Covariant Chiral Perturbation Theory Research Articles

Long-range S -wave DD* interaction in covariant chiral effective field theory

Motivated by the recent lattice QCD study of the DD* interaction at unphysical quark masses, we perform a theoretical study of the DD* interaction in covariant chiral effective field theory. In particular, we calculate the relevant leading-order two-pion exchange contributions. The results compare favorably with the lattice QCD results, supporting the conclusion that the intermediate-range DD* interaction is dominated by two-pion exchanges and the one-pion exchange contribution is absent. At a quantitative level, the covariant chiral perturbation theory results agree better with the lattice QCD results than their nonrelativistic counterparts, showing the relevance of relativistic corrections in the charm sector. Published by the American Physical Society 2024

Proton and neutron electromagnetic radii and magnetic moments from lattice QCD

We present results for the electromagnetic form factors of the proton and neutron computed on the (2 + 1)-flavor Coordinated Lattice Simulations (CLS) ensembles including both quark-connected and -disconnected contributions. The Q2-, pion-mass, lattice-spacing, and finite-volume dependence of our form factor data is fitted simultaneously to the expressions resulting from covariant chiral perturbation theory including vector mesons amended by models for lattice artefacts. From these fits, we determine the electric and magnetic radii and the magnetic moments of the proton and neutron, as well as the Zemach radius of the proton. To assess the influence of systematic effects, we average over various cuts in the pion mass and the momentum transfer, as well as over different models for the lattice-spacing and finite-volume dependence, using weights derived from the Akaike Information Criterion (AIC).

Nucleon Self-Energy Including Two-Loop Contributions

The nucleon self-energy is calculated in SU(2) covariant chiral perturbation theory to study the pion mass dependence of the nucleon mass up to chiral order O(q6), i.e., including two-loop diagrams. The contributions of the diagrams are expressed by a small set of (scalar) master integrals. The extended-on-mass-shell (EOMS) renormalization scheme is applied by systematically subtracting infrared regular parts of the integrals (besides the divergences) to ensure that the renormalized results are consistent with the power counting. The master integrals are evaluated in two ways: Firstly, they are calculated by means of the chiral expansion in d dimensions, using the strategy of regions to differentiate between the infrared singular and regular part. This yields the physical nucleon mass in a 1/m-expansion and is in agreement with the infrared-renormalized result. Secondly, the master integrals are solved numerically without relying on the 1/m-expansion using the sector decomposition method.

Isovector electromagnetic form factors of the nucleon from lattice QCD and the proton radius puzzle

We present results for the isovector electromagnetic form factors of the nucleon computed on the CLS ensembles with $N_f=2+1$ flavors of $\mathcal{O}(a)$-improved Wilson fermions and an $\mathcal{O}(a)$-improved vector current. The analysis includes ensembles with four lattice spacings and pion masses ranging from 130 MeV up to 350 MeV and mainly targets the low-$Q^2$ region. In order to remove any bias from unsuppressed excited-state contributions, we investigate several source-sink separations between 1.0 fm and 1.5 fm and apply the summation method as well as explicit two-state fits. The chiral interpolation is performed by applying covariant chiral perturbation theory including vector mesons directly to our form factor data, thus avoiding an auxiliary parametrization of the $Q^2$ dependence. At the physical point, we obtain $\mu=4.71(11)_{\mathrm{stat}}(13)_{\mathrm{sys}}$ for the nucleon isovector magnetic moment, in good agreement with the experimental value and $\langle r_\mathrm{M}^2\rangle~=~0.661(30)_{\mathrm{stat}}(11)_{\mathrm{sys}}\,~\mathrm{fm}^2$ for the corresponding square-radius, again in good agreement with the value inferred from the $ep$-scattering determination [Bernauer et~al., Phys. Rev. Lett., 105, 242001 (2010)] of the proton radius. Our estimate for the isovector electric charge radius, $\langle r_\mathrm{E}^2\rangle = 0.800(25)_{\mathrm{stat}}(22)_{\mathrm{sys}}\,~\mathrm{fm}^2$, however, is in slight tension with the larger value inferred from the aforementioned $ep$-scattering data, while being in agreement with the value derived from the 2018 CODATA average for the proton charge radius.

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.

Threshold pion electro- and photoproduction off nucleons in covariant chiral perturbation theory

Pion electro- and photoproduction off the nucleon close to threshold is studied in covariant baryon chiral perturbation theory at O($p^3$) in the extended-on-mass-shell scheme, with the explicit inclusion of the $\Delta(1232)$ resonance. The relevant low energy constants are fixed by fitting the available experimental data with the theoretical model. The inclusion of the $\Delta$ resonance as an explicit degree of freedom substantially improves the agreement with data and the convergence of the model.

Pion photoproduction off nucleons in covariant chiral perturbation theory

Pion photoproduction off the nucleon close to threshold is studied in covariant baryon chiral perturbation theory at O($p^3$) in the extended-on-mass-shell scheme, with the explicit inclusion of the $\Delta(1232)$ resonance using the $\delta$ counting. The theory is compared to the available data of cross sections and polarization observables for all the charge channels. Most of the necessary low energy constants are well known from the analysis of other processes and the comparison with data strongly constrains some of the still unknown ones. The $\Delta(1232)$ contribution is significant in improving the agreement with data, even at the low energies considered.

Light front Hamiltonian for boson form of QED (1 + 1) in Pauli–Villars regularization

Light front (LF) Hamiltonian for QED in [Formula: see text] dimensions is constructed using the boson form of this model with additional Pauli–Villars-type ultraviolet regularization. Perturbation theory, generated by this LF Hamiltonian, is proved to be equivalent to usual covariant chiral perturbation theory. The obtained LF Hamiltonian depends explicitly on chiral condensate parameters which enter in a form of some renormalization of coupling constants. The obtained results can be useful when one attempts to apply LF Hamiltonian approach for [Formula: see text]-dimensional models like QCD.

Neutral-current weak pion production off the nucleon in covariant chiral perturbation theory

Neutral current single pion production induced by neutrinos and antineutrinos on nucleon targets has been investigated in manifestly relativistic baryon chiral perturbation theory with explicit Δ(1232) degrees of freedom up to O(p3). At low energies, where chiral perturbation theory is applicable, the total cross sections for the different reaction channels exhibit a sizable non-resonant contribution, which is not present in event generators of broad use in neutrino oscillation and cross section experiments such as GENIE and NuWro.

Weak pion production off the nucleon in covariant chiral perturbation theory

Weak pion production off the nucleon at low energies has been systematically investigated in manifestly relativistic baryon chiral perturbation theory with explicit inclusion of the $\Delta$(1232) resonance. Most of the involved low-energy constants have been previously determined in other processes such as pion-nucleon elastic scattering and electromagnetic pion production off the nucleon. For numerical estimates, the few remaining constants are set to be of natural size. As a result, the total cross sections for single pion production on neutrons and protons, induced either by neutrino or antineutrino, are predicted. Our results are consistent with the scarce existing experimental data except in the $\nu_\mu n\to \mu^-n\pi^+$ channel, where higher-order contributions might still be significant. The $\Delta$ resonance mechanisms lead to sizeable contributions in all channels, especially in $\nu_\mu p\to \mu^- p\pi^+$, even though the considered energies are close to the production threshold. The present study provides a well founded low-energy benchmark for phenomenological models aimed at the description of weak pion production processes in the broad kinematic range of interest for current and future neutrino-oscillation experiments.

Electromagnetic form factors of spin- 1/2 doubly charmed baryons

We study the electromagnetic form factors of the doubly charmed baryons, using covariant chiral perturbation theory within the extended on-mass-shell (EOMS) scheme. Vector-meson contributions are also taken into account. We present results for the baryon magnetic moments, charge and magnetic radii. While some of the chiral Lagrangian parameters could be set to values determined in previous works, the available lattice results for $\Xi_{cc}^+$ and $\Omega_{cc}^+$ only allow for robust constraints on the low-energy constant (LEC) combination, $c_{89}(=-\frac{1}{3}c_8+4c_9)$. The couplings of the doubly charmed baryons to the vector mesons have been estimated assuming the Okubo--Zweig--Iizuka (OZI) rule. We also give the expressions for the form factors of the double beauty baryons considering the masses predicted in the framework of quark models. A comparison of our results with those obtained in heavy baryon chiral perturbation theory (HBChPT) at the same chiral order is made.

Octet baryon magnetic moments at next-to-next-to-leading order in covariant chiral perturbation theory

We calculate the octet baryon magnetic moments in covariant baryon chiral perturbation theory with the extended-on-mass-shell renormalization scheme up to next-to-next-to-leading order. At this order, there are nine low-energy constants, which cannot be uniquely determined by the seven experimental data alone. We propose two strategies to circumvent this problem. First, we assume that chiral perturbation theory has a certain convergence rate and use this as one additional constraint to fix the low-energy constants by fitting to the experimental data. Second, we fit to lattice QCD simulations to determine the low-energy constants. We then compare the resulting predictions of the light and strange quark mass dependence of the octet baryon magnetic moments by the three mostly studied formulations of baryon chiral perturbation theory, namely, the extended-on-mass-shell, the infrared, and the heavy baryon approaches. It is shown that once more precise lattice data become available, one will learn more about the convergence pattern of baryon chiral perturbation theory.

Systematic study of octet-baryon electromagnetic form factors in covariant chiral perturbation theory

We perform a complete and systematic calculation of the octet-baryon form factors within the fully covariant approach of SU(3) chiral perturbation theory at O(p^3). We use the extended on-mass shell renormalization scheme, and include explicitly the vector mesons and the spin-3/2 decuplet intermediate states. Comparing these predictions with data including magnetic moments, charges, and magnetic radii, we determine the unknown low-energy constants, and give predictions for yet unmeasured observables, such as the magnetic moment of the Sigma^0, and the charge and magnetic radii of the hyperons.

Nucleon-pion-state contribution in lattice calculations of the nucleon chargesgA,gTandgS

We employ leading order covariant chiral perturbation theory to compute the nucleon-pion-state contribution to the 3-point correlation functions one typically measures in lattice QCD to extract the isovector nucleon charges $g_A,g_T$ and $g_S$. We estimate the impact of the nucleon-pion-state contribution on both the plateau and the summation method for lattice simulations with physical pion masses. The nucleon-pion-state contribution results in an overestimation of all charges with both methods. The overestimation is roughly equal for the axial and the tensor charge, and about fifty percent larger for the scalar charge.

Predictions of covariant chiral perturbation theory for nucleon polarisabilities and polarised Compton scattering

We update the predictions of the SU(2) baryon chiral perturbation theory for the dipole polarisabilities of the proton, $\{\alpha_{E1},\,\beta_{M1}\}_p=\{11.2(0.7),\,3.9(0.7)\}\times10^{-4}$fm$^3$, and obtain the corresponding predictions for the quadrupole, dispersive, and spin polarisabilities: $\{\alpha_{E2},\,\beta_{M2}\}_p=\{17.3(3.9),\,-15.5(3.5)\}\times10^{-4}$fm$^5$, $\{\alpha_{E1\nu},\,\beta_{M1\nu}\}_p=\{-1.3(1.0),\,7.1(2.5)\}\times10^{-4}$fm$^5$, and $\{\gamma_{E1E1},\,\gamma_{M1M1},\,\gamma_{E1M2},\,\gamma_{M1E2}\}_p=\{-3.3(0.8),\,2.9(1.5),\,0.2(0.2),\,1.1(0.3)\}\times10^{-4}$fm$^4$. The results for the scalar polarisabilities are in significant disagreement with semi-empirical analyses based on dispersion relations, however the results for the spin polarisabilities agree remarkably well. Results for proton Compton-scattering multipoles and polarised observables up to the Delta(1232) resonance region are presented too. The asymmetries $\Sigma_3$ and $\Sigma_{2x}$ reproduce the experimental data from LEGS and MAMI. Results for $\Sigma_{2z}$ agree with a recent sum rule evaluation in the forward kinematics. The asymmetry $\Sigma_{1z}$ near the pion production threshold shows a large sensitivity to chiral dynamics, but no data is available for this observable. We also provide the predictions for the polarisabilities of the neutron: $\{\alpha_{E1},\,\beta_{M1}\}_n=\{13.7(3.1),\,4.6(2.7)\}\times10^{-4}$fm$^3$, $\{\alpha_{E2},\,\beta_{M2}\}_n=\{16.2(3.7),\,-15.8(3.6)\}\times10^{-4}$fm$^5$, $\{\alpha_{E1\nu},\,\beta_{M1\nu}\}_n=\{0.1(1.0),\,7.2(2.5)\}\times10^{-4}$fm$^5$, and $\{\gamma_{E1E1},\,\gamma_{M1M1},\,\gamma_{E1M2},\,\gamma_{M1E2}\}_n=\{-4.7(1.1),\,2.9(1.5),\,0.2(0.2),\,1.6(0.4)\}\times10^{-4}$fm$^4$. The neutron dynamical polarisabilities and multipoles are examined too. We also discuss subtleties related to matching dynamical and static polarisabilities.

Chiral dynamics in the [formula omitted] reaction

We investigate the neutral pion photoproduction on the proton near threshold in covariant chiral perturbation theory with the explicit inclusion of Δ degrees of freedom. This channel is specially sensitive to chiral dynamics and the advent of very precise data from the Mainz microtron has shown the limits of the convergence of the chiral series for both the heavy baryon and the covariant approaches. We show that the inclusion of the Δ resonance substantially improves the convergence leading to a good agreement with data for a wider range of energies.

The strangeness content of the nucleon from effective field theory and phenomenology

We revisit the classical relation between the strangeness content of the nucleon, the pion–nucleon sigma term and the SU(3)F breaking of the baryon masses in the context of Lorentz covariant chiral perturbation theory with explicit decuplet-baryon resonance fields. We find that a value of the pion–nucleon sigma term of ∼60 MeV is not necessarily at odds with a small strangeness content of the nucleon, in line with the fulfillment of the OZI rule. Moreover, this value is indeed favored by our next-to-leading order calculation. We compare our results with earlier ones and discuss the convergence of the chiral series as well as the uncertainties of chiral approaches to the determination of the sigma terms.

Background field approach to electromagnetic properties of baryons

We investigate the self-energies of particles in an external magnetic field $B$. The dependence is generally of the type $\sqrt{P(B)}$ with $P$ a polynomial in $B$ and the participating masses. The non-analytic point depends on the mass and charge constellations, is unproblematic for stable particles but constrains the linear energy shift approximation for resonances. We calculate the $B$ dependent self-energies of the nucleon and $\Delta(1232)$-isobar in the SU(2) covariant chiral perturbation theory and outline a way to obtain finite volume corrections to the nucleon anomalous magnetic moment without using the three point function method. We show that finite volume corrections might explain present discrepancies of lattice QCD and chiral perturbation theory results in the small pion mass region.

Finite-volume effects on octet-baryon masses in covariant baryon chiral perturbation theory

We study finite-volume effects on the masses of the ground-state octet baryons using covariant baryon chiral perturbation theory (ChPT) up to next-to-leading order by analyzing the latest $n_f=2+1$ lattice Quantum ChromoDynamics (LQCD) results from the NPLQCD collaboration. Contributions of virtual decuplet baryons are taken into account using the "consistent" coupling scheme. We compare our results with those obtained from heavy baryon ChPT and show that, although both approaches can describe well the lattice data, the underlying physics is different: In HBChPT, virtual decuplet baryons play a more important role than they do in covariant ChPT. This is because the virtual octet baryon contributions to finite-volume corrections are larger in covariant ChPT than in HBChPT, while the contributions of intermediate decuplet baryons are smaller, because of relativistic effects. We observe that for the octet baryon masses, at fixed $m_\pi L$ ($\gg1$) finite-volume corrections decrease as $m_\pi$ approaches its physical value, provided that the strange quark mass is at or close to its physical value, as in most LQCD setups.

Electromagnetic structure of the lowest-lying decuplet resonances in covariant chiral perturbation theory

We present a calculation of the leading SU(3)-breaking $\mathcal{O}({p}^{3})$ corrections to the electromagnetic moments and charge radius of the lowest-lying decuplet resonances in covariant chiral perturbation theory. In particular, the magnetic dipole moment of the members of the decuplet is predicted fixing the only low-energy constant (LEC) present up to this order with the well-measured magnetic dipole moment of the ${\ensuremath{\Omega}}^{\ensuremath{-}}$. We predict ${\ensuremath{\mu}}_{\ensuremath{\Delta}}^{++}=6.04(13)$ and ${\ensuremath{\mu}}_{\ensuremath{\Delta}}^{+}=2.84(2)$, which agree well with the current experimental information. For the electric quadrupole moment and the charge radius, we use state-of-the-art lattice QCD results to determine the corresponding LECs, whereas for the magnetic octupole moment there is no unknown LEC up to the order considered here, and we obtain a pure prediction. We compare our results with those reported in large ${N}_{c}$, lattice QCD, heavy-baryon chiral perturbation theory, and other models.