Lattice extraction of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mi>π</mml:mi><mml:mi>π</mml:mi></mml:math>amplitudes to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml

Laiho, Jack; Soni, Amarjit

doi:10.1103/physrevd.65.114020

Cited by 47 publications

(149 citation statements)

References 28 publications

(51 reference statements)

Supporting

Mentioning

146

Contrasting

Order By: Relevance

“…Other recent work for related observables has made use of the p-regime, with T ≫ L [51,52,53]. There have also been extensive NLO computations at infinite volume [54], which is a special limit of the p-regime. Note that if 1/F L ≪ 1 as our power-counting rules assume, and we consider an observable that is independent of the topological charge ν, then the ǫ and p-regimes should in principle be continuously connected to each other (cf.…”

Section: Further Remarksmentioning

confidence: 99%

Probing the chiral weak Hamiltonian at finite volumes

Hernández¹,

Laine²

2006

J. High Energy Phys.

View full text Add to dashboard Cite

Non-leptonic kaon decays are often described through an effective chiral weak Hamiltonian, whose couplings ("low-energy constants") encode all non-perturbative QCD physics. It has recently been suggested that these low-energy constants could be determined at finite volumes by matching the non-perturbatively measured three-point correlation functions between the weak Hamiltonian and two left-handed flavour currents, to analytic predictions following from chiral perturbation theory. Here we complete the analytic side in two respects: by inspecting how small ("ǫ-regime") and intermediate or large ("p-regime") quark masses connect to each other, and by including in the discussion the two leading ∆I = 1/2 operators. We show that the ǫ-regime offers a straightforward strategy for disentangling the coefficients of the ∆I = 1/2 operators, and that in the p-regime finite-volume effects are significant in these observables once the pseudoscalar mass M and the box length L are in the regime M L < ∼ 5.0. July 20061 pilar.hernandez@ific.uv.es 2

show abstract

Section: Further Remarksmentioning

confidence: 99%

Probing the chiral weak Hamiltonian at finite volumes

Hernández¹,

Laine²

2006

J. High Energy Phys.

View full text Add to dashboard Cite

show abstract

“…5 is missing. This together with a different treatment of the m 2 K L π contributions generated by diagram f is the origin of the above discrepancy 7 . Let us point out in this context that I checked my full NLO K → ππ amplitude on which the results above are based with the output of the Mathematica package provided in [19] and found complete agreement.…”

Section: Resultsmentioning

confidence: 99%

“…Finally, the lowest order masses and decay constants of these lower order graphs have to be shifted to their renormalized physical value, up to the required chiral order. This two last contributions are represented by diagram d. 7 private communication with the author of [15]. 8 The full expression can be obtained from the author.…”

Section: B the Calculation Of The K → ππ Double Logsmentioning

confidence: 99%

“…The determination of the leading log contributions is thus the only possibility to get an estimate of the corrections one has to expect at NLO and NNLO. In [7] a method has been proposed to provide the LEC's needed for the K → ππ amplitude from lattice simulations. The outline of the paper is as follows: In section 2 I introduce some notation and the chiral Lagrangians used in the calculation.…”

Section: Lo Nlo Nnlo Double Logsmentioning

confidence: 99%

See 1 more Smart Citation

The chiral logs of the K→ππ amplitude

Buchler¹

2006

Physics Letters B

View full text Add to dashboard Cite

I calculate the leading logarithmic contributions up to two-loop order of the octet part of the K 0 → ππ amplitude. This sector of the weak chiral Lagrangian is believed to be the main source of the enhancement of the I = 0 relative to the I = 2 K 0 → ππ amplitude, the so-called ∆I = 1/2 rule. I discuss the procedure of chiral extrapolations of lattice data specific to K → ππ decays and study the implication of the present calculation on these numerically. The latter reinforces the fact that one has to expect a large enhancement of the I = 0 part of the amplitude due to re-scattering effects between the three mesons.

show abstract

“…This method requires 3-momentum insertion, and it is not yet clear if it can be extended to the ∆I = 1/2, K → ππ amplitudes. In our previous paper [13], an alternative method was proposed for constructing the physical K → ππ amplitudes to NLO for all (∆I = 1/2 and 3/2) operators of interest. For the ∆I = 3/2 amplitudes this requires K → K; K → π, ∆I = 3/2; and K → ππ, ∆I = 3/2 at one of (at least) two unphysical kinematics points where the Maiani-Testa theorem can be bypassed.…”

Section: Introductionmentioning

confidence: 99%

Lattice extraction ofK→ππamplitudes to next-to-leading order in partially quenched and in full chiral perturbation theory

Laiho

Soni

2005

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

We show that it is possible to construct ǫ ′ /ǫ to NLO using partially quenched chiral perturbation theory (PQChPT) from amplitudes that are computable on the lattice. We demonstrate that none of the needed amplitudes require three-momentum on the lattice for either the full theory or the partially quenched theory; non-degenerate quark masses suffice. Furthermore, we find that the electro-weak penguin (∆I = 3/2 and 1/2) contributions to ǫ ′ /ǫ in PQChPT can be determined to NLO using only degenerate (m K = m π ) K → π computations without momentum insertion. Issues pertaining to power divergent contributions, originating from mixing with lower dimensional operators, are addressed. Direct calculations of K → ππ at unphysical kinematics are plagued with enhanced finite volume effects in the (partially) quenched theory, but in simulations when the sea quark mass is equal to the up and down quark mass the enhanced finite volume effects vanish to NLO in PQChPT. In embedding the QCD penguin left-right operator onto PQChPT an ambiguity arises, as first emphasized by Golterman and Pallante. With one version (the "PQS") of the QCD penguin, the inputs needed from the lattice for constructing K → ππ at NLO in PQChPT coincide with those needed for the full theory. Explicit expressions for the finite logarithms emerging from our NLO analysis to the above amplitudes are also given.

show abstract

Lattice extraction ofK→ππamplitudes toO(p4

Cited by 47 publications

References 28 publications

Probing the chiral weak Hamiltonian at finite volumes

Probing the chiral weak Hamiltonian at finite volumes

The chiral logs of the K→ππ amplitude

Lattice extraction ofK→ππamplitudes to next-to-leading order in partially quenched and in full chiral perturbation theory

Contact Info

Product

Resources

About