As Christoph Greub embarks on a well-deserved retirement, we take this opportunity to celebrate his remarkable career and lasting contributions. Over the years, Christoph has been a pillar of excellence, known for his unwavering commitment and expertise in B physics. This tribute reflects on his professional journey, the impact he has had on colleagues, young collaborators and the legacy he leaves behind. With deep appreciation, we honour Christoph’s accomplishments and wish him the best in this exciting new chapter of life.

In this review, we present a comprehensive overview of some of our work carried out in numerous collaborations on important topics in the context of higher-order calculations in perturbative quantum field theories. The approach of this review is one where analytical methods are given prominence. Thus, we primarily concern ourselves with the study of multi-loop scalar Feynman integrals appearing in simplified and idealized models on the one hand, and on the other, to methods for obtaining analytic results for such integrals that are amenable to an implementation on Mathematica as the computer algebra software of choice. After a preliminary discussion of some of the commonly used parametric representations for Feynman integrals, we review (a) the construction of an algorithm and an automated program to find the ‘regions’ of Feynman integrals using Landau equations and power geometry, (b) the analysis of a non-trivial two-loop non-planar Feynman integral using Hopf algebras, (c) some basic aspects of multi-variable hypergeometric functions, namely, their regions of convergence and analytic continuations, (d) the interplay between the theory of multi-variable hypergeometric functions and Feynman integrals, including an algorithmic method for finding series representations for multi-fold Mellin-Barnes representations of Feynman integrals, the interpretation of Feynman integrals as GKZ hypergeometric functions and an automated program that uses this idea for obtaining series solutions, the ϵ -expansion for multi-variable hypergeometric functions arising from dimensionally regularized Feynman integrals, algebraic relations for products of propagators, and (e) the summation of large logarithms for renormalizable as well as non-renormalizable quantum field theories.

The striking success of the Standard Model in explaining precision data and, at the same time, its lack of explanations for various fundamental phenomena, such as dark matter or the baryon asymmetry of the universe, suggests new physics at an energy scale much larger than the electroweak scale. In the absence of a short-range-long-range conspiracy, the Standard Model can be viewed as the leading term of an effective "remnant" theory (referred to as the SMEFT) of a more fundamental structure. Over the last years, many aspects of the SMEFT have been investigated and it has become a standard tool to analyze experimental results in an integral way. In this article, after briefly presenting the salient features of the Standard Model, we review the construction of the SMEFT. We discuss the range of its applicability and bounds on its coefficients imposed by general theoretical considerations. Since new physics models are likely to exhibit exact or approximate accidental global symmetries, especially in the flavor sector, we also discuss their implications for the SMEFT. The main focus of our review is the phenomenological analysis of experimental results. We show explicitly how to use various effective field theories to study the phenomenology of theories beyond the Standard Model. We give a detailed description of the matching procedure and the use of the renormalization group equations, allowing to connect multiple effective theories valid at different energy scales. Explicit examples from low-energy experiments and from high-$p_T$ physics illustrate the workflow. We also comment on the non-linear realization of the electroweak symmetry breaking and its phenomenological implications.

Abstract The weak decays K± → π±a offer a powerful probe of axion-like particles (ALPs). In this work, we provide a comprehensive analysis of these processes within chiral perturbation theory, extending existing calculations by including complete next-to-leading order (NLO) contributions and isospin-breaking corrections at first order in (md – mu). We show that the consistent incorporation of ALPs in the QCD and weak chiral Lagrangians requires a non-trivial extension of the corresponding operator bases, which we describe in detail. Furthermore, we show that in the presence of an ALP the so-called “weak mass term”, which is unobservable in the Standard Model, is non-redundant already at leading order. We find that NLO corrections associated with flavor-violating ALP couplings modify the leading-order result by a few percent, with negligible uncertainties. NLO corrections proportional to flavor-conserving ALP couplings lead to potentially larger corrections, which, however, are accompanied by sizable uncertainties mainly due to the currently limited knowledge of various low-energy constants. We study how these corrections impact bounds on the ALP couplings, first model independently, and then specializing to the case of an ALP with flavor-universal couplings in the UV. Our findings confirm that the decays K± → π±a provide the strongest particle-physics constraints for ma ≲ 300 MeV. In addition, we point out that these bounds have interesting implications for the ALP couplings to nucleons, which were so far only constrained by astrophysical measurements and non-accelerator experiments.

The pseudoscalar particles pions, kaons and the $η$-particle are considerably lighter than the other hadrons such as protons or neutrons. Their lightness was understood as a consequence of approximate chiral symmetry breaking. This led to current algebra, a way to express the relations imposed by the symmetry breaking. It was realized by Weinberg that because of their low mass, it is possible to formulate a purely pionic (effective) field theory at experimental energies, which carries all information on the (non-perturbative) dynamics, symmetries, and their spontaneous breaking of quantum chromodynamics (QCD) and allows for systematic calculations of observables. In this review, we trace these developments and present recent activities in this field. We make the connection to other effective theories, more generally introduced by Wilson, as approximate field theories at low energies. Indeed, principles and paradigms introduced first for pions have become ubiquitous in particle physics and the standard model. Lastly, we turn to the latest development where the present (fundamental) standard model itself is considered as an effective field theory of a - yet to be formulated - even more fundamental theory. We also discuss important techniques that were developed in order to turn chiral perturbation theory into a predictive framework and briefly review some connections between lattice QCD and chiral perturbation theory (ChPT).

Compartmental models, such as the well-known SEIR model, which divides the population into Susceptible (to the infection), Exposed, Infectious and Recovered persons, and mathematically models their interdependence, are paradigms of mathematical epidemiology. It is therefore natural that epidemiologists attempt to use appropriate variations of such models to forecast quantities of interest and importance to policymakers during the COVID-19 pandemic. Common to all these models and variations is that they are based on the complex mathematics of differential equations. Although differential equations prove appropriate to model a great variety of processes in very different fields, this is not granted in every single case and for every task. To appreciate more easily possible problems or weaknesses in their use for forecasting, we do not argue on a purely abstract level, but in the context of representative models and their evolution equations. Two examples of models that are presently used are described in [1] and called there BT and CZ. They are implemented on icumonitoring.ch, a platform developed for short-term forecasting of intensive care unit (ICU) occupancy in Switzerland during the present pandemic. Currently, the platform provides forecasts derived by yet one further model, termed the MG model, which implements forecasting based on data-driven time series [2]. As far as we know, this model has not been published yet. In the following, we briefly sketch the mathematical content of model BT. Readers not familiar with ordinary differential equations may skip this material and proceed directly to the section “Performance of icumonitoring.ch” where we show that the performance of the models used by icumonitoring.ch has been poor in the past. In the third section, we discuss conceptual shortcomings of models BT and CZ that are likely to contribute to their poor performance. In the next section, we argue on general grounds that differential equations are neither well suited, nor actually needed for short-term forecasting of the impact of infectious diseases. In the last section, we propose a very simple hands-on method for short-term forecasting (in the spirit of recent proposals described in [3]). We now turn to Model BT. This model consists of systems of ordinary differential equations describing the time evolution of the following quantities: The number of susceptible individuals, S(t), the number of exposed individuals, E(t), and the number of infected individuals, I(t), at time t. The relevant equations are: dS/dt = ‒ SβI, dE/dt = SβI ‒ τE, dI/dt = τE ‒ γI. In writing these equations we have replaced S(t) by S, etc. for ease of notation. This system of equations is extended by the following two equations for the numbers of hospitalised patients, H(t), and of ICU patients, U(t): dH/dt = εH γI ‒ γHH, dU/dt = γH εH21 H ‒ γU U. The (posterior) distributions of the parameters β, τ, γ, γH, γU, εH, and εH21 are determined at a cantonal level, using standard techniques and tools; but this is of no importance in the following. For details, as well as for a similar system of deterministic ordinary differential equations, corresponding to the model CZ, and parameters appearing in the equations, we refer the reader to [1]. Forecasting the number of ICU patients is then done as follows. If, on a day t = t0, the true numbers S(t0), E(t0), I(t0), H(t0) and U(t0) are known from direct observation or inferred from other, directly observable quantities, and assuming the distribution of the above parameters is known, we can calculate the distribution of U(t0 + Δ), for Δ > 0, by solving the above system of differential equations with initial values S(t0) = Strue (t0), etc. Among the forecasts provided by icumonitoring.ch are the mean values and the 95% confidence intervals of U(t0 + Δ), for Δ equal to 3 and 7 days. Correspondence: Prof. Daniel Wyler, PhD, Institut für Theoretische Physik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Wyler[at]physik.uzh.ch

The method of using Hopf algebras for calculating Feynman integrals developed by Abreu et al. is applied to the two-loop non-planar on-shell diagram with massless propagators and three external mass scales. We show that the existence of the method of cut Feynman diagrams comprising of the coproduct, the first entry condition and integrability condition that was found to be true for the planar case also holds for the non-planar case; furthermore, the non-planar symbol alphabet is the same as for the planar case. This is one of the main results of this work, and they have been obtained by a systematic analysis of the relevant cuts, using the symbolic manipulation codes HypExp and PolyLogTools. The obtained result for the symbol is cross-checked by an analysis of the known two-loop original Feynman integral result. In addition, we also reconstruct the full result from the symbol. This is the other main result in this paper.

AbstractThe effective reproductive numberRtof COVID-19 is determined indirectly from data that are only incompletely known. Approaches based on reconstructing these data by sampling time lags from suitable distributions introduce noise effects that can result in distorted estimates ofRt. This, in turn, may lead to misleading interpretations of the efficacy of the various measures taken to limit COVID-19 transmission. We discuss in some detail a study used for real time monitoring of the reproductive number in Switzerland; seehttps://ncs-tf.ch/en/situation-report.We argue that the method used to derive the above curve is systematically flawed and leads to an underestimation of the efficacy of the lockdown. The method adopted by the Robert Koch Institute suffers from similar deficiencies, their impact is however smaller.

Leading (large) logarithms in non-renormalizable theories have been investigated in the recent past. Besides some general considerations, explicit results for the expansion coefficients (in terms of leading logarithms) of partial wave amplitudes and of scalar and vector form factors have been given. Analyticity and unitarity constraints have been used to obtain the expansion coefficients of partial waves in massless theories, yielding form factors and the scalar two-point function to five-loop order in the O(4)/O(3) model. Later, all order solutions for the partial waves in any O(N + 1)/O(N) model were found. Also, results up to four-loop order exist for massive theories. Here we extend the implications of analyticity and unitarity constraints on the leading logarithms to arbitrary loop order in massless theories. We explicitly obtain the scalar and vector form factors as well as the scalar two-point function in any O(N) and SU(N) type models. We present relations between the expansion coefficients of these quantities and those of the relevant partial waves. Our work offers a consistency check on the published results in the O(N) models for form factors, and new results for the scalar two-point function. For the SU(N) type models, we use the known expansion coefficients for partial waves to obtain those for scalar and vector form factors as well as for the scalar two-point function. Our results for the form factor offer a check for the known and future results for massive O(N) and SU(N) type models when the massless limit is taken. Mathematica notebooks which can be used to calculate the expansion coefficients are provided as supplementary material.

We explore oscillations of the solar $^8$B neutrinos in the Earth in detail. The relative excess of night $\nu_e$ events (the Night-Day asymmetry) is computed as function of the neutrino energy and the nadir angle $\eta$ of its trajectory. The finite energy resolution of the detector causes an important attenuation effect, while the layer-like structure of the Earth density leads to an interesting parametric suppression of the oscillations. Different features of the $\eta-$ dependence encode information about the structure (such as density jumps) of the Earth density profile; thus measuring the $\eta$ distribution allows the scanning of the interior of the Earth. We estimate the sensitivity of the DUNE experiment to such measurements. About 75 neutrino events are expected per day in 40 kt. For high values of $\Delta m^2_{21}$ and $E_\nu > $11 MeV, the corresponding D-N asymmetry is about 4\% and can be measured with $15\%$ accuracy after 5 years of data taking. The difference of the D-N asymmetry between high and low values of $\Delta m^2_{21}$ can be measured at the $4\sigma$ level. The relative excess of the $\nu_e$ signal varies with the nadir angle up to 50\%. DUNE may establish the existence of the dip in the $\eta-$ distribution at the $(2 - 3) \sigma$ level.

We describe a novel approach to dimensional reduction in classical field theory. Inspired by ideas from noncommutative geometry, we introduce extended algebras of differential forms over space-time, generalized exterior derivatives, and generalized connections associated with the “geometry” of space-times with discrete extra dimensions. We apply our formalism to theories of gauge- and gravitational fields and find natural geometrical origins for an axion- and a dilaton field, as well as a Higgs field.

The solar neutrino's 7Be line (Eν = 0.862 MeV) has a width of order the temperature in the center of the Sun (∼ 1 keV).The regeneration of neutrinos from remote structures of the Earth is suppressed due to the averaging of the effect over the width of the 7Be line (oscillation dying effect). We discuss a possibility of measuring the width of the beryllium line at large liquid scintillator detector (LENA) by measuring the electron neutrino flux at different nadir angles of neutrino trajectories.

The axino, the fermionic superpartner of the axion, is a well-motivated candidate for cold dark matter if it is the lightest supersymmetric particle. Since the axino couples very weakly to the matter multiplets, the next-to-lightest supersymmetric particle (NLSP) has a long lifetime, which has important consequences for both cosmology and collider phenomenology. Assuming that a charged slepton is the NLSP, we calculate the complete leading one- and two-loop contributions to its decay. We analyze in detail constraints on the parameter space from cosmology and discuss how this scenario can be probed at colliders. Scenarios in which both the axino and the gravitino are lighter than the long-lived charged slepton are also explored with particular emphasis on cosmological constraints and collider phenomenology.

Based on a recent idea by Krohn and Yavin, we construct a little Higgs model with an internal parity that is not broken by anomalous Wess-Zumino-Witten terms. The model is a modification of the "minimal moose" models by Arkani-Hamed et al. and Cheng and Low. The new parity prevents large corrections to oblique electroweak parameters and leads to a viable dark matter candidate. It is shown how the complete Standard Model particle content, including quarks and leptons together with their Yukawa couplings, can be implemented. Successful electroweak symmetry breaking and consistency with electroweak precision constraints is achieved for natural parameters choices. A rich spectrum of new particles is predicted at the TeV scale, some of which have sizable production cross sections and striking decay signatures at the LHC.

We study skyrmions in the littlest Higgs model and discuss their possible role as dark matter candidates. Stable massive skyrmions can exist in the littlest Higgs model also in absence of an exact parity symmetry, since they carry a conserved topological charge due to the non-trivial third homotopy group of the SU(5)/SO(5) coset. We find a spherically symmetric skyrmion solution in this coset. The effects of gauge fields on the skyrmion solutions are analyzed and found to lead to an upper bound on the skyrmion mass. The relic abundance is in agreement with the observed dark matter density for reasonable parameter choices.

In the popular littlest Higgs model, T-parity can be broken by Wess-Zumino-Witten (WZW) terms induced by a strongly coupled UV completion. On the other hand, certain models with multiple scalar multiplets (called moose models) permit the implementation of T-parity such that it is not broken by the WZW terms. Here we present a concrete realization of such a. model, and discuss the phenomenology at the Large Hadron Collider, in particular differences with respect to the littlest Higgs model.

We discuss the kinematics of the particles that make up a Reggeon in field theory, using the terminology of the soft collinear effective theory (SCET). Reggeization sums a series of strongly ordered collinear emissions resulting in an overall Reggeon exchange that falls in the Glauber or Coulomb kinematic region. This is an extremely multiscale problem and appears to fall outside of the usual organizing scheme of SCET.

Several models for physics beyond the Standard Model predict new particles with a decay signature including hard photons and missing energy. Two well-motivated examples are supersymmetry with gauge-mediated breaking (GMSB) and the standard model with two universal extra dimensions. Both models lead to decay chains with similar collider signatures, including hard photon emission. The main discriminating feature are the spins of the new particles. In this paper we discuss how information about the spins of the particles can be extracted from lepton-photon or quark-photon invariant mass distributions at the Large Hadron Collider. The characteristic shapes of the distributions are derived analytically and then studied in a realistic Monte-Carlo simulation. We find that for a typical GMSB mass spectrum with particle masses below 1 TeV, already 10 fb−1 integrated luminosity at 14 TeV center-of-mass energy are sufficient to discriminate the two models with high significance.

Considering axino cold dark matter scenarios with a long-lived charged slepton, we study constraints on the Peccei–Quinn scale fa and on the reheating temperature TR imposed by the dark matter density and by big bang nucleosynthesis (BBN). For an axino mass compatible with large-scale structure, ma˜≳100keV, temperatures above 109GeV become viable for fa>3×1012GeV. We calculate the slepton lifetime in hadronic axion models. With the dominant decay mode being two-loop suppressed, this lifetime can be sufficiently large to allow for primordial bound states leading to catalyzed BBN of lithium-6 and beryllium-9. This implies new upper limits on fa and on TR that depend on quantities which will be probed at the Large Hadron Collider.