arXiv subjects

Konstantin Ottnad

Publications and source records attributed to Konstantin Ottnad.

At least 55 records · Page 3Linked to original sources

arXiv2022

The isovector axial form factor of the nucleon from lattice QCD

The isovector axial form factor of the nucleon plays a key role in interpreting data from long-baseline neutrino oscillation experiments. We perform a lattice-QCD based calculation of this form factor, introducing a new method to directly extract its $z$-expansion from lattice correlators. Our final parametrization of the form factor, which extends up to spacelike virtualities of $0.7\,{\rm GeV}^2$ with fully quantified uncertainties, agrees with previous lattice calculations but is significantly less steep than neutrino-deuterium scattering data suggests.

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arXiv2022

Isoscalar electromagnetic form factors of the nucleon in $N_\mathrm{f} = 2 + 1$ lattice QCD

We present results for the isoscalar electromagnetic form factors of the nucleon computed on the Coordinated Lattice Simulations (CLS) ensembles with $N_\mathrm{f} = 2 + 1$ flavors of $\mathcal{O}(a)$-improved Wilson fermions and an $\mathcal{O}(a)$-improved conserved vector current. In order to estimate the excited-state contamination, we employ several source-sink separations and apply the summation method. For the computation of the quark-disconnected diagrams, a stochastic estimation based on the one-end trick is performed, in combination with a frequency-splitting technique and the hopping parameter expansion. By these means, we obtain a clear signal for the form factors including the quark-disconnected contributions, which have a statistically significant effect on our results.

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arXiv2022

Pion-pole contribution to HLbL from twisted mass lattice QCD at the physical point

We report on our computation of the pion transition form factor ${\cal F}_{P\rightarrow γ^*γ^*}$ from twisted mass lattice QCD in order to determine the numerically dominant light pseudoscalar pole contribution in the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon $a_μ=(g-2)_μ$. The pion transition form factor is computed directly at the physical point. We present first results for our estimate of the pion-pole contribution with kinematic setup for the pion at rest.

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arXiv2022

The hadronic contribution to the running of the electromagnetic coupling and electroweak mixing angle

As present and future experiments, on both the energy and precision frontiers, look to identify new physics beyond the Standard Model, we require more precise determinations of fundamental quantities, like the QED and electroweak couplings at various momenta. These can be obtained either entirely from experimental measurements, or from one such measurement at a particular virtuality combined with the couplings' virtuality dependence computed within the SM. Thus, a precise, entirely theoretical determination of the running couplings is highly desirable, even more since the preliminary results of the E989 experiment in Fermilab were published. We give results for the hadronic contribution to the QED running coupling $α(Q^2)$ and weak mixing angle $\sin^2θ_W(Q^2)$ in the space-like energy region $(0, 7]~\text{GeV}^2$ with a total relative uncertainty of $2\%$ at energies $Q^2 \ll 1~\text{GeV}^2$, and $1\%$ at $Q^2 > 1~\text{GeV}^2$.

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arXiv2021

Isovector Axial Vector Form Factors of the Nucleon from Lattice QCD with $N_{f}=2+1$ $\mathcal O(a)$-improved Wilson Fermions

We present the analysis of isovector axial vector nucleon form factors on a set of $N_f=2+1$ CLS ensembles with $\mathcal O(a)$-improved Wilson fermions and Lüscher-Weisz gauge action. The set of ensembles covers a pion mass range of $130-353\,$MeV with lattice spacings between $0.05\,$fm and $0.09\,$fm. In particular, the set includes a $L/a=96$ ensemble at the physical pion mass. For the purpose of the form factor extraction, we employ both the summed operator insertion method (summation method) and explicit two-state fits in order to account for excited-state contributions to the nucleon correlation functions. To describe the $Q^{2}$-behavior of the form factors, we perform $z$-expansion fits. Finally, we present HBChPT-inspired chiral and continuum extrapolations of the axial charge and radius.

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arXiv2021

Improved analysis of nucleon isovector charges and twist-2 matrix elements on CLS $N_f=2+1$ ensembles

Preliminary results are presented for nucleon isovector charges and twist-2 matrix elements which have been obtained employing an improved analysis strategy to deal with excited-state contamination. The set of CLS $N_f=2+1$ gauge ensembles in this study has been extended compared to our 2018 calculation, including an ensemble at physical quark masses. Besides the addition of new ensembles, the number of gauge configurations and measurements has been increased on several of the existing ensembles and the analysis has been extended to include additional source-sink separations. The ensembles cover a range of the light quark mass corresponding to $M_π\approx 0.130\,\mathrm{MeV} \ldots 350\,\mathrm{MeV}$, four values of the lattice spacing $a\approx0.05\,\mathrm{fm}\ldots0.09\,\mathrm{fm}$ and a large range of volumes. Results at the physical point are computed for each observable from a combined chiral, continuum and finite-volume extrapolation.

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arXiv2021

Quark and gluon momentum fractions in the pion from $N_f=2+1+1$ lattice QCD

We perform the first full decomposition of the pion momentum into its gluon and quark contributions. We employ an ensemble generated by the Extended Twisted Mass Collaboration with $N_f=2 + 1 +1$ Wilson twisted mass clover fermions at maximal twist tuned to reproduce the physical pion mass. We present our results in the $\overline{\mathrm{MS}}$ scheme at $2\gev$. We find $\avgx_{u+d}=0.601(28)$, $\avgx_s=0.059(13)$, $\avgx_c=0.019(05)$, and $\avgx_g=0.52(11)$ for the separate contributions, respectively, whose sum saturates the momentum sum rule.

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arXiv2021

Hadronic light-by-light contribution to $(g-2)_μ$ from lattice QCD: a complete calculation

We compute the hadronic light-by-light scattering contribution to the muon $g-2$ from the up, down, and strange-quark sector directly using lattice QCD. Our calculation features evaluations of all possible Wick-contractions of the relevant hadronic four-point function and incorporates several different pion masses, volumes, and lattice-spacings. We obtain a value of $a_μ^{\text{Hlbl}} = 106.8(14.7) \times 10^{-11}$ (adding statistical and systematic errors in quadrature), which is consistent with current phenomenological estimates and a previous lattice determination. It now appears conclusive that the hadronic light-by-light contribution cannot explain the current tension between theory and experiment for the muon $g-2$.

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arXiv2021

Excited states in nucleon structure calculations

Excited state contributions represent a formidable challenge for hadron structure calculations in lattice QCD. For physical systems that exhibit an exponential signal-to-noise problem they often hinder the extraction of ground state matrix elements, introducing a major source of systematic error in lattice calculations of such quantities. The development of methods to treat the contribution of excited states and the current status of related lattice studies are reviewed with focus on nucleon structure calculations that are notoriously affected by excited state contamination.

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arXiv2020

Model-independent determination of the nucleon charge radius from lattice QCD

Lattice QCD calculations of nucleon form factors are restricted to discrete values of the Euclidean four-momentum transfer. Therefore, the extraction of radii typically relies on parametrizing and fitting the lattice QCD data to obtain its slope close to zero momentum transfer. We investigate a new method, which allows to compute the nucleon radius directly from existing lattice QCD data, without assuming a functional form for the momentum dependence of the underlying form factor. The method is illustrated for the case of the isovector mean square charge radius of the nucleon $\langle r^2_\mathrm{isov} \rangle$ and the quark-connected contributions to $\langle r^2_p\rangle$ and $\langle r^2_n \rangle$ for the proton and neutron, respectively. Computations are performed using a single gauge ensemble with $N_f=2+1+1$ maximally twisted mass clover-improved fermions at physical quark mass and a lattice spacing of $a=0.08\mathrm{fm}$.

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arXiv2020

On the generalised eigenvalue method and its relation to Prony and generalised pencil of function methods

We discuss the relation of three methods to determine energy levels in lattice QCD simulations: the generalised eigenvalue, the Prony and the generalised pencil of function methods. All three can be understood as special cases of a generalised eigenvalue problem. We show analytically that the leading corrections to an energy $E_l$ in all three methods due to unresolved states decay asymptotically exponentially like $\exp(-(E_{n}-E_l)t)$. Using synthetic data we show that these corrections behave as expected also in practice. We propose a novel combination of the generalised eigenvalue and the Prony method, denoted as GEVM/PGEVM, which helps to increase the energy gap $E_{n}-E_l$. We illustrate its usage and performance using lattice QCD examples.

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arXiv2019

The hadronic contribution to the running of the electromagnetic coupling and the electroweak mixing angle

The electromagnetic coupling $α$ and the electroweak mixing angle $θ_{\mathrm{W}}$ are parameters of the Standard Model (SM) that enter precision SM tests and play a fundamental rôle in beyond SM physics searches. Their values are energy dependent, and non-perturbative hadronic contributions are the main source of uncertainty to the theoretical knowledge of the running with energy. We present a lattice study of the leading hadronic contribution to the running of $α$ and $\sin^2θ_{\mathrm{W}}$. The former is related to the hadronic vacuum polarization (HVP) function of electromagnetic currents, and the latter to the HVP mixing of the electromagnetic current with the vector part of the weak neutral currents. We use the time-momentum representation (TMR) method to compute the HVP on the lattice, estimating both connected and disconnected contributions on $N_{\mathrm{f}}=2+1$ non-perturbatively $O(a)$-improved Wilson fermions ensembles from the Coordinated Lattice Simulations (CLS) initiative. The use of different lattice spacings and quark masses allows us to reliably extrapolate the results to the physical point.

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arXiv2019

Strange electromagnetic form factors of the nucleon with $N_f = 2 + 1$ $\mathcal{O}(a)$-improved Wilson fermions

We present results for the strange contribution to the electromagnetic form factors of the nucleon computed on the CLS ensembles with $N_f=2+1$ flavors of $\mathcal{O}(a)$-improved Wilson fermions and an $\mathcal{O}(a)$-improved vector current. Several source-sink separations are investigated in order to estimate the excited-state contamination. We calculate the form factors on six ensembles with lattice spacings in the range of $a=0.049-0.086\,\text{fm}$ and pion masses in the range of $m_π=200-360\,\text{MeV}$, which allows for a controlled chiral and continuum extrapolation. In the computation of the quark-disconnected contributions we employ hierarchical probing as a variance reduction technique.

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arXiv2019

The leading hadronic vacuum polarization contribution to the muon anomalous magnetic moment using $N_f=2+1$ O($a$) improved Wilson quarks

We present a lattice calculation of the leading hadronic contribution to the anomalous magnetic moment of the muon. This work is based on a subset of the CLS ensembles with $N_f = 2+1$ dynamical quarks and a quenched charm quark. Noise reduction techniques are used to improve significantly the statistical precision of the dominant light quark contribution. The main source of systematic error comes from finite size effects which are estimated using the formalism described in Ref. [7] and based on our knowledge of the timelike pion form factor. The strange and charm quark contributions are under control and an estimate of the quark-disconnected contribution is included. Isospin breaking effects will be studied in a future publication but are included in the systematic error using an estimate based on published lattice results. Our final result, $a_μ^{\rm hvp} = (720.0\pm 12.4 \pm 6.8)\times 10^{-10}$, has a precision of about 2%.

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arXiv2019

Strange nucleon form factors and isoscalar charges with $N_f=2+1$ $\mathcal{O}(a)$-improved Wilson fermions

We report on our calculation of the strange contribution to the vector and axial vector form factors. The strange charge radii, magnetic moment, and axial charge are extracted by model independent $z$-expansion fits to the $Q^2$-dependence of the respective form factors. Furthermore, the isoscalar contribution to the axial and tensor charge is investigated by combining the calculation of connected and disconnected diagrams. The required renormalization is performed with the Rome-Southampton method. We make use of the CLS $N_f=2+1$ $\mathcal{O}(a)$-improved Wilson fermion ensembles. Results are reported for pion masses in the range $m_π=200-360\,\text{MeV}$ and lattice spacings $a=0.05-0.086\,\text{fm}$.

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arXiv2019

Nucleon isovector charges and twist-2 matrix elements with $N_f=2+1$ dynamical Wilson quarks

We present results from a lattice QCD study of nucleon matrix elements at vanishing momentum transfer for local and twist-2 isovector operator insertions. Computations are performed on gauge ensembles with non-perturbatively improved $N_f=2+1$ Wilson fermions, covering four values of the lattice spacing and pion masses down to $M_π\approx200$MeV. Several source-sink separations (typically ~1.0fm to ~1.5fm) allow us to assess excited-state contamination. Results on individual ensembles are obtained from simultaneous two-state fits across all observables and all available source-sink separations with the energy gap as a common fit parameter. Renormalization has been performed non-perturbatively using the Rome-Southampton method for all but the finest lattice spacing for which an extrapolation has been used. Physical results are quoted in the $\overline{MS}$ scheme at a scale of $μ=2$GeV and are obtained from a combined chiral, continuum and finite-size extrapolation. For the nucleon isovector axial, scalar and tensor charges we find physical values of $g_A^{u-d}=1.242(25)_\text{stat}(\genfrac{}{}{0pt}{2}{+00}{-31})_\text{sys}$, $g_S^{u-d}=1.13(11)_\text{stat}(\genfrac{}{}{0pt}{2}{+07}{-06})_\text{sys}$ and $g_T^{u-d}=0.965(38)_\text{stat}(\genfrac{}{}{0pt}{2}{+13}{-41})_\text{sys}$, respectively, where individual systematic errors in each direction from the chiral, continuum and finite-size extrapolation have been added in quadrature. Our final results for the isovector average quark momentum fraction and the isovector helicity and transversity moments are given by $\langle x\rangle_{u-d}=0.180(25)_\text{stat}(\genfrac{}{}{0pt}{2}{+14}{-06})_\text{sys}$, $\langle x\rangle_{Δu-Δd}=0.221(25)_\text{stat}(\genfrac{}{}{0pt}{2}{+10}{-00})_\text{sys}$ and $\langle x\rangle_{δu-δd}=0.212(32)_\text{stat}(\genfrac{}{}{0pt}{2}{+20}{-10})_\text{sys}$, respectively.

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arXiv2019

Pseudoscalar flavor-singlet mesons from lattice QCD

We investigate the masses and mixing of $η$, $η'$ mesons in the framework of twisted mass lattice QCD with $N_f=2+1+1$ dynamical quark flavors. For the first time we perform a controlled chiral and continuum extrapolation to obtain physical results. To this end, we have analyzed 17 gauge ensembles with pion masses ranging from $220\,\mathrm{MeV}$ to $500\,\mathrm{MeV}$ and at three values of the lattice spacing. This calculation became feasible through the application of a powerful variance reduction technique for the computation of quark-disconnected diagrams together with several improvements in the final analysis, including a correction of the relevant correlation functions for residual topological finite volume effects. We obtain physical results for the masses $M_η=557(11)_\mathrm{stat}(03)_{χ\mathrm{PT}}\,\mathrm{MeV}$ and $M_{η'}=911(64)_\mathrm{stat}(03)_{χ\mathrm{PT}}\,\mathrm{MeV}$, as well as the mixing angle in the quark flavor basis $ϕ=38.8(2.2)_\mathrm{stat}(2.4)_{χ\mathrm{PT}}^\circ$, in excellent agreement with other results from phenomenology. Similarly, for the physical values of the decay constant parameters we find $f_l=125(5)_\mathrm{stat}(6)_{χ\mathrm{PT}}\,\mathrm{MeV}$ and $f_s=178(4)_\mathrm{stat}(1)_{χ\mathrm{PT}}\,\mathrm{MeV}$. Finally, we present a test of the Veneziano Witten formula using our lattice data.

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arXiv2019

The leading hadronic contribution to $(g-2)_μ$ from lattice QCD with $N_{\rm f}=2+1$ flavours of O($a$) improved Wilson quarks

The comparison of the theoretical and experimental determinations of the anomalous magnetic moment of the muon $(g-2)_μ$ constitutes one of the strongest tests of the Standard Model at low energies. In this article, we compute the leading hadronic contribution to $(g-2)_μ$ using lattice QCD simulations employing Wilson quarks. Gauge field ensembles at four different lattice spacings and several values of the pion mass down to its physical value are used. We apply the O($a$) improvement programme with two discretizations of the vector current to better constrain the approach to the continuum limit. The electromagnetic current correlators are computed in the time-momentum representation. In addition, we perform auxiliary calculations of the pion form factor at timelike momenta in order to better constrain the tail of the isovector correlator and to correct its dominant finite-size effect. For the numerically dominant light-quark contribution, we have rescaled the lepton mass by the pion decay constant computed on each lattice ensemble. We perform a combined chiral and continuum extrapolation to the physical point, and our final result is $ a_μ^{\rm hvp}=(720.0\pm12.4_{\rm stat}\,\pm9.9_{\rm syst})\cdot10^{-10}$. It contains the contributions of quark-disconnected diagrams, and the systematic error has been enlarged to account for the missing isospin-breaking effects.

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