The strange quark content of the nucleon N |ss|N is calculated in dynamical lattice QCD employing the overlap fermion formulation. For this quantity, exact chiral symmetry guaranteed by the Ginsparg-Wilson relation is crucial to avoid large contamination due to a possible operator mixing withūu +dd. Gauge configurations are generated with two dynamical flavors on a 16 3 × 32 lattice at a lattice spacing a ≃ 0.12 fm. We directly calculate the relevant three-point function on the lattice including a disconnected strange quark loop utilizing the techniques of the all-to-all quark propagator and low-mode averaging. Our result f Ts = m s N |ss|N /M N = 0.032(8) stat (22) sys , where m s and M N are strange quark and nucleon masses, is in good agreement with our previous indirect estimate using the Feynman-Hellmann theorem.
We calculate the strange quark content of the nucleon hNj" ssjNi in 2 þ 1 -flavor lattice QCD. Chirally symmetric overlap fermion formulation is used to avoid the contamination from up and down quark contents due to an operator mixing between strange and light scalar operators, " ss and " uu þ " dd. At a lattice spacing a ¼ 0:112ð1Þ fm, we perform calculations at four values of degenerate up and down quark masses m ud , which cover a range of the pion mass M ' 300-540 MeV. We employ two different methods to calculate hNj" ssjNi. One is a direct method where we calculate hNj" ssjNi by directly inserting the " ss operator. The other is an indirect method where hNj" ssjNi is extracted from a derivative of the nucleon mass in terms of the strange quark mass. With these two methods we obtain consistent results for hNj" ssjNi with each other. Our best estimate f T s ¼ m s hNj" ssjNi=M N ¼ 0:009ð15Þ stat ð16Þ sys is in good agreement with our previous studies in two-flavor QCD.
We calculate the strange quark content of the nucleon N|ss|N directly from its disconnected three-point function in N f = 2 + 1 QCD. Chiral symmetry is crucial to avoid a possibly large contamination due to operator mixing, and is exactly preserved by employing the overlap quark action. We also use the all-to-all quark propagator and the low-mode averaging technique in order to accurately calculate the relevant nucleon correlator. Our preliminary result extrapolated to the physical point is f T s = m s N|ss|N /M N = 0.013(12)(16), where m s and M N are the masses of strange quark and nucleon. This is in good agreement with our previous estimate in N f = 2 QCD as well as those from our indirect calculations using the Feynman-Hellmann theorem.
Numerical simulation of the low-energy dynamics of quarks and gluons is now feasible based on the fundamental theory of strong interaction, i.e. quantum chromodynamics (QCD). With QCD formulated on a 4D hypercubic lattice (called lattice QCD or LQCD), one can simulate the QCD vacuum and hadronic excitations on the vacuum using teraflop-scale supercomputers, which have become available in the last decade. A great deal of work has been done on this subject by many groups around the world; in this article we summarize the work done by the JLQCD and TWQCD collaborations since 2006. These collaborations employ Neuberger's overlap fermion formulation, which preserves the exact chiral and flavor symmetries on the lattice, unlike other lattice fermion formulations. Because of this beautiful property, numerical simulation of the formulation can address fundamental questions on the QCD vacuum, such as the microscopic structure of the quark-antiquark condensate in the chirally broken phase of QCD and its relation to SU(3) gauge field topology. Tests of the chiral effective theory, which is based on the assumption that the chiral symmetry is spontaneously broken in the QCD vacuum, can be performed, including the pion-loop effect test. For many other phenomenological applications, we adopt the all-to-all quark propagator technique, which allows us to compute various correlation functions without substantial extra cost. The benefit of this is not only that the statistical signal is improved but that disconnected quark-loop diagrams can be calculated. Using this method combined with the overlap fermion formulation, we study a wide range of physical quantities that are of both theoretical and phenomenological interest.
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