#
Unveiling the MSSM Neutral Higgs Bosons

with Leptons and a Bottom Quark

###### Abstract

We investigate the prospects for the discovery of neutral Higgs bosons produced with a bottom quark where the Higgs decays into a pair of tau leptons and the taus decay into an electron-muon pair, i.e. , . Our study has been done within the framework of the Minimal Supersymmetric Standard Model. We consider the dominant physics backgrounds including the production of Drell-Yan processes ( and ), top quark pair (), and with realistic acceptance cuts and efficiencies. We present discovery contours for the neutral Higgs bosons in the () plane as well as the region with a favored light Higgs mass (123 GeV 129 GeV). Promising results are found for the CP-odd pseudoscalar () and the heavier CP-even scalar () Higgs bosons with masses up to 800 GeV and at the LHC with a center of mass energy () of 14 TeV and an integrated luminosity () of 300 fb. With 14 TeV and 3000 fb, LHC will be able to discover the Higgs pseudoscalar and the heavier Higgs scalar beyond GeV.

###### pacs:

14.80.Cp, 14.80.Ly, 12.60.Jv, 13.85Qk^{†}

^{†}preprint: The University of Oklahoma OUHEP-130923 arXiv: [hep-ph] December 2013

## I Introduction

Recent discovery of the Higgs boson by the ATLAS and the CMS experiments atlas-higgs-discovery (); cms-higgs-discovery () has completed the remaining piece of the standard electroweak symmetry breaking (EWSB) puzzle and has one more time confirmed the success of the Standard Model (SM). Despite its success we know that the Standard Model is not a complete theory and there is new physics to be discovered at or beyond the electroweak scale. After this remarkable achievement, the goal is now to discover signs of new physics with particles and interactions beyond the Standard Model.

One of the most studied new physics candidate is the supersymmetric extension of the Standard Model. Supersymmetry (SUSY) is very well motivated both theoretically and phenomenologically and its realization with minimal particle content is called the Minimal Supersymmetric Standard Model (MSSM). The extensive search for the signs of SUSY and MSSM has so far only returned exclusion limits for SUSY particle masses. For simplified models, the current limits are above a TeV for gluinos and first/second generation squarks, and hundreds of GeV for electroweak gauginos ATLAS-SUSY-exclusion1 (); ATLAS-SUSY-exclusion2 (); CMS-SUSY-exclusion1 ().

The MSSM Higgs sector consists of two doublets and that couple to fermions with weak isospin and , respectively Guide (). After spontaneous symmetry breaking, there remain five physical Higgs bosons: a pair of singly charged Higgs bosons , two neutral CP-even scalars (heavier) and (lighter), and a neutral CP-odd pseudoscalar . At the tree level, all properties of the Higgs sector are fixed by two parameters that are usually chosen to be the Higgs pseudoscalar mass () and the ratio of the vacuum expectation values of the two Higgs doublets (). In the decoupling limit Gunion:1984yn () with and , the light Higgs scalar behaves like the SM Higgs boson, while the heavy Higgs scalar () and the Higgs pseudoscalar () are almost degenerate in mass with dominant decays into () and () final states.

A supersymmetric light Higgs boson of mass implies large loop corrections to the tree level Higgs mass which requires a heavy stop and/or large trilinear couplings Baer:2011ab (); Akula:2011aa (). These large loop corrections also indicate large fine tuning. Although low fine tuned MSSM is still a possibility Baer:2013gva (), the available parameter space is shrinking. Non-observation of superpartners so far indicate a heavy SUSY particle spectrum ATLAS-SUSY-exclusion1 (); ATLAS-SUSY-exclusion2 (); CMS-SUSY-exclusion1 () which may be beyond the reach of the LHC or a relatively light but highly compressed spectrum compressed-SUSY-1 () with soft decay products that escape detection. MSSM Higgs searches are complementary to searches for colored scalars and electroweak gauginos.

The production modes of the neutral MSSM Higgs bosons are similar to those of the SM Higgs boson with the most significant contributions coming from gluon fusion, weak boson fusion, and associated production with heavy quarks. The associated production with one quark Choudhury (); Huang (); Scott2002 (); Cao (); Dawson:2007ur () or two quarks Dicus1 (); hbbmm (); Plumper (); Dittmaier (); Dawson:2003kb () can be enhanced by a large and can produce a large cross section for even a heavy pseudoscalar Higgs. These enhanced production modes with Higgs decaying into bottom quark pairs hbbb1 (); hbbb2 () and muon pairs hbmm (), as well as Higgs decaying into tau pairs hbll () provide promising channels to discover the neutral Higgs bosons of the MSSM. The best tau pair discovery channel for Higgs bosons has one tau decaying into a tau-jet ( or ) and another decaying into a light charged lepton ( or ). ATLAS and CMS groups have also looked into these channels and set put limits on the masses and of the neutral MSSM Higgs bosons ATLAS-MSSM-Higgs (); CMS-MSSM-Higgs ().

The inclusive tau pair discovery channel Kunszt (); Richter-Was (); Carena:2005ek (); Carena:2013qia () () has been found to be very promising for the the search of neutral MSSM Higgs boson at the LHC. In this article we study the associated production of neutral MSSM Higgs bosons with a single quark with the Higgs decaying subsequently into pairs followed by the decay of ’s into leptons (). Although the decay rate is lower compared to the -jet + lepton channel, this channel does not suffer from the difficulties and uncertainties to tag a -jet and provides an alternative with a cleaner signal containing two leptons. In the following sections we study the Higgs signal with SUSY correction as well as the physics background, describe the acceptance cuts we employ and exhibit the LHC discovery potential of the MSSM neutral Higgs bosons in this channel.

## Ii The Higgs Signal with Leptons

The signal we consider is the associated production of a neutral MSSM Higgs boson with a single quark followed by the decay of the Higgs into a pair and taus decaying into opposite sign different flavor leptons () and neutrinos, i.e.

where . This search channel is complementary to the other important final state with a larger branching fraction . Furthermore, this discovery channel offers a cleaner signal without the uncertainties involved with tau tagging and avoids the physics background from decay and the QCD background involving jets.

We calculate the cross section of the Higgs signal in collisions with a Breit-Wigner resonance via . In our parton level calculations we use the leading order (LO) parton distribution function of CTEQ6L1 cteq6l1 (). To include the next-to-leading order (NLO) effects we choose both the factorization and renormalization scales to be Willenbrock (); Boos (); Dawson:2004sh () with a K factor to be one.

The leading SM QCD and SUSY corrections to the bottom quark Yukawa coupling can be calculated by using an effective Lagrangian approach Carena:1999py (). For large , the effective Lagrangian expressed in terms of the physical Higgs fields is given by

(1) |

where denotes the running bottom quark mass including SM QCD corrections which we evaluate with (pole) = 4.7 GeV, is the Higgs vacuum expectation value (VEV), and is the mixing angle between the CP-even states and . The function includes loop suppressed threshold corrections from sbottom-gluino and stop-higgsino loops. In the large and limit reads Hall:1993gn (); Carena:1994bv ()

(2) |

where the auxiliary function is given by

(3) |

In our analysis of SUSY effects, we adopt the conventions in Refs. Dawson:2007ur (); Dawson:2007wh (). The branching width of the neutral Higgs bosons into the final state is also affected by these SUSY corrections which indirectly affect the branching width into the final state as well. In the large limit, these branching ratios Carena:2005ek () are approximately given by

(4) | |||||

(5) |

Therefore the cross section of our Higgs signal is approximately

(6) |

which has only a mild dependence on . Depending on the sign of , which determines the sign of , these SUSY corrections can enhance () or suppress () our signal. We study the neutral MSSM Higgs sector up to a TeV and assume all SUSY particles are heavy and above the Higgs sector. For , and this corresponds to a drop in our signal cross section, for , and we get a suppression of . Since these effects are small for a large , we neglect them in the rest of our analysis.

## Iii Higgs Mass Reconstruction

The decay mode of the Higgs generates large missing transverse momentum due to the neutrinos in the final state which would normally make the mass reconstruction difficult. But since the neutral Higgs bosons are much more massive than ’s (), ’s produced in a Higgs decay are highly boosted, and their decay products –leptons and neutrinos are almost collinear in the lab frame. We exploit this kinematic feature and reconstruct the Higgs mass in the collinear approximation Hagiwara:1989fn (); Plehn:1999xi (). In the collinear limit, the decay product of each lepton can be identified by the fraction of energy it carries. Denoting these energy fractions with and , the total missing transverse momentum can be expressed in terms of the transverse lepton momenta as

(7) |

Given the measurements of the transverse momentum of charged leptons and the missing transverse momentum, the above relation can be used to determine the momenta of ’s:

(8) |

Thus the Higgs mass can be reconstructed from the invariant mass of the pairs Plehn:1999xi (); Ellis:1987xu () as

(9) |

For a physical solution, should be between 0 and 1. This physical solution requirement is one of the most effective cuts to reduce the SM background. To avoid large determinants that would also imply large uncertainties in the solution we require the leptons not to be back to back in the transverse plane () ATLAS-htata (); CMS-htata (). We also require the leptons not to be parallel in the transverse plane in order to reduce the Drell-Yan and backgrounds () ATLAS-htata ().

In Figure 1 we present the invariant mass distribution of the tau pairs for the Higgs signal via , as well as the SM backgrounds due to Drell-Yan production and top pair production. In this figure we have applied all acceptance cuts discussed in the next two sections except the requirement on invariant mass.

## Iv The Physics Background

The physics background consists of the following processes

(10) | |||||

where represents a light jet. We use the notation of to denote a light jet misidentified as a -jet and to denote a -jet that escapes detection. At low mass, due to the large mass peak the dominant background is the Drell-Yan process and . At intermediate and high masses, Drell-Yan processes are suppressed as we move away from the pole and and quickly become dominant. The background is small due to the destructive interference between the Feynman diagrams that contribute to the same final states and due to the requirement of a light jet to be mistagged as a -jet.

For the Drell-Yan processes, the different flavor leptons that we require in the final state can only be produced through an initial pair. But for the remaining background processes they can be produced directly from ’s or indirectly by intermediate ’s. The branching ratio for leptonically decaying (’s) is about . Hence each intermediate suppresses a channel approximately by the same amount. We calculate all the contributions (0,1,2 intermediate ) except for the background for which we only consider ’s decaying directly into or since the cross section of this process is already quite small.

## V Acceptance cuts

To simulate the detector effects, we apply Gaussian smearing with the energy measurement uncertainty parametrized by an energy dependent term and an energy independent term added in quadrature as

(11) |

where we use and for jets (leptons) following the ATLAS and CMS TDR ATLAS-TDR (); CMS-TDR (). We assume a constant -tagging efficiency throughout the detector with the rate , and constant mistagging rates of -jets and light jets as -jets with the rates an .

Acceptance cuts (LL,HL) | |
---|---|

In order to account for the noisy detector environment due to pile-up, we employ two sets of cuts specific for low and high luminosity (LL,HL). We require exactly one high transverse momentum -tagged jet and two opposite sign different flavor leptons in the event. The -jet is required to have (LL) or (HL) and . To reduce the background we veto two jet events with and CMS:2013aea (). We require both leptons to be isolated by imposing and to have (LL) or (HL). We apply a (LL) and (HL) cut on the missing transverse momentum which we define as the negative sum of the transverse momenta of the visible objects in the event. We finally require the reconstructed Higgs mass to be within (LL) or (HL) of the pseudoscalar Higgs mass . A summary of the basic cuts we employed is displayed in Table 1.

We use MadGraph MadGraph5 () to generate HELAS HELAS () subroutines to compute the matrix elements for the tree level signal and background processes. We introduce the NLO corrections to the SM background processes as factors. We apply a factor 1.3 for the Drell-Yan processes Drell-Yan-kfactor (), a factor of 2 for top pair production ttbar-kfactor-1 (); ttbar-kfactor-2 (), a factor of 1.58 for production tw-kfactor (), and a factor of 1 for background. Cross sections and signal significance for benchmark points are displayed in Table 2.

Figure 2 shows the signal and background cross sections with TeV and acceptance cuts for low luminosity (LL) and high luminosity (HL) as a function of the pseudoscalar Higgs mass . The signal is shown for and 50, with a common mass for scalar quarks, scalar leptons, gluino, and the parameter from the Higgs term in the superpotential, TeV. All tagging efficiencies and factors discussed above are included.

100 | 200 | 400 | 800 | |
---|---|---|---|---|

15.85 | 8.847 | 1.176 | 0.052 | |

344.0 | 196.8 | 29.82 | 1.496 | |

57.40 | 0.517 | 0.061 | 0.004 | |

2.867 | 9.158 | 10.25 | 5.792 | |

4.884 | 14.96 | 14.71 | 7.521 | |

0.054 | 0.153 | 0.144 | 0.067 | |

8.513 | 6.745 | 0.959 | 0.059 | |

90.64 | 69.65 | 19.02 | 1.637 |

We use to further reduce the Standard Model backgrounds, which is a global and fully inclusive variable designed to determine the mass scale involved in a scattering event with missing energy shatmin (). It is defined as

(12) |

where is the total mass of all invisible particles produced in an event. In our case the invisible particles are neutrinos hence we set .

For the Higgs signal, the mass of the Higgs particle determines the minimum center of mass energy of the process since the Higgs is mostly on-shell. Similarly for the background, intermediate on-shell particles determine the mass scale. For the main background the mass scale is . So this variable is effective in reducing the and backgrounds in the high mass region where . What we actually get from is not exactly the mass of the intermediate particles but an event by event lower bound of the center of mass energy of the hard interaction. Therefore we expect this variable to be effective well above the threshold. To optimize our cut, we determine the value for which the cut

(13) |

maximizes the signal significance, i.e. . Since the mass scale for the Higgs signal changes with , the optimum cut depends on as well. To determine its dependence we do a scan over in the range [500 GeV, 1000 GeV] for and compute the optimum cut. We display the result of this scan in Figure 3.

We observe that the shape of the distribution for the SM background does not change significantly with our Higgs mass window cut, but for the Higgs signal it shifts towards higher values with increasing Higgs mass while broadening due to more missing energy carried away by neutrinos. This results in an almost linear relation between the optimum cut and which we determine to be . As can be seen from Figure 3 the optimum value has a small dependence as well. In the rest of our analysis we use for simplicity.

## Vi The Discovery Potential at the LHC

To calculate the LHC reach, we scan the plane and display the discovery contours for with an integrated luminosity as well as with integrated luminosities , , in Figures 4 and 5. In addition, we also show the improvement with the addition of the cut.

We define the signal to be observable if the lower limit on the signal plus background is larger than the corresponding upper limit on the background HGG (); Brown (), namely,

(14) |

which corresponds to

(15) |

Here is the integrated luminosity, is the signal cross section, and is the background cross section. Both cross sections are taken to be within a bin of width centered at . In this convention, corresponds to a 5 signal.

For , and are almost degenerate when 125 GeV, while and are very close to each other for 125 GeV Higgsmass1 (); Higgsmass2 (). Therefore, when computing the realistic discovery reach, we add the cross sections of the and the for GeV and those of the and the for GeV Kao:1995gx ().

We use FeynHiggs FeynHiggs () to calculate the light Higgs mass at two loop level Ellis:1990nz (); Heinemeyer:1998np (); Degrassi:2002fi (). To cope with the remaining theory uncertainty in the light Higgs mass which is about 2-3 GeV Degrassi:2002fi (), we define a favored light Higgs mass band (for a 126 GeV light Higgs) to be the range 123 GeV 129 GeV.

Figure 4 shows the 5 discovery contour in the () plane for the neutral MSSM Higgs bosons at the LHC with 8 TeV and fb. Also shown is the parameter region excluded by LEP II LEP2 (). In addition, we present the favored region of a light Higgs boson (123 GeV 129 GeV) for TeV and TeV, where is the trilinear coupling for scalar top.

Figure 5 shows the 5 discovery contours for the MSSM Higgs bosons at the LHC with 14 TeV with and fb. We display again the regions with a favored light Higgs mass (123 GeV 129 GeV) for and . We find that the discovery contour even dips below for GeV GeV depending on luminosity. Below our approximation of mass degeneracy of MSSM Higgs bosons breaks down; therefore we include only one Higgs boson in our calculations to simplify the numerical analysis. For GeV the Higgs cross section becomes kinematically suppressed while for lower masses ( GeV), the Higgs cross section is reasonably large. Therefore, for GeV even the CP-odd pseudoscalar alone can lead to an observable signal with . High mass regions with can be probed if is large. Specifically for and , MSSM neutral Higgs bosons can provide a discovery signal with an integrated luminosity of .

## Vii Conclusions

We have studied the production of neutral MSSM Higgs bosons at the LHC associated with a single quark followed by Higgs decay into tau pairs and tau leptons decaying to electron-muon pairs. This production channel is enhanced for large and this specific final state offers a clean signal albeit a smaller branching ratio compared to the more promising tau pair discovery channel with . The channel does not require tau jet tagging hence eliminates the uncertainties involved with it, and the physics background for our signal from decay and the QCD backgrounds containing light jets are more suppressed.

Motivated with the latest non-observation of super partners, we have considered a heavy SUSY spectrum with squarks, sleptons and the gluino above the Higgs sector. After all the cuts are applied, the Higgs signal cross section is about for and at the LHC running at 14 TeV center of mass energy. We have calculated the relevant background processes which are Drell-Yan, , and productions with full spin correlation. The Drell-Yan background is dominant at low mass and backgrounds are dominant at high mass regions. Our calculation shows that the discovery contour for an integrated luminosity of extends to for and up to almost for with the help of the variable.

###### Acknowledgements.

We are grateful to Howie Baer, Sally Dawson and Phil Gutierrez for useful discussions. The computing for this project was performed at the OU Supercomputing Center for Education & Research (OSCER) at the University of Oklahoma. This research was supported in part by the U.S. Department of Energy under Grant No. DE-FG02-13ER41979.## References

- (1) G. Aad et al. [ATLAS Collaboration], Phys. Lett. B 716, 1 (2012) [arXiv:1207.7214 [hep-ex]].
- (2) S. Chatrchyan et al. [CMS Collaboration], Phys. Lett. B 716, 30 (2012) [arXiv:1207.7235 [hep-ex]].
- (3) G. Aad et al. [ATLAS Collaboration], Phys. Rev. D 87, 012008 (2013) [arXiv:1208.0949 [hep-ex]].
- (4) The ATLAS collaboration, ATLAS-CONF-2013-047.
- (5) S. Chatrchyan et al. [CMS Collaboration], Eur. Phys. J. C 73, 2568 (2013) [arXiv:1303.2985 [hep-ex]].
- (6) J. Gunion, H. Haber, G. Kane and S. Dawson, The Higgs Hunter’s Guide (Addison-Wesley, Redwood City, CA, 1990).
- (7) J. F. Gunion and H. E. Haber, Nucl. Phys. B 272, 1 (1986) [Erratum-ibid. B 402, 567 (1993)].
- (8) H. Baer, V. Barger and A. Mustafayev, Phys. Rev. D 85, 075010 (2012) [arXiv:1112.3017 [hep-ph]].
- (9) S. Akula, B. Altunkaynak, D. Feldman, P. Nath and G. Peim, Phys. Rev. D 85, 075001 (2012) [arXiv:1112.3645 [hep-ph]].
- (10) H. Baer, V. Barger and D. Mickelson, Phys. Rev. D 88, 095013 (2013) [arXiv:1309.2984 [hep-ph]].
- (11) H. K. Dreiner, M. Kramer and J. Tattersall, Europhys. Lett. 99, 61001 (2012) [arXiv:1207.1613 [hep-ph]].
- (12) D. Choudhury, A. Datta and S. Raychaudhuri, hep-ph/9809552.
- (13) C. S. Huang and S. H. Zhu, Phys. Rev. D 60, 075012 (1999) [hep-ph/9812201].
- (14) J. M. Campbell, R. K. Ellis, F. Maltoni and S. Willenbrock, Phys. Rev. D 67, 095002 (2003) [hep-ph/0204093].
- (15) J. Cao, G. Gao, R. J. Oakes and J. M. Yang, Phys. Rev. D 68, 075012 (2003) [hep-ph/0210211].
- (16) S. Dawson and C. B. Jackson, Phys. Rev. D 77, 015019 (2008) [arXiv:0709.4519 [hep-ph]].
- (17) D. A. Dicus and S. Willenbrock, Phys. Rev. D 39, 751 (1989).
- (18) S. Dawson, D. Dicus and C. Kao, Phys. Lett. B 545, 132 (2002) [hep-ph/0208063].
- (19) B. Plumper, DESY-THESIS-2002-005.
- (20) S. Dittmaier, M. Kramer and M. Spira, Phys. Rev. D 70, 074010 (2004) [arXiv:hep-ph/0309204].
- (21) S. Dawson, C. B. Jackson, L. Reina and D. Wackeroth, Phys. Rev. D 69, 074027 (2004) [arXiv:hep-ph/0311067].
- (22) C. Kao, S. Sachithanandam, J. Sayre and Y. Wang, Phys. Lett. B 682, 291 (2009) [arXiv:0908.1156 [hep-ph]].
- (23) H. Baer, C. Kao and J. Sayre, Phys. Rev. D 85, 035021 (2012) [arXiv:1112.5922 [hep-ph]].
- (24) S. Dawson, D. Dicus, C. Kao and R. Malhotra, Phys. Rev. Lett. 92, 241801 (2004) [hep-ph/0402172].
- (25) C. Kao, D. A. Dicus, R. Malhotra and Y. Wang, Phys. Rev. D 77, 095002 (2008) [arXiv:0711.0232 [hep-ph]].
- (26) G. Aad et al. [ATLAS Collaboration], JHEP 1302, 095 (2013) [arXiv:1211.6956 [hep-ex]].
- (27) S. Chatrchyan et al. [CMS Collaboration], Phys. Lett. B 713, 68 (2012) [arXiv:1202.4083 [hep-ex]].
- (28) Z. Kunszt and F. Zwirner, Nucl. Phys. B 385, 3 (1992) [hep-ph/9203223].
- (29) E. Richter-Was, D. Froidevaux, F. Gianotti, L. Poggioli, D. Cavalli and S. Resconi, Int. J. Mod. Phys. A 13, 1371 (1998).
- (30) M. S. Carena, S. Heinemeyer, C. E. M. Wagner and G. Weiglein, Eur. Phys. J. C 45, 797 (2006) [hep-ph/0511023].
- (31) M. Carena, S. Heinemeyer, O. StÃ¥l, C. E. M. Wagner and G. Weiglein, Eur. Phys. J. C 73, 2552 (2013) [arXiv:1302.7033 [hep-ph]].
- (32) J. Pumplin, D. R. Stump, J. Huston, H. L. Lai, P. M. Nadolsky and W. K. Tung, JHEP 0207, 012 (2002) [hep-ph/0201195].
- (33) J. M. Campbell, R. K. Ellis, F. Maltoni and S. Willenbrock, Phys. Rev. D 67, 095002 (2003) [hep-ph/0204093].
- (34) E. Boos and T. Plehn, Phys. Rev. D 69, 094005 (2004) [hep-ph/0304034].
- (35) S. Dawson, C. B. Jackson, L. Reina and D. Wackeroth, Phys. Rev. Lett. 94, 031802 (2005) [hep-ph/0408077].
- (36) M. S. Carena, D. Garcia, U. Nierste and C. E. M. Wagner, Nucl. Phys. B 577, 88 (2000) [hep-ph/9912516].
- (37) L. J. Hall, R. Rattazzi and U. Sarid, Phys. Rev. D 50, 7048 (1994) [arXiv:hep-ph/9306309].
- (38) M. S. Carena, M. Olechowski, S. Pokorski and C. E. M. Wagner, Nucl. Phys. B 426, 269 (1994) [arXiv:hep-ph/9402253].
- (39) S. Dawson, C. Kao and Y. Wang, Phys. Rev. D 77, 113005 (2008) [arXiv:0710.4331 [hep-ph]].
- (40) K. Hagiwara, A. D. Martin and D. Zeppenfeld, Phys. Lett. B 235, 198 (1990).
- (41) T. Plehn, D. L. Rainwater and D. Zeppenfeld, Phys. Rev. D 61, 093005 (2000) [hep-ph/9911385].
- (42) R. K. Ellis, I. Hinchliffe, M. Soldate and J. J. van der Bij, Nucl. Phys. B 297, 221 (1988).
- (43) G. Aad et al. [ATLAS Collaboration], JHEP 1209, 070 (2012) [arXiv:1206.5971 [hep-ex]].
- (44) R. Kinnunen and S. Lehti, CERN-CMS-NOTE-2006-075.
- (45) G. Aad et al. [The ATLAS Collaboration], arXiv:0901.0512 [hep-ex] (2009).
- (46) G. L. Bayatian et al. [CMS Collaboration], CERN-LHCC-2006-001.
- (47) CMS Collaboration, CMS-PAS-TOP-12-040.
- (48) J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer and T. Stelzer, JHEP 1106, 128 (2011) [arXiv:1106.0522 [hep-ph]].
- (49) H. Murayama, I. Watanabe and K. Hagiwara, KEK-91-11.
- (50) J. M. Campbell, R. K. Ellis, F. Maltoni and S. Willenbrock, Phys. Rev. D 69, 074021 (2004) [hep-ph/0312024].
- (51) R. Bonciani, S. Catani, M. L. Mangano and P. Nason, Nucl. Phys. B 529, 424 (1998) [Erratum-ibid. B 803, 234 (2008)] [hep-ph/9801375].
- (52) P. Nason, S. Dawson and R. K. Ellis, Nucl. Phys. B 303, 607 (1988).
- (53) S. Zhu, Phys. Lett. B 524, 283 (2002) [Erratum-ibid. B 537, 351 (2002)].
- (54) P. Konar, K. Kong and K. T. Matchev, JHEP 0903, 085 (2009) [arXiv:0812.1042 [hep-ph]].
- (55) H. Baer, M. Bisset, C. Kao and X. Tata, Phys. Rev. D 46, 1067 (1992).
- (56) N. Brown, Z. Phys. C 49, 657 (1991).
- (57) M. S. Carena, J. R. Espinosa, M. Quiros and C. E. M. Wagner, Phys. Lett. B 355, 209 (1995) [hep-ph/9504316].
- (58) S. Heinemeyer, W. Hollik and G. Weiglein, Phys. Rev. D 58, 091701 (1998) [hep-ph/9803277].
- (59) C. Kao and N. Stepanov, Phys. Rev. D 52, 5025 (1995) [hep-ph/9503415].
- (60) S. Heinemeyer, W. Hollik and G. Weiglein, Comput. Phys. Commun. 124, 76 (2000) [hep-ph/9812320].
- (61) J. R. Ellis, G. Ridolfi and F. Zwirner, Phys. Lett. B 257, 83 (1991).
- (62) S. Heinemeyer, W. Hollik and G. Weiglein, Eur. Phys. J. C 9, 343 (1999) [hep-ph/9812472].
- (63) G. Degrassi, S. Heinemeyer, W. Hollik, P. Slavich and G. Weiglein, Eur. Phys. J. C 28, 133 (2003) [hep-ph/0212020].
- (64) S. Schael et al. [ALEPH and DELPHI and L3 and OPAL and LEP Working Group for Higgs Boson Searches Collaborations], Eur. Phys. J. C 47, 547 (2006) [hep-ex/0602042].