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Register a new userStandard-model prediction for direct CP violation in $Ktopipi$ decay
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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.
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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.
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.
Techniques for performing model-independent searches for direct CP violation in three and four-body decays are discussed. Comments on the performance and the optimisation of a binned chisquare approach and an unbinned approach, known as the energy test, are made. The use of the energy test in the presence of background is also studied. The selection and treatment of the coordinates used to describe the phase-space of the decay are discussed. The conventional model-independent techniques, which test for P-even CP violation, are modified to create a new approach for testing for P-odd CP violation. An implementation of the energy test using GPUs is described.
We study a mechanism that generates the baryon asymmetry of the Universe during a tachyonic electroweak phase transition. We utilize as sole source of CP violation an operator that was recently obtained from the Standard Model by integrating out the quarks.
Using large scale real-time lattice simulations, we calculate the baryon asymmetry generated at a fast, cold electroweak symmetry breaking transition. CP-violation is provided by the leading effective bosonic term resulting from integrating out the fermions in the Minimal Standard Model at zero temperature, and performing a covariant gradient expansion [1]. This is an extension of the work presented in [2]. The numerical implementation is described in detail, and we address issues specifically related to using this CP-violating term in the context of Cold Electroweak Baryogenesis. The results support the conclusion of [2], that Standard Model CP-violation may be able to reproduce the observed baryon asymmetry in the Universe in the context of Cold Electroweak Baryogenesis.
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