Four Generations in Phenomenology

Nuclear Physics B (Proc. Suppl.) 177–178 (2008) 241–245 www.elsevierphysics.com

Four Generations in Phenomenology Graham D. Kribs

a

Tilman Plehn

b

Michael Spannowsky

c

Tim M.P. Tait

d

a

Department of Physics, University of Oregon, Eugene, OR 97403, USA

b

SUPA, School of Physics, University of Edinburgh, Edinburgh EH9 3JZ, Scotland (HCP speaker)

c

ASC, Department f¨ ur Physik, Ludwig-Maximilians-Universit¨ at M¨ unchen, 80333 M¨ unchen, Germany

d

HEP Division, Argonne National Laboratory, 9700 Cass Ave., Argonne, IL 60439, USA

In four–generation models Higgs masses of 115-315 GeV are perfectly allowed by electroweak precision data. In this mass range we find dramatic effects on Higgs phenomenology at hadron colliders: production rates are enhanced, weak–boson–fusion channels are suppressed, angular distributions are modified, Higgs pairs can be observed, and Higgs decays to Majorana neutrinos can lead to exotic signals.

One the simplest kinds of new physics is a simple replication of the three generations of chiral matter. Such a fourth generation has been considered and forgotten or discarded many times, wrongly [1] leaving the impression that it is either ruled out or highly disfavored by experimental data. This article follows a recent complete analysis of the phenomenology of four–generation models, Ref. [2]. Its impact on Higgs physics has been tentatively discussed before [3–5], but unfortunately without properly accounting for direct search bounds and oblique–parameter constraints. We enlarge the Standard Model by a complete sequential fourth generation of chiral matter (Q4 , u4 , d4 , L4 , e4 ) as well as a single right-handed neutrino ν4 [6]. Neutrino masses can arise from either a hierarchy in Yukawa couplings or righthanded neutrino masses or some combination. Here, we only consider heavy Dirac neutrinos. A particularly robust lower bound on fourth– generation masses comes from LEP II. The bound on unstable charged leptons is around 100 GeV, similar to the bound on unstable neutral Dirac neutrinos decaying as ν4 →  + W . These limits only suffer at the 10 GeV level when the neutrino has Majorana mass. The Tevatron has significant sensitivity for fourth–generation quarks. The strongest bound is from the CDF search for u4 u4 → qqW + W − , obtaining mu4 > 258 GeV [7]. 0920-5632/$ – see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.nuclphysbps.2007.11.116

For simplification we adopt this bound as CKMindependent throughout. The CKM matrix elements Vu4 i , Vjd4 are constrained by flavor physics. Flavor-violating neutral current effects occur in loops and are automatically GIM suppressed. Rough constraints on the mixing between the first/second and fourth generation can be extracted requiring unitarity in combination with the Standard–Model 3 × 3 submatrix [1]. The observed single top production [8] translates into Vtb > 0.68 and still allows for large 3-4 mixing. It seems likely that fourth family decays will be mostly into heavy SM quarks.

1. Electroweak and other Constraints There are three important effects that can mitigate the contribution to ΔS. The first, and most important, is exploiting the relative experimental insensitivity along ΔS  ΔT : slightly split electroweak doublets are in far better agreement with electroweak data because of their ΔT contribution. Secondly, split fourth–generation multiplets can have a reduced contribution to S. The last, and least important effect is introducing a Majorana mass for the heavy neutrino [9,10]. Splitting the up-type from down-type masses in the same doublet can give a negative contribution to S. For heavy fermions the contribution to S

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mu4 md4 mH ΔStot ΔTtot (a) 310 260 115 0.15 0.19 (b) 320 260 200 0.19 0.20 (c) 330 260 300 0.21 0.22 Table 1 Examples for ΔS and ΔT . The lepton masses are fixed to mν4 = 100 GeV and m4 = 155 GeV. The best fit to data is (S, T ) = (0.06, 0.11). All points are within the 68% CL contour defined by the LEP EWWG.

The second constraint is potentially stronger. Requiring that the Higgs quartic remain perturbative we find that the maximum cutoff scale rapidly becomes small as the Higgs mass is increased. For our choices of fourth– generation masses, the Yukawa interactions remain perturbative to slightly beyond the Higgs meta-stability/triviality bounds for all considered Higgs masses.

becomes [11,12] ΔS =

Nf 6π

  m2 1 − 2Y ln u2 md

2. Higgs Searches (1)

where Y is the hypercharge of the fermion doublet. For leptons alone with masses mν,  100, 155 GeV we find (ΔSν , ΔTν )  (0.00, 0.05). In Table 1 we provide some examples of fourth– generation fermion masses within the 1σ ellipse of the electroweak constraints. The fit to electroweak data is in agreement with the existence of a fourth generation and a light Higgs about as well as the fit to the Standard Model alone with mH = 115 GeV. Using suitable contributions from the fourth–generation quarks, heavier Higgs masses up to 315 GeV remain in agreement with the 1σ limits. Heavier Higgs masses up to 750 GeV are permitted if the agreement with data is relaxed to 2σ. Since the Yukawa couplings of the new quarks exceed 1.5, our effective theory breaks down at a scale that may not be far above the TeV scale. There are two well-known constraints: the first is the possibility that the quartic coupling is driven negative, destabilizing the electroweak scale by producing large field minima through quantum corrections [13]. We can estimate the metastability bound by requiring that the life time before tunneling into another vacuum is much smaller the age of the Universe. This gives is a minimum scale where new physics is required, which, however, does not need to be strongly coupled. This is important because weakly coupled physics with masses created by e.g. supersymmetry breaking will not affect our Higgs results.

A fourth generation has significant effects on Higgs searches at the Tevatron and at the LHC. Two additional heavy quarks are well known to increase the effective ggH coupling by roughly a factor of 3 and hence to increase the production cross section σgg→H by a factor of 9 [14]. The Yukawa couplings exactly compensate the large decoupling quark masses in the denominator of the loop integral [15]. This result is nearly independent of the mass of the heavy quarks, once they are heavier than the top. It allows D0 to very recently rule out a Higgs in a four–generation model within 150 < mH < 185 GeV [16]. The increase in the ggH coupling also dramatically increases the decay rate of H → gg. For small Higgs masses this at the LHC invisible decay effectively suppresses all other two–body decays by roughly a factor 0.6. Only once the decay mode H → W W ∗ with its larger tree–level coupling opens this suppression vanishes. More subtle effects occur for the second loop–induced decay H → γγ. For a light Higgs boson this implies a suppression of the branching ratio BR(γγ) by roughly a factor 1/9. Of course, this scaling factor breaks down for the top threshold region around 350 GeV and subsequent heavy-quark thresholds. We show the complete set of branching ratios in Fig. 1. All predictions for Higgs decays are computed with a modified version of Hdecay [17] which includes radiative corrections also to the fourth–generation decays, but no off-shell effects for these decays. For a light Higgs below 200 GeV the effects on different gluon–fusion channels are

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gg

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Significance, 30 fb

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Zγ

γγ

gg → H qq → Hqq

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[GeV]

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Figure 1. Branching ratio of the Higgs with fourth–generation effects in the parameter point (b).

roughly summarized by      σgg BR(γγ) σgg BR(γγ) G4 SM     σgg BR(ZZ)  (5 · · · 8) σgg BR(ZZ) G4 SM     σgg BR(f f)  5 σgg BR(f f ) (2) G4

SM

In Figure 2 we show a set of naively scaled discovery contours for a generic compact LHC detector, modifying all known discovery channels for a generic compact LHC detector [18]. The enhancement of the production cross section implies that the ‘golden mode’ H → ZZ → 4μ can be used throughout the Higgs mass range, from the LEP II bound to beyond 500 GeV. Both W W channels [19,20] are still relevant, but again the gluon–fusion channel (which in CMS analyses for a SM Higgs tends to be more promising that the weak–boson–channel, while Atlas simulation show the opposite [21]) wins due to the fourth– generation enhancement. As mentioned above, the weak–boson–fusion discovery decay H → τ τ¯ becomes relatively less important, even though its significance is only slightly suppressed. Weak–boson–fusion Higgs production has interesting features beyond its total rate. Most importantly, it has the advantage of allowing us to extract a Higgs sample only based on cuts on the two forward tagging jets. For two W bosons cou-

100

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500 600

mH[GeV]

Figure 2. Scaled LHC discovery contours for the fourth–generation model. The significances are naively scaled by total rates using the fourth– generation parameters of reference point (b).

pling to the Higgs proportional to the metric tensor we find that the azimuthal angle correlation between the tagging jets is flat. This correlation can be used to determine the Lorentz structure of the W W H couplings [22]. The modification to the ggH coupling from a fourth generation leads to a larger relative size of the gluon–fusion process in the H+2 jets sample. This causes the modification in the angular correlation shown in Fig. 3 [23]. A very interesting modification to Higgs signals occurs if the mixing between the fourth– generation leptons and the other generations is very small. In this case, the fourth–generation neutrinos escape the detector as missing energy. This will be the case, for example, when one contemplates the fourth–generation neutrino as dark matter. LEP II bounds on missing energy plus an initial–state photon are relatively weak, and thus the fourth–generation neutrino can be as light as about MZ /2. For Higgs masses below 140 GeV, the invisible decay H → ν4 ν 4 can even dominate. Such a signature is among the more challenging at the LHC, in particular because the most likely channel to observe an invisible Higgs is weak bo-

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λHHH mH σgg→HH σHH BR(4W ) SM λSM 200 8.54 4.61 SM 0 200 25.73 13.89 (b) λSM 200 96.2 51.30 (b) 0 200 241.3 128.6 Table 2 Total cross section for Higgs pair production at the LHC for reference point (b). All masses are given in units of GeV, all rates in units of fb.

0.7 4 Generations: WBF+GF Standard Model: WBF+GF Standard Model: WBF

0.6

1 dσ σ dΔφjj

0.5 0.4 0.3 0.2 0.1 0

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Figure 3. Angular distribution of vector-boson fusion channel assuming reference point (a) with its Higgs mass mH = 200 GeV

son fusion, so not enhanced by fourth–generation loop effects [24]. If the mixing is not too small, the fourth– generation neutrino promptly decays via an MNS mixed charged current. Given the LEP bounds, for this two–body decay to be open the Higgs must be heavier than about 200 GeV. This means that the new signal is H → ν4 ν 4 → + − W + W − where the lepton flavor depends on which MNS mixing element dominates. The branching ratio of this mode, shown in Fig. 1, is roughly 5%. When combined with the branching ratio of the W ’s into leptons, we can estimate that the rate into four leptons plus missing energy is BR(H → ν4 ν 4 → 4)  1.1 BR(H → ZZ → 4)



 BR(H → ν4 ν 4 ) 0.1 (3)

This is comparable to the rate for H → ZZ → 4. One subtlety is that the decay ν4 → W likely proceeds to third generation leptons, if indeed the 3-4 mixing is largest. It might nevertheless be worthwhile to study the four lepton signal characteristics, i.e., such as searching for events with accompanying missing energy. In the case where the fourth–generation neu-

trino has an electroweak scale Majorana mass, ν M44 ∼ vy44 , half of the time the same two–body decay proceeds to same-sign leptons H → ν4 ν4 → ± ± W ∓ W ∓ . This is a rather unusual signal of the Higgs with little physics background, except potentially Higgs pair production, with each Higgs decaying into W pairs. Finally, Higgs pair production is resurrected by fourth–generation loop effects, since the enhanced effective ggH and ggHH couplings should allow for a proper measurement of λHHH [25]. While total rates are notoriously difficult observables at hadron colliders, the Higgs self coupling can be beautifully extracted from the threshold behavior of the gg → HH amplitude. At threshold, this process is dominated by the two form factors FΔ, proportional to the metric tensor, which arise from the triangular and box diagrams. The Higgs–coupling analysis makes use of the fact that at threshold the two contributions cancel: FΔ = −F + O(ˆ s/m2t ). This cancellation explains the increase in rate when we set λHHH to zero, as shown in Table 2. Similarly to the ggH form factors the decoupling of the top quarks is numerically not as perfect as for the additional fourth–generation quarks. Once the process is dominated by heavier quarks the variation of mHH with λHHH becomes significantly more pronounced, so there is little doubt that we can use it to measure the Higgs self coupling. 3. Discussion If Nature does indeed have a fourth generation, the ordering of discoveries could proceed by Tevatron discovering the Higgs, with an usually

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