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## Proposals for Master or PhD thesis at LPTHE

### Challenges in supersymmetric theories of fields and strings

*Advisor: Ignatios Antoniadis*

The last decade has been very important for our understanding of the Universe. The discovery of the Higgs boson at the Large Hadron Collider at CERN has completed the searches for the building blocks of the Standard Model (SM) of particle physics. On the other hand, recent cosmological observations have confirmed the SM of cosmology. Measurements have allowed establishing the content of our Universe: besides the visible matter, there is a large amount of dark matter and dark energy. Moreover, the recent discovery of gravitational waves has opened a whole new way of perceiving the Universe. Despite this success of our present theories, the Standard Models of particle physics and cosmology and General Relativity, several fundamental questions emerged and have become of central importance for research in fundamental physics. Those relevant to the proposed thesis are:

The LHC has not shown yet any signal of new physics beyond the SM. A well motivated extension is based on supersymmetry that relates bosons and fermions, providing a dark matter candidate and explaining the stability of the mass hierarchy problem. What is the role of supersymmetry in Nature and what is its breaking scale?

What is the origin of inflation and what is the inflation field: a fundamental scalar, or composite, or an effective degree of freedom? Are there associated symmetries protecting its mass? What determines the initial conditions for inflation?

What is the nature of dark energy? Is it a cosmological constant or the effect of a dynamical field? What makes it so small?

What is the origin of the very different scales appearing in particle physics, gravitation and cosmology? Is the physics associated to these scales independent or are there connections due to the same underlying theory?

String theory has been proposed as the candidate to describe gravity at high energies where quantum effects begin to become important. It ought to shed light on the dynamics of the early Universe. Two important ingredients of string theory, necessary for its theoretical consistency, are extra dimensions and supersymmetry. In fact, string (or M-) theory appears in a few forms living in ten (or eleven) dimensions. Unfortunately, at the present stage of knowledge, going from ten or eleven to four dimensions leads to an extremely large number of vacua. The presence of this vast landscape of ground states for string theory weakens its predictive power. Still, the question whether there exist any de Sitter vacua amongst the plethora of possibilities is a long-standing issue and a subject of an ongoing debate today.

The expected duration of the thesis is three years. During the first months, the candidate should rather study the literature in these highly competitive subjects, in order to improve her/his level and to be able to choose the precise research direction depending on personal interests.

A Master internship is possible, prior to the start of the PhD thesis.

### Gravitational waves and BSM physics

*Advisor: Karim Benakli*

Gravitational waves detected on earth might have been produced a long time ago and have traveled a long way through space. Therefore they provide a new mean for the observation of the early universe, along with electromagnetic radiations. The spectrum of gravitational waves depends both on the production mechanism and on the content of the universe it crossed. The subject of this thesis is to continue the investigation of the form and kind of information on physics beyond the Standard Model of particle physics that can be obtained from detection of gravitational waves at different wavelengths.

### Phenomenology of Dark Matter Indirect Detection

*Advisor: Marco Cirelli*

*Format: Master 2 internship + PhD thesis project*

*Timing: Internship in Spring 2020, PhD starting in Fall 2020*

About 85% of the matter in the Universe is in the form of an unknown substance dubbed Dark Matter (DM). While some of its general properties are known, its actual nature is still undetermined. The most popular hypothesis is that it consists of a new, yet-to-be-discovered elementary particle. One of the possible strategies to investigate it is via the so-called Indirect Detection (ID): studying the possible excesses in cosmic rays that could produced by the annihilations (or decays) of DM particles in the galactic halo, and comparing them with the theoretical predictions from particle physics models.

Within this broad context, the proposed PhD project will proceed in different stages. The first part of the work will consist in extending and upgrading a set of numerical tools used in the DM ID studies (PPPC4DMID, based on arXiv:1012.4515). After an initial study of the basic concepts in the literature, this part will be rather technical and will require familiarizing with the Mathematica software and other numerical tools. The second part will consist in exploiting the upgraded tools and applying them to the actual physics searches, including the comparison with data from cosmic ray experiments. Different directions are here possible, concerning gamma-rays, charged cosmic rays or neutrinos. The choice will be dictated by the emergence of possible new results and by the interest in the community.

Following the typical course, a (Master 2) internship lasting a few months during Spring 2020 is strongly encouraged. In this period the student will familiarize with the basics of the physics and with some numerical tools. Subject to mutual agreement, the student can then apply for a PhD fellowship (from the local Doctoral School or from other sources) and, if successful, start the PhD in Fall 2020, for a duration of 3 years.

Candidates should send by email to marco.cirelli_at_gmail.com: i. their CV, ii. a transcript of their academic records, iii. a short description of their interests (optional, and in any case no longer than 1 page). They should also arrange for 1 or 2 short letters of recommendation to be sent to the same address, by scientists familiar with their studies and academic record.

### Pushing the precision frontier of LHC physics: Automating QCD resummation for new physics

*Advisor: Benjamin Fuks, Co-advisor: Hua-Sheng Shao*

The Standard Model of particle physics is an extremely successful theory, with (almost) all observations performed so far perfectly matching the predictions. However, the present experimental status also reveals several of the conceptual issues and practical limitations of the Standard Model, like the absence of a candidate for dark matter or the hierarchy problem. The Standard Model is therefore acknowledged as an effective theory that should originate from a more fundamental one yet to be discovered, and new phenomena are expected at energies well below the Planck scale. Whilst there are currently numerous intriguing features that provide hints that new physics could be accessible at energies that are already probed, none of these are yet significant enough to exclude the standard paradigm. However, as more data is being collected, we have reason to be optimistic towards the close future.

One interesting avenue in the searches for new physics relies on indirect probes in which precision theoretical predictions are confronted to accurate experimental measurements. The state-of-the-art for new physics predictions for the LHC consists in Monte Carlo simulations in which matrix elements including the next-to-leading order corrections driven by quantum chromodynamics (QCD) are matched with parton showers. While the accuracy of parton shower is quite limited so far, QCD resummation procedure provides a systematic way to improve it. In more details, fixed-order QCD perturbative computations are only justified when the perturbative series is controlled by a small expansion parameter. Close to the production threshold or when QCD emission are soft and/or collinear, large logarithmic terms need to be resummed. Whilst such a resummation can be handled through parton showers, its accuracy is limited so that analytical computations are in order to provide a better description at the hard-scattering level.

This thesis fits within this context and aims to automate perturbative QCD resummation calculations for various observables relevant for the LHC, both in the framework of the Standard Model and for new physics. The planned research will extend two existing programs developed at the LPTHE and that are widely used in the high-energy physics community, namely MADGRAPH5_aMC@NLO [1] and RESUMMINO [2]. Whilst we plan to start studying standard candles (total rates, invariant mass and transverse-momentum distributions of one or more final state particles) in the Standard Model, phenomenological applications to new physics will be conducted later on. We indeed plan to focus both on well-motivated ultraviolet-complete models (such as models featuring a strong dynamics at a high-energy scale or supersymmetric models) and effective field theories extending the Standard Model by higher-dimensional operators.

The technical part of the project consists in understanding how next-to-leading order calculations in QCD work and in devising an efficient method to extract the components allowing for performing all-order QCD resummation. Whilst a first training on the Standard Model and supersymmetry for which analytical results exist will be achieved, generalisation to any process from any theory will be foreseen in a second step. The deliverable consists in the building of a plugin linking MADGRAPH5_aMC@NLO and RESUMMINO, so that any physicist could compute precision predictions for any model. Moreover, tables of total and differential cross sections relevant for LHC and future collider physics will be provided, as this is known as relevant inputs for the high-energy physics community.

Within this project, the candidate is expected to develop a deep knowledge of new physics models and phenomenology, as well as acquire strong computing skills in QCD. Achieving the predefined goals will allow the candidate to obtain a strong expertise both in the development and in the usage of various tools widely used in our community, which is a valuable expertise for most research groups in the world.

[1] J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, H.S. Shao, T. Stelzer, P. Torrielli and M. Zaro, *The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations*, JHEP 1407 (2014) 079.

[2] B. Fuks, M. Klasen, D.R. Lamprea and M. Rothering, *Precision predictions for electroweak superpartner production at hadron colliders with Resummino*, Eur. Phys. J. C 73 (2013) 2480.

### Perturbative and non-perturbative aspects of three-dimensional gauge-field theories

*Advisor: Sofian Teber*

One of the most fascinating and challenging problems of theoretical physics is the understanding of the origin of the mass of particles. Historically, according to the textbook [1], it is probably Landau, Abrikosov and Khlatnikov who first suggested that a fermion mass may be dynamically generated in quantum gauge-field theories; in their 1956 paper [2], they wrote: “it can evidently be supposed that... the mass of an electron is of wholly electromagnetic origin”; they also recognized that such a phenomenon is beyond the reach of simple perturbation theory. Interestingly, it is within the field of condensed matter physics that the first example of a theory displaying dynamical symmetry breaking (DSB) was given: the Bardeen-Cooper-Schrieffer theory of superconductivity (1957) whereby a gap in the fermion spectrum is dynamically generated due to fermion pairing. Soon after (1960), Nambu realized that the particle physics counterpart of this phenomenon was the dynamical generation of a fermion mass. Since then, there has been extensive theoretical work carried out to understand DSB both in non-relativistic and relativistic models. To this day, the understanding of such complicated phenomena in even-, e.g., (3 + 1)-, dimensional gauge field theories such as QED4 and QCD4 is still incomplete.

In the 80s, the study of simpler models, such as QED in (2 + 1)-dimensions or QED3, was advocated by Pisarski [3]. Since then, this model has attracted considerable attention because it shares many features with QCD4 (asymptotic freedom and confinement). A salient feature of the model is that it displays dynamical chiral (or flavour) symmetry breaking when the number of fermion flavours, N, is below a critical value, Nc; for N < Nc a dynamical mass is generated. Of interest is, for example, to compute the precise value of Nc [4]. Recently, this has become a very hot topic again attracting the attention of physicists from different communities (from condensed matter physics to string theory), see, e.g., [5, 6, 7, 8]. One of the most robust prediction is based on a recent analytic solution of next-to-leading order (1/N2) Schwinger-Dyson equations, see [9] for a review. This is a promising field-theoretic achievement opening the way to further important developments with respect to variants of QED3 and, eventually, to higher dimensional models where many challenging problems remain to be solved.

The subject of the PhD thesis will be devoted to the field theoretic study of (strongly coupled) three-dimensional gauge-field theories. The central issues are to explore the perturbative structure of three-dimensional gauge theories which is more subtle and less well-known than the one of four-dimensional models; and to apply/develop methods consisting of using the perturbative data as an input to understand non-perturbative features of the model. Applications will be related (but not limited to) to condensed matter physics of planar systems. Familiarity with advanced multi-loop techniques is not required and proper training on these techniques will be given. The interested applicant should however have a basic knowledge of relativistic quantum field theory, e.g., at the level of ICFP Theoretical Physics Master 2 and, preferably, good programming skills (C, Python).

The expected duration of the PhD thesis is three years. A Master 2 internship on the subject is also possible before starting the thesis.

Key words: quantum field theory, three-dimensional models, renormalization group, radiative corrections, Feynman diagrams, multi-loop calculations, Schwinger-Dyson equations, large-N approximation, dynamical mass generation, planar condensed matter physics systems.

References

[1] V. A. Miransky, *Dynamical symmetry breaking in quantum field theories*, Singapore, Singapore: World Scientific (1993).

[2] L. D. Landau, A. Abrikosov and I. M. Khalatnikov, *On the quantum theory of fields*, Nuovo Cimento 3 80 (1956).

[3] R. D. Pisarski, *Chiral Symmetry Breaking in Three-Dimensional Electrodynamics*, Phys. Rev. D 29 (1984) 2423.

[4] T. Appelquist, D. Nash and L. C. R. Wijewardhana, *Critical Behavior in (2+1)-Dimensional QED*, Phys. Rev. Lett. 60 (1988) 2575

[5] S. Giombi, G. Tarnopolsky and I. R. Klebanov, *On CJ and CT in Conformal QED*, JHEP 1608 (2016) 156

[6] I. F. Herbut, *Chiral symmetry breaking in three-dimensional quantum electrodynamics as fixed point annihilation*, Phys. Rev. D 94 (2016) 025036

[7] V. P. Gusynin and P. K. Pyatkovskiy, *On the critical number of fermions in three-dimensional QED*, arXiv:1607.08582 [hep-ph]

[8] A. V. Kotikov and S. Teber, *Critical behaviour of (2 + 1)-dimensional QED: 1/Nf-corrections in an arbitrary non-local gauge*, arXiv:1609.06912 [hep-th]

[9] S. Teber, *Field theoretic study of electron-electron interaction effects in Dirac liquids*, arXiv:1810.08428 [cond-mat.mes-hall].