Final-state Rescattering Research Articles

Effects of final state interactions on Landau singularities

In certain kinematic and particle mass configurations, triangle singularities may lead to line-shapes which mimic the effects of resonances. This well-known effect is scrutinized here in the presence of final-state rescattering. The goal is achieved first by utilizing general arguments provided by Landau equations, and second by applying a modern scattering formalism with explicit two- and three-body unitarity.

Final state rescattering effects in axio-hadronic η and η′ decays

It has been long-understood that final state rescattering effects provide O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(1) corrections to hadronic meson decays rates, such as η → πππ and η′ → ηππ. Hence, one would expect that such effects would be just as important in axio-hadronic η and η′ decays, such as η(′) → ππa, where a is an axion or axion-like particle (ALP). And indeed they are, as we show in this paper by using the treatment of dispersion relations to include the effects of strong final state interactions in several axio-hadronic processes, namely, η(′) → π0π0a, η(′) → π+π−a, and η′ → ηπ0a. We also compute the perturbative, leading order decay rates for multiple ALP emission, such as in η(′) → π0aa, η′ → ηaa and η(′) → aaa, and briefly discuss the expected corrections from strong interactions and the processes that must be considered for an accurate rate estimation of these multi-ALP decay channels.

Determination of the structure of the K → πππ amplitudes from recent data

This Letter provides a new determination of the ten real coefficients that describe the structure of the K→πππ amplitudes in the limit where isospin is conserved and complex phases, due to either CP violation or final-state rescattering, are neglected. This determination is obtained through a fit to the data on the Dalitz-plot structures and partial-decay rates collected during the last twenty years by several high-precision experiments. The fitting procedure and the way the experimental data have been handled in the fit are discussed in detail. Our fit leads to a more precise determination of the coefficients describing the linear and quadratic slopes of the K→πππ amplitudes.

CP violation in quasi-two-body D→VP decays and three-body D decays mediated by vector resonances

We reexamine direct $CP$ violation in the quasi-two-body $D\ensuremath{\rightarrow}VP$ decays and study $CP$ asymmetries in three-body $D$ decays proceeding through intermediate vector resonances within the framework of the topological amplitude approach for tree amplitudes and the QCD factorization approach for penguin amplitudes. Using the same mechanism of incorporating long-distance penguin-exchange amplitude induced from final-state rescattering that nicely accounts for the $CP$ asymmetry difference between ${D}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$ and ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ modes, we find that $CP$ asymmetry can also occur at the per mille level in many of the $D\ensuremath{\rightarrow}VP$ channels or otherwise be negligibly small. We point out six golden modes which have sufficiently large branching fractions and direct $CP$ violation of order ${10}^{\ensuremath{-}3}$. In particular, the direct $CP$ asymmetry difference $\mathrm{\ensuremath{\Delta}}{a}_{CP}^{VP}$ between ${D}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{*\ensuremath{-}}$ and ${\ensuremath{\pi}}^{+}{\ensuremath{\rho}}^{\ensuremath{-}}$ is predicted to be $(\ensuremath{-}1.61\ifmmode\pm\else\textpm\fi{}0.33)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, very similar to the counterpart in the $PP$ sector. Besides, we find a positive and large $CP$ asymmetry of order ${10}^{\ensuremath{-}3}$ in ${D}^{0}\ensuremath{\rightarrow}{K}_{S}{K}^{*0}$, an example of the asymmetry induced at tree level. We take into account the flavor-singlet QCD-penguin contributions to calculate their effects on the modes such as $D\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\phi}$ and $D\ensuremath{\rightarrow}\ensuremath{\eta}\ensuremath{\phi}$. We compare our results with the other approach in detail. For three-body $D$ decays, we perform the Dalitz plot analysis of those decays mediated by several vector resonances with the same mass but different electric charges. Local $CP$ asymmetry varies in magnitude and sign from region to region and can reach the percent level in certain local regions of phase space due to interference.

Production of f2(1270) meson in pp collisions at the LHC via gluon-gluon fusion in the kt-factorization approach

We calculate inclusive cross section for f2(1270) tensor meson production via color singlet gluon-gluon fusion in the kt-factorization approach with unintegrated gluon distribution functions (UGDFs). The process may be potentially interesting in the context of searches for saturation effects. The energy-momentum tensor, equivalent to helicity-2 coupling, and helicity-0 coupling are used for the g⁎g⁎→f2(1270) vertex. Two somewhat different parametrizations of helicity-2 and helicity-0 tensorial structure from the literature are used in our calculations. Some parameters are extracted from γγ→f2(1270)→ππ reactions. Different modern UGDFs from the literature are used. The results strongly depend on the parametrization of the g⁎g⁎→f2(1270) form factor. Our results for transverse momentum distributions of f2 are compared to preliminary ALICE data. We can obtain agreement with the data only at larger f2(1270) transverse momenta only for some parametrizations of the g⁎g⁎→f2(1270) form factor. No obvious sign of the onset of saturation is possible. At low transverse momenta one needs to include also the ππ final-state rescattering. The agreement with the ALICE data can be obtained by adjusting probability of formation and survival of f2(1270) in a harsh quark-gluon and multipion environment. The pomeron-pomeron fusion mechanism is discussed in addition and results are quantified.

Influence of rescattering effects on the helicity dependence of [formula omitted] near threshold and its implication to the E-asymmetry and the GDH sum rule

This work deals with investigation of the helicity dependence of the γ→d→→πNN reaction channels near threshold and its implication to the helicity E-asymmetry and the Gerasimov-Drell-Hearn sum rule. Our formalism based on the one loop corrections to the impulse approximation due to nucleon and pion rescattering, uses the realistic Paris NN potential model for the deuteron wave function and the unitary isobar MAID-2007 model for the elementary γN → πN amplitude. We present results for the doubly polarized differential and total cross sections for parallel and antiparallel helicity states, the deuteron spin asymmetry, the helicity E-asymmetry, and the deuteron GDH integral in the near-threshold region. The influence of NN and πN final-state rescattering on the estimated results has been discussed. It is shown that the inclusion of NN rescattering is important, and its inclusion strongly affected the estimated results in both π ± - and π0-production channels. The inclusion of πN rescattering is found to be insignificant in π ± -production, but it has a non- negligible contribution in the case of π0-production. A comparison with predictions of other theoretical models is given.

Beam-target double spin asymmetries in the reaction [formula omitted] near threshold with final-state rescattering effects

Near-threshold incoherent pion photoproduction on the deuteron including final-state rescattering effects is investigated with special emphasize on the beam-target double spin asymmetries. The elementary γN→πN amplitude is taken from the unitary isobar MAID-2007 model which describes well the threshold region. We present the first results on all possible double spin asymmetries of the differential and total cross sections for both the charged- and neutral-pion production channels near threshold. We discuss the sensitivity of the estimated results to the NN and πN final-state rescattering effects. It turns out that the role of NN-rescattering is significant, and its inclusion strongly affected the results for double spin asymmetries in the charged- and neutral-pion channels. We also find that the πN-rescattering effect is insignificant in the case of charged-pion channels, whereas it has a noticeable contribution on most of double spin asymmetries in the neutral-pion channel.

Revisiting CP violation in D→PP and VP decays

Direct CP violation in the hadronic charm decays provides a good testing ground for the Kobayashi-Maskawa mechanism in the Standard Model. Any significant deviations from the expectation would be indirect evidence of physics beyond the Standard Model. In view of improved measurements from LHCb and BESIII experiments, we re-analyze the Cabibbo-favored $D \to P\!P$ and $V\!P$ decays in the topological diagram approach. By assuming certain SU(3)-breaking effects in the tree-type amplitudes, we make predictions for both branching fractions and CP asymmetries of the singly Cabibbo-suppressed decay modes. While the color-allowed and -suppressed amplitudes are preferred to scale by the factor dictated by factorization in the $P\!P$ modes, no such scaling is required in the $V\!P$ modes. The $W$-exchange amplitudes are found to change by 10\% to 50\% and depend on whether $d\overline{d}$ or $s\overline{s}$ pair directly emerges from $W$-exchange. The predictions of branching fractions are generally improved after these SU(3) symmetry breaking effects are taken into account. We show in detail how the tree-type, QCD-penguin, and weak penguin-annihilation diagrams contribute and modify CP asymmetry predictions. Future measurements of sufficiently many direct CP asymmetries will be very useful in removing a discrete ambiguity in the strong phases as well as discriminating among different theory approaches. In particular, we predict $a_{CP}(K^+K^-)-a_{CP}(\pi^+\pi^-) = (-1.14 \pm 0.26) \times 10^{-3}$ or $(-1.25 \pm 0.25) \times 10^{-3}$, consistent with the latest data, and $a_{CP}(K^+K^{*-})-a_{CP}(\pi^+\rho^-) = (-1.52 \pm 0.43) \times 10^{-3}$, an attractive and measurable observable in the near future. Moreover, we observe that such CP asymmetry differences are dominated by long-distance penguin-exchange through final-state rescattering.

Quark-mass dependence in omega rightarrow 3pi decays

We study the quark-mass dependence of omega rightarrow 3pi decays, based on a dispersion-theoretical framework. We rely on the quark-mass-dependent scattering phase shift for the pion–pion P-wave extracted from unitarized chiral perturbation theory. The dispersive representation then takes into account the final-state rescattering among all three pions. The described formalism may be used as an extrapolation tool for lattice QCD calculations of three-pion decays, for which omega rightarrow 3pi can serve as a paradigm case.

Cusps and exotic charmonia

A simple, causal and analytic model of final state rescattering is used to describe all available data on the exotic resonances [Formula: see text] and [Formula: see text]. The model provides a compelling and accurate representation of experiment with no need for poles in the scattering matrix.

Exclusive π−Electroproduction off the Neutron in Deuterium in the Resonance Region

The goal of our research is to provide the exclusive γ*(n) → p+π− reaction cross section from deuterium data using the correction factor that account for the final state re-scattering that can be determined from the data set itself. The “e1e” Jefferson Lab CLAS data set that we analyze includes both a hydrogen and deuterium target run period, which allows a combined analysis of pion electroproduction off the free proton, the bound proton, and the bound neutron under the same experimental conditions. Hence it will provide the experimentally best possible information about the off-shell and final state interaction effects in deuterium, which must be considered in order to extract the neutron information. This data set will provide results with a kinematic coverage for the hadronic invariant mass W up to 1.7 GeV and in the momentum transfer Q2 range of 0.4 − 1.0 GeV/c2. The cross section analysis of this data set is currently underway, which will considerably improve our knowledge of the Q2 evolution of π−p electroproduction cross sections off bound neutron needed for the extraction of excited neutron state electrocouplings for the first time.

Comprehensive study ofB¯0→K0(K¯0)K∓π±decays in the factorization approach

Using the factorization approach, we investigate the ${\overline{B}}^{0}\ensuremath{\rightarrow}{\overline{K}}^{0}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${\overline{B}}^{0}\ensuremath{\rightarrow}{K}^{0}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ decays individually including the resonant and nonresonant contributions. Under the flavor SU(3) symmetry, we obtain the total branching fraction $BR[{\overline{B}}^{0}\ensuremath{\rightarrow}({\overline{K}}^{0}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}+{K}^{0}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+})]=(7.1{7}_{\ensuremath{-}0.53\ensuremath{-}1.42\ensuremath{-}0.07}^{+0.50+1.97+0.08})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, which is in agreement with the recent measurements of BABAR and LHCb within errors. For the decay ${\overline{B}}^{0}\ensuremath{\rightarrow}{\overline{K}}^{0}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, the nonresonant background and ${a}_{0}^{+}(1450)$ pole in the current-induced process provide a large contribution, the latter of which has not been included in previous studies. On the contrary, the decay ${\overline{B}}^{0}\ensuremath{\rightarrow}{K}^{0}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ is dominated by the nonresonant background and the off-shell ${\ensuremath{\rho}}^{\ensuremath{-}}$ pole. When the flavor SU(3) symmetry breaking and the final-state rescattering are considered under two different scenarios, the results can also accommodate the experimental data with large uncertainties. Moreover, the direct $CP$ asymmetry of ${\overline{B}}^{0}\ensuremath{\rightarrow}{\overline{K}}^{0}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ is found to be sensitive to the matrix element of scalar density. These predictions could be further tested in the LHCb experiment or Super-b factory in the future.

Branching fractions and directCPviolation in charmless three-body decays ofBmesons

Charmless three-body decays of B mesons is studied using a simple model based on the framework of the factorization approach. Hadronic three-body decays receive both resonant and nonresonant contributions. Dominant nonresonant contributions to tree-dominated three-body decays arise from the $b\to u$ tree transition which can be evaluated using heavy meson chiral perturbation theory valid in the soft meson limit. For penguin-dominated decays, nonresonant signals come mainly from the penguin amplitude governed by the matrix elements of scalar densities $<M_1M_2|\bar q_1 q_2|0>$. We use the measurements of $\bar B^0\to K_SK_SK_S$ to constrain the nonresonant component of $<K\bar K|\bar ss|0>$. The intermediate vector meson contributions to three-body decays are identified through the vector current, while the scalar meson resonances are mainly associated with the scalar density. While the calculated direct CP violation in $B^-\to K^+K^-K^-$ and $B^-\to \pi^+\pi^-\pi^-$ decays agrees well with experiment in both magnitude and sign, the predicted CP asymmetries in $B^-\to \pi^- K^+K^-$ and $B^-\to K^-\pi^+\pi^-$ are wrong in signs when confronted with experiment. It has been conjectured recently that a possible resolution to this CP puzzle may rely on final-state rescattering of $\pi^+\pi^-$ and $K^+K^-$. Assuming a large strong phase associated with the matrix element $<K\pi|\bar sq|0>$ arising from some sort of power corrections, we fit it to the data of $K^-\pi^+\pi^-$ and find a correct sign for $\pi^- K^+K^-$.

DirectCPviolation in two-body hadronic charmed meson decays

Motivated by the recent observation of $CP$ violation in the charm sector by LHCb, we study direct $CP$ asymmetries in the standard model (SM) for the singly Cabibbo-suppressed two-body hadronic decays of charmed mesons using the topological-diagram approach. In this approach, the magnitude and the phase of topological weak annihilation amplitudes, which arise mainly from final-state rescattering, can be extracted from the data. Consequently, direct $CP$ asymmetry ${a}_{\mathrm{dir}}^{(\mathrm{tree})}$ at tree level can be reliably estimated. In general, it lies in the range ${10}^{\ensuremath{-}4}&lt;{a}_{\mathrm{dir}}^{(\mathrm{tree})}&lt;{10}^{\ensuremath{-}3}$. Short-distance QCD penguins and penguin annihilation are calculated using QCD factorization. Their effects are generally small, especially for $D\ensuremath{\rightarrow}VP$ modes. Since weak penguin annihilation receives long-distance contributions from the color-allowed tree amplitude followed by final-state rescattering, it is expected to give the dominant contribution to the direct $CP$ violation in the decays ${D}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$ and ${D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, in which ${a}_{\mathrm{dir}}^{(\mathrm{tree})}$ is absent. The maximal $\ensuremath{\Delta}{a}_{CP}^{\mathrm{dir}}$, the direct $CP$ asymmetry difference between the above-mentioned two modes, allowed in the SM is around $\ensuremath{-}0.25%$, more than $2\ensuremath{\sigma}$ away from the current world average of $\ensuremath{-}(0.645\ifmmode\pm\else\textpm\fi{}0.180)%$.

Predictions of HBT parameters in Pb + Pb collisions at √s NN = 2.76 TeV from a hadronic rescattering model

A kinematic model based on the superposition of p + p collisions, relativistic geometry and final-state hadronic rescattering is used to predict two-boson HBT parameters in √sNN = 2.76 TeV Pb + Pb collisions. A short proper time for hadronization is assumed. Previous calculations using this model which were performed for √sNN = 200 GeV Au + Au collisions were shown to describe reasonably well the trends of two-pion HBT in experiments carried out at that energy, giving the present predictions for Pb + Pb at higher energy some degree of credibility.

THEORETICAL REVIEW ON HADRONIC D/Ds DECAYS

A brief review on the theoretical status of hadronic charm decays is presented. We emphasize the analyses based on the diagrammatic approach and the connection of weak annihilation with final-state rescattering. The topics on the [Formula: see text] mixing and the baryonic charm decay [Formula: see text] are sketched.

Energy dependence of elliptic flow from heavy-ion collision models

We have compared the experimental data on charged particle elliptic flow parameter (v2) in Au+Au collisions at midrapidity for \surd sNN = 9.2, 19.6, 62.4 and 200 GeV with results from various models in heavy-ion collisions like UrQMD, AMPT, and HIJING. We observe that the average <v2> from the transport model UrQMD agrees well with the measurements at \surd sNN = 9.2 GeV but increasingly falls short of the experimental <v2> values as the beam energy increases. The difference in <v2> being of the order of 60% at \surd sNN = 200 GeV. The <v2> results from HIJING is consistent with zero, while those from AMPT with default settings, a model based on HIJING with additional initial and final state rescattering effects included, gives a <v2> value of about 4% for all the beam energies studied. This is in contrast to increase in <v2> with beam energy for the experimental data. A different version of the AMPT model, which includes partonic effects and quark coalescence as a mechanism of hadronization, gives higher values of <v2> among the models studied and is in agreement with the measured <v2> values at \surd sNN = 200 GeV. These studies show that the experimental < v2 > has substantial contribution from partonic interactions at \surd sNN = 200 GeV whose magnitude reduces with decrease in beam energy. We also compare the available data on the transverse momentum and pseudorapidity dependence of v2 to those from the above models.

Phases of augmented hadronic light-front wave functions

It is an important question whether the final/initial state gluonic interactions which lead to naive-time-reversal-odd single-spin asymmetries and diffraction at leading twist can be associated in a definite way with the light-front wave function hadronic eigensolutions of QCD. We use light-front time-ordered perturbation theory at the lowest nontrivial order to obtain augmented light-front wave functions which contain an imaginary phase which depends on the choice of advanced or retarded boundary condition for the gauge potential in light-cone gauge. We apply this formalism to the wave functions of the valence Fock states of nucleons and pions, and show how this illuminates the factorization properties of naive-time-reversal-odd transverse momentum dependent observables which arise from rescattering. In particular, one calculates the identical leading-twist Sivers function from the overlap of augmented light-front wave functions that one obtains from explicit calculations of the single-spin asymmetry in semi-inclusive deep inelastic lepton–polarized nucleon scattering where the required phases come from the final-state rescattering of the struck quark with the nucleon spectators.

Dynamic versus Static Hadronic Structure Functions

“Static” structure functions are the probabilistic distributions computed from the square of the light-front wavefunctions of the target hadron. In contrast, the “dynamic” structure functions measured in deep inelastic lepton-hadron scattering include the effects of rescattering associated with the Wilson line. Initial- and final-state rescattering, neglected in the parton model, can have a profound effect in QCD hard-scattering reactions, producing single-spin asymmetries, diffractive deep inelastic scattering, diffractive hard hadronic reactions, the breakdown of the Lam-Tung relation in Drell-Yan reactions, nuclear shadowing, and non-universal nuclear antishadowing—novel leading-twist physics not incorporated in the light-front wavefunctions of the target computed in isolation. I also review how “direct” higher-twist processes – where a proton is produced in the hard subprocess itself – can explain the anomalous proton-to-pion ratio seen in high centrality heavy ion collisions.

Understanding [formula omitted] in the Standard Model

The rare decay B¯d0→J/ψϕ can proceed via four distinct mechanisms: (i) production of the ϕ via tri-gluon fusion, (ii) photoproduction of the J/ψ or ϕ, (iii) final-state rescattering of Ds(∗)Ds(∗) produced in the B¯d decay to J/ψϕ, and (iv) production of the ϕ via ω–ϕ mixing. In this work, we examined the contributions of photoproduction and final-state rescattering to B¯d0→J/ψϕ and found that the corresponding branching ratios were of the orders 10−11 and 10−9, respectively. Hence, this decay is dominated by the ω–ϕ mixing effect.