Radiative Pion Research Articles

Radiative pion photoproduction in covariant chiral perturbation theory

We present a calculation of radiative pion photoproduction in the framework of covariant chiral perturbation theory with explicit $\Delta(1232)$ degrees of freedom. The analysis is performed employing the small scale expansion scheme adjusted for the $\Delta$ region. Depending on the channel, we include contributions up to next-to-next-to-leading order. We fit the available experimental data for the reaction $ \gamma p\to\gamma p\pi^0 $ and extract the value of the $\Delta^+$ magnetic moment. Errors from the truncation of the small scale expansion are estimated using the Bayesian approach. We compare our results both with the previous studies within the $\delta$-expansion scheme and with the $\Delta$-less theory. We also give predictions for radiative charged-pion photoproduction.

Phenomenology of τ−→π−ντγ using light cone sum rules

We present the study of radiative tau decay (${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}}\ensuremath{\gamma}$), computing the structure dependent contribution using light cone sum rules. This decay includes the same form factors as the radiative pion decay with the crucial difference that the momentum transfer squared, $t$, between the pion-photon system is positive, which makes these form factors timelike and also as $t$ can now take values up to ${m}_{\ensuremath{\tau}}^{2}$, it can produce real hadronic resonances. The analytical form for these form factors has been calculated using the light cone sum rules method and the invariant mass spectrum in the $\ensuremath{\pi}\ensuremath{-}\ensuremath{\gamma}$ system and the decay width are presented. The structure dependent parameter, $\ensuremath{\gamma}$, the ratio of the axial vector to vector form factor is found to be in good agreement with the experimental determination.

Comparison of lattice QCD+QED predictions for radiative leptonic decays of light mesons with experimental data

We present a comparison of existing experimental data for the radiative leptonic decays $P\to\ell\nu_\ell\gamma$, where $P=K$ or $\pi$ and $\ell=e$ or $\mu$, from the KLOE, PIBETA, E787, ISTRA+ and OKA collaborations with theoretical predictions based on the recent non-perturbative determinations of the structure-dependent vector and axial-vector form factors, $F_V$ and $F_A$ respectively. These were obtained using lattice QCD+QED simulations at order $O(\alpha_{\mathrm{em}})$ in the electromagnetic coupling. We find good agreement with the KLOE data on $K\to e\nu_e\gamma$ decays from which the form factor $F^+=F_V+F_A$ can be determined. For $K\to\mu\nu_\mu\gamma$ decays we observe differences of up to 3\,-\,4 standard deviations at large photon energies between the theoretical predictions and the data from the E787, ISTRA+ and OKA experiments and similar discrepancies in some kinematical regions with the PIBETA experiment on radiative pion decays. A global study of all the kaon-decay data within the Standard Model results in a poor fit, largely because at large photon energies the KLOE and E787 data cannot be reproduced simultaneously in terms of the same form factor $F^+$. The discrepancy between the theoretical and experimental values of the form factor $F^-=F_V-F_A$ is even more pronounced. These observations motivate future improvements of both the theoretical and experimental determinations of the structure-dependent form factors $F^+$ and $F^-$, as well as further theoretical investigations of models of "new physics" which might for example, include possible flavor changing interactions beyond $V - A$ and/or non-universal corrections to the lepton couplings.

Vector and Axial-vector form factors in radiative kaon decay and flavor SU(3) symmetry breaking

We study the vector and axial-vector form factors of radiative kaon decay within the framework of the gauged nonlocal effective chiral action from the instanton vacuum, focusing on the effects of flavor SU(3) symmetry breaking. The general tendency of the results are rather similar to those of radiative pion decays: The nonlocal contributions make the results of the vector form factor increased by about 20%, whereas they reduce those of the axial-vector form factor by almost 50%. Suppressing the prefactors consisting of the kaon mass and the pion decay constant, we scrutinize how the kaon form factors undergo changes as the mass of the strange current quark is varied. Those related to the vector and second axial-vector form factors tend to decrease monotonically as the strange quark mass increases, whereas that for the axial-vector form factor decreases. When K→eνγ decay is considered, both the results of the vector and axial-vector form factors at the zero momentum transfer are in good agreement with the experimental data. The results are also compared with those from chiral perturbation theory to p6 order.

Compton scattering off pions and electromagnetic polarizabilities

The electric [Formula: see text] and magnetic [Formula: see text] Compton polarizabilities of both the charged and the neutral pion are of fundamental interest in the low-energy sector of quantum chromodynamics (QCD). Pion polarizabilities affect the shape of the [Formula: see text] Compton scattering angular distribution at back scattering angles and [Formula: see text] absolute cross sections. Theory derivations are given for the [Formula: see text] Compton scattering differential cross section, dispersion relations, and sum rules in terms of the polarizabilities. We review experimental charged and neutral polarizability studies and theoretical predictions. The [Formula: see text] polarizabilities were deduced from DESY Crystal Ball [Formula: see text] data, but with large uncertainties. The charged pion polarizabilities were deduced most recently from (1) radiative pion Primakoff scattering [Formula: see text] at CERN COMPASS, (2) two-photon pion pair production [Formula: see text] at SLAC Mark II, and (3) radiative pion photoproduction [Formula: see text] from the proton at MAMI in Mainz. A stringent test of chiral perturbation theory (ChPT) is possible based on comparisons of precision experimental charged pion polarizabilities with ChPT predictions. Only the CERN COMPASS charged pion polarizability measurement has acceptably small uncertainties. Its value [Formula: see text] agrees well with the two-loop ChPT prediction [Formula: see text], strengthening the identification of the pion with the Goldstone boson of chiral symmetry breaking in QCD.

Radiative pion capture in H2 , He3 , and H3

The $\pi^- + {^2{\rm H}} \rightarrow \gamma + n + n$, $\pi^- + {^3{\rm He}} \rightarrow \gamma + {^3{\rm H}}$, $\pi^- + {^3{\rm He}} \rightarrow \gamma + n + d$, $\pi^- + {^3{\rm He}} \rightarrow \gamma + n + n + p$ and $\pi^- + {^3{\rm H}} \rightarrow \gamma + n + n + n$ capture reactions are studied with the AV18 two-nucleon potential and the Urbana~IX three-nucleon potential. We provide for the first time realistic predictions for the differential and total capture rates for all these processes, treating consistently the initial and final nuclear states. Our results are based on the single nucleon Kroll-Ruderman-type transition operator and concentrate on the full treatment of the nuclear final state interactions. They are compared with older theoretical predictions and experimental data.

Investigation of Rare Pion Decays with the PIBETA Spectrometer

Experimental results on pion decays obtained with the PIBETA spectrometer at the Paul Scherrer Institute (PSI) are reviewed. For pion beta decay π+ → π0е+ν (πβ), a precision measurement of relative probability yields Г(πβ) = [1.036 ± 0.004(stat) ± 0.004(syst) ± 0.003(π+→е+ν)] × 10–8, which implies Vud = 0.9728(30) for the corresponding element of the Cabibbo–Kobayashi–Maskawa mixing matrix. Using a sample of 65 × 103 events, relative probability of the π+→е+νγ radiative pion decay (RPD) in the kinematic region of Eγ > 10 MeV and θeγ > 40° is measured as Bexp = 73.86(54) × 10–8. A statistical analysis of measured Ee+ and Eγ distributions for this decay yield the values FV = 0.0258(17) and FA = 0.0117(17) for the pion weak formfactors. Assuming that FV linearly depends on the е+ν invariant mass q2 as FV(q2) = FV(0)(1 + aq2), the slope parameter is extracted as а = 0.10(6). The pion polarizability and neutral-pion lifetime are estimated as αE = 2.78(10) × 10–4 fm3 and τ(π0) = (8.5 ± 1.1) × 10–17 s, respectively. The data for decays π+→ е+ ν and $${\mu ^ + } \to {e^ + }v\bar v\gamma $$ have been collected and are being processed. The follow-up PEN experiment aims at reducing the uncertainty on the π+ → е+ ν relative probability by almost an order of magnitude (to 5 × 10–4).

In medium dispersion relation effects in nuclear inclusive reactions at intermediate and low energies

In a well-established many-body framework, successful in modeling a great variety of nuclear processes, we analyze the role of the spectral functions (SFs) accounting for the modifications of the dispersion relation of nucleons embedded in a nuclear medium. We concentrate in processes mostly governed by one-body mechanisms, and study possible approximations to evaluate the particle–hole propagator using SFs. We also investigate how to include together SFs and long-range RPA-correlation corrections in the evaluation of nuclear response functions, discussing the existing interplay between both type of nuclear effects. At low energy transfers (≤50MeV), we compare our predictions for inclusive muon and radiative pion captures in nuclei, and charge–current (CC) neutrino–nucleus cross sections with experimental results. We also present an analysis of intermediate energy quasi-elastic neutrino scattering for various targets and both neutrino and antineutrino CC driven processes. In all cases, we pay special attention to estimate the uncertainties affecting the theoretical predictions. In particular, we show that errors on the σμ∕σe ratio are much smaller than 5%, and also much smaller than the size of the SF+RPA nuclear corrections, which produce significant effects, not only in the individual cross sections, but also in their ratio for neutrino energies below 400 MeV. These latter nuclear corrections, beyond Pauli blocking, turn out to be thus essential to achieve a correct theoretical understanding of this ratio of cross sections of interest for appearance neutrino oscillation experiments. We also briefly compare our SF and RPA results to predictions obtained within other representative approaches.

Limits on tensor-type weak currents from nuclear and neutronβdecays

The limits on time-reversal invariant tensor-type weak currents from nuclear and neutron $\beta$ decays are evaluated including most recent experimental data. We find that $ -0.14 \times 10^{-2} < (C_T + C^\prime_T)/C_A < 1.4 \times 10^{-2} $ and $ -0.16 < (C_T - C^\prime_T)/C_A < 0.16$ (90% C.L.), while for the case $C_T = C^\prime_T$ the limits are $ | C_T/C_A | < 3.7 \times 10^{-3} $. These limits are shown to be more stringent than those from recent measurements of the radiative pion decay. In addition, the sensitivity of future $10^{-3}$-level correlation measurements is investigated.

ChPT calculations of pionic formfactors

An overview on chiral perturbation theory calculations of form factors is presented. The main focus is given on the form factors related to the lightest meson, pion, namely: pion decay constant, pion vector and scalar form factor, radiative pion decay and transition form factor. A pure calculation within the effective theory can be extended using further methods, as resonance chiral theory and leading logarithm calculations.

Form factors of radiative pion decays in nonlocal chiral quark models

We study the radiative pion decay pi+ -> e+ nu_e gamma within nonlocal chiral quark models that include wave function renormalization. In this framework we analyze the momentum dependence of the vector form factor F_V(q^2), and the slope of the axial-vector form factor F_A(q^2) at threshold. Our results are compared with available experimental information and with the predictions given by the NJL model. In addition we calculate the low energy constants l_5 and l_6, comparing our results with the values obtained in chiral perturbation theory.

Probing novel scalar and tensor interactions from (ultra)cold neutrons to the LHC

Scalar and tensor interactions were once competitors to the now well-established $V\ensuremath{-}A$ structure of the standard model weak interactions. We revisit these interactions and survey constraints from low-energy probes (neutron, nuclear, and pion decays) as well as collider searches. Currently, the most stringent limit on scalar and tensor interactions arise from ${0}^{+}\ensuremath{\rightarrow}{0}^{+}$ nuclear decays and the radiative pion decay $\ensuremath{\pi}\ensuremath{\rightarrow}e\ensuremath{\nu}\ensuremath{\gamma}$, respectively. For the future, we find that upcoming neutron beta decay and LHC measurements will compete in setting the most stringent bounds. For neutron beta decay, we demonstrate the importance of lattice computations of the neutron-to-proton matrix elements to setting limits on these interactions, and provide the first lattice estimate of the scalar charge and a new average of existing results for the tensor charge. Data taken at the LHC is currently probing these interactions at the ${10}^{\ensuremath{-}2}$ level (relative to the standard weak interactions), with the potential to reach the $\ensuremath{\lesssim}{10}^{\ensuremath{-}3}$ level. We show that, with some theoretical assumptions, the discovery of a charged spin-0 resonance decaying to an electron and missing energy implies a lower limit on the strength of scalar interactions probed at low energy.

Study of the radiative pion decay

We study the radiative pion decay of $\pi ^{+} \to e^{+}\nu_{e}\gamma$ in the chiral perturbation theory (ChPT) and light front quark model (LFQM). The vector and axial-vector hadronic form factors ($F_{V,A}$) for the $\pi\to\gamma$ transition are evaluated in the whole allowed momentum transfer. In terms of these momentum dependent form factors, we calculate the decay branching ratio and compare our results with the experimental data and other theoretical predictions in the literature. We also constrain the possible size of the tensor interaction in the LFQM.

Pion radiative weak decays in nonlocal chiral quark models

We analyze the radiative pion decay π+→e+νeγ within nonlocal chiral quark models that include wave function renormalization. In this framework we calculate the vector and axial-vector form factors FV and FA at q2=0 — where q2 is the e+νe squared invariant mass — and the slope a of FV(q2) at q2→0. The calculations are carried out considering different nonlocal form factors, in particular those taken from lattice QCD evaluations, showing a reasonable agreement with the corresponding experimental data. The comparison of our results with those obtained in the (local) NJL model and the relation of FV and a with the form factor in π0→γ⁎γ decays are discussed.

Neutral current neutrino–nucleon scattering within a consistent isobar model and the [formula omitted] resonance-background interference

One-pion production in neutrino scattering off nucleons and nuclei plays and important role as a source of relevant data on hadronic structure and in the analysis of neutrino oscillation experiments. Here we develop a consistent model to describe these processes in the case of neutral currents, which treats the resonant and background contributions to the cross sections in a coherent way. Previously we have used this model to describe the elastic and radiative pion–nucleon scattering, pion-photoproduction reactions and the single-pion production in charged current neutrino–nucleon scattering. In this paper we have extended the model to describe the single-pion production in neutral current neutrino–nucleon scattering for πN invariant-mass distributions up to 2 GeV. For that purpose we include the effects of finite size of hadrons by introducing an appropriate form factor. Good agreement is found between our results and available experimental data for the total cross sections and the invariant-mass distributions of the πN system, as well as with simulations in the case of scattering on free nucleons.

Single pion production in CC [formula omitted] scattering within a consistent effective Born approximation

The one pion production in charged current νμN scattering is analyzed within an extended version of a model used previously to include the Δ(1232) contribution in elastic and radiative pion–nucleon scattering, and in pion photoproduction. Because the resonant amplitude needs to be invariant under contact transformations, we identify the correct forms of the Δ propagator and the W−NΔ vertex that are consistent with this requirement. The only free parameter of the model, the axial form factor at zero momentum transfer, is fixed from data on the differential cross section for νμp→μ−pπ+ scattering. A reasonable agreement with the experimental data of all the νN→μN′π total cross sections is obtained. We show that the use of the complete Δ propagator instead of the Rarita–Schwinger one improves the theoretical results, leading to differences ranging from 10 to 30%, depending on the specific process.

On the radiative pion decay

A reanalysis of the radiative pion decay together with the calculation of the radiative corrections within chiral perturbation theory (CHPT) is performed. The amplitude of this decay contains an inner Bremsstrahlung contribution and a structure-dependent part, which are both accessible in experiments. In order to obtain a reliable estimate of the hadronic contributions we combine the CHPT result with a large-Nc expansion and experimental data on other decays, which makes it possible to determine the occurring coupling constants.

Chiral effective-field theory in theΔ(1232)region. II. Radiative pion photoproduction

We present a theoretical study of the radiative pion photoproduction on the nucleon ($\ensuremath{\gamma}N\ensuremath{\rightarrow}\ensuremath{\pi}N{\ensuremath{\gamma}}^{\ensuremath{'}}$) in the $\ensuremath{\Delta}$-resonance region, with the aim to determine the magnetic dipole moment (MDM) of the ${\ensuremath{\Delta}}^{+}(1232)$. The study is done within the framework of chiral effective-field theory, where the expansion is performed (to next-to-leading order) in the $\ensuremath{\delta}$ power-counting scheme, an extension of chiral perturbation theory to the $\ensuremath{\Delta}$-resonance energy region. We present the results for the absorptive part of the $\ensuremath{\Delta}$ MDM, as well as perform a sensitivity study of the dependence of $\ensuremath{\gamma}N\ensuremath{\rightarrow}\ensuremath{\pi}N{\ensuremath{\gamma}}^{\ensuremath{'}}$ observables on the real part of the $\ensuremath{\Delta}$ MDM. We find that an asymmetry for circular polarization of the photon beam may provide a model-independent way to measure the $\ensuremath{\Delta}$ MDM.

Radiative charged pion photoproduction and pion polarizabilities: An analysis within heavy baryon chiral perturbation theory

We analyze the amplitude for radiative charged pion photoproduction within the framework of heavy baryon chiral perturbation theory and discuss the best experimental setup for the extraction of the pion polarizabilities from the differential cross section.

Form factors in the radiative pion decay

We perform an analysis of the form factors that rule the structure-dependent amplitude in radiative pion decay. The resonance contributions to π→eνeγ decays are computed through the proper construction of the vector and axial-vector form factors by setting the QCD driven asymptotic properties of the three-point Green functions 〈VVP〉 and 〈VAP〉, and by demanding the smoothening of the form factors at high transfer of momentum. A comparison between theoretical and experimental determination of the form factors is also carried out. We also consider and evaluate the role played by a non-standard tensor form factor. We conclude that, at present and due to the hadronic uncertainties, the search for new physics in this process is not feasible.