Master Thesis Proposals: Particles and Gravitation

The characteristic vibrational modes of a black hole are known as “quasinormal modes”, and they describe the response of a black hole after a perturbation and its subsequent gravitational wave emission. In this project, we will analyze the quasinormal modes of black holes in general relativity  (GR) and beyond. In the case of GR, the perturbations of Kerr black holes are described by the Teukolsky equation. We will employ Leaver’s continued fraction method to solve the Teukolsky equation and obtain the quasinormal mode frequencies of Kerr black holes, reproducing important results in the literature. Then we will consider a modified Teukolsky equation that describes perturbations of rotating black holes in extensions of GR and we will generalize the continued fraction method to solve this modified equation. We will compute the corrections to the Kerr quasinormal mode frequencies due to beyond-GR physics and we will study their phenomenological consequences. If time permits, we will also analyze the case of near-extremal black holes, which requires different methods.  

In this thesis, you will make predictions for the forthcoming measurements of baryon form factors by the HADES collaboration [1].

The project can be carried in Barcelona and/or remotely with weekly Zoom meetings with the supervisor.

Do not hesitate to contact the supervisor for more details, without any commitment. 

The sensitivity of the rare decays η/η'→π0γγ to signatures of Beyond the Standard particles in the MeV-GeV mass range will be analyzed in this work. By adding new fundamental scalar (S) and vector (V) bosons through the decay channels η/η'→π0S→π0γγ and η/η'→Vγ→π0γγ, respectively, to the Standard Model contributions from vector, tensor and scalar meson exchanges, and employing experimental data for the associated branching ratios, this project will set constraints on the new particle fundamental properties -mass and coupling to the Standard Model particles. The results will be relevant for the dark-sector particles search programs at existing and forthcoming light-meson factories, such as BESIII (China) and Jefferson Lab Eta Factory (USA) experiments

The work will require state-of-the-art reading, as well as analytical and computational skills. It will be developed at the University of Barcelona, but remote supervision is possible.

A neutron star merger is a highly dynamical system in which the four fundamental forces of nature—electromagnetic, weak, strong, and gravitational—play significant roles. This makes it an intriguing laboratory for studying fundamental physics, which can be explored experimentally through both gravitational and electromagnetic waves. To model this system, instead of solving quantum chromodynamics, one replaces this by a much simpler description based on fluid dynamics. This motivates the study of relativistic hydrodynamics, which is also useful for the description of the quark-gluon plasma or cosmological scenarios.

The project consists in studying basic aspects of relativistic hydrodynamics and obtaining solutions in simple set ups. We can potentially include viscous effects, which are required to improve the state of the art simulations of neutron star mergers. This could lead to the publication of a research paper.

In this thesis, you’ll develop a model describing the photoproduction of tensor mesons based on the model from Ref. [1] and the data from Refs. [2-4]. You will learn some standard techniques and theories used in particle physics such as the helicity formalism, the decomposition into partial waves, the S-matrix (or scattering) theory and Regge theory. 
The project can be carried in Barcelona and/or remotely with weekly Zoom meetings with the supervisor.

Do not hesitate to contact the supervisor for more details, without any commitment. 

[1] V.~Mathieu \textit{et al.} [JPAC], ``Exclusive tensor meson photoproduction,'' Phys. Rev. D \textbf{102} (2020) no.1, 014003 doi:10.1103/PhysRevD.102.014003 [arXiv:2005.01617 [hep-ph]].

[2] M.~Carver \textit{et al.} [CLAS], ``Photoproduction of the $f_2(1270)$ meson using the CLAS detector,'' Phys. Rev. Lett. \textbf{126} (2021) no.8, 082002 doi:10.1103/PhysRevLett.126.082002 [arXiv:2010.16006 [nucl-ex]].

[3] A.~Celentano \textit{et al.} [CLAS], ``First measurement of direct photoproduction of the $a_2(1320)^0$ meson on the proton,'' Phys. Rev. C \textbf{102} (2020) no.3, 032201 doi:10.1103/PhysRevC.102.032201 [arXiv:2004.05359 [nucl-ex]].

[4] The GlueX Collaboration, to appear soon.

In this thesis, you will develop a model for a strange cascade, that is, a reaction in which several baryons containing strange quarks are produced. The GlueX collaboration (Hall D at the Thomas Jefferson Lab) is exploring the possibilities of setting up a polarized proton target [1]. A polarized target could potentially help in the determination of the quantum numbers of the produced strange baryon. To investigate this possibility, you will develop models for various spin-parity baryons and test their differences in the polarized target observables.

The project can be carried in Barcelona and/or remotely with weekly Zoom meetings with the supervisor.

Do not hesitate to contact the supervisor for more details, without any commitment. 

[1] F.~Afzal, M.~M.~Dalton, A.~Deur, P.~Hurck, C.~D.~Keith, V.~Mathieu, S.~Sirca and Z.~Yu, ``White Paper on Polarized Target Studies with Real Photons in Hall D,'' [arXiv:2407.06429 [nucl-ex]].

In this thesis, you will make predictions for the forthcoming measurements of baryon form factors by the HADES collaboration [1].

The project can be carried in Barcelona and/or remotely with weekly Zoom meetings with the supervisor.

Do not hesitate to contact the supervisor for more details, without any commitment. 

[1] R.~Abou Yassine \textit{et al.} [HADES], ``First measurement of massive virtual photon emission from N* baryon resonances,'' [arXiv:2205.15914 [nucl-ex]].

In this thesis, you will develop a powerful technique to analyze baryon resonances produced in photoproduction through the angular decomposition of their decay product. You will generalize the formalism developed in Ref~[1] to the baryon system.

The project can be carried in Barcelona and/or remotely with weekly Zoom meetings with the supervisor.

Do not hesitate to contact the supervisor for more details, without any commitment. 

[1] V.~Mathieu \textit{et al.} [JPAC], ``Moments of angular distribution and beam asymmetries in $\eta\pi^0$ photoproduction at GlueX,'' Phys. Rev. D \textbf{100} (2019) no.5, 054017 doi:10.1103/PhysRevD.100.054017 [arXiv:1906.04841 [hep-ph]].

The X(3872) is an exotic quarkonium state which can not be explained within the quark model. Several configurations have been proposed for the internal structure of this state, being the most popular ones the compact tetraquark and the hadronic molecule. Recently, the X(3872) has been observed in heavy-ion collisions, in which a hot QCD medium is created. Studying how the medium modifies the properties of the X(3872) we can obtain additional information that might allow us to determine whether this state is a tetraquark or a molecule. In this thesis, we are going to build on the results of Phys. Rev. D 107, 054014 that studied this mysterious bound state within the molecule approximation using an approach based on chiral perturbation theory. The goal is to obtain the finite temperature potential of the X(3872), allowing us to make phenomenological predictions. On one hand, we will be able to determine up to which temperatures the bound state solution is still valid. On the other hand, the wave function of the state can be used to analyze recombination within the coalescence model.

When the densest stars in the universe (neutron star or neutron star-black hole pairs) orbit each other, they get closer due to emitted gravitational radiation. Neutron stars have a solid exterior crust that may shatter in this extreme encounters. In this project, you will explore whether the star can shatter like a glass does when a singer hits its resonant note. This depends on the properties of dense matter and, in particular, on the symmetry energy parameter that is predicted from nuclear physics. Furthermore, if detectors can see gamma rays from such a shattering process just before measuring the gravitational waves emission from the merger, we may find the resonant frequency at which the crust shatters. This could potentially help constrain the properties of the crust and nuclei, bridging the gap between 20 orders of magnitude in spatial extent. 

The Standard Model of Cosmology, the so-called ΛCDM model [1], is afflicted by
several discrepancies with observations that might be calling for new physics. The Hubble tension between the local measurement of H0 by SH0ES and Planck’s CMB-inferred value already reaches the ~5σ C.L. Others attain the 2-3σ C.L., as the tension between the growth of large-scale structures measured with weak lensing and galaxy clustering probes and Planck. Both have been there for already a decade. See the review [2] and references therein for details. The growth rate tension is usually quantified in terms of the parameter σ8, which is the root-mean-square mass fluctuations at a scale of R8=8h-1Mpc, with h=H0/(100km/s/Mpc) the reduced Hubble parameter. It has been recently argued that the use of σ8 might introduce a bias in cosmological analyses of models with a value of H0 quite different from the one preferred by ΛCDM (h~0.67) [3]. This has been proved to be true in the context of early dark energy models [4] and modified theories of gravity [5].

In this thesis the student will quantify the bias introduced by the use of σ8 in fitting analyses of several dynamical dark energy models. This bias could be playing a crucial role in the assessment of the aforesaid cosmological tensions, and could also be of utmost importance to understand their interplay. The student will derive the most relevant cosmological equations at the background and linear perturbation levels for the various models and familiarize with the Einstein-Boltzmann code CLASS [6], the use of Monte Carlo techniques and samplers, and basic concepts of Bayesian statistics [7], This analysis is expected to shed light on the discussion of the cosmological tensions and give rise to a publication in a high-impact journal in the field.

The solution of quantum field theories is one of the most challenging topics in modern theoretical physics. Recently, promising advances have relied on the use of variational approaches that exploit machine learning techniques [1]. These approaches encode the gauge symmetries in the architecture of neural networks [2], which provides advantages with respect to other sampling techniques [3]. Variational solutions to quantum field theories can be then exploited to find numerical solutions to these problems [4].  

In this project, you will employ machine learning techniques to address a simplified quantum field theories, and solve it variationally. The results you will obtain will be  benchmarked with other methods, including lattice field theory. You will study and analyze the quality of the variational ansatz depending on different architectures. You will look into the efficiency of these new variational techniques, as well as different sampling and optimization strategies.

The quark-gluon plasma is a new state of matter that can be formed by colliding heavy ions at ultrarelativistic velocities. From all the particles formed in these collisions, heavy quarkonium is one of the most promosing probes to obtain information about this new state of matter. One of the most succesful approaches to the study of the evolution of quarkonium in a medium is to model it as a Markovian open quantum system. Recently, it has been found using this approach that regeneration is crucial to reproduce experimental data on quarkonium excited states. However, it has been observed that after including regeneration the number of detected Upsilon(2S) states over Upsilon (1S) increases but the ratio of Upsilon(3S) over Upsilon(2S) decreases. This result is unintuitive because s-wave quarkonium states are ordered in size and, therefore, we expect larger states to be more suppressed by the medium. We propose to find the reason of this behaviour by studying the evolution of quarkonium with a recently proposed numerical method, the Jumptime unravelling. References:N. Brambilla, M.A. Escobedo, J. Soto and A. Vairo, Quarkonium suppression in heavy-ion collisions: an open quantum system approach, Phys. Rev. D \textbf{96} (2017) no.3, 034021 [arXiv:1612.07248 [hep-ph]].

Dark matter is a mysterious constituent of the universe, 5 times more abundant than ordinary (or visible) matter. The characterisation of its properties remains one of the most pressing problems of particle physics. In particular, dark matter could be in a degenerate quantum state in some galaxies, with novel phenomenological consequences. The proposed work would consist in studying a toy model of fermions with attractive long range interaction to mimic the peculiar properties of these galaxies, which can be done using state-of-the-art tensor network techniques. The student is expected to investigate the ground state (and thermal) properties of this quantum model, and understand which new properties may appear in the final virialized states ('halos') from quantum degeneracy pressure as compared to their classical counterpart. Because of its interdisciplinary nature, this work would be done in co-supervision with Prof. Diego Blas from Universitat Autònoma de Barcelona, and Prof. Mari Carmen Bañuls from Max Planck Institute for Quantum Optics (Garching, Germany). The student would moreover have the opportunity to visit the MPQ to work closely with Prof. Bañuls for a period of one to a few weeks (all expenses covered).

Localization is a technique to compute functional integrals exactly. The location technique applied to the calculation of exact physical observables is one of the most spectacular recent results in non-abelian gauge theories.
This led to the calculation of the exact partition function, Wilson loop operators in supersymmetric theories, including all perturbative and non-perturbative contributions, with an exact account on all instanton effects. This master thesis will investigate several open problems in relation to four-dimensional non-abelian gauge theories by means of supersymmetric localization of path integrals.

Superstring theory in anti de Sitter space is dual to superconformal field theories, that is, to field theories invariant under scale symmetries and supersymmetries. In the last 20 years, this AdS/CFT duality has led to multiple applications, including classical and quantum gravitational physics, condensed matter, integrability and several aspects of superstring theory, representing the main trending topic in theoretical physics. This master thesis will study conformal field theories in spaces which are direct product of anti de sitter spaces and spheres, with the aim of understanding boundary anomalies and their AdS/CFT counterpart.

The gauge/gravity duality, or holography, is a versatile tool to study the strongly coupled dynamics of gauge theory matter. One of areas were the holographic principle shows its strengths is in the computation of the phase diagram of quantum field theories with known gravity duals. For certain realisations of the duality, the field theory enjoys non-trivial phase diagrams, including phase transitions of different degrees. The goal of this project is to determine the effective action of a particular class of models and to relate this effective action to their known phase structure.

Dark energy (DE) is believed to be the physical cause that produces the measured accelerated expansion of the universe. Within the standard model of cosmology (i.e. the current paradigm) the DE is identified with a strict cosmological constant. However, the plain simplicity of this idea lies at the root of its unconvincing theoretical status. In addition, phenomenologically, the standard model is also disputable at present. Tensions of various sorts and of different degrees are known to be present among existing datasets within such framework. For example, the recently measured local value of the Hubble parameter, H0, is significantly higher than the one inferred from the measurements of the anisotropies in the cosmic microwave background (CMB) by the Planck satellite. Also, the current paradigm predicts exceeding structure formation power as compared to the observations etc. The possibility that these facts are actually pointing to serious 'cracks' in the current cosmological paradigm is slowly but strongly setting in.

In this work, the student will have the opportunity to explore the nature of these cosmological problems as well as some theoretical models of dynamical DE capable to alleviate them. Among these models, the dynamical vacuum models are well-motivated from the theoretical point of view (e.g. within quantum field theory in curved spacetime). Interestingly, they also predict a possible time variation of the fundamental "constants" of Nature, including the masses and couplings of the elementary particles, what could act as an additional signature of physics beyond the standard models both of particle physics and cosmology.

Despite the vacuum energy and in general the dark energy (DE) is postulated as being the physical cause that produces the measured accelerated expansion of the universe, the usual prediction in quantum field theory (QFT) is much too large as compared to the critical density of the Universe. The mismatch is ultimately responsible for the "Cosmological Constant Problem", which is the biggest conundrum of fundamental physics ever. The main problem stems from the usually proposed renormalization procedures of the energy-momentum tensor in QFT, which lead to contributions proportional to the quartic powers of the mass of the quantum fields (i.e. proportional to $m^4$). However, if one considers an appropriate variant of the adiabatic regularization and renormalization of quantum fields in a FLRW background it is possible to provide a well defined result which can elude the $m^4$ terms and ultimately provides a dynamical vacuum energy density $\rho_{vac}(H)$ evolving as powers of the Hubble rate, H, and its derivatives, therefore sufficiently small.

In this work, the student will have the opportunity to perform such a QFT calculation in an appropriate context, in which matter is represented by a scalar field non-minimally coupled to curvature. He/she will verify that $\rho_{vac}(H)$ evolves as a constant term (representing the cosmological constant part of the final result) plus some dynamical components of order $H^2$ and $H^4$. The higher powers are relevant for the early universe only, where they can trigger fast inflation through effective string-theory effects generating those terms. These are induced by the presence of anomalous Chern-Simon couplings involving the Kalb-Ramond field of the gravitational multiplet. At present, $\rho_{vac}(H)$ is dominated by the additive constant term accompanied by a tiny dynamical component of order $H^2$. This result tells us that the vacuum energy density is not just constant but evolves with time. Its current variation is small enough, but still potentially measurable. At the phenomenological level, it looks as a kind of effective quintessence behavior. In point of fact, however, there is not a real quintessence field but an underlying QFT vacuum changing ('running') very mildly with the cosmic expansion.

The so called final state interacions or rescattering effects give rise to large uncertainties in the cross sections of hadronic collisions. They are due to the fact that the hadrons produced in a collision may suffer non-negligible interactions between themselves before reaching the detector. A recently proposed effective theory [1] may be instrumental to systematically address this problem. We propose to initially explore this issue in the scattering of scalar particles, and eventually in the relevant case of the Chiral Lagrangian [2].

The plethora of charmonium (and some bottomonium) resonances discovered during the last decade, the so called XYZ states [1], challenge our current understanding of QCD. An important ingredient to describe those states is the interaction of heavy quarkonia with heavy-light meson pairs. We propose to include a realistic estimate of this interaction in the calculation of the heavy quarkonium spectrum. The estimate should be first obtained by fitting lattice QCD data on the string breaking phenomena of refs. [2,3], and extrapolating them to realistic values of the light quark masses [4]. The outcome should be then incorporated in a coupled-channel Schrödinger equation and the spectrum calculated numerically.

The LHCb detector at the LHC has observed a number of small deviations with respect to the Standard Model predictions in b -> sll transitions, most notably in tests of Lepton Universality comparing the couplings to muons and electrons. While a pattern is emerging, it is of uttermost importance to confirm if these deviations are present in the whole family of b -> sll decays. A first measurement of Lepton Universality with Lambda_b decays was performed by LHCb with a fraction of the collected data, with results consistent with the deviations observed in the meson sector but also with the SM predictions. It is thus critical to update this measurement with the full dataset. In particular, optimisation of the event selection and a study of the pK spectrum will enable improvements beyond the pure statistical gain from the size of the analysed data sample.

General Relativity encompasses a huge variety of physical phenomena, from the collision of astrophysical black holes, to the dynamics (via holography) of strongly-coupled plasmas and the spontaneous symmetry-breaking in superconductors. Black holes play a central role in all this. However, their equations are exceedingly hard to solve. The apparent lack of a generic tunable parameter that allows to solve the theory perturbatively (like the electric coupling constant in electrodynamics, or the rank of the gauge group in large-NYang-Mills theory) is arguably the single most important obstacle for generic efficient approaches to the physics of strong gravity and black holes. In General Relativity, one natural parameter suggests itself: the number of dimensions D. Recently we have demonstrated that the limit of large D is optimally tailored for the investigation of black holes, classical and potentially also quantum. We have derived a simple set of nonlinear equations that describe the dynamical evolution of black holes, strings and branes that efficiently capture a surprisingly large amount of black hole physics.

The study of the dark energy is a central subject in cosmology and fundamental physics. Despite the many efforts, our theoretical understanding of the ultimate nature of the dark energy component of the universe still lags well behind the astounding experimental evidence achieved from the increasingly sophisticated observational tools at our disposal. While the canonical possibility is a strict cosmological constant, the exceeding simplicity of this possibility lies also at the root of its unconvincing theoretical status. In this work the student will have the opportunity to explore the cosmological implications of the dynamical models of the vacuum energy. Some of these models are actually well-motivated from the theoretical point of view (e.g. within quantum field theory in curved spacetime) and may provide a rich phenomenology that could be explored in future observations. In particular, the dynamics of vacuum can affect the Hubble expansion and the details of structure formation, as collected e.g. from the data on type Ia supernovae, the Cosmic Microwave Background and the Baryonic Acoustic Oscillations. In this study the cosmology of some these models will be solved and confronted with the data. At the same time the relation of these vacuum models on possible evidence of dynamical dark energy recently pointed out in the literature will also be addressed.

Presently LHC has observed a state which is compatible with the Standard Model Higgs Scalar responsible for electroweak symmetry breaking (EWSM) . On the other hand no direct signature of new physics staes has been observed.

This allows to parametrize the possible effects of NP in the electroweak symmetry breaking sector in terms of an effective lagrangian containing higher dimension operators. Recently we have performed an analysis of the existing data in order to constraint the coefficients of these operators. The proyect will review this subject and will evaluate the maximum allowed deviations from the SM predictions in the Higgs related signatures at the future high precision runs of the LHC.

During the last 15 years neutrino oscillation experiments have produced results which show that neutrinos are massive and oscillate in flavour. One of the most recent results come from the Daya-Bay experiment which measures the disappearance of reactor antineutrinos at distances of the order of km. This experiment was the first one to provide with statistical significance a measurement of the last mixing angle of the leptonic mixing matrix, theta_13 based on the observation of a deficit in the observed over expected number of events. This summer Daya-Bay has released their data on the energy spectrum of their events which can provide additional information. The project proposes to review the formalism of neutrino oscillations and to proceed wiht the relevant computations to make an statistical analysis of the observed energy spectrum.

We will use the equivalence between strongly coupled gauge theories and gravity in Anti de Sitter space to study various aspects of gauge theories.

If dark matter particles are very heavy, they may form bound states mediated by the interaction with Standard Model particles. Direct detection experiments may be sensitive to break-up events. We propose to build an effective field theory in which dark matter particles are non-relativistic, and explore the possible existence of bound states, both in the case that the SU_L(2) x U_Y(1) symmetry is linearly realized and in the case that it is non-linearly realized (composite Higgs).

The Jefferson Laboratory in Virginia hosts two experiments (GlueX and CLAS12) dedicated to the study of meson interaction. These experiments are searching for exotic mesons produced by photons on a hydrogen target. The most promising signal of an exotic meson, in this case a state composed of a q qbar together with an extra gluon, has been observed in the P-wave of the eta+pi0 final state. However the confirmation of this discovery requires a comparison between theoretical predictions and experimental observables.
The project consists in studying the reaction gamma + p --> eta + pi0 + p at high energies and developing a model for the production of exotic meson in this reaction (to be compared with GlueX preliminary data)

Gravitational waves are constantly passing us. However, even the strongest waves that come from merging black holes have a tiny effect on the arms of the gravitational wave detectors on Earth. They stretch and squeeze them by a thousand of the width of a proton.

You will search for gravitational waves in LIGO-Virgo data to find short unknown signals. You will demonstrate the potential of the maximum entropy method to determine the properties of exotic, unknown signals. This technique recovers coherent signals from a network of gravitational wave detectors. It assumes that signal behaves differently from noise, i.e., that the signal is correlated at different detectors in the network, while the noise is uncorrelated. You will learn numerical methods, noise modelling, some of the mathematics behind the data analysis, and practice on real detector data. You will start by reconstructing very short events of possible exotic origin like GW190521.

Requirements: linear algebra, python, complex analysis

Just like light waves, gravitational waves are most generally characterized by their propagation direction and time-dependent waveform in each of two independent polarization states. These properties of incident gravitational plane waves can be inferred from observations made in a properly oriented network of detectors. You will learn to characterize the wave polarization via its (frequency dependent) Stokes parameters to infer important, general properties of the wave's source: e.g., point sources of circularly polarized radiation must be non-axisymmetric and radiating angular momentum, while point sources of linearly polarized waves must be either axisymmetric or oriented so that the direction of angular momentum loss is orthogonal to the observer line-of-sight. This is particularly interesting for more exotic sources, e.g., black hole binaries with high spin or high eccentricity. You will find the regions of the gravitational wave sky where the LIGO-Virgo network is sensitive to both gravitational wave polarizations, and estimate the number of sources.

The first event where both polarizations were detected is GW170814. You will start by computing the Stokes parameters for this event.