SU(3) breaking in neutral current axial matrix elements and the spin content of the nucleon

Abstract

We examine the effects of SU͑3͒ breaking in the matrix elements of the flavor-diagonal axial-vector currents between octet baryon states. Our calculations of K, , and loops indicate that the SU͑3͒ breaking may be substantial for some matrix elements and at the very least indicate large uncertainties. In particular, the strange axial matrix element in the proton determined from the measurements of g 1 (x) is found to have large uncertainties and might yet be zero. We estimate the strange axial matrix element in the proton to be Ϫ0.35Շ⌬sՇ0 and the matrix element of the flavor-singlet current in the proton to be Ϫ0.1Շ⌺Շϩ0.3 from the E143 measurement of ͐dxg 1 (x)ϭ0.127Ϯ0.004Ϯ0.010. The up-quark content of the ⌶ Ϫ is discussed and its implications for nonleptonic weak processes discussed. We also estimate the matrix element of the axialvector current coupling to the Z 0 between all octet baryon states. This may be important for neutrino interactions in dense nuclear environments, where hyperons may play an important role. ͓S0556-2821͑97͒00709-1͔ PACS number͑s͒: 12.15. Ji, 12.39.Fe, 14.20.Dh One of the more exciting realizations in hadronic physics of the last few years is that the strange quark may play an important role in the structure of the nucleon ͓1͔. While this may seem somewhat unnatural in the context of the most naive quark model, it is perfectly natural from the standpoint of QCD. Matrix elements of the strange vector current must vanish at zero-momentum transfer between states with zero net strangeness; however, matrix elements of the axial-vector current need not. Recent measurements suggest that the matrix element of the strange axial-vector current in the proton is ⌬sϭϪ0.12Ϯ0.04 ͓2͔. In addition, one would like to know what fraction of the nucleon spin is carried by the quarks themselves, which is equivalent to determining the matrix element of flavor-singlet axial-vector current in the proton ⌺. This is, of course, intimately related to the matrix element of the strange axial-vector current and present analysis suggests that ⌺ϭ0.2Ϯ0.1 ͓2͔, much smaller than the quark model estimate of ⌺ϳ0.58. There have been intense theoretical and experimental efforts to extract ⌬s and ⌺ to address the present ''spin crisis'' and such efforts continue ͑for recent reviews, see ͓3,4͔͒.A vital ingredient in the present determination of ⌺ and ⌬s is the matrix element of the j 5 ,8 ϭū␥ ␥ 5 uϩd␥ ␥ 5 d Ϫ2s␥ ␥ 5 s axial-vector current in the nucleon, which cannot be measured directly but must be inferred from the approximate SU͑3͒ symmetry observed in nature. The question of SU͑3͒ breaking in the matrix element of the j 5 ,8 current and its impact upon the extraction of ⌬s and ⌺ has been previously addressed ͓5-10͔. In ͓5,6͔ it was assumed that the breaking in the matrix elements of the axial-vector currents was proportional to the breaking in the octet baryon masses and in ͓7͔ a model of the SU͑3͒ breaking was employed. Studies in the Skyrme model ͓9͔ suggest that ⌺ is relatively insensitive to SU͑3͒ breaking while ⌬s sh...

Axial form factors of the octet baryons in a covariant quark model

“…Using the SU F (3) symmetry we can represent the baryon-meson interactions in terms of an SU (3) chiral perturbation theory Lagrangian parametrized by three quantities, namely, the Cabibbo angle (θ C ), and the antisymmetric F and the symmetric D couplings [6,7]. Some of those models may also be refereed to as the Cabibbo theory [6,56] or the heavy baryon chiral perturbation theory [7,[57][58][59][60].…”

“…In this case the transition currents are expressed in terms of the octet baryon states, or by the 3 × 3 baryon matrix and flavor-transition operators in the corresponding octet vector space [7,57,59,116].…”

“…The axial form factors of the octet baryons, including the nucleon, have been studied using constituent and chiral quark models [13,[25][26][27][28][29][30][31][32][33][34][35][36][37], based on the DysonSchwinger equations [38][39][40][41], models with meson cloud dressing [42][43][44][45][46][47][48][49][50][51][52][53][54], large-N C and chiral perturbation theory [5,[55][56][57][58][59][60][61][62][63][64][65] and QCD sum rules [66][67][68]. Recently, lattice QCD simulations for the nucleon became available for Q 2 = 0 [69][70][71]…”

Strange isosinglet versus octet scalar axial vector current

“…The effect of one-loop corrections on the suppression of the nucleon matrix element of the octet axial vector current has been considered in Ref. [10] within the framework of chiral perturbation theory. There, the strong dependence of the result on the nucleon -∆ mass splitting was revealed and the necessity for higher order corrections discussed.…”

Chiral extrapolation of strange matrix elements in the nucleon

“…Further, ongoing experiments are expected to map out the strange electric and magnetic form factors [3,[5][6][7] in the near future. For the determinations of m s N|ss|N and ∆s, an expansion about the SU(3) flavor symmetry limit, in which the u-, d-and s-quarks are degenerate, is used but, unfortunately, in the absence of further experimental inputs, higher order SU(3) symmetry breaking effects [8] can only be estimated with hadronic models or with the leading non-analytic contributions from kaon loops computed in three-flavor chiral perturbation theory (χPT). To accommodate the sometimes slower than expected convergence of the SU(3) expansion in the baryon sector, conservative error estimates inevitably lead to large uncertainties.…”