arXiv subjects

V. Bernard

Publications and source records attributed to V. Bernard.

At least 37 records · Page 2Linked to original sources

arXiv2004

Radiative tritium beta-decay and the neutrino mass

The shape of the electron energy spectrum in 3H beta-decay permits a direct assay of the absolute scale of the neutrino mass; a highly accurate theoretical description of the electron energy spectrum is necessary to the empirical task. We update Sirlin's calculation of the outer radiative correction to nuclear beta-decay to take into account the non-zero energy resolution of the electron detector. In previous 3H beta-decay studies the outer radiative corrections were neglected all together; only Coulomb corrections to the spectrum were included. This neglect artificially pushes m_nu^2 < 0 in a potentially significant way. We present a computation of the theoretical spectrum appropriate to the extraction of the neutrino mass in the sub-eV regime.

hep-ph↗

arXiv2004

Orthonormalization procedure for chiral effective nuclear field theory

We show that the Q-box expansion of nuclear many-body physics can be applied in nuclear effective field theory with explicit pions and external sources. We establish the corresponding power counting and give an algorithm for the construction of a hermitean and energy-independent potential for arbitrary scattering processes on nucleons and nuclei to a given order in the chiral expansion. Various examples are discussed in some detail.

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arXiv2004

Improved analysis of neutral pion electroproduction off deuterium in chiral perturbation theory

Near threshold neutral pion electroproduction on the deuteron is studied in the framework of heavy baryon chiral perturbation theory. We include the next-to-leading order corrections to the three-body contributions. We find an improved description of the total and differential cross section data measured at MAMI. We also obtain more precise values for the threshold S-wave multipoles. We discuss in detail the theoretical uncertainties of the calculation.

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arXiv2004

Radiative neutron beta-decay in effective field theory

We consider radiative β--decay of the neutron in heavy baryon chiral perturbation theory, with an extension including explicit Δdegrees of freedom. We compute the photon energy spectrum as well as the photon polarization; both observables are dominated by the electron bremsstrahlung contribution. Nucleon-structure effects not encoded in the weak coupling constants g_A and g_V are determined at next-to-leading order in the chiral expansion, and enter at the {\cal O}(0.5%)-level, making a sensitive test of the Dirac structure of the weak currents possible.

hep-ph↗

arXiv2002

Near threshold neutral pion electroproduction on deuterium in chiral perturbation theory

Near 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. We develop the multipole decomposition for pion production off spin-1 particles appropriate for the threshold region. The existing data at photon virtuality k^2 = -0.1 GeV^2 can be described satisfactorily. Furthermore, the prediction for the S-wave multipole E_d at the photon point is in good agreement with the data.

nucl-th↗

arXiv2002

The S-Wave Pion-Nucleon Scattering Lengths from Pionic Atoms using Effective Field Theory

The pion-deuteron scattering length is computed to next-to-next-to-leading order in baryon chiral perturbation theory. A modified power-counting is then formulated which properly accounts for infrared enhancements engendered by the large size of the deuteron, as compared to the pion Compton wavelength. We use the precise experimental value of the real part of the pion-deuteron scattering length determined from the decay of pionic deuterium, together with constraints on pion-nucleon scattering lengths from the decay of pionic hydrogen, to extract the isovector and isoscalar S-wave pion-nucleon scattering lengths, a^- and a^+, respectively. We find a^-=(0.0918 \pm 0.0013) M_π^{-1} and a^+=(-0.0034 \pm 0.0007) M_π^{-1}.

hep-ph↗

arXiv2001

Further comment on pion electroproduction and the axial form factor

We show that a recent claim (H.Haberzettl, Phys. Rev. Lett. 85 (2000) 3576) that one cannot extract the nucleon weak axial form factor G_A (t) from charged pion threshold electroproduction is incorrect. Thus previous calculations remain valid and threshold charged pion electroproduction experiments can indeed be used to determine G_A (t), and they should certainly be pursued.

hep-ph↗

arXiv2000

On neutral pion electroproduction off deuterium

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.

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arXiv1999

Novel approach to pion and eta production in proton-proton collisions near threshold

We evaluate the threshold matrix-element for the reaction $pp \to ppπ^0$ in a fully relativistic Feynman diagrammatic approach. We employ a simple effective range approximation to take care of the S-wave $pp$ final-state interaction. The experimental value for the threshold amplitude ${\cal A} = (2.7 - i 0.3)$ fm$^4$ can be reproduced by contributions from tree level chiral (long-range) pion exchange and short-range effects related to vector meson exchanges, with $ω$ exchange giving the largest individual contribution. Pion loop effects appear to be small. We stress that the commonly used heavy baryon formalism is not applicable in the NN-system above the pion production threshold due to the large external momentum, $|\vec p | \simeq \sqrt {Mm_π}$, with $M$ and $m_π$ the nucleon and the pion mass, respectively. We furthermore investigate the reaction $pp\to p n π^+$ near threshold within the same approach. We extract from the data the triplet threshold amplitude as ${\cal B}= (2.8 -i 1.5)$ fm$^4$. Its real part can be well understood from (relativistic) tree level meson-exchange diagrams. In addition, we investigate the process $pp \to pp η$ near threshold. We use a simple factorization ansatz for the $ppη$ final-state interaction and extract from the data the modulus of the threshold amplitude, $|{\cal C}| = 1.32 $fm$^4$. With $g_{ηN}=5.3$, this value can be reproduced by (relativistic) tree level meson-exchange diagrams and $η$-rescattering, whose strength is fixed by the $ηN$ scattering length. We also comment on the recent near threshold data for $η'$-production.

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arXiv1997

The isoscalar S-wave pi-N scattering length a+ from pi-deuteron scattering

We consider constraints on the isoscalar S-wave pi-N scattering length a+ from pi-deuteron scattering, to third order in small momenta and pion masses in chiral perturbation theory. To this order, the pi-deuteron scattering length is determined by a+ together with three-body corrections that involve no undetermined parameters. We extract a novel value for a combination of dimension two low-energy constants which is in agreement with previous determinations.

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arXiv1997

Quark-antiquark resonances in the NJL model

The problem of the $ρ$ meson resonance solution in the extended NJL model is studied. It has been shown previously that the solution for the $ρ$ meson changes smoothly from a bound state to a "virtual state" when the vector channel attraction becomes too weak to support bound state solutions. We have found that together with these solutions a separate resonance branch appears which is not connected smoothly with the bound state solutions. At small values of constituent quark mass, $m\sim 200$ MeV, it corresponds to the physical vector meson resonance solution in the quark-continuum region. The $a_1$ and $σ$ resonances are also discussed.

hep-ph↗

arXiv1997

The reaction $πN \to ππN$ above threshold in chiral perturbation theory

Single pion production off nucleons is studied in the framework of relativistic baryon chiral perturbation theory at tree level with the inclusion of the terms from the dimension two effective pion-nucleon Lagrangian. The five appearing low-energy constants are fixed from pion-nucleon scattering data. Despite the simplicity of the approach, most of the existing data for total and differential cross sections as well as for the angular correlation functions for incoming pion kinetic energies up to 400 MeV can be satisfactorily described.

hep-ph↗

arXiv1997

Neutral pion photoproduction on deuterium in baryon chiral perturbation theory to order q^4

Threshold neutral pion photoproduction on the deuteron is studied in the framework of baryon chiral perturbation theory beyond next-to--leading order in the chiral expansion. To fourth order in small momenta, the amplitude is finite and a sum of two- and three-body interactions with no undetermined parameters. With accurate theoretical and experimental input from the single nucleon sector for the proton amplitude, we investigate the sensitivity of the threshold cross section to the elementary $γn \to π^0 n$ amplitude. A precise measurement of the threshold cross section for $γd \to π^0 d$ is called for.

hep-ph↗

arXiv1997

Aspects of chiral pion-nucleon physics

The next-to-leading order chiral pion-nucleon Lagrangian contains seven finite low-energy constants. Two can be fixed from the nucleon anomalous magnetic moments and another one from the quark mass contribution to the neutron-proton mass splitting. We find a set of nine observables, which to one loop order do only depend on the remaining four dimension two couplings. These are then determined from a best fit. We also show that their values can be understood in terms of resonance exchange related to $Δ$ excitation as well as vector and scalar meson exchange. In particular, we discuss the role of the fictitious scalar-isoscalar meson. We also investigate the chiral expansion of the two P-wave scattering volumes $P_1^-$ and $P_2^+$ as well as the isovector S-wave effective range parameter $b^-$. The one-loop calculation is in good agreement with the data. The difference $P_1^- - P_2^+$ signals chiral loop effects in the $πN$ P-waves. The calculated D- and F-wave threshold parameters compare well with the empirical values.

hep-ph↗

arXiv1996

Nucleon electroweak form factors: Analysis of their spectral functions

We investigate the imaginary parts of the nucleon electromagnetic and axial form factors close to threshold in the framework of heavy baryon chiral perturbation theory. For the isovector electromagnetic form factors, we recover the well known strong enhancement near threshold. For the isoscalar ones, we show that there is no visible enhancement due to the three--pion continuum. This justifies the use of vector meson poles only in dispersion--theoretical calculations. We also calculate the imaginary part of the nucleon isovector axial form factor and show that it is small in the threshold region.

hep-ph↗

arXiv1996

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

We calculate the one--loop contributions of order $M_π^4$ to the difference $Δ_R$ between the on--shell pion--nucleon scattering amplitude $\bar{D}^+(0,2M_π^2)$ at the Cheng--Dashen point $ν=0$, $t=2M_π^2$ and the scalar form factor $σ(2M_π^2)$ in the framework of heavy baryon chiral perturbation theory. We proof that to this order $Δ_R$ contains $no$ chiral logarithms and therefore it vanishes simply as $M_π^4$ in the chiral limit. Numerically, we find as an upper limit $Δ_R \simeq 2\,$MeV.

hep-ph↗

arXiv1996

Double neutral pion photoproduction at threshold

We consider the chiral expansion of the threshold amplitude for the reaction $γp \to π^0 π^0 p$ to order ${\cal O}(M_π^2)$. 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.

nucl-th↗

arXiv1996

Chiral corrections to the Kroll-Ruderman theorem

We calculate the one--loop corrections to the Kroll--Ruderman low--energy theorems for charged pion photoproduction in the framework of heavy baryon chiral perturbation theory. We predict the threshold S--wave multipole $E_{0+}$ to be $E_{0+}^{\rm thr}(γp \to π^+ n) = ( 28.2 \pm 0.6 )\cdot 10^{-3}/M_π$ and $E_{0+}^{\rm thr} (γn \toπ^- p) = ( -32.7 \pm 0.6 )\cdot 10^{-3}/M_π$, respectively, for a fixed pion--nucleon coupling constant, $g_{πN} = 13.4$. A comparison to the existing data is also given.

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