Issues in Phenomenology of Heavy Quarks And Leptons
The Standard Model (SM) of the particle physics, based on the gauge group SU(3) ×SU(2)L × U(1)Y , has been a successful theory which provides consistent description of all phenomena ranging from the nuclear beta decay to known processes at the high energy colliders like the LHC which operates at the TeV scale. Nevertheless, the SM is considered to be only a low energy (weak scale) theory and not a theory that is valid up to an energy scale (∼ 1019 GeV) where the effects of gravity are expected to be strong. The reasons for this view include the sensitivity of the higgs mass to the high energy scale (the hierarchy and the fine tuning problems), lack of explanation, within the SM, of the observation that the matter in the Universe dominates the anti-matter by orders of magnitude, lack of explanation for the number of fermion generations etc. Many extensions of the SM have been proposed so far which come with their own phenomenology to be tested at the high energy particle colliders like the LHC. Many of these extensions offer a special role to the heavy fermions of the SM, viz., the third generation leptons and quarks, the top quark in particular. An example of such a model is the Minimal Supersymmetric Standard Model. The special role given to top quarks is because of the closeness of the mass of the top quark mt (∼ 173 GeV) to the scale of the electroweak √ symmetry breaking (v/ 2 ∼ 175 GeV, where v is the vacuum expectation value of the Higgs field). This also means that the coupling of the top quark to the Higgs boson is large O(1) which makes the top quark loops major contributors to the fine tuning and hierarchy problems of the Higgs sector. Moreover, the interactions of the third generation fermions are the places where some room is left for new physics to appear as the experimental measurements of the properties of the first two generation fermions are very precise. Hence, the third generation particles, and the top quark in particular are expected to have new non-SM couplings to particles that are expected in this Beyond the Standard Model(BSM) physics. These particles can be either fermions or bosons. We focus first on a simple model that has a new fermion generation with the same quantum numbers as the corresponding SM fermions. This model is called the fourth generation Standard Model. Note that the Standard Model has no explanation for the number of fermion generations. The number of neutrinos extracted from the invisible Z-boson decay width at LEP is consistent with three. But this constrain can be evaded when the fourth generation neutrino is sufficiently heavy: mν′ ≳ mZ /2, where mZ is the mass of the Z-boson. Direct search constraints on the charged lepton of the fourth generation put it’s mass above ∼ 100 GeV. The lower bounds on the masses of fourth generation quarks t′ and b′ (mt′ , mb′ , respectively) have changed very much since the beginning of our work. We had used a model independent lower bound mt′,b′ > 290 GeV that was available at the time of our work. One can easily see that the fourth generation fermions were necessarily heavy, heavier than the top quark, at the time of our work. Since then the lower bounds only moved up. The present limits are mt′ > 700 GeV and mb′ > 675 GeV, if they decay through charged current processes. One important aspect of the fourth generation fermions is that they do not decouple when they are heavy. This affects the precision EW observables (see Introduction) through the loops. Earlier works focusing mainly on low Higgs mass (mh) suggested that the precision EW constraints imply a mass splitting |mt′ −mb′ | ≲ mW , where mW is the mass of the W boson. Another important effect of the heavy fourth generation fermions is that some of the tree-level scattering amplitudes like t′t′ → t′t′ at high energies, grow as GF m2f′ , where GF is the Fermi’s constant and m f ′ is the mass of the fourth generation fermion f ′ = t′,b′,ν′,τ′, which could be of O(1), potentially violating the tree level perturbative unitarity of the S-matrix. We combined the constraints from the precision EW observables -the S,T,U parameters, and the perturbative unitarity constraints to find available fourth generation SM parameter space in the light of a heavy Higgs as required by the then available LHC Higgs exclusion limits. We allowed for a small mixing between the third and fourth generation fermions: sin θ34 ≲ 0.3, where θ34 is the mixing angle of the third and the fourth generation quarks. This necessitated inclusion of amplitudes involving the top quark along with those of t′ and b′ in the perturbative unitarity analysis which had not been done before. We found that a heavy higgs with mass mh ≳ 800 GeV allowed large mass splitting between t′ and b′ and τ′ and ν′: |mt′ − mb′ | and mτ′ − mν′ could be greater than mW as long as sin θ34 ≤ 0.3. This meant that there was a non-negligible possibility that t′ → b′W /b′ → t′W and τ′ → ν′W could be open. Further we showed that the branching ratios for t′ → b′W or b′ → t′W could be close to unity (100%) for sin θ34 ≲ 0.05. The implication for the direct search experiments, which till then had not considered such decay modes, was that the search strategies should be altered to include these decay modes. Another important aspect of our result is that the large mass splittings mentioned above could be achieved even with one Higgs doublet, in contrast to earlier works which obtained such mass splittings only with two Higgs doublets. An epilogue is necessary here. The main point of our work was to show that a heavy Higgs could be allowed when a fourth generation of heavy fermions were present. At the time of the publication of this work, hints, but not a discovery, for a light Higgs appeared at the LHC. We did not take these hints to constitute as an evidence at that time. The discovery of a 125 GeV higgs boson at the LHC rules out the simple picture we had considered in our work. This was due to the huge suppression of the B.R of h → γγ channel by two orders of magnitude relative to it’s SM value despite a factor ten enhancement relative to the SM of the production channel gg → h. This results in a net suppression of the gg → h process relative to it’s SM value. Even after the Higgs discovery, a fourth generation model with a two Higgs doublet model could, however, still be viable. The top quark has an important property which is not shared by any other known quarks: Once produced, it decays before it can form any hadron. Hence, information about it’s spin state is transferred to the kinematical distributions of it’s decay products. One of the forms in which the spin information is revealed is via the kinematical distributions of decay products of the top which are sensitive to the polarization of the top quark. Different distributions have different sensitivity to the top polarization. The polarization of the top gives information about the chiral structure of the interaction responsible for the production. In the SM, the main mode of top production is the tt¯ pair production through QCD interactions. Due to the parity conserving nature of the QCD interactions (in other words, purely vector interactions), the polarization of the top quarks along their direction of motion is very small-less than about a percent. On the other hand, the single top production process which involves vector-axial-vector (maximally parity violating) weak interactions, produces highly polarized top quarks. Any possible chiral new physics interaction in the top production could affect the polarization of the produced top quarks. Hence, the top polarization can be a probe of new physics in top production. However, when any possible new physics effects appear in the top decay vertex, such as the W tb vertex associated with t → bW , measurement of top polarization is affected. This is because of the new Lorentz structures induced by the new physics which affect the kinematic distributions of the decay products. These additional couplings can be induced by higher order SM loops also. The possible deviations of these coefficients from the SM value are called anomalous couplings. Different kinematic distributions have different sensitivities to the anomalous couplings. In the second work, we constructed asymmetries from four kinematic distributions: θℓlab, xℓ = 2Eℓlab/mt , u = Eℓlab/(Eℓlab + Eblab) and z = Eℓlab/Etlab; ℓ and b denote the charged lepton and the b-quark from the top decay. The superscript lab denotes that our asymmetries are evaluated in the lab frame. Lab frame asymmetries do not need full reconstruction of a top event. We compare the four asymmetries for their sensitivity to the top polarization and the anomalous coupling f2R (The anomalous couplings of the W tb vertex are denoted as f1R, f2L, f2R (we set f1L = 1). Due to the strong indirect constraints from the measured branching ratio of b → sγ, we considered only one anomalous coupling, i.e f2R). We focused on a particular scenario where the top is highly boosted in the lab frame. Since a typical new physics process is expected to be in the TeV scale, the top produced through such processes would be highly boosted in the lab frame. Since effects of a possible chiral new physics in the top production appear in the top polarization and in the top decay, through the anomalous couplings like f2R of W tb, a simultaneous constraint on the top polarization and anomalous couplings is very useful, as it does not rely upon any specific assumptions on the decay or production. We combined asymmetries in a χ2 analysis to determine how much they can constrain the longitudinal top polarization (polarization along the direction of motion) and the anomalous W tb coupling f2R simultaneously. We also studied the effects of systematic uncertainties in the asymmetries and found that our asymmetries were sensitive to both P and f2R at a level of O(10−2) −O(10−1), for systematic uncertainties upto 5%. The top quarks are produced at the LHC dominantly as tt¯ pairs through QCD interactions. The other modes of production that have been observed include the single top (t-channel), associated production with a electroweak gauge boson etc. But the top can also be produced through possible new physics processes such as the one where a heavy new physics particle decays into a top quark. The couplings of the top with the heavy particle determine it’s polarization, in the rest frame of the heavy particle, for given masses of the parent and the daughter particles that are produced along with the top. The polarization of the top is a frame dependent quantity. For example, if we define the top polarization in the helicity basis, i.e. taking the direction of motion of the top in a given frame as it’s spin quantization axis, the polarization of the top in the rest frame of the heavy particle is not the same as it’s value in the lab frame. This is because the helicity states of the top are not invariant under the Lorentz transformations which are not along the direction of motion of the top. The probes of top polarization defined in the lab frame, do not require a full reconstruction of the event which is complicated by the possible presence of missing energy at the detectors. To probe the mechanism of the top production through the measured top polarization in the lab frame, a prediction of the polarization of the top in the lab frame as a function of the dynamical parameters of a theory like the couplings, mixing angles etc. is needed. In the third work, we studied how the top polarization in the rest frame of the heavy particle can be related to it’s value in the lab frame. In particular, we provide a simple procedure of calculation of top polarization in the lab frame given the dynamical parameters of the theory and the masses of the particles involved in the decay. We show that this can be achieved by the convolution of the velocity distribution of the heavy particle in the lab frame with a formula for top polarization in the lab frame. This formula depends only on the velocity of the heavy particle in the lab frame and not it’s direction of motion. We derive the formula and provide a simple explanation for the absence of the dependence on the direction of motion of the heavy particle. We illustrate our formula with two examples: the top produced from the decay of a gluino, and the top produced in the decay of stop. The analytical expression which we have derived gives the value of top polarization in any boosted frame. We establish the validity of our formula through a Monte Carlo simulation. We also give how finite width effects can be included. We find that a simple approach of folding the expression for the top polarization (after convoluting with the velocity distribution of the heavy particle) with a Breit-Wigner form for the distribution of mass of the heavy particle around it’s on-shell mass is sufficient in most of the cases. To summarize, we explored some aspects of the phenomenology of heavy quarks and leptons which are currently known or which are hypothetical. The first work focuses on the fourth generation Standard Model in the light of an LHC exclusion limit on Higgs boson. Taking into consideration all the indirect constraints, including the precision electroweak tests, we found that a heavy Higgs boson allowed a large mass splitting between the fourth generation fermions which implied that the direct search strategies need to include some more decays of fourth generation fermions. In the second work, we constructed observables which are sensitive to top polarization and used them to constrain possible anomalous couplings associated with the W tb vertex. We studied these observables for their potential to constrain both the top polarization and the possible anomalous couplings of W tb vertex. In the third work, we gave a simple procedure to calculate the top polarization in the lab frame, when the top quarks are produced in the decays of heavy particle. We showed that the lab frame polarization of the top could be obtained simply by convoluting the velocity distribution of the heavy particle in the lab frame with an expression for top polarization. We derived the expression and gave reasons for why the analytical expression does not depend on the direction of motion of the heavy particle. We demonstrated use of a simple procedure to include the effects of finite width of the heavy particle.