The e+e- --> pi+pi-pi0pi0 reaction cross section as a function of the incident energy is calculated using a model that is an extension of our recently published model of the e+e- annihilation into four charged pions. The latter considered the intermediate states with the pi, rho, and a_1 mesons and fixed the mixing angle of the a_1-rho-pi Lagrangian and other parameters by fitting the cross section data. Here we supplement the original intermediate states with those containing omega(782) and h_1(1170), but keep unchanged the values of those parameters that enter both charged and mixed channel calculations. The inclusion of omega is vital for obtaining a good fit to the cross section data, while the intermediate states with h_1 further improve it. Finally, we merge our models of the e+e- --> pi+pi-pi0pi0 and e+e- --> pi+pi-pi+pi- reactions and obtain a simultaneous good fit.
A parametrization of the Bose-Einstein correlation function of pairs of identical pions produced in hadronic e+e- annihilation is proposed within the framework of a model (the tau-model) in which space-time and momentum space are very strongly correlated. Using information from the Bose-Einstein correlations as well as from single-pion spectra,it is then possible to reconstruct the space-time evolution of pion production.
We assume that nucleon antinucleon annihilation is a fast process leading to a classical coherent pion pulse. We develop the quantum description of such pion waves based on the method of coherent states. We study the consequences of such a description for averages of charge types and moments of distributions of pion momenta with iso-spin and four-momentum conservation taken into account. We briefly discuss the applicability of our method to annihilation at rest, where we find agreement with experiment, and suggest other avenues for its use.
We consider an alternative explanation of newly found growth of neutral pion transition form factor with virtuality of one of photon. It is based on Sudakov suppression of quark-photon vertex. Some applications to scattering and annihilation channels are considered including the relevant experiments with lepton-proton scattering.
Process of muon (pion) pair production with small invariant mass in the electron-positron high-energy annihilation, accompanied by emission of hard photon at large angles, is considered. We find that the Dell-Yan picture for differential cross section is valid in the charge-even experimental set-up. Radiative corrections both for electron block and for final state block are taken into account.
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…
The process of the muon (pion) pair production with small invariant mass in the electron--positron high--energy annihilation, accompanied by emission of hard photon at large angles, is considered. We find that the Drell--Yan picture for differential cross section is valid in the charge--even experimental set--up. Radiative corrections both for electron block and for final state block are taken into account.
The Monte Carlo event generator PHOKHARA, which simulates hadron and muon production at electron-positron colliders through radiative return, has been extended to final states with three pions. A model for the form factor based on generalized vector dominance has been employed, which is consistent with presently available experimental observations.
Forward-backward (charge) asymmetry in the processes of $e^+e^-$ annihilation into a pair of charged pseudoscalar mesons is recalculated in the one-loop approximation. The exact dependence on the meson masses is taken into account. Results known in the literature are partially corrected. The bulk of the charge asymmetry appears due to double-photon exchange in $s$ channel. Experimental studies of the asymmetry can be used to verify the point-like approximation used in calculation of radiative corrections due to emission of photons by pions or kaons.
We calculate the processes e+ e- -> 4 pions and tau -> nu_tau + 4 pions to O(p^4) in the low-energy expansion of the standard model. The chiral amplitudes of O(p^4) can be extended via resonance exchange to energies around 1 GeV. Higher-order effects have been included in the form of omega, a_1 and double rho exchange and by performing a resummation of the pion form factor. The predicted cross sections and the branching ratios BR(rho -> 4 pions) are in good agreement with available data.
We discuss pion pair production in two-photon collisions in two different kinematical regimes. When both photons are real and at moderately large center-of-mass energy s we elaborate on partonic transverse momentum and Sudakov corrections within the hard scattering approach. We also point out the difference between our approach and that of other authors. When one of the photons is highly virtual the produced pion pair can be described in terms of a two-pion distribution amplitude, for which we derive the perturbative limit at large s.
The photon pair production by pion annihilation in a hot and dense medium at the chiral phase transition is investigated within a chiral quark model. As a direct consequence of this transition the $σ$ meson appears as a bound state in the domain of temperatures and chemical potentials where the condition $M_σ(T,μ) \approx 2 M_π(T,μ)$ is fulfilled. This effect results in a strong enhancement of the cross section for the pion annihilation process $2 π\to 2 γ$ compared with the vacuum case. The calculation of the photon pair production rate as function of the invariant mass shows a strong enhance…
The processes of muons (tau) and charged pions pairs production at electron-positron annihilation with first order radiative corrections are considered. The calculation results are presented assuming the energies of final particles (cms implied) to be not far significantly from threshold production. The invariant mass distributions for the muon (tau) and pion pairs are obtained both for the initial and final state radiation. Some analytical calculations are illustrated numerically. The pions were assumed to be point-like objects and scalar QED was applied for calculation. The QED radiative cor…
Based on the S-matrix approach, we introduce a modified formula for the $π^{\pm}$ electromagnetic form factor which describes very well the experimental data in the energy region $2m_π \leq \sqrt{s} \leq 1.1$ GeV. Using the CVC hypothesis we predict $B(\tpp) = (24.75 \pm 0.38)\% $, in excellent agreement with recent experiments.
In frame of a phenomenological approach based on Compton-like Feynman amplitudes, we study multi-pion production in antiproton nucleon collisions. The main interest of this reaction is related to the possibility to study the properties of the presumable $\bar N N$ atom and of its resonances. For the case of formation of a scalar or pseudoscalar resonant state, with $I^G(J^{P})=1^-(0^{\pm}),~0^+(0^-)$ numerical results are obtained. The differential cross section in an experimental set-up where the pions invariant mass is measured, is given with explicit dependence on the lepton pair and pions …
We study inelastic meson-meson scattering that is governed by quark-antiquark annihilation and creation involving a quark and an antiquark annihilating into a gluon, and subsequently the gluon creating another quark-antiquark pair. The resultant hadronic reactions include for I=1: pion + pion to rho + rho, kaon + antikaon to kaon* + antikaon*, kaon + antikaon* to kaon* + antikaon*, kaon* + antikaon to kaon* + antikaon*, as well as pion + pion to kaon + antikaon, pion + rho to kaon + antikaon*, pion + rho to kaon* + antikaon, and kaon + antikaon to rho + rho. In each reaction, one or two Feynma…
We revise the pion-pion and quark-quark annihilation mechanisms of dilepton production during relativistic heavy-ion collisions. We focus on the modifications caused by the specific features of intramedium pion states rather than by medium modification of the rho-meson spectral density. The main ingredient emerging in our approach is a form-factor of the multi-pion (multi-quark) system. Replacing the usual delta-function the form-factor plays the role of distribution which, in some sense, "connects" the 4-momenta of the annihilating and outgoing particles. The difference between the c.m.s. vel…
The excitation curve of e+e- annihilation into four charged pions in the rho(770) region is calculated using three existing models with rho mesons and pions in intermediate states supplemented by Feynman diagrams with the a_1(1260)pi intermediate states. A two-term phenomenological Lagrangian of the a_1-rho-pi interaction is used. The mixing angle is determined by fitting the e+e- --> pi+pi-pi+pi- cross section data of the Novosibirsk CMD-2 collaboration and also its combination with the low-energy part of the BaBar collaboration data. It is shown that the inclusion of the a_1-pi intermediate …
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.
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.
We present an analysis of the process $e^+e^-\to V^*\toππγ$, where $V=γ$ or $V=Z$ boson, in the kinematical region where $\sqrt{s}$, the c.m. energy of the $e^+e^-$ pair, is large but much below the $Z$-pole. The subprocess $V^*\to ππγ$ can be described by the convolution of the hard scattering coefficient $V\to q \bar{q} γ$ and the general distribution amplitude of two pions $q\bar{q}\to ππ$. In the case of neutral pion production, $V=γ$ is the dominant process, which can therefore be used to access the GPAs of the pion, especially their $C$-even parts. The $γZ$ interference term provides an …
In this work we discuss the interest of measuring the ratio of of $p\bar p$ annihilation into kaon and pion pairs near the threshold region, where $S$ state dominates. It is shown that a good agreement with existing data on the ratio of the yields of charged kaon to pion pairs is obtained taking into account not only quark rearrangement in the incident hadrons, but also vacuum excitations.
The process of $e^+e^-$ annihilation into a $π^+π^-$ pair with radiation of a photon is considered. The amplitude of the reaction $e^+e^-\toπ^+π^-γ$ consists of the model independent initial-state radiation (ISR) and model-dependent final-state radiation (FSR). The general structure of the FSR tensor is constructed from Lorentz covariance, gauge invariance and discrete symmetries in terms of the three invariant functions. To calculate these functions we apply Chiral Perturbation Theory (ChPT) with vector and axial-vector mesons. The contribution of $e^+e^-\toπ^+π^-γ$ process to the muon anomal…
The process of $e^+ e^-$ annihilation into $π^+ π^-$ pair with radiation of the photon is considered. The amplitude of the reaction $e^+ e^- \to π^+ π^- γ$ consists of the model independent initial-state radiation (ISR) and model dependent final-state radiation (FSR). The general structure of the FSR tensor is constructed from Lorentz covariance, gauge invariance and discrete symmetries in terms of the three invariant functions. To calculate these functions we apply Chiral Perturbation Theory (ChPT) with vector and axial-vector mesons. The contribution of $e^+ e^- \to π^+ π^- γ$ process to the…
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…
An improved description of four-pion production in electron-positron annihilation and in tau lepton decays is presented. The model amplitude is fitted to recent data from BaBar which cover a wide energy range and which were obtained exploiting the radiative return. Predicting tau decay distributions from e+e- data and comparing these predictions with ALEPH and CLEO results, the validity of isospin symmetry is confirmed within the present experimental errors. A good description of two- and three-pion sub-distributions is obtained. Special emphasis is put on the predictions for omega pi (-> pi+p…
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 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…
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…
There is evidence of a second neutral pion from: (1) the anomalous branching ratios in the reactions p-bar p -> pi pi and p-bar d -> pi pi N, and (2) the 1960's results of Tsai-Chu et al. for antinucleon annihilation stars in emulsions. The anomaly of (1) is eliminated if the two neutral pions in the reactions p-bar p -> pi_0 pi_0 and p-bar d -> pi_0 pi_0 n are not identical. Tsai-Chu et al. observed a second neutral pion that ``decays more rapidly into electron pairs with larger opening angles and more frequently into double pairs.'' One antineutron annihilation event produced three neutral p…
Using a model calculation of dihadron fragmentation functions, we fit the spin asymmetry recently extracted by HERMES for the semi-inclusive pion pair production in deep-inelastic scattering on a transversely polarized proton target. By evolving the obtained dihadron fragmentation functions, we make predictions for the correlation of the angular distributions of two pion pairs produced in electron-positron annihilations at BELLE kinematics. Our study shows that the combination of two-hadron inclusive deep-inelastic scattering and electron-positron annihilation measurements can provide a valid …
An $ω$-meson in motion with respect to a nuclear medium can couple to a $σ$-meson through a particle-hole excitation. This coupling is large. We investigate its consequences for the width of $ω$-mesons in matter and for the s-wave annihilation of pions into lepton pairs which can take place in relativistic heavy ion collisions. We find that the two pion decay of $ω$-mesons, resulting from the $ω-σ$ transition and the subsequent $2π$ decay of the $σ$-meson, leads to a substantial broadening of $ω$-mesons in matter and possibly to an observable effect in experiments measuring the $e^+e^-$ decay …
New precise data on the low energy electron-positron annihilation into hadrons from Novosibirsk are used to obtain bounds on the elasticity parameter and the difference between the phase of the pion form factor and that of pion pion scattering
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 production and annihilation of antiprotons in the hadronic phase of heavy-ion collisions is evaluated within a thermal equilibrium approach. It is shown that the inverse reaction of $p\bar p$ annihilation (i.e., multi-pion annihilation $N_ππ\to p\bar p$ with $N_π\simeq$~5-7) in connection with oversaturation of pion phase space (i.e., finite pion chemical potentials) plays an important role in understanding the observed antiproton yields at SpS energies within the standard picture of subsequent chemical and thermal freezeout. Implications for RHIC energies are also addressed.
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.
In this paper, by employing the $k_{T}$ factorization theorem, we made the first calculation for the space-like scalar pion form factor $Q^2 F(Q^2)$ at the leading order (LO) and the next-to-leading order (NLO) level, and then found the time-like scalar pion form factor $F'^{(1)}_{\rm a,I}$ by analytic continuation from the space-like one. From the analytical evaluations and the numerical results, we found the following points: (a) the NLO correction to the space-like scalar pion form factor has an opposite sign with the LO one but is very small in magnitude, can produce at most $10\%$ decreas…
We evaluate the cross section for anti-p p -> l+ l- pi0 in the forward direction and for large lepton pair invariant mass. In this kinematical region, the leading-twist amplitude factorises into a short-distance matrix element, long-distance dominated antiproton Distribution Amplitudes and proton to pion Transition Distribution Amplitudes (TDA). Using a modelling inspired from the chiral limit for these TDAs, we obtain a first estimate of this cross section, thus demonstrating that this process can be measured at GSI-FAIR.
Starting from the low-energy structure derived from QCD, we extend the amplitudes for four-pion production in e+ e- annihilation and tau decays up to invariant four-pion masses of 1 GeV. Cross sections and branching ratios BR(rho^0 -> 4 pi) are compared with available data.
A new statistical model for multiparticle production in $e^+e^-$ annihilation is proposed based on the idea of the longitudinal phase space with limited transverse momentum. The longitudinal rapidity space is divided into cells of equal size in order to take into account the Bose-Einstein correlations(BEC) with a finite correlation length $δy$. The maximum entropy method is used to determine the probability distributions of the final state pions (or $ρ$ mesons) for a given mean multiplicity, mean transverse momentum and mean total energy. Event simulation based on our model is performed in two…
We study finite temperature effects on dilepton production from pion-pion annihilation in hot hadronic matter. The softening of the pion dispersion relation in a medium is found to enhance the production rate of dileptons with invariant masses in the region of $2m^*_π(T)<M<m_ρ$. On the other hand, the reduction of the pion electromagnetic form factor at finite temperature leads to a suppression of the dilepton production rate. Including both effects, we have found that the dilepton yield is slightly enhanced in the invariant mass region $M= 270\sim 600$ MeV but is suppressed around the vector …
For a long time doubts have existed on the existence of the f0(1370) meson as an individual object distinct and separated from the sigma meson. 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 squared ltl. These data confirm in the two charged pions decay channel the existence of the f0(1370) as an isolated well identified structure that was previously observed in K+K-, KsKs, 4 neutral …
We present new functional form of pion and kaon fragmentation functions up to next-to-leading order obtained through a global fit to single-inclusive electron-positron annihilation data and also employ, the semi-inclusive deep inelastic scattering asymmetry data from HERMES and COMPASS to determine fragmentation functions. Also we apply very recently electron-positron annihilation data from BaBar and Belle at $\sqrt{s}=10.54$ GeV and $\sqrt{s}=10.52$ GeV, respectively. In this analysis we consider the impression of semi-inclusive deep inelastic scattering asymmetry data on the fragmentation fu…
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.
Differential distributions in the $π_0π_0γ$ system created in the annihilation channel of an electron-positron collision are considered. The energy fractions of the pions (Dalitz-plot) distribution are presented in a general form and in approximation of intermediate vector mesons (excited and ordinary ones).It is pointed out that in relevant experiments the generalized polarizability of the neutral pion can be measured. Numerical illustrations are presented.
A way to explain the puzzling difference between the pion form factor as measured in e+ e- annihilations and in tau decays is discussed. We show that isospin symmetry breaking, beside the already identified effects, produces also a full mixing between the rho0, omega and phi mesons which generates an isospin 0 component inside the rho0 meson. This effect, not accounted for in current treatments of the problem, seems able to account for the apparent mismatch between e+ e- and tau data below the phi mass.
The main aim of this paper is a new determination of transverse momentum dependence of unpolarized fragmentation function (TMD FFs) in single inclusive hadron production in electron-positron annihilation (SIA) process. Motivated by the need for a reliable and consistent determination of TMD FFs, we use the most recent TMD production cross sections of charged pions ($π^\pm$), kaons ($K^\pm$) and protons/antiprotons ($p/\bar{p}$) measured in inclusive $e^+e^-$ collisions by Belle Collaboration. These datasets are the first transverse momentum dependence of identified light charged hadron measure…
The s-channel annihilation of proton and antiproton into a neutral pion and a real or virtual photon followed by lepton pair emission is studied. Such mechanism is expected to play a role at moderate values of the total energy $\sqrt{s}$, when the pion is emitted around $90^{\circ}$ in the center of mass. A fair comparison with the existing data is obtained taking into account scattering and annihilation channels. The cross section is calculated and numerical results are given in the kinematical range accessible in the PANDA experiment at FAIR.
Processes of electron-positron annihilation into charged pions and kaons are considered. Radiative corrections are taken into account exactly in the first order and within the leading logarithmic approximation in higher orders. A combined approach for accounting exact calculations and electron structure functions is used. An accuracy of the calculation can be estimated about 0.2%.
In frame of a phenomenological approach based on Compton-like Feynman amplitudes, we study the annihilation channel in antiproton nucleon collisions with production of a single charged or neutral pion and a lepton-antilepton pair. These reactions allow to access nucleon and axial electromagnetic form factors in time-like region and offer a unique possibility to study the kinematical region below two nucleon threshold. The differential cross section in an experimental set-up where the pion is fully detected is given with explicit dependence on the relevant nucleon form factors. The possibility …
Charmonium production in association with a forward or backward pion in nucleon-antinucleon annihilation is one of the most promising reaction to access nucleon-to-pion transition distribution amplitudes (TDAs) at PANDA. We briefly review the description of this reaction in terms of πN TDAs within the collinear factorization approach and present the first results of dedicated feasibility studies for the PANDA experimental setup.
I present a first determination of a set of collinear fragmentation functions of charged pions using the NNPDF methodology. The analysis is based on a wide set of single-inclusive electron-positron annihilation data, including recent measurements from $B$-factory experiments, and is performed up to next-to-next-to-leading order accuracy in perturbative quantum chromodynamics. I discuss the results of the fits, highlighting their quality in the description of the data, their stability upon the inclusion of higher-order corrections, and their comparison to other sets of fragmentation functions.
The inclusive decay rate into pions of the charmed $D_s$ meson is surprisingly larger than estimates expected from the $W$ annihilation, adopting commonly used values of current-algebra up and down quark masses. We then go beyond this tree diagram and consider possible QCD effects that might cause such a large rate. There are two; the first one is related to the spectator decay $ c{\bar s} \rightarrow s{\bar s} + u {\bar d}$ followed by $ s {\bar s} \rightarrow d{\bar d}~,~ u{\bar u}$ via two-gluon exchange box diagram. The second one is a gluon emission in weak annihilation for which the usua…
