Partially-quenched Chiral Perturbation Theory Research Articles

Extracting the low-energy constant at three flavors from pion-kaon scattering

Based on our analysis of the contributions from the connected and disconnected contraction diagrams to the pion-kaon scattering amplitude, we provide the first determination of the only free low-energy constant at , known as , in SU (4∣1) Partially-Quenched Chiral Perturbation theory using the data from the Extended Twisted Mass collaboration, . The theory uncertainties originate from the unphysical scattering length, the physical low-energy constants, the higher-order chiral corrections, the (lattice) meson masses and the pion decay constant, respectively.

Applicability of the two-particle quantization condition to partially-quenched theories

Partial quenching allows one to consider correlation functions and amplitudes that do not arise in the corresponding unquenched theory. For example, physical $s$-wave pion scattering can be decomposed into $I=0$ and 2 amplitudes, while, in a partially-quenched extension, the larger symmetry group implies that there are more than two independent scattering amplitudes. It has been proposed that the finite-volume quantization condition of L\"uscher holds for the correlation functions associated with each of the two-particle amplitudes that arise in partially-quenched theories. Using partially-quenched chiral perturbation theory, we show that this proposal fails for those correlation functions for which the corresponding one-loop amplitudes do not satisfy $s$-wave unitarity. For partially-quenched amplitudes that, while being unphysical, do satisfy one-loop $s$-wave unitarity, we argue that the proposal is plausible. Implications for previous work are discussed.

Contraction diagram analysis in pion-kaon scattering

We study the contributions from the connected and disconnected contraction diagrams to the pion-kaon scattering amplitude within the framework of SU(4|1) partially-quenched chiral perturbation theory. Combining this with a finite-volume analysis, we demonstrate that a lattice calculation of the easier computable connected correlation functions is able to provide valuable information of the noisier disconnected correlation functions, and may serve as a theory guidance for the future refinement of the corresponding lattice techniques.

Constraints on disconnected contributions in \u03c0\u03c0 scattering

The accuracy of the lattice QCD computation of hadron-hadron scattering at low isospin depends critically on the ability to compute correlation functions with fermionic disconnected Wick contractions. This happens, for instance, in isospin I = 0 ππ scattering, which receives contributions from rectangular and vacuum types of contractions among other easier calculable ones. Combining Lüscher’s formula and partially-quenched chiral perturbation theory, we provide precise theory predictions of the discrete energy levels extracted from specific linear combinations of lattice correlation functions corresponding to various types of contractions. Expressions are provided for extracting the unphysical low-energy constants in the partially-quenched chiral perturbation theory from the energy levels for these contractions. The predictions for the rectangular and vacuum contractions may serve as solid tests of the accuracy for existing and future lattice studies of ππ scattering.

Connected and disconnected contractions in pion–pion scattering

We show that the interplay of chiral effective field theory and lattice QCD can be used in the evaluation of so-called disconnected diagrams, which appear in the study of the isoscalar and isovector channels of pion–pion scattering and have long been a major challenge for the lattice community. By means of partially-quenched chiral perturbation theory, we distinguish and analyze the effects from different types of contraction diagrams to the pion–pion scattering amplitude, including its scattering lengths and the energy-dependence of its imaginary part. Our results may be used to test the current degree of accuracy of lattice calculation in the handling of disconnected diagrams, as well as to set criteria for the future improvement of relevant lattice computational techniques that may play a critical role in the study of other interesting QCD matrix elements.

Finite volume for three-flavour Partially Quenched Chiral Perturbation Theory through NNLO in the meson sector

We present a calculation of the finite volume corrections to meson masses and decay constants in three flavour Partially Quenched Chiral Perturbation Theory (PQChPT) through two-loop order in the chiral expansion for the flavour-charged (or off-diagonal) pseudoscalar mesons. The analytical results are obtained for three sea quark flavours with one, two or three different masses. We reproduce the known infinite volume results and the finite volume results in the unquenched case. The calculation has been performed using the supersymmetric formulation of PQChPT as well as with a quark-flow technique. Partial analytical results can be found in the appendices. Some examples of cases relevant to lattice QCD are studied numerically. Numerical programs for all results are available as part of the CHIRON package.

BKwith two flavors of dynamical overlap fermions

We present a two-flavor QCD calculation of ${B}_{K}$ on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}32$ lattice at $a\ensuremath{\sim}0.12\text{ }\text{ }\mathrm{fm}$ (or equivalently ${a}^{\ensuremath{-}1}=1.67\text{ }\text{ }\mathrm{GeV}$). Both valence and sea quarks are described by the overlap fermion formulation. The matching factor is calculated nonperturbatively with the so-called RI/MOM scheme. We find that the lattice data are well described by the next-to-leading order (NLO) partially quenched chiral perturbation theory (PQChPT) up to around a half of the strange quark mass (${m}_{s}^{\mathrm{phys}}/2$). The data at quark masses heavier than ${m}_{s}^{\mathrm{phys}}/2$ are fitted including a part of next-to-next-to-leading order terms. We obtain ${B}_{K}^{\overline{\mathrm{MS}}}(2\text{ }\text{ }\mathrm{GeV})=0.537(4)(40)$, where the first error is statistical and the second is an estimate of systematic uncertainties from finite volume, fixing topology, the matching factor, and the scale setting.

Generalized parton distributions of the pion in partially-quenched chiral perturbation theory

We consider the pion matrix elements of the isoscalar and isovector combinations of the vector and tensor twist-two operators that determine the moments of the various pion generalized parton distributions. Our analysis is performed using partially-quenched chiral perturbation theory. We work in the SU(2) and $\mathrm{SU}(4|2)$ theories and present our results at infinite volume and also at finite volume where some subtleties arise. These results are useful for extrapolations of lattice calculations of these matrix elements at small momentum transfer to the physical regime.

Strong-isospin violation in the neutron–proton mass difference from fully-dynamical lattice QCD and PQQCD

We determine the strong-isospin violating component of the neutron–proton mass difference from fully-dynamical lattice QCD and partially-quenched QCD calculations of the nucleon mass, constrained by partially-quenched chiral perturbation theory at one-loop level. The lattice calculations were performed with domain-wall valence quarks on MILC lattices with rooted staggered sea-quarks at a lattice spacing of b = 0.125 fm , lattice spatial size of L = 2.5 fm and pion masses ranging from m π ∼ 290 MeV to ∼ 350 MeV . At the physical value of the pion mass, we predict M n − M p | d − u = 2.26 ± 0.57 ± 0.42 ± 0.10 MeV where the first error is statistical, the second error is due to the uncertainty in the ratio of light-quark masses, η = m u / m d , determined by MILC [C. Aubin, et al., MILC Collaboration, Phys. Rev. D 70 (2004) 114501, hep-lat/0407028], and the third error is an estimate of the systematic due to chiral extrapolation.

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

We show that it is possible to construct ${ϵ}^{\ensuremath{'}}/ϵ$ to next-to-leading order (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 3-momentum on the lattice for either the full theory or the partially quenched theory; nondegenerate quark masses suffice. Furthermore, we find that the electro-weak penguin ($\ensuremath{\Delta}I=3/2$ and $1/2$) contributions to ${ϵ}^{\ensuremath{'}}/ϵ$ in PQChPT can be determined to NLO using only degenerate (${m}_{K}={m}_{\ensuremath{\pi}}$) $K\ensuremath{\rightarrow}\ensuremath{\pi}$ computations without momentum insertion. Issues pertaining to power divergent contributions, originating from mixing with lower dimensional operators, are addressed. Direct calculations of $K\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ 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'' (patially quenched singlet)] of the QCD penguin, the inputs needed from the lattice for constructing $K\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ 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 also are given.

Quark mass dependence of pseudoscalar masses and decay constants on a lattice

Our previous calculations of the sea- and valence-quark mass dependence of the pseudoscalar meson masses and decay constants is repeated on a 16^3x32 lattice which allows for a better determination of the quantities in question. The conclusions are similar as before on the 16^4 lattice [1]. The two light dynamical quark flavours we simulate have masses in the range 1/4 m_s < m_{u,d} < 2/3 m_s. The sea quark mass dependence of f_pi and m_pi^2/m_q is well described by the next-to-leading order (NLO) Chiral Perturbation Theory (ChPT) formulas and clearly shows the presence of chiral logarithms. The valence quark mass dependence requires the presence of NNLO contributions in Partially Quenched ChPT (PQChPT) -- in addition to the NLO terms. The O(a) lattice artifacts in these quantities turn out to be small.

Nucleon properties at finite lattice spacing in chiral perturbation theory

Properties of the proton and neutron are studied in partially-quenched chiral perturbation theory at finite lattice spacing. Masses, magnetic moments, the matrix elements of isovector twist-2 operators and axial-vector currents are examined at the one-loop level in a double expansion in the light-quark masses and the lattice spacing. This work will be useful in extrapolating the results of simulations using Wilson valence and sea quarks, as well as simulations using Wilson sea quarks and Ginsparg-Wilson valence quarks, to the continuum.

Baryons in partially-quenched chiral perturbation theory

I discuss the inclusion of baryons into partially-quenched chiral perturbation theory and describe one-loop calculations that have been performed.

Partially quenched chiral perturbation theory and numerical simulations

The dependence of the pseudoscalar meson mass and decay constant is compared to one-loop partially quenched chiral perturbation theory (PQChPT) in a numerical simulation with two light dynamical quarks. The characteristic behaviour with chiral logarithms is observed. The values of the fitted PQChPT-parameters are in a range close to the expectation in continuum in spite of the fact that the lattice spacing is still large, namely a≃0.28 fm.

Nucleons in two-flavor partially-quenched chiral perturbation theory

Properties of the proton and the neutron are explored in partially-quenched chiral perturbation theory with two non-degenerate light flavors. Masses, magnetic moments, matrix elements of isovector twist-2 operators and axial-vector currents are computed at the one-loop level in the chiral expansion.