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Register a new userDetermination of the $A_2$ amplitude of $K rightarrow pipi$ decays
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We review the status of recent calculations by the RBC-UKQCD collaboration of the complex amplitude $A_2$, corresponding to the decay of a kaon to a two pion state with total isospin 2. In particular, we present preliminary results from two new ensembles: $48^3 times 96$ with $a^{-1}=1.73$ GeV and $64^3 times 128$ with $a^{-1}=2.3$ GeV, both at physical kinematics. Both ensembles were generated Iwasaki gauge action and domain wall fermion action with 2+1 flavours. These results, in comparison to our earlier ones on a $32^3$ DSDR lattice with $a^{-1}=1.36$ GeV, enable us to significantly reduce the discretization errors. The partial cancellation between the two dominant contractions contributing to Re($A_2$) has been confirmed and we believe that this cancellation is a major contribution to the $Delta I=1/2$ rule.
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We describe the computation of the amplitude A_2 for a kaon to decay into two pions with isospin I=2. The results presented in the letter Phys.Rev.Lett. 108 (2012) 141601 from an analysis of 63 gluon configurations are updated to 146 configurations giving Re$A_2=1.381(46)_{textrm{stat}}(258)_{textrm{syst}} 10^{-8}$ GeV and Im$A_2=-6.54(46)_{textrm{stat}}(120)_{textrm{syst}}10^{-13}$ GeV. Re$A_2$ is in good agreement with the experimental result, whereas the value of Im$A_2$ was hitherto unknown. We are also working towards a direct computation of the $Kto(pipi)_{I=0}$ amplitude $A_0$ but, within the standard model, our result for Im$A_2$ can be combined with the experimental results for Re$A_0$, Re$A_2$ and $epsilon^prime/epsilon$ to give Im$A_0/$Re$A_0= -1.61(28)times 10^{-4}$ . Our result for Im,$A_2$ implies that the electroweak penguin (EWP) contribution to $epsilon^prime/epsilon$ is Re$(epsilon^prime/epsilon)_{mathrm{EWP}} = -(6.25 pm 0.44_{textrm{stat}} pm 1.19_{textrm{syst}}) times 10^{-4}$.
We present new results for the amplitude $A_2$ for a kaon to decay into two pions with isospin $I=2$: Re$A_2 = 1.50(4)_mathrm{stat}(14)_mathrm{syst}times 10^{-8}$ GeV; Im$A_2 = -6.99(20)_mathrm{stat}(84)_mathrm{syst}times 10^{-13}$ GeV. These results were obtained from two ensembles generated at physical quark masses (in the isospin limit) with inverse lattice spacings $a^{-1}=1.728(4)$ GeV and $2.358(7)$ GeV. We are therefore able to perform a continuum extrapolation and hence largely to remove the dominant systematic uncertainty from our earlier results, that due to lattice artefacts. The only previous lattice computation of $Ktopipi$ decays at physical kinematics was performed using an ensemble at a single, rather coarse, value of the lattice spacing ($a^{-1}simeq 1.37(1)$ GeV). We confirm the observation that there is a significant cancellation between the two dominant contributions to Re$A_2$ which we suggest is an important ingredient in understanding the $Delta I=1/2$ rule, Re$A_0$/Re$A_2simeq 22.5$, where the subscript denotes the total isospin of the two-pion final state. Our result for $A_2$ implies that the electroweak penguin contribution to $epsilon^prime/epsilon$ is Re($epsilon^prime/epsilon)_textrm{EWP}=-(6.6pm 1.0)times 10^{-4}$.
The Dalitz plot distribution of $B^0 rightarrow bar{D}^0 K^+ pi^-$ decays is studied using a data sample corresponding to $3.0rm{fb}^{-1}$ of $pp$ collision data recorded by the LHCb experiment during 2011 and 2012. The data are described by an amplitude model that contains contributions from intermediate $K^*(892)^0$, $K^*(1410)^0$, $K^*_2(1430)^0$ and $D^*_2(2460)^-$ resonances. The model also contains components to describe broad structures, including the $K^*_0(1430)^0$ and $D^*_0(2400)^-$ resonances, in the $Kpi$ S-wave and the $Dpi$ S- and P-waves. The masses and widths of the $D^*_0(2400)^-$ and $D^*_2(2460)^-$ resonances are measured, as are the complex amplitudes and fit fractions for all components included in the amplitude model. The model obtained will be an integral part of a future determination of the angle $gamma$ of the CKM quark mixing matrix using $B^0 rightarrow D K^+ pi^-$ decays.
The first untagged decay-time-integrated amplitude analysis of $B^{0}_{s} rightarrow K^{0}_{textrm{S}} K^{pm}pi^{mp}$ decays is performed using a sample corresponding to $3.0,$fb$^{-1}$ of $pp$ collision data recorded with the LHCb detector during 2011 and 2012. The data are described with an amplitude model that contains contributions from the intermediate resonances $K^{*}(892)^{0,+}$, $K^*_2(1430)^{0,+}$ and $K^*_0(1430)^{0,+}$, and their charge conjugates. Measurements of the branching fractions of the decay modes $B^{0}_{s} rightarrow K^{*}(892)^{pm}K^{mp}$ and $B^{0}_{s} rightarrow K^{*}(892)^{0}kern 0.2emoverline{kern -0.2em K}{}^{0}, kern 0.2emoverline{kern -0.2em K}{}^{*}(892)^{0}K^{0}$ are in agreement with, and more precise than, previous results. The decays $B^{0}_{s} rightarrow K^*_0(1430)^{pm} K^{mp}$ and $B^{0}_{s} rightarrow K^{*}_{0}(1430)^{0}kern 0.2emoverline{kern -0.2em K}{}^{0}, kern 0.2emoverline{kern -0.2em K}{}^{*}_{0}(1430)^{0}K^{0}$ are observed for the first time, each with significance over 10 standard deviations.
A search for $CP$ violation in the Cabibbo-suppressed $D^0 rightarrow K^+ K^- pi^+ pi^-$ decay mode is performed using an amplitude analysis. The measurement uses a sample of $pp$ collisions recorded by the LHCb experiment during 2011 and 2012, corresponding to an integrated luminosity of 3.0 fb$^{-1}$. The $D^0$ mesons are reconstructed from semileptonic $b$-hadron decays into $D^0mu^- X$ final states. The selected sample contains more than 160000 signal decays, allowing the most precise amplitude modelling of this $D^0$ decay to date. The obtained amplitude model is used to perform the search for $CP$ violation. The result is compatible with $CP$ symmetry, with a sensitivity ranging from 1% to 15% depending on the amplitude considered.
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