Higgs Search Constraints on Fourth Generation Scenarios with General Lepton Sectors
aa r X i v : . [ h e p - ph ] O c t UCI-TR-2011-23October, 2011
Higgs Search Constraints on Fourth Generation Scenarios with General LeptonSectors
Linda M. Carpenter Department of Physics and AstronomyUniversity of California, Irvine, CA [email protected]
I present a general exclusion bound for the Higgs in fourth generation scenarios with a generallepton sector. Recent Higgs searches in fourth generation scenarios rule out the entire Higgs massregion between 120 and 600 GeV. That such a large range of Higgs masses are excluded is due tothe presence of extra heavy flavors of quarks, which substantially increase Higgs production fromgluon fusion over the Standard Model rate. However, if heavy fourth generation neutrinos are lessthan half of the Higgs mass, they can dominate the Higgs decay branching fraction, overtaking thestandard h → W W ∗ decay rate. The Higgs mass exclusion in a fourth generation scenario is shownmost generally to be 155-600 GeV, and is highly dependent on the fourth generation neutrino mixingparameter. PACS numbers:
I. INTRODUCTION
A fourth generation is a simple and compelling extension of the Standard Model. The most general fourth generationmodel consists of the addition of up and down type quarks, a charged lepton and a neutrino which most generallymay have both a Dirac and Majorana mass term. Bounds on the fourth generation lepton sector were set by LEP II,the leptons may be quite light. Bounds on charged leptons are around 100 GeV. Bounds on unstable pure Majorananeutrinos which decay to a W boson and a hard lepton, are 90.7, 89.5 and 80.5 GeV respectively for e, µ and τ finalstate leptons [1]. While bounds on stable neutrinos are set by the Z invisible width at half of the Z mass [2][3]. Theexistence of mixed mass terms in the fourth generation lepton sector however, allows for even lighter neutrino masses,the bounds are as low as 62.1 GeV for unstable neutrinos which decay to τ leptons [4], and below half of the Z mass,33.5 for stable neutrinos [5]. Many collider searches for fourth generation leptons have been proposed with a variety ofinteresting final state topologies such as jets plus missing energy, or like sign dileptons plus multi-jets. [5][6][7][8]. Inaddition, the fact that fourth generation neutrinos may be fairly light offers an exciting possibility for Higgs physics,that a Higgs with mass under 160 GeV may dominantly decay to these states if they are kinematically accessible.Such a possibility was explored both for unstable neutrinos and for stable neutrinos by [9][10] [11] as well as [12].Current Higgs searches seem to severely constrain fourth generation scenarios. At the two signa level, ATLASrules out the standard model Higgs with masses between 155-190 GeV and 300-450 [13]. The current CMS searchesrule out the Standard Model Higgs in the regions between 149 - 206 GeV and 300 - 400 GeV, and this search isinterpreted in fourth generation scenarios as ruling out a very large span of Higgs masses, between 120 and 600 GeV[14]. This is because when a fourth generation is present, the Higgs production cross section is enhanced by a largefactor, of almost 9 over the Standard Model, due to the loop contributions of fourth generation quarks [15][16]. If theHiggs then decayed abundantly into the standard W W ∗ channel which the CMS search relies heavily on, as it doesin some SM4 models, the scenario would be highly constrained by the LHC Higgs searches. This situation is highlyconstraining to fourth generation models. The situation may be ameliorated by extending fourth generation models toeither suppress Higgs production, or soak up the Higgs branching fraction [17], however apparently excluded regionsof standard fourth generation parameter may be shown viable without the addition of extra fields.This paper addresses the possibility that in a fourth generation scenario the Higgs may decay dominantly to fourthgeneration neutrinos which are less than half the Higgs mass. Therefore a Higgs with mass under 160 GeV mayeffectively decay into hidden channels, and would not have been excluded by current Higgs searches. Diverging from[12] this paper considers the constraints and presents exclusions on the general Fourth Generation lepton parameterspace. This work details the allowed fourth generation parameter space still open, and finds that Higgs masses under155 GeV are allowed. It is found however, that the allowed parameter space is highly sensitive the neutrino mixingangle, as the Higgs coupling to fourth generation neutrinos is quite dependent on their Majorana/ Dirac field content.This paper proceeds as follows, Section 2 reviews fourth generation neutrino masses and couplings, Section 3 discussedHiggs production and decay, Section 4 details the constrains on fourth generation parameter space from Higgs searchesand Section 5 concludes. II. FOURTH GENERATION NEUTRINO MASSES AND COUPLINGS
In the most general scenario fourth generation neutrinos have both Dirac and Majorana masses. Using the notationof [18], the Lagrangian for neutrinos is L = m D L N R + M N N + m D v HL i N R The neutrino mass matrix is given by, L m = −
12 ( Q cR N cR ) (cid:18) m D m d M (cid:19) (cid:18) Q R N R (cid:19) + h.c. (1)where ψ c = − iγ ψ ∗ . Diagonalizing the mass matrix there are two Majorana neutrinos with different mass eigenvalues: M = − ( M/
2) + q m D + M / M = ( M/
2) + q m D + M / N = cos θQ cL + sin θN R + cos θQ L + sin θN cR N = − i sin θQ cL + i cos θN R + i sin θQ L − i cos θN cR with neutrino mixing angle tan θ = m /m D The Higgs couples to the neutrino mass eigenstates proportional to powers of the neutrino mixing angle. The Higgscoupling to neutrinos pairs is given by m D v h HN N sin (2 θ ) + m D v h HN N sin (2 θ ) + m D v h HN N icos (2 θ ) . The neutrino mixing angle varies between π/ π/ m D approaches zero, and the Higgs decouples from neutrinos.While for pure Dirac states the coupling is maximal.The neutrinos couple to the charged and neutral currents like gW + µ J µ + + gW − µ J µ − + gZ µ J µ where J µ = 12 cos θ W ( − c θ ¯ N γ µ γ N − is θ c θ ¯ N γ µ N − s θ ¯ N γ µ γ N )) J µ + = c i ( c θ N − is θ N ) γ µ l iL The heavy neutrino may decay to the light neutrino through an or offshell Z. The lightest neutrino may be absolutelystable, or it may decay to a standard model charged lepton though an on or offshell W.
III. HIGGS PRODUCTION AND DECAY
The greatest source of Higgs production at hadron colliders is a single Higgs produced by gluon fusion through aheavy quark loop. The gg → h production cross section is given by σ ( gg → h ) = 116 Γ( h → gg ) 16 π sm h Z m h /s dxx g ( x ) g ( m h sx ) , where Γ( h → gg ) is the Higgs to gluon decay widthΓ( h → gg ) = α s G F m h √ π Σ i ( τ i (1 + (1 − τ i ) f ( τ i )))with τ i = 4 m f i m h , f ( τ i ) = ( sin − p /τ i ) Here, one is summing over all heavy flavors of quarks. In fourth generation models, there exist both an extra heavyup and down type quark with large Yukawa couplings which contribute to the Higgs gluon decay width. This decaywidth is thus substantially increased over that of the Standard Model by a factor larger than 8. For calculationsof Higgs production cross sections in the SM see for example [20] and [16] in fourth generation models. The Higgsproduction cross section at LHC is quite large, remaining over 10 picobarns for Higgs masses up to ∼
500 GeV.The main LHC Higgs decay channels in which one looks for a Higgs produced though gluon fusion are h → γγ and h → W W . The Higgs decay width into
W W ∗ are given in [21] and are proportional toΓ( h → V V ) ∼ G F m V m h π These begin And begins to take up a large portion of the Higgs branching fraction for Higgs masses just undertwice the W mass. Once the vector bosons are on shell, they completely dominate the Higgs branching fraction.
100 500200 3001501.0000.5000.1000.0500.0100.005 mH (GeV) b . f . WW ZZ NN gg bb _ t t _ FIG. 1: Higgs branching fractions vs Higgs mass in a fourth generation scenario for the benchmark point m n = 63 GeV , m n = 300 GeV . The Higgs may decay to photons through a one loop process involving with W bosons and charged fermions theloop. It has been noted that Higgs branching fraction to photons in fourth generation models is suppressed relativeto the standard model due to destructive interference between gauge bosons and heavy quarks in the loop. Perviouswork has claimed that the total Higgs branching fraction to photons is suppressed relative to the SM by a factor of9 [15]. In fourth generation scenario is, as discussed above, the effective Higgs coupling to gluons is substantiallyincreased over the standard model. This means that the Higgs decay channel to gluons can take up a large portionof the branching of a light Higgs.Higgs decays to fermions are proportional to their Yukawa couplings and are given byΓ D = m h y D π (1 − m d m h ) / In the standard model, the dominant fermionic decay model of the Higgs is to the third generation quarks. If thetop is kinematically inaccessible, the largest fermionic branching fraction will be to bottoms. However, the bottomsdo not have a particularly large Yukawa coupling, if other heavy states are kinematically accessible they may easilyovertake to bottom branching fraction. As seen in Section 2, the Higgs couples to fourth generation neutrinos. Thiscoupling varies depending on neutrino mixing angle, and is maximized for pure Dirac type neutrinos. Stable orunstable neutrinos may be quite light, and if the neutrinos are under half of the Higgs mass, the Higgs will have alarge branching fraction into heavy neutrinos that have an appreciable Dirac component. The Higgs decay width intoneutrinos is given by Γ D = m h m N v π sin θ (1 − m d m h ) / Figure 1 is a plot of Higgs branching fractions reproduced from Figure 2 of reference [10] in a fourth generationscenario for a benchmark point in which the lightest fourth generation neutrino is kinematically accessible for Higgsdecay. One sees that for Higgs masses under half of the W mass, fourth generation neutrinos may dominate thebranching fraction.
40 60 80 1000.20.40.60.8 mN (GeV) Γ h NN _ > m =130 GeVm =150GeVm =160 GeVm =170 GeV h h h h FIG. 2: Plot of the Higgs branching fraction to Fourth Generation neutrinos as a function of the mass of the lightest neutrino N . Here The mass of the heavier neutrino N has been set at 400 GeV. The branching fraction is shown for Higgs mass valuesof 170,160,150 and 130 GeV IV. HIGGS MASS BOUNDS
The current Higgs mass bounds in fourth generation scenarios are inferred from the CMS combined search. Onecan see by looking at Plot 6 of reference [14], that the main Higgs exclusions tracks the h → W W decay channel fairlyclosely, except for a small region of parameter space around Higgs masses of 120 GeV where the Higgs to photon searchhas sensitivity. However in fourth generation scenarios we have seen that the Higgs to photon branching fraction issuppressed thus we expect that only the h → W W channel can be used to extract Higgs mass constraints in fourthgeneration scenarios.Current Higgs mass exclusions are claimed in fourth generation scenarios from 120-600 GeV. These exclusions aremuch larger than those claimed for the Standard Model due to the fact that fourth generation scenarios are assumedto produce many more h → W W ∗ events than the Standard Model. The total number of such events - proportionalto σ gg → h SM × Γ h → W W ∗ SM - is much larger than the number expected in the Standard Model due to the extremelylarge Higgs production cross section.However, the Higgs mass exclusion for the fourth generation was made under the assumption that the there were noadditional light states that the Higgs could decay into. We have seen that fourth generation neutrinos can make upthe dominant branching fraction for a Higgs with mass under twice m W . Figure 2 shows the Higgs branching fractionvs. light neutrino mass for a variety of Higgs masses. One see that the Higgs branching fraction into neutrinos isvery high for light Higgs masses, and doesn’t drop substantially until the onshell gauge bosons become kinematicallyaccessible to the Higgs. Standard Higgs searches are not sensitive to Higgs final states which result from neutrinodecay; if the Higgs decays to the stable lightest neutrinos, its decay will be invisible, in the case of unstable neutrinos,the Higgs will decay via the process h → N N → ℓℓW ∗ W ∗ , a decay chain most likely ending in hard leptons plusmulti-jets.One may see that the Higgs branching fraction to offshell gauge bosons is reduced by a substantial factor in FourthGeneration scenarios with light neutrinos as opposed to scenarios without them. Figure 3a shows the ratio of Higgs to W W ∗ branching fractions of two Fourth Generation scenarios, one with neutrinos kinematically accessible for Higgsdecays and the other entirely without them. The ratio of branching fractions is everywhere less than 1, and is quitesmall in much of the parameter space. One can see the Higgs mass exclusion down to 120 GeV only holds where theHiggs has effectively no decay width into onshell fourth generation neutrinos.Alternatively, Figure 3b shows the ratio of Higgs branching fractions to W W ∗ in the Fourth Generation with lightneutrinos to the Standard Model. Again, in a large region of parameter space, this ratio may be quite small. Infact, in some region of parameter space, the branching fraction of Higgses to offshell gauge bosons may be reduced bymore than the factor of 8-9 by which the Higgs production cross section was increased by adding a fourth generationof particles. In this way the total number of h → W W ∗ events from the Fourth Generation need not be extremelyincreased over the number of events one expects from the Standard Model. Thus the claim of Higgs exclusions downto 120 GeV does not apply.To see what regions of Fourth Generation space are ruled out by the current Higgs search, we must calculate thetotal number of h → W W ∗ events for each point in parameter space and compare to the CMS exclusion limits forthe h → W W ∗ search. One sees that in some regions of parameter space, the h → W W ∗ branching fraction is quitesmall. However, the Higgs coupling to neutrinos (and hence the relevant branching fraction) is also very sensitive tothe neutrino mixing angle, and is different at each point in the neutrino mass plane.
20 40 60 80 100050010001500200025003000 m N ( G e V ) mN (GeV)0.21 0.35 0.49 0.85
20 40 60 80 100050010001500200025003000 mN (GeV) m N ( G e V ) FIG. 3: Contour plot in the N N mass plane. Right: ratio between the decay widths h → W W ∗ in a fourth generationmodel with Majorana neutrinos light vs. in the Standard Model. Left: ratio between the decay widths h → W W ∗ in a fourthgeneration model with Majorana neutrinos light vs. in a fourth generation model without light Majorana neutrinos. Plots areshown for a benchmark Higgs mass of 150 GeV Higgs Figure 5 shows the allowed regions of parameter space in the neutrino mass plane for several contours of Higgs massvalues. Of course no parameter space is present for neutrinos greater than half of the Higgs mass. There is a sharpfalloff in the amount of allowed parameter space once the Higgs becomes sufficiently massive, here the gauge bosonsare getting closer to being onshell and beginning to take up more of the Higgs branching fraction. Notice that thereis parameter space for Higgs up to 155 GeV. Also, the most parameter space allowed is greatest where the neutrinosare the most well mixed between Dirac and Majorana masses. As the neutrinos become more Majorana, the massdifference between the neutrino states grows and the coupling to the Higgs decreases, decreasing the Higgs branchingfraction into neutrinos.
20 40 60 80 100050010001500200025003000 mN (GeV) m N ( G e V ) mh=150 GeVmh=140 GeVmh=130 GeVmh=155 GeV FIG. 4: Allowed regions in n1 n2 mass plane.
The Higgs branching fraction at high Higgs mass is almost entirely taken up by onshell diboson production. Onecan see that the Higgs decay width to dibosons goes like mh . As the Higgs becomes much heavier than twice thegauge boson mass, the branching ratio basically becomes a constant. In this regime, the branching ratio to heavyfermions can not overtake the diboson ratio. As one increases the Yukawa coupling, which is proportional to the diracneutrino mass component, one increases the mass of the neutrino and will pay a phase space factor as a consequence.Thus at larger Higgs masses, the Higgs branching fraction will be overwhelmingly taken up by the gauge bosons. Onlya few percent of the branching ratio is taken up by fourth generation neutrinos at high Higgs mass. Therefore oneexpects that the upper bound of the Higgs exclusion at 600 GeV must hold. V. CONCLUSIONS
There exists fourth generation parameter space in which a Higgs may dominantly decay to fourth generationneutrinos. For Higgs masses under 155 GeV current LHC searches do not rule out fourth generation scenarios despitethat fact the Higgs production in such a scenario is increased over standard model production by a substantial factor.The Higgs may decay invisibly if fourth generation neutrinos are stable or, if the neutrinos decay to W bosons andstandard model leptons, the Higgs may decay to dibosons plus hard leptons.Finding a Higgs in such a scenario could be quite challenging and presents an interesting avenue for further work.The authors of [9] have inquired into the situation of looking at Higgs decays in the case of stable lightest neutrino. Thishowever required the Higgs to decay into the second lightest neutrino which then cascaded h → N N → ZZN N .If the second neutrino is not kinematically accessible, the Higgs signal will be pure missing energy. In the case thatthe lightest neutrinos are unstable, the Higgs may decay to dibosons plus hard leptons h → N N → W W ℓℓ . If theHiggs is under 160 GeV, existing inclusive like-sign dilepton searches constrain the final state lepton in this scenarioto be a tau. The case that the Higgs decays to like sign taus plus jets presents a challenging but interesting search.
VI. ACKNOWLEDGEMENT