23,850 research outputs found

    Induced pseudoscalar form factor of the nucleon at two-loop order in chiral perturbation theory

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    We calculate the imaginary part of the induced pseudoscalar form factor of the nucleon GP(t)G_P(t) in the framework of two-loop heavy baryon chiral perturbation theory. The effect of the calculated three-pion continuum on the pseudoscalar constant gP=(mμ/2M)GP(t=0.877mμ2)g_P = (m_\mu/2M) G_P(t=-0.877m_\mu^2) measurable in ordinary muon capture μpνμn\mu^-p\to \nu_\mu n turns out to be negligibly small. Possible contributions from counterterms at two-loop order are numerically smaller than the uncertainty of the dominant pion-pole term proportional to the pion-nucleon coupling constant gπN=13.2±0.2g_{\pi N}= 13.2\pm 0.2. We conclude that a sufficiently accurate representation of the induced pseudoscalar form factor of the nucleon at low momentum transfers tt is given by the sum of the pion-pole term and the Adler-Dothan-Wolfenstein term: GP(t)=4gπNMfπ/(mπ2t)2gAM2/3G_P(t) = 4g_{\pi N} M f_\pi/ (m_\pi^2 -t)- 2g_A M^2 /3, with =(0.44±0.02) = (0.44 \pm 0.02) fm2^2 the axial mean square radius of the nucleon.Comment: 6 pages, 2 figures, accepted for publication in Physical Review

    On neutral pion electroproduction off deuterium

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    Threshold neutral pion electroproduction on the deuteron is studied in the framework of baryon chiral perturbation theory at next-to-leading order in the chiral expansion. To this order in small momenta, the amplitude is finite and a sum of two- and three-body interactions with no undetermined parameters. We calculate the S-wave multipoles for threshold production and the deuteron S-wave cross section as a function of the photon virtuality. We also discuss the sensitivity to the elementary neutron amplitudes.Comment: 6 pp, revtex, 3 figs, corrected version, to appear in Phys. Rev.

    Momentum Dependent Vertices σγγ\sigma \gamma \gamma, σργ\sigma \rho \gamma and σρρ\sigma \rho \rho : The NJL Scalar Hidden by Chiral Symmetry

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    We calculate the momentum dependence of three particle vertices σγγ\sigma \gamma \gamma, σργ\sigma \rho \gamma and σρρ\sigma \rho \rho in the context of a Nambu Jona Lasinio type model. We show how they influence the processes γγσππ\gamma \gamma \rightarrow \sigma \rightarrow \pi \pi, ργσ\rho \rightarrow \gamma \sigma and γγρρ\gamma \gamma \rightarrow \rho \rho and how chiral symmetry shadows the presence of the σ\sigma.Comment: 9 pages (latex), 5 figures available from the authors, preprint Coimbra 940506, IJS-TP-94/10, accepted for publication in Zeit. f. Physik

    On the analysis of the pion--nucleon σ\sigma--term: The size of the remainder at the Cheng--Dashen point

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    We calculate the one--loop contributions of order Mπ4M_\pi^4 to the difference ΔR\Delta_R between the on--shell pion--nucleon scattering amplitude Dˉ+(0,2Mπ2)\bar{D}^+(0,2M_\pi^2) at the Cheng--Dashen point ν=0\nu =0, t=2Mπ2t=2M_\pi^2 and the scalar form factor σ(2Mπ2)\sigma (2M_\pi^2) in the framework of heavy baryon chiral perturbation theory. We proof that to this order ΔR\Delta_R contains nono chiral logarithms and therefore it vanishes simply as Mπ4M_\pi^4 in the chiral limit. Numerically, we find as an upper limit ΔR2\Delta_R \simeq 2\,MeV.Comment: 7 pp, LaTeX, uses epsf, 1 figure in separate PS fil

    Aspects of Nucleon Compton Scattering

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    We consider the spin-averaged nucleon forward Compton scattering amplitude in heavy baryon chiral perturbation theory including all terms to order O(q4){\cal O} (q^4). The chiral prediction for the spin-averaged forward Compton scattering amplitude is in good agreement with the data for photon energies ω110\omega \le 110 MeV. We also evaluate the nucleon electric and magnetic Compton polarizabilities to this order and discuss the uncertainties of the various counter terms entering the chiral expansion of these quantities.Comment: 17 pp, TeX, 7 figures available from the authors, preprint CRN-93/5

    Spin structure of the nucleon at low energies

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    The spin structure of the nucleon is analyzed in the framework of a Lorentz-invariant formulation of baryon chiral perturbation theory. The structure functions of doubly virtual Compton scattering are calculated to one-loop accuracy (fourth order in the chiral expansion). We discuss the generalization of the Gerasimov-Drell-Hearn sum rule, the Burkhardt-Cottingham sum rule and moments of these. We give predictions for the forward and the longitudinal-transverse spin polarizabilities of the proton and the neutron at zero and finite photon virtuality. A detailed comparison to results obtained in heavy baryon chiral perturbation theory is also given.Comment: 29 pp, 14 fig

    Double neutral pion photoproduction at threshold

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    We consider the chiral expansion of the threshold amplitude for the reaction γpπ0π0p\gamma p \to \pi^0 \pi^0 p to order O(Mπ2){\cal O}(M_\pi^2). We substantiate a claim that this photoproduction channel is significantly enhanced close to threshold due to pion loops. A precise measurement of the corresponding cross sections is called for which allows to test chiral perturbation theory.Comment: 8 pp, LaTe

    The pion charge radius from charged pion electroproduction

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    We analyze a low-energy theorem of threshold pion electroproduction which allows one to determine the charge radius of the pion. We show that at the same order where the radius appears, pion loops induce a correction to the momentum dependence of the longitudinal dipole amplitude L0+()L_{0+}^{(-)}. This model-independent correction amounts to an increase of the pion charge radius squared from the electroproduction data by about 0.26~fm2^2. It sheds light on the apparent discrepancy between the recent determination of the pion radius from electroproduction data and the one based on pion-electron scattering.Comment: 3 pp, REVTeX, uses eps

    Threshold Two-Pion Photo- and Electroproduction: More neutrals than expected

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    We present an exploratory study of two pion photo-- and electroproduction off the nucleon in the threshold region. To calculate the pertinent amplitudes, we make use of heavy baryon chiral perturbation theory. We show that due to finite chiral loops the production cross section for final states with two neutral pions is considerably enhanced. The experimental implications are briefly discussed.Comment: 23pp, plain TeX, 11 figures available upon request, CRN 94/1

    Low--Energy Theorems for Weak Pion Production

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    We derive novel low--energy theorems for single pion production off nucleons through the isovector axial current. We find that the k2k^2-dependence of the multipole L0+(+)L_{0+}^{(+)} at threshold is given by the nucleon scalar form factor, namely σ(k2Mπ2)/(3πMπFπ)\sigma(k^2-M_\pi^2 ) /(3 \pi M_\pi F_\pi ). The relation to PCAC results for soft pions including electroweak form factors is also clarified.Comment: 9 pp, TeX, 2 figures available as ps files, CRN 93-5
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