Emerging Understanding of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Δ</mml:mi><mml:mi>I</mml:mi><mml:mo mathvariant="bold">=</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:math>Rule from Lattice QCD

Boyle, P.A.; Christ, Norman H.; Garrón, Nicolas; Goode, Elaine; Janowski, T.; Lehner, Christoph; Liu, Q.; Lytle, Andrew; Sachrajda, C.T.; Soni, Amarjit; Zhang, D.

doi:10.1103/physrevlett.110.152001

Cited by 73 publications

(84 citation statements)

References 18 publications

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“…The only previous lattice computation of K → ππ decays at physical kinematics was performed using an ensemble at a single, rather coarse, value of the lattice spacing [a −1 ≃ 1.37(1) GeV]. We confirm the observation reported in [3] that there is a significant cancellation between the two dominant contributions to ReA 2 which we suggest is an important ingredient in understanding the ∆I = 1/2 rule, ReA 0 /ReA 2 ≃ 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 ǫ ′ /ǫ is Re(ǫ ′ /ǫ) EWP = −(6.6 ± 1.0) × 10 −4 .…”

supporting

confidence: 79%

“…A very interesting feature of our earlier calculation of A 2 was the observation that the two dominant contributions to Re A 2 show a significant numerical cancellation [3]. We argued in [3] that this cancellation is an important element in the explanation of the ∆I = 1/2 rule, ReA 0 /ReA 2 ≃ 22.5.…”

Section: (2)mentioning

confidence: 89%

“…We argued in [3] that this cancellation is an important element in the explanation of the ∆I = 1/2 rule, ReA 0 /ReA 2 ≃ 22.5. We confirm this cancellation in the present calculation.…”

Section: (2)mentioning

confidence: 99%

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K→ππΔI=3/2decay amplitude in the

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supporting

confidence: 79%

Section: (2)mentioning

confidence: 89%

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K→ππΔI=3/2decay amplitude in the

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“…8 A full-error-budget calculation is now being implemented by the RBC/UKQCD collaboration [88,89,90]. The methodology is fully in place, results for the I = 2 final state with a complete error budget are available [91], and complete results for the more challenging I = 0 final states should become available in the next few years.…”

Section: K → ππmentioning

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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ϵK and ϵ′/ϵ in a diquark model

Chen

Nomura²

2019

J. High Energ. Phys.

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Based on the calculations using the lattice QCD by the RBC-UKQCD collaboration and a large N c dual QCD, the resulting ϵ′/ϵ, which is less than the experimental data by more than a 2σ in the standard model (SM), suggests the necessity of a new physics effect. In order to complement the insufficient ϵ′/ϵ, we study the extension of the SM with a colored scalar in a diquark model. In addition to the pure diquark box diagrams, it is found that the box diagrams with one W-boson and one diquark, ignored in the literature, play an important role in the ΔS = 2 process. The mass difference between K L and K S in the diquark model is well below the current data, whereas the Kaon indirect CP violation ϵ K gives a strict constraint on the new parameters. Three mechanisms are classified in the study of ϵ′/ϵ. They include a tree-level diagram, QCD and electroweak (EW) penguins, and chromomagnetic operators (CMOs). Taking the Kobayashi-Maskawa phase as the unique CP source, we analyze each contribution of the three mechanisms in detail and conclude that with the exception of QCD and EW penguins, the tree and CMO effects can singly enhance ϵ′/ϵ to be of $$ \mathcal{O} $$ O (10−3), depending on the values of the free parameters, when the bound from ϵ K is satisfied.

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Emerging Understanding of theΔI=1/2Rule from Lattice QCD

Cited by 73 publications

References 18 publications

K→ππΔI=3/2decay amplitude in the

K→ππΔI=3/2decay amplitude in the

Multi-Hadron Observables from Lattice Quantum Chromodynamics

ϵK and ϵ′/ϵ in a diquark model

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