Precise theoretical predictions derived from the Standard Model are a key ingredient in searches for new physics in the flavor sector. The large mass and long lifetime of the $b$ quark make processes involving $b$ quarks of particular interest. We us
e lattice simulations to perform nonperturbative QCD calculations for semileptonic $B_{(s)}$ decays. We present results from our determinations of $B_sto D_s ell u$ and $B_sto K ell u$ semileptonic form factors and provide an outlook for our $Bto piell u$ calculation. In addition we discuss the determination of $R$-ratios testing lepton-flavor universality and suggest use of an improved ratio. Our calculations are based on the set of 2+1 flavor domain wall Iwasaki gauge field configurations generated by the RBC-UKQCD collaboration featuring three lattice spacings of $1/a = 1.78$, $2.38$, and $2.79,text{GeV}$. Heavy $b$-quarks are simulated using the relativistic heavy quark action.
We present a study of the IR behaviour of a three-dimensional super-renormalisable quantum field theory (QFT) consisting of a scalar field in the adjoint of $SU(N)$ with a $varphi^4$ interaction. A bare mass is required for the theory to be massless
at the quantum level. In perturbation theory the critical mass is ambiguous due to infrared (IR) divergences and we indeed find that at two-loops in lattice perturbation theory the critical mass diverges logarithmically. It was conjectured long ago in [Jackiw 1980, Appelquist 1981] that super-renormalisable theories are nonperturbatively IR finite, with the coupling constant playing the role of an IR regulator. Using a combination of Markov-Chain-Monte-Carlo simulations of the lattice-regularised theory, both frequentist and Bayesian data analysis, and considerations of a corresponding effective theory we gather evidence that this is indeed the case.
A nonperturbative determination of the energy-momentum tensor is essential for understanding the physics of strongly coupled systems. The ability of the Wilson flow to eliminate divergent contact terms makes it a practical method for renormalizing th
e energy-momentum tensor on the lattice. In this paper, we utilize the Wilson flow to define a procedure to renormalize the energy-momentum tensor for a three-dimensional massless scalar field in the adjoint of $SU(N)$ with a $varphi^4$ interaction on the lattice. In this theory the energy-momentum tensor can mix with $varphi^2$ and we present numerical results for the mixing coefficient for the $N=2$ theory.
We present updates for our nonperturbative lattice QCD calculations to determine semileptonic form factors for exclusive $Bto piell u$, $Bto D ell u$, $B_sto Kell u$, and $B_sto D_sell u$ decays. Our calculation is based on RBC-UKQCDs set of $2+1$-d
ynamical-flavor gauge field ensembles. In the valence sector we use domain wall fermions for up/down, strange and charm quarks, whereas bottom quarks are simulated with the relativistic heavy quark action. The continuum limit is based on three lattice spacings. Using kinematical $z$ expansions we aim to obtain form factors over the full $q^2$ range. These form factors are the basis for predicting ratios addressing lepton flavor universality or, when combined with experimental results, to obtain CKM matrix elements $|V_{ub}|$ and $|V_{cb}|$.
In the holographic approach to cosmology, cosmological observables are described in terms of correlators of a three-dimensional boundary quantum field theory. As a concrete model, we study the 3$d$ massless $SU(N)$ scalar matrix field theory. In this
work, we focus on the renormalisation of the energy-momentum tensor 2-point function, which can be related to the CMB power spectra. Here we present a non-perturbative procedure to remove divergences resulting from the loss of translational invariance on the lattice, by imposing Ward identities. This will allow us to make predictions for the CMB power spectra in the regime where the dual QFT is non-perturbative.
Semi-leptonic $B_s to K ell u$ and $B_s to D_s ell u$ decays provide an alternative $b$-decay channel to determine the CKM matrix elements $|V_{ub}|$ and $|V_{cb}|$ or to obtain $R$-ratios to investigate lepton flavor universality violations. In ad
dition, these decays may shed further light on the discrepancies seen in the analysis of inclusive vs. exclusive decays. Using the nonperturbative methods of lattice QCD, theoretical results are obtained with good precision and full control over systematic uncertainties. This talk will highlight ongoing efforts of the $B$-physics program by the RBC-UKQCD collaboration.
A determination of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon from lattice QCD aiming at a precision of $1%$ requires to include isospin breaking corrections in the computation. We present a lattice cal
culation of the QED and strong isospin breaking corrections to the hadronic vacuum polarization with Domain Wall fermions. The results are obtained using quark masses which are tuned such that pion and kaon masses agree with their physical values including isospin breaking corrections.
First-principles studies of strongly-interacting hadronic systems using lattice quantum chromodynamics (QCD) have been complemented in recent years with the inclusion of quantum electrodynamics (QED). The aim is to confront experimental results with
more precise theoretical determinations, e.g. for the anomalous magnetic moment of the muon and the CP-violating parameters in the decay of mesons. Quantifying the effects arising from enclosing QED in a finite volume remains a primary target of investigations. To this end, finite-volume corrections to hadron masses in the presence of QED have been carefully studied in recent years. This paper extends such studies to the self-energy of moving charged hadrons, both on and away from their mass shell. In particular, we present analytical results for leading finite-volume corrections to the self-energy of spin-0 and spin-$frac{1}{2}$ particles in the presence of QED on a periodic hypercubic lattice, once the spatial zero mode of the photon is removed, a framework that is called $mathrm{QED}_{mathrm{L}}$. By altering modes beyond the zero mode, an improvement scheme is introduced to eliminate the leading finite-volume corrections to masses, with potential applications to other hadronic quantities. Our analytical results are verified by a dedicated numerical study of a lattice scalar field theory coupled to $mathrm{QED}_{mathrm{L}}$. Further, this paper offers new perspectives on the subtleties involved in applying low-energy effective field theories in the presence of $mathrm{QED}_{mathrm{L}}$, a theory that is rendered non-local with the exclusion of the spatial zero mode of the photon, clarifying recent discussions on this matter.
We present results for the decay constants of the $D$ and $D_s$ mesons computed in lattice QCD with $N_f=2+1$ dynamical flavours. The simulations are based on RBC/UKQCDs domain wall ensembles with both physical and unphysical light-quark masses and l
attice spacings in the range 0.11--0.07$,$fm. We employ the domain wall discretisation for all valence quarks. The results in the continuum limit are $f_D=208.7(2.8)_mathrm{stat}left(^{+2.1}_{-1.8}right)_mathrm{sys},mathrm{MeV}$ and $f_{D_{s}}=246.4(1.3)_mathrm{stat}left(^{+1.3}_{-1.9}right)_mathrm{sys},mathrm{MeV}$ and $f_{D_s}/f_D=1.1667(77)_mathrm{stat}left(^{+57}_{-43}right)_mathrm{sys}$. Using these results in a Standard Model analysis we compute the predictions $|V_{cd}|=0.2185(50)_mathrm{exp}left(^{+35}_{-37}right)_mathrm{lat}$ and $|V_{cs}|=1.011(16)_mathrm{exp}left(^{+4}_{-9}right)_mathrm{lat}$ for the CKM matrix elements.
Semi-leptonic $B$ decays provide promising channels to test the Standard Model, search for signs of new physics, or determine fundamental parameters like CKM matrix elements. We present an update on our calculation of short distance contributions to
GIM suppressed rare $B$ decays focusing in particular on $B_sto phi ell^+ ell^-$ decays. Furthermore we show first results for our calculation of $B_{(s)}to D_{(s)}^{(*)}ell u$ semi-leptonic decays involving $bto c$ transitions. Our calculations are based on RBC-UKQCDs 2+1 flavor domain-wall fermion and Iwasaki gauge field configurations featuring three lattice spacings in the range $1.73$ GeV $le a^{-1} le 2.77$ GeV and pion masses down to the physical value. We calculate the form factors by simulating $b$-quarks using the relativistic heavy quark action, create light $u/d$ and $s$ quarks with standard domain-wall kernel, and use optimised Mobius domain-wall fermions for charm quarks.
