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An amplitude analysis of the $\overline{N}N \to π^- π^+$ reaction  [PDF]
W. M. Kloet,F. Myhrer
Physics , 1995, DOI: 10.1103/PhysRevD.53.6120
Abstract: A simple partial wave amplitude analysis of $\overline{p}p \rightarrow \pi^- \pi^+$ has been performed for data in the range p$_{\sl lab}$ = 360 -- 1000 MeV/c. Remarkably few partial waves are required to fit the data, while the number of required $J$ values barely changes over this energy range. However, the resulting set of partial wave amplitudes is not unique. We discuss possible measurements with polarized beam and target which will severely restrict and help resolve the present analysis ambiguities. New data from the reaction $\overline{p}p \rightarrow \pi^0 \pi^0$ alone, are insufficient for that purpose.
Comprehensive Amplitude Analysis of $γγ\rightarrow π^+π^-, π^0π^0$ and $\overline{K} K$ below 1.5 GeV  [PDF]
Ling-Yun Dai,Michael R. Pennington
Physics , 2014, DOI: 10.1103/PhysRevD.90.036004
Abstract: In this paper we perform an amplitude analysis of essentially all published pion and kaon pair production data from two photon collisions below 1.5 GeV. This includes all the high statistics results from Belle, as well as older data from Mark II at SLAC, CELLO at DESY, Crystal Ball at SLAC. The purpose of this analysis is to provide as close to a model-independent determination of the $\gamma\gamma$ to meson pair amplitudes as possible. Having data with limited angular coverage, typically $|\cos \theta| < 0.6-0.8$, and no polarization information for reactions in which spin is an essential complication, the determination of the underlying amplitudes might appear an intractable problem. However, imposing the basic constraints required by analyticity, unitarity, and crossing-symmetry makes up for the experimentally missing information. Final state interactions among the meson pairs are critical to this analysis. To fix these, we include the latest $\pi\pi\to\pi\pi$, ${\overline K}K$ scattering amplitudes given by dispersive analyses, supplemented in the ${\overline K}K$ threshold region by the recent precision Dalitz plot analysis from BaBar. With these hadronic amplitudes built into unitarity, we can constrain the overall description of $\gamma\gamma\to\pi\pi$ and $\overline{K}K$ datasets, both integrated and differential cross-sections, including the high statistics charged and neutral pion, as well as $K_sK_s$ data from Belle. Since this analysis invokes coupled hadronic channels, having data on both $\gamma\gamma\to\pi\pi$ and $\overline{K}K$ reduces the solution space to essentially a single form. We present the partial wave amplitudes, show how well they fit all the available data, and give the two photon couplings of scalar and tensor resonances that appear. These partial waves are important inputs into forthcoming dispersive calculations of hadronic light-by-light scattering.
Separation of S- wave pseudoscalar and pseudovector amplitudes in pi^- p---> pi^+ pi^- n reaction on polarized target  [PDF]
R. Kaminski,L. Lesniak,K. Rybicki
Physics , 1996, DOI: 10.1007/s002880050372
Abstract: A new analysis of S-wave production amplitudes for the reaction $\pi^- p_{\uparrow} \rightarrow \pi^+ \pi^- n$ on a transversely polarized target is performed. It is based on the results obtained by the CERN-Cracow -Munich collaboration in the pion-pion energy range from 600 MeV to 1600 MeV at 17.2 GeV/c $\pi^-$ momentum. Energy-independent separation of the S-wave pseudoscalar amplitude ($\pi$ exchange) from the pseudovector amplitude ($a_{1}$ exchange) is carried out using assumptions much weaker than those in all previous analyses. We show that, especially around 1000 MeV and around 1500 MeV, the $a_{1}$ exchange amplitude cannot be neglected. The scalar-isoscalar $\pi\pi$ phase shifts are calculated using fairly weak assumptions. Below the $K\overline{K}$ threshold we find two solutions for the $\pi-\pi$ phase shifts, for which the phases increase slower with the effective $\pi-\pi$ mass than the P-wave phases. Both solutions are consistent with a broad $f_{0}(500)$ but only one is similar to the well-known "down" solution. We find also the third solution (with a somewhat puzzling behavior of inelasticity) which exhibits a narrow $f_{0}(750)$ claimed by Svec. All the solutions undergo a rapid change at the $K\overline{K}$ threshold. Above 1420 MeV the phase shifts increase with energy faster than those obtained without the polarized-target data. This phase behavior as well as an increase of the modulus of the $a_{1}$-exchange amplitude can be due to the presence of the $f_{0}(1500)$.
A note on $ {|overline{N}, p_n; delta|_k} $ summability factors of in nite series  [cached]
Poorvi Sinha,Hirdesh Kumar
Tamkang Journal of Mathematics , 2008, DOI: 10.5556/j.tkjm.39.2008.193-198
Abstract: In this paper a general theorem on $ | overline{N}, p_n; delta|_k $ summability factors which generalizes a theorem of Bor [4] on for $ |overline{N}, p_n|_k $ summability factors of infinite series.
Model-independent aspects of the reaction $\bar{K} + N \to K + Ξ$  [PDF]
Benjamin Jackson,Yongseok Oh,Helmut Haberzettl,Kanzo Nakayama
Physics , 2013, DOI: 10.1103/PhysRevC.89.025206
Abstract: Various model-independent aspects of the $\bar{K} N \to K \Xi$ reaction are investigated, starting from the determination of the most general structure of the reaction amplitude for $\Xi$ baryons with $J^P=\frac12^\pm$ and $\frac32^\pm$ and the observables that allow a complete determination of these amplitudes. Polarization observables are constructed in terms of spin-density matrix elements. Reflection symmetry about the reaction plane is exploited, in particular, to determine the parity of the produced $\Xi$ in a model-independent way. In addition, extending the work of Biagi $\mathrm{\textit{et al. } [Z. Phys.\ C \textbf{34}, 175 (1987)]}$, a way is presented of determining simultaneously the spin and parity of the ground state of $\Xi$ baryon as well as those of the excited $\Xi$ states.
A further analysis of $Θ^+$ production in $γ+D \to Λ+n+K^{+}$ reaction  [PDF]
V. Guzey
Physics , 2006,
Abstract: We analyse Theta+ production in the gamma+D -> \Lambda+n+K+ reaction and study the dependence of the gamma+D -> \Lambda+n+K+ differential cross section on the nK+ invariant mass and on the momentum of the final neutron p_n. We examine the important role of the interference between the signal and background contributions to the gamma+D -> \Lambda+n+K+ amplitude in the extraction of the Theta+ signal from the gamma+D -> \Lambda+n+K+ cross section. We demonstrate that as a result of the cancellation between the interference and signal contributions, the Theta+ signal almost completely washes out after the integration over p_n. This is consistent with the CLAS conclusion that no statistically significant structures in the analysis of the gamma+D -> \Lambda+n+K+ reaction were observed. Therefore, there is no disagreement between the theory and the experiment and the CLAS result does not refute the existence of the Theta+.
Formation spectra of light kaonic nuclei by in-flight (${\bar K},N$) reactions with chiral unitary amplitude  [PDF]
J. Yamagata-Sekihara,D. Jido,H. Nagahiro,S. Hirenzaki
Physics , 2008, DOI: 10.1103/PhysRevC.80.045204
Abstract: We study theoretically the in-flight ($K^-,N$) reactions for the formation of light kaonic nuclear systems to get deeper physical insights on the expected spectra, and to investigate the experimental feasibility of the reaction at new facilities like J-PARC. We show the expected spectra for the formation of the $K^-pp, K^-pn$, $K^-nn$ and $K^-$-$^{11}$B systems which are accessible by the ($K^-,N$) experiments. By considering the conversion part of the Green's function, we can show the missing mass spectra of the ($K^-,N$) reactions coincidence with the particle emissions due to ${\bar K}$ absorption in ${\bar K}N\to \pi Y$ processes. To calculate the cross sections, we use the so-called $T\rho$ approximation to evaluate the optical potential. As for the amplitude $T$, we adopt the chiral unitary amplitude of ${\bar K}N$ channel in vacuum for simplicity, and we also check the medium effects by applying the chiral amplitude at finite density. The effects of the p-wave optical potential of $\Sigma$(1385) channel and the contribution from ${\bar K^0}$ mixing in $^3$He($K^-,n$) reaction are also evaluated numerically. To understand the meanings of the spectrum shape, we also study the behavior of the poles of kaon Green's function in nuclear matter. We conclude that $^3$He($K^-,n$) and $^3$He($K^-,p$) reactions coincident with the $\pi\Sigma$ emission due to ${\bar K}$ absorption may show the certain structure in the bound region spectra indicating the existence of the unstable kaonic nuclear bound states. As for the $^{12}$C($K^-,p$) spectra with the $\pi\Sigma$ emission, we may also observe the structure in the bound region, however, we need to evaluate the medium effects carefully for larger nuclei.
$\bar{K} + N \to K + Ξ$ reaction and $S=-1$ hyperon resonances  [PDF]
Benjamin C. Jackson,Yongseok Oh,H. Haberzettl,K. Nakayama
Physics , 2015, DOI: 10.1103/PhysRevC.91.065208
Abstract: The $\bar{K} + N \to K + \Xi$ reaction is studied for center-of-momentum energies ranging from threshold to 3 GeV in an effective Lagrangian approach that includes the hyperon $s$- and $u$-channel contributions as well as a phenomenological contact amplitude. The latter accounts for the rescattering term in the scattering equation and possible short-range dynamics not included explicitly in the model. Existing data are well reproduced and three above-the-threshold resonances were found to be required to describe the data, namely, the $\Lambda(1890)$, $\Sigma(2030)$, and $\Sigma(2250)$. For the latter resonance we have assumed the spin-parity of $J^P=5/2^-$ and a mass of 2265 MeV. The $\Sigma(2030)$ resonance is crucial in achieving a good reproduction of not only the measured total and differential cross sections, but also the recoil polarization asymmetry. More precise data are required before a more definitive statement can be made about the other two resonances, in particular, about the $\Sigma(2250)$ resonance that is introduced to describe a small bump structure observed in the total cross section of $K^- + p \to K^+ + \Xi^-$. The present analysis also reveals a peculiar behavior of the total cross section data in the threshold energy region in $K^- + p \to K^+ + \Xi^-$, where the $P$- and $D$-waves dominate instead of the usual $S$-wave. Predictions for the target-recoil asymmetries of the $\bar{K} + N \to K + \Xi$ reaction are also presented.
The $K^- d \to πΣn$ reaction revisited  [PDF]
Daisuke Jido,Eulogio Oset,Takayasu Sekihara
Physics , 2012, DOI: 10.1140/epja/i2013-13095-6
Abstract: The appearance of some papers dealing with the $K^- d \to \pi \Sigma n$ reaction, with some discrepancies in the results and a proposal to measure the reaction at forward $n$ angles at J-PARC justifies to retake the theoretical study with high precision to make accurate predictions for the experiment and extract from there the relevant physical information. We do this in the present paper showing results using the Watson approach and the truncated Faddeev approach. We argue that the Watson approach is more suitable to study the reaction because it takes into account the potential energy of the nucleons forming the deuteron, which is neglected in the truncated Faddeev approach. Predictions for the experiment are done as well as spectra with the integrated neutron angle.
Permutation-equivariant quantum K-theory III. Lefschetz' formula on $\overline{M}_{0,n}/S_n$ and adelic characterization  [PDF]
Alexander Givental
Mathematics , 2015,
Abstract: We continue our study of the genus-$0$ permutation-equivariant quantum K-theory of the target $X=pt$, and completely determine the "big J-function" of this theory. The computation is based on the application of Lefschetz' fixed point formula to the action of $S_n$ on $\overline{M}_{0,n+1}$. It is an instance of the general "adelic characterization" (which we state at the end with reference to arXiv:1106.3136) of quantum K-theory for any target $X$ in terms of quantum cohomology theory. Yet, some simplifications of non-conceptual nature occur in this example, making it a lucid illustration to the general theory.
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