Mathias Becker
We investigate a minimal neutrino portal dark matter (DM) model where a right-handed neutrino both generates the observed neutrino masses and mediates between the SM and the dark sector, which consists of a fermion and a boson. In contrast to earlier work, we explore regions of the parameter space where DM is produced via freeze-in instead of freeze-out motivated by the small neutrino Yukawa couplings in case of $\mathcal{O} \left( \mathrm{TeV} \right)$ heavy neutrinos. \\ For a non-resonant production of DM, its energy density is independent of the DM mass. Assuming a democratic coupling structure we find $M_N \approx 10 \, \mathrm{TeV}$. For the resonant production of DM, we find that it can be produced via freeze-in or freeze-out even with couplings of $\mathcal{O} \left( 10^{-5} \right)$. However, the measurement of the Lyman-$α$ forest rules out the feeble coupled freeze-out case completely, while the resonant freeze-in production is only viable for $m_{DM} \gtrsim 3 \, \mathring{keV}$.
Mathias Becker, Emanuele Copello, Julia Harz, Kirtimaan A. Mohan, Dipan Sengupta
The existence of a dark matter model with a rich dark sector could be the reason why WIMP dark matter has evaded its detection so far. For instance, colored co-annihilation naturally leads to the prediction of heavier dark matter masses. Importantly, in such a scenario the Sommerfeld effect and bound state formation must be considered in order to accurately predict the relic abundance. Based on the example of the currently widely studied $t$-channel simplified model with a colored mediator, we demonstrate the importance of considering these non-perturbative effects for correctly inferring the viable model parameters. We emphasize that a flat correction factor on the relic abundance is not sufficient in this context. Moreover, we find that parameter space thought to be excluded by direct detection experiments and LHC searches remains still viable. Additionally, we illustrate that long-lived particle searches and bound-state searches at the LHC can play a crucial role in probing such a model. We demonstrate how future direct detection experiments will be able to close almost all of the remaining windows for freeze-out production, making it a highly testable scenario.
Mathias Becker, Wei-Chih Huang
We propose a novel mechanism to realize two-component asymmetric dark matter of very different mass scales through bound state formation and late freeze-in decay. Assuming a particle-antiparticle asymmetry is initially shared by SM baryons and two dark matter components, we demonstrate that the existence of bound states formed by the heavy component can efficiently transfer the asymmetry from the heavy to the light component via late decay. In this case, the energy densities of the two components can be comparable, and the correct relic density is reproduced.
Mathias Becker, Dominik Döring, Siddhartha Karmakar, Heinrich Päs
We study the dark matter phenomenology of Standard Model extensions addressing the reported anomaly in the $R_K$ observable at one-loop. The article covers the case of fermionic singlet DM coupling leptophilically, quarkphilically or amphiphilically to the SM. The setup utilizes a large coupling of the new particle content to the second lepton generation to explain the $R_K$ anomaly, which in return tends to diminish the dark matter relic density. Further, dark matter direct detection experiments provide stringent bounds even in cases where the dark matter candidate only contributes a small fraction of the observed dark matter energy density. In fact, direct detection rules out all considered models as an explanation for the $R_K$ anomaly in the case of Dirac dark matter. Conversely, for Majorana dark matter, the $R_K$ anomaly can be addressed in agreement with direct detection in coannihilation scenarios. For leptophilic dark matter this region only exists for $M_\text{DM} \lesssim 1000 \, \mathrm{GeV}$ and dark matter is underabundant. Quarkphilic and amphiphilic scenarios even provide narrow regions of parameter space where the observed relic density can be reproduced while offering an explanation to $R_K$ in agreement with direct detection experiments.
Mathias Becker, Heinrich Päs
We discuss the leptonic flavor structure generated by a brane shifted extra dimensional seesaw model with a single right handed neutrino in the bulk. In contrast to previous works, no unitarity approximation for the $3 \times 3$ submatrix has been employed. This allows to study phenomenological signatures such as lepton flavor violating decays. A strong prediction of the model, assuming CP conservation, are the ratios of flavor violating charged lepton decay and Z decay branching ratios which are correlated with the neutrino mixing angles and the neutrino mass hierarchy. Furthermore, it is possible to obtain branching ratios for $μ\rightarrow e γ$ close to the experimental bounds even with Yukawa couplings of order one.
Mathias Becker, Emanuele Copello, Julia Harz, Carlos Tamarit
We study thermal corrections to a model of real scalar dark matter (DM) interacting feebly with a SM fermion and a gauge-charged vector-like fermion mediator. We employ the Closed-Time-Path (CTP) formalism for our calculation and go beyond previous works by including the full dependence on the relevant mass scales as opposed to using (non)relativistic approximations. In particular, we calculate the DM production rate by employing 1PI-resummed propagators constructed from the leading order term in the loop expansion of the 2PI effective action, beyond the Hard-Thermal-Loop (HTL) approximation. We compare our findings to commonly used approximation schemes, including solving the Boltzmann equation using momentum-independent thermal masses in decay processes and as regulators for $t$-channel divergences. We also compare with the result when employing HTL propagators and their tree-level limit. We find that the DM relic abundance when using thermal masses in the Boltzmann approach deviates between $-10\%$ and $+30\%$ from our calculation, where the size and sign strongly depend on the mass splitting between the DM candidate and the gauge-charged mediator. The HTL-approximated result is more accurate at small gauge couplings, only deviating by a few percent at large mass splittings, whereas it overestimates the relic density up to $25\%$ for small mass splittings. Calculations using tree-level propagators in the CTP formalism or semiclassical Boltzmann equations without scatterings underestimate the dark matter abundance and can lead to deviations of up to $-100\%$ from the 1PI-resummed result.
Mathias Becker, Francesco D'Eramo, Ville Vaskonen
We introduce a novel class of bosonic dark matter candidates that we dub wallions, featuring boundaries in field space. The wallion mass is exponentially suppressed when the separation between boundaries far exceeds their intrinsic width and remains radiatively stable under self-interactions. We study the early-universe evolution of wallions and the associated cosmological signatures. Finally, we show that instanton effects can dynamically generate field-space boundaries and discuss possible experimental probes once the wallion couples to Standard Model fields.
Mathias Becker, Kåre Fridell, Julia Harz, Chandan Hati
The mechanism behind the generation of the baryon asymmetry of the Universe (BAU) is one of the biggest open questions of (astro-)particle physics. Popular mechanisms to generate the observed baryon asymmetry include CP-violating out-of-equilibrium decays and scatterings of heavy particles. If these heavy non-relativistic particles feature long-range interactions, the formation of bound states can impact the generation of the baryon asymmetry. We outline the general conditions for when bound states are important for decay and scattering dominated baryogenesis and present the necessary Boltzmann equations for the first time. We demonstrate that bound states can impact baryogenesis in three different ways: They (i) strongly impact abundances of particles sourcing the BAU, (ii) act as a source term of the asymmetry, and (iii) mediate additional washout channels.
Mathias Becker, Emanuele Copello, Julia Harz, Jonas Lang, Yong Xu
We investigate the production of particle Dark Matter (DM) in a minimal freeze-in model considering a non-instantaneous reheating phase after inflation. We demonstrate that for low reheating temperatures, bosonic or fermionic reheating from monomial potentials can lead to a different evolution in the DM production and hence to distinct predictions for the parent particle lifetime and mass, constrained by long-lived particle (LLP) searches. We highlight that such scenario predicts parent particle decay lengths larger compared to using the instantaneous reheating approximation. Moreover, we demonstrate the importance of an accurate definition of the reheating temperature and emphasize its relevance for the correct interpretation of experimental constraints. We explore different models of inflation, which can lead to the considered reheating potential. We find that the extent to which the standard DM freeze-in production can be modified crucially depends on the underlying inflationary model. Based on the latest CMB constraints, we derive lower limits on the decay length of the parent particle and confront these results with the corresponding reach of LLP searches. Our findings underscore the impact of the specific dynamics of inflation on DM freeze-in production and highlight their importance for the interpretation of collider signatures. At the same time, our results indicate the potential for LLP searches to shed light on the underlying dynamics of reheating.
Jonathan L. Feng, Felix Kling, Mary Hall Reno, Juan Rojo, Dennis Soldin, Luis A. Anchordoqui, Jamie Boyd, Ahmed Ismail, Lucian Harland-Lang, Kevin J. Kelly, Vishvas Pandey, Sebastian Trojanowski, Yu-Dai Tsai, Jean-Marco Alameddine, Takeshi Araki, Akitaka Ariga, Tomoko Ariga, Kento Asai, Alessandro Bacchetta, Kincso Balazs, Alan J. Barr, Michele Battistin, Jianming Bian, Caterina Bertone, Weidong Bai, Pouya Bakhti, A. Baha Balantekin, Basabendu Barman, Brian Batell, Martin Bauer, Brian Bauer, Mathias Becker, Asher Berlin, Enrico Bertuzzo, Atri Bhattacharya, Marco Bonvini, Stewart T. Boogert, Alexey Boyarsky, Joseph Bramante, Vedran Brdar, Adrian Carmona, David W. Casper, Francesco Giovanni Celiberto, Francesco Cerutti, Grigorios Chachamis, Garv Chauhan, Matthew Citron, Emanuele Copello, Jean-Pierre Corso, Luc Darmé, Raffaele Tito D'Agnolo, Neda Darvishi, Arindam Das, Giovanni De Lellis, Albert De Roeck, Jordy de Vries, Hans P. Dembinski, Sergey Demidov, Patrick deNiverville, Peter B. Denton, Frank F. Deppisch, P. S. Bhupal Dev, Antonia Di Crescenzo, Keith R. Dienes, Milind V. Diwan, Herbi K. Dreiner, Yong Du, Bhaskar Dutta, Pit Duwentäster, Lucie Elie, Sebastian A. R. Ellis, Rikard Enberg, Yasaman Farzan, Max Fieg, Ana Luisa Foguel, Patrick Foldenauer, Saeid Foroughi-Abari, Jean-François Fortin, Alexander Friedland, Elina Fuchs, Michael Fucilla, Kai Gallmeister, Alfonso Garcia, Carlos A. García Canal, Maria Vittoria Garzelli, Rhorry Gauld, Sumit Ghosh, Anish Ghoshal, Stephen Gibson, Francesco Giuli, Victor P. Gonçalves, Dmitry Gorbunov, Srubabati Goswami, Silvia Grau, Julian Y. Günther, Marco Guzzi, Andrew Haas, Timo Hakulinen, Steven P. Harris, Julia Harz, Juan Carlos Helo Herrera, Christopher S. Hill, Martin Hirsch, Timothy J. Hobbs, Stefan Höche, Andrzej Hryczuk, Fei Huang, Tomohiro Inada, Angelo Infantino, Ameen Ismail, Richard Jacobsson, Sudip Jana, Yu Seon Jeong, Tomas Ježo, Yongsoo Jho, Krzysztof Jodłowski, Dmitry Kalashnikov, Timo J. Kärkkäinen, Cynthia Keppel, Jongkuk Kim, Michael Klasen, Spencer R. Klein, Pyungwon Ko, Dominik Köhler, Masahiro Komatsu, Karol Kovařík, Suchita Kulkarni, Jason Kumar, Karan Kumar, Jui-Lin Kuo, Frank Krauss, Aleksander Kusina, Maxim Laletin, Chiara Le Roux, Seung J. Lee, Hye-Sung Lee, Helena Lefebvre, Jinmian Li, Shuailong Li, Yichen Li, Wei Liu, Zhen Liu, Mickael Lonjon, Kun-Feng Lyu, Rafal Maciula, Roshan Mammen Abraham, Mohammad R. Masouminia, Josh McFayden, Oleksii Mikulenko, Mohammed M. A. Mohammed, Kirtimaan A. Mohan, Jorge G. Morfín, Ulrich Mosel, Martin Mosny, Khoirul F. Muzakka, Pavel Nadolsky, Toshiyuki Nakano, Saurabh Nangia, Angel Navascues Cornago, Laurence J. Nevay, Pierre Ninin, Emanuele R. Nocera, Takaaki Nomura, Rui Nunes, Nobuchika Okada, Fred Olness, John Osborne, Hidetoshi Otono, Maksym Ovchynnikov, Alessandro Papa, Junle Pei, Guillermo Peon, Gilad Perez, Luke Pickering, Simon Plätzer, Ryan Plestid, Tanmay Kumar Poddar, Mudit Rai, Meshkat Rajaee, Digesh Raut, Peter Reimitz, Filippo Resnati, Wolfgang Rhode, Peter Richardson, Adam Ritz, Hiroki Rokujo, Leszek Roszkowski, Tim Ruhe, Richard Ruiz, Marta Sabate-Gilarte, Alexander Sandrock, Ina Sarcevic, Subir Sarkar, Osamu Sato, Christiane Scherb, Ingo Schienbein, Holger Schulz, Pedro Schwaller, Sergio J. Sciutto, Dipan Sengupta, Lesya Shchutska, Takashi Shimomura, Federico Silvetti, Kuver Sinha, Torbjörn Sjöstrand, Jan T. Sobczyk, Huayang Song, Jorge F. Soriano, Yotam Soreq, Anna Stasto, David Stuart, Shufang Su, Wei Su, Antoni Szczurek, Zahra Tabrizi, Yosuke Takubo, Marco Taoso, Brooks Thomas, Pierre Thonet, Douglas Tuckler, Agustin Sabio Vera, Heinz Vincke, K. N. Vishnudath, Zeren Simon Wang, Martin W. Winkler, Wenjie Wu, Keping Xie, Xun-Jie Xu, Tevong You, Ji-Young Yu, Jiang-Hao Yu, Korinna Zapp, Yongchao Zhang, Yue Zhang, Guanghui Zhou, Renata Zukanovich Funchal
Mathias Becker, Maria Jose Fernandez Lozano, Julia Harz, Carlos Tamarit
We present an improved calculation of the freeze-in production rate for scalar dark matter (DM) from a gauge-charged parent particle via a renormalizable interaction. Building on the previously developed 1PI-resummed framework to accurately capture the relevant regime $T \sim M$, we expand the analysis to include the Landau-Pomeranchuk-Migdal (LPM) effect, which contributes at leading order $g^2 T$ to the interaction rate in the ultra-relativistic limit. To this end, we derive an equation for the LPM rate of a scalar particle for the first time and combine it with the previous 1PI results, providing a new state-of-the art calculation. In contrast to the 1PI results, the LPM treatment neglects vacuum mass scales such that a phenomenological switch-off function between the ultra-relativistic and non-relativistic regime is required. We propose a new function motivated by a thermal loop contribution and compare it to other approaches in the literature, quantifying the resulting uncertainty of this method. Depending on the gauge coupling and mass splitting between DM and mediator particles, the LPM effect contributes between 1% and 27% to the relic density, with the impact increasing for larger gauge couplings and smaller mass splittings. Additionally, we compare our results to commonly used semi-classical Boltzmann approaches. For instance, when these include decays and scatterings regulated with thermal masses, we find deviations ranging from -30% to +20% depending on the mass splitting. Finally, we compare to results based on hard-thermal-loop (HTL) approximations.
Chiara Arina, Benjamin Fuks, Luca Panizzi, Michael J. Baker, Alan S. Cornell, Jan Heisig, Benedikt Maier, Rute Pedro, Dominique Trischuk, Diyar Agin, Alexandre Arbey, Giorgio Arcadi, Emanuele Bagnaschi, Kehang Bai, Disha Bhatia, Mathias Becker, Alexander Belyaev, Ferdinand Benoit, Monika Blanke, Jackson Burzynski, Jonathan M. Butterworth, Antimo Cagnotta, Lorenzo Calibbi, Linda M. Carpenter, Xabier Cid Vidal, Emanuele Copello, Louie Corpe, Francesco D'Eramo, Aldo Deandrea, Aman Desai, Caterina Doglioni, Sunil M. Dogra, Mathias Garny, Mark D. Goodsell, Sohaib Hassan, Philip Coleman Harris, Julia Harz, Alejandro Ibarra, Alberto Orso Maria Iorio, Felix Kahlhoefer, Deepak Kar, Shaaban Khalil, Valery Khoze, Pyungwon Ko, Sabine Kraml, Greg Landsberg, Andre Lessa, Laura Lopez-Honorez, Alberto Mariotti, Vasiliki A. Mitsou, Kirtimaan Mohan, Chang-Seong Moon, Alexander Moreno Briceño, María Moreno Llácer, Léandre Munoz-Aillaud, Taylor Murphy, Anele M. Ncube, Wandile Nzuza, Clarisse Prat, Lena Rathmann, Thobani Sangweni, Dipan Sengupta, William Shepherd, Sukanya Sinha, Tim M. P. Tait, Andrea Thamm, Michel H. G. Tytgat, Zirui Wang, David Yu, Shin-Shan Yu
This report, summarising work achieved in the context of the LHC Dark Matter Working Group, investigates the phenomenology of $t$-channel dark matter models, spanning minimal setups with a single dark matter candidate and mediator to more complex constructions closer to UV-complete models. For each considered class of models, we examine collider, cosmological and astrophysical implications. In addition, we explore scenarios with either promptly decaying or long-lived particles, as well as featuring diverse dark matter production mechanisms in the early universe. By providing a unified analysis framework, numerical tools and guidelines, this work aims to support future experimental and theoretical efforts in exploring $t$-channel dark matter models at colliders and in cosmology.
Mathias Becker, Wolfgang Konig
Consider an arbitrary transient random walk on $\Z^d$ with $d\in\N$. Pick $α\in[0,\infty)$ and let $L_n(α)$ be the spatial sum of the $α$-th power of the $n$-step local times of the walk. Hence, $L_n(0)$ is the range, $L_n(1)=n+1$, and for integers $α$, $L_n(α)$ is the number of the $α$-fold self-intersections of the walk. We prove a strong law of large numbers for $L_n(α)$ as $n\to\infty$. Furthermore, we identify the asymptotic law of the local time in a random site uniformly distributed over the range. These results complement and contrast analogous results for recurrent walks in two dimensions recently derived by Černý \cite{Ce07}. Although these assertions are certainly known to experts, we could find no proof in the literature in this generality.
Mathias Becker, Emanuele Copello, Julia Harz, Martin Napetschnig
In the universal framework of simplified $t$-channel dark matter models, the calculation of the relic abundance can be dominated by mediator annihilation when the dark matter and mediator masses are almost degenerate. We analyze four representative models with scalar and fermionic mediators, confront them with direct detection limits and highlight the differences and common features between them. The mediator annihilations are considerably enhanced by the Sommerfeld effect and bound state formation. Albeit their effect is subdominant in the coannihilation regime, excited bound state levels are included as well. We find that Sommerfeld and bound-state effects can lead to order one corrections to the constraints on the DM mass in the coannihilating regime, with the precise magnitude depending on the specific model realization. In addition we provide SE+BSF4DM, an intuitive and easy to use add-on to micrOMEGAs, allowing for an automated inclusion of these effects for a generic $t$-channel Dark Matter Model, which is publicly available on Github.
Mathias Becker, Julia Harz, Enrico Morgante, Cristina Puchades-Ibáñez, Pedro Schwaller
Previous computations of feebly interacting particle production have encountered issues with unphysical (negative) interaction rates at soft momenta. We address this problem by studying the production of Axion-Like Particles (ALPs) coupled to $U(1)$-gauge fields, employing the full form of 1PI-resummed gauge boson propagators. This approach avoids the need for matching or subtraction procedures, ensuring physically consistent results. We find that the ALP production rate remains positive across all momentum scales and identify the dominant production mechanisms. At soft ALP momenta ($p \lesssim g^2 T$), interactions involving two spacelike gauge bosons dominate the production rate, surpassing other channels by an order of magnitude. In particular, using the full gauge boson propagator suggests that at even softer momenta ($p \lesssim g^4 T$), production involving two timelike gauge bosons becomes significant, potentially exceeding other contributions by another order of magnitude. Using these insights, we update the thermal ALP abundance and refine the estimate of the average ALP momentum, providing important input for structure formation constraints on ALP dark matter in the keV mass range.
Georg Hille, Johannes Steffen, Max Dünnwald, Mathias Becker, Sylvia Saalfeld, Klaus Tönnies
This study's objective was to segment spinal metastases in diagnostic MR images using a deep learning-based approach. Segmentation of such lesions can present a pivotal step towards enhanced therapy planning and validation, as well as intervention support during minimally invasive and image-guided surgeries like radiofrequency ablations. For this purpose, we used a U-Net like architecture trained with 40 clinical cases including both, lytic and sclerotic lesion types and various MR sequences. Our proposed method was evaluated with regards to various factors influencing the segmentation quality, e.g. the used MR sequences and the input dimension. We quantitatively assessed our experiments using Dice coefficients, sensitivity and specificity rates. Compared to expertly annotated lesion segmentations, the experiments yielded promising results with average Dice scores up to 77.6% and mean sensitivity rates up to 78.9%. To our best knowledge, our proposed study is one of the first to tackle this particular issue, which limits direct comparability with related works. In respect to similar deep learning-based lesion segmentations, e.g. in liver MR images or spinal CT images, our experiments showed similar or in some respects superior segmentation quality. Overall, our automatic approach can provide almost expert-like segmentation accuracy in this challenging and ambitious task.
Mathias Becker, Emanuele Copello, Julia Harz, Martin Napetschnig
This manual describes the usage and implementation of SE+BSF4DM, an add-on package for micrOMEGAs that includes the Sommerfeld effect and bound state formation in the numerical evaluation of the dark matter relic density for QCD-colored dark sectors, applicable to any model that can be mapped onto a simplified t-channel framework. The package seamlessly integrates these non-perturbative effects into the standard micrOMEGAs workflow, requiring minimal user modification. This document provides a comprehensive guide to the installation, configuration, and usage of SE+BSF4DM, serving as a practical user guide for dark matter phenomenologists.
Mathias Becker, Wolfgang König
Fix $p>1$, not necessarily integer, with $p(d-2)<d$. We study the $p$-fold self-intersection local time of a simple random walk on the lattice $\Z^d$ up to time $t$. This is the $p$-norm of the vector of the walker's local times, $\ell_t$. We derive precise logarithmic asymptotics of the expectation of $\exp\{θ_t \|\ell_t\|_p\}$ for scales $θ_t>0$ that are bounded from above, possibly tending to zero. The speed is identified in terms of mixed powers of $t$ and $θ_t$, and the precise rate is characterized in terms of a variational formula, which is in close connection to the {\it Gagliardo-Nirenberg inequality}. As a corollary, we obtain a large-deviation principle for $\|\ell_t\|_p/(t r_t)$ for deviation functions $r_t$ satisfying $t r_t\gg\E[\|\ell_t\|_p]$. Informally, it turns out that the random walk homogeneously squeezes in a $t$-dependent box with diameter of order $\ll t^{1/d}$ to produce the required amount of self-intersections. Our main tool is an upper bound for the joint density of the local times of the walk.