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===== Interference effects in the search for heavy Higgs bosons =====

//Interested people: Stefan Liebler, Jérémie Quevillon, Sabine Kraml, Alexandra Carvalho, Ramona Gröber, Tetiana Berger-Hryn'ova, Fabio Maltoni [add your names]//

Motivation:
The search for additional heavy Higgs bosons is often carried out in the narrow width approximation, i.e. interferences of the Higgs bosons with the SM background as well as the light Higgs boson or other heavy Higgs bosons are neglected.
The first analysis taking into account such interferences was carried out by ATLAS in the $t\bar t$ final state [ATLAS-CONF-2016-073]. Such interference terms are usually strongly final state and model dependent.

Idea:
To classify the free parameters setting the interference terms starting with the $VV$ and $HH$ final states. Try to provide a guidance where interferences are expected to be sizable.

The below table gives a hint where large interference among the heavy Higgs bosons $\phi_i$, the SM Higgs $H$ and the SM background $B$ are to be expected depending on the final state under consideration:\\
Notation: Heavy (CP-admixed) Higgs bosons $\phi_i$, SM Higgs $H$, SM background $B$

^     ^ $b\bar b/\tau^+\tau^-$ ^ $t\bar t$ ^ $\gamma\gamma$ ^ $VV$ ^ $HH$ ^
| Int. between $\phi_i$ and $\phi_j$ | yes | yes | yes | yes | yes |
| Int. between $\phi_i$ and $B$      |     | yes | yes | yes | yes |
| Int. between $\phi_i$ and $H$      |     |     |     | yes | yes |

The final state $HH$ is (also) discussed in the [[2017:groups:higgs:2h | di-Higgs group]].

Discussion 20/06/2017:

{{:2017:groups:higgs:img_20170620_183954.jpg?400| Blackboard}}

Discussion 22/06/2017:

Work plan:
  - Calculate $d\sigma^X/dm_{VV}$ or $dm_{HH}$ for $gg\to VV/HH$ at LO QCD and at partonic level for $X=S,I_B$ and $I_H$ for the subsequent parameters and store them as a function of $m_{VV}/m_{HH}$ in a table that ranges from $m_\Phi-10\Gamma_\Phi$ to $m_\Phi+10\Gamma_\Phi$ with sufficient data points:
  - $VV$: $c_ge^{i\theta_g}$, $m_\Phi$, $\Gamma_\Phi$, $\kappa_V$ (in a first step choose $\sqrt{1-\kappa_V^2}$ for the SM $HVV$ coupling).
  - $HH$: $c_ge^{i\theta_g}$, $m_\Phi$, $\Gamma_\Phi$, $\lambda_{Hhh}, \lambda_{hhh}$
  - Read in the table (with Mathematica) and calculate relative correction factors named $(\eta^-,\eta^+,\eta)$, see slides, or apply a similar method (e.g. arXiv:1510.03450) to quantify the relevance of the interferences.
  - Try to classify the relevant regions, where interferences are of relevance (check also $\Gamma_\Phi/m_\Phi\cdot \sigma^S/\sigma^B$).

**References: **

**for the different final states:**

$t\bar t/gg/\gamma\gamma$:
  - Signal-background interference in $gg \rightarrow \Phi \rightarrow t\bar{t}$ and $gg \rightarrow \Phi \rightarrow \gamma\gamma$, A. Djouadi, J. Ellis and J. Quevillon [[https://arxiv.org/pdf/1605.00542.pdf | arXiv:1605.00542 ]]
  - Signal-background interference in $gg \rightarrow \Phi \rightarrow t\bar{t}$, M. Carena and Z. Liu [[https://arxiv.org/pdf/1608.07282.pdf | arXiv:1608.07282 ]] 
  - Signal-background interference in $gg \rightarrow \Phi \rightarrow t\bar{t}$ with higher order QCD effects (simplified model and 2HDM), B. Hespel, F. Maltoni, E. Vryonidou [[https://arxiv.org/pdf/1606.04149.pdf | arXiv:1606.04149 ]]
  - Signal-background interference for a singlet spin-zero digluon resonance, S.P. Martin [[https://arxiv.org/pdf/1606.03026.pdf | arXiv:1606.03026 ]]
  - Production of heavy Higgs bosons and decay into top quarks at the LHC, W. Bernreuther, P. Galler, C. Mellein, Z. Si, P. Uwer [[https://arxiv.org/pdf/1511.05584.pdf | arXiv:1511.05584 ]]
  - Production of heavy Higgs bosons and decay into top quarks at the LHC. II: Top-quark polarization and spin correlation effects, W. Bernreuther, P. Galler, Z. Si, P. Uwer [[https://arxiv.org/pdf/1702.06063.pdf | arXiv:1702.06063 ]]

$VV$:
  - Interference effects in Heavy Higgs production via gluon fusion in the Singlet Extension of the Standard Model, E. Maina [[https://arxiv.org/pdf/1501.02139.pdf | arXiv:1501.02139 ]]
  - Heavy Higgs signal–background interference in $gg\to VV$ in the Standard Model plus real singlet, N. Kauer, C. O'Brien [[https://arxiv.org/pdf/1502.04113.pdf | arXiv:1502.04113 ]]
  -  Dip or nothingness of a Higgs resonance from the interference with a complex phase, S. Jung, J. Song, Y. Yoon [[https://arxiv.org/pdf/1505.00291.pdf | arXiv:1505.00291 ]]
  - Interference Effects in Higgs production through Vector Boson Fusion in the Standard Model and its Singlet Extension, A. Ballestrero, E. Maina [[https://arxiv.org/pdf/1506.02257.pdf | arXiv:1506.02257 ]]
  - Interference effect on a heavy Higgs resonance signal in the $\gamma\gamma$ and $ZZ$ channels, S. Jung, Y. Yoon, J. Song [[https://arxiv.org/pdf/1510.03450.pdf | arXiv:1510.03450 ]]
  - Interference contributions to gluon initiated heavy Higgs production in the Two-Higgs-Doublet Model, N. Greiner, S. Liebler, G Weiglein [[https://arxiv.org/pdf/1512.07232.pdf | arXiv:1512.07232 ]]

$HH$:
  - Higgs pair production via gluon fusion in the Two-Higgs-Doublet Model, B. Hespel, D. Lopez-Val, E. Vryonidou [[https://arxiv.org/pdf/1407.0281.pdf | arXiv:1407.0281 ]]
  - NLO Corrections to Double Higgs Production in the Higgs Singlet Model, S. Dawson, I. Lewis [[https://arxiv.org/pdf/1508.05397.pdf | arXiv:1508.05397 ]]

**for two interfering heavy Higgs bosons:**

$\phi_i\phi_j$:
  - Interference effects in BSM processes with a generalised narrow-width approximation, E. Fuchs, G. Weiglein [[https://arxiv.org/pdf/1411.4652.pdf | arXiv:1411.4652 ]]
  - Impact of CP-violating interference effects on MSSM Higgs searches, E. Fuchs, G. Weiglein [[https://arxiv.org/pdf/1705.05757.pdf | arXiv:1705.05757 ]]
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