Interference effects in heavy $W^{\prime }$-boson searches at the LHC

Interference effects are widely neglected in searches for new physics. This is the case in recent publications on searches for $W^{\prime }$ bosons using leptonic final states. We examine the effects of interference on distributions frequently used to determine mass limits for possible $W^{\prime }$ bosons and show that there are important qualitative effects on the behavior of the new physics signal. There are two main consequences. First, exclusion limits where interferences effects have not been considered are likely to have been overestimated. Second, presenting experimental results as a function of a transverse mass cut rather than in terms of the contribution of new physics to the total cross section would be more informative.

Figure 1

(a) Differential cross section in the dilepton transverse mass for $m_{W^{\prime }}=2000\mathrm{GeV}$, considering 7 TeV $pp$ collisions. The magenta dashed line shows the SM background plus the pure $W^{\prime }$-boson contribution as implemented in PYTHIA. The blue solid line gives the complete theoretical distribution, including the interference term between $W$ and $W^{\prime }$ bosons. The yellow dotted line represents the SM irreducible background as a reference. (b) Same for $m_{W^{\prime }}=2400\mathrm{GeV}$. The inset plots display the interference term normalized to the complete theoretical prediction.

Figure 2

(a) Ratio between the differential cross section in the dilepton transverse mass for the prediction of the model and the SM irreducible background, considering 7 TeV $pp$ collisions. The blue solid line shows the ratio obtained when including the interference. The magenta dashed line represents the ratio without taking into account the interference. We consider $m_{W^{\prime }}=2000\mathrm{GeV}$. (b) Same for $m_{W^{\prime }}=2400\mathrm{GeV}$.

Figure 3

(a) Differential cross section in the dilepton transverse mass for $m_{W^{\prime }}=2000\mathrm{GeV}$, considering 7 TeV $pp$ collisions. The magenta dashed line shows the pure $W^{\prime }$-boson signal as implemented in PYTHIA. The blue solid line gives the theoretical distribution of the BSM signal, including the interference term between $W$ and $W^{\prime }$ bosons. The yellow dotted line represents the SM irreducible background as a reference. (b) Same for $m_{W^{\prime }}=2400\mathrm{GeV}$.

Figure 4

(a) $W^{\prime }$ signal cross section as a function of the minimum $m_T$ cut for $m_{W^{\prime }}=2000\mathrm{GeV}$, considering 7 TeV $pp$ collisions. The magenta dashed line shows the pure $W^{\prime }$-boson contribution as implemented in PYTHIA. The blue solid line gives the BSM signal, including the interference term between $W$ and $W^{\prime }$ bosons. (b) Same for $m_{W^{\prime }}=2400\mathrm{GeV}$.

Figure 5

(a) Differential cross section in the dilepton transverse mass for $z=0.8$ and $m_{W2}=2000\mathrm{GeV}$, considering 7 TeV $pp$ collisions. The magenta dashed line shows the SM background plus the pure $W_{1,2}$-boson contribution. The blue solid line gives the complete theoretical distribution, including the interference term between $W$ and $W_{1,2}$ bosons. The yellow dotted line represents the SM irreducible background as a reference. (b) Same for $m_{W2}=2400\mathrm{GeV}$. The inset plots display the interference term normalized to the complete theoretical prediction.

Figure 6

(a) Ratio between the differential cross section in the dilepton transverse mass for the prediction of the model and the SM irreducible background, considering 7 TeV $pp$ collisions. The blue solid line shows the ratio obtained when including the interference. The magenta dashed line represents the ratio without taking into account the interference. We consider $z=0.8$ and $m_{W2}=2000\mathrm{GeV}$. (b) Same for $m_{W2}=2400\mathrm{GeV}$.

Figure 7

(a) Differential cross section in the dilepton transverse mass for $z=0.8$ and $m_{W2}=2000\mathrm{GeV}$, considering 7 TeV $pp$ collisions. The magenta dashed line shows the pure $W_{1,2}$-boson contribution. The blue solid line gives the theoretical distribution of the BSM signal, including the interference term between $W$ and $W_{1,2}$ bosons. The yellow dotted line represents the SM irreducible background as a reference. (b) Same for $m_{W2}=2400\mathrm{GeV}$.

Figure 8

(a) $W_{1,2}$ signal cross section as a function of the minimum $m_T$ cut for $z=0.8$ and $m_{W2}=2000\mathrm{GeV}$, considering 7 TeV $pp$ collisions. The magenta dashed line shows the pure $W_{1,2}$-boson contribution. The blue solid line gives the BSM signal, including the interference term between $W$ and $W_{1,2}$ bosons. (b) Same for $m_{W2}=2400\mathrm{GeV}$.