arXiv subjects

Patrick Fritzsch

Publications and source records attributed to Patrick Fritzsch.

At least 55 records · Page 3Linked to original sources

arXiv2018

Controlling quark mass determinations non-perturbatively in three-flavour QCD

The determination of quark masses from lattice QCD simulations requires a non-perturbative renormalization procedure and subsequent scale evolution to high energies, where a conversion to the commonly used MS-bar scheme can be safely established. We present our results for the non-perturbative running of renormalized quark masses in Nf=3 QCD between the electroweak and a hadronic energy scale, where lattice simulations are at our disposal. Recent theoretical advances in combination with well-established techniques allows to follow the scale evolution to very high statistical accuracy, and full control of systematic effects.

hep-lat↗

arXiv2018

Non-perturbative quark mass renormalisation and running in $N_f=3$ QCD

We determine from first principles the quark mass anomalous dimension in Nf=3 QCD between the electroweak and hadronic scales. This allows for a fully non-perturbative connection of the perturbative and non-perturbative regimes of the Standard Model in the hadronic sector. The computation is carried out to high accuracy, employing massless O(a)-improved Wilson quarks and finite-size scaling techniques. We also provide the matching factors required in the renormalisation of light quark masses from lattice computations with O(a)-improved Wilson fermions and a tree-level Symanzik improved gauge action. The total uncertainty due to renormalisation and running in the determination of light quark masses in the SM is thus reduced to about 1%.

hep-lat↗

arXiv2018

A non-perturbative exploration of the high energy regime in $N_\text{f}=3$ QCD

Using continuum extrapolated lattice data we trace a family of running couplings in three-flavour QCD over a large range of scales from about 4 to 128 GeV. The scale is set by the finite space time volume so that recursive finite size techniques can be applied, and Schrödinger functional (SF) boundary conditions enable direct simulations in the chiral limit. Compared to earlier studies we have improved on both statistical and systematic errors. Using the SF coupling to implicitly define a reference scale $1/L_0\approx 4$ GeV through $\bar{g}^2(L_0) =2.012$, we quote $L_0 Λ^{N_{\rm f}=3}_{\overline{\rm MS}} =0.0791(21)$. This error is dominated by statistics; in particular, the remnant perturbative uncertainty is negligible and very well controlled, by connecting to infinite renormalization scale from different scales $2^n/L_0$ for $n=0,1,\ldots,5$. An intermediate step in this connection may involve any member of a one-parameter family of SF couplings. This provides an excellent opportunity for tests of perturbation theory some of which have been published in a letter [1]. The results indicate that for our target precision of 3 per cent in $L_0 Λ^{N_{\rm f}=3}_{\overline{\rm MS}}$, a reliable estimate of the truncation error requires non-perturbative data for a sufficiently large range of values of $α_s=\bar{g}^2/(4π)$. In the present work we reach this precision by studying scales that vary by a factor $2^5= 32$, reaching down to $α_s\approx 0.1$. We here provide the details of our analysis and an extended discussion.

hep-lat↗

arXiv2017

openQ*D simulation code for QCD+QED

The openQ*D code for the simulation of QCD+QED with C$^\star$ boundary conditions is presented. This code is based on openQCD-1.6, from which it inherits the core features that ensure its efficiency: the locally-deflated SAP-preconditioned GCR solver, the twisted-mass frequency splitting of the fermion action, the multilevel integrator, the 4th order OMF integrator, the SSE/AVX intrinsics, etc. The photon field is treated as fully dynamical and C$^\star$ boundary conditions can be chosen in the spatial directions. We discuss the main features of openQ*D, and we show basic test results and performance analysis. An alpha version of this code is publicly available and can be downloaded from http://rcstar.web.cern.ch/ .

hep-lat↗

arXiv2016

Non-perturbative running of quark masses in three-flavour QCD

We present our preliminary results for the computation of the non-perturbative running of renormalized quark masses in $N_f = 3$ QCD, between the electroweak and hadronic scales, using standard finite-size scaling techniques. The computation is carried out to very high precision, using massless $\mathcal{O}(a)$-improved Wilson quarks. Following the strategy adopted by the ALPHA Collaboration for the running coupling, different schemes are used above and below a scale $μ_0 \sim m_b$, which differ by using either the Schrödinger Functional or Gradient Flow renormalized coupling. We discuss our results for the running in both regions, and the procedure to match the two schemes.

hep-lat↗

arXiv2016

The determination of $α_s$ by the ALPHA collaboration

We review the ALPHA collaboration strategy for obtaining the QCD coupling at high scale. In the three-flavor effective theory it avoids the use of perturbation theory at $α> 0.2$ and at the same time has the physical scales small compared to the cutoff $1/a$ in all stages of the computation. The result $Λ_\overline{MS}^{(3)}=332(14)$~MeV is translated to $α_\overline{MS}(m_Z)=0.1179(10)(2)$ by use of (high order) perturbative relations between the effective theory couplings at the charm and beauty quark "thresholds". The error of this perturbative step is discussed and estimated as $0.0002$.

hep-lat↗

arXiv2016

Determination of the QCD $Λ$-parameter and the accuracy of perturbation theory at high energies

We discuss the determination of the strong coupling $α_\mathrm{\overline{MS}}^{}(m_\mathrm{Z})$ or equivalently the QCD $Λ$-parameter. Its determination requires the use of perturbation theory in $α_s(μ)$ in some scheme, $s$, and at some energy scale $μ$. The higher the scale $μ$ the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the $Λ$-parameter in three-flavor QCD, we perform lattice computations in a scheme which allows us to non-perturbatively reach very high energies, corresponding to $α_s = 0.1$ and below. We find that (continuum) perturbation theory is very accurate there, yielding a three percent error in the $Λ$-parameter, while data around $α_s \approx 0.2$ is clearly insufficient to quote such a precision. It is important to realize that these findings are expected to be generic, as our scheme has advantageous properties regarding the applicability of perturbation theory.

hep-ph↗

arXiv2016

Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\rm f}=3$ QCD

Using a finite volume Gradient Flow (GF) renormalization scheme with Schrödinger Functional (SF) boundary conditions, we compute the non-perturbative running coupling in the range $2.2 \lesssim {\bar g}_\mathrm{GF}^2(L) \lesssim 13$. Careful continuum extrapolations turn out to be crucial to reach our high accuracy. The running of the coupling is always between one-loop and two-loop and very close to one-loop in the region of $200\,{\rm MeV} \lesssim μ=1/L \lesssim 4\,{\rm GeV}$. While there is no convincing contact to two-loop running, we match non-perturbatively to the SF coupling with background field. In this case we know the $μ$ dependence up to $\sim 100\,{\rm GeV}$ and can thus connect to the $Λ$-parameter.

hep-lat↗

arXiv2015

Non-perturbative renormalization of tensor bilinears in Schrödinger Functional schemes

We present preliminary result for the study of the renormalization group evolution of tensor bilinears in Schrödinger Functional (SF) schemes for $N_f=0$ and $N_f=2$ QCD with non-perturbatively $\mathcal{O}(a)$-improved Wilson fermions. First $N_f=2+1$ results (proceeding in parallel with the ongoing computation of the running quark masses [1] are also discussed. A one-loop perturbative calculation of the discretisation effects for the relevant step scaling functions has been carried out for both Wilson and $\mathcal{O}(a)$-improved actions and for a large number of lattice resolutions. We also calculate the two-loop anomalous dimension in SF schemes for tensor currents through a scheme matching procedure with RI and $\overline{\rm MS}$. Thanks to the SF iterative procedure the non-perturbative running over two orders of magnitude in energy scales, as well as the corresponding Renormalization Group Invariant operators, have been determined.

hep-lat↗

arXiv2015

A status update on the determination of $Λ_{\overline{\rm MS}}^{N_{\rm f}=3}$ by the ALPHA collaboration

The ALPHA collaboration aims to determine $α_s(m_Z)$ with a total error below the percent level. A further step towards this goal can be taken by combining results from the recent simulations of 2+1-flavour QCD by the CLS initiative with a number of tools developed over the years: renormalized couplings in finite volume schemes, recursive finite size techniques, two-loop renormalized perturbation theory and the (improved) gradient flow on the lattice. We sketch the strategy, which involves both the standard SF coupling in the high energy regime and a gradient flow coupling at low energies. This implies the need for matching both schemes at an intermediate switching scale, $L_{\rm swi}$, which we choose roughly in the range 2-4 GeV. In this contribution we present a preliminary result for this matching procedure, and we then focus on our almost final results for the scale evolution of the SF coupling from $L_{\rm swi}$ towards the perturbative regime, where we extract the $N_{\rm f} = 3$ $Λ$-parameter, $Λ_{\overline{\rm MS}}^{N_{\rm f}=3}$, in units of $L_{\rm swi}$ . Connecting $L_{\rm swi}$ and thus the $Λ$-parameter to a hadronic scale such as $F_K$ requires 2 further ingredients: first, the connection of $L_{\rm swi}$ to $L_{\rm max}$ using a few steps with the step-scaling function of the gradient flow coupling, and, second, the continuum extrapolation of $L_{\rm max} F_K$.

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

Determination of c_sw in N_f=3+1 Lattice QCD with massive Wilson fermions

We develop a strategy for the non-perturbative determination of the O(a)-improvement coefficient c_sw for Wilson fermions with massive sea quarks. The improvement condition is defined via the PCAC relation in the Schrödinger functional. It is imposed along a line of constant physics designed to be close to the correct mass of the charm quark. The numerical work uses the tree-level improved Lüscher-Weisz gauge action in N_f=3+1 Lattice QCD.

hep-lat↗

arXiv2013

Critical slowing down and the gradient flow coupling in the Schrödinger functional

We study the sensitivity of the gradient flow coupling to sectors of different topological charge and its implications in practical situations. Furthermore, we investigate an alternative definition of the running coupling that is expected to be less sensitive to the problems of the HMC algorithm to efficiently sample all topological sectors.

hep-lat↗

arXiv2013

The gradient flow coupling in the Schrödinger Functional

We study the perturbative behavior of the Yang-Mills gradient flow in the Schrödinger Functional, both in the continuum and on the lattice. The energy density of the flow field is used to define a running coupling at a scale given by the size of the finite volume box. From our perturbative computation we estimate the size of cutoff effects of this coupling to leading order in perturbation theory. On a set of Nf=2 gauge field ensembles in a physical volume of L ~ 0.4 fm we finally demonstrate the suitability of the coupling for a precise continuum limit due to modest cutoff effects and high statistical precision.

hep-lat↗

arXiv2012

B-physics from non-perturbatively renormalized HQET in two-flavour lattice QCD

We report on the ALPHA Collaboration's lattice B-physics programme based on N_f=2 O(a) improved Wilson fermions and HQET, including all NLO effects in the inverse heavy quark mass, as well as non-perturbative renormalization and matching, to fix the parameters of the effective theory. Our simulations in large physical volume cover 3 lattice spacings a ~ (0.08-0.05) fm and pion masses down to 190 MeV to control continuum and chiral extrapolations. We present the status of results for the b-quark mass and the B_(s)-meson decay constants, f_B and f_{B_s}.

hep-lat↗

arXiv2012

The strange quark mass and Lambda parameter of two flavor QCD

We complete the non-perturbative calculations of the strange quark mass and the Lambda parameter in two flavor QCD by the ALPHA collaboration. The missing lattice scale is determined via the kaon decay constant, for whose chiral extrapolation complementary strategies are compared. We also give a value for the scale r_0 in physical units as well as an improved determination of the renormalization constant Z_A.

hep-lat↗

arXiv2012

Parameters of Heavy Quark Effective Theory from Nf=2 lattice QCD

We report on a non-perturbative determination of the parameters of the lattice Heavy Quark Effective Theory (HQET) Lagrangian and of the time component of the heavy-light axial-vector current with Nf=2 flavors of massless dynamical quarks. The effective theory is considered at the 1/mh order, and the heavy mass mh covers a range from slightly above the charm to beyond the beauty region. These HQET parameters are needed to compute, for example, the b-quark mass, the heavy-light spectrum and decay constants in the static approximation and to order 1/mh in HQET. The determination of the parameters is done non-perturbatively. The computation reported in this paper uses the plaquette gauge action and two different static actions for the heavy quark described by HQET. For the light-quark action we choose non-perturbatively O(a)-improved Wilson fermions.

hep-lat↗

arXiv2011

M_b and f_B from non-perturbatively renormalized HQET with Nf=2 light quarks

We present an updated analysis of the non-perturbatively renormalized b-quark mass and B meson decay constant based on CLS lattices with two dynamical non-perturbatively improved Wilson quarks. This update incorporates additional light quark masses and lattice spacings in large physical volume to improve chiral extrapolations and to reach the continuum limit. We use Heavy Quark Effective Theory (HQET) including 1/m_b terms with non-perturbative coefficients based on the matching of QCD and HQET developed by the ALPHA collaboration during the past years.

hep-lat↗