Spin observables in pion photoproduction from a unitary and causal effective field theory
A. M. Gasparyan, M. F. M. Lutz
备注：
10 pages, 5 figures, writeup of two talks presented at the NAPP 2010 conference and the Crystal-Ball Collaboration meeting in Dubrovnik, October 2010, revised version - corrected an error in Fig. 2 and Fig. 4
Pion photoproduction is analyzed with the chiral Lagrangian. Partial-wave amplitudes are obtained by an analytic extrapolation of subthreshold reaction amplitudes computed in chiral perturbation theory, where the constraints set by electromagnetic-gauge invariance, causality and unitarity are used to stabilize the extrapolation. The experimental data set is reproduced up to energies $\sqrt{s}\simeq 1300$ MeV in terms of the parameters relevant at order $Q^3$. We present and discuss predictions for various spin observables.
Dubnicka-Dubnickova-Kuraev (DDK) sum rules are considered. It is shown that integrals over differences of the total photoproduction cross-sections on octet baryons could be understood in terms of unitary symmetry approach. All the DDK sum rules for these quantities are expressed in terms of only three parameters.
We study the neutral pion photoproduction at near-threshold energies in fully covariant chiral perturbation theory up to O(p^3). When including only nucleonic virtual states in the model, the convergence is too slow. Therefore we test the model when introducing the Delta(1232) resonance as an additional degree of freedom. Some low-energy constants were fitted, converging to values in good agreement with those expected from literature.
The pion and nucleon mass differences generate a very pronounced cusp in the photoproduction reaction of a single neutral pion on the proton. A nonrelativistic effective field theory to describe this reaction is constructed. The approach is rigorous in the sense that it is an effective field theory with a consistent power counting scheme. Expressions for the S- and P-wave multipole amplitudes at one loop are given. The relation of the phase of the electric multipole E_0+ to the phase of the S-wave of pi^0 p --> pi^0 p scattering is discussed.
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 $Δ(1232)$ resonance. The relevant low energy constants are fixed by fitting the available experimental data with the theoretical model. The inclusion of the $Δ$ resonance as an explicit degree of freedom substantially improves the agreement with data and the convergence of the model.
Around $θ_π= 90^\circ$, the coupling to the $ρ^\circ N$ channel leads to a good accounting of the charged pion exclusive photoproduction cross section in the energy range 3 $<E_γ<$ 10 GeV, where experimental data exist. Starting from a Regge Pole approach that successfully describes vector meson production, the singular part of the corresponding box diagrams (where the intermediate vector meson-baryon pair propagates on-shell) is evaluated without any further assumptions (unitarity). Such a treatment provides an explanation of the $s^{-7}$ scaling of the cross section. Elastic rescattering of …
The top triangle moose $(TTM)$ model, which can be seen as the deconstructed version of the topcolor-assisted technicolor ($TC2$) model, predicts the existence of the charged top-pions $ π_{t}^{\pm}$ in low energy spectrum. In the context of this model, we consider photoproduction of $π^{\pm}_{t}$ via the subprocesses $γb\to t π_{t}^{-}$ and $γ\bar{b}\to \bar{t} π_{t}^{+}$ at the large hadron-electron collider ($LHeC$), in which high energy photon beams are generated by using the Compton backscatting method. We find that, as long as the charged top-pions are not too heavy, they can be abundant…
The neutral pion photoproduction on the proton near threshold has a very small scattering cross section when compared to the charged channels, which in ChPT is explained by strong cancellations between the lowest order pieces. Therefore it is very sensitive to higher-order corrections of chiral perturbation theory. We perform a fully covariant calculation up to chiral order p^3 and we investigate the effect of the inclusion of the Delta(1232) resonance as an explicit degree of freedom. We show that the convergence improves, leading to a much better agreement with data at a wide range of energi…
We derive and apply the finite energy sum rules to pion photoproduction. We evaluate the low energy part of the sum rules using several state-of-the-art models. We show how the differences in the low energy side of the sum rules might originate from different quantum number assignments of baryon resonances. We interpret the observed features in the low energy side of the sum rules with the expectation from Regge theory. Finally, we present a model, in terms of a Regge-pole expansion, that matches the sum rules and the high-energy observables.
A sizable $\cos 4ϕ$ azimuthal asymmetry in exclusive di-pion production near $ρ^0$ resonance peak in ultraperipheral heavy ion collisions recently has been reported by STAR collaboration. We show that both elliptic gluon Wigner distribution and final state soft photon radiation can give rise to this azimuthal asymmetry. The fact that the QED effect alone severely underestimates the observed asymmetry might signal the existence of the nontrivial correlation in quantum phase distribution of gluons.
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 $Δ(1232)$ resonance using the $δ$ 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 $Δ(1232)$ contribution is significant in improving the a…
We study the photoproduction of the charged top-pion predicted by the top triangle moose ($TTM$) model (a deconstructed version of the topcolor-assisted technicolor $TC2$ model) via the processes $pp\rightarrow p γp \rightarrow π^\pm_t t +X$ at the 14 $TeV$ Large Hadron Collider ($LHC$) including next-to-leading order ($NLO$) $QCD$ corrections. Our results show that the production cross sections and distributions are sensitive to the free parameters $\sinω$ and $M_{π_t}$. Typical $QCD$ correction value is $7\% \sim 11\%$ and does not depend much on $\sinω$ as well as the forward detector accep…
Masses, widths and photocouplings of baryon resonances are determined in a coupled-channel partial wave analysis of a large variety of data. The Bonn-Gatchina partial wave formalism is extended to include a decomposition of t- and u-exchange amplitudes into individual partial waves. The multipole transition amplitudes for $γp\to pπ^0$ and $γp\to nπ^+$ are given and compared to results from other analyses.
The reaction $γp \to π^0 p$ is investigated in the energy range above the resonance region. The amplitudes include the leading Regge singularities in the cross-channel and correctly describe the differential cross section for beam energies above 4 GeV and for the $s-$channel scattering angle $\cosθ_s\ge 0.6$. The energy dependence of the beam asymmetry and the reaction $γn \to π^0 n$ seem is quantitative consistent with the Regge-pole dominance.
The pion and nucleon mass differences generate a very pronounced cusp in the photoproduction reaction of a single pion on the nucleon. A nonrelativistic effective field theory to describe this reaction is constructed. The approach is rigorous in the sense that it is an effective field theory with a consistent power counting scheme. Expressions for the S- and P-wave multipole amplitudes for all four reaction channels at two loops are given.
Within the framework of non-local quark model of Nambu--Jona-Lasinio type the two-photon decay of radial excited state of $π_0$-meson -- $π_0'$ -- is found to be $3.6\KeV$. The radial excitation of pion is described with the use of polynomial formfactor of second order over $\vec q^2$ where $\vec q$ is the transverse momentum, which corresponds to relative motion of quark-antiquark pair within the energy range from 0 up to $1\GeV$. The probabilities of production of $π_0'$ and $(π_0'+γ)$ states in the electron-positron colliders are estimated. The production of $π_0'$-meson in the interaction …
Within a dynamical coupled-channels model which has already been fixed from analyzing the data of the pi N -> pi N and gamma N -> pi N reactions, we present the predicted double pion photoproduction cross sections up to the second resonance region, W< 1.7 GeV. The roles played by the different mechanisms within our model in determining both the single and double pion photoproduction reactions are analyzed, focusing on the effects due to the direct gamma N -> pi pi N mechanism, the interplay between the resonant and non-resonant amplitudes, and the coupled-channels effects. The model parameters…
We investigate pion photoproduction off the proton in a manifestly gauge-invariant chiral unitary extension of chiral perturbation theory. In a first step, we consider meson-baryon scattering taking into account all next-to-leading order contact interactions. The resulting low-energy constants are determined by a fit to s-wave pion-nucleon scattering and the low-energy data for the reaction pi- p --> eta n. To assess the theoretical uncertainty, we perform two different fit strategies. Having determined the low-energy constants, we then analyse the data on the s-wave multipole amplitudes E0+ o…
A unified description of single-pion photoproduction data, together with pion- and eta-hadroproduction data, has been achieved in a Chew-Mandelstam parametrization which is consistent with unitarity at the two-body level. Energy-dependent and single-energy partial wave analyses of pion photoproduction data have been performed and compared to previous SAID fits and multipoles from the Mainz and Bonn-Gatchina groups.
We analyze the $γN\toπN$ process in the negative parity channel with Hamiltonian effective filed theory which is successful in studying the nucleon resonances associated with the meson-nucleon scattering and lattice QCD simulations. We provide the scattering amplitude of pion photoproduction and extract the electric dipole amplitudes $E_{0+}$. The triquark component in $N^*(1535)$ is important for improving the consistence between our results and the experimental data.
Hybrid/exotic meson spectroscopy searches at Jefferson Lab require the accurate theoretical description of the production mechanism in peripheral photoproduction. We develop a model for $πΔ$ photoproduction at high energies ($5 \leq E_{\text{lab}} \leq 16~\text{GeV}$) that incorporates both the absorbed pion and natural-parity cut contributions. We fit the available observables, providing a good description of the energy and angular dependencies of the experimental data. We also provide predictions for the photon beam asymmetry of charged pions at $E_{\text{lab}} = 9~\text{GeV}$ which is expec…
Energy-dependent and single-energy fits to the existing pion photoproduction database have been updated to cover the region from threshold to 2.7 GeV in the laboratory photon energy. Revised resonance photo-decay couplings have been extracted and compared to previous determinations. The influence of recent measurements is displayed. Remaining problems and future approaches are discussed.
We argue that the reaction mechanism for the coherent pion production is not known with sufficient accuracy to determine the neutron radius of 208Pb to the claimed precision of 0.03 fm.
Dispersion relations and the $Δ$ contributions into the amplitudes $M_{1+}^{3/2},E_{1+}^{3/2}$ from new VPI partial-wave analysis of pion photoproduction
We apply the nuclear model with explicit mesons to photoproduction of neutral pions off protons at the threshold. In this model the nucleons do not interact with each other via a potential but rather emit and absorb mesons that are treated explicitly on equal footing with the nucleons. We calculate the total cross section of the reaction for energies close to threshold and compare the calculations with available experimental data. We show that the model is able to reproduce the experimental data and determine the range of the parameters where the model is compatible with the experiment.
We study the reaction of pion photoproduction on the nucleon in the framework of chiral perturbation theory with explicit $Δ(1232)$ degrees of freedom. In the covariant approach, we give results up to order $ε^3$ in the small scale expansion scheme. Furthermore, we provide $Δ$-less and $Δ$-full results obtained in the heavy-baryon scheme to analyze the differences to the covariant approach. Low energy constants are fitted to multipole amplitudes using theoretical truncation errors estimated by a Bayesian approach. We also compare our findings to data of neutral pion production cross sections a…
We study the effects of the $Δ$(1232) resonance as an effective degree of freedom for charged and neutral pion photo-production on nucleons. Different observables have been calculated for these processes by using relativistic chiral perturbation theory up to $\mathcal{O}(p^3)$ in the $ δ$ counting, thus, including pion loops. We compare our model with a large database containing the available experimental data and constrain some unknown low energy constants.
We study the photoproduction of exclusive $2π^+2π^-$ mesons in ultra-peripheral heavy-ion collisions at RHIC and LHC energies. Predictions in photon-nucleus interactions are calculated for various resonances at central and forward rapidities. The recent H1 preliminary data are utilized to improve the description of the poorly known $γp \to 4π^\pm p$ process. We present the comparisons of our results to the available STAR data at RHIC, and made predictions for LHC energies.
We present a calculation of radiative pion photoproduction in the framework of covariant chiral perturbation theory with explicit $Δ(1232)$ degrees of freedom. The analysis is performed employing the small scale expansion scheme adjusted for the $Δ$ 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 $ γp\toγpπ^0 $ and extract the value of the $Δ^+$ magnetic moment. Errors from the truncation of the small scale expansion are estimated using the Bayesian approach. We compare our results both with…
We have applied a new approach to determine the pole positions and residues from pion photoproduction multipoles. The method is based on a Laurent expansion of the partial wave T-matrices, with a Pietarinen series representing the regular part of energy-dependent and single-energy photoproduction solutions. The method has been applied to multipole fits generated by the MAID and GWU/SAID groups. We show that the number and properties of poles extracted from photoproduction data correspond very well to results from $π$N elastic data and values cited by Particle Data Group (PDG). The photoproduct…
