A model for the $B^\pm \to π^-π^+π^\pm$ decay amplitude is proposed to study the large CP violation observed at the high mass region of the Dalitz plane. A short distance $ b \to u $ amplitude with the weak phase $γ$ is considered together with the contribution of a hadronic charm loop and a s-wave $D\bar{D}\to ππ$ rescattering. In the model, the $χ_c^0$ appears as a narrow resonant state of the $D\bar D$ system below threshold. It is introduced in an unitary two channel S-matrix model of the coupled $D\bar D$ and $ππ$ channels, where the $χ_c^0$ complex pole in $D\bar D$ channel shows its signature in the off-diagonal matrix element and in the associated $D\bar{D}\to ππ$ transition amplitude. The strong phase of the resulting decay amplitude has a sharp sign change at the $D\bar D$ threshold, changing the sign of the CP asymmetry, as it is observed in the data. We conclude that the hadronic charm loop and rescattering mechanism are relevant to the broadening of the CP asymmetry around the $χ_c^0$ resonance in the $ππ$ channel. This novel mechanism provides a possible interpretation of the CP asymmetry defier experimental result presented by the LHCb collaboration for the $B^\pm \to π^-π^+π^\pm$ decay in the high mass region.
We study the process $B^- \to K^- χ_{c0}$ considering intermediate charmed meson rescattering effects. For this decay mode the naive factorization ansatz would predict a vanishing amplitude. We estimate contributions from the $D^{(*)}_{s} D^{(*)}\to K^- χ_{c0}$ rescattering amplitudes, and compare the result with recent experimental measurements. We find that rescattering effects are able to produce a large branching ratio consistent with measurements by Belle Collaboration. We also consider rescattering effects in $B^- \to K^- J/ψ$, arguing that they play a similar role in producing a large b…
Following the experimental results from LHCb on the rare decay $B^+_c \to K^-K^+π^+$, we investigate the possibility where this process is dominated by a double charm rescattering. The $B_c$ decay to double charm channels have a weak topology that is favoured in comparison with the direct production of $K^-K^+π^+$ in the final state, suppressed by quark annihilation. The decay amplitude for $B^+_c \to K^-K^+π^+$ with $B_c$ decaying first to double charm channels is described by a charm penguin diagram, represented by charm hadronic triangle loops, which reach the final state of interest after …
We investigate the processes $e^+e^-$ annihilating to $J/ψππ$, $ψ^\primeππ$ and $h_cππ$. The coupled-channel effects induced by the couplings between the widely accepted $D$-wave charmonium $ψ(4160)$ and $D_1D$, $D_1D^*$ and $D_2D^*$ charmed meson pairs in the $S$-wave state with couplings given by heavy quark spin symmetry are analyzed. The line shapes show the presence of cusps that result from the singularities of the rescattering loops, which could be helpful in understanding the nature of $Y(4260)$, $Y(4360)$, $Z_c(3900)$/$Z_c(3885)$ and $Z_c(4020)$/$Z_c(4025)$.
The doubly charmed baryon $Ξ_{cc}^{++}$ was recently observed by LHCb via the decay processes of $Ξ_{cc}^{++}\to Λ_c^+ K^-π^+π^+$ and $Ξ_c^+π^+$. These discovery channels were successfully predicted in the framework that the short-distance contributions are calculated under the factorization hypothesis and the long-distance contributions are estimated using the rescattering mechanism for the final-state-interaction effects. In this paper, we illustrate the above framework in details by systematic studies on the two-body baryonic decays $\mathcal{B}_{cc}\to\mathcal{B}_{c}P$ involving the doubly…
The $B^{-} \to χ_{c0} K^{-}$ decay which has no visible factorizable amplitude, could be induced by the Cabibbo-allowed, color-favored $B^{-} \to D_{s}D^{*0}$, $B^{-} \to D^{*0}_{s}D^{0}$ and $B \to D_{s}^{*}D^{*}$ via the rescattering of these charmed mesons to $χ_{co} K^{-}$. In this talk I would like to discuss a recent calculation \cite{Colangelo} of these effects for $B^{-} \to χ_{c0} K^{-}$ and $B^{-} \to J/ψK^{-}$ decays. We find that charmed scattering effects seem capable of producing a large $B^{-} \to χ_{c0} K^{-}$ branching ratio measured by the Babar and Belle Collaboration and ma…
Assuming that Y(4140) is the second radial excitation of the P-wave charmonium $χ_{cJ}^{\prime\prime}$ ($J=0, 1$), the hidden charm decay mode of Y(4140) is calculated in terms of the rescattering mechanism. Our numerical results show that the upper limit of the branching ratio of the hidden charm decay $Y(4140)\to J/ψϕ$ is on the order of $10^{-4}\sim 10^{-3}$ for both of the charmonium assumptions for Y(4140), which disfavors the large hidden charm decay pattern indicated by the CDF experiment. It seems to reveal that the pure second radial excitation of the P-wave charmonium $χ_{cJ}^{\prime…
A new mechanism for heavy quarkonium production in high-energy collisions called the "s-channel cut" was proposed in 2005 by Lansberg, Cudell, and Kalinovsky. We identify this mechanism physically as the production of a heavy quark and anti-quark that are on-shell followed by their rescattering to produce heavy quarkonium. We point out that in the NRQCD factorization formalism this rescattering mechanism is a contribution to the color-singlet model term at next-to-next-to-leading order in perturbation theory. Its leading contribution to the production rate can be calculated without introducing…
Implications of two-channel rescattering for charm CP violation from precise dispersive data
Universitat de València – Consejo Superior de Investigaciones Científicas（瓦伦西亚大学 - 西班牙高等科学研究委员会）；PSI Center for Neutron and Muon Sciences（保罗谢勒研究所中子与缪子科学中心）；Universität Zürich（苏黎世大学）；Universidad Cardenal Herrera-CEU（卡迪纳尔埃雷拉-CEU大学）
The current wealth of charmless B decay data may suggest the presence of final state rescattering. In a factorized amplitude approach, better fits are found by incorporating two SU(3) rescattering phase differences, giving delta ~ 65 degree and sigma ~ 90 - 100 degree. Fitting with unitarity phase phi_3 as a fit parameter gives phi_3 ~ 96 degree, the CP asymmetries A_{pi pi}, S_{pi pi} agree better with BaBar, and the sigma phase is slightly lower. Keeping phi_3 = 60 degree fixed in fit gives S_{pi pi} ~-0.9, which agrees better with Belle. With the sizable delta, sigma rescattering phases as …
A method for modelling the prompt production of molecular states using the hadronic rescattering framework of the general-purpose Pythia event generator is introduced. Production cross sections of possible exotic hadronic molecules via hadronic rescattering at the LHC are calculated for the $χ_{c1}(3872)$ resonance, a possible tetraquark state, as well as three possible pentaquark states, $P_c^+(4312)$, $P_c^+(4440)$, and $P_c^+(4457)$. For the $P_c^+$ states, the expected cross section from $Λ_b$ decays is compared to the hadronic-rescattering production. The $χ_{c1}(3872)$ cross section is c…
The doubly charmed baryon $Ξ^{++}_{cc}$ was observed by LHCb cooperation in 2017. The branching fractions of two-body doubly charmed baryon decays were predicted in the framework of rescattering mechanism, and some $SU(3)_F$ relations were investigated in the topological amplitudes. In this work, we study the correlation between topological diagram at quark level and rescattering triangle diagram at hadron level in the doubly charmed baryon decay. The completeness of our framework is confirmed from the fact that all the twelve possible structures of meson-baryon scattering appear once each in …
We study the final-state interaction (FSI) effects in charmless B_{u,d,s} to PP decays. We consider a FSI approach with both short- and long-distance contributions, where the former are from in-elastic channels and are contained in factorization amplitudes, while the latter are from the residual rescattering among PP states. Flavor SU(3) symmetry is used to constrain the residual rescattering S-matrix. We fit to all available data on the CP-averaged decay rates and CP asymmetries, and make predictions on unmeasured ones. Our main results are as follows: (i) Results are in agreement with data i…
Final-state interaction effects in charmless B_{u,d,s} to PP decays are studied. We investigate the B(bar)^0 to pi^+ pi^-, pi^0 pi^0 rates and the K pi direct CP violations, which lead to the so-called K pi puzzle in CP violation (Delta A). We found that sizable and complex color-suppressed tree amplitudes, which are crucial for the large pi^0 pi^0 rate and Delta A, are generated through exchange rescattering. The correlation of the ratio B(pi^0 pi^0)/B(pi^+ pi^-) and Delta A is studied. Predictions on B_s rates, direct and time-dependent CP asymmetries are made.
On the basis of the generalized eikonal approximation we study the exclusive reactions $\bar p d \to J/ψ\, n$ and $\bar p d \to ψ^\prime\, n$ in vicinity of the thresholds for charmonium production on a free proton target. It is shown that the rescattering of the incoming antiproton and outgoing charmonium on the spectator neutron leads to a depletion of the charmonium production at low- and to an enhancement at high transverse momenta. This is in qualitative agreement with previous studies of hard proton knockout in proton-deuteron collisions. We analyze different physical sources of uncertai…
Various rescattering sources are analyzed in the context of the SU(3) flavor symmetry. In particular, the possibility to account for intermediate charm at the hadronic level in B to PP is thoroughly investigated. Then, the rescattering sources are compared in light of recent B to two charmless pseudoscalar decay measurements, with emphasis on the size of strong phases and on patterns of direct CP-asymmetries.
Various new measurements in charmless $B_{u,d,s}\to PP$ modes, where $P$ is a low lying pseudoscalar meson, are reported by Belle and LHCb. These include the rates of $B^0\toπ^0π^0$, $ηπ^0$, $B_s\toη'η'$, $B^0\to K^+K^-$ and $B^0_s\toπ^+π^-$ decays. Some of these modes are highly suppressed and are among the rarest $B$ decays. Direct CP asymmetries on various modes are constantly updated. It is well known that direct CP asymmetries and rates of suppressed modes are sensitive to final state interaction (FSI). As new measurements are reported and more data will be collected, it is interesting an…
A kinematic model based on the superposition of p+p collisions, relativistic geometry and final-state hadronic rescattering is used to predict various hadronic observables in \surd sNN = 2.76 TeV Pb+Pb collisions. Predictions for rapidity and transverse momentum distributions, elliptic flow, and two-boson femtoscopy are presented. A short proper time for hadronization is assumed. Previous calculations using this model which were performed for \surd sNN = 200 GeV Au+Au collisions were shown to describe reasonably well the trends of observables in experiments carried out at that energy, giving t…
The $σ$ resonance was observed as a conspicuous $π^+π^-$ peak in hadronic decays like $J/ψ\to π^+π^-ω$ or $D^+\toπ^+π^-π^+$. The phase of the $σ\toπ^+π^-$ amplitude, extracted from production data within the conventional isobar model, is assumed to coincide with that in $ππ$ elastic scattering. We check the validity of this assumption by using Lehmann-Symanzik-Zimmermann (LSZ) reduction and unitarity. The rescattering effects in the final three-particle states are shown to generate a correction to the phase given by a naive application of Watson theorem. We briefly discuss the implications of …
In a recent article we presented a model for hadronic rescattering, and some results were shown for pp collisions at LHC energies. In order to extend the studies to pA and AA collisions, the Angantyr model for heavy-ion collisions is taken as the starting point. Both these models are implemented within the general-purpose Monte Carlo event generator Pythia, which makes the matching reasonably straightforward, and allows for detailed studies of the full space--time evolution. The rescattering rate is significantly higher than in pp, especially for central AA collisions, where the typical primar…
We study the effects of hadronic rescattering on hadron distributions in high-energy nuclear collisions by using an integrated dynamical approach. This approach is based on a hybrid model combining (3+1)-dimensional ideal hydrodynamics for the quark gluon plasma (QGP), and a transport model for the hadron resonance gas. Since the hadron distributions are the result of the entire expansion history of the system, understanding the QGP properties requires investigating how rescattering during the hadronic stage affects the final distributions of hadrons. We include multistrange hadrons in our stu…
In this article, a framework for hadronic rescattering in the general-purpose Pythia event generator is introduced. The starting point is the recently presented space-time picture of the hadronization process. It is now extended with a tracing of the subsequent motion of the primary hadrons, including both subsequent scattering processes among them and decays of them. The major new component is cross-section parameterizations for a range of possible hadron-hadron combinations, applicable from threshold energies upwards. The production dynamics in these collisions has also been extended to cope…
We study the energy distributions of dipion transitions $Υ(5S)$ to $Υ(1S,2S,3S)π^+π^-$ in the final state rescattering model. Since the $Υ(5S)$ is well above the open bottom thresholds, the dipion transitions are expected to mainly proceed through the real processes $Υ(5S)\to B^{(*)}\bar{B}^{(*)}$ and $B^{(*)}\bar{B}^{(*)}\to Υ(1S,2S,3S)π^+π^-$. We find that the energy distributions of $Υ(1S,2S,3S)π^+π^-$ markedly differ from that of $Υ(5S)\to B^{(*)}\bar{B}^{(*)}$. In particular, the resonance peak will be pushed up by about 7-20 MeV for these dipion transitions relative to the main hadronic …
The significance of final-state interactions in B_d-->ππdecays is phenomenologically demonstrated by taking elastic ππ--ππand inelastic ππ--D\bar{D} rescattering effects into consideration. We find that the present experimental data on B^0_d-->π^+π^- can well be understood in this approach without fine-tuning of the input parameters, and large CP-violating asymmetries are expected to manifest themselves in such charmless rare processes.
Using purely phenomenological approach we show that the peaking structures observed in the psi(2S) pi+ and chi_c1 pi+ mass spectra in B -> psi(2S)(chi_c1) pi+ K decays can be result of (D \bar{D}^(*))+ -> (ccbar)_res pi+ rescattering in the decays B -> D_sJ (-> \bar{D}(*) K) D(*). In particular, the position of the peak in the chain B -> D_s(2S) D+ -> K- \bar{D}*0 D+ -> K- psi(2S) pi+ coincides well with the measured Z(4430) mass, assuming the mass of D_s(2S) (the first radial excitation of D_s) to be 2610 MeV/c2. The widths of the Z(4430) peak is also well reproduced in this approach independ…
There exist many experimental indications that final-state interactions (FSIs) may play a prominent role not only in charmful B decays but also in charmless B ones. We examine the final-state rescattering effects on the hadronic B decay rates and their impact on direct CP violation. The color-suppressed neutral modes such as $B^0\to D^0π^0,π^0π^0,ρ^0π^0,K^0π^0$ can be substantially enhanced by long-distance rescattering effects. The direct CP-violating partial rate asymmetries in charmless B decays to $ππ/πK$ and $ρπ$ are significantly affected by final-state rescattering and their signs are g…
Final-state rescattering effects on the hadronic B decays and their impact on direct CP violation are examined. The phenomenology of the polarization anomaly in $B\toϕK^*$ decays is discussed.
A way of circumventing the gauge and infrared problems with effective Wilson coefficients is shown. Implications of experimentally measured charmless $B$ decays are discussed.
Identification of charmonium states at hadron colliders has mostly been limited to leptonic decays of the J/ψ. In this paper we present and algorithm to identify hadronic decays of charmonium states (J/ψ, ψ(2S), χ_{c0,1,2}) which make up the large majority of all decays. The algorithm is able to identify hadronic $J/ψ$ decays with an efficiency of 36\% while suppressing a background of quark and gluon jets by a factor 100.
In a previous paper we suggested an explanation for the peak designated as $Z(4430)^+$ in the $ψ^\primeπ^+$ mass spectrum, observed by Belle in ${\bar{\!B}} \to {ψ^\prime} π^+ K$ decays, as an effect of $\bar{\!D}{}^{\,*0}D^{\,+} \to ψ^\primeπ^+$ rescattering in the decays ${\bar{\!B}} \to {D_{s}^{\,\prime -}} {D}$, where the $D_{s}^{\,\prime -}$ is an as-yet unobserved radial excitation of the pseudoscalar ground state $D_{s}^{\,-}$-meson. In this paper, we demonstrate that this hypothesis provides an explanation of the double $Z^+$-like peaking structures, which were studied by LHCb with muc…
We estimate effects of the final state interactions in B -> pi pi decays coming from rescattering of pi pi via exchange of rho, sigma, f_0 mesons. Then we include the rho rho rescattering via exchange of pi, omega, a_1 mesons and finally we consider contributions of the a_1 pi rescattering via exchange of rho. The absorptive parts of amplitudes for these processes are determined. In the case of pi^+ pi^- decay mode, due to model uncertainties, the calculated contribution is |M_A| =< 1.7 x 10^-8 GeV. This produces a small relative strong phase for the tree and color-suppressed B -> pi pi amplit…
New results going beyond those obtained from isospin and flavor symmetry and subject to clear experimental tests are obtained for effects of FSI in $B^\pm$ decays to charmless strange final states containing neutral flavor-mixed mesons like $ω$, $ϕ$, $η$ and $η'$. The most general strong-interaction diagrams containing arbitrary numbers of quarks and gluons are included with the assumptions that any $q \bar q$ pair created by gluons must be a flavor singlet, and that there are no hairpin diagrams in which a final meson contains a $q \bar q$ pair from the same gluon vertex. The smallness of $K^…
Hadronic resonance propagators which take into account the analytical properties of decay processes are built in terms of the dispersion relation technique. Such propagators can describe multi-component systems, for example, those when quark degrees of freedom create a resonance state, and decay products correct the corresponding pole by adding hadronic deuteron-like components. Meson and baryon states are considered, examples of particles with different spins are presented.
We study the observed $B^-\rightarrow X(3823)K^-$ decay via rescattering mechanism and show that this branching ratio is well reproduced by this mechanism. We further extend this theoretical framework to investigate the decays of $B^-\toη_{c2} (^1D_2)/ψ_3(^3D_3)K^-$, where the $η_{c2} (^1D_2)$ and the $ψ_3(^3D_3)$ are $D$-wave charmonium partners of the $X(3823)$. Our results show that the branching ratios, $B^-\to η_{c2}(^1D_2) K^-$ and $B^-\to ψ_3(^3D_3) K^-$, are of the order of $10^{-5}$, which can be accessible at LHCb, Belle and forthcoming BelleII.
We present a first model-independent calculation of $ππ$ intermediate states in the hadronic-light-by-light (HLbL) contribution to the anomalous magnetic moment of the muon $(g-2)_μ$ that goes beyond the scalar QED pion loop. To this end we combine a recently developed dispersive description of the HLbL tensor with a partial-wave expansion and demonstrate that the known scalar-QED result is recovered after partial-wave resummation. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box, $a_μ^{π\text{-box}}=-15.9(2)\times 10^…
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 $D^0$-$\bar D^0$ mixing and the baryonic charm decay $D_s^+\to p\bar n$ are sketched.
We investigate the processes $e^+e^-$$\to$$γJ/ψϕ$, $γJ/ψω$ and $π^0 J/ψη$ to search for the charmnium-like states with hidden $s\bar{s}$, such as $Y(4140)$, $Y(4274)$, $X(4350)$ and $X(3915)$. These processes will receive contributions from the charmed-strange meson rescatterings. When the center-of-mass energies of the $e^+e^-$ scatterings are taken around the $D_{s0}(2317)D_s^{*}$, $D_{s1}(2460)D_s$ or $D_{s1}(2460)D_s^{*}$ threshold, the anomalous triangle singularities can be present in the rescattering amplitudes, which implies a non-resonance explanation about the resonance-like structur…
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 $a_{dir}^{\rm (tree)}$ at tree level can be reliably estimated. In general, it lies in the range $10^{-4}<a_{dir}^{\rm (tree)}<10^{-3}$. Sh…
We perform a model dependent fit to recent data on charmless hadronic B decays and determine $γ$, the phase of $V^*_{ub}$. We find $γ= 114^{+25}_{-21}$ degrees, which disfavors the often quoted $γ\sim 60^\circ$ at the two standard deviation level. We also fit for the form factors $F_0^{Bπ}$ and $A_0^{Bρ}$, and the strange-quark mass. They are consistent with theoretical expectations, although $m_s$ is somewhat low. Such agreement and the good $χ^2$ for the fit may be interpreted as a confirmation of the adequacy of our model assumptions.
In this work, we investigate the open-charm decay process $ψ\toΛ_c\barΛ_c$ via the hadronic loop mechanism for vector charmonia above $Λ_c\barΛ_c$ threshold. The branching ratios of these vector charmonium states to $Λ_c\barΛ_c$ are estimated. The charmonium explanation of the $Y(4630)$ observed in $e^+e^- \to Λ_c\barΛ_c$ is tested. Furthermore, for the predicted higher vector charmonia above 4.7 GeV, the branching ratios $\mathcal{B}[ψ(nS)\toΛ_c\barΛ_c]$ with $n=7,8,9$ are found to be of the order of magnitude of $10^{-4}-10^{-3}$ while $\mathcal{B}[ψ(mD)\toΛ_c\barΛ_c]$ with $m=6,7,8$ are of …
I discuss the effect of final state interactions on the determination of the CKM angle γfrom B -> K + pi decays. Using a simple Regge-based model for rescattering processes, I argue that such effects could be substantial enough to make it problematic to obtain reliable limits on γin this way. Fortunately, an analysis of B -> K + K decays may provide model-independent bounds on rescattering contributions.
The large localized CP asymmetries observed by LHCb in three-body charmless decays of $B$ mesons brings new challenge for experimentalists and their traditional models to fit data. With higher statistics, rescattering and three-body effects, previously ignored on data analysis, become more visible. The time is ripe to use better theoretical assumptions as an ingredient in order to improve the analysis. In this paper we address the issue of rescattering effects in the charmless three-body decays of $B$ mesons. In particular, we study the case of the $B^+ \to π^-π^+π^+$ decay and show that the p…
A calculation of the hadronic matrix elements for K\toππincluding π-πrescattering effects in a dispersion integral is presented. I study the dependence of the results on the matching scale μand use them to calculate the CP-parameter (ε\prime/ε). I find improved stability on the matching scale and good agreement with the experimental results.
Charm penguin diagrams are known to be the main contribution to charmless B decay process with strangeness variation equal to minus one, which is the case of $B^\pm \to K^\pm K^+ K^-$ decay. The large phase space available in this and other B three-body decays allows non trivial final state interactions with all sort of rescattering processes and also access high momentum transfers in the central region of the Dalitz plane. In this work we investigate the charm Penguin contribution to $B^\pm \to K^\pm K^+ K^-$, described by a hadronic triangle loop in nonperturbative regions of the phase space…
We study phi photoproduction with various hadronic rescattering contributions included, in addition to the Pomeron and pseudoscalar meson-exchange diagrams. We find that the hadronic box diagrams can explain the recent experimental data in the vicinity of the threshold. In particular, the bump-like structure at the photon energy E_gamma \approx 2.3$ GeV is well explained by the K Lambda(1520) rescattering amplitude in the intermediate state, which is the dominant contribution among other hadronic contributions. We also find that the hadronic box diagrams are consistent with the observed spin-d…
Using a relativistic hydrodynamics + hadronic afterburner simulation we explore resonance production in PbPb collisions at 5.02 TeV, and demonstrate that many resonance yields, mean transverse momenta, and flows are very sensitive to the late stage hadronic rescattering. Out of all measured resonances $Λ(1520)$ is affected strongest by the hadronic rescattering stage, which allows to estimate its duration, and even constrain branching ratios of $Σ^* \to Λ(1520)π$ decays. Strong suppression of $Λ(1520)$, which in vacuum has a lifetime of 12.6 fm/$c$, is explained by its small lifetime in a hadr…
