PLB34087S03702693(18)30702010.1016/j.physletb.2018.09.010The Author(s)PhenomenologyTable 1The experimental data on the hyperon semileptonic decay constants [2] and the singlet axialvector constant taken from Ref. [33].Table 1Experimental dataReferences
g1/f1(n→p)1.2723 ± 0.0023PDG [2]
g1/f1(Λ→p)0.718 ± 0.015PDG [2]
g1/f1(Σ−→n)−0.340 ± 0.017PDG [2]
g1/f1(Ξ−→Λ)0.25 ± 0.05PDG [2]
g1/f1(Ξ0→Σ+)1.22 ± 0.05PDG [2]
gA(0)0.36 ± 0.03Bass et al. [33]
Table 2Numerical values of the dynamical parameters ai.Table 2a1a2a3a4a5a6
−3.509 ± 0.0113.437 ± 0.0280.604 ± 0.030−1.213 ± 0.0680.479 ± 0.025−0.735 ± 0.040
Table 3Pseudoscalar strong coupling constants of the baryon octet, divided by 4π. The second column lists the results for the SUf(3) symmetric case, whereas the third one does those with explicit SUf(3) symmetry breaking taken into account. The fourth and fifth columns list the values of the coupling constants taken from the Nijmegen and Jülich–Bonn hyperon–nucleon potentials, respectively.Table 3P8B8B8gP8B8B8(0)gP8B8B8(total)ESC08a [8]Jülich–Bonn [4,7]
πNN3.524 ± 0.0123.638 ± 0.0183.6393.795
πΛΣ3.129 ± 0.0113.229 ± 0.0163.3282.629
πΣΣ3.356 ± 0.0143.197 ± 0.0193.2903.036
πΞΞ−1.240 ± 0.009−0.985 ± 0.015−1.475⋯
KNΛ−3.185 ± 0.030−3.189 ± 0.032−3.217−3.944
KNΣ0.820 ± 0.0090.905 ± 0.0110.9750.759
KΛΞ1.076 ± 0.0131.316 ± 0.0170.942⋯
KΣΞ−3.855 ± 0.037−3.793 ± 0.037−3.980⋯
Table 4Pseudovector coupling constants for the P8B8B10 vertices. The second column lists the results for the SUf(3) symmetric case, whereas the third one does those with explicit SUf(3) symmetry breaking taken into account. The last column lists the values of the coupling constants taken from the Jülich–Bonn hyperon–nucleon potential.Table 4M8B8B10fP8B8B10(0)fP8B8B10(total)Jülich–Bonn [4]
πNΔ1.646 ± 0.0061.777 ± 0.0081.68
πΛΣ⁎1.164 ± 0.0041.178 ± 0.0061.18
πΣΣ⁎−1.164 ± 0.004−1.059 ± 0.007−0.68
πΞΞ⁎1.164 ± 0.0041.111 ± 0.007⋯
KΣΔ−4.815 ± 0.046−4.551 ± 0.045−4.90
KNΣ⁎−3.404 ± 0.032−3.667 ± 0.038−2.00
KΞΣ⁎3.404 ± 0.0323.450 ± 0.033⋯
KΣΞ⁎3.404 ± 0.0323.167 ± 0.032⋯
KΛΞ⁎−5.897 ± 0.056−6.535 ± 0.064⋯
KΞΩ8.339 ± 0.0798.130 ± 0.080⋯
Table 5Partial (Γi) and full decay widths (Γ) for the decays B10 → B8 + π in units of MeV.Table 5Decay modesΓi(0)Γi(total)ΓΓ(Exp.) [2]
Δ → Nπ75.98 ± 1.0188.58±1.31116–120

Σ⁎+ → Σ0π+2.59 ± 0.033.22 ± 0.0636.25 ± 0.4236.0 ± 0.7
Σ⁎+ → Σ+π03.17 ± 0.052.62 ± 0.05
Σ⁎+ → Λπ+29.68 ± 0.2630.41 ± 0.33

Σ⁎0 → Σ0π00037.21 ± 0.6936 ± 5
Σ⁎0 → Σ+π−3.61 ± 0.112.98 ± 0.1
Σ⁎0 → Σ−π+2.78 ± 0.12.30 ± 0.09
Σ⁎0 → Λπ031.15 ± 0.4731.92 ± 0.52

Σ⁎− → Σ−π03.50 ± 0.062.89 ± 0.0638.18 ± 0.4839.4 ± 2.1
Σ⁎− → Σ0π−3.64 ± 0.063.01 ± 0.06
Σ⁎− → Λπ−31.50 ± 0.3032.28 ± 0.37

Ξ⁎0 → Ξ0π04.76 ± 0.054.33 ± 0.0611.26 ± 0.179.1 ± 0.5
Ξ⁎0 → Ξ−π+7.61 ± 0.086.93 ± 0.10

Ξ⁎− → Ξ−π04.76 ± 0.054.33 ± 0.0613.01 ± 0.219.9−1.9+1.7
Ξ⁎− → Ξ0π−8.20 ± 0.138.68 ± 0.16
Table 6Pseudovector coupling constants for the P8B10B10 vertices. The second column lists the results for the SUf(3) symmetric case, whereas the third one does those with explicit SUf(3) symmetry breaking taken into account.Table 6P8B10B10fP8B10B10(0)fP8B0B10(total)
πΔΔ0.769 ± 0.0030.780 ± 0.004
πΣ⁎Σ⁎0.688 ± 0.0030.703 ± 0.004
πΞ⁎Ξ⁎0.421 ± 0.0020.469 ± 0.002
πΩΩ00
KΔΣ⁎−1.423 ± 0.014−1.375 ± 0.014
KΣ⁎Ξ⁎−2.013 ± 0.020−2.014 ± 0.020
KΞ⁎Ω−2.466 ± 0.024−2.507 ± 0.025
Table 7Pseudoscalar strong coupling constants gηB8B8 and gη′B8B8 divided by 4π. The second column lists the results for the SUf(3) symmetric case, whereas the third one corresponds to those from a4, a5, and a6 of the collective operator for the axialvector constants given in Eq. (4). The fourth one represents the corrections from the symmetrybreaking parts of the collective wavefunctions in Eq. (6). The fifth column presents the total results of the coupling constants. The sixth one lists the values of the coupling constants taken from the Nijmegen potentials.Table 7P8B8B8gP8B8B8(0)gP8B8B8(op)gP8B8B8(wf)gP8B8B8(total)ESC08a [8]
ηNN1.583 ± 0.126−0.328 ± 0.027−0.015 ± 0.0021.241 ± 0.1031.933
η′NN1.241 ± 0.103−0.637 ± 0.0440.007 ± 0.0010.611 ± 0.0882.443
ηΛΛ−1.947 ± 0.1531.169 ± 0.097−0.053 ± 0.005−0.831 ± 0.086−1.572
η′ΛΛ3.189 ± 0.1992.272 ± 0.1550.024 ± 0.0025.486 ± 0.3294.634
ηΣΣ3.772 ± 0.288−1.026 ± 0.086−0.006 ± 0.0032.740 ± 0.2144.547
η′ΣΣ0.790 ± 0.113−2.531 ± 0.1710.003 ± 0.001−1.738 ± 0.1732.168
ηΞΞ−3.590 ± 0.2741.470 ± 0.124−0.042 ± 0.004−2.161 ± 0.177−2.986
η′ΞΞ4.346 ± 0.2663.747 ± 0.2530.019 ± 0.0018.111 ± 0.4845.981
Table 8Pseudovector coupling constants fηB8B10 and fη′B8B10 divided by 4π. The second column lists the results for the SUf(3) symmetric case, whereas the third one corresponds to those from a4, a5, and a6 of the collective operator for the axialvector constants given in Eq. (4). The fourth one represents the corrections from the symmetrybreaking parts of the collective wavefunctions in Eq. (6). The fifth column presents the total results of the coupling constants.Table 8P8B8B10fP8B8B10(0)fP8B8B10(op)fP8B8B10(wf)fP8B8B10(total)
ηΣΣ⁎3.21 ± 0.25−0.74 ± 0.060.02 ± ±0.012.48 ± 0.20
η′ΣΣ⁎3.46 ± 0.31−3.00 ± 0.20−0.01 ± 0.010.45 ± 0.28
ηΞΞ⁎3.21 ± 0.25−0.68 ± 0.06−0.10 ± 0.012.42 ± 0.19
η′ΞΞ⁎3.46 ± 0.31−3.04 ± 0.210.08 ± 0.010.49 ± 0.28
Table 9Pseudovector strong coupling constants of the baryon decuplet with η and η′, divided by 4π. The second column lists the results for the SUf(3) symmetric case, whereas the third one corresponds to those from a4, a5, and a6 of the collective operator for the axialvector constants given in Eq. (4). The fourth one represents the corrections from the symmetrybreaking parts of the collective wavefunctions in Eq. (6). The fifth column presents the total results of the coupling constants.Table 9P8B10B10fP8B10B10(0)fP8B0B10(op)fP8B0B10(wf)fP8B0B10(total)
ηΔΔ1.77 ± 0.15−0.21 ± 0.02−0.04 ± 0.011.51 ± 0.13
η′ΔΔ4.58 ± 0.35−0.83 ± 0.060.04 ± 0.013.79 ± 0.32
ηΣ⁎Σ⁎1.16 ± 0.100.02 ± 0.01−0.01 ± 0.011.17 ± 0.11
η′Σ⁎Σ⁎5.06 ± 0.37−0.01 ± 0.010.01 ± 0.015.05 ± 0.37
ηΞ⁎Ξ⁎0.56 ± 0.070.21 ± 0.02−0.03 ± 0.010.75 ± 0.08
η′Ξ⁎Ξ⁎5.53 ± 0.390.83 ± 0.060.02 ± 0.016.39 ± 0.43
ηΩΩ−0.04 ± 0.05−0.22 ± 0.02−0.01 ± 0.01−0.27 ± 0.06
η′ΩΩ6.00 ± 0.41−0.83 ± 0.060.01 ± 0.015.18 ± 0.38
Meson–baryon coupling constants of the SU(3) baryons with flavor SU(3) symmetry breakingGhilSeokYangaghsyang@ssu.ac.krHyunChulKimbc⁎hchkim@inha.ac.kraDepartment of Physics, Soongsil University, Seoul 06978, Republic of KoreaDepartment of PhysicsSoongsil UniversitySeoul06978Republic of KoreabDepartment of Physics, Inha University, Incheon 22212, Republic of KoreaDepartment of PhysicsInha UniversityIncheon22212Republic of KoreacSchool of Physics, Korea Institute for Advanced Study (KIAS), Seoul 02455, Republic of KoreaSchool of PhysicsKorea Institute for Advanced Study (KIAS)Seoul02455Republic of Korea⁎Corresponding author at: Department of Physics, Inha University, Incheon 22212, Republic of Korea.Department of PhysicsInha UniversityIncheon22212Republic of KoreaEditor: J.P. BlaizotAbstractWe investigate the strong coupling constants for the baryon octet–octet, decuplet–octet, and decuplet–decuplet vertices with pseudoscalar mesons within a general framework of the chiral quarksoliton model, taking into account the effects of flavor SU(3) symmetry breaking to linear order in the expansion of the strange current quark mass. All relevant dynamical parameters are fixed by using the experimental data on hyperon semileptonic decays and the singlet axialvector constant of the nucleon. The results of the strong coupling constants for the baryon octet and the pseudoscalar meson octet are compared with those determined from the Jülich–Bonn potential and the Nijmegen extended softcore potential for hyperon–nucleon scattering. The results of the strong decay widths of the baryon decuplet are in good agreement with the experimental data. The effects of SUf(3) symmetry breaking are sizable on the η′ coupling constants. We predict also the strong coupling constants for the Ω baryons.KeywordsMeson–baryon coupling constantsStrong decay widthsThe chiral quarksoliton model1IntroductionThe meson–baryon coupling constants are the essential quantities in understanding the structure of SU(3) baryons and in describing various productions such as meson–baryon scattering, baryon–baryon scattering, photoproduction and electroproduction of hadrons. The strong coupling constants are often determined with flavor SUf(3) symmetry assumed. Knowing the πNN coupling constants and the ratio α=F/(F+D), where F and D are the two couplings arising from the SU(3) Wigner–Eckart theorem for computing the matrix elements of the axialvector current [1], one can determine the pseudoscalar meson octet (P8) and baryon octet (B8) coupling constants:(1)gP8iB8jB8k=g[iαfijk+(1−α)dijk], with g=gπNN. The ratio α can be found from the five known experimental data on hyperon semileptonic decay (HSD) constants (g1/f1)B8′→B8 [2,3]. Almost all theoretical works on the hyperon–nucleon interaction use it obtained in this way [4–9]. However, the empirical values of F and D determined from the HSD constants contain tacitly the effects of flavor SUf(3) symmetry breaking, though F and D are defined with SUf(3) symmetry assumed.The strong coupling constants for the baryon decuplet (B10)octet and pseudoscalar meson octet vertices are less known. Even the πNΔ coupling constant, which is the essential quantity in describing the NN and πN interactions, is not at all given in consensus. The πNΔ coupling constant is usually determined by the decay width of Δ→πN, which yields fπNΔ≈2.24. In describing πN scattering, fπNΔ≈2.0−2.5 was used [10–12]. On the other hand, the full Bonn potential for the NN interaction [13], fπNΔ=1.678 was employed, which was taken from the relation in an SU(6) quark model fπNΔ2=72fπNN2/25 [14]. A recent work determined fπNΔ=1.256, which is much smaller than that from the decay width, based on the global fit to the πN and γN data [15]. When it comes to the coupling constants for the other members of the baryon decuplet, information is much less known.In the mean time, new experimental programs with strangeness of S=−3 are now under way at the JPARC [16] and a new excited Ω resonance was reported by the Belle Collaboration [17]. The HAL Collaboration in lattice QCD predicted the dibaryon (ΩΩ) with strangeness S=−6 [18]. The NΩ interaction was studied in a mesonexchange picture [19] very recently. The baryon decuplet and octet interactions were investigated [20]. In this regard, it is highly required to provide information on the baryon and pseudoscalar meson coupling constants in a quantitative manner.In the present work, we want to study the coupling constants for the vertices of the baryon decuplet–octet (also decuplet) and pseudoscalar mesons in a pion meanfield approach that is often called the chiral quarksoliton model (χSM). In Refs. [21,22], we reexamined the mass splittings of the SU(3) baryon octet and the decuplet, fixing all the parameters unequivocally to the experimental data. The effects of SUf(3) symmetry breaking and isospin symmetry breaking due to both the electromagnetic interaction and current quark mass difference [21,23] were systematically included, which made it possible to exploit the experimental data to fix the parameters. Since we have fixed all unknown parameters in the baryon wavefunctions, we can proceed to the study of the axialvector transitions, again fixing relevant parameters by utilizing the experimental data on the HSD constants and the flavorsinglet axialvector charge gA(0). Though similar works were done already [24–27], it was then not possible to fix all the parameters unambiguously because of the absence of isospin symmetry breaking which is inevitable in incorporating the experimental data for the baryon octet. Recently, we have shown that all the relevant parameters for the HSD constants can be fixed without any ambiguity [28]. Once they are known, we can compute all possible axialvector transitions between the baryon multiplets. As a result, we are able to determine the coupling constants for the vertices of the baryon decuplet–octet (decuplet) and pseudoscalar mesons without any additional parameters introduced, taking into account the effects of explicit SU(3) symmetry breaking.This paper is outlined as follows: Section 2, we briefly review the general formalism of the χSM to compute the axialvector transitions between the baryon multiplets and show how to fix the parameters for the axialvector transitions. In Sec. 3, we present the results of the coupling constants for the baryon multiplets and pseudoscalar meson vertices. We show also the decay widths of the baryon decuplet to the octet. In Sect. 4, we discuss the results for the η (η′), and baryon coupling constants, applying a usual mixing between the octet η8 and the singlet η0. In the final section we summarize the present work and draw conclusions.2Baryon matrix elements of the axialvector currentsThe baryon matrix elements of the axialvector currents are expressed in terms of three form factors(2)〈B8AμiB8′〉=u¯B8′(p2,s2)[g1B8′→B8(q2)γμ+ig2B8′→B8(q2)σμνqνMB8′+g3B8′→B8(q2)qμMB8′]γ5uB8(p1,s1), where the axialvector currents are defined as(3)Aμi(x)=ψ¯(x)γμγ512λiψ(x). The λi stand for flavor GellMann matrices for strangeness conserving ΔS=0 transitions (i=3,8,(1±i2)) and for ΔS=1 ones (i=4±i5), respectively. The q2=−Q2 denotes the square of the momentum transfer q=p2−p1. The form factors gi are real quantities due to CPinvariance, depending only on the square of the momentum transfer. We can neglect g3B8′→B8, because its contribution to the decay rate is proportional to the ratio ml2/MB8′2≪1, where ml represents a mass of the lepton (e or μ) in the final state and that of the baryon in the initial state, MB8′, respectively. The g2B8′→B8 is finite only with the effects of SUf(3) symmetry and isospin symmetry breakings because of its opposite G parity to the axialvector current, so it is very small for the baryon octet.In the χQSM, the collective operator for the axialvector constants can be defined in terms of the SUf(3) Wigner D functions [24–26]:(4)gˆ1=a1DX3(8)+a2dpq3DXp(8)Jˆq+a33DX8(8)Jˆ3+a43dpq3DXp(8)D8q(8)+a5(DX3(8)D88(8)+DX8(8)D83(8))+a6(DX3(8)D88(8)−DX8(8)D83(8)), where ai denote dynamical parameters encoding the specific dynamics of a χQSM [29–31]. Note that a1 parametrizes the leadingorder contribution, a2 and a3 come from the rotational 1/Nc corrections, and a4, a5 and a6 are originated from SUf(3) symmetry breaking, in which the strange current quark mass ms is contained. Jˆq and Jˆ3 stand for the qth and third components of the collective spin operator of the baryons, respectively. The Dab(8) are the SU(3) Wigner D functions in the octet representation.The baryon wavefunctions for the baryon octet and decuplet are written in terms of the SUf(3) Wigner D functions in the χSM [21,32]:(5)〈AR,B(YTT3,Y′JJ3)〉=Ψ(R⁎;Y′JJ3)(R;YTT3)(A)=dim(R)(−)J3+Y′/2D(Y,T,T3)(−Y′,J,−J3)(R)⁎(A), where R designates the allowed irreducible representations of the SUf(3) group, i.e. R=8,10,⋯. Y,T,T3 denote the corresponding hypercharge, isospin and its third component, respectively. The right hypercharge is constrained to be Y′=1 in such a way that it selects a tower of allowed SUf(3) representations. The baryon octet and decuplet, which are the lowest representations, coincide with those of the quark model. This has been considered as a success of the collective quantization and gives a hint about certain duality between the chiral soliton picture and the constituent quark model.When the effects of SUf(3) symmetry breaking are taken into account, a baryon state is no more pure state but the state mixed with those in higher representations. Thus, the wavefunctions for the baryon octet and the decuplet are given by(6)B8〉=81/2,B〉+c10‾B10‾1/2,B〉+c27B271/2,B〉,B10〉=103/2,B〉+a27B273/2,B〉+a35B353/2,B〉, where the spin indices J3 have been dropped from the states. The mixing coefficients in Eq. (6) contain the strange current quark mass ms and are expressed as(7)c10‾B=c10‾[5050],c27B=c27[6326],a27B=a27[15/223/20],a35B=a35[5/1425/735/1425/7], respectively in the bases [N,Λ,Σ,Ξ] and [Δ,Σ⁎,Ξ⁎,Ω] with(8)c10‾=−I215(ms−mˆ)(α+12γ),c27=−I225(ms−mˆ)(α−16γ),a27=−I28(ms−mˆ)(α+56γ),a35=−I224(ms−mˆ)(α−12γ),d8=I215(ms−mˆ)(α+12γ),d27=−I28(ms−mˆ)(α−76γ),d35‾=−I24(ms−mˆ)(α+16γ). Here I2 is a moment of inertia for the soliton. α and γ are the parameters appearing in the collective Hamiltonian. As for the explicit definitions of I2, α and γ, we refer to Ref. [21], where one can find also a detailed discussion as to how they are fixed unambiguously, and relevant references.Since the baryon wavefunctions contain the corrections of linear SUf(3) symmetry breaking as shown in Eq. (6), the axialvector transition constants g1B8′→B8 acquire yet another linear ms corrections, when the collective operator gˆ1 is sandwiched between the baryon states. Thus, we have the two different linear ms corrections to the axialvector transition constants, i.e., one from a4, a5 and a6, and the other from the baryon wavefunctions. Recently, we have shown how the parameters ai are unequivocally fixed in detail [28]. The experimental data on the HSD constants (g1/f1)B8′→B8 and the flavorsinglet axialvector charge gA(0), listed in Table 1, will be the input for fixing ai. The parameters ai are related to the experimentally known axialvector HSD constants and gA(0) in a form of the matrix equation:(9)g=B⋅a, where(10)g=((g1/f1)n→p,(g1/f1)Λ→p,(g1/f1)Σ−→n,g=((g1/f1)Ξ−→Λ,(g1/f1)Ξ0→Σ+,gA0),(11)B=[−730−13c10‾−245c27760−13c10‾−445c27160−16c10‾+115c27−11270−19−115−215+16c10‾+130c27115+16c10‾+115c27130+112c10‾−120c271450−130115−145c27−130−245c27115+130c27−1270−145130−130−130c27160−115c27120+120c27−1180130−130−730+16c10‾+145c27760+16c10‾+245c27160+112c10‾−130c27115401181300010−1515],(12)a=(a1,a2,a3,a4,a5,a6). Inverting B, we can easily derive the parameters ai of which the numerical values are listed in Table 2. All other unmeasured HSD constants for the baryon octet and decuplet were predicted in Ref. [28].3Coupling constants for the P8–B8–B10 and P8–B10–B10 verticesThe matrix elements of the B10→B8 and B10→B10 transitions with the axialvector current are parametrized in terms of the Adler form factors CiA,B10→B8 [34–36](13)〈B8(p′,s′)AμiB10(p,s)〉=u‾(p′,s′)[{C3A,B10→B8(q2)M8γα+C4A,B10→B8(q2)M82pα}(qαgμν−qνgαμ)+C5A,B10→B8(q2)gμν+C6A,B10→B8(q2)M82qμqν]uν(p,s),(14)〈B10(p′,s′)AμiB10(p,s)〉=u‾α(p′,s′)[gαβ(h1(q2)γμγ5+h3(q2)qμ2M10γ5)+qαqβ4M102(h1′(q2)γμγ5+h3′(q2)qμ2M10γ5)]uβ(p,s), where the uν represents the Rarita–Schwinger spinor for the baryon decuplet. qμ denotes the momentum transfer qμ=(p′−p)μ. The axialvector constant C5A,B10→B8 can be related to the strong coupling constants for P8–B8–B10 and P8–B10–B10 vertices by the partially conserved axialvector current (PCAC) hypothesis. The pseudoscalar meson decay constant f8 is defined as the transition matrix element of the axialvector current from the physical pion state to the vacuum(15)〈0Aμa(x)πb(p)〉=ipμf8e−ip⋅xδab, which will be used for the relations of the pseudovector coupling constants fP8B8B10 and fP8B10b10 to the Adler form factors. In the present work, we will determine only C5A and h1.The effective Lagrangians for the P8B8B10 and P8B10B10 vertices are expressed as(16)LP8B8B10=fP8B8B10m8B‾10μZμνI(32,12)B8∂νM8+h.c.,LP8B10B10=fP8B10B10m8B‾10αZαβνI(32,32)B10β∂νM8+h.c., where the pseudovector coupling constants are defined as(17)fP8B8B10=m8f8C5A(0),(18)fP8B10B10=m8f8h1(0), m8 denotes the mass of the pseudoscalar meson. The field operators B10μ, B8, and P8 correspond respectively to a decuplet baryon, an octet baryon, and a pseudoscalar octet meson. The Zμν and Zαβν stand for the tensors including the offshell effects arising from the Rarita–Schwinger field quantization, defined as Zμν=gμν−xΔγμγν with the offshell parameter xΔ. I(3/2,1/2) and I(3/2,3/2) are isospin transition matrices.For completeness, we also want to mention that the pseudoscalar strong coupling constants can be derived from the generalized Goldberger–Treiman (GT) relation [37,38], which is defined as(19)gP8B8B10≈M8+M10f8C5A(0). However, there is a caveat in Eq. (19). Keeping in mind that certain effects on the GT relation will arise from the flavor SUf(3) symmetry breaking. In Ref. [39], it was shown that loop corrections to the GT relation, which come from the pion mass, are indeed very small (∼2%). So, we expect that the strange current quark mass will not yield much effects on the relation. Thus, as often assumed in the hyperon–nucleon potentials, one still can use Eq. (19), if one wants to derive the strong coupling constants gP8B8B10.In effect, the numerical values of the C5A(0) were already presented in the previous work [28]. Thus, we will show the results for the pseudovector coupling constants and decay widths of the baryon decuplet in this work, using the experimental data on the meson decay constants, fπ=92.4MeV and fK=113.0MeV. In Table 3, we list the results of the pseudoscalar coupling constants for the various P8B8B8 vertices, i.e. gP8B8B8/4π. The second column represents those in the SUf(3) symmetric case, whereas the third one denotes those with explicit SUf(3) symmetry breaking taken into account. The results are compared with those determined from the extended softcore Nijmegen hyperon–nucleon (YN) potential (ESC08a) [8] and Jülich–Bonn YN potential, employing the generalized GT relation for kaon vertices. Except for the coupling constants of the vertices πΞΞ and KΞΛ, the present results are in good agreement with the those from both the Nijmegen and Jülich–Bonn potentials. When the effects of the SUf(3) symmetry breaking are taken into account, the present results are more deviated from those taken from the Nijmegen potential. Note that both the Nijmegen and Jülich–Bonn potentials have assumed SUf(3) symmetry and the following relations for the P8B8B10 vertices are obtained in exact SUf(3):(20)fπNΔ=2fπΛΣ⁎=−2fπΣΣ⁎=2fπΞΞ⁎,fKΣΔ=2fKNΣ⁎=−2fKΞΣ⁎=−2fKΣΞ⁎=2/3fKΛΞ⁎=−1/3fKΞΩ, which can be found in various works already.In Table 4 we list the results of the pseudovector coupling constants for the P8B8B10 vertices. We find that the present value of fπΣΣ⁎ is different from that taken from the Jülich–Bonn potential by almost 50%. The value of fKNΣ⁎ differs by approximately 45%. However, we want to emphasize that the present results of the coupling constants reproduce the experimental data on the decay widths of the decuplet hyperons very well, which will be discussed now.The partial width for the decay from the baryon decuplet to the octet and pseudoscalar meson P8 is expressed in terms of the pseudovector coupling constant as follows(21)ΓB10→φB8=k38πm82M8M10fP8B8B102, where k denotes the three momentum of the pseudoscalar meson in the rest frame of the baryon decuplet. m8 represents the mass of the pseudoscalar meson involved in the decay process. Summing all possible transitions with averaging over the initial states, we can write the decay width for each member of the baryon decuplet as(22)Γ[Δ→πN]=32Γ[Δ+→π0p],Γ[Σ⁎→πΛ]=Γ[Σ⁎0→π0Λ],Γ[Σ⁎→πΣ]=2Γ[Σ⁎+→π0Σ+],Γ[Ξ⁎→πΞ]=3Γ[Ξ⁎0→π0Ξ0]. Except for the Δ decay, the present results are in good agreement with the experimental data as shown in Table 5. There exist also experimental data on the ratio of the decay widths for Σ⁎→Σ and Σ⁎→Λ. The present result is comparable with the data as shown in the following(23)Γ[Σ⁎→Σ]Γ[Σ⁎→Λ]=0.180±0.002(experimental data [2]: 0.135±0.011).In Table 6, we list the results on the pseudovector coupling constants for the P8B10B10 vertices. The πΩΩ coupling constant vanishes, since the isoscalar Ω baryon can not be coupled to the pion. Note that as the absolute value of strangeness increases, the magnitude of the P8B10B10 coupling constant tends to increase. For example, the magnitude of fKΞ⁎Ω is approximately three times larger than that of fπΔΔ.4Coupling constants for the η–B–B, η′–B–B veticesIn this section, we provide the numerical values of the coupling constants when η and η′ are involved. In order to compute them, we have to consider the mixing between the octet η8 and the singlet η0 coupling constants. Following the mixing scheme suggested in Ref. [8] given as(24)gηB8B8=cosθpgη8B8B8−sinθpgη0B8B8,(25)gη′B8B8=sinθpgη8B8B8+cosθpgη0B8B8, one can easily determine the coupling constants for the η and η′ coupling constants. Using the values of fη=94.0MeV, fη′=89.1MeV taken from Refs. [40–42] and mixing angle θp=−23.00∘ from Ref. [8], we obtain the pseudoscalar coupling constants for the ηB8B8 and η′B8B8 coupling constants.The corresponding numerical results are listed in Table 7 and are compared with those from the Nijmegen potentials. Since the effects of SU(3) symmetry breaking seem rather important, we examine the contributions from the SU(3) symmetry breaking more closely. In the case of exact SUf(3) symmetry, the results are very similar to those from the Nijmegen potentials. However, when the effects of explicit SUf(3) symmetry breaking are taken into account, the values of the η and η′ coupling constants are in general much changed. As shown in Table 7, there are two different contributions of the SUf(3) symmetry breaking: The one arises directly from the collective operator for the axialvector constant given in Eq. (4) and the other comes from the wavefunctions mixed with the states from higher representations as in Eq. (6). As clearly shown in the fourth column of Table 7, the wavefunction corrections are negligibly small. However, the linear ms corrections from the collective operator, in particular, when it comes to the η′B8B8 coupling constants, are sizable, even compared with the contributions of the SUf(3) symmetric terms.In order to understand this, we need to examine carefully the expression for the singlet axialvector constant gA(0). As discussed in detail In Ref. [26], the singlet axialvector operator gˆA(0) is written as(26)gˆA(0)2=a3Jˆ3+3(a5−a6)D83(8), where the leadingorder contribution with a1 vanish. It means that a3, which is subleading in the 1/Nc expansion, plays a leading role [43,44]. The parameter a3 in Eq. (26) comes from the anomalous part of the effective chiral action in the χQSM while in the Skyrme model it arises from the Wess–Zumino term and vanishes in the version of the pseudoscalar mesons. Thus, the effects of SUf(3) symmetry breaking are crucial in determining the value of gA(0) quantitatively. Since a5 and a6 have different signs as shown in Table 2, the ms correction given in the second term of Eq. (26) becomes large. As a result, the effects of SUf(3) symmetry breaking turn out to be sizable, in particular, in the case of the η′B8B8 coupling constants for which the singlet contributions are large. Thus, the present results imply physically that the effects of SUf(3) symmetry breaking are crucial in determining the η and η′ coupling constants quantitatively.In Table 8, we list the results of the ηB8B10 and η′B8B10 coupling constants. In general, the effects of explicit SUf(3) symmetry breaking reduce the magnitudes of these coupling constants noticeably. Table 9 lists the results of the η and η′ coupling constants for the baryon decuplet. Interestingly, the effects of explicit SUf(3) symmetry breaking are marginal except for the ηΩΩ coupling constant, since the matrix elements of D83(8) are small for the baryon decuplet. Note that the η′Σ⁎Σ⁎ does not acquire any contribution from explicit SUf(3) symmetry breaking. In general, the values of the η′ coupling constants are much larger than those of the η ones.5Summary and conclusionIn the present work, we have investigated the strong coupling constants for the meson–baryon–baryon vertices within the general framework of the chiral soliton model, taking into account the effects of flavor SU(3) symmetry breaking to linear order. All the relevant dynamical parameters were fixed by using the experimental data on the hyperon semileptonic decays and the singlet axialvector constant. We were able to determine the strong coupling constants for the baryon octet and pseudoscalar meson octet vertices, those for the transition from the baryon decuplet to the baryon and pseudoscalar meson octets, and those for the baryon decuplet and pseudoscalar meson octet vertices. Except for the πΞΞ, πΣΣ⁎ and KNΣ⁎ vertices, the present results were in good agreement with those determined from the Nijmegen and Jülich–Bonn potentials. We also computed the decay widths of the baryon decuplet to the baryon octet and the pion. Apart from the Δ decays, the results are in good agreement with the experimental data. We also presented the strong coupling constants for the η and η′ mesons. The effects of SUf(3) symmetry breaking are in general quite sizable on the η′ coupling constants. This can be understood that the leading contribution to the singlet axialvector constant vanishes in the 1/Nc expansion within the present framework and the subleadingorder terms play a leading role. Thus, the corrections of the strange current quark mass become relatively more important in the case of the η′ coupling constants.The strong coupling constants for the vector mesons and the baryon octet and decuplet can be examined within the same framework. Since the vector mesons have spin 1, the structure of the coupling constants is more involved. The related work is under investigation.AcknowledgementsH.Ch.K. is grateful to M.V. Polyakov for the discussion and hospitality during his visit to the Institute für Theoretical Physics II, RuhrUniversität Bochum, where part of the work was done. 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