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Register a new user$K_L-K_S$ mass difference from lattice QCD
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We report on the first complete calculation of the $K_L-K_S$ mass difference, $Delta M_K$, using lattice QCD. The calculation is performed on a 2+1 flavor, domain wall fermion ensemble with a 330MeV pion mass and a 575 MeV kaon mass. We use a quenched charm quark with a 949 MeV mass to implement Glashow-Iliopoulos-Maiani cancellation. For these heavier-than-physical particle masses, we obtain $Delta M_K =3.19(41)(96)times 10^{-12}$ 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.
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We develop and demonstrate techniques needed to compute the long distance contribution to the $K_{L}$-$K_{S}$ mass difference, $Delta M_K$, in lattice QCD and carry out a first, exploratory calculation of this fundamental quantity. The calculation is performed on 2+1 flavor, domain wall fermion, $16^3times32$ configurations with a 421 MeV pion mass and an inverse lattice spacing $1/a=1.73$ GeV. We include only current-current operators and drop all disconnected and double penguin 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 GIM mechanism by introducing a valence charm quark. The inclusion of the charm quark makes the complete calculation accessible to lattice methods provided the discretization errors associated with the charm quark can be controlled. The long distance effects are discussed for each parity channel separately. While we can see a clear signal in the parity odd channel, the signal to noise ratio in the parity even channel is exponentially decreasing as the separation between the two weak operators increases. We obtain a mass difference $Delta M_K$ which ranges from $6.58(30)times 10^{-12}$ MeV to $11.89(81)times 10^{-12}$ MeV for kaon masses varying from 563 MeV to 839 MeV. Extensions of these methods are proposed which promise accurate results for both $Delta M_K$ and $epsilon_K$, including long distance effects.
In this work, we used a $32^3 times 64 times 32$, 2+1 flavor domain wall lattice with Iwasaki+DSDR gauge action. The pion mass is 171 MeV and the kaon mass is 492 MeV. We implement the Glashow-Iliopoulos-Maiani (GIM) cancellation using charm quark masses of 750 MeV and 592 MeV. This is an intermediate calculation, in that we are using both a coarse lattice spacing (1/a = 1.37GeV) so we expect significant discretization error coming from charm quark mass and we are also using unphysical kinematics for the pion. The main purpose of this calculation is to study the contribution from the two-pion intermediate state when the energy of a two-pion state is lower than that of the kaon, as well as the corresponding finite volume correction to the $Delta M_K$.
The real and imaginary parts of the $K_L-K_S$ mixing matrix receive contributions from all three charge-2/3 quarks: up, charm and top. These give both short- and long-distance contributions which are accessible through a combination of perturbative and lattice methods. We will discuss a strategy to compute both the mass difference, $Delta M_K$ and $epsilon_K$ to sub-percent accuracy, looking in detail at the contributions from each of the three CKM matrix element products $V_{id}^*V_{is}$ for $i=u, c$ and $t$ as described in Ref. [1]
The RBC and UKQCD collaborations have recently proposed a procedure for computing the K_L-K_S mass difference. A necessary ingredient of this procedure is the calculation of the (non-exponential) finite-volume corrections relating the results obtained on a finite lattice to the physical values. This requires a significant extension of the techniques which were used to obtain the Lellouch-Luscher factor, which contains the finite-volume corrections in the evaluation of non-leptonic kaon decay amplitudes. We review the status of our study of this issue and, although a complete proof is still being developed, suggest the form of these corrections for general volumes and a strategy for taking the infinite-volume limit. The general result reduces to the known corrections in the special case when the volume is tuned so that there is a two-pion state degenerate with the kaon.
We present a new method to evaluate with high precision isospin breaking effects due to the small mass difference between the up and down quarks using lattice QCD. Our proposal is applicable in principle to any hadronic observable which can be computed on the lattice. It is based on the expansion of the path-integral in powers of the small parameter md-mu. In this paper, we apply this method to compute the leading isospin breaking effects for several physical quantities of interest: the kaon meson masses, the kaon decay constant, the form factors of semileptonic Kl3 decays and the neutron-proton mass splitting.
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