Research projects

The research projects within

International PhD studies in Fundamental Problems of Quantum Gravity and Quantum Field Theory

Subject of thesis: Hadron light-front wave functions based on AdS/QCD duality, supervised by prof. Stanisław D. Głazek, University of Warsaw

Outline of the project: Structure and interaction of hadrons are known at the probability level. A deeper understanding at the level of amplitude is required for conceptually clear and quantitatively precise description of processes that involve hadrons, such as collisions of protons or their interaction with electrons and photons. This project aims at construction of the renormalized wave functions of hadrons using insights from AdS/QCD duality and light-front holography. Since cross-sections in processes that involve hadrons can be expressed in terms of their generalized parton distributions and form factors, the graduate student would be expected to compute the relevant observables using the derived wave functions. Two main results provide foundation for this project. The general theoretical framework in the study will be the similarity renormalization group procedure for Hamiltonians that was originally formulated by Głazek and Wilson and subsequently developed by Głazek and his students in the University of Warsaw in application to QCD. This framework is a natural candidate for incorporating the vast amount of information from the phenomenology of hadronic wave functions developed by Brodsky and his collaborators, based on the development of AdS/QCD correspondence and light-front holography.

Stays abroad: SLAC, at least 6 months, likely extension to 12 months.

Foreign partner: Prof. S. J. Brodsky , SLAC, Stanford University, California, USA

Subject of thesis: Strong interaction corrections to the weak radiative B-meson decay at order O(alpha_s^2) with exact dependence on the c-quark mass'', supervised by prof. UW dr hab. Mikołaj Misiak, University ofWarsaw.

Outline of the project: The inclusive radiative decay rate of the B-meson is known to provide strong constraints on new particles and their interactions at scales up to 1 TeV. For this reason, efforts towards improving accuracy of the decay rate determination are undertaken on both the experimental and theoretical sides. At present, both uncertainties amount to around 7%. A reduction of the experimental error by a factor of 2 or more is expected from the future measurements at Belle-II and Super-B. On the theory side, one of the most important goals is to remove an uncertainty that stems from interpolation in the charm quark mass of some of the O(alpha_s^2)
corrections. Evaluation of these corrections for an arbitrary value of the c-quark mass is the subject of the Ph.D. project. The calculation requires long-term access to powerful computers with total RAM in the Terabyte
range. The student is supposed to spend between 6 and 24 months at both partner institutions (combining the time spent at RWTH Aachen and at the Karlsruhe Institute of Technology). He is expected to collaborate on the problem
described above with the research staff of both institutions, in particular with our main partners there (M. Czakon and M. Steinhauser, espectively).                

Stays abroad: RWTH Aachen and Karlruhe Institute of Technology, 6 to 24 months.      

Foreign Partners: Prof. M. Czakon, RWTH Aachen, Germany, and Prof. M. Steinhauser, KIT, Karlsruhe, Germany.

Subject of thesis: Flavour Constraints on Supersymmetric Grand Unified Theories, supervised by prof. UW dr hab. Mikołaj Misiak, University of Warsaw

Outline of the project: The strong, weak and electromagnetic interactions are phenomenologically very different at low energies but become similar at high energies, and are likely to unify into a single interaction. Quantum numbers of all the known particles “miraculously” fit into few basic representations of SU(5) and/or SO(10) that are among the smallest simple groups containing the Standard Model SU(3) × SU(2) × U(1) gauge group as a subgroup. Grand Unified Theories (GUTs) are non-abelian gauge theories based on such groups. At a certain scale M_GUT, the Higgs mechanism reduces their gauge symmetry to the SM one. The three SM gauge couplings must be close to each other at that scale, which implies M_GUT ≈ 10¹⁵ ÷ 10¹⁷ GeV. Stabilization of the hierarchy between the GUT and electroweak (O(250 GeV)) scales becomes natural in softly broken supersymmetric theories, provided the soft breaking scale is small enough. The Minimal Supersymmetric Standard Model (MSSM) is consistent with the GUT paradigm and free of parameter fine-tuning so long as the soft breaking scale M_SUSY is close to the electroweak one. The MSSM renormalization group equations “miraculously” lead to numerically acceptable unification of all the three gauge couplings at M_GUT, with no need for new dynamics at intermediate scales (contrary to the SM case). The same is true for unification of the tau and bottom Yukawa couplings that must take place in any SU(5)-like GUT. In SO(10)-like GUTs, also the top Yukawa coupling must unify with them, which requires adjusting the ratio of vacuum expectation values of the two MSSM Higgs doublets. In any viable GUT, one should verify unification of     the 3 × 3 Yukawa coupling matrices rather than just restrict to considering the third generation. It is well known that no automatic unification occurs for the first two generations. However, since the corresponding Yukawa couplings are small, considerable contributions to them can arise from various sources. One may introduce higher-dimensional Higgs field representations, higher-dimensional operators at the GUT scale, or flavour-non-diagonal soft supersymmetry breaking terms that cause threshold effects at M_SUSY in the renormalization group evolution. Studying the latter option is the main task for the proposed Ph.D. project. In particular, it should be verified whether threshold effects at M_SUSY alone could lead to proper Yukawa matrix unification, without violating constraints from the observed flavour-changing processes in the quark and neutrino sectors. This important question has received relatively little attention in the past. A new analysis including the most recent experimental constraints from the B-factories, neutrino facilities and the LHC is necessary. The work is going to be a part of the common effort of many researchers to answer the basic question: “What is the simplest supersymmetric GUT that works?”. A student is expected to collaborate on the problem described above with the research staff of CERN and Karlsruhe Institute of Technology, in particular with our main partners there (C. Grojean and U. Nierste, respectively).

Stays abroad:  between 6 and 24 months total at both partner institutions

Foreign partners: Dr. C. Grojean, CERN, Geneva, Switzerland, and Prof. U. Nierste, Karlsruhe Institute of Technology, Karlsruhe, Germany

Subject of thesis: F-theory unification and its implications to the LHC physics, supervised by prof. UW dr hab. Jacek Pawełczyk, University of Warsaw

Outline of the project: Data from LHC (Large Hadron Collider in CERN, Geneva) experiments are expected to provide numerous hints for the structure of unification theory of all fundamental forces. Among the most attractive possibilities are the so-called Grand Unified Theory (GUT) models and their recently revived string theory version, i.e. F-theory GUT’s. The aim of the project is to study properties of the F-theory GUT’s as the candidate for the unification model. This will involve analysis of the structure of the F-theory GUT's and its ability to solve some theoretical problems of the particle physics such as supersymmetry breaking and generation of scales for various terms of the effective low energy supersymmetry theory. Besides the theoretical issues the project aims to find preliminary answers to some phenomenological consequences for the LHC physics. This includes searching for, e.g., exotic matter, possible new gauge interaction, and supersymmetric particles. Some issues relating particle physics and cosmology (e.g. searching for dark matter candidates) are also planned to study. Members of our research team have a proper background in theoretical issues of string model building for the unification program as well as good background in phenomenological aspects of these models. Emilian Dudas is a world recognized expert in string theory and its application to particle physics and unification. During the stay at Ecole Polytechnique a student will learn advanced methods of both theoretical and phenomenological analysis of the string unification models.

Stays abroad: Ecole Polytechnique, 2x4 = 8 months

Foreign partner: Prof. E. Dudas, Ecole Polytechnique, Centre de Physique Theorique (CphT), Palaiseau Cedex, France

Subject of thesis: Knots as possible excitations of quantum Yang-Mills fields, supervised by prof. Jerzy Lewandowski, University of Warsaw

Outline of the project: Faddeev described a model where knot-like structure of a solution guarantees its stability. It is a type of nonlinear sigma-model where the nonlinear field takes values in two-dimensional sphere. The solutions are minimizing energy functional proposed by Faddeev. It is a linear combination of traditional sigma-model Hamiltonian and Maxwell energy of magnetic field. Using this model, Faddeev has recently pointed out that there could be a connection between knotted solitons and quantum Yang-Mills field. He stated the hypothesis that particles of Yang-Mills field could be knot-like solitons. This project is aimed to develop the idea proposed by Faddeev. It is of great importance to particle physics and to mathematical physics, it may shed some light on the "Mass-Gap" problem, one of the famous Clay Millenium Problems. The research will involve constant cooperation with St. Petersburg Department of Steklov Mathematical Institute. During four stays lasting 6 months each, a student will: learn the quantum theory of solitons and consult the project with Professor Faddeev in Steklov Mathematical Institute. Professor Ludwig D. Faddeev, a mathematical physicist is famous for the discovery of Faddeev-Popov ghosts and Faddeev equations. His work led to the invention of quantum groups.

Stays abroad: SMI, 4x6=24 months.

Foreign partner: Prof. L.D. Faddeev, St. Petersburg Department of Steklov Mathematical Insitute, Russia

Subject of thesis: Effective low-energy theories from the Randall-Sundrum model with soft branes, supervised by prof. Bohdan Grządkowski, University of Warsaw

Outline of the project: The Standard Model (SM) of electroweak and strong interactions has been verified up to an impressive precision by many experiments. Nevertheless, it is commonly believed that it is only an effective low-energy approximation of some unknown, more fundamental theory. The model suffers from a number of basic drawbacks:

• the hierarchy problem,
• lack of a dark matter (DM) candidate,
• the strong CP problem,
• no explanation for dark energy.

Some of the above problems could be attacked assuming the existence of 5-dimensional space-time with 5th dimension smoothly compactified. The goal of this project is to investigate 5-dimensional models with both gravity and multiple scalar fields propagating in the 5-dim bulk, such that classical (background) solutions of field equations would describe kink-like periodic functions while the metric tensor would have Randall-Sundrum (RS) type warping towards the 5th dimension. Kinks corresponding to localized energy are suppose to constitute branes necessary within the standard RS setup. In that scenario singularities (caused by infinitely thin branes) appearing in the RS model would be replaced by smooth soft branes made of scalar fields.

The following specific issues could be investigated within this project:

• Determination of potentials for scalar fields for which kink-like periodic solutions (scalar background) exist in the presence of non-minimal couplings to gravity.
• Stability of background solutions for a system of several scalar fields coupled to gravity.
• Cosmology with soft branes.
• Localization of fermions in the extra dimension.

The issue no. 1 has been already initiated together with prof. Jose Wudka from University of California Riverside, therefore a student visiting Riverside could easily join the project. A student is expected to spend between 6 and 24 months at both partner institutions (combining time spent at University of California Davis and Riverside). A student will have a chance to work on the research project specified in this application either with the counterpart researchers (J.Gunion and J.Wudka, respectively) or with other faculty members.

Stays abroad: UCD and UCR, 6 to 24 months

Foreign partners: Prof. J. Gunion, University of California Davis, USA and Prof. J. Wudka, University of California Riverside, USA

Subject of thesis: Multi-singlet extensions of the Standard Model, supervised by prof. Bohdan Grządkowski, University of Warsaw

Outline of the project: The goal of this project is to investigate the simplest extensions of the Standard Model (SM) which would ameliorate the hierarchy problem and possibly offer a candidate for DM, while preserving all the successes of the SM. The approach we propose is very pragmatic, so we would extend the SM in a simplest manner which guarantees the cancellation of quadratic divergences at the one-loop level by adding a number of scalars that are singlets under the SM gauge symmetry [see B. Grzadkowski and J. Wudka, Phys. Rev. Lett. 103, 091802 (2009)]. Since higher loop contributions to the quadratic divergence remain non-vanishing, therefore the solution we propose to investigate is applicable only below certain UV cutoff of the order of few TeV. Nevertheless, since the SM cutoff is as low as about 600 GeV, the simple model we propose constitutes a substantial increase of the region of validity for the model. To some extend the multi-singlet scalar extensions are also motivated by so called unparticles, a scenario which recently attracted a lot of attention after being proposed by Georgi. It has been conjectured that unparticles could be "decomposed" into an infinite series of extra degrees of freedom, e.g. gauge singlet scalars, as in our proposal. It turned out that scalar singlets provides candidates for DM. Of course, the scenario considered here requires some amount of fine tuning between parameters, nevertheless the fine tuning is less dramatic than in the SM. If the proposed extension is indeed realized in Nature, some unknown UV completion of the model is required, however its typical scale is of the order of few TeV.

Within this project the following issues could be investigated:

• Leptogenesis in the presence of singlets.
• Cosmological consequences of the presence of singlets.
• Electroweak phase transitions with scalars.
• Existing experimental constraints on multi-scalar extension of the SM.
• LHC tests of the multi-scalar extension of the SM.
• Multi-doublet extensions of the SM.

The 4th issue has been already initiated together with prof. John Gunion from the University of California Davis, therefore a student visiting Davis could easily join the project. A student is expected to spend between 6 and 24 months at both partner institutions (combining time spent at University of California Davis and Riverside). A student will have a chance to work on the research project specified in this application either with the counterpart researchers (J.Gunion and J.Wudka, respectively) or with other faculty members.

Stays abroad: UCD and UCR, 6 to 24 months

Foreign partners: Prof. J. Gunion, University of California Davis, USA and Prof. J. Wudka, University of California Riverside, USA

Subject of thesis: Heat kernels in the study of quantum spacetimes, supervised by prof. Jerzy Kowalski-Glikman, University of Wrocław

Outline of the project: Doubly-special relativity is one of many theoretical approaches to quantum gravity, initially proposed by Giovanni Amelino-Camelia in 2002. It is based on an assumption, that along with speed of light, there is another physical constant (namely the Planck energy), that on a scale comparable to it the "ordinary" physics breaks down. This poses a need for modification (or "deformation") of the symmetry group of the theory, and the proposed structure of spacetime as well. A well-established mathematical tool to probe this structure is a heat kernel - a fundamental solution to the heat dissipation equation. The exact form of the kernel depends heavily on the space on which the equation is solved and thus may be used to infer key properties of the space. We plan to investigate them for a gamut of quantum spacetimes, with emphasis on the key example of kappa-Minkowski, being the most natural deformation of the ordinary special relativistic Minkowski spacetime. Part of the work will be conducted in the University of Utrecht during six-month-long stays, preferably two or three, depending on actual needs. During these periods the student will learn the theory of Hopf algebras and Hopf spaces and discuss the project with the UU staff.

Stays abroad: UU, 3x6=18 months

Foreign partners: Dr. M. Arzano, Universiteit Utrecht, the Netherlands

Subject of thesis: Applications of the spin networks and Spin Foam Models in Quantum Field Theory and quantum gravity, supervised by prof. Jerzy Lewandowski, University of Warsaw

Outline of the project: Spin networks and spin foam models are new tools of modern quantum theory. The quantum states of gauge potential can be represented by Penrose’s spin networks. After Ponzano-Regge and Rovelli, we understand that a time evolution of those quantum states should be characterized by a suitable spin foam model. Those models are known in the cases of the Chern-Simons theory and the lower dimensional gravity. However a correct model describing 4-dimensional quantum gravity has not been found yet. The aim of this project is to investigate the applications of spin networks and spin foams in the quantum theory of gravity with special attention to cosmological models. The research includes quantum gravity in terms of the Ashtekar variables. The research will involve constant cooperation with Université de la Méditerranée Centre de Physique Théorique in Marseille, France. During three stays lasting 3 months each, a student will: learn the Spin Foam Models methods at Centre de Physique Théorique in Marseille. Prof. Jerzy Lewandowski is one of the main contributors to formulation and development of Loop Quantum Gravity. Prof. Rovelli is one of the leaders of quantum gravity and pioneers in Loop Quantum Gravity.

Stays abroad: UdlM, 3x3=9 months

Foreign partners: Prof. C. Rovelli, Université de la Méditerranée Centre de Physique Théorique, Institut Universitaire de France, Marseille, France