arXiv subjects

Nicolas Garron

Publications and source records attributed to Nicolas Garron.

At least 19 recordsLinked to original sources

arXiv2026

$F_K/F_\pi$ as a precision test of a new four flavor Domain Wall Fermion action

We present a new set of lattice QCD ensembles with four flavors of smeared M\"obius Domain Wall Fermions with good chiral symmetry and small fifth-dimensional extent. A modest amount of computing resources was sufficient to generate 30 publicly-available ensembles spanning five lattice spacings and a broad range of pion masses down to physical. To scrutinize our action we determine $F_{K^{\pm}}/F_{\pi^{\pm}} = 1.1962(34)$, a key quantity for precision CKM unitarity tests, heralding a future of inexpensive high-precision calculations of hadronic observables with chiral fermions.

hep-lat↗

arXiv2025

Lattice Calculation of Short-Range Contributions to Neutrinoless Double-Beta Decay $\pi^-\to\pi^+ ee$ at Physical Pion Mass

Neutrinoless double-beta ($0\nu\beta\beta$) decays provide an excellent probe for determining whether neutrinos are Dirac or Majorana fermions. The short-range matrix elements associated with the $\pi^- \to \pi^+ ee$ process contribute at leading order in the $0\nu\beta\beta$ decay channel $nn \to ppee$ through pion exchange between nucleons. However, current lattice calculations show notable discrepancies in predicting these short-range contributions. To address this issue, we perform a lattice QCD calculation of the $\pi^- \to \pi^+ ee$ matrix elements using domain wall fermion ensembles at the physical pion mass generated by the RBC and UKQCD Collaborations. To mitigate contamination from around-the-world effects, we develop a new method to reconstruct and subtract them directly from lattice data. We then perform a nonperturbative renormalization using the RI/SMOM scheme. Compared with previous studies, this work reduces the uncertainties in the matrix elements and provides an independent cross-check that helps to reconcile the discrepancies among previous lattice calculations.

hep-lat↗

arXiv2024

Kaon mixing beyond the standard model with physical masses

We present non-perturbative results for beyond the standard model kaon mixing matrix elements in the isospin symmetric limit ($m_u=m_d$) of QCD, including a complete estimate of all dominant sources of systematic error. Our results are obtained from numerical simulations of lattice QCD with $N_f = 2+1$ flavours of dynamical domain wall fermions. For the first time, these quantities are simulated directly at the physical pion mass $m_\pi$~$\sim$~$139\,\mathrm{MeV}$ for two different lattice spacings. We include data at three lattice spacings in the range $a = 0.11 $ - $ 0.07\,\mathrm{fm}$ and with pion masses ranging from the physical value up to 450$\,\mathrm{MeV}$. Compared to our earlier work, we have added both direct calculations at physical quark masses and a third lattice spacing making the removal of discretisation effects significantly more precise and eliminating the need for any significant mass extrapolation beyond the range of simulated data. We renormalise the lattice operators non-perturbatively using RI-SMOM off-shell schemes. These schemes eliminate the need to model and subtract non-perturbative pion poles that arises in the RI-MOM scheme and, since the calculations are performed with domain wall fermions, the unphysical mixing between chirality sectors is suppressed. Our results for the bag parameters in the $\overline{\mathrm{MS}}$ scheme at $3\,\mathrm{GeV}$ are $B_K~\equiv~\mathcal{B}_1 = 0.5240(17)(54)$, $\mathcal{B}_2 = 0.4794(25)(35)$, $\mathcal{B}_3 = 0.746(13)(17)$, $\mathcal{B}_4 = 0.897(02)(10)$ and $\mathcal{B}_5 = 0.6882(78)(94)$, where the first error is from lattice uncertainties and the second is the uncertainty due to the perturbative matching to $\overline{\mathrm{MS}}$.

hep-lat↗

arXiv2019

Lattice QCD Determination of $g_A$

The nucleon axial coupling, $g_A$, is a fundamental property of protons and neutrons, dictating the strength with which the weak axial current of the Standard Model couples to nucleons, and hence, the lifetime of a free neutron. The prominence of $g_A$ in nuclear physics has made it a benchmark quantity with which to calibrate lattice QCD calculations of nucleon structure and more complex calculations of electroweak matrix elements in one and few nucleon systems. There were a number of significant challenges in determining $g_A$, notably the notorious exponentially-bad signal-to-noise problem and the requirement for hundreds of thousands of stochastic samples, that rendered this goal more difficult to obtain than originally thought. I will describe the use of an unconventional computation method, coupled with "ludicrously'" fast GPU code, access to publicly available lattice QCD configurations from MILC and access to leadership computing that have allowed these challenges to be overcome resulting in a determination of $g_A$ with 1% precision and all sources of systematic uncertainty controlled. I will discuss the implications of these results for the convergence of $SU(2)$ Chiral Perturbation theory for nucleons, as well as prospects for further improvements to $g_A$ (sub-percent precision, for which we have preliminary results) which is part of a more comprehensive application of lattice QCD to nuclear physics. This is particularly exciting in light of the new CORAL supercomputers coming online, Sierra and Summit, for which our lattice QCD codes achieve a machine-to-machine speed up over Titan of an order of magnitude.

hep-lat↗

arXiv2018

SU(3)-breaking ratios for $D_{(s)}$ and $B_{(s)}$ mesons

We present results for the $SU(3)$ breaking ratios of decay constants $f_{D_s}/f_D$ and $f_{B_s}/f_B$ and - for the first time with physical pion masses - the ratio of bag parameters $B_{B_s}/B_{B_d}$, as well as the ratio $\xi$, forming the ratio of the nonpeturbative contributions to neutral $B_{(s)}$ meson mixing. Our results are based on Lattice QCD simulations with chirally symmetric 2+1 dynamical flavors of domain wall fermions. Eight ensembles at three different lattice spacing in the range $a = 0.11 - 0.07\,\mathrm{fm}$ enter the analysis two of which feature physical light quark masses. Multiple heavy quark masses are simulated ranging from below the charm quark mass to half the bottom quark mass. The $SU(3)$ breaking ratios display a very benign heavy mass behaviour allowing for extrapolation to the physical bottom quark mass. The results in the continuum limit including all sources of systematic errors are $f_{D_s}/f_D = 1.1740(51)_\mathrm{stat}(^{+68}_{-68})_\mathrm{sys}$, $f_{B_s}/f_B = 1.1949(60)_\mathrm{stat}(^{+\hphantom{0}95}_{-175})_\mathrm{sys}$, $B_{B_s}/B_{B_d} = 0.9984(45)_\mathrm{stat}(^{+80}_{-63})_\mathrm{sys}$ and $\xi = 1.1939(67)_\mathrm{stat}(^{+\hphantom{0}95}_{-177})_\mathrm{sys}$. Combining these with experimentally measured values we extract the ratios of CKM matrix elements $|V_{cd}/V_{cs}| = 0.2164(57)_\mathrm{exp}(^{+12}_{-12})_\mathrm{lat}$ and $|V_{td}/V_{ts}| = 0.20329(41)_\mathrm{exp}(^{+162}_{-301})_\mathrm{lat}$.

hep-lat↗

arXiv2018

Beyond the Standard Model Kaon Mixing with Physical Masses

We present results from a calculation of beyond the standard model (BSM) kaon mixing including data physical with light quark masses. We simulate $N_f=2+1$ QCD with Iwasaki gauge and domain wall fermion action on 8 ensembles, spanning 3 lattice spacings and pion masses from the physical value up to 430MeV. The ratio of the BSM to standard model (SM) matrix elements are extracted from the correlation functions and renormalised using the RI-SMOM Rome-Southampton method with non-exceptional kinematics. The results at the physical point continuum limit are found by performing a simultaneous continuum chiral extrapolation. In this work we gain consistency with our previous results and achieve a reduction in both the statistical and systematic error.

hep-lat↗

arXiv2018

A percent-level determination of the nucleon axial coupling from Quantum Chromodynamics

The $\textit{axial coupling of the nucleon}$, $g_A$, is the strength of its coupling to the $\textit{weak}$ axial current of the Standard Model of particle physics, in much the same way as the electric charge is the strength of the coupling to the electromagnetic current. This axial coupling dictates the rate at which neutrons decay to protons, the strength of the attractive long-range force between nucleons and other features of nuclear physics. Precision tests of the Standard Model in nuclear environments require a quantitative understanding of nuclear physics rooted in Quantum Chromodynamics, a pillar of the Standard Model. The prominence of $g_A$ makes it a benchmark quantity to determine theoretically - a difficult task because quantum chromodynamics is non-perturbative, precluding known analytical methods. Lattice Quantum Chromodynamics provides a rigorous, non-perturbative definition of quantum chromodynamics that can be implemented numerically. It has been estimated that a precision of two percent would be possible by 2020 if two challenges are overcome: contamination of $g_A$ from excited states must be controlled in the calculations and statistical precision must be improved markedly. Here we report a calculation of $g_A^{QCD} = 1.271\pm0.013$, using an unconventional method inspired by the Feynman-Hellmann theorem that overcomes these challenges.

hep-lat↗

arXiv2017

BSM Kaon Mixing at the Physical Point

We present a progress update on the calculation of beyond the standard model (BSM) kaon mixing matrix elements at the physical point. Simulations are performed using 2+1 flavour domain wall lattice QCD with the Iwasaki gauge action at 3 lattice spacings and with pion masses ranging from 430 MeV to the physical pion mass.

hep-lat↗

arXiv2017

Nucleon axial coupling from Lattice QCD

We present state-of-the-art results from a lattice QCD calculation of the nucleon axial coupling, $g_A$, using Möbius Domain-Wall fermions solved on the dynamical $N_f = 2 + 1 + 1$ HISQ ensembles after they are smeared using the gradient-flow algorithm. Relevant three-point correlation functions are calculated using a method inspired by the Feynman-Hellmann theorem, and demonstrate significant improvement in signal for fixed stochastic samples. The calculation is performed at five pion masses of $m_π\sim \{400, 350, 310, 220, 130\}$~MeV, three lattice spacings of $a\sim\{0.15, 0.12, 0.09\}$~fm, and we do a dedicated volume study with $m_πL\sim\{3.22, 4.29, 5.36\}$. Control over all relevant sources of systematic uncertainty are demonstrated and quantified. We achieve a preliminary value of $g_A = 1.285(17)$, with a relative uncertainty of 1.33\%.

hep-lat↗

arXiv2017

Controlling the Sign Problem in Finite Density Quantum Field Theory

Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analogue. The smallness arises from an almost uniform distribution for the phase of the fermion determinant. Large cancellations upon integration is the origin of a poor signal to noise ratio. We study three alternatives for this integration: the Gaussian approximation, the "telegraphic" approximation, and a novel expansion in terms of theory-dependent moments and universal coefficients. We have tested the methods for QCD at finite densities of heavy quarks. We find that for two of the approximations the results are extremely close - if not identical - to the full answer in the strong sign problem regime.

hep-lat↗

arXiv2017

BSM Kaon Mixing at the Physical Point

We present new preliminary results for bag parameters and ratios of the BSM kaon mixing operators measured at the physical point. The results are obtained from simulations of domain wall fermion QCD with 2+1 flavours with an Iwasaki gauge, and now include pion and kaon masses very close to the physical point. We compare these results to our collaboration's previous results obtained from heavier simulated quarks.

hep-lat↗

arXiv2016

Tackling the sign problem with a moment expansion and application to Heavy dense QCD

Heavy-Dense QCD (HDQCD) is a popular theory to investigate the sign problem in quantum field theory. Besides its physical applications, HDQCD is relatively easy to implement numerically: the fermionic degrees of freedom are integrated out, and the fermion determinant factorises into local ones. The theory has a sign problem, the severeness of which depends on the value of the chemical potential, which makes this theory ideal to test the reach of new algorithms. We use the LLR approach to obtain the probability distribution of the phase of the fermion determinant. Our goal is the calculation of the phase factor expectation value, which appears as Fourier transform of this probability distribution. We here propose a new and systematic moment expansion for this phase factor. We compare the answer from the moment expansion order by order with the exact answer. We find that this expansion converge quickly and works very well in the strong sign problem region.

hep-lat↗

arXiv2016

Neutral Kaon Mixing Beyond the Standard Model with $n_f=2+1$ Chiral Fermions Part 1: Bare Matrix Elements and Physical Results

We compute the hadronic matrix elements of the four-quark operators relevant for $K^0-{\bar K^0}$ mixing beyond the Standard Model. Our results are from lattice QCD simulations with $n_f=2+1$ flavours of domain-wall fermion, which exhibit continuum-like chiral-flavour symmetry. The simulations are performed at two different values of the lattice spacing ($a\sim0.08$ and $a\sim 0.11 \, \fm $) and with lightest unitary pion mass $\sim 300\, \MeV$. For the first time, the full set of relevant four-quark operators is renormalised non-perturbatively through RI-SMOM schemes; a detailed description of the renormalisation procedure is presented in a companion paper. We argue that the intermediate renormalisation scheme is responsible for the discrepancies found by different collaborations. We also study different normalisations and determine the matrix elements of the relevant four-quark operators with a precision of $\sim 5\%$ or better.

hep-lat↗

arXiv2016

Anatomy of the sign-problem in heavy-dense QCD

QCD at finite densities of heavy quarks is investigated using the density-of-states method. The phase factor expectation value of the quark determinant is calculated to unprecedented precision as a function of the chemical potential. Results are validated using those from a reweighting approach where the latter can produce a significant signal-to-noise ratio. We confirm the particle-hole symmetry at low temperatures, find a strong sign problem at intermediate values of the chemical potential, and an inverse Silver Blaze feature for chemical potentials close to the onset value: here, the phase quenched theory underestimates the density of the full theory.

hep-lat↗

arXiv2015

CP violation and Kaon weak matrix elements from Lattice QCD

In this short review, I present the recent lattice computations of kaon weak matrix elements relevant to $K \to ππ$ decays and neutral kaon mixing. These matrix elements are key to the theoretical determination of the CP violation parameters $ε$ and $ε'$ . Impressive progress have been achieved recently, in particular the first realistic computation of $ε'/ε$ with physical kinematics has been reported in [1]. The novelty is the $ΔI = 1/2$ channel, whereas the $ΔI = 3/2$ contribution is now computed at several values of the lattice spacing and extrapolated to the continuum limit. I will also present the status of $B_K$ and discuss its error budget, with a particular emphasis on the perturbative error. Finally I will review the matrix elements of neutral kaon mixing beyond the standard model and will argue that the discrepancy observed by different collaborations could be explained by the renormalisation procedure of the relevant four-quark operators.

hep-lat↗

arXiv2015

$N_f=2+1+1$ renormalisation of four-quark operators

When several four-quark operators are allowed to mix through renormalisation, this can considerably amplify the problems coming from perturbative truncation and discretisation effects. In this work we investigate whether our previous $B_K$ strategy can conveniently be generalised to a wider set of operators, corresponding to the so-called "SUSY $B_K$" basis of four-quark operators. We show that the discretisation effects, when plotted as a function of $ap$, are surprisingly independent of the lattice spacing. They appear reasonably under control up to very large energy scales. This allows us to discuss the effect of varying the intermediate scale on which the perturbative matching is done, and therefore the prospects of future high-precision studies with a Rome-Southampton renormalisation.

hep-lat↗

arXiv2015

B-meson spectroscopy in HQET at order 1/m

We present a study of the B spectrum performed in the framework of Heavy Quark Effective Theory expanded to next-to-leading order in 1/m and non-perturbative in the strong coupling. Our analyses have been performed on Nf=2 lattice gauge field ensembles corresponding to three different lattice spacings and a wide range of pion masses. We obtain the Bs-meson mass and hyperfine splittings of the B- and Bs-mesons that are in good agreement with the experimental values and examine the mass difference m_{Bs}-m_B as a further cross-check of our previous estimate of the b-quark mass. We also report on the mass splitting between the first excited state and the ground state in the B and Bs systems.

hep-lat↗

arXiv2015

The kaon semileptonic form factor in Nf=2+1 domain wall lattice QCD with physical light quark masses

We present the first calculation of the kaon semileptonic form factor with sea and valence quark masses tuned to their physical values in the continuum limit of 2+1 flavour domain wall lattice QCD. We analyse a comprehensive set of simulations at the phenomenologically convenient point of zero momentum transfer in large physical volumes and for two different values of the lattice spacing. Our prediction for the form factor is f+(0)=0.9685(34)(14) where the first error is statistical and the second error systematic. This result can be combined with experimental measurements of K->pi decays for a determination of the CKM-matrix element for which we predict |Vus|=0.2233(5)(9) where the first error is from experiment and the second error from the lattice computation.

hep-lat↗