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# S-wave pi-K scattering length from lattice QCD

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### Abstract

The $$S$$-wave $$\pi K$$ scattering lengths are calculated for both the isospin 1/2 and 3/2 channels in the lattice QCD by using the finite size formula. We perform the calculation with $$N_f=2+1$$ gauge configurations generated on $$32^3 \times 64$$ lattice using the Iwasaki gauge action and nonperturbatively $$O(a)$$-improved Wilson action at $$1/a = 2.17$$ GeV. The quark masses correspond to $$m_\pi = 0.30 - 0.70$$ GeV. For $$I=1/2$$, to separate the contamination from excited states, we construct a $$2 \times 2$$ matrix of the time correlation function and diagonalize it. Here, we adopt the two kinds of operators, $$\bar{s}u$$ and $$\pi K$$. It is found that the signs of the scattering lengths are in agreement with experiment, namely attraction in $$I=1/2$$ and repulsion in $$I=3/2$$. We investigate the quark-mass dependence of the scattering lengths and also discuss the limitation of chiral perturbation theory.

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###### Journal
2009-11-01
0911.0228