Predictions for the Top Quark Decay Width in BSM Models

Various models based on BSM physics exist which predict top quark decay width values significantly larger or smaller than the results from SM computations as presented before. The following section introduces some of these alternative models, which predict a different decay widthΓt and which have become very popular over the last decades.

This section intends to give an overview of those alternative models although the latest LHC results are in tension with some of them. The focus is laid on a brief introduction of these BSM models and a presentation of their possible impact onΓt to motivate the direct measurement of the top quark decay width. A detailed discussion on how probable individual models are, based on current exclusion limits, cannot be covered in this thesis.

Supersymmetric Models

One of the most famous extensions of the Standard Model is supersymmetry (SUSY). In particular, effects of the R parity conserving Minimal Supersymmetric Standard Model (MSSM) on the top quark decay width have been discussed in the past[176, 177]. However, the theoretical models presented in the following could not be experimentally verified in the past despite intensive searches at the Tevatron or the LHC, making the existence of supersymmetric particles more and more improbable. According to SUSY, all SM particles possess a super-partner called “sparticle” which differs by half a unit of spin. This means that sfermions as spin-0 scalars are the super-partners of the SM fermions while spin-1 gauge bosons have spin-1/2 gauginos as super-partners. In the MSSM, two complex weak isospin Higgs doublets:

‚ H₂⁺ H₂⁰

Œ

and

‚ H₁⁰ H₁⁻

Œ

denote the partners of the SM spin-0 Higgs field having opposite hypercharge,Y = +1 andY=−1, respectively, to ensure anomaly cancellation between fermionic particles. The physical chargino and neutralino states originate, in general, from mixtures of the Higgsinos ˜H and gauginos, namely the two charged Higgsinos mix with the winos ˜W^±to charginos whereas the neutral Higgsinos mix with the neutral gauginos ˜Zand ˜γto be the neutralinos. The lightest neutralino is in many SUSY

2 . 3 T O P Q U A R K D E C AY W I D T H

models a weakly interacting stable particle and may thus offer an explanation of the dark matter in the universe, as described in Sec. 2.1.2, leading to its popularity[25, 26].

The two Higgs doublets are associated with eight degrees of freedom - out of which three are absorbed to give mass to the three massive SM bosonsW^±andZ. Five physical states remain for five different types of Higgs bosons: two neutral scalars h⁰ and H⁰, a pseudoscalar A⁰ and two charged Higgs bosonsH^±. The decay of the top quark into those particles will be discussed later in this subsection.

The existence of SUSY may have an impact on the top quark decay width in two ways: Firstly, unexpected radiative corrections to the dominant SM decay process t →W b may affectΓ_t and, secondly, some of the SUSY particles introduced above may have smaller masses than the top quark leading to possible new decay channels of this quark directly modifying its decay width.

Standard Model corrections of Γt are shown in Table 2.7. The MSSM, if it exists, may impose further (perturbative) quantum effects on Γt caused by one-loop corrections mediated by SUSY particles[178, 179]. Those corrections often depend on tanβ, which is defined as the ratio of the two vacuum expectation values corresponding to the expectation valuesv₁andv₂of the two neutral Higgs doublets so that tanβ=v₁/v2. These values are related to the SM vacuum expectation value viav²=v₁²+v₂².

SUSY EW quantum corrections can reduce the top quark decay width by about 1-10% (negative corrections), depending on the choice of several SUSY parameters and in particular on tanβ. SUSY QCD corrections are also negative but smaller than the SUSY EW corrections and can reach a few percent. These SUSY corrections toΓ(t →W b)have the same sign as the SM QCD ones and can reach half the size of these SM corrections for large tanβvalues[176, 178, 179].

In case of the existence of a light charged Higgs boson, the top quark will also decay via t→H⁺b.

The partial decay width for this processΓ(t→H⁺b)depends strongly on tanβ. If this parameter is small or large enough, this partial width is comparable to the SM decay width of the top quark when it reaches a minimum at around tanβ≈6. This MSSM decay process of the top quark is very sensitive to radiative corrections of different types. Partial decay widths of the top quark as well as such radiative corrections for a large range of possible tanβvalues are visualised in Fig. 2.13.

Fig. 2.13a shows a summary of different scenarios leading to alternative values of Γ(t →H⁺b) compared to the SM decay width which is naturally independent of tanβ. In a scenario where the Higgsino mass parameterµis negative, the SUSY QCD corrections are opposite in sign to the SM QCD corrections, thus cancelling the strong SM QCD corrections for increasing tanβwhereas for positive parameter values of µboth SUSY and SM QCD corrections possess the same sign. This results in the large negative corrections.

Fig. 2.13b illustrates the relative radiative corrections toΓ(t→H⁺b), revealing an almost linear behaviour of the dominant SUSY contributions. In contrast to the SM EW contribution, which is close to being negligible, the SM QCD contribution to this process reaches a maximum at around tanβ ≈ 10. For tanβ ≈ 35, the SUSY QCD corrections cancel out the SM ones. Hence, for certain values of tanβ, the partial decay width for a top quark decay into charged Higgs bosons will

(a) (b)

Figure 2.13: (a) The partial decay widthΓ(t → H⁺b)compared to the SM top quark decay width as a function oftanβ^form_H±=120GeV. Shown are curves for different scenarios of SUSY parameters as the Higgsino mass parameterµwhich is set to±150GeV. (b) Relative SUSY and SM radiative corrections to the processΓ(t→H⁺b)^[176].

drastically modify the total decay widthΓt. Such a large impact improves the experimental discovery reach of such processes with a direct measurement ofΓt significantly [176]. The corresponding calculations are, for example, also described in[180–182].

In addition, there may also be top quark decays into supersymmetric particles predicted by certain SUSY models. In such cases, the top quark decays, for example, into a sbottom quark and a chargino, into a stop quark and a gluino or into a stop quark and a neutralino. In particular the latter process changesΓt significantly. Depending on the gluino mass, the corresponding radiative corrections may decreaseΓt by up to 20%[183]. Also the decays of top quarks into more than two particles can be studied which may modify the top quark decay width by a few percent[176].

FCNC Processes

The existence of flavour changing neutral current (FCNC) decays of the top quark in BSM models can also affect the top quark decay width[184]. FCNC processes where a Z boson, a photon or a gluon act as a mediator do not exist at tree level in the Standard Model. They occur solely via loop induced processes which are highly suppressed in the SM and reach branching ratios of about 10⁻¹⁰−10⁻¹⁵[185].

Alternative models as, e.g., some SUSY models predict significantly larger branching ratios for FCNC decays of the top quark. For instance, SUSY EW charged current interactions can induce FCNC processes. Depending on the decay channel, branching ratios of FCNC top quark decays can reach up to 10⁻⁴−10⁻⁵(for decays of the top quark into ac quark and a gluon or a neutral Higgs boson). This contribution is still relatively small but at least more than five orders of magnitude larger than the corresponding SM processes[176, 186]and thus much closer to the precision that can be achieved with today’s particle physics experiments[187–189].

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Vector-Like Top Quarks or a Fourth Quark Generation

The CKM matrix elementV_{t b} is presumed to be close to one due to unitarity constraints from the 3×3 CKM matrix. Once the unitarity requirement is relaxed, V_{t b} may have a measurable value different from one. Two minimal extensions of the SM that permit such a difference by introducing new quarks directly affecting the decay width of the third generation top quark are described in this paragraph.

The first model[190]introduces a vector-like top singlet which causes a global rescaling ofV_{t d},V_ts andV_{t b}. The latter may differ from one even if the ratioR=|V_{t b}|²/(|V_{t d}|²+|V_ts|²+|V_{t b}|²)is close to one. Ris invariant under a rescaling of theV_{t i}entries satisfyingV_{t i}⁽¹⁾=V_{t i}cosθwithi=d,s,b. This rescaling can be implemented with an additional vector-like quark havingQ= +2/3. In case such a hypothetical quark has a mass around the electroweak scale, it mixes with its direct neighbour, the SM top quark, which extends the known CKM matrix as follows:

V_4×3=

‚ 12×2 0 0 U_2×2

Œ ‚ V_3×3 0

Œ

with V_4×3V_4×3^† 6=1_4×4^.

On the assumption that the mass of the additional top quark t⁰is not dominated by the vacuum expectation value of the SM Higgs doublet, the mixing angle is required to be less thanπ/4. A criterion onV_{t b} can thus be defined as a lower bound:|V_{t b}| ≈ |cosθ|>1/p

2≈0.71. Thet⁰quark has three decay modes at leading order: t⁰→W b, as the third generation top quark, as well as the modes t⁰→Z t andt⁰→H t. The total decay width oft⁰depending on the t⁰mass is shown in Fig. 2.14a while Fig. 2.14b contains the branching fractions of the three decay modes of t⁰, again depending on the t⁰mass for a set of the underlying parametersm_H, m_t and cosθ. The shown mass range is almost excluded by many recent searches for at⁰quark. Nevertheless, the motivation of such a model and the trend towards larger masses becomes visible.

(a) (b)

Figure 2.14:(a) The total decay width of thet⁰quark and (b) the corresponding branching ratios of the contributing decay modes oft⁰at leading order as a function of its mass. The underlying parameters are chosen to bem_H=120GeV,m_t=174GeV andcosθ=0.71[190].

The number of decay modes depend on the t⁰mass. With larger masses more decay modes con-tribute; for masses above around 300 GeV all listed LO decay modes need to be considered. Also the parameter choice is relevant for the calculated branching ratios; the branching ratio oft⁰→W b is reduced with increasing cosθ.

The second model[190–193]adds a complete fourth generation of quarks to the known 3×3 CKM matrix. This implies the existence of another unitary V_4×4 mixing matrix which does not allow FCNC decays withZbosons at leading order, as they need to be considered for the above vector-like t⁰quark model. If CP-violating phases beyond the CKM matrix are neglected, the new 4×4 matrix includes three further mixings which can be parametrised by[194]:

V_4×4=R₃₄(θu)R₂₄(θv)R₁₄(θw)·

‚ V_3×3 0_3×1 0_3×1 1

Π.

The rotation in the flavour planei jis given by theR_{i j} with the mixing anglesθu,θvandθw. In this case, the dominant decay channel is expected to be t⁰→W b⁰. Also decays of t⁰ into aW boson and lighter quarks like the top quark can contribute although these decays may be suppressed.

Latest measurement excludedt⁰quarks with masses below around 500-700 GeV, depending on the analysed decay channel[28].

Depending on the corresponding t⁰masses, decays of such vector-like top quarks may contribute to the SM signal of top quark decays and thus directly modify the decay widthΓt.

These days, limits on those BSM models presented in this section are mainly set by the LHC experi-ments. For reasons of simplicity, particularly basic models like the MSSM model are delineated here as an example of such alternative models which can affect the measured value of the decay width Γ_t. There are many other more complex models which are not excluded by the LHC yet, starting with N-MSSM (next-to-MSSM) models, which may contain, e.g., an additional singlet state leading to seven instead of five Higgs bosons. A detailed introduction of those models is beyond the scope of this thesis.