arXiv subjects

Ruben Flores-Mendieta

Publications and source records attributed to Ruben Flores-Mendieta.

At least 19 recordsLinked to original sources

arXiv2025

Use of $SU(3)$ flavor projection operators to construct baryon-meson scattering amplitudes in the $1/N_c$ expansion

An $SU(3)$ flavor projection operator technique is implemented to construct the baryon-meson scattering amplitude in the framework of the $1/N_c$ expansion of QCD, where $N_c$ is the number of color charges. The operator technique is implemented to evaluate not only the lowest-order scattering amplitude but also effects coming from first-order perturbative $SU(3)$ flavor symmetry breaking and strong isospin breaking. The most general expression is obtained by accounting for explicitly the effects of the decuplet-octet baryon mass difference. At order $\mathcal{O}(1/N_c^2)$, a large number of unknown operator coefficients appear, so there is little additional predictive power unless leading and subleading terms are retained. Although the resultant expression is general enough that it can be applied to any incoming and outgoing baryons and pseudo scalar mesons, provided that the Gell-Mann--Nishijima scheme is respected, results for $Nπ\to Nπ$ scattering processes are explicitly dealt with.

hep-ph↗

arXiv2025

Leading vector coupling in baryon semileptonic decays in large-$N_c$ chiral perturbation theory revisited: Extension to decuplet baryons

The leading vector coupling defined in the semileptonic decay of a baryon is revisited in the framework of large-$N_c$ baryon chiral perturbation. Aspects of $SU(3)$ flavor symmetry breaking are taken into account in two ways: Explicitly through perturbative symmetry breaking and implicitly through the integrals occurring in the one-loop corrections. The analysis of perturbative breaking is performed by using flavor projection operators which are exceptionally helpful in understanding previously unidentified issues. The approach is extended to theoretically evaluate the leading vector coupling in the transition $Ω^-\to {Ξ^*}^0$. A fitting procedure to data reveals that second-order symmetry breaking corrections, while small, can have a significant impact on the evaluation of the baryon vector coupling, potentially increasing its overall strength due to the involved interplay of both explicit and implicit contributions.

hep-ph↗

arXiv2025

Universality of the baryon axial vector current operator in large-$N_c$ chiral perturbation theory

The baryon axial vector current is computed in a combined formalism in $1/N_c$ and chiral corrections. Flavor $SU(3)$ symmetry breaking is accounted for in two ways: Implicitly through the integrals occurring in the one-loop graphs and explicitly through perturbative symmetry breaking. Loop integrals can be expanded in a power series in the ratio of the decuplet-octet baryon mass difference to the pseudoscalar meson mass and the first three terms in the series are retained and evaluated. The universal baryon axial vector current so constructed is neither diagonal nor off-diagonal in the sense that it can connect baryon states of either different or equal spins to obtain appropriate axial vector couplings. Processes of interest are found in octet-baryon and decuplet-baryon semileptonic decays and strong decays of decuplet baryons. A fit to the available experimental information is performed to determine the free parameters in the formalism, which allows one to estimate, for instance, the leading axial vector coupling in the semileptonic decay $Ω^- \to{Ξ^*}^0\ell^-\overlineν_\ell$.

hep-ph↗

arXiv2024

An alternative approach to baryon masses in the $1/N_c$ expansion of QCD

The baryon mass operator is studied within a combined expansion in $1/N_c$ and perturbative $SU(3)$ flavor symmetry breaking, where $N_c$ denotes the number of quark charges. Flavor projection operators are used to classify the baryon operators involved in the expansion, which fall into the flavor representations $1$, $8$, $10+\overline{10}$, $27$, $35+\overline{35}$ and $64$. This approach allows one to incorporate up to third-order flavor symmetry breaking in the baryon mass operator in a rigorous and systematic way. Previous work on the subject is considered to validate the approach. A fit to data is performed to evaluate the free parameters in the theory and to produce some numerical values of baryon masses. Results are consistent and reaffirm the striking success of the $1/N_c$ expansion.

hep-ph↗

arXiv2021

Baryon magnetic moment in large-$N_c$ chiral perturbation theory: Complete analysis for $N_c=3$

Baryon magnetic moments are computed in baryon chiral perturbation theory in the large-$N_c$ limit at one-loop order, where $N_c$ is the number of color charges. Orders $\mathcal{O}(m_q^{1/2})$ and $\mathcal{O}(m_q \ln m_q)$ corrections are both evaluated including all the operator structures that participate at the physical value $N_c=3$. The complete expressions for octet and decuplet baryon magnetic moments in addition to decuplet-octet baryon transition moments are thus compared to their available counterparts obtained in heavy baryon chiral perturbation theory for degenerate intermediate baryons in the loops. Theoretical expressions fully agree at the physical values $N_c=3$ and $N_f=3$ flavors of light quarks. Some numerical evaluations are produced via a least-squares fit to explore the free parameters in the analysis. Results point out the necessity of incorporating the effects of non-degenerate intermediate baryons in the loops for a consistent determination of these free parameters.

hep-ph↗

arXiv2021

Contribution of $SU(3)$ quadratic Casimir squared to rotational bands in the interacting boson model

Rotational bands are commonly used in the analysis of the spectra of atomic nuclei. The early version of the interacting boson model of Arima and Iachello has been foundational to the description of rotations in nuclei. The model is based on a unitary spectrum generating algebra $U(6)$ and an orthogonal (angular momentum) symmetry algebra $SO(3)$. A solvable limit of the model contains $SU(3)$ in its dynamical symmetry chain. The corresponding Hamiltonian is written as a linear combination of linear and quadratic Casimir invariants of all the algebras in the chain. Prompted by these facts, a Hamiltonian containing the $SU(3)$ quadratic Casimir squared is proposed to evaluate its effects on rotational bands. The additional term yields three undetermined parameters into the theory, which need be obtained from experiment. The lack of data does not allow one to perform a detailed numerical analysis, but a rather restricted one in terms of a one-parameter fit. Nevertheless, these additional terms provide a good description of rotational bands of two nuclei of interest, $^{156}\mathrm{Ga}$ and $^{234}\mathrm{U}$.

nucl-th↗

arXiv2021

Baryon axial vector current in large-$N_c$ chiral perturbation theory: Complete analysis for $N_c=3$

The baryon axial vector current is computed in heavy baryon chiral perturbation theory in the large-$N_c$ limit, where $N_c$ is the number of color charges. One-loop nonanalytic corrections of order $m_q \ln m_q$ are comprised in the analysis, with contributions of both intermediate octet and decuplet baryon states, to all orders in the $1/N_c$ expansion of the axial vector current relevant for $N_c=3$. Theoretical expressions are obtained in the limit of vanishing decuplet-octet mass difference only, which allows one to carry out a full comparison with conventional heavy baryon chiral perturbation theory results for three flavors of light quarks and at the physical value $N_c=3$. Both approaches perfectly agree to all orders considered. Furthermore, a numerical analysis via a least-squares fit is performed in order to extract the values of the free parameters of the theory, using the experimental data available. The predictions of formalism are remarkable.

hep-ph↗

arXiv2020

Spin and flavor projection operators in the $SU(2N_f)$ spin-flavor group

The quadratic Casimir operator of the special unitary $SU(N)$ group is used to construct projection operators, which can decompose any of its reducible finite-dimensional representation spaces contained in the tensor product of two and three adjoint spaces into irreducible components. Although the method is general enough, it is specialized to the $SU(2N_f) \to SU(2)\otimes SU(N_f)$ spin-flavor symmetry group, which emerges in the baryon sector of QCD in the large-$N_c$ limit, where $N_f$ and $N_c$ are the numbers of light quark flavors and color charges, respectively. The approach leads to the construction of spin and flavor projection operators that can be implemented in the analysis of the $1/N_c$ operator expansion. The use of projection operators allows one to successfully project out the desired components of a given operator and subtract off those that are not needed. Some explicit examples in $SU(2)$ and $SU(3)$ are detailed.

hep-ph↗

arXiv2020

Precision radiative corrections to the muon polarization in the semileptonic decay of a charged kaon

An expression for the Dalitz plot of the semileptonic decay of a charged kaon, including radiative corrections to order O[απ)(q/M_1)], where q is the four-momentum transfer and M_1 is the mass of the decaying kaon, is obtained. Contributions of both the three- and four-body regions are accounted for. Besides, the emitted muon is considered to be polarized so the analysis is also focused on evaluating the radiative corrections to the longitudinal, transverse, and normal polarization components of the muon. The final formulas, with the triple integration of the bremsstrahlung photon variables ready to be performed numerically, are general enough to be used in model-independent experimental analyses whether or not the real photon is discriminated. With the numerical values of the weak form factors and slope parameters of the process, the radiative corrections to the components of the muon polarization are found to be very small compared to their respective uncorrected values.

hep-ph↗

arXiv2020

Baryon quadrupole moment in the 1/N(c) expansion of QCD

The quadrupole moments of ground state baryons are discussed in the framework of the 1/N(c) expansion of QCD, where N(c) is the number of color charges. Theoretical expressions are first provided assuming an exact SU(3) flavor symmetry, and then the effects of symmetry breaking are accounted for to linear order. The rather scarce experimental information available does not allow a detailed comparison between theory and experiment, so the free parameters in the approach are not determined. Instead, some useful new relations among quadrupole moments, valid even in the presence of first-order symmetry breaking, are provided. The overall predictions of the 1/N(c) expansion are quite enlightening.

hep-ph↗

arXiv2019

S-wave baryon nonleptonic decay amplitude in large-N_c chiral perturbation theory

The s-wave decay amplitude in the nonleptonic decay of baryons is analyzed within heavy baryon chiral perturbation theory in the large-N_c limit at one-loop order, where N_c is the number of color charges. Loop graphs with octet and decuplet intermediate states are systematically incorporated into the analysis and the effects of the decuplet-octet mass difference are accounted for. There are large-N_c cancellations between different one-loop graphs as a consequence of the large-N_c spin-flavor symmetry of QCD baryons. The predictions of large-N_c baryon chiral perturbation theory are in very good agreement both with the expectations from the 1/N_c expansion and with the experimental data.

hep-ph↗

arXiv2017

Sum rules for leading vector form factors in hyperon semileptonic decays

By considering that the weak currents and the electromagnetic current are members of the same SU(3) octet, two sum rules involving leading vector form factors in hyperon semileptonic decays are derived in the limit of exact flavor SU(3) symmetry. Deviations from this limit arise from second-order SU(3) symmetry-breaking effects, according to the Ademollo-Gatto theorem. The 1/N_c expansion of QCD is used to evaluate such effects. One sum rule vanishes identically even in the presence of symmetry breaking and the other one obtains contributions mainly from the 10+\overline{10} representation. Results obtained in (heavy) baryon chiral perturbation theory are used to test the validity of these sum rules. To order O(p^2) in the chiral expansion, results are encouraging.

hep-ph↗

arXiv2016

Four-body Dalitz plot contribution to the radiative corrections in K_{l3}^0 decays and its role in the determination of |V_{us}|

The four-body contribution of the model-independent radiative corrections to the Dalitz plot of the semileptonic decays of neutral kaons are computed to order (α/π)(q/M_1), where q is the momentum transfer and M_1 is the kaon mass. The final result is presented in two forms. The first one is given in terms of the triple integration of the bremsstrahlung photon ready to be performed numerically; the second one is a fully analytical expression. This paper is organized to make it accessible and reliable in the analysis of the Dalitz plot of precision experiments involving kaons and is not compromised to fixing the form factors at predetermined values. As a byproduct, gathering together three- and four-body contributions of radiative corrections yields, through a least-squares fit to the measured kaon decay rates, the value f_+^{K^0π^-}|V_{us}| = 0.2168(3).

hep-ph↗

arXiv2015

Dirac form factors and electric charge radii of baryons in the combined chiral and 1/N_c expansions

The baryon Dirac form factor is computed at one-loop order in large-N_c baryon chiral perturbation theory, where N_c is the number of color charges. Loop graphs with octet and decuplet intermediate states are systematically incorporated into the analysis and the effects of the decuplet-octet mass difference are accounted for. There are large-N_c cancellations between different one-loop graphs as a consequence of the large-N_c spin-flavor symmetry of QCD baryons. As a byproduct, the mean-square charge radius is also computed through a detailed numerical analysis. The predictions of large-N_c baryon chiral perturbation theory are in very good agreement both with the expectations from the 1/N_c expansion and with the experimental data.

hep-ph↗

arXiv2015

Radiative corrections to the Dalitz plot of K_{l3}^0 decays

A model-independent expression for the Dalitz plot of semileptonic decays of neutral kaons, K_{l3}^0, including radiative corrections to order (α/π)(q/M_1), where q is the momentum transfer and M_1 is the mass of the kaon, is presented. The model dependence of radiative corrections is kept in a general form within this approximation, which is suitable for model-independent experimental analyses. Expressions for bremsstrahlung radiative corrections are presented in two forms: one with the triple integral over the kinematical variables of the photon ready to be performed numerically and the other one in a fully analytical form. The final result is restricted to the so-called three-body region of the Dalitz plot and it is not compromised to fixing the values of the form factors at predetermined values.

hep-ph↗

arXiv2014

The baryon vector current in the combined chiral and 1/Nc expansions

The baryon vector current is computed at one-loop order in large-Nc baryon chiral perturbation theory, where Nc is the number of colors. Loop graphs with octet and decuplet intermediate states are systematically incorporated into the analysis and the effects of the decuplet-octet mass difference and SU(3) flavor symmetry breaking are accounted for. There are large-Nc cancellations between different one-loop graphs as a consequence of the large-Nc spin-flavor symmetry of QCD baryons. The results are compared against the available experimental data through several fits in order to extract information about the unknown parameters. The large-Nc baryon chiral perturbation theory predictions are in very good agreement both with the expectations from the 1/Nc expansion and with the experimental data. The effect of SU(3) flavor symmetry breaking for the |Delta S|=1 vector current form factors f1(0) results in a reduction by a few percent with respect to the corresponding SU(3) symmetric values.

hep-ph↗

arXiv2014

Baryon magnetic moments in large-N_c chiral perturbation theory: Effects of the decuplet-octet mass difference and flavor symmetry breaking

The magnetic and transition magnetic moments of the ground-state baryons are computed in heavy baryon chiral perturbation theory in the large-$N_c$ limit, where N_c is the number of colors. SU(3) symmetry breaking is systematically studied twofold: On the one hand, one-loop nonanalytic corrections of orders m_q^{1/2} and m_q ln m_q are included, with contributions of baryon intermediate states from both flavor octet and flavor decuplet multiplets, assuming degeneracy between baryon states within a given flavor multiplet but nondegeneracy between baryons of different multiplets. On the other hand, perturbative SU(3) symmetry breaking is also analyzed by including all relevant leading-order operators that explicitly break SU(3) at linear order. The resultant expressions are compared with the available experimental data and with other determinations in the context of conventional heavy baryon chiral perturbation theory for three flavors of light quarks and at the physical value $N_c=3$. The agreement reached is quite impressive.

hep-ph↗

arXiv2012

Renormalization of the baryon axial vector current in large-N_c chiral perturbation theory: Effects of the decuplet-octet mass difference and flavor symmetry breaking

The baryon axial vector current is computed at one-loop order in large-N_c baryon chiral perturbation theory, where N_c is the number of colors. Loop graphs with octet and decuplet intermediate states are systematically incorporated into the analysis and the effects of the decuplet-octet mass difference and SU(3) flavor symmetry breaking are accounted for. As expected, large-N_c cancellations between different one-loop graphs are observed as a consequence of the large-N_c spin-flavor symmetry of QCD baryons. Fitting our analytical formulas against experimental data on baryon semileptonic decays and the strong decays of decuplet baryons, a detailed numerical analysis regarding the determination of the basic parameters of large-N_c baryon chiral perturbation theory as well as the extraction of the baryon axial vector couplings is performed. The large-N_c baryon chiral perturbation theory predictions are in very good agreement both with the expectations from the 1/N_c expansion and with the experimental data.

hep-ph↗