Transport models cannot simultaneously explain very recent data on pion multiplicities and pion charged ratios of Sn+Sn in the reaction at 0.27 A GeV. This stimulates further investigations on the pion dispersion relation, in-medium $Nπ\to Δ$ cross sections and $Δ\to N π$ decay widths near the threshold energy or at subthreshold energy of pion production in isospin asymmetric nuclear matter. In this study, the pion dispersion relation, in-medium $Nπ\to Δ$ cross section and $Δ\to N π$ decay width near the threshold energy are investigated in isospin asymmetric nuclear matter by using the one-boson-exchange model. With the consideration of the energy conservation effect, the in-medium $Nπ\toΔ$ cross sections are enhanced at $s^{1/2}<1.11$ GeV in nuclear medium. The prediction of pion multiplicity and $π^-/π^+$ ratios near the threshold energy can be modified if this effect is considered in transport model simulations.
Recent experiment indicates that the behavior exhibited by the ratios $E_{1^+}/M_{1^+}$ and $S_{1^+}/M_{1^+}$ of the $γ^* N \leftrightarrow Δ$ transition remain small and negative for $Q^2 \le 4.0 GeV^2$. It implies that the perturbative QCD is still not applicable at these momentum transfers. We show that these data can be explained in a dynamical model for electromagnetic production of pions, together with a simple scaling assumption for the bare $γ^* N Δ$ form factors. Within our model we find that the bare $Δ$ is almost spherical and the electric E2 and Coulomb C2 quardrupole excitations o…
We investigate the possibility of measuring the pion dispersion relation in nuclear matter through the anomalous coupling in the reaction γ- γ' π_0. It is shown that this reaction permits the study of pionic modes for space-like momenta. If the pion is softened in nuclear matter due to mixing with the delta-hole state, significant strength for this reaction is expected to move into the space-like region. Competing background processes are evaluated, and it is concluded that useful insight can be obtained experimentally, but only through a difficult exclusive measurement.
We put forward a formalism to calculate the relativistic particle - hole and delta - hole excitation polarization insertion for pion propagator by using the particle - hole - antiparticle representation of nucleon and delta propagators in nuclear matter. The real and the imaginary part of the polarization insertion and the dispersion relation for pion propagator are calculated numerically. We find that the short range correlation enhances the delta - hole excitation but suppresses the particle - hole excitation, it also suppresses the pion condensation. We find that the effect of the short ran…
A new result for the nucleon sigma term from an updated pion-nucleon partial-wave and dispersion relation analysis of the Virginia Polytechnic Institute (now George Washington University) group is discussed. Using a method similar to that of Gasser, Leutwyler, Locher, and Sainio, we obtain Sigma=90 +/- 8 MeV (preliminary), in disagreement with the canonical result 64 +/- 8 MeV, but consistent with expectations based on new information on the $π$NN coupling constant, pionic atoms, and the Delta resonance width.
In symmetrical nuclear matter the solutions of pion dispersion equation are investigated in the complex plane of the pion frequency ω. There are three well-known branches of solutions on the physical sheet : sound, pion and isobar, at the matter density less than the critical one ρ<ρ_c. At ρ>ρ_c the fourth branch appears on the physical sheet. For this branch the condition ω^2_c\leq0 (in general case Reω^2_c\leq0) takes place. This points out the instability of the ground state which is possibly related to the pion condensation.
We investigate the influence of medium corrections to the pion dispersion relation on the pion dynamics in intermediate energy heavy ion collisions. To do so a pion potential is extracted from the in-medium dispersion relation and used in QMD calculations and thus we take care of both, real and imaginary part of the pion optical potential. The potentials are determined from different sources, i.e. from the $Δ$--hole model and from phenomenological approaches. Depending on the strength of the potential a reduction of the anti-correlation of pion and nucleon flow in non-central collisions is obs…
Our extraction of the pion-nucleon coupling constant from πp elastic scattering data is outlined. A partial wave analysis (T_π < 2100 MeV) is performed simultaneously with a fixed-t dispersion relation analysis (T_π < 800 MeV). The πNN coupling constant g^2/4πis searched to find the best fit. The result 13.73 \pm 0.01 \pm 0.07 (first error statistical, second systematic) is found to be insensitive to database changes and Coulomb barrier corrections. This value satisfies important elements of low energy QCD like the Goldberger-Treiman discrepancy, the Dashen-Weinstein sum rule, and chiral pertu…
We give predictions for the partial wave amplitudes of pion photoproduction near threshold by means of dispersion relations at fixed t. The free parameters of this approach are determined by a fit to experimental data in the energy range 160 MeV $\le E_γ \le$ 420 MeV. The observables near threshold are found to be rather sensitive to the amplitudes in the resonance region, in particular to the $Δ$ (1232) and $N^*$ (1440). We obtain a good agreement with the existing threshold data for both charged and neutral pion production. Our predictions also agree well with the results of chiral perturbat…
Two approaches for analysis of pion photo- and electroproduction on nucleons in the resonance energy region are checked at $Q^2=0$ using the results of GWU(VPI) partial-wave analysis of photoproduction data. The approaches are based on dispersion relations and unitary isobar model. Within dispersion relations good description of photoproduction multipoles is obtained up to $W=1.8 GeV$. Within unitary isobar model, modified with increasing energy by incorporation of Regge poles, and with unified Breit-Wigner parametrization of resonance contributions, good description of photoproduction multipo…
The $NΔ\to NN$ cross sections, which take into account the $Δ$-mass dependence of M-matrix and momentum $p_{NΔ}$, are applied on the calculation of pion production within the framework of the UrQMD model. Our study shows that UrQMD calculations with the $Δ$-mass dependent $NΔ\to NN$ cross sections enhance the pion multiplicities and decrease the $π^-/π^+$ ratios. By analyzing the time evolution of the pion production rate and the density in the overlapped region for Au+Au at the beam energy of 0.4A GeV, we find that the pion multiplicity probes the symmetry energy in the region of 1-2 times no…
Neutral pion photo- and electroproduction at threshold is analyzed in the framework of dispersion relations. For this purpose, we evaluate the real threshold amplitudes in terms of Born contributions and dispersion integrals determined by the imaginary parts of the MAID and SAID multipoles. The results show considerable cancellations between Born terms and resonance contributions. Good agreement with the data is found for photoproduction. While our dispersion analysis suggests considerable discrepancies for electroproduction, the present state of the experimental multipole analysis at finite Q…
In this paper we consider instability of nuclear matter which takes place when the frequencies of the collective excitations turn to zero. We investigate collective excitations with pion quantum numbers J^π=0^-. We study the dependence of zero-frequency solutions of the pion dispersion equation on the value of the spin-isospin quasiparticle interaction G'. The solutions of the pion dispersion equation describe the different types of the excitations in the matter, ω_i(k). At the critical density ρ=ρ_c one of solutions of the definite type turns to zero: ω_{i0}(k_c)=0. When ρ>ρ_c, the excitation…
We study the deuteron production via the deuteron pion and nucleon catalysis reactions, $πp n \leftrightarrow πd$ and $N p n \leftrightarrow N d$, by employing stochastic multi-particle reactions in the hadronic transport approach SMASH for the first time. This is an improvement compared to previous studies, which introduced an artificial fake resonance $d'$ to simulate these $3 \leftrightarrow 2$ reactions as a chain of $2\leftrightarrow 2$ reactions. The derivation of the stochastic criterion for multi-particle reactions is presented in a comprehensive fashion and its implementation is teste…
A new partial wave analysis of pion photoproduction has been obtained in the framework of fixed-t dispersion relations valid form threshold up to 500 MeV. It is based on new Mainz data for π^{0} and π^{+} production off the proton and both older and more recent data from Bonn, Frascati and TRIUMF for π^{+} and π^{-}. At threshold we obtain a good agreement with the existing data for both charged and neutral pion production. In the resonance region we have precisely determined the electromagnetic properties of the Δ(1232) resonance, in particular the E2/M1 ratio R_{EM}=(-2.5 \pm 0.1) %. We show…
We reply to the Comment by Fil'kov and Kashevarov, arXiv:0805.4486 [hep-ph]. We show that the discrepancies between ChPT and dispersion theory, reported for the polarizability of the pion, result from applying dispersion theory to non-analytic functions.
The multichannel S- and P-wave amplitudes for the pion-pion scattering, constructed requiring analyticity and unitarity of the S-matrix and using the uniformization procedure, are elaborated using the dispersion relations with imposed crossing symmetry condition. The amplitudes are modified in the low-energy region to improve their consistency with experimental data and the dispersion relations. Agreement with data is achieved for both amplitudes from the threshold up to 1.8 GeV and with dispersion relations up to 1.1 GeV. Consequences of the applied modifications, e.g. changes of the S-wave l…
By looking at the complex plane of the pion-mass squared we establish a dispersion relation which the static quantities, such as baryon masses, magnetic moments, polarizabilities, should obey. This dispersion relation yields insight into the differences between the heavy-baryon and relativistic calculations in the baryon sector of chiral perturbation theory.
The possibility of pion--pair formation in a hot pion gas, based on the bosonic gap equation, is pointed out and discussed in detail. The critical temperature for condensation of pion pairs (Evans--Rashid transition) is determined as a function of the pion density. As for fermions, this phase transition is signaled by the appearance of a pole in the two--particle propagator. In bose systems there exists a second, lower critical temperature, associated with the appearance of the single--particle condensate. Between the two critical temperatures the pion dispersion relation changes from the usua…
Recent attempts to determine the pion polarizability by dispersion relations yield values that disagree with the predictions of chiral perturbation theory. These dispersion relations are based on specific forms for the absorptive part of the Compton amplitudes. The analytic properties of these forms are examined, and the strong enhancement of intermediate-meson contributions is shown to be connected to non-analytic structures
We study the behavior of the pion dispersion relation in a pion medium at finite density and temperature. We introduce a pion chemical potential to describe the finite pion number density and argue that such description is valid during the hadronic phase of a relativistic heavy-ion collision between chemical and thermal freeze-out. We make use of an effective Lagrangian that explicitly respects chiral symmetry through the enforcement of the chiral Ward identities. The pion dispersion relation is computed through the computation of the pion self-energy in a non-perturbative fashion by giving an…
The solutions to the zero-sound frequency equation and pion dispersion equation are considered for the different values of the parameters of the effective particle-hole interaction. The branches of solutions, responsible for the long-wave instability [Pomeranchuk] of the nuclear matter ω_P(k) are presented for the both equations. It is shown that in the pion dispersion equation the solutions ω_P(k) result in the instability not only for values of the spin-isospin constant g'\leq -1/2, violating stability criteria, but for all g' < g'_p (|g'_p|\ll 1 and g'_p < 0). At g' > g'_p the branches ω_P(…
We develop one-loop effective vertices and propagators in the linear sigma model at finite temperature satisfying the chiral Ward identities. We use these in turn to compute the pion dispersion relation in a pion medium for small momentum and temperatures on the order of the pion mass at next to leading order in the parameter m_pi^2/4pi^2f_pi^2 and to zeroth order in the parameter (m_pi/m_sigma)^2. We show that this expansion reproduces the result obtained from chiral perturbation theory at leading order. The main effect is a perturbative, temperature-dependent increase of the pion mass. We fi…
We present a dispersion relation in the pion-mass squared, which static quantities (nucleon mass, magnetic moment, etc.) obey under the assumption of analyticity in the entire complex $m_π^2$ plane modulo a cut at negative $m_π^2$ associated with pion production. The relation is verified here in a number of examples of nucleon and $Δ$-isobar properties computed in chiral perturbation theory up to order $p^3$. We outline a method to obtain relations for other mass-dependencies, and illustrate it on a two-loop example.
Coulomb and mass difference corrections to low-energy pion-nucleon scattering are calculated and compared with previous work including potential models, dispersion relation methods and chiral perturbation theory calculations. Particular attention is paid to their role in testing isospin breaking.
In this work, dispersion relations of $π^0$ and $π^{\pm}$ have been studied in vacuum in the limit of weak external magnetic field using a phenomenological pion-nucleon $(πN)$ Lagrangian. For our purpose, we have calculated the results up to one loop order in self energy diagrams with the pseudoscalar $(PS)$ and pseudovector $(PV)$ pion-nucleon interactions. By assuming weak external magnetic field it is seen that the effective mass of pion gets explicit magnetic field dependence and it is modified significantly for the case of PS coupling. However, for the PV coupling, only a modest increase …
Recent attempts to determine the pion polarizability by dispersion relations yield values that disagree with the predictions of chiral perturbation theory. These dispersion relations are based on specific forms for the absorptive part of the Compton amplitudes. The analytic properties of these forms are examined, and the strong enhancement of intermediate-meson contributions is shown to be connected with spurious singularities. If the basic requirements of dispersion relations are taken into account, the results of dispersion theory and effective field theory are not inconsistent.
We review our recent analysis of $πK$ scattering data in terms of forward dispersion relations, and also present the parameters of the strange resonances. This work consists of fits to the data that are constrained to satisfy analyticity requirements. The method yields a set of simple and consistent parameterizations that are compatible with forward dispersion relations up to 1.6 GeV while still describing the data. We also obtain the pole parameters of the $K^*_0(800)$ and the $K^*(892)$ resonances.
We calculate dispersion relations and propagators for the $σ$, $ω$, $π$, $ρ$, $δ$, $η$ and $a_1$ mesons in relativistic, dense, hot, symmetric nuclear matter. In addition to the usual mixing of the $σ-ω$ system, we obtain mixing of the $δ$ with the longitudinal $ρ$ mode and of the tranverse $ρ$ with the transverse $a_1$ mode. Finally, the component of the $a_1$ polarization along the transferred momentum modifies the in-medium pion propagator in a way similar to the Migdal contact interaction, but with the opposite sign. The spurious pion condensate as well as the additional contribution from …
The saturation properties of the nuclear matter taking pion correlations into account is studied. We construct a Bogoliubov transformations for the pion pair operators and calculate the energy associated with the pion pairs. The pion dispersion relation is investigated. We next study the correlation energy due to one pion exchange in nuclear matter and neutron matter at random phase approximation using the generator coordinate method. The techniques of the charged pion correlations are discussed in the neutron matter calculations. We observe that there is no sign of the pion condensation in th…
The relativistic amplitudes of pion photoproduction are evaluated by dispersion relations at t=const. The imaginary parts of the amplitudes are taken from the MAID model covering the absorption spectrum up to center-of-mass energies W = 2.2 GeV. For sub-threshold kinematics the amplitudes are expanded in powers of the two independent variables νand t related to energy and momentum transfer. Subtracting the loop corrections from this power series allows one to determine the counter terms of covariant baryon chiral perturbation theory. The proposed continuation of the amplitudes into the unphysi…
An analysis of different dispersion sum rules (DSRs) for the dipole and quadrupole pion polarizabilities is carried out. We prove the absence of additional spurious singularities in these approaches. The results of the calculations of the polarizabilities in the framework of DSRs are compared with ChPT predictions and with data obtained in different experiments.
A dynamical model for S-- and P--wave correlated $2 π$ (and $K \bar K$) exchange between a kaon and a nucleon is presented, starting from corresponding $N \bar N \rightarrow K \bar K$ amplitudes in the pseudophysical region, which have been constructed from nucleon, $Δ$--isobar and hyperon ($Λ$, $Σ$) exchange Born terms and a realistic meson exchange model of the $ππ\rightarrow K \bar K$ and $K \bar K \rightarrow K \bar K$ amplitude. The contribution in the s--channel is then obtained by performing a dispersion relation over the unitarity cut. In the $ρ$--channel, considerable ambiguities exis…
We have analysed pion photoproduction imposing constraints from fixed t dispersion relations and unitarity. Coupled integral equations for the S and P wave multipoles were derived from the dispersion relations and solved by the method of Omnes and Muskhelishvili. The free parameters were determined by a fit to the most recent data for π^{+} and π^{0} production on the proton as well as π^{-} production on the neutron, in the energy We have analysed pion photoproduction imposing constraints from fixed t dispersion relations and unitarity. Coupled integral equations for the S and P wave multipol…
Neutrino-induced pion and photon production from nucleons and nuclei are important for the interpretation of neutrino-oscillation experiments, and these processes are potential backgrounds in the MiniBooNE experiment [A. A. Aquilar-Arevalo \textit{et al.} (MiniBooNE Collaboration), Phys.\ Rev.\ Lett.\ {\bf 100}, 032301 (2008)]. Pion and photon production are investigated at intermediate energies, where the $Δ$ resonance becomes important. The Lorentz-covariant effective field theory contains nucleons, pions, Deltas, isoscalar scalar ($σ$) and vector ($ω$) fields, and isovector vector ($ρ$) fie…
The time dependent Schroedinger equation for two identical and charged pions is solved using wavepacket states. It is shown that the expected Coulomb distortion in the momentum correlation function is obliterated by the dispersion of the localized states, and therefore becomes unobservable.
We utilize precise weak interaction experiments on atomic muon capture and beta decay in the A = 3 nuclei, and take into account the effects of nuclear "anomalous thresholds" to extract the pseudoscalar pi-^3He-^3H coupling parameter, G^{eff}(m_π^2) = 45.8+- 2.4. This is an order of magnitude improvement in precision over that from the use of pion-nuclear scattering data and dispersion relations.
The statement of the authors of the article Phys. Rev. C 77, 065211 (2008) that spurious singularities occur in the dispersion relation approach, where imaginary parts of the amplitudes of the process γγ->ππare saturated by the contributions of meson resonances by using Breit-Wigner expressions, is analyzed. It is shown that there are no any additional singularities in this approach and the disagreement between the predictions of the dispersion relations and the chiral perturbation theory for (α_1-β_1)_π^{\pm} remains.
The isoscalar and isovector scattering lengths (b_0,b_1) are determined using a unitarized coupled channel approach based on chiral Lagrangians. Using experimental values of pionic hydrogen and deuterium as well as low energy pi N scattering data, the free parameters of the model are calculated. Isospin violation is incorporated to a certain extent by working with physical particle masses. For the deuterium scattering length a_{pi-d} new significant corrections concerning real and imaginary parts are evaluated, putting new constraints from pi-d scattering on the values of (b_0,b_1). In particu…
We propose an intensity-dependent pion-nucleon coupling Hamiltonian within a unitary multiparticle-production model of the Auerbach- Avin-Blankenbecler-Sugar (AABS) type in which the pion field is represented by the thermal-density matrix.Using this Hamiltonian, we explain the appearance of the negative-binomial (NB) distribution for pions and the well-known empirical relation, the so-called Wr\' oblewski relation, in which the dispersion $D$ of the pion- multiplicity distribution is linearly related to the average multiplicity $<n>$ : $D = A <n> + B$, with the coefficient $A < 1$. The Hamilto…
The inclusive A(gamma,pi+ pi-)X reaction is studied theoretically. A sizeable enhancement of the cross section is found, in comparison with the scaling of the deuteron cross section (sigma_deuteron * A/2). This enhancement is due to the modifications in the nuclear medium of the gamma N ----> pi pi N amplitude and the pion dispersion relation. The enhancement is found to be bigger than the one already observed in the (pi,pi pi) reaction in nuclei.
I discuss the absorption and dispersion of pions in hot matter. A two-loop calculation in the framework of chiral perturbation theory is presented and its result is compactly written in terms of the two- and three-particle forward $ππ$ scattering amplitudes. At modest temperatures, $T \le 100$ MeV, the change in the pion mass is small and its dispersion law closely resembles the free space one. At these temperatures, all quantities of interest are given to a good degree of accuracy by the first term in the virial expansion which is linear in the density. (BUTP-93/16, uses espcrc1.sty from Nort…
Working within the linear sigma model at finite temperature, we construct effective one-loop vertices and propagators satisfying the chiral Ward identities, for small pion momentum and mass compared to the sigma mass. We obtain an expansion for the pion dispersion relation up to second order in the parameter m_pi^2/4pi^2f_pi^2. At leading order, this expansion reproduces the dispersion curve obtained in chiral perturbation theory. We also study pion damping and compute the mean free path for pions traveling in the medium before forming a sigma resonance. These results are also in good agreemen…
We study the quark spectrum at finite temperature near and above the pseudocritical temperature of the chiral phase transition incorporating the effects of the collective modes with the quantum number of the sigma (parasigma) and pion (parapion) in a chiral effective model with a nonzero current quark mass. Below the pion zero-binding temperature where the pionic modes are bound, the quark self-energy has van Hove singularity induced by the scattering of quarks with the composite bound pions with a nonhyperbolic dispersion curve. This singularity is found to cause a drastic change in the quark…
Neutrino-induced productions (neutrinoproduction) of photons and pions from nucleons and nuclei are important for the interpretation of neutrino-oscillation experiments, as they are potential backgrounds in the MiniBooNE experiment [A. A. Aquilar-Arevalo et al. (MiniBooNE Collaboration), Phys. Rev. Lett. {\bf 100}, 032301 (2008)]. These processes are studied at intermediate energies, where the Δ(1232) resonance becomes important. The Lorentz-covariant effective field theory, which is the framework used in this series of study, contains nucleons, pions, Δs, isoscalar scalar (σ) and vector (ω) f…
We calculate the spin-polarizabilities of the nucleon by means of dispersion relation, where the pion photoproduction amplitude predicted by chiral soliton model is utilized. We consider the $Nπ$ and $Δπ$ channels in the pion-photoproduction amplitude, and also evaluate the contribution of the anomalous term of the $π^0γγ$ process. In a narrow decay-width limit of the $Δ$ particle the result coincides with that in heavy baryon chiral perturbation theory (HBChPT) except for the interference part of the electric and magnetic amplitudes. A comparison with the multipole analysis is given.
Transport simulations including in-medium properties derived in a microscopic pi + nucleon-hole + delta-hole model in infinite nuclear matter are presented. In-medium pion dispersion relations, partial delta decay widths, pion absorption cross sections and delta cross sections are incorporated into the transport description by means of a local-density approximation. Strong modifications of pi and delta production and absorption rates are found, but only small effects on pion observables.
The behavior of the pion dispersion relation in a pion medium is strongly modified by the introduction of a finite chemical potential associated to the finite pion number density. Such behavior is particularly important during the hadronic phase of a relativistic heavy-ion collision, between chemical and thermal freeze-out, where the pion number changing processes, driven by the strong interaction, can be considered to be frozen. We make use of an effective Lagrangian that explicitly respects chiral symmetry through the enforcement of the chiral Ward identities. The pion dispersion relation is…
The invariant amplitudes for pion electroproduction on the nucleon are evaluated by dispersion relations at constant t with MAID as input for the imaginary parts of these amplitudes. In the threshold region these amplitudes are confronted with the predictions of several low-energy theorems derived in the soft-pion limit. In general agreement with Chiral Perturbation Theory, the dispersive approach yields large corrections to these theorems because of the finite pion mass.
The pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon $(g-2)_μ$ is fully determined by the doubly-virtual pion transition form factor. Although this crucial input quantity is, in principle, directly accessible in experiment, a complete measurement covering all kinematic regions relevant for $(g-2)_μ$ is not realistic in the foreseeable future. Here, we report in detail on a reconstruction from available data, both space- and time-like, using a dispersive representation that accounts for all the low-lying singularities, reproduces the corr…
In this third paper of a series dedicated to a dispersive treatment of the hadronic light-by-light (HLbL) tensor, we derive a partial-wave formulation for two-pion intermediate states in the HLbL contribution to the anomalous magnetic moment of the muon $(g-2)_μ$, including a detailed discussion of the unitarity relation for arbitrary partial waves. We show that obtaining a final expression free from unphysical helicity partial waves is a subtle issue, which we thoroughly clarify. As a by-product, we obtain a set of sum rules that could be used to constrain future calculations of $γ^*γ^*\toππ$…
The differential cross sections for $π^- p \to γn$ and $π^+ n \to γp$ are computed up to $O(p^3)$ in heavy baryon chiral perturbation theory (HBChPT). The expressions at $O(p)$ and $O(p^2)$ have no free parameters. There are three unknown parameters at $O(p^3)$, low energy constants of the HBChPT Lagrangian, which are determined by fitting to experimental data. Two acceptable fits are obtained, which can be separated by comparing with earlier dispersion relation calculations of the inverse process. Expressions for the multipoles, with emphasis on the p-wave multipoles, are obtained and evaluat…
The Fubini-Furlan-Rossetti sum rule for pion photoproduction on the nucleon is evaluated by dispersion relations at constant t, and the corrections to the sum rule due to the finite pion mass are calculated. Near threshold these corrections turn out to be large due to pion-loop effects, whereas the sum rule value is closely approached if the dispersion integrals are evaluated for sub-threshold kinematics. This extension to the unphysical region provides a unique framework to determine the low-energy constants of chiral perturbation theory by global properties of the excitation spectrum.
In this paper we make a further step towards a dispersive description of the hadronic light-by-light (HLbL) tensor, which should ultimately lead to a data-driven evaluation of its contribution to $(g-2)_μ$. We first provide a Lorentz decomposition of the HLbL tensor performed according to the general recipe by Bardeen, Tung, and Tarrach, generalizing and extending our previous approach, which was constructed in terms of a basis of helicity amplitudes. Such a tensor decomposition has several advantages: the role of gauge invariance and crossing symmetry becomes fully transparent; the scalar coe…
We consider the electromagnetic and transition pion form factors. Using dispersion relations we simultaneously describe both the hadronic, time-like region and the asymptotic region of large energy-momentum transfer. For the latter we propose a novel mechanism of Regge fermion exchange.
Recent experimental results on the proton and neutron polarizabilities are examined from the point of view of backward dispersion relations. Results are found to be in reasonable agreement with the measured values. A rigorous relationship between the nucleon and pion polarizabilities is derived and shown to be in excellent agreement with several models.
