Mass and decays of Brout-Englert-Higgs scalar with extra generations

J.M. Frere A.N. Rozanov M.I. Vysotsky ITEP, Moscow, Russia

November 8, 2004

Abstract

The higher bound on the mass of the Brout-Englert-Higgs scalar boson (BEH boson for brevity) arising from radiative correcions is not stable when the Standard Model is extended to include non-decoupling particles. In particular additional generations of fermions allow for a heavier scalar. We investigate how the decay branchings of scalar boson are affected by the opening of new channels.

The precision measurement of Z-boson parameters, W -boson mass, top quark mass and the value of the running electromagnetic coupling constant at the Z-boson mass allow to predict the mass of the Brout-Englert-Higgs (BEH) boson in the framework of the Standard Model.

Table 1 contains the LEPTOP fit of electroweak observables to the experimental data updated in spring 2004. The increase of the t-quark mass according to the D0 reanalysis pushes the scalar boson mass up:

(M_{BEH})_{Standard Model}^{2004} = (103 + 55 − 40) GeV ,  (1)

and the quality-of-fit is good:

N_{G} = 0 :  χ^{2}/n_{d.o.f.} = 16.7/12 .  (2)

So, in the framework of the 3-generations Standard Model, the central value of M_{BEH} is close to the direct-search lower bound from LEP II, m > 115 GeV. Most probably it should be lighter than 200 GeV. This prediction originates from the electroweak radiative corrections, which in first approximation look like:

δV_{i} ≈ (m_{t}/M_{Z})^{2} − s^{2} ln(\frac{M_{BEH}}{M_{Z}})^{2} ,  (3)

where s ≡ sin θ, θ is the electroweak mixing angle, while the definitions of functions V_{i} are given in [1]. It is evident that introducing heavy fermionic generations will add new contributions to the first term on right hand side of eq.(3) and in order for functions V_{i} to remain the same M_{BEH} should become larger. Indeed, it was noted in paper [2] that a

Table 1: LEPTOP fit of the precision observables.

Observ. Exper. LEPTOP Pull
data  fit
ΓZ [GeV]  2.4952(23) 2.4969(15) -0.7
σ_{h} [nb]  41.540(37) 41.481(14) 1.6
R_{l}  20.767(25) 20.736(18) 1.2
A_{F B}^{l} 0.0171(10) 0.0164(2) 0.7
A_{τ}  0.1465(33) 0.1480(11) -0.5
R_{b}  0.2164(7) 0.2156(1)  1.2
R_{c}  0.172(3)  0.1723(1)  -0.1
A_{F B}^{b}  0.0997(16) 0.1038(8)  -2.6
A_{F B}^{c}  0.0706(35) 0.0742(6)  -1.0
s2 l (Q_{F B})  0.2324(12) 0.2314(1)  0.8
s2 l (A_{LR})  0.2310(3) 0.2314(1)  -1.6
A_{b}  0.925(20) 0.9348(1)  -0.5
A_{c}  0.670(26) 0.6683(5)  0.1
mW [GeV]  80.426(34) 80.391(20) 1.0
mt [GeV] 178.0(4.3) 177.5(3.9) 0.1
MBEH [GeV]  103_{−39}^{+54}
α̂_{s}  0.1183(27)
ᾱ^{−1}  128.936(49) 128.924(48) 0.2
χ^{2}/n_{dof}  16.7/12

500 GeV scalar does not contradict electroweak precision data if accompanied by a fourth generation. In paper [3], the five-dimensional parameter space of the model with a fourth generation (M_{BEH}, m_{U}, m_{D}, m_{E}, m_{N}) was investigated and the values of new quark and lepton masses which allow for a heavy scalar were obtained.

In the present paper we investigate how the BEH-scalar decay branching ratios change when new generations are added to the Standard Model. Let us first determine how many new generations can be added. New quarks contributions to the radiative corrections depend mainly on the difference of the masses of up and down quarks. Concerning leptons the difference of masses of neutral and charged isodoublet members matters as well, however anew aspect emerges: the χ^{2} diminishes rapidly when the new neutral lepton mass approaches one half of the Z-boson mass, m_{N} ≈ 50 GeV.

To perform our fit we take initially a ”typical value” M_{BEH} = 600 GeV, m_{U}+m_{D} = 450 GeV and m_{E} = 200 GeV and allow m_{U} −m_{D} and m_{N} to vary. If N_{g} is the number of extra generations, for N_{g} = 1 , we obtain the exclusion plot shown in Fig. 1. The minimum of χ^{2} is at m_{N} = 52.5 GeV and almost degenerate U- and D-quarks, m_{U} − m_{D} = 2 GeV, and it is equal to:

N_{G} = 1 :  χ^{2}/n_{d.o.f.} = 15.8/11 ,  (4)

so the quality of fit is the same as that of the Standard Model, eq. (2).

In Fig. 2 the exclusion plot is given for N_{G} = 2. In case of 2 extra generations we take masses of new fermions to be degenerate: m_{U_{4}} = m_{U_{5}} = m_{U}, m_{D_{4}} = m_{D_{5}} = m_{D}, m_{E_{4}} = m_{E_{5}} = m_{E}, m_{N_{4}} = m_{N_{5}} = m_{N} in order to avoid a multiplication of the number of fitted parameters. While we have not exhausted the full parameter space, some other

Figure 1: Exclusion plot for one extra generation.

attempts did not give more encouraging results. At χ^{2} minimum up and down quarks are still degenerate, like in case of one extra generation. Neutral leptons become a little bit heavier, m_{N} ≈ 60 GeV., but the quality of fit worsens considerably:

N_{G=2} :  χ^{2}/n_{d.o.f.} = 21.7/11  (5)

We analyze the case with 3 extra generations in the same manner as that of 2 extra generations, taking new quarks and leptons with the same isospin projection degenerate and allow m_{N} and m_{U} − m_{D} to vary. We get:

N_{G} = 3 :  χ^{2}/n_{d.o.f.} = 30.4/11 ,  (6)

and comparing with eq.(4) we conclude that 3 extra generations with such parameters are excluded at the level of 4 standard deviations.

So, not more than two extra fermionic generations (at least with the mass pattern considered) are allowed by current precision data.

The BEH scalar boson widths to pairs of intermediate vector bosons are given by the following formulas:

Γ_{BEH→W W} = \frac{αM_{BEH}^{3}}{16s^{2}M_{W}^{2}} [1 − (\frac{2M_{W}}{M_{BEH}})^{2} + 12(\frac{M_{W}}{M_{BEH}})^{4}] [1 − \frac{4M_{W}^{2}}{M_{BEH}^{2}} ]^{1/2} ,  (7)

Figure 2: Exclusion plot for two extra generations.

Γ_{BEH→ZZ} = \frac{αM_{BEH}^{3}}{32s^{2}c^{2}M_{Z}^{2}} [1 − (\frac{2M_{Z}}{M_{BEH}})^{2} + 12(\frac{M_{Z}}{M_{BEH}})^{4}] [1 − \frac{4M_{Z}^{2}}{M_{BEH}^{2}} ]^{1/2} ,  (8)

and they rapidly increase when the scalar particle becomes heavier.

The decay widths to fermion pairs read:

Γ_{BEH→ff̄} = N_{c} \frac{M_{BEH}}{8π} (\frac{m_{f}}{η})^{2} [1 − \frac{4m_{f}^{2}}{M_{BEH}^{2}} ]^{3/2} ,  (9)

where N_{c} = 1 for lepton, N_{c} = 3 for quarks and η is the scalar boson expectation value.

An extra factor 1− \frac{4m_{f}^{2}}{M_{BEH}^{2}} = v_{f}^{2} (v_{f} is the fermion velocity) is due to the fact that Dirac fermions are produced in P -wave when a scalar particle decays. In order to compare the width of fermionic decays to the width of the vector bosons channel, it is convenient to present eq.(9) in the following way:

Γ_{BEH→ff̄} = N_{c} \frac{αM_{BEH}}{8s^{2}} (\frac{m_{f}}{M_{W}})^{2} [1 − \frac{4m_{f}^{2}}{M_{BEH}^{2}} ]^{3/2} .  (10)

As long as the BEH boson decays to the pair of vector bosons is kinematically forbidden (M_{BEH} < 160 GeV), fermionic decays dominate. In the case of the 3-generations Standard Model it is the decay to bb̄ pair, see [4]. If extra generations are present and if the decay

Figure 3: Branching ratios for scalar boson decays in Standard Model.

to the pair of heavy neutral leptons is kinematically allowed, then it dominates [5]. The possibility of observing such an ”invisible” BEH boson decay at the LHC was discussed in a recent paper [6].

In the opposite case of very heavy BEH boson, M_{BEH} = 600 GeV, the vector boson decay channel dominates in the strict Standard Model. Let us investigate if decays to new fermions can considerably diminish this branching ratio. Let us adjust the mass of fermions in such a way that the BEH boson width to this channel becomes maximal. According to eq.(10) this happens for m_{f}^{2} = M_{BEH}^{2}/10:

(Γ_{BEH→ff̄})_{max} ≈ 0.09N_{c} \frac{αM_{BEH}^{3}}{16s^{2}M_{W}^{2}} ,  (11)

and for one extra degenerate fermion generation the sum over all// fermionic modes gives^{1}:

Γ_{BEH→new degenerate fermions} = 0.09 · 8\frac{αM_{BEH}^{3}}{16s^{2}M_{W}^{2}} .  (12)

1It follows from the first part of the paper that in order to allow a heavy BEH boson, masses in fermion isodoublets should be split. We take however degenerate doublets here for a quick estimation in order to diminish the parameter space; it is clear that the pattern of heavy BEH boson decays will not alter drastically if the splitting is taken into account.

Figure 4: Branching ratios for scalar boson decays in case of one extra generation.

Finally, the BEH boson decay to the pair tt̄ should also be included :

Γ_{BEH→tt̄} = \frac{3αM_{BEH}}{8s^{2}} (\frac{m_{t}}{M_{W}})^{2} [1 − \frac{4m_{t}^{2}}{M_{BEH}^{2}} ]^{3/2} .  (13)

In order to calculate BEH boson width eq.(7 - 9) were used, m_{f} = 190 GeV were taken and numerical values s^{2} = 0.23, c^{2} = 0.77, η = 246GeV, α = 1/129 were substituted.

For the case M_{BEH} = 600 GeV we obtain:

Γ_{new degenerate fermions} Γ_{W W} Γ_{ZZ} Γ_{tt} Γ_{BEH}
53  70 32 18 173

All widths are in GeV. The doubling of the BEH boson width which occur in case of 2 extra generations would lead to four times less events of BEH boson decay to “golden mode” BEH → ZZ around the cross-section maximum:

σ_{pp→BEH→ZZ} ∼ \frac{Γ_{BEH→ZZ}Γ_{BEH→gg}}{(E − M_{BEH})^{2} + Γ_{BEH}^{2}/4} .  (14)

However since the gg → BEH fusion proceeds through quark triangles, new quarks enhance it [7]. In the Standard Model the triangle with top quark dominates; as far as masses of new quarks are close to that of top, the production amplitude in case of two extra generations is enhanced by factor 5 (contribution of U_{4}, U_{5}, D_{4}, D_{5} should be taken into account), hence , the production cross section is about 25 times that of the Standard Model.

We have thus seen that the noncoherent effect of heavy BEH boson(M_{BEH} ∼ 500−600 GeV) decay to new quarks diminishes slightly the effect of coherent enhancement of BEH bosons production in gluon fusion. However, relatively light scalars (M_{BEH} < 200 GeV) would be much more severely affected by the now-predominant decay channel into a pair of neutral leptons, possibly making such a BEH invisible. Consequences of the additional fermion families on the BEH boson production at Tevatron and LHC was discussed in some details in [8].

Acknowledgements

JMF wants to acknowledge the support of the IISN and of the Belgian science policy office (IAP V/27); ANR.....; MV acknowledge the support of the program FS NTP FYaF 40.052.1.1.1112 and grant N SH - 2328.2003.2.

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