## Heavy-to-light decays on the lattice

##### Abstract

Precise predictions of hadronic matrix elements in heavy meson decays are important
to constrain the fundamental parameters in the Standard Model of particle physics.
The CKM matrix element Vub can be extracted from experimental data on the decay
B → πℓν if the hadronic form factor is known. In addition, loop suppressed rare decays
of B-mesons, such as B → K∗γ and B → K(∗)ℓℓ, provide valuable insight into new
physics models.
Hadronic form factors for exclusive meson decays can be calculated in the framework
of lattice QCD. As the wavelength of heavy quarks is not resolved on currently available
lattices I use an effective nonrelativistic theory to discretise the heavy degrees of
freedom. In addition, the discretisation errors in the final state meson are reduced
by working in a moving frame.
I review the phenomenology of rare B decays and describe how lattice QCD can
contribute to calculating the relevant form factors. As the short distance physics in
the effective theory is different from that of QCD, the Lagrangian and decay currents
need to be renormalised. I show how this can be achieved in the framework of lattice
perturbation theory.
I calculate the perturbative renormalisation constants of the leading order operators
in the heavy quark Lagrangian. Motivated by nonperturbative studies I extend
this approach to higher order kinetic terms which break rotational invariance. In
combination with simulations in the weak coupling regime of the theory, results from
diagrammatic lattice perturbation theory are used to calculate the heavy quark selfenergy
corrections and predict the fundamental parameters of QCD. I calculate the one
loop correction on a finite lattice with twisted boundary conditions which is used for
the extraction of higher order perturbative corrections. I renormalise the heavy-light
current to one loop order in lattice mNRQCD and present results from nonperturbative
studies. Finally, I discuss how the results are used in the calculation of hadronic form
factors.