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Semileptonic Kaon Decay in Staggered Chiral Perturbation Theory
High Energy Physics - Lattice · Submitted 29 Nov 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We provide the one-loop partially quenched staggered chiral perturbation theory expressions that may be employed to analyze staggered simulations of $f_+(q^2)$ with three light flavors.
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The abstract, sentence by sentence
The determination of $\vert V_{us}\vert$ from kaon semileptonic decays requires the value of the form factor $f_+(q^2=0)$, which can be calculated precisely on the lattice. We provide the one-loop partially quenched staggered chiral perturbation theory expressions that may be employed to analyze staggered simulations of $f_+(q^2)$ with three light flavors. We consider both the case of a mixed action, where the valence and sea sectors have different staggered actions, and the standard case where these actions are the same. The momentum transfer $q^2$ of the form factor is allowed to have an arbitrary value. We give results for the generic situation where the $u$, $d$, and $s$ quark masses are all different, $N_f=1+1+1$, and for the isospin limit, $N_f=2+1$. The expression we obtain for $f_+(q^2)$ is independent of the mass of the (valence) spectator quark. In the limit of vanishing lattice spacing, our results reduce to the one-loop continuum partially quenched expression for $f_+(q^2)$, which has not previously been reported in the literature for the $N_f=1+1+1$ case. Our expressions have already been used in staggered lattice analyses of $f_+(0)$, and should prove useful in future calculations as well.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The determination of $\vert V_{us}\vert$ from kaon semileptonic decays requires the value of the form factor $f_+(q^2=0)$, which can be calculated precisely on the lattice. | background 1.00 | 0.07 | 0.06 | asserted 0.98 |
| s1 | We provide the one-loop partially quenched staggered chiral perturbation theory expressions that may be employed to analyze staggered simulations of $f_+(q^2)$ with three light flavors. | contribution 0.98 | 0.93 | 0.38 | hedged possibility 0.87 |
| s2 | We consider both the case of a mixed action, where the valence and sea sectors have different staggered actions, and the standard case where these actions are the same. | contribution 0.55 | 0.76 | 0.04 | asserted 0.96 |
| s3 | The momentum transfer $q^2$ of the form factor is allowed to have an arbitrary value. | contribution 0.52 | 0.72 | 0.04 | asserted 0.91 |
| s4 | We give results for the generic situation where the $u$, $d$, and $s$ quark masses are all different, $N_f=1+1+1$, and for the isospin limit, $N_f=2+1$. | contribution 0.76 | 0.83 | 0.08 | asserted 1.00 |
| s5 | The expression we obtain for $f_+(q^2)$ is independent of the mass of the (valence) spectator quark. | result 1.00 | 0.92 | 0.10 | asserted 1.00 |
| s6 | In the limit of vanishing lattice spacing, our results reduce to the one-loop continuum partially quenched expression for $f_+(q^2)$, which has not previously been reported in the literature for the $N_f=1+1+1$ case. | result 0.64 | 0.84 | 0.24 | asserted 1.00 |
| s7 | Our expressions have already been used in staggered lattice analyses of $f_+(0)$, and should prove useful in future calculations as well. | future work 0.49 | 0.25 | 0.11 | asserted 0.82 |
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The paper
Original abstract
The determination of $\vert V_{us}\vert$ from kaon semileptonic decays requires the value of the form factor $f_+(q^2=0)$, which can be calculated precisely on the lattice. We provide the one-loop partially quenched staggered chiral perturbation theory expressions that may be employed to analyze staggered simulations of $f_+(q^2)$ with three light flavors. We consider both the case of a mixed action, where the valence and sea sectors have different staggered actions, and the standard case where these actions are the same. The momentum transfer $q^2$ of the form factor is allowed to have an arbitrary value. We give results for the generic situation where the $u$, $d$, and $s$ quark masses are all different, $N_f=1+1+1$, and for the isospin limit, $N_f=2+1$. The expression we obtain for $f_+(q^2)$ is independent of the mass of the (valence) spectator quark. In the limit of vanishing lattice spacing, our results reduce to the one-loop continuum partially quenched expression for $f_+(q^2)$, which has not previously been reported in the literature for the $N_f=1+1+1$ case. Our expressions have already been used in staggered lattice analyses of $f_+(0)$, and should prove useful in future calculations as well.
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References
How the literature uses it
7 arXiv papers cite this in 16 sentences
Papers citing it · 9 sentences without a confident label
Uses its method or tool 4 papers
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We perform the interpolation to the physical masses and the continuum using next-to-next-to-leading-order (NNLO) continuum $χ$PT [ref] , supplemented by next-to-leading-order (NLO) partially quenched, staggered $χ$PT [ref] .
Determination of $|V_{us}|$ from a lattice-QCD calculation of the $K\to\pi\ell\nu$ semileptonic form factor with physical quark masses · Introduction · 1.00
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Following the same strategy as in our asqtad $N_f=2+1$ analysis, we use partially quenched staggered $χ$PT (PQS$χ$PT) at NLO [ref] plus regular continuum $χ$PT at NNLO [ref] , and add the discretization effects mentioned above and the dominant $a^2$ corrections that respect the AG theorem (other than those included explicitly by the NLO PQS$χ$PT), i. e., $((m_K^2-m_π^2)^2α_s a^2, (m_K^2-m_π^2)^2α_s^2 a^2)$ terms.
K semileptonic form factor with HISQ fermions at the physical point · Chiral-continuum interpolation/extrapolation · 0.99
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We use the same fit function as in our 2014 analysis, a NLO partially quenched staggered ChPT (PQSChPT) expression [ref] , plus regular NNLO continuum ChPT terms [ref] , plus extra analytic terms which parametrize higher order discretization and chiral effects:
Kaon semileptonic decays with $N_f=2+1+1$ HISQ fermions and physical light-quark masses · New simulation data · 0.99
Cites it as background 1 paper
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Earlier ChPT work on $K_ℓ3$ and related form-factors is the original one-loop work [ref] , the two-loop work without [ref] and with [ref] isospin breaking and the one-loop partially quenched staggered calculation [ref] .
Chiral Perturbation Theory at Finite Volume and/or with Twisted Boundary Conditions · $K_ℓ3$ · 0.98
What it cites · 55 sentences without a confident label
Uses the method or tool of 2 papers
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The meson field $ϕ$ is a matrix in flavor-taste space, where the flavor indices run over valence and sea indices.[We will assume that we will use the quark flow or the replica method [ref] to remove the valence-quark determinant; any needed replica indices in the latter case will be implicit.] We write [equation] where $ϕ^a$ is itself a matrix in flavor (really flavor-replica) space, and the Hermitian taste generators $T_a$ are the same as in Eq. ([ref]).
Partially Quenched Chiral Perturbation Theory and the Replica Method · Mixed theory chiral Lagrangian at leading order · 0.86
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However, it is often easier to use the quark flow approach [ref] to locate the loops, and then to simply insert the factors of $1/4$ by hand.
Quenched Chiral Logarithms · Introduction · 0.93
Compares with 1 paper
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We note that, after we worked out the properties of staggered mixed-action chiral perturbation theory, we discovered Ref. [ref] , which developed mixed action staggered chiral perturbation theory several years ago, and found many of the results that are given in this section.
$B_K$ using HYP-smeared staggered fermions in $N_f=2+1$ unquenched QCD · Staggered chiral perturbation theory with a mixed staggered action · 0.85
Cites as background 1 paper
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We will assume that there are three light sea-quark flavors ($u$, $d$, and $s$), but $N_f$ in general will be larger than three to accommodate valence quarks (and either additional ghost quarks or replicas), in order to allow for partial quenching [ref] .
Partially Quenched Chiral Perturbation Theory and the Replica Method · Basics of Staggered Chiral Perturbation theory · 0.81
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