo and compare to the most recent antiproton spectrum of the PAMELA experiment. We obtain useful constraints on the size of the effective interactions that are comparable to those deduced from collider and gamma-ray experiments.
We consider dark matter annihilation into a general set of final states of Standard Model particles, including two-body and four-body final states that result from the decay of intermediate states. For dark matter masses ~10-10^5 GeV, we use updated data from Planck and from high gamma-ray experiments such as Fermi-LAT, MAGIC, and VERITAS to constrain the annihilation cross section for each final state. The Planck constraints are the most stringent over the entire mass range for annihilation into light leptons, and the Fermi-LAT constraints are the most stringent for four-body final states up …
If the dark matter particle is a Majorana fermion, annihilations into two fermions and one gauge boson could have, for some choices of the parameters of the model, a non-negligible cross-section. Using a toy model of leptophilic dark matter, we calculate the constraints on the annihilation cross-section into two electrons and one weak gauge boson from the PAMELA measurements of the cosmic antiproton-to-proton flux ratio. Furthermore, we calculate the maximal astrophysical boost factor allowed in the Milky Way under the assumption that the leptophilic dark matter particle is the dominant compon…
Using the latest AMS-02 cosmic ray antiproton flux data, we search for potential dark matter annihilation signal. The background parameters about the propagation, source injection, and solar modulation are not assumed {\it a priori}, but based on the results inferred from the recent B/C ratio and proton data measurements instead. The possible dark matter signal is incorporated into the model self-consistently under a Bayesian framework. Compared with the astrophysical background only hypothesis, we find that a dark matter signal is favored. The rest mass of the dark matter particles is $\sim 2…
Recent measurements of very low-energy ($p_{L}<100$ MeV/c) $\bar p$ annihilation on light nuclei reveal apparent suppression of annihilation upon increasing the atomic charge $Z$ and mass number $A$. Using $\bar p$-nucleus optical potentials $V_{\rm opt}$, fitted to $\bar p$-atom energy-shifts and -widths, we resolve this suppression as due to the strong effective repulsion produced by the very absorptive $V_{\rm opt}$. The low-energy $\bar p$-nucleus wavefunction is kept substantially outside the nuclear surface and the resulting reaction cross section saturates as function of the strength of…
