Background estimation

14.4 Background estimation

The QCD multijet background is the primary background of both searches. It is estimated with a data-driven approach, using the shape of the data minus other MC backgrounds, whose uncertainties are incorporated into the fit, in a control region multiplied by a polynomial transfer factor to the signal regions, whose order is determined by an $F$ -test. This is described in more detail below. The parameters of the transfer factor are estimated with a simultaneous fit in the signal and fail regions. Other minor backgrounds include top quark and vector boson plus jets, which are estimated from MC simulation.

Correction factors are applied to the W and Z boson samples to match the generator-level $p_{T}$ distributions with those predicted by the highest available order in the perturbative expansion. The $W +$ jets and $Z +$ jets MC samples are corrected to approximately NNLO in QCD and then further reweighted to incorporate the reduction of the cross section at high $p_{T}$ due to higher-order electroweak effects (EWK).

The QCD event yields in the signal, or “pass”, and fail regions are related by a smoothly parametrized transfer factor $R_{P ∕ F}$ :

n {(QCD)}_{b}^{pass} = R_{P ∕ F} (m) n {(QCD)}_{b}^{fail},

(14.4.1)

where $n {(QCD)}_{b}$ is the QCD yield in bin $b$ , and $n {(QCD)}_{b}^{fail}$ is estimated to be the data in the fail region minus non-QCD backgrounds. In the nonresonant case, separate transfer factors are used for each signal region $R$ ( $\in$ {ggF, VBF}), each of which is parametrized by the coefficients $a_{k}^{R}$ of the set of $n^{R} + 1$ Bernstein basis polynomials $b_{k, n^{R}}$ of order $n^{R}$ in $m_{reg}^{bb}$ :

R_{P ∕ F nonresonant}^{Region R} (m_{reg}^{bb}) = \sum_{k = 0}^{n_{m_{reg}^{bb}}^{R}} a_{k}^{R} b_{k, n_{m_{reg}^{bb}}^{R}} (m_{reg}^{bb}),

(14.4.2)

while in the resonant case it is generalised to two dimensions, as a function of $m^{jj}$ and $m_{reg}^{VV}$ :

R_{P ∕ F resonant} (m^{jj}, m_{reg}^{VV}) = \sum_{k = 0}^{n_{m^{jj}}} \sum_{l = 0}^{n_{m_{reg}^{VV}}} a_{k, l} [b_{k, n_{m^{jj}}} (m^{jj}) b_{l, n_{m_{reg}^{VV}}} (m_{reg}^{VV})] .

(14.4.3)

The optimal orders of the polynomials are determined to be $n_{m_{reg}^{bb}}^{ggF} = 0$ , $n_{m_{reg}^{bb}}^{VBF} = 1$ , $n_{m^{jj}} = 2$ , and $n_{m_{reg}^{VV}} = 1$ by a Fisher F-test. This iteratively tests each polynomial order, starting from the lowest considered, against higher order polynomials to see if the latter provide significantly better fits. The lowest order tested is 0 for all but the nonresonant VBF region, for which we require the transfer factor to be at least linear to account for observed shift in the simulated QCD $m_{reg}^{bb}$ shape (due to the higher $m_{H H}$ phase space of this region).