Photon-initiated production of a dilepton final state at the LHC: Cross section versus forward-backward asymmetry studies

We explore the effects of photon induced (PI) production of a dilepton final state in the Large Hadron Collider environment. Using QED parton distribution function (PDF) sets we can treat the photons as real partons inside the protons and compare their yield directly to that of the Drell-Yan (DY) process. In particular, we concentrate on an error analysis of the two mechanisms. In order to do so, we use the neural network parton distribution functions (NNPDF) set, which comes with a set of replicas to estimate the systematic PDF error, and the CT14 set. On the one hand, we find that the PI contribution becomes dominant over DY above a dilepton invariant mass of 3 TeV. On the other hand, the PI predictions are affected by a large uncertainty coming from the QED PDFs, well above the one affecting the DY mode. We assess the impact of these uncertainties in the context of resonant and nonresonant searches for a neutral massive vector boson ($Z^{\prime }$) through the differential cross section and forward-backward asymmetry (AFB) observables as a function of the dilepton invariant mass. While the former is subject to the aforementioned significant residual errors the latter shows the systematic error cancellation expected (recall that AFB is a ratio of cross sections) even in presence of PI contributions, so that the recently emphasized key role played by AFB as a valid tool for both $Z^{\prime }$ discovery and interpretation in both resonant and nonresonant mode is further consolidated.

Figure 1

Photon induced process contributing to the dilepton final state.

Figure 2

(a) PI differential cross section in the dilepton invariant mass for the LHC at 8 TeV (blue line) and 13 TeV (red line). (b) Ratio of the two differential cross sections at 13 TeV and 8 TeV (magenta line) compared with the analogous ratio for the DY case (green line). Standard acceptance cuts are applied: $|{\eta }_l|<2.5$ and $p_T^l>20\mathrm{GeV}$.

Figure 3

(a) Relative importance of the PI term in the dilepton SM background at the LHC with energies of 8 TeV (blue line) and 13 TeV (red line). Standard acceptance cuts are applied ($|{\eta }_l|<2.5$ and $p_T^l>20\mathrm{GeV}$). (b) Number of events expected in the dielectron channel as a function of the lower cut applied on the dielectron invariant mass. The solid lines represent the pure DY background while the dashed ones include also the PI contribution. Different colors refer to different stages of the LHC as described in the legend. Standard acceptance cuts are applied ($|{\eta }_l|<2.5$ and $p_T^l>20\mathrm{GeV}$) as well as the declared efficiency of the electron channel [12]. NNLO QCD corrections are accounted for in the DY term [47].

Figure 4

(a) Ratio between the central values of the photon induced dilepton spectrum obtained with the MRST2004QED and the NNPDF2.3QED sets. (b) Same as (a) but now comparing the MRST2004QED and the CT14QED sets. (c) Ratio between the dilepton spectrum at two different factorization scales, $Q^2=\widehat{s}$ and $Q^2=P_T^2$, for MRST2004QED (dashed lines), for CT14QED (dotted lines) and NNPDF2.3QED (solid lines) at the 8 TeV LHC (blue lines) and the 13 TeV LHC (red lines). (d) Differential cross section distribution for the PI process as predicted by the three PDF collaborations specified. Standard acceptance cuts are applied ($|{\eta }_l|<2.5$ and $p_T^l>20\mathrm{GeV}$).

Figure 5

(a) DY dilepton spectrum for the 100 NNPDF replicas. (b) Central value and PDF error for the DY dilepton spectrum via NNPDF. (c) Relative size of the PDF error for the DY process at the 8 TeV (blue line) and 13 TeV (red line) LHC. Standard acceptance cuts are applied ($|{\eta }_l|<2.5$ and $p_T^l>20\mathrm{GeV}$).

Figure 6

(a) PI dilepton spectrum for the 100 NNPDF replicas. (b) Central value and PDF error for the PI dilepton spectrum in NNPDF. (c) PI dilepton spectrum for the first 15 CT14 tables, which parametrize an initial momentum fraction of the proton total momentum carried by the photon ranging from 0.00% to 0.11%. (d) Central value and PDF error for the PI dilepton spectrum extracted from CT14 tables and upper limits on the momentum fraction as quoted in [35]. Standard acceptance cuts are applied $|{\eta }_l|<2.5$ and $p_T^l>20\mathrm{GeV}$.

Figure 7

(a) Prediction of the $\mathrm{DY}+\mathrm{PI}$ dilepton spectrum for the 100 NNPDF replicas. (b) central value for the DY (black line) and $\mathrm{DY}+\mathrm{PI}$ (red line) dilepton spectrum from NNPDF including the PDF error band for the two cases. (c) Relative impact of the PDF uncertainties with (magenta line) and without (blue line) the PI contribution. Standard acceptance cuts are applied ($|{\eta }_l|<2.5$ and $p_T^l>20\mathrm{GeV}$).

Figure 8

(a) Number of SM events expected in the dielectron channel from the DY process as a function of the lower cut on the dilepton invariant mass. The error bands include only the statistical error, as the PDF error is here subdominant. (b) Same result with the inclusion of the PI contribution. In the error bands is now included the overall PDF uncertainty in addiction to the statistical error. Standard acceptance cuts are applied ($|{\eta }_l|<2.5$ and $p_T^l>20\mathrm{GeV}$) as well as the declared efficiency of the electron channel [12]. NNLO QCD corrections are accounted for in the DY term [47].

Figure 9

(a) Reconstructed AFB for the DY process and the combined ($\mathrm{DY}+\mathrm{PI}$) process. (b) Absolute PDF error on the reconstructed AFB observable with and without the inclusion of the PI process. Standard acceptance cuts are applied ($|{\eta }_l|<2.5$ and $p_T^l>20\mathrm{GeV}$).

Figure 10

(a) The acceptance of the PI contribution to the dilepton spectrum for different cuts in ${\eta }_l$ and $p_T^l$ with respect to the differential cross section obtained with the standard acceptance cuts: $|{\eta }_l|<2.5$ and $p_T^l>20\mathrm{GeV}$. (b) Same for the DY process.

Figure 11

(a) Differential cross section predicted within the $E_6^{\chi }$ model with a $Z^{\prime }$-boson of mass $M_{Z^{\prime }}=3.5\mathrm{TeV}$. The black solid line represents the combined ($\mathrm{DY}+\mathrm{PI}$) background including PDFs uncertainty and the red line the full contribution including the $Z^{\prime }$ signal. (b) Reconstructed AFB distribution for the same benchmark including PDF uncertainty. The line color code is the same as in (a). Standard acceptance cuts are applied ($|{\eta }_l|<2.5$ and $p_T^l>20\mathrm{GeV}$).

Figure 12

(a) Differential cross section significance within the $E_6^{\chi }$ model with a $Z^{\prime }$ of mass $M_{Z^{\prime }}=3.5\mathrm{TeV}$. The black line represents the case where only the default DY process is accounted for as a SM background. The red line represents the case where the combined ($\mathrm{DY}+\mathrm{PI}$) process is taken into account as SM background. The integrated luminosity is $L=300{\mathrm{fb}}^{-1}$. (b) Same as (a) for a $Z^{\prime }$ with $M_{Z^{\prime }}=4.5\mathrm{TeV}$ and an integrated luminosity $L=3{\mathrm{ab}}^{-1}$. (c) Significance of the reconstructed AFB distribution with and without the PI contribution, for a $Z^{\prime }$ boson of mass $M_{Z^{\prime }}=3.5\mathrm{TeV}$ and an integrated luminosity $L=300{\mathrm{fb}}^{-1}$. (d) Same as (c) for a $Z^{\prime }$ with $M_{Z^{\prime }}=4.5\mathrm{TeV}$ and an integrated luminosity $L=3{\mathrm{ab}}^{-1}$. Standard acceptance cuts are applied ($|{\eta }_l|<2.5$ and $p_T^l>20\mathrm{GeV}$) as well as the declared efficiencies of the electron and muon channels [12]. NNLO QCD corrections are accounted for in the DY term [47]. The overall significance is the combination of the significances in the two lepton channels. The binning has been chosen to represent an average of the two channel resolutions.

Figure 13

(a) Differential cross section predicted within the GSM-SSM model with a $Z^{\prime }$-boson of mass $M_{Z^{\prime }}=3\mathrm{TeV}$ and $\mathrm{\Gamma }/M_{Z^{\prime }}=20\%$. The black dashed line represents the pure DY background as default reference, the black solid line the combined ($\mathrm{DY}+\mathrm{PI}$) background including the PDFs uncertainty and the red line the full contribution including the $Z^{\prime }$ signal. (b) Reconstructed AFB distribution for the same benchmark including PDF uncertainty. The line color code is the same as in (a). Standard acceptance cuts are applied ($|{\eta }_l|<2.5$ and $p_T^l>20\mathrm{GeV}$).

Figure 14

(a) Differential cross section significance within the GSM-SSM model with a $Z^{\prime }$-boson of mass $M_{Z^{\prime }}=3\mathrm{TeV}$ and $\mathrm{\Gamma }/M_{Z^{\prime }}=20\%$. The black line represents the case where only the default DY process is accounted for as a SM background. The red line represents the case where the combined ($\mathrm{DY}+\mathrm{PI}$) process is taken into account as SM background. The integrated luminosity is $L=300{\mathrm{fb}}^{-1}$. (b) Same as (a) for a $Z^{\prime }$ with $M_{Z^{\prime }}=3.2\mathrm{TeV}$ and an integrated luminosity $L=3{\mathrm{ab}}^{-1}$. (c) Significance of the reconstructed AFB distribution with and without the PI contribution, for a $Z^{\prime }$ boson of mass $M_{Z^{\prime }}=3\mathrm{TeV}$ and an integrated luminosity $L=300{\mathrm{fb}}^{-1}$. (d) Same as (c) for a $Z^{\prime }$ with $M_{Z^{\prime }}=3.2\mathrm{TeV}$ and an integrated luminosity $L=3{\mathrm{ab}}^{-1}$. Standard acceptance cuts are applied ($|{\eta }_l|<2.5$ and $p_T^l>20\mathrm{GeV}$) as well as the declared efficiencies of the electron and muon channels [12]. NNLO QCD corrections are accounted for in the DY term [47]. The overall significance is the combination of the significances in the two lepton channels. The binning has been chosen to represent an average of the two channel resolutions.