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Register a new userEmerging understanding of the Delta I = 1/2 Rule from Lattice QCD
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There has been much speculation as to the origin of the Delta I = 1/2 rule (Re A_0/Re A_2 simeq 22.5). We find that the two dominant contributions to the Delta I=3/2, K to pi pi{} correlation functions have opposite signs leading to a significant cancellation. This partial cancellation occurs in our computation of Re A_2 with physical quark masses and kinematics (where we reproduce the experimental value of A_2) and also for heavier pions at threshold. For Re A_0, although we do not have results at physical kinematics, we do have results for pions at zero-momentum with m_pi{} simeq 420 MeV (Re A_0/Re A_2=9.1(2.1)) and m_pi{} simeq 330 MeV (Re A_0/Re A_2=12.0(1.7)). The contributions which partially cancel in Re A_2 are also the largest ones in Re A_0, but now they have the same sign and so enhance this amplitude. The emerging explanation of the Delta I=1/2 rule is a combination of the perturbative running to scales of O(2 GeV), a relative suppression of Re A_2 through the cancellation of the two dominant contributions and the corresponding enhancement of Re A_0. QCD and EWP penguin operators make only very small contributions at such scales.
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We present a lattice QCD calculation of the $Delta I=1/2$, $Ktopipi$ decay amplitude $A_0$ and $varepsilon$, the measure of direct CP-violation in $Ktopipi$ decay, improving our 2015 calculation of these quantities. Both calculations were performed with physical kinematics on a $32^3times 64$ lattice with an inverse lattice spacing of $a^{-1}=1.3784(68)$ GeV. However, the current calculation includes nearly four times the statistics and numerous technical improvements allowing us to more reliably isolate the $pipi$ ground-state and more accurately relate the lattice operators to those defined in the Standard Model. We find ${rm Re}(A_0)=2.99(0.32)(0.59)times 10^{-7}$ GeV and ${rm Im}(A_0)=-6.98(0.62)(1.44)times 10^{-11}$ GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result ${rm Re}(A_0)=3.3201(18)times 10^{-7}$ GeV. These results for $A_0$ can be combined with our earlier lattice calculation of $A_2$ to obtain ${rm Re}(varepsilon/varepsilon)=21.7(2.6)(6.2)(5.0) times 10^{-4}$, where the third error represents omitted isospin breaking effects, and Re$(A_0)$/Re$(A_2) = 19.9(2.3)(4.4)$. The first agrees well with the experimental result of ${rm Re}(varepsilon/varepsilon)=16.6(2.3)times 10^{-4}$. A comparison of the second with the observed ratio Re$(A_0)/$Re$(A_2) = 22.45(6)$, demonstrates the Standard Model origin of this $Delta I = 1/2$ rule enhancement.
We present the first chiral-continuum extrapolated up, down and strange quark spin contribution to the proton spin using lattice QCD. For the connected contributions, we use eleven ensembles of 2+1+1-flavor of Highly Improved Staggered Quarks (HISQ) generated by the MILC Collaboration. They cover four lattice spacings $a approx {0.15,0.12,0.09,0.06}$ fm and three pion masses, $M_pi approx {315,220,135}$ MeV, of which two are at the physical pion mass. The disconnected strange calculations are done on seven of these ensembles, covering the four lattice spacings but only one with the physical pion mass. The disconnected light quark calculation was done on six ensembles at two values of $M_pi approx {315,220}$ MeV. High-statistics estimates on each ensemble for all three quantities allow us to quantify systematic uncertainties and perform a simultaneous chiral-continuum extrapolation in the lattice spacing and the light-quark mass. Our final results are $Delta u equiv langle 1 rangle_{Delta u^+} = 0.777(25)(30)$, $Delta d equiv langle 1 rangle_{Delta d^+} = -0.438(18)(30)$, and $Delta s equiv langle 1 rangle_{Delta s^+} = -0.053(8)$, adding up to a total quark contribution to proton spin of $sum_{q=u,d,s} (frac{1}{2} Delta q) = 0.143(31)(36)$. The second error is the systematic uncertainty associated with the chiral-continuum extrapolation. These results are obtained without model assumptions and are in good agreement with the recent COMPASS analysis $0.13 < frac{1}{2} Delta Sigma < 0.18$, and with the $Delta q$ obtained from various global analyses of polarized beam or target data.
We present the first results for the Kl3 form factor from simulations with 2+1 flavours of dynamical domain wall quarks. Combining our result, namely f_+(0)=0.964(5), with the latest experimental results for Kl3 decays leads to |V_{us}|=0.2249(14), reducing the uncertaintity in this important parameter. For the O(p^6) term in the chiral expansion we obtain Delta f=-0.013(5).
We present the first result for the hyperon vector form factor f_1 for Xi^0 -> Sigma^+ l bar{nu} and Sigma^- -> n l bar{nu} semileptonic decays from fully dynamical lattice QCD. The calculations are carried out with gauge configurations generated by the RBC and UKQCD collaborations with (2+1)-flavors of dynamical domain-wall fermions and the Iwasaki gauge action at beta=2.13, corresponding to a cutoff 1/a=1.73 GeV. Our results, which are calculated at the lighter three sea quark masses (the lightest pion mass down to approximately 330 MeV), show that a sign of the second-order correction of SU(3) breaking on the hyperon vector coupling f_1(0) is negative. The tendency of the SU(3) breaking correction observed in this work disagrees with predictions of both the latest baryon chiral perturbation theory result and large N_c analysis.
The pi+pi+ s-wave scattering phase-shift is determined below the inelastic threshold using Lattice QCD. Calculations were performed at a pion mass of m_pi~390 MeV with an anisotropic n_f=2+1 clover fermion discretization in four lattice volumes, with spatial extent L~2.0, 2.5, 3.0 and 3.9 fm, and with a lattice spacing of b_s~0.123 fm in the spatial direction and b_t b_s/3.5 in the time direction. The phase-shift is determined from the energy-eigenvalues of pi+pi+ systems with both zero and non-zero total momentum in the lattice volume using Luschers method. Our calculations are precise enough to allow for a determination of the threshold scattering parameters, the scattering length a, the effective range r, and the shape-parameter P, in this channel and to examine the prediction of two-flavor chiral perturbation theory: m_pi^2 a r = 3+O(m_pi^2/Lambda_chi^2). Chiral perturbation theory is used, with the Lattice QCD results as input, to predict the scattering phase-shift (and threshold parameters) at the physical pion mass. Our results are consistent with determinations from the Roy equations and with the existing experimental phase shift data.
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