arXiv subjects

Fabio Bernardoni

Publications and source records attributed to Fabio Bernardoni.

15 recordsLinked to original sources

arXiv2019

Extraction of bare Form Factors for $\mathrm B_\mathrm s \to \mathrm K \ell ν$ Decays in non-perturbative HQET

We discuss the extraction of the ground state $\langle \mathrm{K} ({\bf p})|V_μ(0)|\mathrm{B} ({\bf 0})\rangle$ matrix elements from Euclidean lattice correlation functions. The emphasis is on the elimination of excited state contributions. Two typical gauge-field ensembles with lattice spacings $0.075, \; 0.05$ fm and pion masses $330,\;270$ MeV are used from the O($a$)- improved CLS 2-flavour simulations and the final state momentum is $|{\bf p}|=0.5\,{\rm GeV}$. The b-quark is treated in HQET including the $1/m_\mathrm{b}$ corrections. Fits to two-point and three-point correlation functions and suitable ratios including summed ratios are used, yielding consistent results with precision of around 2% which is $not$ limited by the $1/m_\mathrm{b}$ corrections but by the dominating static form factors. Excited state contributions are under reasonable control but are the bottleneck towards precision. We do not yet include a specific investigation of multi-hadron contaminations, a gap in the literature which ought to be filled soon.

hep-lat↗

arXiv2016

Continuum limit of the leading order HQET form factor in $B_s \to K\ellν$ decays

We discuss the computation of form factors for semi-leptonic decays of $\rm B$-, $\rm B_s$- mesons in lattice QCD. Considering in particular the example of the static $\rm B_s$ form factors we demonstrate that after non-perturbative renormalization the continuum limit can be taken with confidence. The resulting precision is of interest for extractions of $V_{\rm ub}$. The size of the corrections of order $1/m_{\rm b}$ is just estimated at present but it is expected that their inclusion does not pose significant difficulties.

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↗

arXiv2014

Form factors for $\mathrm B_\mathrm s \to \mathrm K \ell ν$ decays in Lattice QCD

We present the current status of the computation of the form factor $f_+ (q^2)$ for the semi-leptonic decay $\mathrm B_\mathrm s \to \mathrm K \ell ν$ by the ALPHA collaboration. We use gauge configurations which were generated as part of the Coordinated Lattice Simulations (CLS) effort. They have $N_\mathrm f=2$ non-perturbatively $O(a)$ improved Wilson fermions, and pion masses down to $\approx 250 \,\mathrm {MeV}$ with $m_πL \geq 4$. The heavy quark is treated in non-perturbative Heavy Quark Effective Theory (HQET). We discuss how to extract the form factors from the correlation functions and present first results for the form factor at $q^2 = 21.23\,\mathrm{GeV}^2$ extrapolated to the continuum. Next-to-leading order terms in HQET and the chiral extrapolation still need to be included in the analysis.

hep-lat↗

arXiv2014

Precision lattice QCD computation of the $B^*Bπ$ coupling

The static $B^{*}Bπ$ coupling, $\hat{g}_χ$, a low energy constant in the leading order heavy meson chiral Lagrangian, is determined using $N_\mathrm{f} = 2$ lattice QCD. We use CLS ensembles with lattice spacings and pion masses down to $a = 0.05\mathrm{fm}$ and $m_π=270\mathrm{MeV}$, and perform combined continuum and chiral extrapolations of our results which have a much better accuracy than previous numbers in the literature. As a by-product, we determine the coupling between the first radial excitations in the $B$ and $B^{*}$ channels ($\hat{g}_{22}$). Accounting for all uncertainties, which are dominated by the chiral extrapolation, we obtain $\hat{g}_χ= 0.492(29)$, while $\hat{g}_{22}$ is somewhat smaller. The comparison to a precise quenched computation suggests that there is little influence by the sea quarks and $\hat{g}_χ$ will not change much when a dynamical strange quark is included.

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

B $\to$ $π$ form factor with 2 flavours of $O(a)$ improved Wilson quarks

The determinations of $|V_{\rm ub}|$ from the exclusive branching ratios of $B\to τν$ and $B \to πl ν$ tend to show a tension at the level of $3σ$ \cite{Beringer:1900zz}. On the theoretical side they depend on the lattice computation of the hadronic matrix elements $f_{\rm B}$ and the $B\to π$ form factor $f_+(q^2)$. To understand the tension, improved precision and a careful analysis of the systematics involved are necessary. Working towards this goal, we present preliminary lattice results of the ALPHA collaboration for the $B\to π$ form factor $f_+(q^2)$ with $N_{\rm f}=2$ flavours of $O(a)$-improved Wilson fermions. Our computation uses HQET in the static limit, pion masses ranging down to $\sim250$ MeV, large volumes with $m_πL >4$, three lattice spacings, and non-perturbative renormalization. We describe the techniques adopted to reduce the statistical noise (stochastic all-to-all with full time dilution) and the contamination from excited states (smearing for the B and the pion). We estimate the size of the chiral and continuum extrapolations. We discuss the impact our result could have to clarify the above mentioned discrepancy in the determination of $|V_{\rm ub}|$.

hep-lat↗

arXiv2011

Determination of the Wilson ChPT low energy constant c_2

Following a suggestion by Aoki and Bär, c2 can be extracted by analyzing volume effects in 2-pion states. To this end we consider renormalized ratios of four point to two point correlation functions. We present the results from various CLS lattices, with pion masses ranging from 280 to 450 MeV and lattice spacings of 0.07 fm and 0.08 fm. This low energy constant is useful to understand discretization effects in chiral extrapolations with Wilson fermions, especially for quantities which vanish in the chiral limit, like the pion mass. Since our procedure is computationally cheap and straightforward, it is recommended as a routine study for any Wilson-type simulation, as a check of discretization effects.

hep-lat↗

arXiv2011

Light quark correlators in a mixed-action setup

We report our progress in simulating Neuberger valence fermions on N_f=2 Wilson O(a)-improved sea quarks. We compute correlators with valence quark masses both in the p- and in the epsilon-regime, and we match the results with the predictions of the Chiral Effective Theory in the mixed regime. This allows us to extract the Low Energy Couplings (LECs) of the N_f=2 theory and to test the validity of the approach.

hep-lat↗

arXiv2011

Probing the chiral regime of Nf=2 QCD with mixed actions

We report on our first experiences with a mixed action setup with overlap valence quarks and non-perturbatively O(a) improved Wilson sea quarks. For the latter we employ CLS Nf=2 configurations with light sea quark masses at small lattice spacings. Exact chiral symmetry allows to consider very light valence quarks and explore the matching to (partially quenched) Chiral Perturbation Theory (ChPT) in a mixed epsilon/p-regime. We compute the topological susceptibility and the low-lying spectrum of the massless Neuberger-Dirac operator for three values of the sea quark mass, and compare the sea quark mass dependence to NLO ChPT in the mixed regime. This provides two different determinations of the chiral condensate, as well as information about some NLO low-energy couplings. Our results allow to test the consistency of the mixed-regime approach to ChPT, as well as of the mixed action framework.

hep-lat↗

arXiv2010

Exploring the chiral regime of $N_f=2$ QCD with mixed actions

We report on our simulations with Neuberger valence fermions on CLS $N_f=2$ configurations with non-perturbatively $O(a)$-improved Wilson sea quarks. We consider the matching of QCD to ChPT in the so called mixed-regime in which the sea quarks are in the $p$-regime while the valence quarks are in the $ε$-regime. From this matching, we can get information on $Σ$, $L_6$ and the combination $L_8+2L_6+2L_7$.

hep-lat↗

arXiv2009

Finite-size scaling of heavy-light mesons

We study the finite-size scaling of heavy-light mesons in the static limit. The most relevant effects are due to the pseudo-Goldstone boson cloud. In the HMChPT framework we compute two-point functions of left current densitities as well as pseudoscalar densitites for the cases in which some or all of them lay in the epsilon-regime. As expected, finite volume dependence turns out to be significant in this regime and can be predicted in the effective theory in terms of the infinite-volume low-energy couplings. These results might be relevant for extraction of heavy-light meson properties from lattice simulations.

hep-lat↗

arXiv2009

Heavy-light mesons in the epsilon-regime

We study the finite-size scaling of heavy-light mesons in the static limit. We compute two-point functions of chiral current densities as well as pseudoscalar densities in the epsilon-regime of heavy meson Chiral Perturbation Theory (HMChPT). As expected, finite volume dependence turns out to be significant in this regime and can be predicted in the effective theory in terms of the infinite-volume low-energy couplings. These results might be relevant for extraction of heavy-meson properties from lattice simulations.

hep-lat↗

arXiv2007

Mapping the geometry of the F4 group

In this paper we present a construction of the compact form of the exceptional Lie group F4 by exponentiating the corresponding Lie algebra f4. We realize F4 as the automorphisms group of the exceptional Jordan algebra, whose elements are 3 x 3 hermitian matrices with octonionic entries. We use a parametrization which generalizes the Euler angles for SU(2) and is based on the fibration of F4 via a Spin(9) subgroup as a fiber. This technique allows us to determine an explicit expression for the Haar invariant measure on the F4 group manifold. Apart from shedding light on the structure of F4 and its coset manifold OP2=F4/Spin(9), the octonionic projective plane, these results are a prerequisite for the study of E6, of which F4 is a (maximal) subgroup.

math-ph↗

arXiv2007

Mapping the geometry of the E6 group

In this paper we present a construction for the compact form of the exceptional Lie group E6 by exponentiating the corresponding Lie algebra e6, which we realize as the the sum of f4, the derivations of the exceptional Jordan algebra J3 of dimension 3 with octonionic entries, and the right multiplication by the elements of J3 with vanishing trace. Our parametrization is a generalization of the Euler angles for SU(2) and it is based on the fibration of E6 via a F4 subgroup as the fiber. It makes use of a similar construction we have performed in a previous article for F4. An interesting first application of these results lies in the fact that we are able to determine an explicit expression for the Haar invariant measure on the E6 group manifold.

math-ph↗