# Semileptonic and radiative meson decays from lattice QCD with improved staggered fermions

Donald, Gordon (2013) Semileptonic and radiative meson decays from lattice QCD with improved staggered fermions. PhD thesis, University of Glasgow.

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Printed Thesis Information: https://eleanor.lib.gla.ac.uk/record=b2981673

## Abstract

Improved staggered fermions are a numerically efficient formulation of the fermion action in lattice QCD.
They are used for nonperturbative theoretical calculations of the QCD form factors appearing in the decay rates for radiative and semileptonic meson transitions.
The constituent quarks are bound inside hadrons by the strong interaction, so the decay rate depends on the interactions between the quarks, which are described by QCD.
The fermion action used in these calculations is the Highly Improved Staggered Quark (HISQ) action.

The HISQ Dirac operator, $\slashed{D}_{HISQ}$, contains four tastes of quark equivalent to one continuum quark, which is a consequence of the discretisation.
In gauge configurations including staggered sea quarks, the extra tastes are accounted for by taking the fourth root of the fermion determinant.
The validity of this step relies on the taste structure of $\slashed{D}_{HISQ}$.
To look into this, the interactions of the eigenvectors of $\slashed{D}_{HISQ}$ with the topology of the gauge field is studied.
The results show that the eigenvectors corresponding to the different tastes decouple in the continuum limit in such a way that $\slashed{D}_{HISQ}$ resembles the continuum Dirac operator.

Using the HISQ action for the charm quark, the form factor $V(q^2)$ appearing in the radiative decay rate for $J/\psi \to \eta_c \gamma$ is calculated.
The form factor on the lattice is calculated by computing 3-point correlation functions, which are fitted simultaneously with 2-point correlation functions to obtain the meson transition matrix element.
Only the form factor at $q^2 = 0$ enters the decay rate for a physical photon, so the kinematics of the decay are tuned to calculate $V(0)$.
The lattice operator used for the electromagnetic vector current is nonperturbatively normalised.

Lattice QCD can also be used to calculate matrix elements for the decays of mesons to 2 photons.
The form factor for the radiative decay $\eta_c \to 2\gamma$ is calculated at the physical kinematics using nonperturbatively normalised lattice operators for the currents.
The form factor is the same when calculated on gauge configurations containing $N_f = 2+1$ flavours of asqtad sea quarks and $N_f = 2+1+1$ flavours of HISQ sea quarks.

Lattice 3-point correlators are used to calculate the form factors for the semileptonic decay $D_s \to \phi \ell \nu$.
This interaction is mediated by a weak $W$ boson, so contains vector and axial vector form factors.
Each of these is calculated on the lattice with a nonperturbatively normalised current.
The decay includes a $c \to s$ quark decay, so the experimentally measured decay rate depends on the CKM matrix element $V_{cs}$.
By comparing the theoretical calculation of the decay rate to the measurements, a value of $V_{cs} = 0.975(48)$ is obtained.

Item Type: Thesis (PhD) Doctoral Q Science > QC Physics College of Science and Engineering > School of Physics and Astronomy Davies, Prof. Christine 2013 Mr Gordon Donald glathesis:2013-4325 Copyright of this thesis is held by the author. 30 May 2013 11:52 30 May 2013 11:52 http://theses.gla.ac.uk/id/eprint/4325