arXiv subjects

Gunnar S. Bali

Publications and source records attributed to Gunnar S. Bali.

At least 19 recordsLinked to original sources

arXiv2026

Gauge-invariant Higgs mechanism via gradient-flow regularization

We provide a manifestly gauge-invariant description of the Higgs mechanism in the Standard Model, casting it not as the breaking of a local symmetry, but as a smooth, analytic crossover from a high-temperature symmetric phase to a low-temperature Higgs phase. Taking the vacuum expectation value of a gauge-invariant local scalar operator and constructing composite quasi-particle states from the original fields of the Lagrangian usually introduces contact-term divergences. Previous attempts to circumvent this issue via bilocal operators remain unsatisfactory. Here we demonstrate that the gradient flow at a flow time $t$ provides a clean, structurally sound, and Lorentz-covariant regularization that permits a consistent, renormalon-free matching onto the standard $\overline{\text{MS}}$ scheme at a scale $μ\sim 1/\sqrt{2t}\gg m_t$. Beyond its theoretical appeal, this construction clarifies a number of conceptional and practical questions. We demonstrate the utility of this framework at the one-loop level, thereby establishing the foundation for future electroweak precision physics in this approach.

hep-ph↗

arXiv2023

Octet baryon isovector charges from $N_f = 2 + 1$ lattice QCD

We determine the axial, scalar and tensor isovector charges of the nucleon, sigma and cascade baryons as well as the difference between the up and down quark masses, $m_u-m_d$. We employ gauge ensembles with $N_f=2+1$ non-perturbatively improved Wilson fermions at six values of the lattice spacing in the range $a\approx (0.039 - 0.098) \,$fm, generated by the Coordinated Lattice Simulations (CLS) effort. The pion mass $M_π$ ranges from around $430 \, $MeV down to a near physical value of $130 \, $MeV and the linear spatial lattice extent $L$ varies from $6.5\,M_π^{-1}$ to $3.0\,M_π^{-1}$, where $L M_π\geq 4$ for the majority of the ensembles. This allows us to perform a controlled interpolation/extrapolation of the charges to the physical mass point in the infinite volume and continuum limit. Investigating SU(3) flavour symmetry, we find moderate symmetry breaking effects for the axial charges at the physical quark mass point, while no significant effects are found for the other charges within current uncertainties.

hep-lat↗

arXiv2023

Scale setting and the light baryon spectrum in $N_f=2+1$ QCD with Wilson fermions

We determine the light baryon spectrum on ensembles generated by the Coordinated Lattice Simulations (CLS) effort, employing $N_f=2+1$ flavours of non-perturbatively improved Wilson fermions. The hadron masses are interpolated and extrapolated within the quark mass plane, utilizing three distinct trajectories, two of which intersect close to the physical quark mass point and the third one approaching the SU(3) chiral limit. The results are extrapolated to the continuum limit, utilizing six different lattice spacings ranging from $a\approx 0.10\,$fm down to below $0.04\,$fm. The light pion mass varies from $M_π\approx 429\,$MeV down to $127\,$MeV. In general, the spatial extent is kept larger than four times the inverse pion mass and larger than $2.3\,$fm, with additional small and large volume ensembles to investigate finite size effects. We determine the Wilson flow scales $\sqrt{t_{0,{\rm ph}}}=0.1449^{(7)}_{(9)}\,$fm and $t_0^*\approx t_{0,{\rm ph}}$ from the octet cascade ($Ξ$ baryon). Determining the light baryon spectrum in the continuum limit, we find the nucleon mass $m_N=941.7^{(6.5)}_{(7.6)}\,$MeV and the other stable baryon masses to agree with their experimental values within sub-percent level uncertainties. Moreover, we determine SU(3) and SU(2) chiral perturbation theory low energy constants, including the octet and the $Ω$ baryon sigma~terms $σ_{πN}=43.9(4.7)\,$MeV, $σ_{πΛ}=28.2^{(4.3)}_{(5.4)}\,$MeV, $σ_{πΣ}=25.9^{(3.8)}_{(6.1)}\,$MeV, $σ_{πΞ}=11.2^{(4.5)}_{(6.4)}\,$MeV and $σ_{πΩ}=6.9^{(5.3)}_{(4.3)}\,$MeV, as well as various parameters, renormalization factors and improvement coefficients that are relevant for simulations with our lattice action.

hep-lat↗

arXiv2022

Leading order mesonic and baryonic SU(3) low energy constants from $N_f = 3$ lattice QCD

We determine the leading order mesonic~($B_0$ and $F_0$) and baryonic~($m_0$, $D$ and $F$) SU(3) chiral perturbation theory low energy constants from lattice QCD. We employ gauge ensembles with $N_f=3$ (i.e., $m_u=m_d=m_s$) non-perturbatively improved Wilson fermions at six distinct values of the lattice spacing in the range $a\approx (0.039 - 0.098)$ fm, which constitute a subset of the Coordinated Lattice Simulations (CLS) gauge ensembles. The pseudoscalar meson mass $M_π$ ranges from around $430$ MeV down to $240$ MeV and the linear spatial lattice extent $L$ from $6.4\,M_π^{-1}$ to $3.3\,M_π^{-1}$, where $ L M_π\geq 4$ for the majority of the ensembles. This allows us to perform a controlled extrapolation of all the low energy constants to the chiral, infinite volume and continuum limits. We find the SU(3) chiral condensate and $F_0$ to be smaller than their SU(2) counterparts while the Gell-Mann--Oakes--Renner parameters $B_0\approx B$ are similar. Regarding baryonic LECs, we obtain $F/D = 0.612^{(14)}_{(12)}$.

hep-lat↗

arXiv2021

Properties of the $η$ and $η^{\prime}$ mesons: Masses, decay constants and gluonic matrix elements

We present results for the $η$ and $η^\prime$ masses and their four independent decay constants at the physical point as well as their anomalous gluonic matrix elements $a_{η^{(\prime)}}$. The chiral and continuum limit extrapolation is performed on twenty-one $N_f = 2+1$ Coordinated Lattice Simulations (CLS) ensembles with non-perturbatively improved Wilson fermions at four different lattice spacings and along two trajectories in the quark mass plane, including one ensemble very close to physical quark masses. For the first time the decay constants are determined directly from the axialvector matrix elements without model assumptions. This allows us to study their QCD scale dependence and to determine all low-energy constants contributing at next-to-leading order in large-$N_c$ ChPT at a well defined QCD renormalization scale. We also discuss higher excited states in the $1400\,\mathrm{MeV}$ region.

hep-lat↗

arXiv2021

Investigating $\mathbf{N \to Nπ}$ axial matrix elements

Excited state contamination is one of the most challenging sources of systematics to tackle in the determination of nucleon matrix elements and form factors. The signal-to-noise problem prevents one from considering large source-sink time separations for the three-point functions to ensure ground state dominance. Instead, relevant analyses consider multi-state fits. Excited state contributions are particularly significant in the axial channel. In this work, we confront the problem directly. Since the major source of contamination is understood to be related to pion production, we consider three-point correlation functions with a nucleon operator at the source and a nucleon-pion interpolating operator at the sink, which allows studies of $N \to Nπ$ matrix elements. We discuss the construction of these three-point correlation functions and we solve the generalized eigenvalue problem (GEVP) using different sets of nucleon and nucleon-pion interpolators. The analysis is performed on the CLS ensemble A653 with $m_π\approx 420$ MeV. Results were generated with valence quark masses corresponding to $m_π\approx 1750$ MeV and $m_π\approx 420$ MeV.

hep-lat↗

arXiv2021

Double parton distributions in the nucleon from lattice QCD

We evaluate nucleon four-point functions in the framework of lattice QCD in order to extract the first Mellin moment of double parton distributions (DPDs) in the unpolarized proton. In this first study, we employ an nf = 2 + 1 ensemble with pseudoscalar masses of mpi = 355 MeV and mK = 441 MeV. The results are converted to the scale mu = 2 GeV. Our calculation includes all Wick contractions, and for almost all of them a good statistical signal is obtained. We analyze the dependence of the DPD Mellin moments on the quark flavor and the quark polarization. Furthermore, the validity of frequently used factorization assumptions is investigated.

hep-lat↗

arXiv2021

Masses and decay constants of the $η$ and $η^\prime$ mesons from lattice QCD

We determine the masses, the singlet and octet decay constants as well as the anomalous matrix elements of the $η$ and $η^\prime$ mesons in $N_f=2+1$ QCD\@. The results are obtained using twenty-one CLS ensembles of non-perturbatively improved Wilson fermions that span four lattice spacings ranging from $a\approx 0.086\,$fm down to $a\approx 0.050\,$fm. The pion masses vary from $M_π=420\,$MeV to $126\,$MeV and the spatial lattice extents $L_s$ are such that $L_sM_π\gtrsim 4$, avoiding significant finite volume effects. The quark mass dependence of the data is tightly constrained by employing two trajectories in the quark mass plane, enabling a thorough investigation of U($3$) large-$N_c$ chiral perturbation theory (ChPT). The continuum limit extrapolated data turn out to be reasonably well described by the next-to-leading order ChPT parametrization and the respective low energy constants are determined. The data are shown to be consistent with the singlet axial Ward identity and, for the first time, also the matrix elements with the topological charge density are computed. We also derive the corresponding next-to-leading order large-$N_{c}$ ChPT formulae. We find $F^8 = 115.0(2.8)~\text{MeV}$, $θ_{8} = -25.8(2.3)^{\circ}$, $θ_0 = -8.1(1.8)^{\circ}$ and, in the $\overline{\mathrm{MS}}$ scheme for $N_f=3$, $F^{0}(μ= 2\,\mathrm{GeV}) = 100.1(3.0)~\text{MeV}$, where the decay constants read $F^8_η=F^8\cos θ_8$, $F^8_{η^\prime}=F^8\sin θ_8$, $F^0_η=-F^0\sin θ_0$ and $F^0_{η^\prime}=F^0\cos θ_0$. For the gluonic matrix elements, we obtain $a_η(μ= 2\,\mathrm{GeV}) = 0.0170(10)\,\mathrm{GeV}^{3}$ and $a_{η^{\prime}}(μ= 2\,\mathrm{GeV}) = 0.0381(84)\,\mathrm{GeV}^{3}$, where statistical and all systematic errors are added in quadrature.

hep-lat↗

arXiv2021

Double parton distributions in the pion from lattice QCD

We perform a lattice study of double parton distributions in the pion, using the relationship between their Mellin moments and pion matrix elements of two local currents. A good statistical signal is obtained for almost all relevant Wick contractions. We investigate correlations in the spatial distribution of two partons in the pion, as well as correlations involving the parton polarisation. The patterns we observe depend significantly on the quark mass. We investigate the assumption that double parton distributions approximately factorise into a convolution of single parton distributions.

hep-lat↗

arXiv2020

Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD

We present the first lattice determination of the two lowest Gegenbauer moments of the leading-twist pion and kaon light-cone distribution amplitudes with full control of all errors. The calculation is carried out on 35 different CLS ensembles with $N_f=2+1$ flavors of dynamical Wilson-clover fermions. These cover a multitude of pion and kaon mass combinations (including the physical point) and 5 different lattice spacings down to $a=0.039\,$fm. The momentum smearing technique and a new operator basis are employed to reduce statistical fluctuations and to improve the overlap with the ground states. The results are obtained from a combined chiral and continuum limit extrapolation that includes three separate trajectories in the quark mass plane. The present arXiv version (v3) includes an Addendum where we update the results using the recently calculated three-loop matching factors for the conversion from the RI'/SMOM to the $\overline{\text{MS}}$ scheme. We find $a_2^π=0.116^{+19}_{-20}$ for the pion, $a_1^K=0.0525^{+31}_{-33}$ and $a_2^K=0.106^{+15}_{-16}$ for the kaon. We also include the previous values, which were obtained with two-loop matching.

hep-lat↗

arXiv2020

Magnetic susceptibility of QCD matter and its decomposition from the lattice

We determine the magnetic susceptibility of thermal QCD matter by means of first principles lattice simulations using staggered quarks with physical masses. A novel method is employed that only requires simulations at zero background field, thereby circumventing problems related to magnetic flux quantization. After a careful continuum limit extrapolation, diamagnetic behavior (negative susceptibility) is found at low temperatures and strong paramagnetism (positive susceptibility) at high temperatures. We revisit the decomposition of the magnetic susceptibility into spin- and orbital angular momentum-related contributions. The spin term -- related to the normalization of the photon lightcone distribution amplitude at zero temperature -- is calculated non-perturbatively and extrapolated to the continuum limit. Having access to both the full magnetic susceptibility and the spin term, we calculate the orbital angular momentum contribution for the first time. The results reveal the opposite of what might be expected based on a free fermion picture. We provide a simple parametrization of the temperature- and magnetic field-dependence of the QCD equation of state that can be used in phenomenological studies.

hep-lat↗

arXiv2020

Nucleon axial structure from lattice QCD

We present a new analysis method that allows one to understand and model excited state contributions in observables that are dominated by a pion pole. We apply this method to extract axial and (induced) pseudoscalar nucleon isovector form factors, which satisfy the constraints due to the partial conservation of the axial current up to expected discretization effects. Effective field theory predicts that the leading contribution to the (induced) pseudoscalar form factor originates from an exchange of a virtual pion, and thus exhibits pion pole dominance. Using our new method, we can recover this behavior directly from lattice data. The numerical analysis is based on a large set of ensembles generated by the CLS effort, including physical pion masses, large volumes (with up to $96^3 \times 192$ sites and $L m_π= 6.4$), and lattice spacings down to $0.039 \, \text{fm}$, which allows us to take all the relevant limits. We find that some observables are much more sensitive to the choice of parametrization of the form factors than others. On the one hand, the $z$-expansion leads to significantly smaller values for the axial dipole mass than the dipole ansatz ($M_A^{\text{$z$-exp}}=1.02(10) \, \text{GeV}$ versus $M_A^{\text{dipole}} = 1.31(8) \, \text{GeV}$). On the other hand, we find that the result for the induced pseudoscalar coupling at the muon capture point is almost independent of the choice of parametrization ($g_P^{\star \ \text{$z$-exp}} = 8.68(45)$ and $g_P^{\star \ \text{dipole}} = 8.30(24)$), and is in good agreement with both, chiral perturbation theory predictions and experimental measurement via ordinary muon capture. We also determine the axial coupling constant $g_A$.

hep-lat↗

arXiv2019

Hyperon couplings from $N_f = 2 + 1$ lattice QCD

We compute various (generalized) isovector charges of the octet baryons. These include $g_A$, $g_T$ and $g_S$ as well as the unpolarized, polarized and transversity parton distribution function (PDF) momentum fractions $\langle x\rangle_{u^+-d^+}$, $\langle x\rangle_{Δu^--Δd^-}$ and $\langle x\rangle_{δu^+-δ^+}$. The simulations are carried out on a subset of the (isospin symmetric) $N_f=2+1$ flavour Coordinated Lattice Simulations (CLS) gauge ensembles with lattice spacings ranging from $a\approx 0.086\,$fm down to $a\approx 0.050\,$fm. First results on the breaking of flavour symmetry and the low energy constants $F$ and $D$ are presented. While SU(3) flavour symmetry violations are found to be sizeable for $g_A=\langle 1\rangle_{Δu^+-Δd^+}$, these are quite small for $g_T=\langle 1\rangle_{δu^--δd^-}$ and $\langle x\rangle_{u^+-d^+}$.

hep-lat↗

arXiv2019

Nucleon generalized form factors from two-flavor lattice QCD

We determine the generalized form factors, which correspond to the second Mellin moment (i.e., the first $x$-moment) of the generalized parton distributions of the nucleon at leading twist. The results are obtained using lattice QCD with $N_f=2$ nonperturbatively improved Wilson fermions, employing a range of quark masses down to an almost physical value with a pion mass of about 150 MeV. We also present results for the isovector quark angular momentum and for the first $x$-moment of the transverse quark spin density. We compare two different fit strategies and find that directly fitting the ground state matrix elements to the functional form expected from Lorentz invariance and parametrized in terms of form factors yields comparable, and usually more stable results than the traditional approach where the form factors are determined from an overdetermined linear system based on the fitted matrix elements.

hep-lat↗

arXiv2019

Light-cone distribution amplitudes of octet baryons from lattice QCD

We present lattice QCD results for the wave function normalization constants and the first moments of the distribution amplitudes for the lowest-lying baryon octet. The analysis is based on a large number of $N_f=2+1$ ensembles comprising multiple trajectories in the quark mass plane including physical pion (and kaon) masses, large volumes, and, most importantly, five different lattice spacings down to $a=0.039\,\mathrm{fm}$. This allows us to perform a controlled extrapolation to the continuum and infinite volume limits by a simultaneous fit to all available data. We demonstrate that the formerly observed violation of flavor symmetry breaking constraints can, indeed, be attributed to discretization effects that vanish in the continuum limit.

hep-lat↗

arXiv2018

Two-current correlations in the pion on the lattice

We perform a systematic study of the correlation functions of two quark currents in a pion using lattice QCD. We obtain good signals for all but one of the relevant Wick contractions of quark fields. We investigate the quark mass dependence of our results and test the importance of correlations between the quark and the antiquark in the pion. Our lattice data are compared with predictions from chiral perturbation theory.

hep-lat↗

arXiv2018

Pion distribution amplitude from Euclidean correlation functions: Exploring universality and higher-twist effects

Building upon our recent study arXiv:1709.04325, we investigate the feasibility of calculating the pion distribution amplitude from suitably chosen Euclidean correlation functions at large momentum. We demonstrate in this work the advantage of analyzing several correlation functions simultaneously and extracting the pion distribution amplitude from a global fit. This approach also allows us to study higher-twist corrections, which are a major source of systematic error. Our result for the higher-twist parameter $δ^π_2$ is in good agreement with estimates from QCD sum rules. Another novel element is the use of all-to-all propagators, calculated using stochastic estimators, which enables an additional volume average of the correlation functions, thereby reducing statistical errors.

hep-lat↗

arXiv2018

Pion and Kaon Distribution Amplitudes from lattice QCD: towards the continuum limit

We present the current status of a non-perturbative lattice calculation of the moments of the pion and kaon distribution amplitudes by the RQCD collaboration. Our investigation is carried out using $N_f=2+1$ dynamical, non-perturbatively O(a)-improved Wilson fermions on the CLS ensembles with 5 different lattice spacings and pion masses down to the physical pion mass. A combined continuum and chiral extrapolation to the physical point is performed along two independent quark mass trajectories simultaneously. We employ momentum smearing in order to decrease the contamination by excited states and increase statistical precision.

hep-lat↗