Forward photoproduction of <math><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> pairs with invariant mass of the order of <math><msub><mi>m</mi><mi>ρ</mi></msub><mo>∼</mo><mn>770</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> is traditionally attributed to Pomeron exchange. Based on a detailed analysis of the CEBAF Large Acceptance Spectrometer photoproduction data collected at photon energies below 4 GeV, it is shown from a study of the angular moments that the dynamics of two-pion photoproduction for <math><mo>|</mo><mi>t</mi><mo>|</mo><mo>≳</mo><mn>0.5</mn><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></math> cannot be explained by Pomeron exchange alone. This motivates the development of a new theoretical model of two-pion photoproduction which incorporates both two-pion and pion-nucleon resonant contributions. After fitting free parameters, the model provides an excellent description of the low moments of the angular distribution measured at CLAS and enables an assessment of the relative contributions of particular production mechanisms and an interpretation of the various features of the data in terms of these mechanisms.

Poland

Łukasz Bibrzycki

Spain

Nadine Hammoud

Vincent Mathieu

Robert J. Perry

United States

Alex Akridge

César Fernández-Ramírez

Gloria Montaña

Italy

Alessandro Pilloni

Arkaitz Rodas

Vanamali Shastry

Wyatt A. Smith

Germany

Daniel Winney

Adam P. Szczepaniak

Studying <math><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> photoproduction beyond Pomeron exchange

The Reggeized pion is expected to provide the main contribution to the forward cross section in light meson photoproduction reactions with charge exchange at high energies. We discuss the Reggeization of pion exchange in charged pion photoproduction with an emphasis on consistency with current conservation. We show that the gauge-invariant amplitude for the exchange of a particle with a generic even spin <math><mi>J</mi><mo>≥</mo><mn>2</mn></math> in the <math><mi>t</mi></math> channel is analytic at <math><mi>J</mi><mo>=</mo><mn>0</mn></math> and that it can be interpreted in terms of the nucleon electric current. This enables us to reconcile the dynamics in the <math><mi>s</mi></math> and <math><mi>u</mi></math> channel, which involves also nucleon exchanges, with the amplitude expressed in terms of <math><mi>t</mi></math>-channel partial waves, as required by Regge theory.

Glòria Montaña

Giorgio Foti

Revisiting gauge invariance and Reggeization of pion exchange

We study the decays of the <math altimg='si1.svg'><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><msup><mrow><mn>1</mn></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math> hybrid nonet using a Lagrangian invariant under the flavor symmetry, parity reversal, and charge conjugation. We use the available experimental data, the lattice predictions, and the flavor constraints to evaluate the coupling strengths of the <math altimg='si2.svg'><msub><mrow><mi>&#960;</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy='false'>(</mo><mn>1600</mn><mo stretchy='false'>)</mo></math> to various two-body mesonic states. Using these coupling constants, we estimate the partial widths of the two-body decays of the hybrid pion, kaon and the isoscalars. We find that the hybrid kaon can be nearly as broad as the <math altimg='si2.svg'><msub><mrow><mi>&#960;</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy='false'>(</mo><mn>1600</mn><mo stretchy='false'>)</mo></math>. Quite remarkably, we find also that the light isoscalar must be significantly narrow while the width of the heavy isoscalar can be matched to the recently observed <math altimg='si3.svg'><msub><mrow><mi>&#951;</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy='false'>(</mo><mn>1855</mn><mo stretchy='false'>)</mo></math>.

Christian S. Fischer

Francesco Giacosa

The phenomenology of the exotic hybrid nonet with <italic>&#960;</italic> <inf>1</inf>(1600) and <italic>&#951;</italic> <inf>1</inf>(1855)

We propose commuting sets of matrix-valued difference operators in terms of trigonometric <math><mrow><mi>GL</mi></mrow><mo>(</mo><mi>N</mi><mo>|</mo><mi>M</mi><mo>)</mo></math>-valued R-matrices thus providing quantum supersymmetric (and possibly anisotropic) spin Ruijsenaars-Macdonald operators. Two types of trigonometric supersymmetric R-matrices are used for this purpose. The first is the one related to the affine quantized algebra <math><msub><mrow><mover><mrow><mi>U</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mrow><mi>gl</mi></mrow><mo>(</mo><mi>N</mi><mo>|</mo><mi>M</mi><mo>)</mo><mo>)</mo></math>. The second is a graded version of the standard <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>n</mi></mrow></msub></math>-invariant <math><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></math> type R-matrix. We show that being properly normalized the latter graded R-matrix satisfies the associative Yang-Baxter equation. Next, we discuss construction of long-range spin chains using the Polychronakos freezing trick. As a result we obtain a new family of spin chains, which extends the <math><mrow><mi>gl</mi></mrow><mo>(</mo><mi>N</mi><mo>|</mo><mi>M</mi><mo>)</mo></math>-invariant Haldane-Shastry spin chain to q-deformed case with possible presence of anisotropy.

Russia

M. Matushko

A. Zotov

Supersymmetric generalization of q-deformed long-range spin chains of Haldane-Shastry type and trigonometric GL( | ) solution of associative Yang-Baxter equation

We study the effects of off-shellness in the generalized parton distributions of the pion. On general grounds, these distributions exhibit a richer structure than in the on-shell case due to absence of the crossing symmetry. In particular, their moments involve additional terms odd in the skewness parameter, associated with new form factors. We bring up relations between the off-shell charge and gravitational form factors, as well as the pion form factor, and discuss their derivations based on the Ward-Takahashi identities. We illustrate the features at the (leading-<math><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math>) one-quark-loop level with the help of the spectral quark model of the pion, constructed to embed the vector meson dominance. Simple analytic expressions for the form factors and the distributions follow. Thus obtained off-shell generalized parton distributions are evolved from the quark model scale to higher scales with the leading-order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equations. We evaluate the corresponding Compton amplitudes which enter the cross section for the electroproduction of the pion off the proton (the Sullivan process). It is found in our model that the effects of off-shellness in the generalized parton distribution are substantial, however, they can be largely canceled by the corresponding off-shell corrections to the pion propagator. In particular, this is the case of the Compton form factors entering the deeply virtual Compton scattering amplitude. As a result, we expect small off-shellness effects in electroproduction reactions, such as the Sullivan process.

Wojciech Broniowski

Enrique Ruiz Arriola

Off-shellness in generalized parton distributions and form factors of the pion

We study the Higgs–Higgs scattering process and the possible emergence of a Higgs–Higgs bound state (Higgsonium) in any Higgs potential with the vacuum expectation value and second derivative matching the corresponding values from the Standard Model (SM). From the tree-level Higgs–Higgs scattering amplitude, we construct the unitarized amplitude using two different unitarization schemes (the well-known on-shell and N/D methods). We reproduce the known result that there is no Higgsonium state in the SM and, in addition, we determine the S-, D-, and G-wave SM scattering lengths, both at tree-level and upon unitarization. In doing so, we refine previous results by checking the convergence of the N/D approach. Next, we extend the calculation for non-SM potentials and investigate under which conditions a formation of a bound state close to the Higgs–Higgs threshold is possible. In this way, the assumption that no Higgsonium exist, imposes certain bounds on the values of the self-interaction parameters that complement those imposed by the vacuum stability condition.

Higgs–Higgs scattering and the (non-)existence of the Higgsonium

Off-shell effects in generalized parton distributions (GPDs) of the pion, appearing, e.g., in the Sullivan process, are considered. Due to the lack of crossing symmetry, the moments of GPDs involve also odd powers of the skewness (longitudinal momentum transfer) parameter, which results in emergence of new off-shell form factors. With current-algebra techniques, we derive exact relations between the four off-shell gravitational form factors of the pion, in analogy to the electromagnetic case. Our results place stringent constraints on the off-shell GPDs of the pion. We provide an explicit realization in terms of a chiral quark model, where we show that the off-shell effects in GPDs are potentially significant in modeling physical processes and should not be neglected.

Off-shell generalized parton distributions and form factors of the pion

We analyze the generalized quasi, Ioffe-time, and pseudodistributions of the valence quarks in the pion at the quark model scale. We use the framework of the Nambu-Jona-Lasinio model and investigate the basic question of how fast the pion has to move to effectively reach the infinite momentum limit, where the approach can provide the information on the generalized parton distribution functions. We consider both the vector distributions and the transversity distributions, related to the spin densities. With the developed analytic expressions, we conclude that to effectively approach the infinite momentum limit in the Ioffe-time distributions for values of the Ioffe-time accessible in lattice QCD, one roughly needs the pion momenta of the order of <math><mrow><mo>∼</mo><mn>3</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. We explore polynomiality of the quasidistributions and study the generalized quasi form factors. The issue of separability of the transverse and longitudinal dynamics in the model is studied with the help of the generalized Ioffe-time distributions, with the conclusion that the breaking is not substantial, unless the momentum transfer <math><mi>t</mi></math> is large. We also provide an estimate of the range of the Ioffe-time values needed to obtain the generalized parton distributions with a reasonable accuracy. Our model results, which are analytic or semianalytic, provide a valuable insight into the theoretical formalism and illustrate the intricate features of the investigated distributions.

Generalized quasi-, Ioffe-time-, and pseudodistributions of the pion in the Nambu–Jona-Lasinio model

We study the two-body decays of mesons using the covariant helicity formalism. In particular, we show how the partial wave analysis of decays constrains the interacting terms entering the Lagrangian describing the decays of mesons with <math><mi>J</mi><mo>=</mo><mn>1</mn></math> and <math><mrow><mi>J</mi><mo>=</mo><mn>2</mn></mrow></math>. We use available information on partial wave analysis to study specific mesonic decays and to make predictions for not yet measured quantities as well as to investigate the isoscalar mixing angle in the axial-vector, pseudovector and pseudotensor sectors. In particular, in the axial-vector sector our result agrees with the LHCb one, and in the pseudotensor sector we confirm a quite large (and negative) angle in the nonstrange-strange basis, which is compatible with a large contribute of the axial anomaly.

Enrico Trotti

Constraints imposed by the partial wave amplitudes on the decays of <math><mi>J</mi><mo>=</mo><mn>1</mn></math>, 2 mesons