The Ratio of W + N jets To Z/gamma + N jets As a Precision Test of the Standard Model

TL;DR

The paper advocates using event-by-event ratios of W+N jets to Z/γ*+N jets as a precision test of the Standard Model, arguing that many experimental and theoretical uncertainties cancel in the ratio, especially at higher jet multiplicities. Through MadGraph and MCFM studies at LO/NLO and using Run I data as a baseline, it demonstrates that the W/Z ratio is significantly less sensitive to jet energy scale, underlying event, and PDFs than the individual cross sections. The work quantifies the residual uncertainties and shows substantial suppression of Q^2-scale and PDF-related errors in the ratio, predicting strong sensitivity to new physics contributions in multiple jet channels. It concludes that ratio-based analyses can provide percent-level precision and enhanced discovery potential for high-multiplicity final states at the Tevatron Run II and the LHC, albeit requiring dedicated experimental studies.

Abstract

We suggest replacing measurements of the individual cross-sections for the production of W + N jets and Z/gamma + N jets in searches for new high-energy phenomena at hadron colliders by the precision measurement of the ratios (W+0 jet)/(Z+0 jet), (W+1 jet)/(Z+1 jet), (W+2 jets)/(Z+2 jets),... (W+N jets)/(Z+N jets), with N as large as 6 (the number of jets in ttbarH). These ratios can also be formed for the case where one or more of the jets is tagged as a b or c quark. Existing measurements of the individual cross sections for Wenu + N jets at the Tevatron have systematic uncertainties that grow rapidly with N, being dominated by uncertainties in the identification of jets and the jet energy scale. These systematics, and also those associated with the luminosity, parton distribution functions (PDF's), detector acceptance and efficiencies, and systematics of jet finding and b-tagging, are expected to substantially cancel in calculating the ratio of W to Z production in each N-jet channel, allowing a greater sensitivity to new contributions in these channels in Run II at the Tevatron and at the LHC.

Figures (8)

• Figure 1: a) The measured cross sections for the signatures $W^{+}(\rightarrow e^+\nu) ~+N~ \text{jets}$ and $Z^0 / \gamma^*~(\rightarrow e^+e^-) +N~ \text{jets}$ versus the number of jets, N, in $W^+$ and $Z^0 / \gamma^*$ production in ${\bar{p}}p$ collisions at ${\sqrt s}=1.8$$\text{\ Te V}$. The data are from the CDF CDF_Wjets collaboration and were originally reported as inclusive cross sections. In computing exclusive cross sections from these, the uncertainties have been calculated in two ways. The dotted error bars were calculated assuming no correlations (giving an upper bound for the uncertainty) and the solid error bars were calculated assuming complete correlation (giving a lower bound); b) the percent uncertainty in the $W^{+}+N~ \text{jets}$ and $Z^0 / \gamma^*~ +N~ \text{jets}$ cross sections. The uncertainties shown are the lower bounds (corresponding to the solid error bars in plot a). The figure shows the rapid growth of the uncertainties with N, the number of jets.
• Figure 2: The plot on the left (a) shows the (normalized) jet $\eta$ distributions for $W^{+}(\rightarrow e^+\nu) ~+1~ \text{jet}$ (dashed) and $Z^0 / \gamma^*~(\rightarrow e^+e^-) +1~ \text{jet}$ (solid) events satisfying the selection criteria described in the text. The plot on the right (b) shows the corresponding jet $E_T$ distributions, log ($dN/dE_T$) versus N. Both plots are predictions at LO using MadGraph 2MadGraph. Uncertainties in the ratios $\sigma(W^{+}+N \text{jets})/\sigma(Z^0 / \gamma^*~+N \text{jets})~$ due to the uncertainty in the jet rapidity cut at $\eta$=2.5 are estimated from the shapes in the left-hand plot, and those due to the uncertainty in the jet energy scale from the right-hand plot.
• Figure 3: A comparison of CDF data (circles) with MadGraph (LO) predictions (triangles) for the ratio of production cross sections times leptonic branching ratios for the signature $W^{+}+N~ \text{jets}$ to the signature $Z^0 / \gamma^*~ +N~ \text{jets}$ , $\sigma(W^{+}+N \text{jets})/\sigma(Z^0 / \gamma^*~+N \text{jets})$ , versus the number of jets, N, in $W^{+}$ and $Z^0 / \gamma^*$ production at ${\sqrt s}=1.8$$\text{\ Te V}$ for the data and at ${\sqrt s}=1.96$$\text{\ Te V}$ for the predictions. The case where two of the jets are b-quark jets are also shown (inverted triangles). The statistical uncertainties on the predictions are smaller than the symbols.
• Figure 4: The ratio of cross sections times branching ratios, $\sigma(W^{+}+N \text{jets})/\sigma(W^{+}+N+1 \text{jets})~$ (left hand plot) and $\sigma(Z^0 / \gamma^*~+N\text{jets})/\sigma(Z^0 / \gamma^*~+N+1 \text{jets})~$ (right hand plot) versus the number of jets, N, in W and Z production at ${\sqrt s}=1.8$$\text{\ Te V}$ for the data and at ${\sqrt s}=1.96$$\text{\ Te V}$ for the predictions. The data (circles) are from the CDF CDF_Wjets and DØ D0_Wjets collaborations; the predictions are at leading order from MadGraph 2MadGraph. The MadGraph cross sections for when the jets are from gluons or light quarks are shown with triangles, while inverted triangles represent when two of the jets are from b-quarks.
• Figure 5: The ratios $\sigma$($W^{+}+N~ \text{jets}$ at $\text{Q}^2 = {\text{M}_{\text{V}}}^2$) to $\sigma$($W^{+}+N~ \text{jets}$ at $\text{Q}^2 = {\text{M}_{\text{V}}}^2 +{\text{P}_{\text{T,V}}}^2$) and $\sigma$($Z^0 / \gamma^*~ +N~ \text{jets}$ at $\text{Q}^2 = {\text{M}_{\text{V}}}^2$) to $\sigma$($Z^0 / \gamma^*~ +N~ \text{jets}$ at $\text{Q}^2 = {\text{M}_{\text{V}}}^2 +{\text{P}_{\text{T,V}}}^2$). Changing the $Q^2$ scale significantly changes the cross sections, by up to approximately 15%. However the ratio of W to Z cross sections changes much less (see Table \ref{['qstudy']}).