# Krzysztof Sliwa: research activities

email : Krzysztof Sliwa

conference presentations and invited talks : Krzysztof Sliwa's talks and presentations

# Tufts ATLAS Group

The Tufts University Elementary Particles Group joined ATLAS in 1994. After deciding to focus on the ATLAS end-cap muon system, the Tufts Group was very active in initial physics simulations and in the construction and testing of the first MDT end-cap muon chamber, with Prof. Mann leading the latter effort. The Tufts Group's high precision computer-controlled machine shop served as a R&D lab for BMC, and later manufactured thousands of small, very precise and custom-designed pieces needed for the MDT chambers and for the entire muon alignment system. At the same time, the Tufts ATLAS Group was very active in studying and planning the world-wide data analysis and reconstruction, needed for the world-wide collaboration like ATLAS. MONARC, a very successful LHC project created jointly by Tufts and Caltech, provided the first realistic modelling of such a world-wide, distributed computer system.

The Tufts ATLAS Group consisted of two faculty - Pierre-Hugues Beauchemin, who joined the group in 2011, and Krzysztof Sliwa. The Tufts Group performed the first analyses of the muon test-beam data, and continued to work on the muon reconstruction software. The Tufts ATLAS Group developed the MuonTrackingGeometry, a completely new description of the entire muon system, including the active and the passive elements, which allows the use of ATLAS common tracking tools in muon reconstruction. The MuonTrackingGeometry is also an essential component of FatRas, a new, fast ATLAS track simulation which models the detector response at the hit level. Tufts ATLAS Group was responsible for simulation of the entire muon system in FatRas, which became part of the Integrated Simulation Framework, a new fast simulation of the entire ATLAS detector.

In physics studies, The Tufts ATLAS Group was involved in W+jets and Z+jets analyses (prof. Beauchemin), top physics, Higgs boson studies (prof. Sliwa), and physics beyond the Standard Model - non-standard Higgs searches, SUSY, extra dimensions et cetera. After discovering the Higgs boson in 2012, the main objective of the LHC analyses is to find out whether the new particle is the Minimal Standard Model Higgs, or some other kind. It would be really exciting if the latter were true. There is also a possibility that, with increased energy of the proton-proton collisions, completely new particles will be found. Here, studies of top quarks are extremely important, as top quarks will constitute the most important background for almost any final states due to “new physics” and have to be understood very well.

The Tufts ATLAS Group has developed a new multidimensional and multiclass analysis technique - an event classifier based on Support Vector Machines (SVM). This novel analysis method, originated by Dr. Ben Whitehouse while working towards his Ph.D. with Prof. Sliwa, allows to take into account simultaneously a large number of physics observables, including correlations between them. In contrast with other multivariate methods, SVM has a sound mathematical foundation in Mercer Theorem. Although SVM were used in other research fields in the past, Tufts was the first group to apply it in collider physics. We applied this new analysis technique to the ATLAS Collaboration data in measurements of the production rate of top quarks in proton-proton collisions at 7 TeV and 8 TeV at LHC. A paper based on our multidimensional and multiclass analysis technique "Measurement of the tt cross section in the lepton+jets channel at 7 TeV using support vector machines" has been published in Phys. Rev. D. arXiv:2022.00571

I have decided not to take part in Run 3 at the LHC, and my involvement with the ATLAS Collaboration will not extend beyond Fall 2023.

I am also a member of the MoEDAL Collaboration at CERN, a small, dedicated, experiment looking for magnetic monopoles. All searches so far were negative. I will continue to take part in the LHC Collider program with the MoEDAL Collaboration beyond 2023.

faculty: Pierre-Hugues Beauchemin, Krzysztof Sliwa

# other activities

I am also interested in topology, differential geometry and other areas of modern mathematics, which I have studied to gain a deeper insight into the meaning of quantum gauge theories, the origin of mass and the structure of space-time, matter and all interactions, including gravity.

In the last few years, I've embarked on studies of geometry and topology of the Universe. In the Standard Cosmological Model (SCM), the starting point is an interpretation of the observed increase of redshifts with the distance of far-away objects as a result of expansion of the Universe. Acceptance of this hypothesis led to the ideas of Big Bang and the Standard Model of Cosmology. Universe locally looks flat, its geometry is R^{1} x R^{3}, or the Minkowski "world". However, interestingly, there is another possibility. Irving Ezra Segal, a mathematician and a mathematical physicist, showed in the second part of XX-th century that the same axioms of physical symmetries - global isotropy and homogeneity of space and time, and its causality properties - are satisfied not only by Minkowski spacetime, but also by a Universe whose geometry is R^{1} x S^{3}. Segal's starting point was to extend the 10 parameter Poincare group to 15 parameter conformal group as the candidate for the underlying symmetry group of physics, as the Maxwell equations are conformally invariant. Locally, such Universe is indistinguishable from the flat Minkowski spacetime. It is the geometry of Einstein static Universe, which Einstein abandoned after the interpretation of the increase of redshift with distance became universally accepted as evidence for expanding Universe. Its spatial part is a 3-sphere, the surface of the unit sphere in 4-dimensional Euclidean space. The redshift in Segal's model arises in a geometric way analogously a distortion which appear when making maps using stereographic projection from S^{2}, the surface of a sphere in 3-dimensional Euclidean space, onto a flat R^{2}. Segal's model provides a verifiable prediction for the dependence of this geometric redshift on the propagation time, or the geodesic distance in S^{3}. In 2017, I have decided to compare the data from the latest redshift catalogues available online with predictions of Segal's cosmology and SCM. The comparison, although in principle very simple, is non-trivial. For more distant objects, one can only estimate the distance using various proxies, for example magnitude, if one assumes that the chosen sources have the same absolute luminosity. Surprisingly, Segal's model has not yet been falsified with the currently available data. The magnitude-redshift data, m(z), for supernovae agree very well with SCM, but it also agrees with Segal's model. For quasars, the agreement is perhaps better with the latter. The number of observed galaxies as a function of redshift, N(< z), is another observable. Assuming that galaxies are uniformly distributed in the Universe, their number in a given fixed angular field of view is proportional to the enclosed volume, and dependence of this volume on the manifold distance is sensitive to the geometry of the Universe. Two Tufts undergraduate students, Maxwell Kaye and Nathan Burwig, joined me in this analysis. We examined the data from several Hubble Deep Fields, and found that the number of observed galaxies as a function of redshift is in very good agreement with Segal's model. Following Segal's original idea that the CMB appears unavoidably as residual light when considering solutions to Maxwell equations travelling over multiple trips around the spatially closed R^{1} x S^{3} Universe, I showed in February 2022 that the observed value of the CMB temperature can indeed be naturally explained. It is also quite likely that the observed structure in the power spectrum of CMB fluctuations can be explained as being due to hierarchy of large scale structures in the Universe - galaxy clusters, superclusters et cetera. Based on these analyses, Max and Nathan wrote Senior Honors Theses at Tufts.

We plan to further study these fundamental questions about the topology and geometry of our Universe. We would like first to reanalyze the updated redshift catalogues and Deep Fields data. We will also try to find new observables that could differentiate between R^{1} x R^{3} versus R^{1} x S^{3} geometries. Also, rather than to study independently the magnitudes and the number of observed galaxies as a function of redshift, m(z) and N(< z), it would be preferable to perform a simultaneous fit to those observables. Augmented with the new data from the James Webb Space Telescope (JWST), the new Deep Field catalogues may allow such analyses. Also, JWST data could provide more information about absorption, which additionally complicates the m(z) and N(<z) observations.

Interestingly, in a recent Nature paper based on JWST data, "A population of red candidate massive galaxies ∼600 Myr after the Big Bang" by Labbe et al, an observation of galaxies of uncharacteristically large mass, given their redshift, was reported. According to the current ideas about evolution of galaxies in expanding Universe, such objects are not expected so early after the Big Bang. Their presence is, of course, naturally explained in a static R^{1} x S^{3} Universe.

A short summary of results can be found in my talk: Tufts Colloquium September 22, 2023