

Abstract
We search for the fermiophobioc Higgs boson ($h_f$), in the context of the two Higgs doublet model (type I), using 3γ + X events in $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV. In this model, $h_f$ is assumed to be produced in association with the charged Higgs boson ($H^{\pm}$) followed by the $H^{\pm}$ decaying to $h_f W^*$ and both of the two $h_f$'s decaying to 2γ.
The data were collected with the CDFII detector at the Fermilab Tevatron collider and correspond to an integrated liminosity of 9.2 fb^{−1}
The number of backgrounds is estimated to be 2.96 ± 0.94 events, where the direct triphoton production dominates the contribution.
The expected numbers of signal events are estimated for a set of the $h_f$ and $H^{\pm}$ mass combinations.
For example, it is 35 events for the $h_f$ mass 75 GeV/c^{2} and the $H^{\pm}$ mass 120 GeV/c^{2}, with $H^0$ mass = 500 GeV/c^{2}, $A^0$ mass = 350 GeV/c^{2}, and $\tan\beta$ = 10.
The observed number of events in the data is 5. From these results, we obtain the limits on $\sigma(p\bar{p}{\rightarrow}h_fH^{\pm})$ $\times$ $\mathcal{B}(H^{\pm}{\rightarrow}h_fW^*)$ $\times$ $[\mathcal{B}(h_f{\rightarrow}2\gamma)]^2$ at the 95% confidence level.
By comparing with the theoretical cross sections, the cross section limits are translated to $h_f$ mass constraints for a given $m_{H^{\pm}}$, which are collectively represented as a rather large excluded region on the $m_{h_f}$ vs. $m_{H^{\pm}}$ plane.

Supporting documents
Public note (11116)

General remarks
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Analysis
Introduction
We search for the fermiophobic Higgs boson using 3γ + X final state emerging from the process
\[
q\bar{q}' \rightarrow h_f H^{\pm} \rightarrow h_f (h_f W^*) \rightarrow
(2\gamma)(2\gamma) + X.
\]
In the previous $h_f$ searches at the LEP, Tevatron and LHC experiments, the vector boson associated production ($q\bar{q}' / e^+e^ \rightarrow h_f V, V = W^{\pm}$ or $Z$) have been conventionally used to produce $h_f$. And the mass limits were calculated by assuming the benchmark scenario, where $h_f VV$ coupling was of the same strength as the SM coupling $\phi^0 VV$.
However, in the framework of the two Higgs doublet model (2HDM) typeI, the vector boson acssociated production is strongly suppressed by a factor of $1/(1 + \tan^2\beta)$ for large $\tan\beta$, and it is possible that a light $h_f$ ($m_{h_f} \lesssim$ 100 GeV/c^{2}) eluded the previous searches.
But since the above $h_f H^{\pm}$ production is not suppressed for large $\tan\beta$, $h_f$ can be explored at the Tevatron using this process even in the region where $q\bar{q}' \rightarrow h_f V$ is suppressed.


Event Selection
This analysis is based on the data collected with the CDFII detcetor between February 2002 and September 2011, corresponding to an integrated luminosity of 9.2 fb^{−1}. The diphoton triggers with $E_T$ > 12 GeV and the triphoton trigger with $E_T$ > 10 GeV are used for our intial data sample.
Events were selected with at least 3 photons with $E_T$ > 15 GeV, $\eta$ < 1.1 and within fiducial regions of the subdetectors. They are also required to be isolated in terms of the caloriteter and the track coneisolation. Then cuts for photon identification were applied based on the EM shower profile. We veto photon candidates if there is an additional nearby cluster found in the EM showermax strip detector to reject $\pi^0/\eta^0 \rightarrow 2\gamma$ decays.


Signal Efficiency
The trigger efficiency is taken to be 100% for our combination of triggers and high $E_T$ photons passing our selection cuts. The rest of the detection efficiency is estimated as a functuion of $h_f$ and $H^{\pm}$ masses using PYTHIA Monte Carlo (MC) data. The generated events are all passed through the full detector simulations. We estimate the efficiency by the simple fraction:
\[
\epsilon = \frac{\mbox{# of HiggsMC events passing the selection cuts}}{\mbox{# of generated HiggsMC events with 4}\gamma}
\]
The plots of the signal efficiencies are shown here. The systematic uncertainties are considered in terms of the photon selection efficiency, particle distrubution functions (PDFs), the initial and final state radiation (ISR/FSR), and the $Q^2$ scale. They are summarized here.


Background Estimation
There are two major background sources which provide 3γ + X events. They are jets misidentified as photons (fake photon backgrounds) and the direct triphoton production (DTP) events.
The fake photon backgrounds are estimated by calculating the fake rate with the datadriven method. The fake rate is presented here as a function of jet $E_T$. The number of the fake photon backgrounds we quote is 3.0 ± 0.2(stat) ± 1.2(syst).
The DTP events are estimated by using MC data based on the MadGraph/MadEvent + PYTHIA partonshower event generation. The number of backgrounds coming from the DTP events are estimated to be 6.9 ± 0.1(stat) ± 2.4(syst).
Another but minor background contributution comes from electroweak (EWK) processes of $Z\gamma$ and $W\gamma$ production. We considered $Z(\rightarrow ee)\gamma$, $W(\rightarrow e\nu)\gamma$, $Z(\rightarrow\tau\tau)\gamma$ and $W(\rightarrow\tau\nu)\gamma$, and the expected total number of EWK events is estimated to be 0.40 ± 0.06(stat) ± 0.28(syst).
In total, we estimate the number of background events to be 10.3 ± 0.2 ± 2.7, whereas the number of observed events is 10.


Final Cut Optimization
After estimating all of the possible backgrounds, we optimize the final cut with respect to $E_T^{\gamma_1} + E_T^{\gamma_2}$ so that we can get the maximum sensitivity for the $h_f$ search. We choose $E_T^{\gamma_1} + E_T^{\gamma_2}$ > 90 GeV, and we predict 2.96 ± 0.94 background events with 0.32 ± 0.16 of fake events, 2.60 ± 0.93 of DTP events, and 0.04 ± 0.03 of EWK events. The number of the observed events passing the final cut is 5.


Analysis Checks
As analysis checks, we look at the region $E_T^{\gamma_1} + E_T^{\gamma_2}$ < 90 GeV with an additional cut of $E_T^{\gamma_3}$ < 24 GeV as the control region. The cut on $E_T^{\gamma_3}$ is to minimize the signal contribution in the control region. Various distributions for 3γ + X events in this control region are shown here. We see reasonable agreements between expectation and data.


Results and Conclusion
The number of background events is estimated to be 2.96 ± 0.94, while the number of observed events is 5, which is consistent each other.
The expected and observed crosssection limits at the 95% C.L. with ±1σ and ±2σ bands for a particular $H^{\pm}$ and $h_f$ mass are presented here. Also, the excluded mass regions are displayed on the $m_{h_f}$  $m_{H^{\pm}}$ plane here.


 