Carregant...
Fitxers
Tipus de document
TesiVersió
Versió publicadaData de publicació
Llicència de publicació
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/119044
Meson-Baryon interactions from effective Chiral Lagrangians
Títol de la revista
Autors
Director/Tutor
ISSN de la revista
Títol del volum
Resum
[eng] The purpose of this thesis has been to study the S=-1 meson-baryon interaction in S-wave employing an effective chiral SU(3) lagrangian up to NLO and implementing unitarization in coupled channels. Such a study requires fixing the NLO coefficients of the lagrangian which are not well established yet.
In general, the low energy constants of an effective lagrangian are obtained from fitting procedures to the experimental available data. These parameters have been constrained to a large set of experimental K^- p scattering data into πΣ,K ̅N, πΛ channels, to γ, R_n and R_c branching ratios, and to the precise SIDDHARTA value of the energy shift and width of kaonic hydrogen. The novelty of our work is the inclusion of the scattering data from K^- p⟶K^+ Ξ^-,K^0 Ξ^0 reactions in the fitting procedure, since they become especially sensitive to higher order terms, as they cannot proceed with the WT term of the lagrangian, except indirectly via unitarization contributions. We have paid a special attention to the effects that a systematic inclusion in the lagrangian of the NLO and Born terms has on the low energy constants, particularly on the NLO coefficients.
The main difference among the models we get from the fits is reflected in the isospin components of the total cross sections of the reactions we study. To check the reliavility of these models, we have performed new fits which take into account data from isospin filtering reactions. The stability and accuracy of the parameters have been tested by including phenomenological resonant contributions to the scattering amplitudes of the reactions that are especially sensitive to the NLO corrections. These resonant terms have been useful to reach better agreement with the experimental data.
In order to explore other processes that take place at higher energies and can provide more information of the NLO parameters, we have studied the Λ_b decay into states containing a J/ψ and meson-baryon pairs. Furthermore, the Λ_b⟶J/ψ ηΛ process has allowed us to study the implications of observing a possible strange partner of the hidden charm pentaquark state P_c (4450). The conclusions and analysis of each chapter are summarized below.
The second chapter is devoted to study the role played by NLO and Born terms, as well as the relevance of certain reactions in obtaining a more reliable parametrization for the NLO coefficients.
We started by comparing different fitting procedures consisting of unitarized calculations employing a kernel in which we include or not the NLO term and which take into account or not the scattering data of the K^- p⟶KΞ reactions. From the results of all these combinations, and particularly from the successful reproduction of the experimental data reached by the WT+NLO model, we have shown for the first time that the NLO order terms of the chiral Lagrangian are absolutely necessary to reproduce the K^- p⟶KΞ reaction data. In this way, the sensitivity of the NLO lagrangian to such reactions has been clearly established. Given this sensitivity and the fact that the existing K^- p⟶KΞ scattering data are limited and suffer from large uncertainty, more accurate data are required before giving a more definitive answer about the values of the NLO coefficients.
Next, contrary to the assumption we made about the little effect of the Born terms in the earlier stage, we have proved that they become non-negligible in the K^- p⟶KΞ reactions. The parametrization of the new fit (WT+NLO+Born) has confirmed the expectations of obtaining significant changes in the NLO coefficients compared to those of the WT+NLO model. Despite this, we do not get any improvement neither in accuracy of the parameters nor in the χ_(d.o.f)^2. This fact has led us to an interesting finding that allows us to understand how such different parametrization could give so similar agreement with the experimental data: the inclusion or non inclusion of the Born terms can seriously modify the isospin decomposition of the K^- p⟶KΞ cross sections due to their sensitivity to the higher order terms. Such differences in the isospin components point to the need of constraining the models with experimental data from reactions that proceed through I=0 or I=1, thus providing more reliable parameters of the meson-baryon lagrangian.
Most of the data employed in our fits are coming from antikaon-proton scattering and therefore contain contributions from both isospin I=0 and I=1 components; being the only exceptions the π^0 Σ^0,πΛ channels, which select I=0 and I=1 respectively. We then have widened the number of experimental observables used in the fits including scattering data from K^- p⟶ηΛ,ηΣ^0 reactions, which are of pure isospin 0 and 1 respectively. These efforts culminated in the WT+NLO+Born (η chan) model that, as far as we know, is the only chiral model in the literature which reproduces K^- p scattering data into all possible S=-1 channels with good agreement. Regarding the parametrization related to this model, the inclusion of these new experimental data has been crucial for obtaining a very homogeneous and accurate set of NLO coefficients, as well as natural sized values for all the subtraction constants. This leads us to think that the inclusion of more experimental data from isospin filtering processes could favor more reliable values for the low energy constants.
The proposed measurement of the K_L^0 p⟶K^+ Ξ^0 reactions in I=1 with a secondary K_L^0 beam at Jlab would complement the information one can obtain from K^- p scattering data to constrain the theoretical models. We have presented our prediction for this reaction employing some of our models, concluding that, as more contributions are taken into account in the interaction kernel and more data are included in the fit, the predicted values are closer to the only two available experimental points of this reaction. None of these two data points have been used in any fitting procedure. This prediction seems to point out towards the reliability of our parametrizations, particularly the WT+NLO+Born (η chan) one, which we consider our best pure chiral model.
In order to improve the description of the experimental K^- p⟶KΞ and K^- p⟶ηΛ scattering data, it is also possible to considerate the inclusion of high-spin resonances in such processes. Since they are the most sensitive reactions to the NLO terms, this could also lead to modifications of the NLO parameters. In this way, we can study the stability and accuracy of the parameters present in the models. This is performed in the third chapter of this thesis.
We first allowed for the explicit contribution of the high spin hyperon resonances Σ(2030) and Σ(2250) to the K^- p⟶KΞ amplitudes, aiming at establishing an appropriate amount for the background, which in this work is associated to the chiral contributions, and, hence, obtaining more reliable values of the associated low energy constants. The resonant amplitude has been calculated by applying the Rarita-Schwinger method while the chiral amplitude has been obtained employing a lagrangian with a WT and NLO contribution giving rise to the NLO+RES model. Since the resonant terms introduce an angular dependence in the amplitudes, we also attempt the description of the KΞ differential cross sections. We find the resonant terms to have a double benefit. On the one hand, they allow for a reasonable overall description of the scattering data, including the total and the differential cross sections of the KΞ production reactions. On the other hand, by absorbing certain structures of the cross section, the inclusion of resonant contributions permit finding a more stable solution and therefore more precise values of the low energy constants of the chiral unitary model.
Then, we have performed a similar study for WT+NLO+Born (η chan) model, which we consider our best chiral model. In contrast to the study carried out previously, this model has been constrained with additional data (K^- p⟶ηΣ^0,ηΛ cross-section data), meaning that, since the K^- p⟶ηΛ reaction is also very senstive to the NLO terms, the corresponding NLO coefficients are more reliable. This makes the analysis of stability acquire a more decisive character. Aiming for this, we have extended the resonant contributions to the K^- p⟶ηΛ process, particularly we have taken into account the contribution of the Λ(1890) resonance which has also been incorporated to the K^- p⟶KΞ amplitudes, in addition to the Σ(2030) and Σ(2250) resonances. The results obtained confirm the previous findings: there is a notable improvement of the agreement with the experimental data and the parameters take similar values to the ones corresponding to the model without resonances. This stability is specially marked for most of the NLO coefficients.
Having proved the effects of the isospin filtering processes on the NLO coefficients, in Chapter 4 we have shown that the Λ_b⟶J/ψ ηΛ decay and, particularly, the Λ_b⟶J/ψ KΞ one provide very valuable information concerning the meson-baryon interaction in the S=-1 and isospin I=0 sector. The dynamics of the reaction, where the light quarks of the Λ_b play a spectator role, is such that it filters I=0 in the final state. This is so because the "u" and "d" quarks in the Λ_b baryon necessarily couple to I=0 and the weak decay favors the b⟶cc ̅s transition, so there is an s-quark at the end of the weak process, which together with the "ud" pair in I=0 gives a total isospin I=0. Thus, these decays may offer complementary information to that obtained from K^- p⟶KΞ scattering data, where both isospin 0 and 1 contributions combine to give the final results.
Our study is based on the models WT+NLO (Model 1) and WT+NLO+Born (η chan) (Model 2) developed in this thesis to describe the K^- p scattering. Both models produce quite different invariant mass distributions for the decay of the Λ_b into KΞ and ηΛ states, which are in turn quite different also from phase space, indicating the sensitivity of these processes to the strong internal dynamics. The differences between models are more visible in the Λ_b⟶J/ψ KΞ decay process. The reason stems from the fact that the decay into ηΛ can proceed at tree level, while the selectivity of the Λ_b decay processes producing the J/ψ does not allow the formation of a KΞ pair in a primary step. This is only produced through rescattering of the K ̅N and ηΛ primary components. Thus the Λ_b⟶J/ψ KΞ reaction is directly proportional to the meson-baryon scattering amplitude, concretely to the ηΛ⟶KΞ and K ̅N⟶KΞ components in I=0, which can lead to a marked pattern of interferences. These models also predict sizable differences for the Λ_b decay in the energy region of KΞ and ηΛ production, reflecting that the I=0 component of the meson-baryon interaction, which is the one playing a role in the Λ_b decay processes studied here, is not very well constrained by the fitting to K^- p⟶KΞ data.
The recent finding of two structures in the J/ψ p invariant mass distribution of the Λ_b⟶J/ψ K^- p decay, associated to two pentaquark states, together with its plausible explanation in terms of a previously predicted hidden charm baryon molecular state, prompted us to study the decay of the Λ_b into J/ψ ηΛ final states. The Λ_b⟶J/ψ ηΛ decay, being a coupled channel of the Λ_b⟶J/ψ K^- p one, will occur with similar strength and one could observe, in the J/ψ Λ invariant mass spectrum, possible strange partners of the two non-strange pentaquark states reported by LHCb collaboration. We recall that when the hidden charm N^* resonances were theoretically predicted as molecular states in several unitary approaches, some partner hidden charm strange Λ^* states were also found. We have taken advantage of this finding and have predicted what signal should one of these states leave in the ηΛ and J/ψ Λ invariant mass distributions of the Λ_b⟶J/ψ ηΛ reaction. We have found that, taking the values of the couplings of the hidden charm Λ^* state to the D ̅^(0*) Ξ_c^' and J/ψ Λ channels obtained in the unitary approaches, one should observe clear and sizable peaks in the J/ψ Λ mass distribution of the Λ_b⟶J/ψ ηΛ decay. We have studied the dependence of our results on reasonable changes in the parameters of the models involved in our description of the process, as well as on the unknown properties of the speculated hidden charm strange pentaquark. We have observed that, while there appear changes in the position of the peak and in the shapes of the distributions, a resonance signal in the J/ψ Λ invariant mass spectrum is clearly seen in all the cases. This gives us confidence that such an experiment should result into a successful proof of the existence of this new state and we encourage the experimental analysis of this decay channel, for which our theoretical study predicts a similar strength than for the Λ_b⟶J/ψ K^- p reaction already analyzed by LHCb.
The present work is our first step toward building a more complete chiral model in S=-1 sector to help analyze the forthcoming more precise data in the KΞ production. In addition, the findings and the features observed in this study indicate that the actual measurement of the complementary observables analyzed here would provide valuable information, novel so far, that would enrich our knowledge of the meson-baryon interaction and help us make progress in our understanding of hadron dynamics.
Descripció
Matèries
Matèries (anglès)
Citació
Citació
FEIJOO ALIAU, Albert. Meson-Baryon interactions from effective Chiral Lagrangians. [consulta: 8 de desembre de 2025]. [Disponible a: https://hdl.handle.net/2445/119044]