arXiv subjects

P. C. Magalhães

Publications and source records attributed to P. C. Magalhães.

16 recordsLinked to original sources

arXiv2026

A dispersive method to study CP asymmetries in hadronic multi-body $B$ decays

We present the details of a dispersive method to construct the amplitudes for hadronic multibody $B$ decays based on the universality of pairwise hadronic final-state interactions at low invariant masses. This approach allows us to split the amplitude into source terms controlled by phenomenological parameters and final-state interactions, governed by the precise knowledge of two-body dynamics, both resonant and non-resonant. As a concrete application, we make use of the well-determined low-energy pion-pion ($ππ$) interactions to understand the enhanced localized CP violation observed in $B^{\pm}\rightarrow K^{\pm}π^+π^-$. Fitting only angle-integrated CP-asymmetry data, the method successfully predicts the Dalitz plot differential distribution of events and of the CP asymmetry in the low-energy region. This allows for a better understanding of the large localized CP asymmetry recently reported by LHCb, which is shown not to be driven by an absolute enhancement of CP-violating effects, but by a suppression of the CP-conserving part resulting from the interplay of several partial waves. Moreover, we show that the widely-neglected non-resonant isospin-2 contributions play an essential role in the description of CP violation in this system. The method can be straightforwardly adapted to other multibody decays, where final-state two-hadron interactions drive the CP violation.

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arXiv2026

Understanding large localized CP violation in $B^\pm\to K^\pmπ^+π^-$ using dispersive methods

We utilize the universality of pion-pion ($ππ$) final-state interactions at small invariant masses to understand the enhanced localized CP violation in $B^\pm\to K^\pmπ^+π^-$, using a dispersive approach. From a fit to the integrated CP-asymmetry data, we successfully predict the Dalitz-plot kinematic distribution of the asymmetry in the low-energy $ππ$ region, including the large localized CP violation recently observed by LHCb. An essential role is played by the contributions of isospin 2. This formalism, whose parameters have a physical meaning, can be adapted straightforwardly to other systems with CP violation enhanced by final-state interactions.

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arXiv2024

Hadronic rescattering to solve helicity puzzle in $B^+\to p\bar p π^+(K^+)$ decays

We explore the contribution of hadronic final state interactions (FSI) to propose a production mechanism and interpret the puzzle on helicity angle distributions in $B^+\to p\bar p π^+$ and $B^+\to p\bar p K^+$ decays. Experimental results indicate opposite helicity angle $θ_p$ distributions in those two channels with the difference presenting a remarkable linear dependence on $\cos θ_p$. We assume the production mechanism is driven by $B^+\to xy\, m^+ \to p\bar p m^+$, where $m =π$ or $K$, and $xy$ represents favorable mesonic decay channels producing $p\bar p$. We develop a model that includes three-body final state interaction between the $p\,,~\bar p$ and $π^+$ or $K^+$ considering the dominance of elastic channels $π^+p$ and $K^+\bar p$ interactions below 2\,GeV/c$^2$. Our three-body framework with FSI explains qualitatively the observed opposite behavior of the helicity distributions and the observed linearity.

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arXiv2024

Giant CP violation in charmless three-body $B$ meson decays at LHCb: all order formalism for meson-meson final state interactions

LHCb has observed giant CP violation in localized regions of the Dalitz plots of B to three charmless light mesons. This has been interpreted as an enhancement due to strong two-body final state interactions. In this talk, we show how such interactions, described with dispersive analyses of data, can be implemented beyond the leading order expansion in the two-body re-scattering amplitude.

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arXiv2023

Dispersive $ππ\rightarrow K\bar K$ amplitude and giant CP violation in B to three light-meson decays at LHCb

The LHCb collaboration has recently reported the largest CP violation effect from a single amplitude, as well as other giant CP asymmetries in several $B$-meson decays into three charmless light mesons. It is also claimed that this is predominantly due to $ππ\rightarrow K\bar K$ rescattering in the final state, particularly in the 1 to 1.5 GeV region. In these analyses the $ππ\rightarrow K\bar K$ amplitude is by default estimated from the $ππ$ elastic scattering amplitude and does not describe the existing $ππ\rightarrow K\bar K$ scattering data. Here we show how the recent model-independent dispersive analysis of $ππ\rightarrow K\bar K$ data can be easily implemented in the LHCb formalism. This leads to a more accurate description of the asymmetry, while being consistent with the measured scattering amplitude and confirming the prominent role of hadronic final state interactions, paving the way for more elaborated analyses.

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arXiv2020

Multibody decay analyses -- a new phenomenological model for meson-meson subamplitudes

Meson-meson amplitudes are important on their own and also play key roles in analyses of heavy-meson and tau decays. In this work we propose a new phenomenological model suited to all $SU(3)$ mesonic two-body final state interactions up to energies around 2 GeV. It is aimed at replacing those entering the old isobar model, produced in the 1960's, long before the development of QCD. The only similarity between our new proposal and amplitudes used in the isobar model concern vector resonances in the elastic regime. In other situations, especially those involving scalar resonances and coupled channels, the isobar model is not compatible with post-QCD dynamics. In order to support these claims convincingly and to motivate our approach, we consider applications to the $ππ$ amplitude and compare our version with the isobar model in several different instances. We also show that the new model provides a clear indication of the mechanism responsible for the sharp rise observed in the $ππ$ phase around $1\,$ GeV. The phenomenological amplitudes proposed here are suited to any number of resonances in a given channel and rely just on masses and coupling constants as free parameters. Concerning theory, they incorporate chiral symmetry at low energies, include coupled channels and respect unitarity whenever appropriate.

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arXiv2018

Multi-Meson Model for the $D^+\to K^+K^-K^+$ decay amplitude

We propose a novel approach to describe the $D^+\to K^+K^-K^+$ decay amplitude, based on chiral effective Lagrangians, which can be used to extract information about $K\bar{K}$ scattering. Our trial function is an alternative to the widely used isobar model and includes both nonresonant three-body interactions and two-body rescattering amplitudes, based on coupled channels and resonances, for S- and P-waves with isospin $0$ and $1$. The latter are unitarized in the $K$-matrix approximation and represent the only source of complex phases in the problem. Free parameters are just resonance masses and coupling constants, with transparent physical meanings. The nonresonant component, given by chiral symmetry as a real polynomium, is an important prediction of the model, which goes beyond the (2+1) approximation. Our approach allows one to disentangle the two-body scalar contributions with different isospins, associated with the $f_0(980)$ and $a_0(980)$ channels. We show how the $K\bar{K}$ amplitude can be obtained from the decay $D^+\to K^+K^-K^+$ and discuss extensions to other three-body final states.

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arXiv2016

Suppressed $B \to PV $ CP asymmetry: CPT constraint

Charge Parity asymmetry in charmless B meson decays is a key issue to be understood. Many theoretical calculations have been performed using short distance factorization approaches which, in general, do not take into account the CPT invariance constraint. For each channel with CP violation there is an equal amount of CP asymmetry in another channel or other channels, with an opposite sign. This happens if these channels are coupled through final state interactions (FSI). In the specific process $B\to PV$, involving one pseudo-scalar and one vector particle in the final state, we argue that the CP asymmetry, inherent from a short distance mechanism, could be suppressed due to the CPT constraint. In this case, we propose a sensitive and practical experimental method to identify even a small CP asymmetry, which provides the values for $A_{CP}$ without the need for an amplitude analysis. This method, if applied directly to data, will enable to extract the CP asymmetry information in a model independent way and check to which extend the suggested suppression due to the CPT constraint is verified.

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arXiv2016

Multi-Meson Model applied to $D^+ \to K^+ K^- K^+$

Matrix elements of weak currents involving light multi-meson states are important in many hadronic decays of both heavy leptons and heavy mesons. In this paper we focus on the latter case where the current size of the data set demands better models. The specific case of three-kaon weak matrix elements is considered and expressed as a relatively simple structure, which generalizes naturally the concept of form factor. We propose a model for the decay $D^+ \to K^+ K^- K^+$ as an alternative to isobar model, with free parameter predicted by the theory to be fine-tuned by a fit to data. An important qualitative outcome is that we encompass naturally all final states topologies, which involve necessarily proper multi-particle structures and cannot be decomposed into simpler two-body processes. This aspect represents a significant improvement when compared to isobar model, often employed in analyses of heavy-meson decay data.

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arXiv2015

Final state interaction on $B^+ \to π^-π^+π^+$

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 presence of hadronic loops shifts the P-wave phase near threshold to below zero, and modify the position of the $ρ$-meson peak and it width, in the Dalitz plot.

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arXiv2015

$D^+ \to K^- π^+ π^+$ - the weak vector current

Studies of D and B mesons decays into hadrons have been used to test the standard model in the last fifteen years. A heavy meson decay involves the combined effects of a primary weak vertex and subsequent hadronic final state interactions, which determine the shapes of Dalitz plots. The fact that final products involve light mesons indicates that the QCD vacuum is an active part of the problem. This makes the description of these processes rather involved and, in spite of its importance, phenomenological analyses tend to rely on crude models. Our group produced, some time ago, a schematic calculation of the decay $D^+ \to K^- π^+ π^+$, which provided a reasonable description of data. Its main assumption was the dominance of the weak vector-current, which yields a non-factorizable interaction. Here we refine that calculation by including the correct momentum dependence of the weak vertex and extending the energy ranges of $ππ$ and $Kπ$ subamplitudes present into the problem. These new features make the present treatment more realistic and bring theory closer to data.

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arXiv2013

D+ -> K- pi+ pi+ : heavy meson decays and final state interactions

We show that final state interactions are important in shaping Dalitz plots for the decay $D^+ \rar K^- \p^+ \p^+$. The theoretical treatment of this reaction requires a blend of several weak and hadronic processes and hence it is necessarily involved. In this talk we present results from a calculation which is still in progress, but has already unveiled the role of important dynamical mechanisms. We do not consider explicit quark degrees of freedom and our study is performed within an effective hadronic framework. In spite of the relatively wide window of energies available in the Dalitz plot for the $D^+$ decay, we depart from $SU(3)\times SU(3)$ chiral perturbation theory and extend its range by means of unitarization. Our present results, which concentrate on the vector weak vertex, describe qualitative features of the modulus of the decay amplitude and agrees well with its phase in the elastic region.

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arXiv2012

Towards three-body unitarity in $D^+ \to K^- π^+ π^+$

We assess the importance of final state interactions in $D^+ \rar K^- \p^+ \p^+$, stressing the consistency between two- and three-body interactions. The basic building block in the calculation is a $Kπ$ amplitude based on unitarized chiral perturbation theory and with parameters determined by a fit to elastic LASS data. Its analytic extension to the second sheet allows the determination of two poles, associated with the $\k$ and the $K^*(1430)$, and a representation of the amplitude based on them is constructed. The problem of unitarity in the three-body system is formulated in terms of an integral equation, inspired in the Faddeev formalism, which implements a convolution between the weak vertex and the final state hadronic interaction. Three different topologies are considered for the former and, subsequently, the decay amplitude is expressed as a perturbation series. Each term in this series is systematically related to the previous one and a re-summation was performed. Remaining effects owing to single and double rescattering processes were then added and results compared to FOCUS data. We found that proper three-body effects are important at threshold and fade away rapidly at higher energies. Our model, based on a vector weak vertex, can describe qualitative features of the modulus of the decay amplitude and agrees well with its phase in the elastic region.

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arXiv2008

Elastic $Kπ$ amplitude: a simple model

We present a chiral model for the $J=0, I=1/2,$ elastic $K\p$ amplitude, suited to be employed in $D^+ \rar K^- \p^+ \p^+$ data analyses and valid between threshold and $1.5 $GeV. Although not as precise as other versions available in the literature, it is rather simple and incorporates the essential physics in this energy domain. In the case of the $K$-matrix approximation, the model allows the pole structure of the $K\p$ amplitude to be understood by solving a quadratic equation in $s$. We show that the solutions to this equation can be well approximated by polynomials of masses and coupling constants. This analytic structure allows a clear understanding why, depending on the values of one of the coupling constants, one may have one or two physical poles. The model yields a pole, associated with the $\k$, at $\sqrt{s}= (0.75 - i 0.24) $GeV.

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arXiv2008

Decay $D^+ \to K^- π^+ π^+$: chiral symmetry and scalar resonances

The low-energy S-wave component of the decay $D^+ \to K^- π^+ π^+$ is studied by means of a chiral SU(3)XSU(3) effective theory. As far as the primary vertex is concerned, we allow for the possibility of either direct production of three pseudoscalar mesons or a meson and a scalar resonance. Special attention is paid to final state interactions associated with elastic meson-meson scattering. The corresponding two-body amplitude is unitarized by ressumming s-channel diagrams and can be expressed in terms of the usal phase shifts $δ$. This procedure preserves the chiral properties of the amplitude at low-energies. Final state interactions also involve another phase $ω$, which describes intermediate two-meson propagation and is theoretically unambiguous. This phase is absent in the K-matrix approximation. Partial contributions to the decay amplitude involve a real term, another one with phase $δ$ and several others with phases $δ+ω$. Our main result is a simple and almost model independent chiral generalization of the usual Breit-Wigner expression, suited to be used in analyses of production data involving scalar resonances.

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arXiv2008

$D^+ \to K^- \p^+ \p^+ $: the low-energy sector

An effective $SU(3)\times SU(3)$ chiral lagrangian, which includes scalar resonances, is used to describe the process $D^+ \rar K^- \p^+ \p^+$ at low-energies. Our main result is a set of five $S$-wave amplitudes, suited to be used in analyses of production data.

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