Title: K_L-K_S mass difference from lattice QCD
Description: The K_L-K_S mass difference is a promising quantity to reveal new phenomena which lie outside the standard model. A state-of-art perturbation theory calculation has be en performed at next-to-next-to-leading order (NNLO) and a 40% error is quoted in the final result. We develop and demonstrate non-perturbative techniques needed to calculate the K_L-K_S mass difference, ΔM_K, in lattice QCD and carry out exploratory calculations. The calculations are performed on a 2+1 flavor, domain wall fermion, 16³ x 32 ensemble with a 421 Mev pion and a 24³ x 64 lattice ensemble with a 329 MeV pion. In the $16^3$ lattice calculation, we drop the double penguin diagrams and the disconnected diagrams. The short distance part of the mass difference in a 2+1 flavor calculation contains a quadratic divergence cut off by the lattice spacing. Here, this quadratic divergence is eliminated through the Glashow-Iliopoulos-Maiani (GIM) mechanism by introducing a quenched charm quark. We obtain a mass difference ΔM_K which ranges from 6.58(30) x 10⁻¹² MeV to 11.89(81) x 10⁻¹² MeV for kaon masses varying from 563 MeV to 839 MeV.

On the 24³ lattice, we include all the diagrams and perform a full calculation. Our result is for a case of unphysical kinematics with pion, kaon and charmed quark masses of 330, 575 and 949 MeV respectively. We obtain ΔM_K=3.19(41)(96) x 10⁻¹² MeV, quite similar to the experimental value. Here the first error is statistical and the second is an estimate of the systematic discretization error. An interesting aspect of this calculation is the importance of the disconnected diagrams, a dramatic failure of the OZI rule.