arXiv subjects

Oliver Bar

Publications and source records attributed to Oliver Bar.

At least 19 recordsLinked to original sources

arXiv2023

$B\pi$ excited-state contamination in lattice calculations of B-meson correlation functions

Multi-particle states with additional pions are expected to result in a difficult-to-control excited-state contamination in lattice simulations. We show that heavy meson chiral perturbation theory can be employed to estimate the contamination due to two-particle $B\pi$ states in various $B$-meson observables like the $B$-meson decay constant and the $BB^*\pi$ coupling. We work in the static limit and to next-to-leading order in the chiral expansion, i.e. including $\rm O(p)$. The $B\pi$ states are found to typically overestimate the observables at the few percent level. We determine two of the LECs from $B\to \pi$ form factor computations of the KEK group and discuss ways to determine the others. In particular two LECs which are associated with smeared interpolating fields seem to be easily accessible and thus open up a way to systematically study the effect of smearing on excited state effects.

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arXiv2022

$B\pi$-state contamination in $B$-meson observables

Multi-particle states with additional pions are expected to result in a non-negligible excited-state contamination in lattice simulations. We show that heavy meson chiral perturbation theory can be employed to calculate the contamination due to two-particle $B\pi$ states in various $B$-meson observables like the $B$-meson decay constant and the $BB^*\pi$ coupling. We work in the static limit and to next-to-leading order in the chiral expansion. The $B\pi$ states are found to typically overestimate the observables at the few percent level depending on the size of two currently unknown NLO low-energy coefficients. A strategy to independently measure one of them with the 3-point function of the light axial vector current will be discussed.

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arXiv2021

Nucleon-pion-state contamination in lattice computations of the nucleon electromagnetic form factors

The nucleon-pion-state contributions to QCD two-point and three-point functions relevant for lattice calculations of the nucleon electromagnetic form factors are studied in chiral perturbation theory. To leading order the results depend on a few experimentally known low-energy constants only, and the nucleon-pion-state contribution to the form factors can be estimated. The nucleon-pion-state contribution to the electric form factor $G_{\rm E}(Q^2)$ is at the +5 percent level for a source-sink separation of 2 fm, and it increases with increasing momentum transfer $Q^2$. For the magnetic form factor the nucleon-pion-state contribution leads to an underestimation of $G_{\rm M}(Q^2)$ by about $-5$ percent that decreases with increasing $Q^2$. For smaller source-sink separations that are accessible in present-day lattice simulations the impact is larger. Although the ChPT results may not be applicable for these time separations a comparison with recent lattice data works reasonably well.

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arXiv2021

$N\pi$-state contamination in lattice calculations of the nucleon electromagnetic form factors

The nucleon-pion-state contribution to QCD two-point and three-point functions relevant for lattice calculations of the nucleon electromagnetic form factors are studied in chiral perturbation theory. To leading order the results depend on a few experimentally known low-energy constants only, and the nucleon-pion-state contribution to the form factors can be estimated. The nucleon-pion-state contribution to the electric form factor $G_{\rm E}(Q^2)$ is at the +5 percent level for a source-sink separation of 2 fm, and it increases with increasing momentum transfer $Q^2$. For the magnetic form factor the nucleon-pion-state contribution leads to an underestimation of $G_{\rm M}(Q^2)$ by about 5 percent that decreases with increasing $Q^2$. For smaller source-sink separations that are accessible in present-day lattice simulations the impact is larger, although the ChPT results may not be applicable for such small time separations. Still, a comparison with lattice data at $t\approx 1.6$ fm works reasonably well.

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arXiv2019

$N\pi$-states and the projection method for the nucleon axial and pseudoscalar form factors

The RQCD collaboration proposed a projection method to remove the excited state contamination in lattice OCD calculations of nuclear form factors. The effectiveness of this method in removing the two-particle nucleon-pion-state contamination is examined using chiral perturbation theory. It is shown that the projection method has practically no impact in the calculation of the axial and induced pseudoscalar form factors. In the pseudoscalar form factor the projection method strongly enhances the nucleon-pion-state contamination. The generalized Goldberger-Treiman relation is satisfied even though large nucleon-pion-state contaminations are present in individual form factors. Therefore, the projection method is not a solution to the excited state problem in nucleon form factor calculations.

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arXiv2019

$N\pi$-excited state contamination in nucleon 3-point functions using ChPT

The $N\pi$-state contribution to nucleon 3-pt functions involving the pseudoscalar density $P(x)$ and the time component $A_4(x)$ of the axial vector current are computed to LO in ChPT. In case of the latter the $N\pi$ contribution is O($M_N$) enhanced compared to the single-nucleon ground state contribution. In addition, a relative sign in two terms of the $N\pi$ contribution leads an almost linear dependence on the operator insertion time, as it is observed in lattice data. In case of the pseudoscalar density the $N\pi$ contribution is strongly dependent on the momentum transfer, leading to a distortion of the pseudoscalar nucleon form factor. Finally, the $N\pi$ state contamination in the form factors result in a violation of the generalized Goldberger-Treiman relation as observed in various lattice calculations.

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arXiv2019

$N\pi$-state contamination in lattice calculations of the nucleon pseudoscalar form factor

The nucleon-pion-state contribution in the QCD 3-point function of the pseudoscalar density is calculated to leading order in chiral perturbation theory. It predicts a nucleon-pion-state contamination in lattice estimates for the pseudoscalar form factor $G_{\rm P}(Q^2)$ determined with the plateau method. Depending on the momentum transfer $Q^2$ the contamination varies between -20% and +50% for a source-sink separation of 2 fm. The nucleon-pion-state contamination also causes violations in the generalized Goldberger-Treiman relation among the pseudoscalar and the axial nucleon form factors, the dominant source being the nucleon-pion-state contamination in the induced pseudoscalar form factor $\tilde{G}_{\rm P}(Q^2)$. Comparing the chiral perturbation theory predictions with lattice results of the PACS collaboration we find reasonable agreement even for source-sink separations as small as 1.3 fm.

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arXiv2018

$N\pi$-state contamination in lattice calculations of the nucleon axial form factors

The nucleon-pion-state contribution to QCD two-point and three-point functions used in lattice calculations of the nucleon axial form factors are studied in chiral perturbation theory. For small quark masses this contribution is expected to be the dominant excited-state contamination at large time separations. To leading order in chiral perturbation theory the results depend on only two experimentally known low-energy constants and the nucleon-pion-state contribution to the form factors can be estimated. The nucleon-pion-state contribution to the axial form factor $G_{\rm A}(Q^2)$ is at the 5 percent level for a source-sink separation of 2 fm and shows almost no dependence on the momentum transfer $Q^2$. In contrast, for the induced pseudoscalar form factor $\tilde{G}_{\rm P}(Q^2)$ the nucleon-pion-state contribution shows a rather strong dependence on $Q^2$ and leads to a 10 to 40 percent underestimation of $\tilde{G}_{\rm P}(Q^2)$ at small momentum transfers. The ChPT results can be used to analytically remove the nucleon-pion-state contribution from lattice data. Performing this removal for lattice data generated by the PACS collaboration we find agreement with experimental data and the predictions of the pion-pole dominance model. The removal works surprisingly well even for source-sink separations as small as 1.3 fm.

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arXiv2018

Nucleon-pion-state contamination in lattice calculations of the axial form factors of the nucleon

The nucleon-pion-state contribution to QCD two- and three-point functions used in the calculation of the axial form factors of the nucleon are studied in chiral perturbation theory. For physically small quark masses the nucleon-pion states are expected to dominante the excited-state contamination at large euclidean time separations. To leading order in chiral perturbation theory the results depend on two experimentally well-known low-energy constants only and the nucleon-pion-state contribution can be reliably estimated. The nucleon-pion-state contribution to the axial form factor $G_{\rm A}(Q^2)$ is at the 5 percent level for source-sink separations of 2 fm and shows almost no dependence on the momentum transfer $Q^2$. In contrast, for the induced pseudo scalar form factor $G_{\rm P}(Q^2)$ the nucleon-pion-state contribution shows a rather strong dependence on $Q^2$ and leads to a 10 to 40 percent underestimation of $G_{\rm P}(Q^2)$ at small momentum transfers. Applying the ChPT results to recent lattice data generated by the PACS collaboration we find agreement with experimental data and the predictions of the pion-pole dominance model.

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arXiv2018

Three-particle $N\pi\pi$ state contribution to the nucleon two-point function in lattice QCD

The three-particle $N\pi\pi$-state contribution to the QCD two-point function of standard nucleon interpolating fields is computed to leading order in chiral perturbation theory. Using the experimental values for two low-energy coefficients the impact of this contribution on lattice QCD calculations of the nucleon mass is estimated. The impact is found to be at the per mille level at most and negligible in practice.

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arXiv2017

Multi-hadron-state contamination in nucleon observables from chiral perturbation theory

Multi-particle states with additional pions are expected to be a non-negligible source of the excited-state contamination in lattice simulations at the physical point. It is shown that baryon chiral perturbation theory (ChPT) can be employed to calculate the contamination due to two-particle nucleon-pion states in various nucleon observables. Results to leading order are presented for the nucleon axial, tensor and scalar charge and three Mellin moments of parton distribution functions: the average quark momentum fraction, the helicity and the transversity moment. Taking into account experimental and phenomenological results for the charges and moments the impact of the nucleon-pion-states on lattice estimates for these observables can be estimated. The nucleon-pion-state contribution leads to an overestimation of all charges and moments obtained with the plateau method. The overestimation is at the 5-10% level for source-sink separations of about 2 fm. Existing lattice data is not in conflict with the ChPT predictions, but the comparison suggests that significantly larger source-sink separations are needed to compute the charges and moments with few-percent precision.

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arXiv2017

Chiral perturbation theory and nucleon-pion-state contaminations in lattice QCD

Multi-particle states with additional pions are expected to be a non-negligible source of excited-state contamination in lattice simulations at the physical point. It is shown that baryon chiral perturbation theory can be employed to calculate the contamination due to two-particle nucleon-pion states in various nucleon observables. Leading order results are presented for the nucleon axial, tensor and scalar charge and three Mellin moments of parton distribution functions (quark momentum fraction, helicity and transversity moment). Taking into account phenomenological results for the charges and moments the impact of the nucleon-pion-states on lattice estimates for these observables can be estimated. The nucleon-pion-state contribution results in an overestimation of all charges and moments obtained with the plateau method. The overestimation is at the 5-10% level for source-sink separations of about 2 fm. The source-sink separations accessible in contemporary lattice simulations are found to be too small for chiral perturbation theory to be directly applicable.

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arXiv2016

Nucleon-pion-state contribution in lattice calculations of moments of parton distribution functions

We employ chiral perturbation theory to calculate the nucleon-pion-state contribution to the 3-point correlation functions measured in lattice QCD to compute various moments of parton distribution functions (quark momentum fraction, helicity and transversity moment). We estimate the impact of the nucleon-pion-state contribution on the plateau method for lattice simulations with a physical pion mass. The nucleon-pion-state contribution results in an overestimation of all three moments. The overestimation is at the 5-20% level for source-sink separations of about 1.5 fm.

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arXiv2016

Nucleon-pion-state contribution in lattice calculations of the nucleon charges $g_A,g_T$ and $g_S$

We employ leading order covariant chiral perturbation theory to compute the nucleon-pion-state contribution to the 3-point correlation functions one typically measures in lattice QCD to extract the isovector nucleon charges $g_A,g_T$ and $g_S$. We estimate the impact of the nucleon-pion-state contribution on both the plateau and the summation method for lattice simulations with physical pion masses. The nucleon-pion-state contribution results in an overestimation of all charges with both methods. The overestimation is roughly equal for the axial and the tensor charge, and about fifty percent larger for the scalar charge.

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arXiv2015

Nucleon-pion-state contribution to nucleon two-point correlation functions

We study the nucleon-pion-state contribution to the QCD two-point function of the standard nucleon interpolating fields. For sufficiently small quark masses these two-particle states are expected to have a smaller total energy than the single-particle excited states. We calculate the nucleon-pion-state contribution to leading order in chiral perturbation theory. Both parity channels are considered. We find the nucleon-pion-state contribution to be small, contributing at the few percent level to the effective mass in the positive parity channel.

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arXiv2015

Nucleon-pion-state contributions in the determination of the nucleon axial charge

The nucleon-pion-state contributions to QCD 2- and 3-point functions used in the calculation of the nucleon axial charge are studied in chiral perturbation theory. For sufficiently small quark masses and large volumes the nucleon-pion states are expected to have smaller total energy than the single-particle excited states. To leading order in chiral perturbation theory the results do not depend on low-energy constants associated with the interpolating nucleon fields and apply to local as well as smeared interpolators. The nucleon-pion-state contribution is found to be at the few percent level.

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arXiv2014

Chiral perturbation theory for gradient flow observables

We construct the next-to-leading order chiral lagrangian for scalar and pseudo-scalar densities defined using the gradient flow. We calculate the chiral condensate and the pion decay constant to this order from operators at positive flow time, and confirm results obtained earlier in the chiral limit. We also calculate the quark mass dependence of the scales $t_0$ and $w_0$ defined from the scalar gluon density and find that nonanalytic terms in the quark mass only enter at next-to-next-to-leading order.

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arXiv2013

The kaon mass in 2+1+1 flavor twisted mass Wilson ChPT

We construct the chiral low-energy effective theory for 2+1+1 flavor lattice QCD with twisted mass Wilson fermions. In contrast to existing results we assume a heavy charm quark mass such that the D mesons are too heavy to appear as degrees of freedom in the effective theory. As an application we compute the kaon mass to 1-loop order in the LCE regime. The result contains a chiral logarithm involving the neutral pion mass which has no analogue in continuum ChPT.

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