arXiv subjects

Hartmut Wittig

Publications and source records attributed to Hartmut Wittig.

At least 73 records · Page 4Linked to original sources

arXiv2019

Testing the strength of the $\text{U}_A(1)$ anomaly at the chiral phase transition in two-flavour QCD

We study the thermal transition of QCD with two degenerate light flavours by lattice simulations using $\mathcal{O}(a)$-improved Wilson quarks. Particular emphasis lies on the pattern of chiral symmetry restoration, which we probe via the static screening correlators. On $32^3$ volumes we observe that the screening masses in transverse iso-vector vector and axial-vector channels become degenerate at the transition temperature. The splitting between the screening masses in iso-vector scalar and pseudoscalar channels is strongly reduced compared to the splitting at zero temperature and is actually consistent with zero within uncertainties. In this proceedings article we extend our studies to matrix elements and iso-singlet correlation functions. Furthermore, we present results on larger volumes, including first results at the physical pion mass.

hep-lat↗

arXiv2019

Iso-vector axial form factors of the nucleon in two-flavour lattice QCD

We present a lattice calculation of the nucleon iso-vector axial and induced pseudoscalar form factors on the CLS ensembles using $N_{\rm f}=2$ dynamical flavours of non-perturbatively $\mathcal{O}(a)$-improved Wilson fermions and an $\mathcal{O}(a)$-improved axial current together with the pseudoscalar density. Excited-state effects in the extraction of the form factors are treated using a variety of methods, with a detailed discussion of their respective merits. The chiral and continuum extrapolation of the results is performed both using formulae inspired by Heavy Baryon Chiral Perturbation Theory (HBChPT) and a global approach to the form factors based on a chiral effective theory (EFT) including axial vector mesons. Our results indicate that careful treatment of excited-state effects is important in order to obtain reliable results for the axial form factors of the nucleon, and that the main remaining error stems from the systematic uncertainties of the chiral extrapolation. As final results, we quote $g_{\rm A} = 1.278 \pm 0.068\genfrac{}{}{0pt}{1}{+0.000}{-0.087}$, $\langle r_{\rm A}^2\rangle = 0.360 \pm 0.036\genfrac{}{}{0pt}{1}{+0.080}{-0.088}~\mathrm{fm}^2$, and $g_{\rm P} = 7.7 \pm 1.8 \genfrac{}{}{0pt}{1}{+0.8}{-2.0}$ for the axial charge, axial charge radius and induced pseudoscalar charge, respectively, where the first error is statistical and the second is systematic.

hep-lat↗

arXiv2019

Lattice QCD and the anomalous magnetic moment of the muon

The anomalous magnetic moment of the muon, a_mu, has been measured with an overall precision of 540 ppb by the E821 experiment at BNL. Since the publication of this result in 2004 there has been a persistent tension of 3.5 standard deviations with the theoretical prediction of a_mu based on the Standard Model. The uncertainty of the latter is dominated by the effects of the strong interaction, notably the hadronic vacuum polarisation (HVP) and the hadronic light-by-light (HLbL) scattering contributions, which are commonly evaluated using a data-driven approach and hadronic models, respectively. Given that the discrepancy between theory and experiment is currently one of the most intriguing hints for a possible failure of the Standard Model, it is of paramount importance to determine both the HVP and HLbL contributions from first principles. In this review we present the status of lattice QCD calculations of the leading-order HVP and the HLbL scattering contributions, a_mu^hvp and a_mu^hlbl. After describing the formalism to express a_mu^hvp and a_mu^hlbl in terms of Euclidean correlation functions that can be computed on the lattice, we focus on the systematic effects that must be controlled to achieve a first-principles determination of the dominant strong interaction contributions to a_mu with the desired level of precision. We also present an overview of current lattice QCD results for a_mu^hvp and a_mu^hlbl, as well as related quantities such as the transition form factor for pi0 -> gamma*gamma*. While the total error of current lattice QCD estimates of a_mu^hvp has reached the few-percent level, it must be further reduced by a factor 5 to be competitive with the data-driven dispersive approach. At the same time, there has been good progress towards the determination of a_mu^hlbl with an uncertainty at the 10-15%-level.

hep-lat↗

arXiv2018

The hadronic vacuum polarization contribution to $(g-2)_μ$ from $2+1$ flavours of O($a$) improved Wilson quarks

We report on our ongoing project to determine the leading-order hadronic vacuum polarisation contribution to the muon $g-2$, using ensembles with $N_f=2+1$ flavours of O($a$) improved Wilson quarks generated by the CLS effort, with pion masses down to the physical value. We employ O($a$) improved versions of the local and conserved vector currents to compute the contributions of the light, strange and charm quarks to $(g-2)_μ$, using the time-momentum representation. We perform a detailed investigation of the systematic effects arising from constraining the long-distance regime of the vector correlator. To this end we make use of auxiliary calculations in the iso-vector channel using distillation and the Lüscher formalism. Our results are corrected for finite-volume effects by computing the timelike pion form factor in finite and infinite volume. For certain parameter choices, the corrections computed in this way can also be confronted with results determined on different volumes. Currently, the overall precision of our results is limited by the uncertainties in the lattice scale.

hep-lat↗

arXiv2018

Nucleon charges and quark momentum fraction with $N_f=2+1$ Wilson fermions

We present a nucleon structure analysis including local isovector charges as well as twist-2 operator insertions. Computations are performed on CLS ensembles with $N_f=2+1$ Wilson fermions, covering four values of the lattice spacing and pion masses down to $M_π\approx 200\,\mathrm{MeV}$. Several source-sink separations (typically $\sim 1.0\,\mathrm{fm}$ to $\sim 1.5\,\mathrm{fm}$) allow us to assess excited-state contaminations. Results on each ensemble are obtained from simultaneous two-state fits including all observables and all available source-sink separations with the mass gap as a free fit parameter. Finally, the chiral, continuum and finite size extrapolation is performed to extract physical results.

hep-lat↗

arXiv2018

Towards leading isospin breaking effects in mesonic masses with open boundaries

We present an exploratory study of leading isospin breaking effects in mesonic masses using $O(a)$ improved Wilson fermions with open boundaries. Isospin symmetry is explicitly broken by distinct masses and electric charges of the up and down quarks. In order to be able to make use of existing isosymmetric QCD gauge ensembles we apply reweighting techniques. The path integral describing QCD+QED is expanded perturbatively in powers of deviations in the quark masses and the inverse strong coupling as well as the electromagnetic coupling. We have constructed QED$_{\mathrm{L}}$, which we use as a finite volume formulation of QED, for open boundaries. We will also give a first insight into contributions from quark disconnected diagrams.

hep-lat↗

arXiv2018

The $H$ dibaryon from lattice QCD with SU(3) flavor symmetry

We show recent results from the Mainz group using $N_f = 2 + 1$ CLS ensembles generated at the $SU(3)$ symmetric point. Temporal correlation functions using two-baryon interpolating operators are calculated with the distillation method. In addition to the spin-0 operators relevant for studying the $H$ dibaryon, we added spin-1 operators to our basis, thereby extending our results to other flavor sectors. These preliminary results show a finite-volume energy below the $ΛΛ$ threshold. Further calculations are necessary to establish whether the $H$ dibaryon is bound at the physical point.

hep-lat↗

arXiv2018

Strange nucleon form factors with $N_f = 2 + 1$ O($a$)-improved Wilson fermions

We present preliminary results for strangeness form factors of the nucleon computed on the CLS ensembles with $N_f=2+1$ flavors of O($a$)-improved Wilson fermions. Our calculations are performed at two values of the lattice spacing ($a \in \{0.064, 0.086\} \,\mathrm{fm}$) and three values of the pion mass ($m_π\in \{ 200, 280, 340\} \,\mathrm{MeV}$). The determination of strangeness form factors proceeds by computing quark-disconnected diagrams, for which we employ hierarchical probing in four dimensions in order to deal with this most challenging part of the calculation. Furthermore, we investigate several source-sink separations to check for excited-state contamination.

hep-lat↗

arXiv2018

Parton distributions and lattice QCD calculations: a community white paper

In the framework of quantum chromodynamics (QCD), parton distribution functions (PDFs) quantify how the momentum and spin of a hadron are divided among its quark and gluon constituents. Two main approaches exist to determine PDFs. The first approach, based on QCD factorization theorems, realizes a QCD analysis of a suitable set of hard-scattering measurements, often using a variety of hadronic observables. The second approach, based on first-principle operator definitions of PDFs, uses lattice QCD to compute directly some PDF-related quantities, such as their moments. Motivated by recent progress in both approaches, in this document we present an overview of lattice-QCD and global-analysis techniques used to determine unpolarized and polarized proton PDFs and their moments. We provide benchmark numbers to validate present and future lattice-QCD calculations and we illustrate how they could be used to reduce the PDF uncertainties in current unpolarized and polarized global analyses. This document represents a first step towards establishing a common language between the two communities, to foster dialogue and to further improve our knowledge of PDFs.

hep-ph↗

arXiv2018

Hadronic light-by-light scattering contribution to the muon g-2 on the lattice

We briefly review several activities at Mainz related to hadronic light-by-light scattering (HLbL) using lattice QCD. First we present a position-space approach to the HLbL contribution in the muon g-2, where we focus on exploratory studies of the pion-pole contribution in a simple model and the lepton loop in QED in the continuum and in infinite volume. The second part describes a lattice calculation of the double-virtual pion transition form factor F_{pi^0 gamma^* gamma^*}(q_1^2, q_2^2) in the spacelike region with photon virtualities up to 1.5 GeV^2 which paves the way for a lattice calculation of the pion-pole contribution to HLbL. The third topic involves HLbL forward scattering amplitudes calculated in lattice QCD which can be described, using dispersion relations (HLbL sum rules), by gamma^* gamma^* -> hadrons fusion cross sections and then compared with phenomenological models.

hep-lat↗

arXiv2017

Hadronic light-by-light scattering amplitudes from lattice QCD versus dispersive sum rules

The hadronic contribution to the eight forward amplitudes of light-by-light scattering ($γ^*γ^*\to γ^*γ^*$) is computed in lattice QCD. Via dispersive sum rules, the amplitudes are compared to a model of the $γ^*γ^*\to {\rm hadrons}$ cross sections in which the fusion process is described by hadronic resonances. Our results thus provide an important test for the model estimates of hadronic light-by-light scattering in the anomalous magnetic moment of the muon, $a_μ^{\rm HLbL}$. Using simple parametrizations of the resonance $M\to γ^*γ^*$ transition form factors, we determine the corresponding monopole and dipole masses by performing a global fit to all eight amplitudes. Together with a previous dedicated calculation of the $π^0\to γ^*γ^*$ transition form factor, our calculation provides valuable information for phenomenological estimates of $a_μ^{\rm HLbL}$. The presented calculations are performed in two-flavor QCD with pion masses extending down to 190\,MeV at two different lattice spacings. In addition to the fully connected Wick contractions, on two lattice ensembles we also compute the (2+2) disconnected class of diagrams, and find that their overall size is compatible with a parameter-free, large-$N$ inspired prediction, where $N$ is the number of colors. Motivated by this observation, we estimate in the same way the disconnected contribution to $a_μ^{\rm HLbL}$.

hep-lat↗

arXiv2017

Light-by-light forward scattering amplitudes in Lattice QCD

We present our preliminary results on the calculation of hadronic light-by-light forward scattering amplitudes using vector four-point correlation functions computed on the lattice. Using a dispersive approach, forward scattering amplitudes can be described by $γ^* γ^* \to$ hadrons fusion cross sections and then compared with phenomenology. We show that only a few states are needed to reproduce our data. In particular, the sum rules considered in this study imply relations between meson$-γγ$ couplings and provide valuable information about individual form factors which are often used to estimate the meson-pole contributions to the hadronic light-by-light contribution to the $(g-2)$ of the muon.

hep-lat↗

arXiv2017

Nucleon average quark momentum fraction with $N_\mathrm{f}=2+1$ Wilson fermions

We report on an analysis of the average quark momentum fraction of the nucleon and related quantities using $N_\mathrm{f}=2+1$ Wilson fermions. Computations are performed on four CLS ensembles covering three values of the lattice spacing at pion masses down to $M_π\approx 200\,\mathrm{MeV}$. Several source-sink separations ($\sim 1.0\,\mathrm{fm}$ to $\sim 1.4\,\mathrm{fm}$) are used to assess the excited-state contamination. To gain further insight, the generalized pencil-of-functions approach has been implemented to reduce the excited-state contamination in the relevant two- and three-point functions. Preliminary results are shown for the isovector nucleon charges from vector, axial vector and tensor derivative (twist-2) operators.

hep-lat↗

arXiv2017

Towards leading isospin breaking effects in mesonic masses with $O(a)$ improved Wilson fermions

We present an exploratory study of leading isospin breaking effects in mesonic masses using $O(a)$ improved Wilson fermions. Isospin symmetry is explicitly broken by distinct masses and electric charges of the up and down quarks. In order to be able to make use of existing isosymmetric QCD gauge ensembles we apply reweighting techniques. The path integral describing QCD+QED is expanded perturbatively in powers of the light quarks' mass deviations and the electromagnetic coupling. We employ QED$_{\mathrm{L}}$ as a finite volume formulation of QED.

hep-lat↗

arXiv2017

Towards extracting the timelike pion form factor on CLS two-flavour ensembles

Results are presented from an ongoing study of the $ρ$ resonance. The focus is on CLS 2-flavour ensembles generated using $\mathcal{O}(a)$ improved Wilson fermions with pion masses ranging from $265$ to $437$ $\mathrm{MeV}$. The energy levels are extracted by solving the GEVP of correlator matrices, created with the distillation approach involving $ρ$ and $ππ$ interpolators. The study is done in the centre-of-mass frame and several moving frames. One aim of this work is to extract the timelike pion form factor after applying the Lüscher formalism. We therefore plan to integrate this study with the existing Mainz programme for the calculation of the hadronic vacuum polarization contribution to the muon $g-2$.

hep-lat↗

arXiv2017

Nucleon form factors and couplings with $N_\mathrm{f} = 2 + 1$ Wilson fermions

We present updated results on the nucleon electromagnetic form factors and axial coupling calculated using CLS ensembles with $N_\mathrm{f}=2+1$ dynamical flavours of Wilson fermions. The measurements are performed on large, fine lattices with a pseudoscalar mass reaching down to 200 MeV. The truncated-solver method is employed to reduce the variance of the measurements. Estimation of the matrix elements is challenging due to large contamination from excited states and further investigation is necessary to bring these effects under control.

hep-lat↗

arXiv2017

On the strength of the $U_A(1)$ anomaly at the chiral phase transition in $N_f=2$ QCD

We study the thermal transition of QCD with two degenerate light flavours by lattice simulations using $O(a)$-improved Wilson quarks. Temperature scans are performed at a fixed value of $N_t = (aT)^{-1}=16$, where $a$ is the lattice spacing and $T$ the temperature, at three fixed zero-temperature pion masses between 200 MeV and 540 MeV. In this range we find that the transition is consistent with a broad crossover. As a probe of the restoration of chiral symmetry, we study the static screening spectrum. We observe a degeneracy between the transverse isovector vector and axial-vector channels starting from the transition temperature. Particularly striking is the strong reduction of the splitting between isovector scalar and pseudoscalar screening masses around the chiral phase transition by at least a factor of three compared to its value at zero temperature. In fact, the splitting is consistent with zero within our uncertainties. This disfavours a chiral phase transition in the $O(4)$ universality class.

hep-lat↗

arXiv2016

Towards extracting the timelike pion form factor on CLS 2-flavour ensembles

Results are presented from an ongoing study of the $ρ$ resonance. We use the distillation approach in order to create correlator matrices involving $ρ$ and $ππ$ interpolators. The study is done in a centre-of-mass frame and several moving frames. We are able to extract energy levels by solving the GEVP of those correlator matrices. The initial exploratory study is being done on a CLS 2-flavour lattice with a pion mass of $451$ $\mathrm{MeV}$ using $\mathcal{O}(a)$ improved Wilson fermions. One aim of this work is to extract the timelike pion form factor after applying the Lüscher formalism. We also plan to integrate this study with the existing Mainz programme for the calculation of the hadronic vacuum polarization contribution to the muon $g-2$ and will extend our study to lower pion masses and larger lattices in the future, including ensembles with $2+1$ flavours.

hep-lat↗