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تسجيل مستخدم جديدCalculation of $K to pipi$ decay amplitudes with improved Wilson fermion
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We present results of our trial calculation of the $K to pipi$ decay amplitudes with the improved Wilson fermion action. Calculations are carried out with $N_f=2+1$ gauge configurations generated with the Iwasaki gauge action and non-perturbatively $O(a)$-improved Wilson fermion action at $a=0.091,{rm fm}$, $m_pi=280,{rm MeV}$ and $m_K=560,{rm MeV} (sim 2 m_pi)$ on a $32^3times 64$ ($La=2.9 {rm fm}$) lattice.
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We present our result for the $Ktopipi$ decay amplitudes for both the $Delta I=1/2$ and $3/2$ processes with the improved Wilson fermion action. Expanding on the earlier works by Bernard {it et al.} and by Donini {it et al.}, we show that mixings wit
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We present results for the $Ktopipi$ decay amplitudes for both the $Delta I=1/2$ and $3/2$ channels. This calculation is carried out on 480 gauge configurations in $N_f=2+1$ QCD generated over 12,000 trajectories with the Iwasaki gauge action and non
-perturbatively $O(a)$-improved Wilson fermion action at $a=0.091,{rm fm}$, $m_pi=280,{rm MeV}$ and $m_K=580,{rm MeV}$ on a $32^3times 64$ ($La=2.9,{rm fm}$) lattice. For the quark loops in the Penguin and disconnected contributions in the $I=0$ channel, the combined hopping parameter expansion and truncated solver techniques work very well for variance reduction. We obtain, for the first time with a Wilson-type fermion action, that ${rm Re}A_0 = 60(36) times10^{ -8},{rm GeV}$ and ${rm Im}A_0 =-67(56) times10^{-12},{rm GeV}$ for a matching scale $q^* =1/a$. The dependence on the matching scale is weak.
We present our result for the $Ktopipi$ decay amplitudes for both the $Delta I=1/2$ and $3/2$ processes with the improved Wilson fermion action. In order to realize the physical kinematics, where the pions in the final state have finite momenta, we c
onsider the decay process $K({bf p}) to pi({bf p}) + pi({bf 0})$ in the nonzero momentum frame with momentum ${bf p}=(0,0,2pi/L)$ on the lattice. Our calculations are carried out with $N_f=2+1$ gauge configurations generated with the Iwasaki gauge action and nonperturbatively $O(a)$-improved Wilson fermion action at $a=0.091,{rm fm}$ ($1/a=2.176,{rm GeV}$), $m_pi=260,{rm MeV}$, and $m_K=570,{rm MeV}$ on a $48^3times 64$ ($La=4.4,{rm fm}$) lattice. For these parameters the energy of the $K$ meson is set at that of two-pion in the final state. We obtain ${rm Re}A_2 = 2.431(19) times10^{ -8},{rm GeV}$, ${rm Re}A_0 = 51(28) times10^{ -8},{rm GeV}$, and $epsilon/epsilon = 1.9(5.7) times10^{-3}$ for a matching scale $q^* =1/a$ where the errors are statistical. The dependence on the matching scale $q^*$ of these values is weak. The systematic error arising from the renormalization factors is expected to be around $1.3%$ for ${rm Re}A_2$ and $11 %$ for ${rm Re}A_0$. Prospects toward calculations with the physical quark mass are discussed.
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