<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>K</mml:mi></mml:math>to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mi>π</mml:mi></mml:math>decay amplitudes from lattice QCD

Blum, Thomas; Boyle, Peter; Christ, Norman H.; Garrón, Nicolas; Goode, Elaine; Izubuchi, Taku; Lehner, Christoph; Liu, Q.; Mawhinney, Robert D.; Sachrajda, Christopher; Soni, Amarjit; Sturm, Christian; Yin, H.; Zhou, R.

doi:10.1103/physrevd.84.114503

Cited by 67 publications

(93 citation statements)

References 29 publications

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“…Instead more sophisticated boundary conditions, mixing quarks and anti-quarks and an isospin rotation, (G-parity boundary conditions) [14], must be used for both the valence and the sea quarks. Exploratory studies [7] suggest that obtaining adequate statistics will be practical with the next generation of machines which will become available to our collaboration within the next few months.…”

Section: Discussionmentioning

confidence: 99%

“…For A 0 however, the two pions have vacuum quantum numbers and the correlation functions are dominated by the vacuum intermediate state. We report on our exploratory work in developing techniques for the efficient subtraction of the vacuum contributions in [7] and look forward to presenting results of a realistic computation of A 0 in the future.…”

Section: Introductionmentioning

confidence: 99%

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K→(ππ)I=2Decay Amplitude from Lattice QCD

Boyle²,

et al. 2012

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We report on the first realistic ab initio calculation of a hadronic weak decay, that of the amplitude A2 for a kaon to decay into two π-mesons with isospin 2. We find Re A2 = (1.436 ± 0.063 stat ± 0.258 syst ) 10 −8 GeV in good agreement with the experimental result and for the hitherto unknown imaginary part we find Im A2 = −(6.83±0.51 stat ±1.30 syst ) 10 −13 GeV. Moreover combining our result for Im A2 with experimental values of Re A2, Re A0 and ǫ ′ /ǫ, we obtain the following value for the unknown ratio Im A0/Re A0 within the Standard Model: Im A0/Re A0 = −1.63(19)stat(20)syst × 10 −4 . One consequence of these results is that the contribution from Im A2 to the direct CP violation parameter ǫ ′ (the so-called Electroweak Penguin, EWP, contribution) is Re(ǫ ′ /ǫ)EWP = −(6.52 ± 0.49 stat ± 1.24 syst ) × 10 −4 . We explain why this calculation of A2 represents a major milestone for lattice QCD and discuss the exciting prospects for a full quantitative understanding of CP-violation in kaon decays.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

K→(ππ)I=2Decay Amplitude from Lattice QCD

Boyle²,

et al. 2012

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“…While the combinations ± p effectively eliminate the error from this contribution, the light-bylight contribution is identical, so the statistical error is only reduced by averaging over independent momenta or the γ µ inserted at the external vertex. Early preliminary work [19] was done on another DWF+Iwasaki ensemble with size 16 3 × 32 and light quark mass m q = 0.01 (m π = 422 MeV). Two muon masses, m µ = 0.4 and 0.1, were used.…”

Section: Qcd Contributionmentioning

confidence: 99%

Hadronic Light-by-Light Scattering Contribution to the Muon Anomalous Magnetic Moment from Lattice QCD

et al. 2015

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The form factor that yields the light-by-light scattering contribution to the muon anomalous magnetic moment is computed in lattice QCD+QED and QED. A non-perturbative treatment of QED is used and is checked against perturbation theory. The hadronic contribution is calculated for unphysical quark and muon masses, and only the diagram with a single quark loop is computed. Statistically significant signals are obtained. Initial results appear promising, and the prospect for a complete calculation with physical masses and controlled errors is discussed.

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“…(5.190) holds for the other endcap 192) while for the correlator sum we obtain 193) where 196) After some algebra, we obtain a relatively simple form 197) where 198) and , which are symmetric under particle interchange.…”

Section: Two-to-two Insertions: Any Number Of Switchesmentioning

confidence: 99%

“…See Refs. [193,194,195,88] for recent examples of the implementation of this formalism on LQCD calculations of the K → ππ decay amplitude. 4 .…”

Section: One-to-two Transition Matrix Elementsmentioning

confidence: 99%

Multi-Hadron Observables from Lattice Quantum Chromodynamics

Hansen¹

2014

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Multi-Hadron Observables from Lattice Quantum Chromodynamics Maxwell T. HansenChair of the Supervisory Committee:Professor Stephen R. Sharpe Department of PhysicsWe describe formal work that relates the finite-volume spectrum in a quantum field theory to scattering and decay amplitudes. This is of particular relevance to numerical calculations performed using Lattice Quantum Chromodynamics (LQCD). Correlators calculated using LQCD can only be determined on the Euclidean time axis. For this reason the standard method of determining scattering amplitudes via the Lehmann-Symanzik-Zimmermann reduction formula cannot be employed. By contrast, the finite-volume spectrum is directly accessible in LQCD calculations. Formalism for relating the spectrum to physical scattering observables is thus highly desirable.In this thesis we develop tools for extracting physical information from LQCD for four types of observables. First we analyze systems with multiple, strongly-coupled two-scalar channels. Here we accommodate both identical and nonidentical scalars, and in the latter case allow for degenerate as well as nondegenerate particle masses. Using relativistic field theory, and summing to all orders in perturbation theory, we derive a result relating the finite-volume spectrum to the two-to-two scattering amplitudes of the coupled-channel theory. This generalizes the formalism of Martin Lüscher for the case of single-channel scattering. Second we consider the weak decay of a single particle into multiple, coupled two-scalar channels. We show how the finite-volume matrix element extracted in LQCD is related to matrix elements of asymptotic two-particle states, and thus to decay amplitudes. This generalizes work by Laurent Lellouch and Martin Lüscher. Third we extend the method for extracting matrix elements by considering currents which insert energy, momentum and angular momentum. This allows one to extract transition matrix elements and form factors from LQCD. Finally we look beyond two-particle systems to those with three-particles in asymptotic states. Working again to all orders in relativistic field theory, we derive a relation between the spectrum and an infinite-volume three-to-three scattering quantity. This final analysis is the most complicated of the four, because the all-orders summation is more difficult for this system, and also because a number of new technical issues arise in analyzing the contributing diagrams.

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Ktoππdecay amplitudes from lattice QCD

Cited by 67 publications

References 29 publications

K→(ππ)I=2Decay Amplitude from Lattice QCD

K→(ππ)I=2Decay Amplitude from Lattice QCD

Hadronic Light-by-Light Scattering Contribution to the Muon Anomalous Magnetic Moment from Lattice QCD

Multi-Hadron Observables from Lattice Quantum Chromodynamics

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