B meson decays, conformal anomalies and gauge invariance
Nabeebaccus, Muhammad Saad
In this thesis, we discuss the calculation of conformal anomalies using curved spacetime and heat-kernel techniques, and QED corrections to semi-leptonic decays of the pseudoscalar B meson at the full differential level. In the first chapter, the basic ideas of conformal field theory are reviewed, including the importance of the trace of the energy-momentum tensor as a measure of conformal symmetry breaking, and the use of curved spacetime in calculations. In the second chapter, we perform computations of the conformal anomalies for the spin-0, spin- 1/2 and spin-1 fields in curved spacetime using the De-Witt-Schwinger point splitting method and heat-kernel techniques. Particular focus is given to the spin-1 gauge field, where it is explicitly shown how gauge invariance is obtained, a result that has been overlooked in the literature, and which is also a source of ambiguities in different regularisation schemes. We then proceed to discuss the application of these results on positivity theorems in Chapter 3. It is shown that they could potentially provide tighter bounds on the conformal window in QCD. In chapter 4, a calculation of the QED corrections to the B¯ → K` ¯ +`− decay process at the double differential rate is introduced, using an effective mesonic Lagrangian. Particular focus is given to the cancellation of infrared soft and collinear divergences between the real and virtual contributions using the phase-space slicing method, which is discussed in Chapter 5. Hard-collinear divergences, appearing in the form of logs of the lepton mass, are shown to cancel depending on the differential variables used and the experimental photon energy cut. Plots and results are given in chapter 6, and some comments on the value of RK and lepton flavour universality are made.