rest frames. Thus, for SUSY signal events, ${\ensuremath{M_R}\xspace}$ is an estimator of ${\ensuremath{M_\Delta}\xspace}$, and for simulated samples we find that the distribution of ${\ensuremath{M_R}\xspace}$ indeed peaks around the true value of ${\ensuremath{M_\Delta}\xspace}$. This definition of ${\ensuremath{M_R}\xspace}$ is improved with respect to the one used in Ref. [@razor2010], to avoid configurations where the razor frame is unphysical.

The razor observable ${\ensuremath{M_\mathrm{T}^R}\xspace}$ is defined as $${\ensuremath{M_\mathrm{T}^R}\xspace}\equiv \sqrt{ \frac{\ETmiss(\pt^{\cPq_1}+\pt^{\cPq_2}) -
    \VEtmiss {\cdot}
    (\ptvec^{\,\cPq_1}+\ptvec^{\,\cPq_2})}{2}},$$ where $\ptvec^{\,\cPq_i}$ is the transverse momentum of megajet ${\cPq_i}$ ($i = 1,2$) and $\pt^{\cPq_i}$ is the corresponding magnitude; similarly, $\VEtmiss$ is the missing transverse momentum in the event and its magnitude.

Given a global estimator ${\ensuremath{M_R}\xspace}$ and a transverse estimator ${\ensuremath{M_\mathrm{T}^R}\xspace}$, the razor dimensionless ratio is defined as $${\ensuremath{R}\xspace}\equiv \frac{{\ensuremath{M_\mathrm{T}^R}\xspace}}{{\ensuremath{M_R}\xspace}}.$$

For signal events, ${\ensuremath{M_\mathrm{T}^R}\xspace}$ has a maximum value (a kinematic endpoint) at ${\ensuremath{M_\Delta}\xspace}$, so ${\ensuremath{R}\xspace}$ has a maximum value of approximately one. Thus, together with the shape of ${\ensuremath{M_R}\xspace}$ peaking at ${\ensuremath{M_\Delta}\xspace}$, this behavior is in stark contrast with, for example, QCD multijet background events, whose distributions in both ${\ensuremath{M_R}\xspace}$ and ${\ensuremath{R^2}\xspace}$ fall exponentially. These properties allow us to identify a region of the two-dimensional (2D) razor space where the contributions of the SM background are reduced while those of 