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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 the order ${m}_{q}\mathrm{ln}{m}_{q}$ 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 in good agreement with the experimental data.

An expression for the Dalitz plot of the semileptonic decay of a charged kaon, including radiative corrections to order O[\alpha \pi)(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., Comment: 20 pages, 4 figures, 3 tables

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 $SU(2{N}_{f})\ensuremath{\rightarrow}SU(2)\ensuremath{\bigotimes}SU({N}_{f})$ 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.

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., Comment: 20 pages, 7 tables

The $s$-wave decay amplitude in the nonleptonic decay of baryons is analyzed within heavy baryon chiral perturbation theory in the $\mathrm{large}\text{\ensuremath{-}}{N}_{c}$ 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 $\mathrm{large}\text{\ensuremath{-}}{N}_{c}$ cancellations between different one-loop graphs as a consequence of the $\mathrm{large}\text{\ensuremath{-}}{N}_{c}$ spin-flavor symmetry of QCD baryons. The predictions of $\mathrm{large}\text{\ensuremath{-}}{N}_{c}$ baryon chiral perturbation theory are in very good agreement both with the expectations from the $1/{N}_{c}$ expansion and with the experimental data.

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., 8 pages

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.

A model-independent expression for the Dalitz plot of semileptonic decays of neutral kaons, ${K}_{l3}^{0}$, including radiative corrections to order $(\ensuremath{\alpha}/\ensuremath{\pi})(q/{M}_{1})$, 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.

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.

The magnetic and transition magnetic moments of the ground-state baryons are computed in heavy baryon chiral perturbation theory in the large-N{sub c} limit, where N{sub 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{sub q}{sup 1/2} and m{sub q} ln m{sub 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{sub c}=3. The agreement reached is quite impressive.

We obtain an expression for the Dalitz plot of semileptonic decays of polarized hyperons including radiative corrections to order {alpha} and neglecting terms of the order {alpha}q/{pi}M{sub 1}, where q is the four-momentum transfer and M{sub 1} is the mass of the decaying hyperon. Our results are specialized to exhibit the angular correlation between such polarization and the momentum of the emitted hyperon. The model dependence of radiative corrections is kept in a general form within this approximation which is suitable for model-independent experimental analysis. Our final result, valid for charged as well as for neutral hyperons, allows us to obtain the angular spin-asymmetry coefficient of the emitted hyperon. {copyright} {ital 1997} {ital The American Physical Society}

Large-Nc chiral perturbation theory is a calculational scheme for baryons that simultaneously exhibits both the mq and 1/Nc expansions, where Nc is the number of colors of quarks. In this work an outline of the calculation of one-loop corrections to the leading baryon axial-vector and vector form factors in baryon semileptonic decays to order O(p 2) in the chiral expansion is provided in order to show how the expansion works.

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.

We calculate the radiative corrections to the Dalitz plot of ${K}_{l3}^{\ifmmode\pm\else\textpm\fi{}}$ decays to order $(\ensuremath{\alpha}/\ensuremath{\pi})(q/{M}_{1})$, where $q$ is the momentum transfer and ${M}_{1}$ is the mass of the kaon. We restrict the analysis to the so-called four-body region, which arises when no discrimination of real photons is made either kinematically or experimentally. We present our results in two ways: the first one with the triple integration over the photon kinematical variables ready to be performed numerically and the second one in a fully analytical form. Our results can be useful in experimental analyses of the Dalitz plot, by evaluating the model-independent coefficients of the quadratic products of the form factors; we provide some numbers as a case example. We find a small, albeit non-negligible, contribution from the four-body region to the radiative correction to the total decay rate of ${K}_{l3}^{\ifmmode\pm\else\textpm\fi{}}$ decays.

We present an overview of the calculation of one‐loop corrections to baryon magnetic moments in large‐Nc chiral perturbation theory, where Nc is the number of colors. Nonanalytic corrections of orders mq1/2 and mq ln mq are explicitly included to relative order 1/Nc3 in the 1/Nc expansion. Comparisons with other theoretical calculations and with experiment are carried out, leading to very good agreements.

The baryon magnetic and transition magnetic moments are computed in heavy baryon chiral perturbation theory in the large-N_c limit, where N_c is the number of colors. One-loop nonanalytic corrections of orders m_q^{1/2} and m_q ln m_q are incorporated into the analysis, where contributions of both intermediate octet and decuplet baryon states are explicitly included. Expressions are obtained in the limit of vanishing baryon mass differences and compared with the current experimental data. Furthermore, a comparison with conventional heavy baryon chiral perturbation theory is carried out for three light quarks flavors and at the physical value N_c=3., RevTex4, 36 pages, 2 eps figures; corrected typos; results agree with the ones of Ref. [26]

We complement the results for the radiative corrections to the s2.l angular correlation of baryon semileptonic decays of Ref. [1] with the final results in the rest frame of the decaying baryon., 7 pages, Revtex4, no figures

We have calculated the radiative corrections to the Dalitz plot of baryon semileptonic decays with angular correlation between polarized emitted baryons and charged leptons. This work covers both charged and neutral decaying baryons and is restricted to the so-called three-body region of the Dalitz plot. Also it is specialized at the center-of-mass frame of the emitted baryon. We have considered terms up to order (alpha/pi)(q/M_1)^0, where q is the momentum-transfer and M_1 is the mass of the decaying baryon, and neglected terms of order (alpha/pi)(q/M_1)^n$ for n >= 1. The expressions displayed are ready to obtain numerical results, suitable for model-independent experimental analyses., 18 pages, 1 figure; some typos corrected; Eq. (24) complemented

Analytical radiative corrections of order (alpha/pi)(q/M) are calculated for the four-body region of the Dalitz plot of baryon semileptonic decays when the s1.l correlation is present. Once the final result is available, it is possible to exhibit it in terms of the corresponding final result of the three-body region following a set of simple changes in the latter, except for a few exceptions. We cover two cases, a charged and a neutral polarized decaying baryon., RevTex, 6 pages, no figures

We give a detailed account of the techniques to compute radiative corrections in baryon semileptonic decays developed over the years by Mexican collaborations. We explain how the method works by obtaining an expression for the Dalitz plot of semileptonic decays of polarized baryons including radiative corrections to order ${\mathcal O}(\alpha q/\pi M_1)$, where $q$ is the four-momentum transfer and $M_1$ is the mass of the decaying baryon. From here we compute the totally integrated spin angular asymmetry coefficient of the emitted baryon and compare its value with other results., Comment: 10 pages. Prepared for the Commemorative Volume of the Divison of Particles and Fields of the Mexican Physical Society

The baryon axial vector current is computed at one-loop order in heavy baryon chiral perturbation theory in the large-N_c limit, where N_c is the number of colors. Loop graphs with octet and decuplet intermediate states cancel to various orders in N_c as a consequence of the large-N_c spin-flavor symmetry of QCD baryons. These cancellations are explicitly shown for the general case of N_f flavors of light quarks. In particular, a new generic cancellation is identified in the renormalization of the baryon axial vector current at one-loop order. A comparison with conventional heavy baryon chiral perturbation theory is performed at the physical values N_c=3, N_f=3., Comment: REVTex4, 29 pages, 2 figures, 6 tables. Equations (32) and (81) corrected. Some typos fixed. Results and conclusions remain unchanged

Analytical radiative corrections of order (\alpha/\pi)(q/M_1) are calculated for the four-body region of the Dalitz plot of baryon semileptonic decays when the s_1 \cdot p_2 correlation is present. Once the final result is available, it is possible to exhibit it in terms of the corresponding final result of the three-body region following a set of simple changes in the latter. We cover two cases, a charged and a neutral polarized decaying baryon., Comment: Revtex4, 7 pages, no figures

The derivation of the 1/N_c expansions for the baryon vector and axial-vector currents, in the SU(3) symmetry limit and including perturbative SU(3) breaking, is reviewed. Symmetry breaking effects in the hyperon semileptonic decay form factors are reanalyzed. Fits to experimental data yield corrections to the leading vector and axial-vector form factors consistent with expectations. The values of the Cabibbo-Kobayashi-Maskawa matrix elements V_{ud} and V_{us} also extracted from the analysis are comparable to the ones recommended by the Particle Data Group., 12 pages, no figures. Based on a talk given at ECT Workshop on Large N_c QCD 2004, Trento, Italy, 5-9 Jul 2004

We calculate the radiative corrections to the angular correlation between the polarization of the decaying baryon and the direction of the emitted charged lepton in the semileptonic decays of spin one-half baryons to order (\alpha/\pi)(q/M_1). The final results are presented, first, with the triple integration of the bremsstrahlung photon ready to be performed numerically and, second, in an analytical form. A third presentation of our results in the form of numerical arrays of coefficients to be multiplied on the quadratic products of form factors is discussed. This latter may be the most practical one to use in Monte Carlo simulations. A series of crosschecks is performed. The results are useful in the analysis of the Dalitz plot of precision experiments involving light and heavy quarks and is not compromised to fixing the form factors at predetermined values. It is assumed that the real photons are kinematically discriminated. Otherwise, our results have a general model-independent applicability., Comment: 8 pages, RevTex4, 5 tables, no figures. Shortened version; results and conclusions remain unchanged

We propose and discuss a numerical use for our previous precision results for the radiative corrections to unpolarized spin one-half baryon semileptonic decays, which is not compromised to fixing the form factors at prescribed values. We present various cross-checks and comparisons with other results available in the literature of such analytical radiative corrections. Our analysis, however, is general and applies to all charge assignments to the baryons allowed by heavy quarks. The procedure is exemplified with the processes ${\ensuremath{\Xi}}^{0}\ensuremath{\rightarrow}{\ensuremath{\Sigma}}^{+}e\overline{\ensuremath{\nu}}$ and ${\ensuremath{\Lambda}}_{c}^{+}\ensuremath{\rightarrow}\ensuremath{\Lambda}{e}^{+}\ensuremath{\nu}$.

A model-independent determination of the CKM matrix element V_{us} from five measured strangeness-changing hyperon semileptonic decays is performed. Flavor SU(3) symmetry breaking effects in the leading vector and axial-vector form factors are analyzed in the framework of the 1/N_c expansion of QCD. A fit to experimental data allows one to extract the value V_{us}=0.2199\pm 0.0026, which is comparable to the one from K_{e3} decays. This reconciliation is achieved through second-order symmetry breaking effects of a few percent in the form factors f_1, which increase their magnitudes over their SU(3) predictions., Comment: 23 pages, Revtex4, 12 tables, no figures

We calculate the radiative corrections to the angular correlation between the polarization of the decaying and the direction of the emitted spin one-half baryons in the semileptonic decay mode. The final results are presented, first, with the triple integration of the bremsstrahlung photon ready to be performed numerically and, second, in an analytical form. A third presentation of our results in the form of numerical arrays of coefficients to be multiplied by the quadratic products of form factors is discussed. This latter may be the most practical one to use in Monte Carlo simulations. A series of crosschecks is performed. Previous results to order (alpha/pi)(q/M_1) for the decays of unpolarized baryons are reviewed, too, where q is the momentum transfer and M_1 is the mass of the decaying baryon. This paper is self-contained and organized to make it accessible and reliable in the analysis of the Dalitz plot of precision experiments involving heavy quarks and is not compromised to fixing the form factors at predetermined values. It is assumed that the real photons are kinematically discriminated. Otherwise, our results have a general model-independent applicability., 34 pages, 4 tables, no figures. Some sections have been shortened. Conclusions remain unchanged

We study the four‐body region of the Dalitz plot for the semileptonic decays of polarized charged baryons. We perform our calculations up to order αq/πM1, where q is the four‐momentum transfer and M1 is the mass of decaying baryon. This work complements previous results obtained for the so called three‐body region of these decays where the radiative corrections are calculated up to order αq/πM1. In this way we will be able to obtain the total Dalitz plot which can be used in ordinary baryon decays and in charmed baryon decays like Λc → Λ0ev.

In semileptonic decays of spin‐1/2 baryons containing heavy quarks up to six charge assignments for the baryons and lepton are possible. We have found that the radiative corrections to four of these possibilities can be directly obtained from the final results of the two possibilities previously studied. In consequence, neither integrals over virtual or real photon momentum nor any traces need to be recalculated.

In semileptonic decays of spin-1/2 baryons containing heavy quarks up to six charge assignments for the baryons and lepton are possible. We show that the radiative corrections to four of these possibilities can be directly obtained from the final results of the two possibilities previously studied. There is no need to recalculate integrals over virtual or real photon momentum or any traces., Comment: 15 pages, 2 figures, RevTex. Extended discussion. Final version to appear in Physical Review D

We give a complete analytical computation of three-point one-loop integrals with one heavy propagator, up to the third tensor rank, for arbitrary values of external momenta and masses., Comment: 10 pages, Latex, to appear in J. Phys. G

We compute nonanalytical pion-loop corrections to baryon masses in a combined expansion in chiral symmetry breaking and 1/N_c, where N_c is the number of colors. Specifically, we compute flavor-27 baryon mass splittings at leading order in chiral perturbation theory. Our results, at the physical value N_c=3, are compared with the expressions obtained in heavy baryon chiral perturbation theory with no 1/N_c expansion., Comment: 7 pages. Based on a talk given at 8th Mexican Workshop on Particles and Fields, Zacatecas, Mexico, 14-20 Nov 2001. To appear in the proceedings

We show how to compute loop graphs in heavy baryon chiral perturbation theory including the full functional dependence on the ratio of the {delta}-nucleon mass difference to the pion mass, while at the same time automatically incorporating the 1/N{sub c} cancellations that follow from the large-N{sub c} spin-flavor symmetry of baryons in QCD. The one-loop renormalization of the baryon axial vector current is studied to demonstrate the procedure. A new cancellation is identified in the one-loop contribution to the baryon axial vector current. We show that loop corrections to the axial vector currents are exceptionally sensitive to deviations of the ratios of baryon-pion axial vector couplings from SU(6) values. (c) 2000 The American Physical Society.

We obtain a model-independent expression for the Dalitz plot of semileptonic decays of polarized hyperons including radiative corrections to order alpha and neglecting terms of order (alpha q)/(pi M_1), where q is the four-momentum transfer and M_1 is the mass of the decaying hyperon. We specialize our results to exhibit the correlation between the charged-lepton momentum and the spin of the decaying hyperon. We present results for the three-body region of the Dalitz plot and for the complete Dalitz plot (which includes the four-body region). From these results we also obtain the corresponding radiative corrections to the integrated lepton spin-asymmetry coefficient. Our formulas are valid for charged as well as for neutral decaying hyperons and are appropriate for model-independent experimental analysis whether the real photon is discriminated or not., Comment: 29 pages, no figures, REVTEX

The baryon axial vector current is considered within the combined framework of large-Nc baryon chiral perturbation theory (where Nc is the number of colors) and the baryon axial vector couplings are extracted. Loop graphs with octet and decuplet intermediate states are systematically incorporated into the analysis.

We discuss how to compute corrections to one-loop order to the baryon axial-vector current and magnetic moments in heavy baryon chiral perturbation theory in the large-Nc limit, where Nc is the number of colors. Loop graphs with octet and decuplet intermediate states cancel to various orders in Nc as a consequence of the large-Nc spin-flavor symmetry of QCD baryons. These cancellations are explicitly shown for the general case of Nf flavors of light quarks. We also indicate how to compare our resultant expressions with the corresponding ones obtained within conventional heavy baryon chiral perturbation theory at the physical values Nc = 3, Nf = 3. We observe an excellent agreement order by order.