We present preliminary results of the non-perturbative heavy quark mass dependence of heavy-light meson observables in the continuum limit of finite-volume two-flavour lattice QCD. These observables, which are derived from heavy-light Schroedinger functional correlation functions and computed over a range of renormalization group invariant heavy quark masses from the charm to beyond the bottom region, allow for a quantitative comparison with the predictions of HQET and are of practical relevance for solving renormalization problems in HQET non-perturbatively by a matching to QCD in finite volume.
By imposing axial and vector Ward identities for flavour-non-singlet currents, we estimate in the quenched approximation the non-perturbative values of combinations of improvement coefficients, which appear in the expansion around the massless case of the renormalization constants of axial, pseudoscalar, vector, scalar non-singlet currents and of the renormalized mass. These coefficients are relevant for the completion of the improvement programme to O(a) of such operators. The simulations are performed with a clover Wilson action non-perturbatively improved.
We apply finite-size recursion techniques based on the Schrodinger functional formalism to determine the renormalization group running of four-fermion operators which appear in the Delta S=2 effective weak Hamiltonian of the Standard Model. Our calculations are done using O(a) improved Wilson fermions with N_f=2 dynamical flavours. Preliminary results are presented for the four-fermion operator which determines the B_K parameter in tmQCD.
We compute non-perturbatively the renormalization constant of the flavour-singlet local vector current $Z_V$ in lattice QCD with 3 massless flavours. Gluons are discretized by the Wilson plaquette action while quarks by the O($a$)-improved Wilson--Dirac operator. The constant $Z_V$ is fixed by comparing the expectation values (1-point functions) of the conserved and local vector currents at finite temperature in the presence of shifted boundary conditions and at non-zero imaginary chemical potential. Monte Carlo simulations with a moderate computational cost allow us to obtain $Z_V$ with an ac…
Using the Schrödinger functional (SF) with a single staggered fermion field we calculate the SF coupling in four-flavour QCD for a wide range of energies and lattice sizes up to $L/a=16$. Preliminary results for the continuum extrapolation of the step-scaling function are presented. To reduce cutoff effects, one-loop ${\rm O}(a)$ improvement has been implemented. Various cross checks are made possible by the use of two independent sets of lattices with either $T=L+a$ or $T=L-a$.
We discuss a 3-flavour lattice QCD action with clover improvement in which the fermion matrix has single level stout smearing for the hopping terms together with unsmeared links for the clover term. With the (tree-level) Symanzik improved gluon action this constitutes the Stout Link Non-perturbative Clover or SLiNC action. To cancel O(a) terms the clover term coefficient has to be tuned. We present here results of a non-perturbative determination of this coefficient using the Schroedinger functional and as a by-product a determination of the critical hopping parameter. Comparisons of the resul…
We non-perturbatively determine the renormalization constant and the improvement coefficients relating the renormalized current and subtracted quark mass in O(a) improved two-flavour lattice QCD. We employ the Schrödinger functional scheme and fix the physical extent of the box by working at a constant value of the renormalized coupling. Our calculation yields results which cover two regions of bare parameter space. One is the weak-coupling region suitable for volumes of about half a fermi. By making simulations in this region, quarks as heavy as the bottom can be propagated with the full rela…
We present results for the light meson masses, the bare strange quark mass and preliminary non-perturbative renormalisation of B_K in 2+1 flavour domain wall QCD. The ensembles used were generated with the Iwasaki gauge action and have a volume of 16^3 x 32 with a fifth dimension size of 16 and an inverse lattice spacing of 1.6 GeV. These ensembles have u and d masses as low as one quarter of the strange quark mass. All data were generated jointly by the UKQCD and RBC collaborations on QCDOC machines.
For the Stout Link Non-perturbative Clover (SLiNC) action we determine in one-loop lattice perturbation theory the critical hopping parameter $κ_c$ and the clover parameter $c_{SW}$ which is needed for $\mathcal{O}(a)$ improvement. Performing this calculation off-shell we are also able to compute the non gauge invariant quark field improvement coefficient $c_{NGI}$. Additionally, we present first results for the renormalization factors of the scalar, pseudoscalar, vector and axial vector currents. We discuss mean field improvement for the SLiNC action.
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 r…
We perform the non-perturbative renormalization of matrix elements of the static-light axial current by a computation of its scale dependence in lattice QCD with two flavours of massless O(a) improved Wilson quarks. The regularization independent factor that relates any running renormalized matrix element of the axial current in the static effective theory to the renormalization group invariant one is evaluated in the Schroedinger functional scheme, where in this case we find a significant deviation of the non-perturbative running from the perturbative prediction. An important technical ingred…
Using Schroedinger Functional methods, we compute the non-perturbative renormalisation and renormalisation group running of several four-fermion operators, in the framework of lattice simulations with two dynamical Wilson quarks. Two classes of operators have been targeted: (i) those with left-left current structure and four propagating quark fields; (ii) all operators containing two static quarks. In both cases, only the parity-odd contributions have been considered, being the ones that renormalise multiplicatively. Our results, once combined with future simulations of the corresponding latti…
We discuss an action in which the fermion matrix has single level stout smearing for the hopping terms together with unsmeared links for the clover term. With the (tree level) Symanzik improved gluon action this constitutes the Stout Link Non-perturbative Clover or SLiNC action. To cancel O(a) terms the clover coefficient, csw, has to be tuned. We present here preliminary results of a non-perturbative determination of csw using the Schrodinger functional and as a by-product also a determination of the critical hopping parameter. A determination of the renormalisation constant for the local vec…
We discuss the status of different determinations of alpha_s, motivating a precise and reliable computation from lattice QCD. In order to suppress perturbative errors, the non-perturbative computation has to reach high energy scales mu. Such results already exist in the SF-scheme for N_f=0,2 and N_f=3. We recently added the running with four massless flavours in a range of alpha from about 0.07 to 0.3 . It is based on our recent determination of the Sheikholeslami Wohlert coefficient in the four-flavour theory.
We present some early results from a high statistics study of the scalar and pseudoscalar singlet sectors of lattice QCD using 2+1 flavours of Asqtad improved staggered fermions. The use of the Asqtad action has allowed us to generate an unprecedented number of configurations at 2 lattice spacings which on completion we hope will give us a significantly improved view of both the scalar and pseudoscalar singlet sectors.
We present a calculation of the finite volume corrections to meson masses and decay constants in three flavour Partially Quenched Chiral Perturbation Theory (PQChPT) through two-loop order in the chiral expansion for the flavour-charged (or off-diagonal) pseudoscalar mesons. The analytical results are obtained for three sea quark flavours with one, two or three different masses. We reproduce the known infinite volume results and the finite volume results in the unquenched case. The calculation has been performed using the supersymmetric formulation of PQChPT as well as with a quark-flow techni…
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…
We study the heavy quark mass dependence of selected observables constructed from heavy-light meson correlation functions in small-volume two-flavour lattice QCD after taking the continuum limit. The light quark mass is tuned to zero, whereas the range of available heavy quark masses $m_h$ covers a region extending from around the charm to beyond the bottom quark mass scale. This allows entering the asymptotic mass-scaling regime as $1/m_h \to 0$ and performing well-controlled extrapolations to the infinite-mass limit. Our results are then compared to predictions obtained in the static limit o…
We estimate the effects of dynamical fermions by extrapolating to positive flavour numbers the results from negative values obtained by adding to the pure gauge sector a fermion action where the fields obey a Bose statistics: the bermions.
We present the results of a non-perturbative determination of the improvement coefficient $c_\mathrm{V}$ and the renormalisation factor $Z_\mathrm{V}$, which define the renormalised vector current in three-flavour $\mathrm{O}(a)$ improved lattice QCD with Wilson quarks and tree-level Symanzik-improved gauge action. In case of the improvement coefficient, we consider both lattice descriptions of the vector current, the local as well as the conserved (i.e., point-split) one. Our improvement and normalisation conditions are based on massive chiral Ward identities and numerically evaluated in the …
In this work I would like to present some ideas on how to improve on the gauge sector in our lattice simulations at finite baryon density. The long standing problem, that we obtain an onset in thermodynamic quantities at a much smaller chemical potential than expected, could be related to an unphysical proliferation of flavours due to hard gluons close to the Brillouin edges. These hard gluons produce flavour non-conserving vertices to the fermion sector. They also produce excessive number of small instantons due to lattice dislocations. Both unphysical effects could increase the propagation i…
We present a study on the direct determination of the $η'$ mass on the full set of SESAM and T$χ$L QCD vacuum configurations with 2 active flavours of Wilson fermions, at $β= 5.6$. We observe a definite dependency of the two-loop correlator on the topological charge sector.
A mixed action composed of valence quark flavours regularized with a fully-twisted tmQCD action and of $N_f=2+1$ flavours of non-perturbatively ${\rm O}(a)$-improved Wilson sea quarks is described. Two procedures for the matching of sea and valence quark masses are discussed. We report about a comparison of the continuum-limit scaling of pseudoscalar meson observables and of quark masses using the sea and valence actions.
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}.
We present preliminary results of a study of Delta S = 2 matrix elements originating from physics beyond the Standard Model. Using 2+1 flavour Domain Wall Fermions we obtain the non-perturbative renormalisation (mixing) matrix in the RI scheme. We also discuss plans for the chiral extrapolation of the renormalised matrix elements in a partially quenched set-up.
We present a strategy how to match the full set of components of the heavy-light axial and vector currents in Heavy Quark Effective Theory (HQET), up to and including 1/m-corrections, to QCD. While the ultimate goal is to apply these matching conditions non-perturbatively, in this study we first have implemented them at tree-level, in order to find good choices of the matching observables with small O(1/m^2) contributions. They can later be employed in the non-perturbative matching procedure which is a crucial part of precision HQET computations of semileptonic decay form factors in lattice QC…
The scaling of the Schr"odinger functional coupling is studied numerically and perturbatively for an SU(3) lattice gauge field coupled to an O(a) improved bosonic spinor field. This corresponds to QCD with minus two light flavours and is used as a numerically less costly test case for real QCD. A suitable algorithm is developed, and the influence of the matter fields on the continuum limit and the lattice artefacts are studied in detail.
We present a general class of operators resembling compact tetraquarks which have a range of colour-flavour-spin structures, transform irreducibly under the symmetries of the lattice and respect other relevant symmetries. These constructions are demonstrated in lattice QCD calculations with light quarks corresponding to $m_π=$ 391 MeV. Using the distillation framework, correlation functions involving large bases of meson-meson and tetraquark operators are computed in the isospin-1 hidden-charm and doubly-charmed sectors, and finite-volume spectra are extracted with the variational method. We f…
We present results for the masses of pseudoscalar mesons in twisted mass lattice QCD with a degenerate doublet of u and d quarks and a non-degenerate doublet of s and c quarks in the framework of next-to-leading order chiral perturbation theory, including lattice effects up to O(a^2). The masses depend on the two twist angles for the light and heavy sectors. For maximal twist in both sectors, O(a)-improvement is explicitly exhibited. The mixing of flavour-neutral mesons is also discussed, and results in the literature for the case of degenerate s and c quarks are corrected.
We report on the non-perturbative computation of the running coupling of two-flavour QCD in the Schr"odinger functional scheme. The corresponding Lambda-parameter, which describes the coupling strength at high energy, is related to a low energy scale which still remains to be connected to a hadronic ``experimentally'' observable quantity. We find the non-perturbative evolution of the coupling indispensable to avoid untolerable errors in the estimated Lambda-parameter.
We convey an idea of the significant recent progress, which opens up good perspectives for high-precision ab-initio computations in heavy flavour physics based on lattice QCD. Rather than surveying the latest results, this contribution focuses on the concept and the challenges of fully non-perturbative computations in the B-meson sector, where the b-quark is treated within an effective theory. We outline its use to determine the b-quark mass and report on the results obtained in the quenched approximation and on the status in the two dynamical flavour theory.
We present data for the axial coupling constant g_A of the nucleon obtained in lattice QCD with two degenerate flavours of dynamical non-perturbatively improved Wilson quarks. The renormalisation is also performed non-perturbatively. For the analysis we give a chiral extrapolation formula for g_A based on the small scale expansion scheme of chiral effective field theory for two degenerate quark flavours. Applying this formalism in a finite volume we derive a formula that allows us to extrapolate our data simultaneously to the infinite volume and to the chiral limit. Using the additional lattic…
A non-perturbative effective model is derived for the Higgs sector of the standard model, described by a simple scalar theory. The renormalized couplings are determined by the derivatives of the Gaussian Effective Potential that are known to be the sum of infinite bubble graphs contributing to the vertex functions. A good agreement has been found with strong coupling lattice simulations when a comparison can be made.
We study strongly-coupled, approximately scale-invariant gauge theories, which develop a mass gap in the infrared. We argue that a large number of fermion flavours is most suitable to provide an ultraviolet completion for the composite Higgs scenario. The holographic approach allows to describe the qualitative features of the non-perturbative dynamics in the Veneziano limit. We introduce new bottom-up holographic models, which incorporate the backreaction of flavour on the geometry, and show that this can correlate the mass gap to the scale of flavour-symmetry breaking. We compute the mass spe…
I review recent progress in lattice computations relevant for $B$- and charm physics, focusing on decay and mixing amplitudes with a direct impact on CKM analysis. Emphasis is put on the interplay with the upcoming new generation of experimental results, and the subsequent challenges for lattice computations in the heavy quark sector.
We review theoretical approaches to form factors that arise in heavy-meson decays and are hadronic expressions of non-perturbative QCD. After motivating their origin in QCD factorisation, we retrace their evolution from quark-model calculations to non-perturbative QCD techniques with an emphasis on formulations of truncated heavy-light amplitudes based upon Dyson-Schwinger equations. We compare model predictions exemplarily for the B\toπtransition form factor and discuss new results for the g_{D*Dπ} coupling in the hadronic D* decay.
We show that supersymmetry Ward identities contain an anomalous term which takes the form of a surface term in Hilbert space. In the one-instanton sector the anomalous term is the integral of a total rho-derivative where rho is the instanton's size. There are cases where the anomalous term is non-zero, and cannot be modified by subtractions. This constitutes a supersymmetry anomaly. The derivation is based on Feynman rules suitable for any non-perturbative sector of a weakly-coupled, renormalizable gauge theory.
