Colquhoun, Brian
(2015)
Bottomonium and B physics with lattice NRQCD b quarks.
PhD thesis, University of Glasgow.
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Abstract
Lattice Nonrelativistic QCD (NRQCD) is a formalism that allows $b$ quarks to be simulated in their bound states in lattice QCD. It requires only a relatively straightforward evolution equation and is therefore much faster than other lattice QCD formalisms. We perform calculations using radially improved NRQCD for mesons that contain $b$ quarks on gluon field configurations generated by the MILC collaboration with $2+1+1$ flavours of sea quarks, and including light quarks down to their physical masses.
We calculate properties of bottomonium mesons; in particular, the $\Upsilon$ and $\eta_b$. The kinetic mass of these states over a range of momenta is calculated and shown to be stable. We determine the $\Upsilon$ and $\Upsilon^{\prime}$ leptonic widths for the first time in lattice QCD after determining a renormalisation factor matching NRQCD to QCD using temporal moments of the meson correlators. We also compare these temporal moments to continuum temporal moments derived from $q^2$derivative moments of the $b$ quark polarisation function in continuum QCD perturbation theory. Finally, we use the NRQCD moments to determine the mass of the $b$ quark and the contribution of a $b$ quark loop to the hadronic piece of the muon anomalous magnetic moment.
The same NRQCD action can be used to simulate the $b$ quark in heavylight mesons. We present results here for the form factor $f_0{(q^2_{\mathrm{max}})}$ of the semileptonic $B\rightarrow \pi \ell \nu$ decay. We show that the soft pion theorem, which states that $f_0{(q^2_{\mathrm{max}})}=f_B/f_{\pi}$ in the chiral limit, holds. This was uncertain previously as simulations were carried out with light quarks that were much heavier than their physical masses. The lattice gluon field configurations with physical light quarks allow us to overcome this issue and simulate at the physical pion mass.
Finally, we briefly discuss the decays $B_s \rightarrow K \ell \nu$ and the fictitious $B_s \rightarrow \eta_s$ decay. These processes again utilise NRQCD $b$ quarks.
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