# Higgs characterisation via vector-boson fusion and associated production: NLO and parton-shower effects

- 714 Downloads
- 31 Citations

## Abstract

Vector-boson fusion and associated production at the LHC can provide key information on the strength and structure of the Higgs couplings to the Standard Model particles. Using an effective field theory approach, we study the effects of next-to-leading order (NLO) QCD corrections matched to a parton shower on selected observables for various spin-0 hypotheses. We find that inclusion of NLO corrections is needed to reduce the theoretical uncertainties on the total rates as well as to reliably predict the shapes of the distributions. Our results are obtained in a fully automatic way via FeynRules and MadGraph5_aMC@NLO.

## Keywords

Parton Shower Gluon Fusion Effective Field Theory Standard Model Case EWSB Scale## 1 Introduction

After the discovery of a new boson at the LHC [1, 2], studies of its properties have become the first priority of the high-energy physics community. A coordinated theoretical and experimental effort is made [3, 4, 5] that aims at maximising the information from the ongoing and forthcoming measurements. On the experimental side, new analyses, strategies and more precise measurements are being performed that cover the wider range of relevant production and decay channels in the Standard Model (SM) and beyond, and the recent measurements of the coupling strength [6, 7] and the spin-parity properties [8, 9] give strong indications that the new particle is indeed the scalar boson predicted by the SM. On the theoretical side, predictions for signal and background are being obtained at higher orders in perturbative expansion in QCD and electroweak (EW) theory, so that a better accuracy in the extraction of the SM parameters can be achieved. In addition, new variables and observables are being proposed that may be sensitive to new physics effects. At the same time, considerable attention is being devoted to the definition of a theoretical methodology and framework to collect and interpret the constraints coming from the experimental side.

The proposal of employing an effective field theory (EFT) that features only SM particles and symmetries at the EW scale has turned out to be particularly appealing. Such a minimal assumption, certainly well justified by the present data, provides not only a drastic reduction of all possible interactions that Lorentz symmetry alone would allow, but also a well-defined and powerful framework where constraints coming from Higgs measurements can be globally analysed together with those coming from precision EW measurements and flavour physics (see for example Refs. [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34], and more in general Refs. [35, 36]).

In this context, the *Higgs Characterisation* (HC) framework has recently been presented [37], which follows the general strategy outlined in Ref. [38]. A simple EFT lagrangian featuring bosons with various spin-parity assignments has been implemented in FeynRules [39, 40] and passed to the MadGraph5_aMC@NLO [41, 42, 43] framework by means of the UFO model file [44, 45]. Such an implementation is simple but general enough to describe any new physics effects coming from higher scales in a fully model-independent way. It has the advantage of being systematically and seamlessly improvable through the inclusion of more operators in the lagrangian on one side and of higher-order corrections, notably those coming from QCD, on the other. The latter, considered in the form of multi-parton tree-level computations (ME+PS) and of next-to-leading order (NLO) calculations matched to parton showers (NLO+PS), are a very important ingredient for performing sensible phenomenological studies.

In Ref. [37] we have provided a study of higher-order QCD effects for inclusive \(pp\rightarrow X(J^P)\) production, with \(J^P=0^+\), \(0^-\), \(1^+\), \(1^-,\) and \(2^+\), and correlated decay of resonances into a pair of gauge bosons, where gluon fusion (\(q{\bar{q}}\) annihilation) is dominant for spin-0 and spin-2 (spin-1) at the LO. In this work, we present the results for the next most important production channels at the LHC, *i.e.*, weak vector-boson fusion (VBF) and associated production (VH), focusing on the most likely spin-0 hypothesis. As already noted in Ref. [37], these processes share the property that NLO QCD corrections factorise exactly with respect to the new physics interactions in Higgs couplings and therefore can be automatically performed within the current MadGraph5_aMC@NLO framework. Given that the Higgs characterisation can also be done automatically in the \(t{\bar{t}}H\) production channel [46], all the main Higgs production channels are covered.

We stress that the spin-parity studies in VBF and VH production nicely complement those in \(H\rightarrow ZZ/WW\) decays [47, 48]. One of the advantages in the VBF and VH channels is that spin-parity observables, *e.g.*, the azimuthal difference between the two tagging jets \(\varDelta \phi _{jj}\) in VBF, do not require a reconstruction of the Higgs resonance, although the separation between the \(Z\) and \(W\) contributions is very difficult. In this study, we focus on the effects of the QCD corrections in Higgs VBF and VH production without considering the decay.

The paper is organised as follows. In the following section we recall the relevant effective lagrangian of Ref. [37], and we define the sample scenarios used to illustrate the phenomenological implications. In Sect. 3 we present the VBF results in the form of distributions of key observables in the inclusive setup as well as with dedicated VBF cuts, while in Sect. 4 we illustrate the \(W^{\pm }H\) and \(ZH\) production. We briefly summarise our findings in the concluding section.

## 2 Theoretical setup

In this section, we summarise the full setup, from the lagrangian, to the choice of benchmark scenarios, to event generation at NLO accuracy.

### 2.1 Effective lagrangian and benchmark scenarios

We construct an effective lagrangian below the electroweak symmetry breaking (EWSB) scale in terms of mass eigenstates. Our assumptions are simply that the resonance structure observed in data corresponds to one bosonic state (\(X(J^P)\) with \(J=0\), \(1\) or \(2\) and a mass of about \(125\) GeV), and that no other new state below the cutoff \(\varLambda \) coupled to such a resonance exists. We also follow the principle that any new physics is dominantly described by the lowest-dimensional operators. This means, for the spin-0 case, that we include all effects coming from the complete set of dimension-six operators with respect to the SM gauge symmetry.

*i.e.*, for the interactions between a spin-0 state and vector bosons, is (Eq. (2.4) in Ref. [37]):

HC model parameters

Parameter | Description |
---|---|

\(\varLambda \) (GeV) | Cutoff scale |

\(c_{\alpha }\,(\equiv \cos \alpha \)) | Mixing between \(0^+\) and \(0^-\) |

\(\kappa _i\) | Dimensionless coupling parameter |

Values in units of \(v\) taken by the couplings \(g_{Xyy'}\) for the EW gauge bosons. \(C=\sqrt{\frac{\alpha _{\scriptscriptstyle \mathrm EM}G_F m_Z^2}{8\sqrt{2}\pi }}\)

\(g_{Xyy'}\times v\ \ \) | \(ZZ/WW\) | \(\gamma \gamma \) | \(Z\gamma \) |
---|---|---|---|

\(X=H\) | \(2m_{Z/W}^2\) | \(47\alpha _{\scriptscriptstyle \mathrm EM}/18\pi \) | \(C(94c^2_W-13)/9\pi \) |

\(X=A\) | 0 | \(4\alpha _{\scriptscriptstyle \mathrm EM}/3\pi \) | \(2C(8c^2_W-5)/3\pi \) |

The corresponding implementation of the dimension-six lagrangian above the EWSB scale, where \(SU(2)_L \times U(1)_Y\) is an exact symmetry, has recently appeared [49], which has overlapping as well as complementary features with respect to our HC lagrangian. We note that the lagrangian of Eq. (1) features 14 free parameters, of which one possibly complex (\(\kappa _{\scriptscriptstyle H\partial W}\)). On the other hand, as explicitly shown in Table 1 of Ref. [49] these correspond to 11 free parameters in the parametrisation above the EWSB due to the custodial symmetry. We stress that the results at NLO in QCD accuracy shown here can be obtained for that lagrangian in exactly the same way.

Benchmark scenarios

Scenario | HC parameter choice |
---|---|

\(0^+\)(SM) | \(\kappa _{\scriptscriptstyle \mathrm SM}=1\ (c_{\alpha }=1)\) |

\(0^+\)(HD) | \(\kappa _{\scriptscriptstyle HZZ,HWW}=1\ (c_{\alpha }=1)\) |

\(0^+\)(HDder) | \(\kappa _{\scriptscriptstyle H\partial Z,H\partial W}=1\ (c_{\alpha }=1)\) |

\(0^+\)(SM\(+\)HD) | \(\kappa _{\scriptscriptstyle SM,HZZ,HWW}=1\ (c_{\alpha }=1,\, \varLambda =v)\) |

\(0^-\)(HD) | \(\kappa _{\scriptscriptstyle AZZ,AWW}=1\ (c_{\alpha }=0)\) |

\(0^{\pm }\)(HD) | \(\kappa _{\scriptscriptstyle HZZ,AZZ,HWW,AWW}=1\ (c_{\alpha }=1/\sqrt{2})\) |

### 2.2 NLO corrections including parton-shower effects

The MadGraph5_aMC@NLO framework is designed to automatically perform the computation of tree-level and NLO cross sections, possibly including their matching to parton showers and the merging of samples with different parton multiplicities. Currently, the full automation is available in a unique and self-contained framework based on MadGraph5 [41] for SM processes with NLO QCD corrections. User intervention is limited to the input of physical quantities, and after event generation, to the choice of observables to be analysed. In Ref. [37] the results for gluon fusion have been presented and compared to predictions coming from ME+PS (MLM-\(k_T\) merging [50, 51, 52]) and NLO +PS. The distributions were found to be compatible between the two predictions. In this work we limit ourselves to NLO+PS results as typical observables are inclusive in terms of extra radiation and such calculations do also provide a reliable normalisation.

aMC@NLO implements matching of any NLO QCD computation with parton showers following the MC@NLO approach [53]. Two independent and modular parts are devoted to the computation of specific contributions to an NLO-matched computation: MadFKS [42] takes care of the Born, the real-emission amplitudes, and it also performs the subtraction of the infrared singularities and the generation of the Monte Carlo subtraction terms, according to the FKS prescription [54, 55]. MadLoop [43] computes the one-loop amplitudes, using the CutTools [56] implementation of the OPP integrand-reduction method [57]. The OpenLoops method [58] is also used for better performance. Once the process of interest is specified by the user, the generation of the code is fully automated. Basic information, however, must be available as regards the model and the interactions of its particles with QCD partons. For MadFKS this amounts to the ordinary Feynman rules. For MadLoop, on the other hand, the Feynman rules, UV counterterms, and special tree-level rules, so-called \(R_2\), necessary to (and defined by) the OPP method, should be provided. While Feynman rules are automatically computed from a given lagrangian (via FeynRules [39, 40]), this is not yet possible for UV counterterms and \(R_2\) rules. At this moment this limitation hampers the automatic computation of NLO QCD corrections for arbitrary processes in generic BSM models, including the HC model. The processes considered in this paper, VBF and VH, are, however, a notable exception as QCD corrections can be computed automatically and in full generality. This is because the corresponding one-loop amplitudes only include SM particles and do not need any UV counterterms and \(R_2\) information from the HC lagrangian. In the case of VBF, this assumes that only vertex loop corrections can be computed, *i.e.*, the pentagon diagrams are discarded, as the contributions only affect interferences between the diagrams, which are negligible already at LO.

### 2.3 Simulation parameters

In our simulations we generate events at the LHC with a centre-of-mass energy \(\sqrt{s}=8\) TeV and set the resonance mass to \(m_{X_0}=125\) GeV. Parton distribution functions (PDFs) are evaluated by using the MSTW2008 (LO/NLO) parametrisation [59], and jets are reconstructed via the anti-\(k_T\) (\(\varDelta R=0.4\)) algorithm [60] as implemented in FastJet [61]. Central values for the renormalisation and factorisation scales \(\mu _{R,F} \) are set to \(\mu _0=m_W\) and \(m_\mathrm{VH}\) for VBF and VH production, respectively, where \(m_\mathrm{VH}\) is the invariant mass of the VH system. We note here that scale (and PDF) uncertainties can be evaluated automatically in the code via a reweighting technique [62], the user only deciding the range of the variation. In addition, such information is available on an event-by-event basis and therefore uncertainty bands can be plotted for any observable of interest. In this work, however, to simplify the presentation that focuses on the differences between the various scenarios, we give this information only for total cross sections and refrain from showing them in the differential distributions. For parton shower and hadronisation we employ HERWIG6 [63] in this paper, while HERWIG++ [64], (virtuality ordered) Pythia6 [65] and Pythia8 [66] are available for use in aMC@NLO. The comparison among the above different shower schemes was done for the SM Higgs boson in VBF in Ref. [67].

## 3 Vector-boson fusion

Predictions for Higgs production via VBF in the SM are known up to NNLO accuracy for the total cross section [68, 69, 70], at the NLO QCD [71, 72, 73, 74, 75, 76] + EW [77, 78] level in a differential way and at NLO in QCD plus parton shower both in the POWHEG BOX [79] and in aMC@NLO [67]. NLO QCD predictions that include anomalous couplings between the Higgs and a pair of vector bosons are available in VBFNLO [80, 81]. Our implementation provides the first predictions for EFT interactions including NLO corrections in QCD interfaced with a parton shower. Many phenomenological studies on Higgs spin, parity and couplings are available in the literature [47, 48, 82, 83, 84, 85, 86, 87, 88], which could now be upgraded to NLO+PS accuracy.

*i.e.*, we set the corresponding \(\kappa _i\) to zero in the simulation), as we focus on SM-like VBF observables. As mentioned above, since our interest is geared towards QCD effects on production distributions, we do not include Higgs decays in our studies either. We stress, however, that decays (as predicted in the HC model) can be efficiently included at the partonic event level (before passing the event to a shower program) via MadSpin [89].

VBF total cross sections with scale uncertainties and corresponding \(K\)-factors at LHC 8TeV for various scenarios

Scenario | \(\sigma _\mathrm{LO}\) (fb) | \(\sigma _\mathrm{NLO}\) (fb) | \(K\) |
---|---|---|---|

\(0^+\)(SM) | 1509(1) \({}^{+4.7~\%}_{-4.4~\%}\) | 1633(2) \({}^{+2.0~\%}_{-1.5~\%}\) | 1.08 |

\(0^+\)(HD) | 69.66(6) \({}^{+7.5~\%}_{-6.6~\%}\) | 67.08(13) \({}^{+2.2~\%}_{-2.3~\%}\) | 0.96 |

\(0^+\)(HDder) | 721.9(6) \({}^{+11.0~\%}_{-9.0~\%}\) | 684.9(1.5) \({}^{+2.3~\%}_{-2.8~\%}\) | 0.95 |

\(0^+\)(SM\(+\)HD) | 3065(2) \({}^{+5.6~\%}_{-5.1~\%}\) | 3144(5) \({}^{+1.6~\%}_{-1.1~\%}\) | 1.03 |

\(0^-\)(HD) | 57.10(4) \({}^{+7.7~\%}_{-6.7~\%}\) | 55.24(11) \({}^{+2.1~\%}_{-2.5~\%}\) | 0.97 |

\(0^\pm \)(HD) | 63.46(5) \({}^{+7.6~\%}_{-6.7~\%}\) | 61.07(13) \({}^{+2.3~\%}_{-2.0~\%}\) | 0.96 |

The lowest inset in Fig. 1 is the ratio of NLO+PS to LO results, while the middle one shows the ratio of NLO+PS to pure NLO. NLO+PS corrections modify in a consistent way LO parton-level predictions with major effects at high invariant mass, *i.e.*, the QCD corrections tend to make the tagging jets softer. In addition, the parton shower affects both the lower and the higher invariant mass regions.

The unitarity violating behaviour of the higher-dimensional interactions, especially for \(0^+\)(HDder), clearly manifests itself in the transverse momentum distributions for the \(X_0\) and the jets. The rapidity distribution of the tagging jets displays the fact that in the case of higher-dimensional interactions the jets as a result are much more central than in the SM case. The same glaring difference appears in the azimuthal correlations between the jets which offer clear handle to discriminate about different interactions type and parity assignments.

In all cases NLO corrections are relevant and cannot be described by an overall \(K\)-factor. Moreover, their impact depends on the applied cuts. Apart from regions in phase space where the jets end up close and therefore are sensitive to NLO/jet reconstruction effects, the parton-shower effect on the shapes is very minor, especially after the VBF cut.

## 4 Vector-boson associated production

Predictions for Higgs production in association with a weak vector boson in the SM are known up to NNLO accuracy [90, 91, 92], including EW corrections [93, 94]. NLO+PS results can be obtained via (a)MC@NLO [95, 96] and the POWHEG BOX [97]. Many phenomenological studies on Higgs spin, parity and couplings are available in the literature [48, 88, 98, 99, 100, 101, 102, 103, 104, 105]. In this section we present the first predictions for EFT interactions including NLO corrections in QCD interfaced with a parton shower in the VH process.

\(pp\rightarrow H(W^+\rightarrow e^+\nu _e)\) total cross sections with scale uncertainties and corresponding \(K\)-factors at LHC 8 TeV for various scenarios

Scenario | \(\sigma _\mathrm{LO}\) (fb) | \(\sigma _\mathrm{NLO}\) (fb) | \(K\) |
---|---|---|---|

\(0^+\)(SM) | 39.58(3) \({}^{+0.1~\%}_{-0.6~\%}\) | 51.22(5) \({}^{+2.2~\%}_{-1.8~\%}\) | 1.29 |

\(0^+\)(HD) | 13.51(1) \({}^{+1.5~\%}_{-1.7~\%}\) | 17.51(1) \({}^{+1.9~\%}_{-1.3~\%}\) | 1.30 |

\(0^+\)(HDder) | 324.2(2) \({}^{+4.7~\%}_{-4.3~\%}\) | 416.1(4) \({}^{+2.3~\%}_{-2.1~\%}\) | 1.28 |

\(0^+\)(SM\(+\)HD) | 118.8(1) \({}^{+3.0~\%}_{-2.9~\%}\) | 154.2(1) \({}^{+1.8~\%}_{-1.6~\%}\) | 1.30 |

\(0^-\)(HD) | 8.386(7) \({}^{+2.6~\%}_{-2.6~\%}\) | 10.89(1) \({}^{+1.8~\%}_{-1.5~\%}\) | 1.30 |

\(0^\pm \)(HD) | 10.96(1) \({}^{+1.9~\%}_{-2.1~\%}\) | 14.22(1) \({}^{+1.8~\%}_{-1.3~\%}\) | 1.30 |

Same as Table 5, but for \(pp\rightarrow H(W^-\rightarrow e^-\bar{\nu }_e)\)

Scenario | \(\sigma _\mathrm{LO}\) (fb) | \(\sigma _\mathrm{NLO}\) (fb) | \(K\) |
---|---|---|---|

\(0^+\)(SM) | 22.46(1) \({}^{+0.0~\%}_{-0.6~\%}\) | 29.86(3) \({}^{+2.3~\%}_{-1.8~\%}\) | 1.33 |

\(0^+\)(HD) | 7.009(5) \({}^{+1.4~\%}_{-1.7~\%}\) | 9.355(9) \({}^{+1.9~\%}_{-1.3~\%}\) | 1.34 |

\(0^+\)(HDder) | 145.7(1) \({}^{+4.1~\%}_{-3.9~\%}\) | 193.8(1) \({}^{+2.1~\%}_{-1.9~\%}\) | 1.33 |

\(0^+\)(SM\(+\)HD) | 57.90(5) \({}^{+2.8~\%}_{-2.9~\%}\) | 77.31(8) \({}^{+1.8~\%}_{-1.6~\%}\) | 1.34 |

\(0^-\)(HD) | 4.151(3) \({}^{+2.5~\%}_{-2.6~\%}\) | 5.550(5) \({}^{+1.7~\%}_{-1.4~\%}\) | 1.34 |

\(0^\pm \)(HD) | 5.583(4) \({}^{+1.8~\%}_{-2.0~\%}\) | 7.445(7) \({}^{+1.8~\%}_{-1.3~\%}\) | 1.33 |

Same as Table 5, but for \(pp\rightarrow H(Z\rightarrow e^+e^-)\)

Scenario | \(\sigma _\mathrm{LO}\) (fb) | \(\sigma _\mathrm{NLO}\) (fb) | \(K\) |
---|---|---|---|

\(0^+\)(SM) | 10.13(1) \({}^{+0.0~\%}_{-0.5~\%}\) | 13.24(1) \({}^{+2.2~\%}_{-1.7~\%}\) | 1.31 |

\(0^+\)(HD) | 2.638(2) \({}^{+1.4~\%}_{-1.7~\%}\) | 3.461(3) \({}^{+1.9~\%}_{-1.3~\%}\) | 1.31 |

\(0^+\)(HDder) | 48.61(4) \({}^{+4.2~\%}_{-3.9~\%}\) | 63.59(5) \({}^{+2.1~\%}_{-1.9~\%}\) | 1.31 |

\(0^+\)(SM\(+\)HD) | 19.95(1) \({}^{+3.1~\%}_{-3.1~\%}\) | 26.24(2) \({}^{+1.8~\%}_{-1.6~\%}\) | 1.32 |

\(0^-\)(HD) | 1.480(1) \({}^{+2.6~\%}_{-2.7~\%}\) | 1.952(1) \({}^{+1.7~\%}_{-1.5~\%}\) | 1.32 |

\(0^\pm \)(HD) | 2.061(1) \({}^{+1.9~\%}_{-2.0~\%}\) | 2.705(2) \({}^{+1.8~\%}_{-1.3~\%}\) | 1.31 |

The results for \(W\) and \(Z\) display very similar features. The scenarios that include contributions from higher-dimensional operators show harder \(p_T\) spectra. This is even more pronounced in the case of the derivative operator (HDder). This fact is also reflected in the shape of the rapidity distributions, *i.e.*, the harder \(p_T\) spectra correspond to a more central rapidity for the VH scattering.

As in Sect. 3, the ratios of NLO+PS to LO (NLO) results are presented in the lowest (middle) inset in Fig. 4. NLO+PS effects are quite important when compared with fixed-order LO predictions, and, in many cases, they cannot be accounted for by applying an overall \(K\)-factor. Conversely, NLO+PS distributions are in almost perfect agreement with fixed-order NLO predictions, witnessing small effects genuinely due to the parton shower.

## 5 Summary

We have studied higher-order QCD effects for various spin-0 hypotheses in VBF and VH production, obtained in a fully automatic way via the model implementation in FeynRules and event generation at NLO accuracy in the MadGraph5_aMC@NLO framework. Our approach to the Higgs characterisation is based on an EFT that takes into account all relevant operators up to dimension six written in terms of fields above the EWSB scale and then expressed in terms of mass eigenstates (\(W,Z,\gamma \) and \(H\)).

We have presented illustrative distributions obtained by interfacing NLO parton-level events to the HERWIG6 parton shower. NLO corrections improve the predictions on the total cross sections by reducing the scale dependence. In addition, our simulations show that NLO+PS effects need to be accounted for to make accurate predictions on the kinematical distributions of the final state objects, such as the Higgs and the jet distributions.

We look forward to the forthcoming LHC experimental studies employing the EFT approach and NLO accurate simulations to extract accurate information on possible new physics effects in Higgs physics.

## Notes

### Acknowledgments

We would like to thank all the members of the Higgs Cross Section Working Group for their encouragement in pursuing the Higgs Characterisation project. We also thank Stefano Frixione for helpful comments on the draft. This work has been performed in the framework of the ERC grant 291377 ‘LHCtheory: Theoretical predictions and analyses of LHC physics: advancing the precision frontier’ and it is supported in part by the Belgian Federal Science Policy Office through the Interuniversity Attraction Pole P7/37. The work of FM is supported by the IISN ‘MadGraph’ convention 4.4511.10, the IISN ‘Fundamental interactions’ convention 4.4517.08. KM is supported in part by the Strategic Research Program ‘High Energy Physics’ and the Research Council of the Vrije Universiteit Brussel. The work of MZ is partially supported by the Research Executive Agency (REA) of the European Union under the Grant Agreement number PITN-GA-2010-264564 (LHCPhenoNet).

## References

- 1.ATLAS Collaboration, G. Aad et al., Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC. Phys. Lett. B
**716**, 1–29 (2012). arXiv:1207.7214 Google Scholar - 2.S. Chatrchyan et al., C.M.S. Collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC. Phys. Lett. B
**716**, 30–61 (2012). arXiv:1207.7235 - 3.LHC Higgs Cross Section Working Group Collaboration, S. Dittmaier et al., Handbook of LHC Higgs Cross Sections: 1. Inclusive Observables, arXiv:1101.0593
- 4.LHC Higgs Cross Section Working Group Collaboration, S. Dittmaier et al., Handbook of LHC Higgs Cross Sections: 2. Differential Distributions, arXiv:1201.3084
- 5.LHC Higgs Cross Section Working Group Collaboration, S. Heinemeyer et al., Handbook of LHC Higgs Cross Sections: 3. Higgs Properties (2013). doi: 10.5170/CERN-2013-004. arXiv:1307.1347
- 6.ATLAS Collaboration, Combined coupling measurements of the Higgs-like boson with the ATLAS detector using up to 25 fb\(^{-1}\) of proton-proton collision data, ATLAS-CONF-2013-034Google Scholar
- 7.CMS Collaboration, S. Chatrchyan et al., Observation of a new boson with mass near 125 GeV in pp collisions at \(\sqrt{s}\) = 7 and 8 TeV, JHEP
**1306**, 081 (2013). arXiv:1303.4571 - 8.ATLAS Collaboration, G. Aad et al., Evidence for the spin-0 nature of the Higgs boson using ATLAS data. Phys. Lett. B
**726**, 120–144 (2013). arXiv:1307.1432 Google Scholar - 9.CMS Collaboration, S. Chatrchyan et al., Study of the mass and spin-parity of the Higgs Boson candidate via Its decays to Z Boson Pairs. Phys.Rev.Lett.
**110**, 081803 (2013). arXiv:1212.6639 Google Scholar - 10.K. Hagiwara, R. Szalapski, D. Zeppenfeld, Anomalous Higgs boson production and decay. Phys. Lett. B
**318**, 155–162 (1993). arXiv:hep-ph/9308347 Google Scholar - 11.G. Giudice, C. Grojean, A. Pomarol, R. Rattazzi, The strongly-interacting light Higgs. JHEP
**0706**, 045 (2007). arXiv:hep-ph/0703164 - 12.B. Gripaios, A. Pomarol, F. Riva, J. Serra, Beyond the minimal composite Higgs model. JHEP
**0904**, 070 (2009). arXiv:0902.1483 ADSCrossRefGoogle Scholar - 13.R. Lafaye, T. Plehn, M. Rauch, D. Zerwas, M. Duhrssen, Measuring the Higgs sector. JHEP
**0908**, 009 (2009). arXiv:0904.3866 ADSCrossRefGoogle Scholar - 14.I. Low, R. Rattazzi, A. Vichi, Theoretical constraints on the Higgs effective couplings. JHEP
**1004**, 126 (2010). arXiv:0907.5413 ADSCrossRefGoogle Scholar - 15.D.E. Morrissey, T. Plehn, T.M. Tait, Physics searches at the LHC. Phys. Rep.
**515**, 1–113 (2012). arXiv:0912.3259 ADSCrossRefGoogle Scholar - 16.R. Contino, C. Grojean, M. Moretti, F. Piccinini, R. Rattazzi, Strong double Higgs production at the LHC. JHEP
**1005**, 089 (2010). arXiv:1002.1011 ADSCrossRefGoogle Scholar - 17.J. Espinosa, C. Grojean, M. Muhlleitner, Composite Higgs search at the LHC. JHEP
**1005**, 065 (2010). arXiv:1003.3251 ADSCrossRefGoogle Scholar - 18.A. Azatov, R. Contino, J. Galloway, Model-independent bounds on a light Higgs. JHEP
**1204**, 127 (2012). arXiv:1202.3415 ADSCrossRefGoogle Scholar - 19.J. Espinosa, C. Grojean, M. Muhlleitner, M. Trott, Fingerprinting Higgs suspects at the LHC. JHEP
**1205**, 097 (2012). arXiv:1202.3697 ADSCrossRefGoogle Scholar - 20.J. Ellis, T. You, Global analysis of experimental constraints on a possible Higgs-like particle with mass 125 GeV. JHEP
**1206**, 140 (2012). arXiv:1204.0464 ADSCrossRefGoogle Scholar - 21.M. Klute, R. Lafaye, T. Plehn, M. Rauch, D. Zerwas, Measuring Higgs couplings from LHC data. Phys. Rev. Lett.
**109**, 101801 (2012). arXiv:1205.2699 ADSCrossRefGoogle Scholar - 22.I. Low, J. Lykken, G. Shaughnessy, Have we observed the Higgs (imposter)? Phys. Rev. D
**86**, 093012 (2012). arXiv:1207.1093 ADSCrossRefGoogle Scholar - 23.T. Corbett, O. Eboli, J. Gonzalez-Fraile, M. Gonzalez-Garcia, Constraining anomalous Higgs interactions. Phys. Rev. D
**86**, 075013 (2012). arXiv:1207.1344 ADSCrossRefGoogle Scholar - 24.J. Ellis, T. You, Global analysis of the Higgs candidate with mass 125 GeV. JHEP
**1209**, 123 (2012). arXiv:1207.1693 ADSCrossRefGoogle Scholar - 25.M. Montull, F. Riva, Higgs discovery: the beginning or the end of natural EWSB? JHEP
**1211**, 018 (2012). arXiv:1207.1716 ADSCrossRefGoogle Scholar - 26.J. Espinosa, C. Grojean, M. Muhlleitner, M. Trott, First Glimpses at Higgs’ face. JHEP
**1212**, 045 (2012). arXiv:1207.1717 ADSCrossRefGoogle Scholar - 27.D. Carmi, A. Falkowski, E. Kuflik, T. Volansky, J. Zupan, Higgs after the discovery: a status report. JHEP
**1210**, 196 (2012). arXiv:1207.1718 ADSCrossRefGoogle Scholar - 28.T. Plehn, M. Rauch, Higgs couplings after the discovery. Europhys. Lett.
**100**, 11002 (2012). arXiv:1207.6108 CrossRefGoogle Scholar - 29.G. Passarino, NLO inspired effective lagrangians for Higgs physics. Nucl. Phys. B
**868**, 416–458 (2013). arXiv:1209.5538 Google Scholar - 30.T. Corbett, O. Eboli, J. Gonzalez-Fraile, M. Gonzalez-Garcia, Robust determination of the Higgs couplings: power to the data. Phys. Rev. D
**87**, 015022 (2013). arXiv:1211.4580 ADSCrossRefGoogle Scholar - 31.K. Cheung, J.S. Lee, P.-Y. Tseng, Higgs precision (Higgcision) era begins. JHEP
**1305**, 134 (2013). arXiv:1302.3794 ADSCrossRefGoogle Scholar - 32.A. Falkowski, F. Riva, A. Urbano, Higgs at last. JHEP
**1311**, 111 (2013). doi: 10.1007/JHEP11(2013)111. arXiv:1303.1812 - 33.R. Contino, M. Ghezzi, C. Grojean, M. Muhlleitner, M. Spira, Effective Lagrangian for a light Higgs-like scalar. JHEP
**1307**, 35 (2013). doi: 10.1007/JHEP07(2013)035. arXiv:1303.3876 - 34.Y. Chen, R. Vega-Morales, Extracting effective Higgs couplings in the golden channel. arXiv:1310.2893
- 35.W. Buchmuller, D. Wyler, Effective lagrangian analysis of new interactions and flavor conservation. Nucl. Phys. B
**268**, 621 (1986)ADSCrossRefGoogle Scholar - 36.B. Grzadkowski, M. Iskrzynski, M. Misiak, J. Rosiek, Dimension-six terms in the standard model lagrangian. JHEP
**1010**, 085 (2010). arXiv:1008.4884 ADSCrossRefGoogle Scholar - 37.P. Artoisenet, P. de Aquino, F. Demartin, R. Frederix, S. Frixione, et al., A framework for Higgs characterisation. JHEP
**1311**, 43 (2013). doi: 10.1007/JHEP11(2013)043. arXiv:1306.6464 - 38.N.D. Christensen, P. de Aquino, C. Degrande, C. Duhr, B. Fuks et al., A Comprehensive approach to new physics simulations. Eur. Phys. J. C
**71**, 1541 (2011). arXiv:0906.2474 ADSCrossRefGoogle Scholar - 39.N.D. Christensen, C. Duhr, FeynRules-Feynman rules made easy. Comput. Phys. Commun.
**180**, 1614–1641 (2009). arXiv:0806.4194 Google Scholar - 40.A. Alloul, N. D. Christensen, C. Degrande, C. Duhr, B. Fuks, FeynRules 2.0-A complete toolbox for tree-level phenomenology. arXiv:1310.1921
- 41.J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, T. Stelzer, MadGraph 5: going beyond. JHEP
**1106**, 128 (2011). arXiv:1106.0522 ADSCrossRefGoogle Scholar - 42.R. Frederix, S. Frixione, F. Maltoni, T. Stelzer, Automation of next-to-leading order computations in QCD: the FKS subtraction. JHEP
**10**, 003 (2009). arXiv:0908.4272 ADSCrossRefGoogle Scholar - 43.V. Hirschi et al., Automation of one-loop QCD corrections. JHEP
**05**, 044 (2011). arXiv:1103.0621 ADSCrossRefGoogle Scholar - 44.C. Degrande, C. Duhr, B. Fuks, D. Grellscheid, O. Mattelaer et al., UFO-the universal FeynRules output. Comput. Phys. Commun.
**183**, 1201–1214 (2012). arXiv:1108.2040 ADSCrossRefGoogle Scholar - 45.P. de Aquino, W. Link, F. Maltoni, O. Mattelaer, T. Stelzer, Automatic libraries of helicity amplitudes for Feynman diagram computations. Comput. Phys. Commun.
**183**, 2254–2263 (2012). arXiv:1108.2041 ADSCrossRefGoogle Scholar - 46.R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, R. Pittau, P. Torrielli, Scalar and pseudoscalar Higgs production in association with a top-antitop pair. Phys. Lett. B
**701**, 427–433 (2011). arXiv:1104.5613 ADSCrossRefGoogle Scholar - 47.K. Hagiwara, Q. Li, K. Mawatari, Jet angular correlation in vector-boson fusion processes at hadron colliders. JHEP
**0907**, 101 (2009). arXiv:0905.4314 ADSCrossRefGoogle Scholar - 48.C. Englert, D. Goncalves-Netto, K. Mawatari, T. Plehn, Higgs quantum numbers in weak Boson fusion. JHEP
**1301**, 148 (2013). arXiv:1212.0843 ADSCrossRefGoogle Scholar - 49.A. Alloul, B. Fuks, V. Sanz, Phenomenology of the Higgs effective lagrangian via FeynRules. arXiv:1310.5150
- 50.M.L. Mangano, M. Moretti, R. Pittau, Multijet matrix elements and shower evolution in hadronic collisions: \(W b \bar{b}\) + \(n\) jets as a case study. Nucl. Phys. B
**632**, 343–362 (2002). arXiv:hep-ph/0108069 - 51.J. Alwall, S. Hoche, F. Krauss, N. Lavesson, L. Lonnblad et al., Comparative study of various algorithms for the merging of parton showers and matrix elements in hadronic collisions. Eur. Phys. J. C
**53**, 473–500 (2008). arXiv:0706.2569 ADSCrossRefGoogle Scholar - 52.J. Alwall, S. de Visscher, F. Maltoni, QCD radiation in the production of heavy colored particles at the LHC. JHEP
**0902**, 017 (2009). arXiv:0810.5350 ADSCrossRefGoogle Scholar - 53.S. Frixione, B.R. Webber, Matching NLO QCD computations and parton shower simulations. JHEP
**06**, 029 (2002). arXiv:hep-ph/0204244 - 54.S. Frixione, Z. Kunszt, A. Signer, Three jet cross-sections to next-to-leading order. Nucl. Phys. B
**467**, 399–442 (1996). arXiv:hep-ph/9512328 Google Scholar - 55.S. Frixione, A general approach to jet cross-sections in QCD. Nucl. Phys. B
**507**, 295–314 (1997). arXiv:hep-ph/9706545 Google Scholar - 56.G. Ossola, C.G. Papadopoulos, R. Pittau, CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes. JHEP
**0803**, 042 (2008). arXiv:0711.3596 ADSCrossRefGoogle Scholar - 57.G. Ossola, C.G. Papadopoulos, R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level. Nucl. Phys. B
**763**, 147–169 (2007). arXiv:hep-ph/0609007 - 58.F. Cascioli, P. Maierhofer, S. Pozzorini, Scattering amplitudes with open loops. Phys. Rev. Lett.
**108**, 111601 (2012). arXiv:1111.5206 ADSCrossRefGoogle Scholar - 59.A. Martin, W. Stirling, R. Thorne, G. Watt, Parton distributions for the LHC. Eur. Phys. J. C
**63**, 189–285 (2009). arXiv:0901.0002 Google Scholar - 60.M. Cacciari, G.P. Salam, G. Soyez, The Anti-k(t) jet clustering algorithm. JHEP
**0804**, 063 (2008). arXiv:0802.1189 ADSCrossRefGoogle Scholar - 61.M. Cacciari, G.P. Salam, G. Soyez, FastJet user manual. Eur. Phys. J. C
**72**, 1896 (2012). arXiv:1111.6097 ADSCrossRefGoogle Scholar - 62.R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, R. Pittau et al., Four-lepton production at hadron colliders: aMC@NLO predictions with theoretical uncertainties. JHEP
**1202**, 099 (2012). arXiv:1110.4738 ADSCrossRefGoogle Scholar - 63.G. Corcella, I. Knowles, G. Marchesini, S. Moretti, K. Odagiri et al., HERWIG 6: an event generator for hadron emission reactions with interfering gluons (including supersymmetric processes). JHEP
**0101**, 010 (2001). arXiv:hep-ph/0011363 - 64.M. Bahr, S. Gieseke, M. Gigg, D. Grellscheid, K. Hamilton et al., Herwig++ physics and manual. Eur. Phys. J. C
**58**, 639–707 (2008). arXiv:0803.0883 ADSCrossRefGoogle Scholar - 65.T. Sjostrand, S. Mrenna, P.Z. Skands, PYTHIA 6.4 physics and manual, JHEP
**0605**, 026 (2006). arXiv:hep-ph/0603175 - 66.T. Sjostrand, S. Mrenna, P.Z. Skands, A brief Introduction to PYTHIA 8.1. Comput. Phys. Commun.
**178**, 852–867 (2008). arXiv:0710.3820 ADSCrossRefGoogle Scholar - 67.S. Frixione, P. Torrielli, M. Zaro, Higgs production through vector-boson fusion at the NLO matched with parton showers. Phys. Lett. B
**726**, 273–282 (2013). arXiv:1304.7927 ADSCrossRefGoogle Scholar - 68.R.V. Harlander, J. Vollinga, M.M. Weber, Gluon-induced weak Boson fusion. Phys. Rev. D
**77**, 053010 (2008). arXiv:0801.3355 - 69.P. Bolzoni, F. Maltoni, S.-O. Moch, M. Zaro, Higgs production via vector-boson fusion at NNLO in QCD. Phys. Rev. Lett.
**105**, 011801 (2010). arXiv:1003.4451 ADSCrossRefGoogle Scholar - 70.P. Bolzoni, F. Maltoni, S.-O. Moch, M. Zaro, Vector boson fusion at NNLO in QCD: SM Higgs and beyond. Phys. Rev. D
**85**, 035002 (2012). arXiv:1109.3717 ADSCrossRefGoogle Scholar - 71.T. Han, G. Valencia, S. Willenbrock, Structure function approach to vector boson scattering in p p collisions. Phys. Rev. Lett.
**69**, 3274–3277 (1992). arXiv:hep-ph/9206246 Google Scholar - 72.T. Figy, C. Oleari, D. Zeppenfeld, Next-to-leading order jet distributions for Higgs boson production via weak boson fusion. Phys. Rev. D
**68**, 073005 (2003). arXiv:hep-ph/0306109 - 73.E.L. Berger, J.M. Campbell, Higgs boson production in weak boson fusion at next-to-leading order. Phys. Rev. D
**70**, 073011 (2004). arXiv:hep-ph/0403194 - 74.T. Figy, D. Zeppenfeld, QCD corrections to jet correlations in weak boson fusion. Phys. Lett. B
**591**, 297–303 (2004). arXiv:hep-ph/0403297 Google Scholar - 75.V. Hankele, G. Klamke, D. Zeppenfeld, T. Figy, Anomalous Higgs boson couplings in vector boson fusion at the CERN LHC. Phys. Rev. D
**74**, 095001 (2006). arXiv:hep-ph/0609075 - 76.T. Figy, S. Palmer, G. Weiglein, Higgs production via weak Boson fusion in the standard model and the MSSM. JHEP
**1202**, 105 (2012). arXiv:1012.4789 ADSCrossRefGoogle Scholar - 77.M. Ciccolini, A. Denner, S. Dittmaier, Strong and electroweak corrections to the production of Higgs + 2jets via weak interactions at the LHC. Phys. Rev. Lett.
**99**, 161803 (2007). arXiv:0707.0381 ADSCrossRefGoogle Scholar - 78.M. Ciccolini, A. Denner, S. Dittmaier, Electroweak and QCD corrections to Higgs production via vector-boson fusion at the LHC. Phys. Rev. D
**77**, 013002 (2008). arXiv:0710.4749 ADSCrossRefGoogle Scholar - 79.P. Nason, C. Oleari, NLO Higgs boson production via vector-boson fusion matched with shower in POWHEG. JHEP
**1002**, 037 (2010). arXiv:0911.5299 ADSCrossRefGoogle Scholar - 80.K. Arnold, M. Bahr, G. Bozzi, F. Campanario, C. Englert et al., VBFNLO: a parton level Monte Carlo for processes with electroweak bosons. Comput. Phys. Commun.
**180**, 1661–1670 (2009). arXiv:0811.4559 ADSCrossRefGoogle Scholar - 81.K. Arnold, J. Bellm, G. Bozzi, M. Brieg, F. Campanario, et al., VBFNLO: a parton level Monte Carlo for processes with electroweak Bosons-manual for version 2.5.0. arXiv:1107.4038
- 82.T. Plehn, D.L. Rainwater, D. Zeppenfeld, Determining the structure of Higgs couplings at the LHC. Phys. Rev. Lett.
**88**, 051801 (2002). arXiv:hep-ph/0105325 Google Scholar - 83.C. Englert, M. Spannowsky, M. Takeuchi, Measuring Higgs CP and couplings with hadronic event shapes. JHEP
**1206**, 108 (2012). arXiv:1203.5788 ADSCrossRefGoogle Scholar - 84.J.R. Andersen, C. Englert, M. Spannowsky, Extracting precise Higgs couplings by using the matrix element method. Phys. Rev. D
**87**, 015019 (2013). arXiv:1211.3011 ADSCrossRefGoogle Scholar - 85.A. Djouadi, R. Godbole, B. Mellado, K. Mohan, Probing the spin-parity of the Higgs boson via jet kinematics in vector boson fusion. Phys. Lett. B
**723**, 307–313 (2013). arXiv:1301.4965 ADSCrossRefGoogle Scholar - 86.C. Englert, D. Goncalves, G. Nail, M. Spannowsky, The shape of spins. Phys. Rev. D
**88**, 013016 (2013). doi: 10.1103/PhysRevD.88.013016. arXiv:1304.0033 - 87.J. Frank, M. Rauch, D. Zeppenfeld, Higgs spin determination in the WW channel and beyond. arXiv:1305.1883
- 88.I. Anderson, S. Bolognesi, F. Caola, Y. Gao, A. V. Gritsan, et al., Constraining anomalous HVV interactions at proton and lepton colliders. arXiv:1309.4819
- 89.P. Artoisenet, R. Frederix, O. Mattelaer, R. Rietkerk, Automatic spin-entangled decays of heavy resonances in Monte Carlo simulations. JHEP
**1303**, 015 (2013). arXiv:1212.3460 ADSCrossRefGoogle Scholar - 90.O. Brein, A. Djouadi, R. Harlander, NNLO QCD corrections to the Higgs-strahlung processes at hadron colliders. Phys. Lett. B
**579**, 149–156 (2004). arXiv:hep-ph/0307206 - 91.G. Ferrera, M. Grazzini, F. Tramontano, Associated WH production at hadron colliders: a fully exclusive QCD calculation at NNLO. Phys. Rev. Lett.
**107**, 152003 (2011). arXiv:1107.1164 - 92.O. Brein, R.V. Harlander, T.J. Zirke, vh@nnlo-Higgs Strahlung at hadron colliders. Comput. Phys. Commun.
**184**, 998–1003 (2013). arXiv:1210.5347 Google Scholar - 93.M. Ciccolini, S. Dittmaier, M. Kramer, Electroweak radiative corrections to associated WH and ZH production at Hadron Colliders. Phys. Rev. D
**68**, 073003 (2003). arXiv:hep-ph/0306234 - 94.A. Denner, S. Dittmaier, S. Kallweit, A. Muck, Electroweak corrections to Higgs-strahlung off W/Z bosons at the Tevatron and the LHC with HAWK. JHEP
**1203**, 075 (2012). arXiv:1112.5142 ADSCrossRefGoogle Scholar - 95.S. Frixione, B.R. Webber, The MC@NLO 3.1 event generator. arXiv:hep-ph/0506182
- 96.O. Latunde-Dada, MC and NLO for the hadronic decay of Higgs bosons in associated production with vector bosons. JHEP
**0905**, 112 (2009). arXiv:0903.4135 ADSCrossRefGoogle Scholar - 97.G. Luisoni, P. Nason, C. Oleari, F. Tramontano, \(HW^{\pm }\)/HZ + 0 and 1 jet at NLO with the POWHEG BOX interfaced to GoSam and their merging within MiNLO. JHEP
**1310**, 083 (2013). arXiv:1306.2542 ADSCrossRefGoogle Scholar - 98.D. Miller, S. Choi, B. Eberle, M. Muhlleitner, P. Zerwas, Measuring the spin of the Higgs boson. Phys. Lett. B
**505**, 149–154 (2001). arXiv:hep-ph/0102023 Google Scholar - 99.N.D. Christensen, T. Han, Y. Li, Testing CP Violation in ZZH Interactions at the LHC. Phys. Lett. B
**693**, 28–35 (2010). arXiv:1005.5393 ADSCrossRefGoogle Scholar - 100.N. Desai, D.K. Ghosh, B. Mukhopadhyaya, CP-violating HWW couplings at the Large Hadron Collider. Phys. Rev. D
**83**, 113004 (2011). arXiv:1104.3327 ADSCrossRefGoogle Scholar - 101.J. Ellis, D.S. Hwang, V. Sanz, T. You, A fast track towards the ‘Higgs’ spin and parity. JHEP
**1211**, 134 (2012). arXiv:1208.6002 ADSCrossRefGoogle Scholar - 102.J. Ellis, V. Sanz, T. You, Associated production evidence against Higgs impostors and anomalous couplings. Eur. Phys. J. C
**73**, 2507 (2013). arXiv:1303.0208 ADSCrossRefGoogle Scholar - 103.R. Godbole, D.J. Miller, K. Mohan, C.D. White, Boosting Higgs CP properties via VH Production at the Large Hadron Collider. arXiv:1306.2573
- 104.G. Isidori, M. Trott, Higgs form factors in associated, production. arXiv:1307.4051
- 105.C. Delaunay, G. Perez, H. de Sandes, W. Skiba, Higgs up-down CP asymmetry at the LHC. arXiv:1308.4930

## Copyright information

**Open Access**This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Funded by SCOAP^{3} / License Version CC BY 4.0