### Conveners

#### Standard Model Parameters

- William Jay (Fermi National Accelerator Laboratory)

#### Standard Model Parameters

- Ruth Van de Water (Fermilab)

#### Standard Model Parameters

- Stefan Sint (Trinity College Dublin)

#### Standard Model Parameters

- Alejandro Vaquero Avilรฉs-Casco (University of Utah)

#### Standard Model Parameters

- Takeshi Yamazaki

#### Standard Model Parameters

- Constantia Alexandrou
- Chris Bouchard (University of Glasgow )

We present recent results on quark masses using N_f=2+1+1 clover-improved twisted mass fermion gauge ensembles simulated by the Extended Twisted Mass Collaboration. The renormalized light, strange and charm quark masses are evaluated in isospin-symmetric QCD and different mesonic and baryonic inputs

are used to set the scale and define the physical point, thus providing a consistency checks...

We perform the complete non-perturbative running of the quark mass from hadronic to electroweak scales in $N_f = 3$ massless QCD. In the present work we use the same configuration ensembles used for a similar calculation arXiv 1802.05243, subject to Schrรถdinger Functional (SF) boundary conditions, whereas we use valence quarks with ($\chi$SF) boundary conditions, which results in O(a)...

We present our progress in the non-perturbative $O(a)$ improvement and renormalisation of quark operators in three-flavour lattice QCD with Wilson-clover fermions. We employ the chirally rotated Schroedinger functional scheme in finite volumes. Our calculations cover both weak- and strong-coupling regions for the RG-running, where step scaling functions are computed.

We have recently performed a determination of the charm quark mass on $N_f = 2+1$ CLS ensembles of non-perturbatively improved Wilson fermions. The extrapolation to the chiral and continuum limits is performed using 5 lattice spacings ranging roughly from 0.09 down to 0.04 fm and pion masses from 420 MeV to 130 MeV. The spatial extent of the ensembles is generally at least $4 / M_\pi$. We will...

Renormalization constants of the scalar and tensor currents are calculated for overlap fermions on domain-wall fermion configurations. We perform zero, one or two steps of hypercubic smearing in constructing the overlap Dirac operator and examine the discretization effects in the renormalization constants of quark bilinears and check the dependence of those effects on the level of smearing....

We construct a method for computing the spectral sum appearing in the Shifman-Vainshtein-Zakharov (SVZ) QCD sum rule. The method gives results consistent with the operator product expansion (OPE) of the $s\bar{s}$ correlation function in the vector channel. The application of this method to other channels is useful for operator renormalization as well as the test of perturbative QCD and OPE.

The interpretation of gradient flow as a Wilsonian renormalization group (RG) transformation allows one to determine the continuous RG beta function. This approach is alternative to the finite-volume step-scaling function. Unlike step-scaling methods, where the lattice volume must provide the only scale, the continuous beta function can be used even in the confining regime. We demonstrate this...

With scale changes set by the gradient flow time, a new beta function emerges from infinite volume extrapolations, matching 3-loop predictions from Harlander and Neumann at weak coupling. Non-perturbative lattice methods are used to get the beta-function in the infrared region at strong coupling. The method was tested in multi-flavor QCD with ten and twelve flavors and compared in contrast...

While the standard model is the most successfully theory to describe all interactions and constituents in elementary particle physics, it has been constantly examined for over four decades. Weak decays of charm quarks can measure the coupling strength of quarks in different families and serve as an ideal probe for CP violation. As the lowest charm-strange baryons with three different...

We present an overview of the RQCD and ALPHA collaboration's combined effort on charm decay constants. Our calcluations are based on the $N_\mathrm{f}=2+1$ CLS ensembles including the physical point. We discuss our analysis strategy and present results for the pseudoscalar and vector decay constants $f_{D_{(\mathrm{s})}}$ and $f_{D_{(\mathrm{s})}^\ast}$ as well as the coupling of the...

We will present a lattice QCD computation of the decay constants for the pseudoscalar mesons K and D(s) in the isosymmetric limit by the Extended Twisted Mass Collaboration (ETMC). Simulations of Nf=2+1+1 dynamical quarks have been performed with the twisted mass fermion action at three values of the lattice spacing, where the masses of the light, strange and charm quarks are all tuned at...

We report on our ongoing determination of the charm quark mass and the masses and decay constants of various charmed mesons, obtained within a mixed-action setup. We employ $N_f=2+1$ CLS ensembles combined with a Wilson twisted mass valence action that eliminates the leading $O(a)$ effects from our target observables. Alongside our preliminary results, we will discuss an exploration of GEVP...

Semileptonic $D \to{}K \ell \nu$ decays provide one angle of attack to get at the CKM matrix element $V_{cs}$, complementary to the study of leptonic $D_s$ decays. Here HPQCD present the results of an improved determination of $V_{cs}$, recently released on the arXiv (2104.09883).

We discuss a new, precise determination of $D\to K$ scalar and vector form factors from a lattice calculation...

We present the results of HPQCD's recent calculation of the $B_c \to J/\psi$ semileptonic form factors and $R(J/\psi)$ for the first time from lattice QCD using the heavy-HISQ method. We also present results from lattice QCD, using the heavy-HISQ method, for the $B_s \to D_s^*$ semileptonic form factors and $R(D_s^*)$. We give a value for $|V_{cb}|$ computed using our results for the full...

A recently proposed approach to inclusive semi-leptonic decay rate on the lattice allows for the calculation of various quantities (differential distributions and moments) in different subchannels. We systematically compare the lattice QCD results for unphysically light bottom and strange quarks with OPE-based predictions, including leading order perturbative and O(1/m^3) power corrections,...

We present HPQCDโs results of the first lattice QCD calculation of the weak matrix elements for $B_c^+ \to D^0 \ell^+ \nu_{\ell}$ facilitated by a $b \to u$ transition. Together with observation of this process from LHCb, our form factors will lead to a new determination of $V_{ub}$. In tandem, we also calculate the form factors for rare $B_c^+ \to D_s^+ \ell^+ \ell^-$. Results are derived...

We consider three-flavor QCD and perform a determination of the low energy coupling $\hat g$ of SU(2) Heavy Meson Chiral Perturbation Theory. It is the $B^*B\pi$ coupling in the limit of static heavy and chiral *light* quarks in $N_\mathrm{f}=2+1$ flavor QCD and has not been determined with precision thus far. The calculation is performed on the $2+1$ flavor CLS ensembles using the summed GEVP...

We apply a novel method to a non-perturbative determination of the hadronic form factors describing the exclusive semileptonic $B \to D^{(*)} \ell \nu_\ell$ decays. The method is based on the non-perturbative calculation of the dispersive bounds due to unitarity and analyticity, and it allows to determine in a model-independent way the form factors in the full kinematical range of the recoil,...

Experimental precision for measurements of $B$ meson decays will continue to improve over the coming years as Belle II collects more data and the LHC returns to operation after its upgrade period. Independent measurements of $V_{ub}$ will soon be possible using rare $B\to\tau\nu$ decays, for which $B$ meson decay constants $f_B$ are a key input.

We present updates from UKQCD/QCDSF/CSSM on...

The desire for additional determinations of the CKM matrix element $V_{ub}$ and a long-standing 2-3$\sigma$ discrepancy between results from inclusive $B\to X_u$ and exclusive $B\to\pi$ processes motivate the study of $B\to\pi$ semileptonic form factors on the lattice. The status of our preliminary $B\to\pi\ell\nu$ results will be discussed by highlighting updates to our analysis. The analysis...

Semileptonic Bs to K and Bs to Ds decays provide additional channels to determine the CKM matrix elements |Vub| and |Vcb| or to investigate lepton flavour universality violation in R-ratios comparing decays with heavy or light final state leptons. We calculate the decay form factors using domain-wall light, strange and charm quarks, with the Columbia formulation of the RHQ action for the...

Our charm program uses a mixed action with twisted-mass valence quarks over non-perturbatively improved Wilson sea quarks, in order to study various quantities in a relativistic and manifestly local framework of full QCD. The sea sector consists of $N_f=2+1$ ensembles generated by the CLS initiative. Thanks to open boundary conditions, this offers access to fine ensembles without topological...

We present the status of a project to calculate $D \rightarrow \pi \ell \nu$, $D \rightarrow K \ell \nu$ and $D_s \rightarrow K \ell \nu$ semileptonic form factors with 2+1f Domain Wall Fermions for both heavy and light quarks. We plan to cover the full kinematic range and three point functions are being computed on the RBC-UKQCD Iwasaki gauge ensembles. Given the exponential growth of noise,...

We present a new method aiming at a non-perturbative, model-independent determination of the momentum dependence of the form factors entering hadronic semileptonic decays using unitarity and analyticity constraints. We extend the original proposal of Ref. [1] and, using suitable two-point functions computed non-perturbatively, we determine the form factors at low-momentum transfer $q^2$ from...

We present new results on heavy meson semileptonic decays using the highly improved staggered quark (HISQ) action for both valence and 2+1+1 sea quarks. The use of the highly improved action, combined with the MILC collaboration's gauge ensembles with lattice spacings down to ~0.042 fm, allows the b quark to be treated with the same discretization as the lighter quarks. This unified treatment...

A very rich place to look for phenomena to challenge our current understanding of physics is the flavor sector of the Standard Model (SM). In particular, the $V_{cb}$ matrix element of the CKM matrix is the subject of a long standing tension, depending on whether it is determined using inclusive or exclusive methods. On top of that, the current average of $R(D^\ast)$ shows a 3$\sigma$ tension...

This talk will report recent results from ongoing calculations of the $D\to\pi$ semileptonic decay by the Fermilab lattice and MILC collaborations.ย Our calculation employs the HISQ action for both sea and valence quarks and includes several ensembles with physical-mass up, down, strange, and charm quarks and lattice spacings ranging from 0.15 fm down to 0.06 fm. At each lattice spacing, an...

We present our current progress on the lattice calculation of decay constants for $B_{(s)}$, $D_{(s)}$ mesons using sequential Bayesian method and the Oktay-Kronfeld (OK) action for the charm and bottom quarks (valence quarks). Here, the masses of charm and bottom quark are determined non-perturbatively. For the light spectator quarks (up, down and strange), we use HISQ action. Lattice...

We develop a methodology for the computation of the $K\to \ell\nu_\ell \ell'^+ \ell'^-$ decay width using lattice QCD and present an exploratory study. We use a scalar function method to account for the momentum dependence of the decay amplitude. We adopt infinite volume reconstruction (IVR) method to solve temporal truncation effects and general finite-volume effects in a systematic way. To...

We have completed a lattice QCD calculation of $\Delta m_K$, the mass difference between the long- and short-lived K mesons. The calculation was performed on a $64^3 \times 128$ lattice using 152 configurations with physical quark masses and an inverse lattice spacing of $a^{-1}=2.36$ GeV. While the statistical error approaches a relatively small size of 9%, several sources of systematic...

Determining the standard model prediction for the decay amplitude of a long-lived neutral kaon into two photons is an important step toward the goal of calculating the two-photon contribution to $K_L\to\mu^+\mu^-$ decay. In this talk we will describe a computational strategy to determine this decay amplitude using lattice QCD. While the lattice QCD calculation is carried out in finite...

The decoupling strategy by the ALPHA collaboration uses simultaneous decoupling of $N_{\rm f}=3$ heavy quark flavours to obtain a controlled connection between the $\Lambda$-parameters in QCD with $N_{\rm f}=3$ and $N_{\rm f}=0$ quark flavours, respectively, in terms of a common decoupling scale. Corrections are either power suppressed in the heavy quark mass, or perturbatively suppressed by...

We present analysis details and new results for the strong coupling $\alpha_s(m_Z)$, determined by the decoupling strategy detailed in the previous talk. Starting from a line of constant physics (LCP) from previous ALPHA Collaboration work, we simulate $N_f=3$ massless quarks to measure a set of renormalization and improvement constants which allow us to determine the simulation parameters for...

The QCD-coupling is a necessary input in the computation of many observables, and the parametric error on input parameters can be a dominant source of uncertainty. The coupling can be extracted by comparing high order perturbative computations and lattice evaluated moments of mesonic two-point functions with heavy quarks, which provide a high energy scale for perturbation theory. The...

Non-perturbative renormalization of composite operators can be achieved by combining the step-scaling method with an intermediate finite volume renormalization scheme. Matching to low energy physics requires that the finite volume scheme can be accurately evaluated at the bare couplings used in simulations of hadronic physics.

In this regime, the gradient flow for the gauge field has been...

We present a calculation of the QCD renormalization constants (RCs) for quark bilinear operators, evaluated non-perturbatively on the lattice in the RI'-MOM scheme. The calculation is performed by using dedicated ensembles with $N_f=4$ degenerate dynamical twisted mass (clover) fermions and the Iwasaki gauge action. A detailed analysis is reported, with emphasis on the control or subtraction...

We determine non-perturbatively the renormalization constant of the flavour-singlet local vector current with $O(a)$-improved Wilson fermions in a moving reference frame. The renormalization constant is fixed by comparing the expectation values (one-point function) of the local vector current and of the conserved one in thermal QCD with a non-zero imaginary chemical potential and in the chiral...

We explore various non-perturbative renormalisation schemes in the framework of the Rome-Southampton method. In particular, we implement several non-exceptional interpolating momentum schemes, where the momentum transfer is not restricted to the symmetric point defined in RI/SMOM. Using flavour non-singlet quark bilinears, we compute the renormalisation factors of the quark mass and wave...

We present an update of the scale setting for $N_f=2+1$ flavor QCD using gradient flow scales and pseudoscalar decay constants. We analyze the latest ensembles with $2+1$ flavors of non-perturbatively improved Wilson fermions generated by CLS for improved precision. Special care is taken to correct for mistuning by measuring directly the mass derivatives of the various observables. We...

Recently a method of measuring static force from the lattice using an insertion of chromoelectric field to an Wilson loop has been proposed to tackle the ambiguities of taking numerical derivative of the static potential. We present the current status of testing the viability of this approach and also expand the calculation for the first time to use gradient flow, which solves the problems...

We consider a mixed action approach where valence Wilson twisted mass

(Wtm) fermions at maximal twist are combined with CLS ensembles

consisting of $N_f$=2+1 flavours of O($a$)-improved Wilson sea quarks. We

present an update of the results of the matching of valence and sea

quarks, and of the subsequent continuum-limit scaling studies of

light-quark observables. A scale setting procedure...

We analyse the leading logarithmic corrections to the $a^2$ scaling of lattice artefacts in QCD, following the seminal work of Balog, Niedermayer and Weisz in the O(n) non-linear sigma model. Limiting to contributions from the action, the leading logarithmic corrections can be determined by the anomalous dimensions of mass-dimension 6 operators. These operators form a minimal on-shell basis of...