etd@IISc Collection:
http://hdl.handle.net/2005/37
2018-01-25T08:35:08ZIssues in Phenomenology of Heavy Quarks And Leptons
http://hdl.handle.net/2005/2687
Title: Issues in Phenomenology of Heavy Quarks And Leptons
Authors: Arunprasath, V
Abstract: 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.2017-09-25T18:30:00ZHigher Spins, Entanglement Entropy And Holography
http://hdl.handle.net/2005/2653
Title: Higher Spins, Entanglement Entropy And Holography
Authors: Datta, Shouvik
Abstract: The idea of holography [1, 2] finds a concrete realization in form of the AdS/CFT correspondence [3, 4]. This duality relates a field theory with conformal symmetries to quantum gravity living in one higher dimension. In this thesis we study aspects of black hole quasinormal modes, higher spin theories and entanglement entropy in the context of this duality. In almost all cases we have been able to subject the duality to some precision tests.
Quasinormal modes encode the spectrum of black holes and the time-scale of pertur-
bations therein [5]. From the dual CFT viewpoint they are the poles of retarded Green's function (or peaks in the spectral function) [6]. Quasinormal modes were previously studied for scalar, gauge field and fermion fluctuations [7]. We solve for these quasinormal modes of higher spin (s _ 2) fields in the background of the BTZ black hole [8, 9]. We obtain an exact solution for a field of arbitrary spin s (integer or half-integer) in the BTZ background. This implies that the BTZ is perhaps the only known black hole background where such an analysis can be done analytically for all bosonic and fermionic fields.
The quasinormal modes are shown to match precisely with the poles of the corresponding Green's function in the CFT living on the boundary. Furthermore, we show that one-loop determinants of higher spin fields can also be written as a product form [10] in terms of these quasinormal modes and this agrees with the same obtained by integrating the heat-kernel [11].
We then turn our attention to dualities relating higher-spin gravity to CFTs with W
algebra symmetries. Since higher spin gravity does go beyond diffeomorphism invariance, one needs re_ned notions of the usual concepts in differential geometry. For example, in general relativity black holes are defined by the presence of the horizon. However, higher spin gravity has an enlarged group of symmetries of which the diffeomorphisms form a subgroup. The appropriate way of thinking of solutions in higher spin gravity is via characterizations which are gauge invariant [12, 13]. We study classical solutions embedded in N = 2 higher spin supergravity. We obtain a general gauge-invariant condition { in terms of the odd roots of the superalgebra and the eigenvalues of the holonomy matrix of the background { for the existence of a Killing spinor such that these solutions are supersymmetric [14].
We also study black holes in higher spin supergravity and show that the partition function of these black holes match exactly with that obtained from a CFT with the same asymptotic symmetry algebra [15]. This involved studying the asymptotic symmetries of the black hole and thereby developing the holographic dictionary for the bulk charges and chemical potentials with the corresponding quantities of the CFT.
We finally investigate entanglement entropy in the AdS3/CFT2 context. Entanglement
entropy is an useful non-local probe in QFT and many-body physics [16]. We analytically evaluate the entanglement entropy of the free boson CFT on a circle at finite temperature (i.e. on a torus) [17]. This is one of the simplest and well-studied CFTs. The entanglement entropy is calculated via the replica trick using correlation functions of bosonic twist operators on the torus [18]. We have then set up a systematic high temperature expansion of the Renyi entropies and determined their finite size corrections. These _nite size corrections both for the free boson CFT and the free fermion CFT were then compared with the one-loop corrections obtained from bulk three dimensional handlebody spacetimes which have higher genus Riemann surfaces (replica geometry) as its boundary [19]. One-loop corrections in these geometries are entirely determined by the spectrum of the excitations present in the bulk. It is shown that the leading _nite size corrections obtained by evaluating the one-loop determinants on these handlebody geometries exactly match with those from the free fermion/boson CFTs. This provides a test for holographic methods to calculate one-loop corrections to entanglement entropy.
We also study conformal field theories in 1+1 dimensions with W-algebra symmetries at
_nite temperature and deformed by a chemical potential (_) for a higher spin current. Using OPEs and uniformization techniques, we show that the order _2 correction to the Renyi and entanglement entropies (EE) of a single interval in the deformed theory is universal [20]. This universal feature is also supported by explicit computations for the free fermion and free boson CFTs { for which the EE was calculated by using the replica trick in conformal perturbation theory by evaluating correlators of twist fields with higher spin operators [21]. Furthermore, this serves as a verification of the holographic EE proposal constructed from Wilson lines in higher spin gravity [22, 23].
We also examine relative entropy [24] in the context of higher-spin holography [25]. Relative entropy is a measure of distinguishability between two quantum states. We confirm the expected short-distance behaviour of relative entropy from holography. This is done by showing that the difference in the modular Hamiltonian between a high-temperature state and the vacuum matches with the difference in the entanglement entropy in the short-subsystem regime.2017-08-20T18:30:00ZModel Studies Of The Hot And Dense Strongly Interacting Matter
http://hdl.handle.net/2005/2518
Title: Model Studies Of The Hot And Dense Strongly Interacting Matter
Authors: Chatterjee, Sandeep
Abstract: Ultra-relativisitic heavy ion collisions produce quark gluon plasma-a hot and dense soup of deconfined quarks and gluons akin to the early universe. We study two models in the context of these collisions namely, Polyakov Quark Meson Model (PQM) and Hadron Resonance Gas Model (HRGM).The PQM Model provides us with a simple and intuitive understanding of the QCD equation of state and thermodynamics at non zero temperature and baryon density while the HRGM is the principle model to analyse the hadron yields measured in these experiments across the entire range of beam energies.
We study the effect of including the commonly neglected fermionic vacuum fluctuations to the (2+1) flavor PQM model. The conventional PQM model suffers from a rapid phase transition contrary to what is found through lattice simulations. Addition of the vacuum term tames the rapid transition and significantly improves the model’s agreement to lattice data. We further investigate the role of the vacuum term on the phase diagram. The smoothening effect of the vacuum term persists even at non zero . Depending on the value of the mass of the sigma meson, including the vacuum term results in either pushing the critical end point into higher values of the chemical potential or excluding the possibility of a critical end point altogether. We compute the fluctuations(correlations) of conserved charges up to sixth(fourth) order. Comparison is made with lattice data wherever available and overall good qualitative agreement is found, more so for the case of the normalised susceptibilities. The model predictions for the ratio of susceptibilities approach to that of an ideal gas of hadrons as in HRGM at low temperatures while at high temperature the values are close to that of an ideal gas of massless quarks.
We examine the stability of HRGMs by extending them to take care of undiscovered resonances through the Hagedorn formula. We find that the influence of unknown resonances on thermodynamics is large but bounded. We model the decays of resonances and investigate the ratios of particle yields in heavy-ion collisions. We find that extending these models do not have much effect on hydrodynamics but the hadron yield ratios show better agreement with experiment. In principle HRGMs are internally consistent up to a temperature higher than the cross over temperature in QCD; but by examining quark number susceptibilities we find that their region of applicability seems to end even below the QCD cross over.2016-04-24T18:30:00ZTopics In Noncommutative Gauge Theories And Deformed Relativistic Theories
http://hdl.handle.net/2005/2468
Title: Topics In Noncommutative Gauge Theories And Deformed Relativistic Theories
Authors: Chandra, Nitin
Abstract: There is a growing consensus among physicists that the classical notion of spacetime has to be drastically revised in order to nd a consistent formulation of quantum mechanics and gravity. One such nontrivial attempt comprises of replacing functions of continuous spacetime coordinates with functions over noncommutative algebra. Dynamics on such noncommutative spacetimes (noncommutative theories) are of great interest for a variety of reasons among the physicists. Additionally arguments combining quantum uncertain-ties with classical gravity provide an alternative motivation for their study, and it is hoped that these theories can provide a self-consistent deformation of ordinary quantum field theories at small distances, yielding non-locality, or create a framework for finite truncation of quantum field theories while preserving symmetries.
In this thesis we study the gauge theories on noncommutative Moyal space. We nd new static solitons and instantons in terms of the so-called generalized Bose operators (GBO). GBOs are constructed to describe reducible representation of the oscillator algebra. They create/annihilate k-quanta, k being a positive integer. We start with giving an alternative description to the already found static magnetic flux tube solutions of the noncommutative gauge theories in terms of GBOs. The Nielsen-Olesen vortex solutions found in terms of these operators also reduce to the ones known in the literature. On the other hand, we nd a class of new instanton solutions which are unitarily inequivalent to the ones found from ADHM construction on noncommutative space. The charge of the instanton has a description in terms of the index representing the reducibility of the Fock space representation, i.e., k. After studying the static soliton solutions in noncommutative Minkowski space and the instanton solutions in noncommutative Euclidean space we go on to study the implications of the time-space noncommutativity in Minkowski space. To understand it properly we study the time-dependent transitions of a forced harmonic oscillator in noncommutative 1+1 dimensional spacetime. We also provide an interpretation of our results in the context of non-linear quantum optics. We then shift to the so-called DSR theories which are related to a different kind of noncommutative ( -Minkowski) space. DSR (Doubly/Deformed Special Relativity) aims to search for an alternate relativistic theory which keeps a length/energy scale (the Planck scale) and a velocity scale (the speed of light scale) invariant. We study thermodynamics of an ideal gas in such a scenario.
In first chapter we introduce the subjects of the noncommutative quantum theories and the DSR. Chapter 2 starts with describing the GBOs. They correspond to reducible representations of the harmonic oscillator algebra. We demonstrate their relevance in the construction of topologically non-trivial solutions in noncommutative gauge theories, focusing our attention to flux tubes, vortices, and instantons. Our method provides a simple new relation between the topological charge and the number of times the basic irreducible representation occurs in the reducible representation underlying the GBO. When used in conjunction with the noncommutative ADHM construction, we nd that these new instantons are in general not unitarily equivalent to the ones currently known in literature.
Chapter 3 studies the time dependent transitions of quantum forced harmonic oscillator (QFHO) in noncommutative R1;1 perturbatively to linear order in the noncommutativity . We show that the Poisson distribution gets modified, and that the vacuum state evolves into a \squeezed" state rather than a coherent state. The time evolutions of un-certainties in position and momentum in vacuum are also studied and imply interesting consequences for modelling nonlinear phenomena in quantum optics.
In chapter 4 we study thermodynamics of an ideal gas in Doubly Special Relativity. We obtain a series solution for the partition function and derive thermodynamic quantities. We observe that DSR thermodynamics is non-perturbative in the SR and massless limits. A stiffer equation of state is found. We conclude our results in the last chapter.2015-08-11T18:30:00Z