arXiv subjects

Matthias F. M. Lutz

Publications and source records attributed to Matthias F. M. Lutz.

At least 19 recordsLinked to original sources

arXiv2026

Decomposition of the axial-vector current in a finite box

We consider the matrix element of the axial-vector current between two nucleon states in a finite box. Starting from the chiral Lagrangian density with nucleon and Delta-isobar degrees of freedom, we study the finite-volume effects at the one-loop level. We show that the standard decomposition into the axial-vector and pseudoscalar form factor is incomplete in a finite box. We derive expressions for the complete set of in-box form factors at one loop, and demonstrate how to extract the full set from lattice correlation functions. We verify that the axial Ward identity holds in the chiral limit. We derive the one-loop expressions for the pseudoscalar form factor and verify that the in-box axial Ward identity away from the chiral limit is fulfilled also. Selected numerical results are shown for two flavor-SU(2) lattice ensembles. Sizable finite-volume effects are observed, with an important role for the Delta-isobar. We discuss the implications of our results for lattice studies of the axial-vector current. We conclude that full finite-box results are crucial for a precise determination of the form factors.

hep-lat↗

arXiv2026

The axial-vector form factor of the nucleon in a finite box

We consider the axial-vector form factor of the nucleon in a finite box. Starting from the chiral Lagrangian with nucleon and Delta-isobar degrees of freedom, we address, at the one-loop level, the impact of two types of finite-volume effects. On the one hand, there are the implicit effects from the in-box values of the nucleon and Delta-isobar masses. On the other hand, there are the explicit effects caused by computing the in-box loop integrals with the values of the nucleon and Delta-isobar masses obtained in the infinite-volume limit. Selected numerical results are shown for three lattice ensembles. We show that the implicit effects dominate the in-box form factor. Our results are presented in terms of a set of basis functions that generalize the Passarino-Veltman reduction scheme to the finite-box case, such that only scalar loop integrals have to be performed. The techniques we developed are more generally relevant for lattice studies of hadronic quantities.

hep-lat↗

arXiv2024

QCD in the chiral SU(3) limit from baryon masses on Lattice QCD ensembles

The baryon masses on CLS ensembles are used to determine the LEC that characterize QCD in the flavor-SU(3) limit with vanishing up, down, and strange quark masses. Here we reevaluate some of the baryon masses on flavor-symmetric ensembles with much-improved statistical precision, in particular for the decuplet states. These additional results then lead to a more significant chiral extrapolation of the Lattice data set to its chiral SU(3) limit. Our results are based on the chiral Lagrangian with baryon octet and decuplet fields considered at the one-loop level. Finite-box and discretization effects of the Lattice data are considered systematically. While in our global fit of the data we insist on large-Nc sum rules for the LEC that enter at N3LO, all other LEC are unconstrained. In particular, we obtain values for the chiral limit of the pion decay constant and the isospin-limit of the quark-mass ratio compatible with the FLAG report.

hep-lat↗

arXiv2024

How much strangeness is needed for the axial-vector form factor of the nucleon?

We consider the axial-vector together with its induced pseudo-scalar form factor of the nucleon as computed from the chiral Lagrangian with nucleon and isobar degrees of freedom. The form factors are evaluated at the one-loop level, where particular emphasis is put on the use of on-shell masses in the loop expressions. Our results are presented in terms of a novel set of basis functions that generalize the Passarino--Veltman scheme to the case where power-counting violating structures are to be subtracted. The particularly important role of the isobar degrees of freedom is emphasized. We obtain a significant and simultaneous fit to the available Lattice QCD results based on flavour SU(2) ensembles for the baryon masses and form factors up to pion masses of about 500 MeV. Our fits includes sizeable finite volume effects that are implied by using in-box values for the hadron masses entering our one-loop expressions. We conclude that from flavour SU(2) ensembles it appears not possible to predict the empirical formfactor at the desired precision. Effects from strange quarks are expected to remedy the situation.

hep-ph↗

arXiv2024

Precise Omega baryons from lattice QCD

In this paper we determine the masses of $I(J^P)=0\left(3/2^+\right)$ and $0\left(3/2^-\right)$ $Ω$-baryon ground states using lattice QCD. We utilise Wilson-clover ensembles with $2+1$ dynamical quark flavours generated by the CLS consortium along a trajectory with a constant trace of the quark-mass matrix. We show that N$^3$LO $\text{SU}(3)_f$ chiral perturbation theory expressions describe the ground-state masses with positive-parity well, and we use them to set the lattice scale. Methodologically, our combination of gauge-fixed wall sources and the generalized Pencil of Functions allows for high-precision determinations of the lattice spacing at a relative error of around $0.3\%$ with controlled excited-state contamination. The fit we perform allows for the continuum value of $t_0$ to vary, thereby determining this quantity with a comparable level of precision to that of the lattice scale. Using the resulting scales our measurement of the negative-parity $Ω^{3/2^{-}}$ state is found to be consistent with the recently-discovered $Ω(2012)^-$, which can therefore be assigned the quantum numbers $I(J^P)=0\left(3/2^-\right)$.

hep-lat↗

arXiv2023

Triangle and box diagrams in coupled-channel systems from the chiral Lagrangian

We perform an analysis of triangle- and box-loop contributions to the generalized potential in the scattering of Goldstone bosons off the J^P= 0^- and 1^- charmed mesons. Particular emphasis is put on the use of on-shell mass parameters in such contributions in terms of a renormalization scheme that ensures the absence of power-counting violating terms. This is achieved with a systematically extended set of Passarino--Veltman basis functions, that leads to manifest power-counting conserving one-loop expressions and avoids the occurrence of superficial kinematical singularities. Compact expressions to chiral order three and four are presented that are particularly useful in coding such coupled-channel systems. Our formal results are generic and prepare analogous computations for other systems, like meson-baryon scattering from the chiral Lagrangian.

hep-ph↗

arXiv2023

Low-energy constants in the chiral Lagrangian with baryon octet and decuplet fields from Lattice QCD data on CLS ensembles

We perform an analysis of Lattice QCD data on baryon octet and decuplet masses based on the chiral SU(3) Lagrangian. Low-energy constants (LEC) are adjusted to describe baryon masses from a large set of CLS ensembles, where finite-box and discretization effects are considered. The set is successfully compared against previous Lattice QCD data from ensembles generated with distinct QCD actions by the ETMC, QCDSF-UKQCD and HSC groups. Discretization effects are modelled by the use of action and lattice-scale dependent leading orders LEC, where uniform values are imposed in the limit of vanishing lattice scales. From the CLS data set we extract a pion-nucleon sigma term, $σ_{πN}= 58.7(1.2)$ MeV, compatible with its empirical value and a sizeable strangeness content of the nucleon with $σ_{sN} = -316(76)$ MeV.

hep-lat↗

arXiv2022

A coupled-channel system with anomalous thresholds and unitarity

We consider the isospin one-half example system, with $D \,π, D\,η, D_s \bar K, D^* π, D^*η, D^*\bar K$ coupled channels in the $J^P = 1^-$ partial wave, chosen such that various phenomena that come with the opening of an anomalous threshold can be illustrated in a step-wise procedure by a suitable variation of up, down and strange quark masses. We use a set of LEC in the chiral Lagrangian that were adjusted to a large set of Lattice QCD results. The six phase shifts and inelasticity parameters are presented for various choices of the pion mass. For a pion mass of 150 MeV there are no anomalous thresholds encountered. The small change from 150 MeV to 145 MeV pion mass causes a dramatic impact of the anomalous threshold on the phase shifts.

hep-ph↗

arXiv2022

Coupled-channel dynamics with chiral long-range forces in the open-charm sector of QCD

We perform an analysis of Lattice QCD data in the open-charm sector based on the chiral SU(3) Lagrangian. The low-energy constants are adjusted to recover the open-charm meson masses on Lattice QCD ensembles from HPQCD, ETMC and HSC with pion and kaon masses smaller than 550 MeV. A significant set of low-energy parameters is obtainable only if the most recent information from HSC on scattering observables is included in our global fit. For the first time our analysis considers the effect of left-hand cuts as developed in terms of a generalized potential approach (GPA) previously by one of the authors. Here we use coupled-channel interaction terms at the one-loop level. The elastic s-wave and p-wave $D\,π$, $D K $ and $D \bar K $ scattering phase shifts on ensembles with nominal pion masses of about 239 MeV and 391 MeV are reproduced faithfully. Based on such low-energy parameters we predict s- and p-wave phase shifts and inelasticities at physical quark masses, where the statistical uncertainties in the phase shifts are smaller than 1 degree always. Most striking would be the exotic s-wave $D_s π$ channel, for which we predict a resonance state at about 2.287 GeV where the phase shift passes through 90 degrees.

hep-ph↗

arXiv2022

Chiral excitations of open-beauty systems

We study the scattering of open-beauty mesons and Goldstone bosons as predicted by the chiral SU(3) Lagrangian. The impact of subleading order chiral interactions to systems with $J^P= 0^+$ and $J^P=1^+$ quantum numbers is worked out. We estimate the relevant low-energy coefficients from the open-charm sector, for which their values have been determined previously from sets of QCD lattice data. The leading order heavy-quark symmetry breaking effects are estimated by matching the $B$-meson ground-state chiral mass formula to the mass formula from the heavy-quark effective theory. We make refined predictions for the flavor anti-triplet and sextet resonances that are generated dynamically by coupled-channel interactions.

hep-ph↗

arXiv2022

The chiral Lagrangian with three flavors and large-Nc sum rules

We reconsider the chiral Lagrangian with three-flavor baryon fields. A systematic analysis of all LEC that contribute to the axial-vector and pseudoscalar currents in the baryon octet and decuplet fields at next-to-leading order is performed. While there are 4 LEC relevant at leading order, the number of relevant LEC at subleading chiral order is 23. For those a leading order large-$N_c$ analysis predicts 3 and 18 sum rules respectively. At the next accuracy level the number of sum rules is reduced to 2 and 8. Our results are illustrated by a tree-level analysis of available axial-vector coupling constants and strong decay widths of the baryon decuplet states.

hep-ph↗

arXiv2022

Axial-vector form factors of the baryon octet and chiral symmetry

We consider the axial-vector form factors of the baryon octet in flavor-SU(3) chiral perturbation theory. The baryon octet and decuplet and the pseudoscalar-meson octet are included as explicit degrees of freedom. We explore the use of on-shell meson and baryon masses in the one-loop contributions to the axial-vector form factors and focus on a consistent treatment in terms of chiral power counting. The convergence properties of such an approach are scrutinized. We discuss the potential for comparison to upcoming QCD lattice data.

hep-ph↗

arXiv2021

From lattice QCD to predictions of scattering phase shifts at the physical point

The Hadron Spectrum Collaboration (HSC) presented new results on two of their ensembles for s-wave scattering phase shifts in the open-charm sector of QCD. For such ensembles we have made predictions that are based on the chiral Lagrangian that were published two years ago. In this talk we confront our phase shifts with those of HSC. A remarkably consistent picture emerges. In particular there is mounting evidence for the existence of a flavor-sextet state in the $D π$ and $D^*π$ channels, that show a striking quark-mass dependence.

hep-lat↗

arXiv2020

A generalized Higgs potential with two degenerate minima for a dark QCD matter scenario

We consider the Higgs potential in generalizations of the Standard Model. The possibility of the potential to develop two almost degenerate minima is explored. This would imply that QCD matter at two distinct sets of quark masses is relevant for astrophysics and cosmology. If in the exotic minimum the QCD matter ground state is electromagnetically neutral, dark matter may consist of QCD matter and antimatter in bubbles of the Higgs field. We predict an abundance of gamma rays in the few MeV region as messengers of dark matter regions in space. In addition the ratio of dark matter to normal matter is expected to show a time dependence.

hep-ph↗

arXiv2020

On the axial-vector form factor of the nucleon and chiral symmetry

We consider the chiral Lagrangian with nucleon, isobar, and pion degrees of freedom. The baryon masses and the axial-vector form factor of the nucleon are derived at the one-loop level. We explore the impact of using on-shell baryon masses in the loop expressions. As compared to results from conventional chiral perturbation theory we find significant differences. An application to QCD lattice data is presented. We perform a global fit to the available lattice data sets for the baryon masses and the nucleon axial-vector form factor, and determine the low-energy constants relevant at N$^3$LO for the baryon masses and at N$^2$LO for the form factor. Partial finite-volume effects are considered. We point out that the use of on-shell masses in the loops results in non-analytic behavior of the baryon masses and the form factor as function of the pion mass, which becomes prominent for larger lattice volumes than presently used.

hep-lat↗

arXiv2020

On a first order transition in QCD with up, down and strange quarks

We consider the quark-mass dependence of the baryon octet and decuplet ground state masses. It is predicted that QCD dynamics implies a first order transition when increasing the strange quark mass from its chiral limit towards its physical value. Our claim relies on a global fit to the available QCD lattice data on such baryon masses. Quantitative results based on an application of the chiral SU(3) Lagrangian at N$^3$LO are discussed. We predict an anomalous sector of QCD where stable baryonic matter would be composed of lambda or anti-lambda particles rather than nucleons and anti-nucleons.

hep-lat↗

arXiv2019

Low-energy constants from charmed baryons on QCD lattices

We study the light quark-mass dependence of charmed baryon masses as measured by various QCD lattice collaborations. A global fit to such data based on the chiral SU(3) Lagrangian is reported on. All low-energy constants that are relevant at next-to-next-to-next-to-leading order (N$^3$LO) are determined from the lattice data sets where constraints from sum rules as they follow from large-Nc QCD at subleading order are considered. The expected hierarchy for the low-energy constants in the 1/Nc expansion is confirmed by our global fits to the lattice data. With our results the low-energy interaction of the Goldstone bosons with the charmed baryon ground states is well constrained and the path towards realistic coupled-channel computations in this sector of QCD is prepared.

hep-lat↗

arXiv2019

On chiral extrapolations of coupled-channel reaction dynamics for charmed mesons

We perform an analysis of QCD lattice data on masses of charmed meson with J^P = 0^- and J^P =1^- quantum numbers. The quark-mass dependence of the data set is used to gain information on the size of counter terms in the chiral Lagrangian formulated with open-charm mesons. Of particular interest are those counter terms that are active in the exotic flavour sextet channel. A chiral expansion scheme is developed and applied to the lattice data set. An accurate reproduction of the lattice data based on ensembles of PACS-CS, MILC, ETMC and HSC with pion and kaon masses smaller than 600 MeV is achieved. It is argued that a unique set of low-energy parameters is obtainable only if additional information from an HSC ensemble on some scattering phase shifts is included in our global fits. Based on such low-energy parameters we find a clear signal for a member of the exotic flavour sextet states in the pi D phase shift, between the eta D and bar K D_s thresholds. A striking dependence of such phase shifts on the values of the up, down and strange quarks is predicted.

hep-lat↗