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Register a new userDirect CP violation and the $Delta I=1/2$ rule in $Ktopipi$ decay from the Standard Model
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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.
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We report the first lattice QCD calculation of the complex kaon decay amplitude $A_0$ with physical kinematics, using a $32^3times 64$ lattice volume and a single lattice spacing $a$, with $1/a= 1.3784(68)$ GeV. We find Re$(A_0) = 4.66(1.00)(1.26) times 10^{-7}$ GeV and Im$(A_0) = -1.90(1.23)(1.08) times 10^{-11}$ GeV, where the first error is statistical and the second systematic. The first value is in approximate agreement with the experimental result: Re$(A_0) = 3.3201(18) times 10^{-7}$ GeV while the second can be used to compute the direct CP violating ratio Re$(varepsilon/varepsilon)=1.38(5.15)(4.59)times 10^{-4}$, which is $2.1sigma$ below the experimental value $16.6(2.3)times 10^{-4}$. The real part of $A_0$ is CP conserving and serves as a test of our method while the result for Re$(varepsilon/varepsilon)$ provides a new test of the standard-model theory of CP violation, one which can be made more accurate with increasing computer capability.
In this document we address an error discovered in the ensemble generation for our calculation of the $I=0$ $Ktopipi$ amplitude (Phys. Rev. Lett. 115, 212001 (2015), arXiv:1505.07863) whereby the same random numbers were used for the two independent quark flavors, resulting in small but measurable correlations between gauge observables separated by 12 units in the y-direction. We conclude that the effects of this error are negligible compared to the overall errors on our calculation.
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.
I review the status of CP violation in the Standard Model from the combination of flavour constraints within the CKMfitter frequentist approach and I describe studies of New Physics restricted to the Delta F=2 sector to explain recent results on neutral-meson mixing. All results have been obtained using data available for the Winter 2012 conferences.
Using the worldline method, we derive an effective action of the bosonic sector of the Standard Model by integrating out the fermionic degrees of freedom. The CP violation stemming from the complex phase in the CKM matrix gives rise to CP-violating operators in the one-loop effective action in the next-to-leading order of a gradient expansion. We calculate the prefactor of the appropriate operators and give general estimates of CP violation in the bosonic sector of the Standard Model. In particular, we show that the effective CP violation for weak gauge fields is not suppressed by the Yukawa couplings of the light quarks and is much larger than the bound given by the Jarlskog determinant.
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