Multiboson interactions at the LHC

This review covers results on the production of all possible electroweak boson pairs and 2-to-1 vector boson fusion at the CERN Large Hadron Collider (LHC) in proton-proton collisions at a center of mass energy of 7 and 8 TeV. The data were taken between 2010 and 2012. Limits on anomalous triple gauge couplings (aTGCs) then follow. In addition, data on electroweak triple gauge boson production and 2-to-2 vector boson scattering yield limits on anomalous quartic gauge boson couplings (aQGCs). The LHC hosts two general purpose experiments, ATLAS and CMS, which have both reported limits on aTGCs and aQGCs which are herein summarized. The interpretation of these limits in terms of an effective field theory is reviewed, and recommendations are made for testing other types of new physics using multigauge boson production.

Figure 1

Diboson production via the Drell-Yan process at a lepton or hadron collider. The red insertion represents using a term from the parametrized Lagrangian in Eq. (1).

Figure 2

VBS in the SM with the exchange of gauge bosons on the left-hand side and the Higgs on the right-hand side needed to preserve perturbative unitarity in the SM.

Figure 3

Examples of VBS contributions from aTGCs and aQGCs.

Figure 4

A demonstration of increased sensitivity of LHC over LEP. The naming conventions are such that our $c_{WWW}$ is their $f_{WWW}/{\mathrm{\Lambda }}^2$ and our $c_B$ is their $f_B/{\mathrm{\Lambda }}^2$, the Wilson coefficients of the operators given in Eq. (9). From [98].

Figure 5

Jet mass distributions in events with a leptonic $W$ boson decay and jets with cuts appropriate for boosted top jets: (a) CMS ([181]) for the muon channel and (b) ATLAS ([52]) for the combined electron and muon channels. A wide variety of MC generators is used to model SM signal and background processes in the figures of this review. We give an overview of the commonly used generators in Sec. 2a, but for the specific details of each analysis see the provided analysis references.

Figure 6

Comparison of $\gamma \gamma$ differential cross-section measurements as a function of (a) the invariant mass ([125]) and (b) transverse momentum ([32]) of the diphoton system with NLO and NNLO predictions.

Figure 7

7 TeV $W\gamma$ inclusive cross section as a function of photon $E_{\mathrm{T}}$: (a) comparison of the CMS measurements with mcfm predictions ([127]) and (b) comparison of the ATLAS measurements with mcfm, sherpa, and alpgen ([210]) predictions, where the latter two have been scaled to match the total number of observed events in data ([31]). Note that mcfm gives an NLO prediction, which is known to increase by $\approx 20\%$ when taking NNLO corrections into account.

Figure 8

Effect of aTGCs in the $W\gamma$ final state at 7 TeV: (a) photon $E_{\mathrm{T}}$ spectrum measured by CMS with an inclusive selection ([113]) and (b) $W\gamma$ cross section measured by ATLAS as a function of photon $E_{\mathrm{T}}$ with an exclusive selection vetoing central jets ([31]).

Figure 9

7 TeV $Z\gamma$ inclusive cross section as a function of photon $E_{\mathrm{T}}$: (a) comparison of the CMS measurements with mcfm predictions ([127]) and (b) comparison of the ATLAS measurements with mcfm and sherpa predictions, where the latter has been scaled to match the total number of observed events in data ([31]). Note that mcfm gives an NLO prediction, which is known to increase by $\approx 8\%$ when taking NNLO corrections into account.

Figure 10

8 TeV $Z\gamma$ inclusive cross section as a function of photon $E_{\mathrm{T}}$ in comparison with mcfm, sherpa, and NNLO predictions: (a) CMS ([191]), where sherpa is normalized to the NNLO cross section, and (b) ATLAS ([54]).

Figure 11

Photon $E_{\mathrm{T}}$ spectrum at 8 TeV for the $Z\gamma \to \nu \overline{\nu }\gamma$ final state and effect of a representative aTGC on the spectrum for (a) CMS ([194]) and (b) ATLAS ([54]) with an exclusive selection vetoing central jets.

Figure 12

Leading lepton $p_{\mathrm{T}}$ spectra in 7 TeV fully leptonic $WW$ candidate events and the impact of different anomalous TGC predictions for (a) CMS ([117]) and (b) ATLAS ([30]). The last bin includes the overflow.

Figure 13

Dilepton mass spectrum in 8 TeV fully leptonic $WW$ candidate events and impact of different anomalous TGC predictions. The last bin includes the overflow. From [195].

Figure 14

Comparison of measured total $WW$ production cross sections at hadron colliders and NNLO theory predictions as a function of $\sqrt{s}$. From [56].

Figure 15

Dijet-$p_{\mathrm{T}}$ spectra in the muon channel of 7 TeV semileptonic $WV$ candidate events and the impact of different anomalous TGC predictions for (a) CMS ([116]) and (b) ATLAS ([48]). The last bin includes the overflow.

Figure 16

68% and 95% C.L. cross-section contours for $WZ$ and $ZZ$ production as observed in $ZV\to b\overline{b}V$ events in comparison with NLO theory predictions. From [128].

Figure 17

Comparison of $W^{\pm }Z$ production cross-section measurements with NLO and NNLO predictions (a) at various center of mass energies ([4]) and (b) in the individual and combined channels at 7 and 8 TeV ([196]).

Figure 18

Observed (a) $p_{\mathrm{T}}$ distribution of the $Z$ boson ([196]) and (b) transverse mass spectrum of the $W^{\pm }Z$ system ([53]) in $W^{\pm }Z$ candidate events at 8 TeV and the impact of different anomalous TGC predictions.

Figure 19

(a) $ZZ$ mass spectrum in the $4\ell$ decay channel ($\ell =e$, $\mu$) and the impact of anomalous TGCs ([122]). (b) Unfolded $ZZ$ fiducial cross sections in the $4\ell$ decay channel in bins of $ZZ$ mass ([33]).

Figure 20

(a) $ZZ$ mass spectrum in the $4\ell$ decay channel ($\ell =e$, $\mu$) and the impact of anomalous TGCs. From [184]. (b) Comparison of $ZZ$ production cross sections measured at hadron colliders and NNLO predictions as a function of center of mass energy. From [5].

Figure 21

Dilepton ($Z$) $p_{\mathrm{T}}$ distributions in $ZZ$ candidate events at 8 TeV in the $2\ell 2\nu$ decay channel ($\ell =e$, $\mu$) and the impact of anomalous TGCs: (a) From [185]. (b) From [5].

Figure 22

$W\gamma \gamma$ candidate events at 8 TeV in the $\ell \nu \gamma \gamma$ final state: (a) $E_{\mathrm{T}}$ spectrum of the leading photon in the electron channel and (b) diphoton invariant mass distribution in the muon channel. From [45].

Figure 23

$Z\gamma \gamma$ candidate events at 8 TeV. (a) Spectrum of the four-body invariant mass $m_{ee\gamma \gamma }$ in the electron channel of the $\ell \ell \gamma \gamma$ final state. (b) Diphoton invariant mass distribution in the exclusive $\nu \nu \gamma \gamma$ final state and potential impact of aQGCs. From [54].

Figure 24

Photon $p_{\mathrm{T}}$ spectrum in $WV\gamma$ candidate events in the $\ell \nu jj\gamma$ final state at 8 TeV and potential impact of aQGCs. From [129].

Figure 25

$W^{\pm }{W}^{\pm }{W}^{\mp }$ candidate events at 8 TeV: (a) spectrum of the trilepton transverse mass in the ${\ell }^{\pm }\nu {\ell }^{\pm }\nu {\ell }^{\mp }\nu$ final state and (b) sum of scalar $p_{\mathrm{T}}$ for all selected objects (leptons, jets, MET) distribution in the ${\ell }^{\pm }\nu {\ell }^{\pm }\nu jj$ final state. The potential impact of aQGCs is shown as well. From [9].

Figure 26

VBF-$W$ candidate events in the $\ell \nu jj$ final state at 8 TeV. (a) Pseudorapidity difference of the tag jets. (b) Dijet mass spectrum of the tag jets. From [199].

Figure 27

(a) BDT output and Monte Carlo expectations for VBF-$Z$ candidate events in the $\ell \ell jj$ final state at 8 TeV. From [183]. (b) Expected and observed 68% and 95% C.L. signal strength contours for EW and DY production of $\ell \ell jj$ at 8 TeV. From [183].

Figure 28

(a) Dijet invariant mass distribution of VBF-$Z$ candidate events in the $\ell \ell jj$ final state at 8 TeV. From [42]. (b) Unfolded normalized differential $Zjj$ production cross section as a function of dijet invariant mass. From [42].

Figure 29

(a) Dijet mass distribution of the tag jets in the $\mu \nu \gamma jj$ final state at 8 TeV. From [193]. (b) $p_{\mathrm{T}}$ spectrum of the $W$ boson in VBS candidate events in the $\ell \nu \gamma jj$ final state at 8 TeV. The effect of a representative aQGC on the spectrum is also shown. From [193].

Figure 30

$W^{\pm }Vjj$ candidate event transverse diboson mass distributions in the ${\ell }^{\pm }\nu (jj/J)jj$ final state at 8 TeV: (a) resolved ($V\to jj$) category for positively charged leptons and (b) merged ($V\to J$) category. The potential impact of aQGCs is shown as well. From [8].

Figure 31

VBS-$W^{\pm }{W}^{\pm }$ candidate events in the ${\ell }^{\pm }\nu {\ell }^{\pm }\nu jj$ final state at 8 TeV: (a) dijet mass of the tag jets and (b) dilepton mass distribution, where the effect of a representative aQGC on the spectrum is also shown. From [189].

Figure 32

VBS-$W^{\pm }{W}^{\pm }$ candidate events in the ${\ell }^{\pm }\nu {\ell }^{\pm }\nu jj$ final state at 8 TeV: (a) dijet mass and (b) rapidity separation of the tag jets. The applied selections are indicated by dotted lines. From [39].

Figure 33

Electroweak $W^{\pm }Zjj$ candidate event distributions in the ${\ell }^{\pm }\nu {\ell }^{\pm }{\ell }^{\mp }jj$ final state at 8 TeV: (a) the difference in the azimuthal angle between reconstructed $W$ and $Z$ boson directions and (b) the scalar sum of the $p_{\mathrm{T}}$ of the three charged leptons. The potential impact of aQGCs is shown as well. From [53].

Figure 34

VBS-$\gamma \gamma \to W^{+}{W}^{-}$ candidate events in the $e^{\pm }\nu {\mu }^{\mp }\nu$ final state in 8 TeV data: (a) the difference in the azimuthal angle between the electron and muon and (b) dilepton $p_{\mathrm{T}}$ distribution before applying the 30 GeV selection cut. The potential impact of aQGCs is shown as well. From [2].

Figure 35

VBS-$\gamma \gamma \to W^{+}{W}^{-}$ candidate events in the $e^{\pm }\nu {\mu }^{\mp }\nu$ final state in 8 TeV data: (a) acoplanarity of the $e\mu$ system and (b) dilepton $p_{\mathrm{T}}$ distribution before applying the 30 GeV selection cut. The potential impact of aQGCs is shown as well. From [198].

Figure 36

Comparison of the most competitive aTGC limits in the LEP scenario for the LHC analyses presented in this review as well as the combination of limits by the D0 ([60]) and LEP ([221]) experiments.

Figure 37

Expected and observed 95% C.L. contours for aTGC limits derived from 8 TeV fully leptonic $WW$ candidate events, illustrating the anticorrelations between (a) ${\lambda }^V$ and (b) $\mathrm{\Delta }{\kappa }^V$ parameters when no constraints between aTGCs are assumed. The aTGCs not shown are set to zero. From [56].

Figure 38

Comparison of the most competitive aTGC EFT limits based on the 8 TeV $WW$ and $WZ$ analyses in leptonic final states by ATLAS (blue) and CMS (red), using the full available data sets.

Figure 39

Expected and observed 68% and 95% C.L. contours for aTGC limits in the EFT formulation derived from 8 TeV fully leptonic $WW$ candidate events illustrating the weak correlations between these EFT parameters, with $c_{WWW}$ set to zero. From [195].

Figure 40

Comparison of the most competitive $Z\gamma \gamma$ and $Z\gamma Z$ limits, set by the LHC analyses presented in this review. All limits are based on the full 8 TeV, $\approx 20{\mathrm{fb}}^{-1}$ data sets.

Figure 41

Expected and observed 95% C.L. contours for aTGC limits derived from 7 TeV $ZZ$ candidate events in the $4\ell$ decay mode for the $f_4^{\gamma }$ vs $f_4^Z$ parameters. aTGCs not shown are set to zero. From [122].

Figure 42

Comparison of the most competitive $ZZ\gamma$ and $ZZZ$ limits, set by the LHC analyses presented in this review.

Figure 43

Comparison of the most competitive limits involving $f_{T,i}$ coefficients, set by the LHC analyses presented in this review. All limits are based on the full 8 TeV, $\approx 20{\mathrm{fb}}^{-1}$ data sets.

Figure 44

Comparison of the most competitive limits involving $f_{M,i}$ coefficients, set by the LHC analyses presented in this review. All limits are based on the full 8 TeV, $\approx 20{\mathrm{fb}}^{-1}$ data sets, except for the $\gamma \gamma \to WW$ analysis by CMS, using in addition the full $\approx 5{\mathrm{fb}}^{-1}$ of the 7 TeV data set.

Figure 45

Expected and observed 95% C.L. contours for aQGC limits in the ${\alpha }_4$ and ${\alpha }_5$ plane derived from 8 TeV $W^{\pm }Vjj$, $W^{\pm }{W}^{\pm }jj$, and $W^{\pm }Zjj$ results by ATLAS. From [8].

Figure 46

Comparison of the available limits involving $f_{S,i}$ coefficients, set by the LHC analyses presented in this review. All limits are based on the full 8 TeV, $\approx 20{\mathrm{fb}}^{-1}$ data sets.

Figure 47

Comparison of the available limits involving ${\alpha }_{4,5}$ coefficients, set by the LHC analyses presented in this review. All limits are based on the full 8 TeV, $\approx 20{\mathrm{fb}}^{-1}$ data sets. A “K” in the ${\mathrm{\Lambda }}_{\mathrm{F}\mathrm{F}}$ column indicates that $K$-matrix unitarization was applied.

Figure 48

Expected CMS performance for $W^{\pm }{W}^{\pm }$ VBS measurements at the HL-LHC: (a) significance of measuring the longitudinal $W^{\pm }{W}^{\pm }$ VBS cross section as a function of integrated luminosity and (b) dilepton mass distribution, where the effect of aQGCs on the spectrum is also From [190].