Partial Wave Analysis Research Articles

Partial-Wave Phase Shift Analysis of Elastic Pion-Nucleon Scattering

Partial-Wave Phase Shift Analysis of Elastic Pion-Nucleon Scattering

Renormalization of one-pion exchange in chiral effective field theory for antinucleon-nucleon scattering

The renormalization of iterated one-pion exchange (OPE) is studied in chiral effective field theory $(\ensuremath{\chi}\mathrm{EFT})$ for the antinucleon-nucleon $(\overline{N}N)$ system. The OPE potential is cut off at a certain distance and contact interactions are represented by a complex spherical well with the same radius. We investigate the dependence on the cutoff radius of the phase shifts, inelasticities, and mixing angles for the low partial waves in $\overline{N}N$ scattering. We show that renormalization requires additional contact interactions compared to the expectation based on naive dimensional analysis. Results after renormalization are compared with the state-of-the-art energy-dependent partial-wave analysis of $\overline{N}N$ data. We compare our conclusions with applications of $\ensuremath{\chi}\mathrm{EFT}$ to the nucleon-nucleon system.

Stopping power of Hetero nuclear di-cluster ions from partial-wave analysis based on semi classical phase shifts


 We apply a semi classical partial-wave scattering method based on the induced density approach (IDA) model. For ion electron scattering, the transport cross section is used to calculate the energy loss. This method yields a non-perturbative exemplification of energy loss, bridging the difference among classical and quantal representations. The focus of this work is the interaction of hetero nuclear di-cluster (He-H) ions with a free gas. The results show three kinds of stopping power in (a.u) (cluster stopping power, self-stopping power and correlated stopping power) of hetero nuclear di-cluster ions (He-H) with velocity at different atomic di-cluster distances at different densities and temperatures. We find that Bragg’s peak of stopping power is directly proportional to density and temperatures and inversely with atomic di-cluster distance . The equations in present work are programmed in fortran-90 for numerical calculations.

On the nature of X(6900) and other structures in the LHCb di-j/ψ spectrum

The LHCb di-J/ψ spectrum is studied within the framework of effective field theory with four coupled channels {J/ψJ/ψ, J/ψψ(2S), J/ψψ(3770), ψ(2S)ψ(2S)}, in order to unveil possible underlying fully-charmed tetraquark states. The partial-wave analysis is performed properly, and the unitarity of the scattering amplitudes is restored via Bethe-Salpeter equation under on-shell approximation. Four states are found in the energy region [6.2 GeV, 7.6 GeV]. For the partial wave with quantum numbers 0 ++, a bound state X(6200) and a narrow resonance X(7200) can be dynamically generated, while for the 2 ++ partial wave, two different resonant states, one named X(6900) with a narrow width and the other X(6680) with a broad width, can be found. Our results of the mass and width of X(6900) agree well with the experimental ones given by the LHCb collaboration. Furthermore, our findings shed first light on the determination of the J P C quantum numbers of these states

Anisotropic dynamics of resonant scattering between a pair of cold aligned diatoms

The collision dynamics between a pair of aligned molecules in the presence of a partial-wave resonance provide the most sensitive probe of the long-range anisotropic forces important to chemical reactions. Here we control the collision temperature and geometry to probe the dynamics of cold (1-3 K) rotationally inelastic scattering of a pair of optically state-prepared D2 molecules. The collision temperature is manipulated by combining the gating action of laser state preparation and detection with the velocity dispersion of the molecular beam. When the bond axes of both molecules are aligned parallel to the collision velocity, the scattering rate drops by a factor of 3.5 as collision energies >2.1 K are removed, suggesting a geometry-dependent resonance. Partial-wave analysis of the measured angular distribution supports a shape resonance within the centrifugal barrier of the l = 2 incoming orbital. Our experiment illustrates the strong anisotropy of the quadrupole-quadrupole interaction that controls the dynamics of resonant scattering.

Partial wave analysis of J/ψ→γη′η′

Using a sample of $(10.09~\pm~0.04)\times10^{9} ~J/\psi$ events collected with the BESIII detector, a partial wave analysis of $J/\psi\to\gamma\eta^{\prime}\eta^{\prime}$ is performed. The masses and widths of the observed resonances and their branching fractions are reported. The main contribution is from $J/\psi\rightarrow\gamma f_0(2020)$ with $f_0(2020)\rightarrow\eta^{\prime}\eta^{\prime}$, which is found with a significance of greater than 25$\sigma$. The product branching fraction ${\cal B}\left(J/\psi\rightarrow\gamma f_0(2020)\right)\cdot{\cal B}\left(f_0(2020)\rightarrow\eta^{\prime}\eta^{\prime}\right)$ is measured to be $(2.63\pm0.06({\rm stat.})^{+0.31}_{-0.46}({\rm syst.}))\times10^{-4}$.

Single-pion contribution to the Gerasimov-Drell-Hearn sum rule and related integrals

Phenomenological amplitudes obtained in partial-wave analyses (PWA) of single-pion photoproduction are used to evaluate the contribution of this process to the Gerasimov-Drell-Hearn (GDH), Baldin, and Gell-Mann--Goldberger--Thirring (GGT) sum rules, by integrating up to $2\phantom{\rule{4pt}{0ex}}\mathrm{GeV}$ in photon energy. Our study confirms that the single-pion contribution to all these sum rules converges even before the highest considered photon energy, but the levels of saturation are very different in the three cases. Single-pion production almost saturates the GDH sum rule for the proton, while a large fraction is missing in the neutron case. The Baldin integrals for the proton and the neutron are both saturated to about four fifths of the predicted total strength. For the GGT sum rule, the wide variability in predictions precludes any definitive statement.

Unitarity bounds on effective field theories at the LHC

Effective Field Theory (EFT) extensions of the Standard Model are tools to compute observables (e.g. cross sections with partonic center-of-mass energy sqrt{hat{s}} ) as a systematically improvable expansion suppressed by a new physics scale M. If one is interested in EFT predictions in the parameter space where M < sqrt{hat{s}} , concerns of self-consistency emerge, which can manifest as a violation of perturbative partial-wave unitarity. However, when we search for the effects of an EFT at a hadron collider with center-of-mass energy sqrt{s} using an inclusive strategy, we typically do not have access to the event-by-event value of sqrt{hat{s}} . This motivates the need for a formalism that incorporates parton distribution functions into the perturbative partial-wave unitarity analysis. Developing such a framework and initiating an exploration of its implications is the goal of this work. Our approach opens up a potentially valid region of the EFT parameter space where M ≪ sqrt{s} . We provide evidence that there exist valid EFTs in this parameter space. The perturbative unitarity bounds are sensitive to the details of a given search, an effect we investigate by varying kinematic cuts.

Constraints imposed by the partial wave amplitudes on the decays of J=1 , 2 mesons

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 $J=1$ and $J=2$. 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.

A Theoretical Study of Scattering of Electrons and Positrons by CO2 Molecule

This article presents a theoretical investigation of the differential, integrated, elastic, inelastic, total, momentum-transfer, and viscosity cross-sections, along with the total ionization cross-section, for elastically scattered electrons and positrons from a carbon dioxide (CO2) molecule in the incident energy range of 1 eV ≤Ei≤ 1 MeV. In addition, for the first time, we report the spin polarization of e±−CO2 scattering systems. The independent atom model (IAM) with screening correction (IAMS) using a complex optical potential was employed to solve the Dirac relativistic equation in partial-wave analysis. The comparison of our results with the available experimental data and other theoretical predictions shows a reasonable agreement in the intermediate- and high-energy regions.

Beam-spin asymmetry Σ for Σ− hyperon photoproduction off the neutron

We report a new measurement of the beam-spin asymmetry, Σ, for the γ→n→K+Σ− reaction using quasi-free neutrons in a liquid-deuterium target. The new dataset includes data at previously unmeasured photon energy and angular ranges, thereby providing new constraints on partial wave analyses used to extract properties of the excited nucleon states. The experimental data were obtained using the CEBAF Large Acceptance Spectrometer (CLAS), housed in Hall B of the Thomas Jefferson National Accelerator Facility (JLab). The CLAS detector measured reaction products from a liquid-deuterium target produced by an energy-tagged, linearly polarised photon beam with energies in the range 1.1 to 2.3 GeV. Predictions from an isobar model indicate strong sensitivity to N(1720)3/2+, Δ(1900)1/2−, and N(1895)1/2−, which corroborates results from a recent combined analysis of all KΣ channels. When our data are incorporated in the fits of partial-wave analyses, one observes significant changes in γ-n couplings of resonances which have small branching ratios to the πN channel.

A direct method for the low energy scattering solution of delta shell potentials

A direct method for the bound states and the low energy scattering from a circular and a spherical delta shell potentials is proposed and the results are compared with the one using the standard partial wave analysis developed for potentials with rotational symmetry. The formulation is presented in momentum space and the scattering solutions are obtained by considering the elementary use of distributions. In this approach, the outgoing boundary conditions are imposed explicitly in contrast to the $i\epsilon$ prescription often used in quantum mechanics.

Nucleon-nucleon scattering with perturbative pions: The uncoupled P -wave channels

The uncoupled $P$-wave channels of nucleon-nucleon scattering are studied in an effective field theory (EFT) including a perturbative dibaryon field and perturbative pions. Good agreement between EFT results and the Nijmegen partial wave analysis is observed up to a center-of-mass momentum $k\ensuremath{\approx}400$ MeV. Using a method that combines renormalization and fitting together, the long-standing convergence problem of EFTs in these channels with perturbative pions, for momenta above the pion mass is addressed from a new perspective.

Application of the single-channel, single-energy amplitude and partial-wave analysis method to K+Λ photoproduction

The new single-channel, single-energy partial-wave analysis method based on a simultaneous use of amplitude and partial-wave analysis called AA-PWA, developed and tested on $\ensuremath{\eta}$ photoproduction in [Phys. Rev. C 102, 064609 (2020)] is applied to the ${K}^{+}\mathrm{\ensuremath{\Lambda}}$ photoproduction for the center-of-mass energy range of $1625\phantom{\rule{4.pt}{0ex}}\text{MeV}&lt;W&lt;2296\phantom{\rule{4.pt}{0ex}}\text{MeV}$. A complete set of multipoles has been created. The advantages of the method have been confirmed and a comparison with the only existing single-energy partial-wave analysis of ${K}^{+}\mathrm{\ensuremath{\Lambda}}$ photoproduction given in [Phys. Rev. Lett. 119, 062004 (2017), Eur. Phys. J. A 53, 242 (2017)] is presented. We confirm the size and shape of Bonn-Gatchina multipoles, but we do not confirm the unambiguous interpretation of the structure in the ${M}_{1\ensuremath{-}}$ multipole as a $N(1880){\frac{1}{2}}^{+}$ resonance. The decisive role of the self-consistency of the world database is emphasized.

Development and application of CATCH: A cylindrical active tracker and calorimeter system for hyperon–proton scattering experiments

In this study, we developed a new proton detector system called CATCH, which was designed for a scattering experiment involving a Σ hyperon and a proton (J-PARC E40). CATCH is a cylindrical detector system covering an inner target that can be used to measure the trajectory and energy of a proton emitted from the target for the kinematic identification of a Σp scattering event. It comprises a cylindrical fiber tracker (CFT), a bismuth germanate (BGO) calorimeter, and a plastic scintillator hodoscope (PiID), which are coaxially arranged from the inner to the outer sides. The CFT is a tracking detector consisting of 5,000 scintillation fibers, and it has two types of cylindrical layers in which the fibers are arranged in straight and spiral configurations. 24 BGO crystals are placed around the CFT to measure the kinetic energy of the recoil proton. The PiID is used to determine whether the recoil proton is stopped in the BGO calorimeter . We performed proton–proton (pp) and proton–carbon (pC) scattering experiments using an 80 MeV proton beam to evaluate the performance of CATCH. The total energy resolution for the recoil proton was 2.8 MeV in σ for the entire angular region after the energy calibrations of the BGO calorimeter and the CFT. The angular resolution of the CFT was 1.27 degrees in σ for the proton, and the time resolution was more than 1.8 ns in σ. We also developed an analysis method for deriving the cross section of the pp scattering using CATCH. The obtained relative differential cross section for the pp elastic scattering was consistent with that obtained by reliable partial wave analysis, and the systematic error was maintained at below 10%. These performance results satisfy our requirements for a reliable detection system for the Σp scattering experiment conducted at J-PARC.

Exotic meson π1(1600) with JPC=1−+ and its decay into ρ(770)π

We study the spin-exotic JPC=1−+ amplitude in single-diffractive dissociation of 190 GeV/c pions into π−π−π+ using a hydrogen target and confirm the π1(1600)→ρ(770)π amplitude, which interferes with a nonresonant 1−+ amplitude. We demonstrate that conflicting conclusions from previous studies on these amplitudes can be attributed to different analysis models and different treatment of the dependence of the amplitudes on the squared four-momentum transfer and we thus reconcile these experimental findings. We study the nonresonant contributions to the π−π−π+ final state using pseudodata generated on the basis of a Deck model. Subjecting pseudodata and real data to the same partial-wave analysis, we find good agreement concerning the spectral shape and its dependence on the squared four-momentum transfer for the JPC=1−+ amplitude and also for amplitudes with other JPC quantum numbers. We investigate for the first time the amplitude of the π−π+ subsystem with JPC=1−− in the 3π amplitude with JPC=1−+ employing the novel freed-isobar analysis scheme. We reveal this π−π+ amplitude to be dominated by the ρ(770) for both the π1(1600) and the nonresonant contribution. These findings largely confirm the underlying assumptions for the isobar model used in all previous partial-wave analyses addressing the JPC=1−+ amplitude.7 MoreReceived 6 August 2021Accepted 8 September 2021DOI:https://doi.org/10.1103/PhysRevD.105.012005Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDiffractive productionHadron-hadron interactionsPhysical SystemsExotic mesonsNuclear Physics

Strange-Meson Spectroscopy – from COMPASS to AMBER

COMPASS is a multi-purpose fixed-target experiment at CERN’s M2 beam line aimed at studying the structure and spectrum of hadrons. It has collected the so far world’s largest data set on diffractive production of the K−π−π+ final state, which in principle gives access to all strange mesons. Based on this data set, we performed an elaborate partial-wave analysis. It reveals signals in the mass region of well-known states, such as the K*2(1430). In addition, we found indications for a resonance-like signal in the mass region of the K(1630). This state would be a supernumerary state and hence could be a candidate for an exotic strange meson. The partial-wave analysis is limited in some areas by the limited kinematic coverage of the final-state particle identification of the COMPASS setup. To overcome this limitation, we propose a new high-precision strange-meson spectroscopy measurement at the AMBER experiment, which will be located at CERN’s M2 beam line.

General Properties of Higher-Spin Fermion Interaction Currents and Their Test in πN-Scattering

The currents of higher-spin fermion interactions with zero- and half-spin particles are derived. They can be used for the N*(J) ↔ Nπ-transitions (N*(J) is thenucleon resonance with the J spin). In accordance with the theorem on currents and fields, the spin-tensors of these currents are traceless, and their products with the γ-matrices and the higher-spin fermion momentum vanish, similarly to the field spin-tensors. Such currents are derived explicitly for J=3/2and 5/2. It is shown that, in the present approach, the scale dimension of a higher spin fermion propagator equals to –1 for any J ≥ 1/2. The calculations indicate that the off-mass-shell N* contributions to the s-channel amplitudes correspond to J = JπN only ( JπN is the total angular momentum of the πN-system). As contrast, in the usually exploited approaches, such non-zero amplitudes correspond to 1/2 ≤ JπN ≤ J. In particular, the usually exploited approaches give non-zero off-mass-shell contributions of the ∆(1232)-resonance to the amplitudes S31, P31( JπN = 1/2) and P33, D33(JπN = 3/2), but our approach – to P33 and D33 only. The comparison of these results with the data of the partial wave analysis on the S31-amplitude in the ∆(1232)-region shows the better agreement for the present approach.

Partial-wave correlations with uncertainties in the two-nucleon system

The nucleon-nucleon scattering problem is usually analyzed in terms of partial waves and the corresponding coupled-channel phase shifts and mixing angles, but the available experiments induce correlations among the corresponding channels with different quantum numbers. Based on the Granada 2013 database we analyze the meaning and impact of those correlations, taking into account both the purely statistical ones reflecting the primary experimental data uncertainties as well as the systematic ones exhibiting the ambiguities in the form of the potential representing the unknown nuclear force for distances below 3 fm. We find that the combined uncertainties not only display a dominance of systematic over statistical effects, but also show that these correlations are almost compatible with zero. These findings support the frequent practice of determining potentials from separated channel-by-channel direct fits to phase shifts with the combined systematic and statistical effects without the full-fledged partial wave analysis inferred from experimental data but only with much larger uncertainties.

Collision‐induced spin‐orbit relaxation of highly vibrationally excited NO near 1 K

AbstractState‐to‐state scattering studies of vibrationally excited molecules in the cold regime extend inelastic scattering investigations into a new territory. Here, we present differential cross‐sections for superelastic scattering of spin‐orbit excited nitric oxide (NO) (v = 10, Ω = 1.5, j = 1.5) with argon near 1 K utilizing our recently developed near‐copropagating beam technique, and compare these to quantum scattering calculations on coupled cluster and multi‐reference potential energy surfaces. At these collision energies, the scattering is mainly governed by resonances and provides a platform to assess the accuracy of the attractive part of the difference potential for the NO–Ar system, which has remained untested. Quantum scattering calculations for such inelastic processes on high‐quality potential energy surfaces at thermal energies have largely been successful at reproducing the key features of experimental results, but cold spin‐orbit changing collisions are shown to test the limits of the current theoretical state‐of‐the‐art. The experimental results clearly exhibit backscattering centered around 3.5 cm−1 collision energy suggesting a scattering resonance; such resonances have never been detected for the well‐studied NO–Ar system. A partial wave analysis based on a multireference potential energy surface suggests the enhanced backscattering arises from overlapping resonances associated with the highest partial wave contributions.Key points We have achieved state‐to‐state spin‐orbit changing collisions of highly vibrationally excited NO with Ar near 1 K utilizing the near‐copropagating beam technique. The experiment reveals the influence of quantum scattering resonances for the well‐studied NO–Ar system for the first time. The results are found to challenge the current theoretical state‐of‐the‐art.