Author:
Nabeebaccus Saad,Zwicky Roman
Abstract
Abstract
Standard interpolating operators for charged mesons, e.g. JB = $$ \overline{b} $$
b
¯
iγ5u for B−, are not gauge invariant in QED and therefore problematic for perturbative methods. We propose a gauge invariant interpolating operator by adding an auxiliary charged scalar ΦB, $$ {\mathcal{J}}_B^{(0)} $$
J
B
0
= JB ΦB, which reproduces all the universal soft and collinear logs. The modified LSZ-factor is shown to be infrared finite which is a necessary condition for validating the approach. At $$ \mathcal{O} $$
O
(α), this is equivalent to a specific Dirac dressing of charged operators. A generalisation thereof, using iterated integrals, establishes the equivalence to all orders and provides a transparent alternative viewpoint. The method is discussed by the example of the leptonic decay B−→ ℓ−$$ \overline{\nu} $$
ν
¯
for which a numerical study is to follow. The formalism itself is valid for any spin, flavour and set of final states (e.g. B−→ π0ℓ−$$ \overline{\nu} $$
ν
¯
).
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
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