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Register a new userSU(3) breaking effects in hyperon beta decay from lattice QCD
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Shoichi Sasaki
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We present results of an exploratory study of flavor SU(3) breaking effects in hyperon beta decays using domain wall fermions. From phenomenological point of view, the significance of this subject is twofold: (1) to extract the element $V_{us}$ of the Cabibbo-Kabayashi-Maskawa mixing matrix from the $Delta S=1$ decay process, and (2) to provide vital information to analysis of the strange quark fraction of the proton spin with the polarized deep inelastic scattering data. In this study, we explore the $Xi^0 to Sigma^+$ beta decay, which is highly sensitive to the SU(3) breaking since this decay corresponds to the direct analogue of neutron beta decay under an exchange between the down quark and the strange quark. We expose the SU(3) breaking effect on $g_A/g_V=g_1(0)/f_1(0)$ up to the first order in breaking. The second-class form factors $g_2$ and $f_3$, of which non-zero values are the direct signals of the SU(3) breaking effect, are also measured. Finally, we estimate $f_1(0)$ up to the second-order correction and then evaluate $|V_{us}|$ combined with the KTeV experiment.
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We present a quenched lattice calculation of all six form factors: vector [f_1(q^2)], weak magnetism [f_2(q^2)], induced scalar [f_3(q^2)], axial-vector [g_1(q^2)], weak electricity [g_2(q^2)] and induce pseudoscalar [g_3(q^2)] form factors in hyperon semileptonic decay Xi^0 -> Sigma^{+} l nu using domain wall fermions. The q^2 dependences of all form factors in the relatively low q^2 region are examined in order to evaluate their values at zero momentum transfer. The Xi^0 -> Sigma^+ transition is highly sensitive to flavor SU(3) breaking since this decay corresponds to the direct analogue of neutron beta decay under the exchange of the down quark with the strange quark. The pattern of flavor SU(3) breaking effects in the hyperon beta decay is easily exposed in a comparison to results for neutron beta decay. We measure SU(3)-breaking corrections to f_1(0), f_2(0)/f_1(0) and g_1(0)/f_1(0). A sign of the leading order corrections, of which the size is less than a few %, on f_1(0) is likely negative, while f_2(0)/f_1(0) and g_1(0)/f_1(0) receive positive corrections of order 16% and 5% respectively. The observed patterns of the deviation from the values in the exact SU(3) limit does not support some of model estimates. We show that there are nonzero second-class form factors in the Xi^0 -> Sigma^+ decay, measuring f_3(0)/f_1(0)=0.14(10) and g_2(0)/g_1(0)=0.68(18), which are comparable to the size of first-order SU(3) breaking. It is also found that the SU(3) breaking effect on g_3(0)/g_1(0) agree with the prediction of the generalized pion-pole dominance.
To check the dual superconductor picture for the quark-confinement mechanism, we evaluate monopole dominance as well as Abelian dominance of quark confinement for both quark-antiquark and three-quark systems in SU(3) quenched lattice QCD in the maximally Abelian (MA) gauge. First, we examine Abelian dominance for the static $Qbar Q$ system in lattice QCD with various spacing $a$ at $beta$=5.8-6.4 and various size $L^3$x$L_t$. For large physical-volume lattices with $La ge$ 2fm, we find perfect Abelian dominance of the string tension for the $Qbar Q$ systems: $sigma_{Abel} simeq sigma$. Second, we accurately measure the static 3Q potential for more than 300 different patterns of 3Q systems with 1000-2000 gauge configurations using two large physical-volume lattices: ($beta$,$L^3$x$L_t$)=(5.8,$16^3$x32) and (6.0,$20^3$x32). For all the distances, the static 3Q potential is found to be well described by the Y-Ansatz: two-body Coulomb term plus three-body Y-type linear term $sigma L_{min}$, where $L_{min}$ is the minimum flux-tube length connecting the three quarks. We find perfect Abelian dominance of the string tension also for the 3Q systems: $sigma^{Abel}_{3Q}simeq sigma_{3Q} simeq sigma$. Finally, we accurately investigate monopole dominance in SU(3) lattice QCD at $beta$=5.8 on $16^3$x32 with 2,000 gauge configurations. Abelian-projected QCD in the MA gauge has not only the color-electric current $j^mu$ but also the color-magnetic monopole current $k^mu$, which topologically appears. By the Hodge decomposition, the Abelian-projected QCD system can be divided into the monopole part ($k_mu e 0$, $j_mu=0$) and the photon part ($j_mu e 0$, $k_mu=0$). We find monopole dominance of the string tension for $Qbar Q$ and 3Q systems: $sigma_{Mo}simeq 0.92sigma$. While the photon part has almost no confining force, the monopole part almost keeps the confining force.
We present the first calculation within lattice QCD of excited light meson resonances with $J^{PC} = 1^{--}$, $2^{--}$ and $3^{--}$. Working with an exact SU(3) flavor symmetry, for the singlet representation of pseudoscalar-vector scattering, we find two $1^{--}$ resonances, a lighter broad state and a heavier narrow state, a broad $2^{--}$ resonance decaying in both $P$- and $F$-waves, and a narrow $3^{--}$ state. We present connections to experimental $omega^star_J, phi^star_J$ resonances decaying into $pi rho$, $Kbar{K}^*$, $eta omega$ and other final states.
We present the first result for the hyperon vector form factor f_1 for Xi^0 -> Sigma^+ l bar{nu} and Sigma^- -> n l bar{nu} semileptonic decays from fully dynamical lattice QCD. The calculations are carried out with gauge configurations generated by the RBC and UKQCD collaborations with (2+1)-flavors of dynamical domain-wall fermions and the Iwasaki gauge action at beta=2.13, corresponding to a cutoff 1/a=1.73 GeV. Our results, which are calculated at the lighter three sea quark masses (the lightest pion mass down to approximately 330 MeV), show that a sign of the second-order correction of SU(3) breaking on the hyperon vector coupling f_1(0) is negative. The tendency of the SU(3) breaking correction observed in this work disagrees with predictions of both the latest baryon chiral perturbation theory result and large N_c analysis.
We calculate $pXi^0$ potentials from the equal-time Bethe-Salpeter amplitude measured in the quenched QCD simulation with the spatial lattice volume, (4.4 fm)$^3$. The standard Wilson gauge action with the gauge coupling $beta=5.7$ on $32^4$ lattice together with the standard Wilson quark action are used. The hopping parameter $kappa_{ud}=0.1678$ is chosen for $u$ and $d$ quarks, which corresponds to $m_{pi}simeq 0.37$ GeV. The physical strange quark mass is used by taking the parameter $kappa_s=0.1643$ which is deduced from the physical $K$ meson mass. The lattice spacing $a=0.1420$ fm is determined by the physical $rho$ meson mass. We find that the $pXi^0$ potential has strong spin dependence. Strong repulsive core is found in $^1S_0$ channel while the effective central potential in the $^3S_1$ channel has relatively weak repulsive core. The potentials also have weak attractive parts in the medium to long distance region (0.6 fm $lsim r lsim 1.2$ fm) in both of the $^1S_0$ and $^3S_1$ channels.
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