### Conveners

#### Weak Decays and Matrix Elements: Weak Decays and Matrix Elements I

- Nicolas Garron (Liverpool Hope University)

#### Weak Decays and Matrix Elements: Weak Decays and Matrix Elements II

- Takeshi Yamazaki (University of Tsukuba)

#### Weak Decays and Matrix Elements: Weak Decays and Matrix Elements III

- Roger Horsley (University of Edinburgh)

#### Weak Decays and Matrix Elements: Weak Decays and Matrix Elements IV

- Oliver Bär (Humboldt-Universität zu Berlin)

#### Weak Decays and Matrix Elements: Weak Decays and Matrix Elements V

- William Jay (MIT)

The standard method for determining matrix elements in lattice QCD requires the computation of three-point correlation functions. This has the disadvantage of requiring two large time separations: one between the hadron source and operator and the other from the operator to the hadron sink. Here we consider an alternative formalism, based on the Dyson expansion leading to the Feynman-Hellmann...

Theoretical calculations of the transition form factors of the hyperons are an important component of the determination of the CKM matrix elements. These calculations historically have been performed using ratios of lattice three point functions and two-point functions to extract the form factors, this requires the careful balancing of control over excited states and the preservation of a...

$V_{ub}$ is the smallest and least known of all CKM matrix elements; the community determines its current value primarily through the exclusive process $B\to\pi\ell\nu$. This talk will present our progress toward a lattice QCD determination of the $V_{ub}$ matrix element from a novel transition - $B \to \pi\pi\ell\nu$ process, where the $\pi\pi$ rescattering features the $\rho(770)$ resonance...

Multi-particle states with additional pions are expected to result in a non-negligible excited-state contamination in lattice simulations at the physical point. We show that heavy meson chiral perturbation theory (HMChPT) can be employed to calculate the contamination due to two-particle $B\pi$ states in various $B$-meson observables like the decay constant $f_B$ and the $B^*B\pi$ coupling...

Combining experimental input, perturbative calculations, and form factors computed in lattice QCD simulations, it is possible to deduce $|V_{ub}|$ from semileptonic decays of B mesons. But the results of the form factors are contaminated by excited-states, which may lead to noticeable systematic errors in the desired CKM matrix element.

This talk presents our recent computations of the...

CKM matrix elements can be obtained from lattice determinations of semileptonic decay form factors by combining them with experimental results for decay rates. We give a status update on our study using the Domain Wall Fermion action for up/down, strange and charm quarks to determine semileptonic form factors for $D \rightarrow \pi \ell \nu$, $D \rightarrow K \ell \nu$ and $D_s \rightarrow K...

We present HPQCD's improved scalar, vector and tensor form factors for $B \to K$ semileptonic decays, using the heavy-HISQ formalism for more accurate normalisation of the weak currents. Working with masses close to the physical $b$ on the finest ensemble and including three ensembles with physical light quarks, we cover the full physical $q^2$ range with good precision. Our uncertainties at...

We study, with lattice QCD, the radiative leptonic decays $P\to \ell\,\nu_\ell\,\ell'^+\,\ell'^-$, where $P$ is a charged pseudoscalar meson and $\ell$ and $\ell^\prime$ are charged leptons. These processes are mediated by the emission of a virtual photon and, in addition to the ``point-like" contribution in which the virtual photon is emitted either from the lepton or the meson treated as a...

In the region of hard photon energies, radiative leptonic decays represent important probes of the internal structure of hadrons.

Moreover, radiative decays can provide independent determinations of Cabibbo-Kobayashi-Maskawa matrix elements with respect to purely leptonic or semileptonic channels.

Prospects for a precise determination of leptonic decay rates with emission of a hard photon...

We developed a strategy to implement RI/MOM schemes on quark bilinear and four-quark operators. In these schemes, the momentum transfer is not restricted to the exceptional point or to the symmetric point. In particular, we study the convergence of the perturbative series and the potential to reduce some systematic errors (discretisation and chiral symmetry breaking effects). In particular, we...

In this talk we present the first RBC-UKQCD lattice calculation of the leading isospin-breaking corrections to the ratio of leptonic decay rates of kaons and pions into muon and neutrino, $\Gamma(K_{\ell 2})/\Gamma(\pi_{\ell 2})$. This computation is performed using domain wall fermions with close-to-physical (light and strange) quark masses. The QED effects are implemented using a...

Analytical techniques to derive the finite-volume dependence of observables calculated in lattice simulations can be used to improve numerical determinations. With the need for (sub-)percent precision in lattice predictions, also isospin-breaking effects have to be considered. When including electromagnetism in the so-called QED$_{\textrm{L}}$ prescription, having good control of the...

In lattice calculations including isospin-breaking effects, low-energy Standard Model predictions can be unambiguously obtained providing external inputs to define the quark masses, the QCD scale and the value of the electromagnetic coupling. However, there is phenomenological interest to define an isospin-symmetric value of a given observable, or to define the corrections coming from the...

We present the comparison of preliminary results of $D\to\pi$ semileptonic

decays from two related projects: the first one is based on unitary Wilson

fermions, and the second uses valence quarks rotated to maximal twist.

While these projects differ by their goals and strategies, both studies

are performed on CLS $N_f=2+1$ configurations, with similar analysis

techniques. The...

We present our results for the kaon semileptonic form factors using the two

sets of the PACS10 configuration, whose physical volumes are more than

(10 fm)$^4$ at the physical point. The lattice spacings are 0.063 and 0.085 fm.

The configurations were generated using the Iwasaki gauge action and $N_f=2+1$

stout-smeared nonperturbatively $O(a)$ improved Wilson quark action. From the...

In this talk we present results on B-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 ~0.03 fm, allows the b quark to be treated with the same discretization as the lighter quarks. The talk will focus...

We present new results on semileptonic decays of D-mesons using the highly improved staggered quark (HISQ) action for both valence and 2+1+1 sea quarks. Our calculation uses lattice spacings ranging from 0.12 fm down to 0.042 fm, including several ensembles with physical-mass pions. The focus on the talk will be on the vector and scalar form factors ($f_+$ and $f_0$) for the decays $D\to\pi$,...

We discuss progress towards the RBC & UKQCD collaborations' next generation of measurements of Standard Model direct CP-violation in kaon decays with G-parity boundary conditions, for which we aim to leverage the power of the upcoming exascale computers to perform the continuum limit and thus eliminate this dominant lattice systematic error.

Since our recent publication on direct CP violation and the Delta I = 1/2 rule in $K \to \pi\pi$ decay which was made with G-parity boundary conditions, we have revisited this problem with a conventional lattice setup employing periodic boundary conditions and two lattice spacings to check our previous result and to improve the precision. We show that the physical amplitude, which corresponds...

We present the status of ongoing work to extract pseudoscalar and vector decay constants for $B^{(*)}$, $B_s^{(*)}$ and $B_c^{(*)}$ mesons and determine phenomenologically interesting ratios such as f_Bs/f_B or f_B*/f_B.

Our calculation is based on $N_f=2+1$ dynamical flavour gauge field ensembles generated by the RBC/UKQCD collaborations using domain wall fermions and the Iwasaki gauge...

We report on our progress in the non-perturbative calculation of the decay rates for inclusive semi-leptonic decays of charmed mesons from lattice QCD. In view of the long-standing tension in the determination of the CKM matrix elements $V_{ub}$ and $V_{cb}$ from exclusive and inclusive processes, recently, the method of lattice QCD has been extended towards the description of inclusive decays...

We address the non-perturbative calculation of the decay rate of the inclusive semi-leptonic $B_{(s)}$ mesons decay from lattice QCD. Precise theoretical Standard Model predictions are key ingredients in searches for new physics. This type of computation may eventually provide new insight into the long-standing tension between the inclusive and exclusive determination of the $V_{cb}$ and...

Among the many anomalies and tensions in flavour physics, one of the most persistent ones is the $V_{cb}$ puzzle, which is a difference of about $2.7 \sigma$ between the inclusive and exclusive estimate of the CKM matrix element $V_{cb}$. In order to understand the origin of this tension from first principles, one needs calculations obtained using lattice QCD.

Over the years, lattice QCD has...

In this talk, we present Lattice QCD measurements for the matrix elements of $\Delta B = 0$ four-quark operators that involve a light spectator quark in a $b$-hadron. These matrix elements contribute to the determination of $V_{ub}$, as well as the lifetime ratios of $b$-hadrons. Though the historical tension in the $\tau(\Lambda_b)/\tau(B_d)$-lifetime ratio has disappeared with newer...