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Meson-Baryon coupling constants in QCD sum rules

Erkol, G., 2006, s.n.. 124 p.

Research output: ThesisThesis fully internal (DIV)Academic

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  • Güray Erkol
There is a long history of describing the baryon-baryon interactions in terms of One Boson Exchange (OBE) models. These phenomenological models give an effective first-order approximation of the complete interaction and provide a very accurate description of the rich nucleon-nucleon (N!N) and the more scarce hyperon-nucleon (YN) scattering data. In these models, the values of the meson-baryon coupling constants are empirically determined so as to reproduce the N!N and Y!N interactions. Calculation of the coupling constants at the hadronic vertices directly from the Quantum Chromodynamics (QCD), which is the gauge theory of the strong interactions involving the quarks and the gluons, is a long-standing problem. QCD has been very successful in the large momentum transfer regime where the quark-gluon coupling constant is small and one can reliably apply perturbative methods. However, at the hadron scale the quark-gluon coupling constant is of order unity and perturbation theory fails. In this regime one should use some non-perturbative methods. Among other approaches, the QCD Sum Rules (QCDSR) method has proven to be a powerful tool to extract qualitative and quantitative information about hadron properties. Our aim in this work is to calculate the meson-baryon coupling constants using the method of QCDSR. There are different approaches in constructing the sum rules. The most convenient one for our purposes is the external-field QCDSR method. Our motivation is to define the coupling constants in terms of QCD parameters which will give us a deeper understanding of the mechanism behind the interactions of two baryon systems in terms of the OBE model. In this framework, we consider the vacuum-to-vacuum transition matrix element of two baryon interpolating fields in an external meson field and calculate the coupling constants of scalar, vector and pseudoscalar mesons to the baryons. One of the advantages of this approach is that it is consistent with the SU(3)-flavor symmetry so that the alpha=F/(F+D) ratios of the meson octets can be determined in a model-independent way. The method allows, as well, to estimate the amount of SU(3) breaking in the couplings, which occurs as a result of the strange-quark mass and the physical masses of the mesons and baryons. This approach provides a very convenient ground for us to compare our results with the ones from the phenomenological potential models. We compare our results for the coupling constants with the values from a model of the N!N and YN interaction, the Nijmegen soft-core potential. In Chapter 3 we use the external-field QCDSR method to evaluate the coupling constants of the light isoscalar-scalar meson ("sigma" or epsilon) to the Sigma, Xi, and Lambda baryons. We evaluate the correlation function of the baryon interpolating fields in the presence of an external constant isoscalar-scalar field sigma and construct the sum rules. We assume ideal mixing and make the analysis in both the qbar{q} and the q^2bar{q}^2 pictures for the scalar mesons. We observe that the scalar meson-baryon coupling constants as obtained from the QCDSR depend on the picture assumed for the structure of the scalar mesons (qbar{q} or q^2bar{q}^2), whereas the F/(F+D) ratio, which is alpha_s=0.55, remains intact in the two pictures. The obtained value of the nucleon-sigma coupling constant as g_{N!Nsigma}= 14.4 pm 3.7, is in agreement with the large value found in OBE models. One of the most significant coupling constants in this framework is the LambdaLambdasigma coupling constant as the sigma exchange plays the most crucial role in LambdaLambda interactions. Our analysis of the LambdaLambdasigma coupling constant in QCDSR both in the SU(3) limit and with the SU(3)-breaking effects reveal that this coupling constant is small as compared to the N Nsigma coupling constant. This implies that the LambdaLambda interaction is weak, in accordance with the recent experimental results. Chapter 4 is devoted to the calculation of the vector and the tensor coupling constants of the vector mesons rho and omega to the N, Lambda, Xi and Sigma baryons using the external-field QCDSR method. For this purpose, we define a constant background tensor-field in order to take account of both the vector and the tensor coupling. Our results for the coupling constants and the F/(F+D) ratio for the vector coupling, which is alpha_v=1, are in agreement with the ones from the OBE potential model and the VMD model. We obtain alpha_m=0.18, for the F/(F+D) ratio of the magnetic coupling, which is about half of the values obtained in NSC potential model results. In Chapter 5, we explore the earlier studies of the pion-nucleon coupling constant with the method of external-field QCDSR. In the literature one encounters two schemes for the pion-nucleon coupling constant: the pseudoscalar coupling and the pseudovector coupling. These two schemes are related to each other with a Goldberger-Treiman relation however their calculations are independent. The experimentally well-known value of the pion-nucleon coupling constant together with the nucleon sum rule evaluated in the presence of the external pion field provide an estimation of the pion susceptibility. We use this estimation to obtain a numerical value for the pion-Delta coupling constant, which is a significant parameter for the pion-nucleon scattering away from threshold and in loop calculations of chiral perturbation theory. We also carry out an independent calculation of the Delta axial coupling from the QCDSR, which is related to the pion-Delta coupling constant with the Goldberger-Treiman relation. We find that the two independent calculations lead to consistent results. Our calculations show that the value of the DeltaDeltapi coupling constant is larger than the N Npi coupling constant.
Original languageEnglish
QualificationDoctor of Philosophy
Supervisors/Advisors
Publisher
Print ISBNs9036727995
Electronic ISBNs9036727987
Publication statusPublished - 2006

    Keywords

  • Proefschriften (vorm), Kwantumchromodynamica, Mesonen , Baryonen, Koppelingsconstan, eigenschappen van specifieke deeltjes, resonanties

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