Added README for rad

radiative-lepton-decay/README.md

+# Radiative lepton decays $`L\to \nu\bar\nu l\gamma`$
+
+References: [[1705.03782]](https://arxiv.org/abs/1705.03782), [[1712.05633]](https://arxiv.org/abs/1712.05633)
+
+Configurations implemented
+
+* Canonical cuts
+ * MEG
+   * full cuts
+   * reduced cuts
+ * PiBeta
+ * BaBar
+   * Full implantation
+   * Only the energy
+   * Invariant mass
+
+In the radiative decay with massive fermions, an IR safe cut needs to
+be applied to the hard photon. However, in the
+$`\mathcal{M}_{n+1}^{(0)}`$ configuration there are two photons. The
+hard one needs to be identified first and then cut.
+
+## Canonical cuts
+The canonical version refers to the values often quoted in the PDG of
+```math
+E_\gamma > 10\,\mathrm{MeV}
+```
+Usually, this also means that we are exclusive, i.e. exactly one
+photon is visible.
+
+## MEG
+
+### Full cuts
+In this configuration, the full MEG cuts are used. We assume a 85%
+polarised muon and require the following cuts
+
+```math
+E_\gamma > 40\,\mathrm{MeV}\,,\qquad E_e> 45\,\mathrm{MeV}
+```
+```math
+|\cos\sphericalangle(\vec p_\gamma,\vec e_z)| \equiv |\cos\theta_\gamma| < 0.35
+\,,\qquad
+|\phi_\gamma| < \frac{2\pi}{3}
+```
+```math
+|\cos\sphericalangle(\vec p_e,\vec e_z)| \equiv |\cos\theta_e| < 0.5
+\,,\qquad
+|\phi_e| < \frac{\pi}{3}
+```
+MEG requires one and only one photon meaning that an event with real
+radiation with energy larger then the detector resolution of roughly 2
+MeV will be discarded if it hits the detector. 
+
+
+### Reduced cuts
+It is also interesting to remove the cuts on the electron angles to
+investigate to which extend the back-to-back approximation used by MEG
+is valid.
+
+
+## PiBeta cuts
+The PiBeta experiment had less stringent cuts when looking at the
+radiative muon decay, producing the current best result for this
+process. 
+
+```math
+E_\gamma > 10\,\mathrm{MeV}\,,\qquad \sphericalangle(\vec p_\gamma,\vec p_e) > 30^\circ
+```
+
+
+## BaBar
+
+BaBar has measured the radiative tau decays in
+[[1502.01784]](https://arxiv.org/pdf/1502.01784.pdf) with rather
+complicated cuts.