arXiv subjects

Felix Tellander

Publications and source records attributed to Felix Tellander.

14 recordsLinked to original sources

arXiv2025

Renormalization of U(1) Gauge Boson Kinetic Mixing

Quantum field theories containing fields with the same quantum numbers allow for mixed kinetic terms in the Lagrangian, leading to off-diagonal elements in the tree-level two-point function. After removing the mixing by a field rotation, the off-diagonal UV divergences cannot be subtracted by a counterterm, still one can show that the theory is renormalizable. We study kinetic mixing of $U(1)$ gauge bosons in an extension of QED with a massive "dark" photon at one-loop order. In general covariant $R_\xi$-gauge, the gauge-fixing function naively obstructs the removal of tree-level mixing but we show that these off-diagonal gauge-dependent contributions cancel. We compare two renormalization schemes: one with and one without kinetic mixing, and relate them via a scale-dependent field transformation, showing that the schemes are equivalent.

hep-ph↗

arXiv2025

Characterizing Cohen-Macaulay One-Loop Feynman Integrals

We study the generalized hypergeometric systems, in the sense of Gel'fand, Kapranov, and Zelevinsky, associated with one-loop Feynman integrals, and determine when their rank is independent of space-time dimension and propagator powers. This is equivalent to classifying when the associated affine semigroup ring is Cohen-Macaulay. For massive one-loop integrals, we prove necessary and sufficient conditions for Cohen-Macaulayness, generalizing previous results on normality for these rings. We show that for Feynman integrals, the Cohen-Macaulay property is fully determined by an integer linear program built from the Newton polytope of the integrand and find a graphical description of its solutions. Furthermore, we provide a sufficient condition for Cohen-Macaulayness of general one-loop integrals.

hep-th↗

arXiv2025

Geometric Singularities of Feynman Integrals

We provide a new method to calculate the full microlocal description of singularities of Feynman integrals. This is done by associating a unique constructible function to the system of partial differential equations (PDEs) annihilating the integral and from this function the singularities can directly be read-off. This function can be constructed explicitly even if the system of PDEs is unknown and describes both the location of the singularities and the number of master integrals on them. Our framework is flexible enough to preform the calculation in any of the Lee-Pomeransky, Feynman, or momentum representations.

hep-th↗

arXiv2025

Spectral Decomposition of Euler-Mellin Integrals

We consider the spectral decomposition of singularities of integrals and their integrands. Our results apply to any integral of Euler-Mellin type, and thus especially to every scalar Feynman integral. Specifically we provide for both the integrand and integral respectively; two explicit constructions of the characteristic variety and characteristic cycle of the constructible function and $D$-module they are associated with. From this we also obtain the singular locus or Landau singularities of the integral. En route we give a simple procedure to compute the local Euler obstruction function of a variety, and using this, to compute the Euler characteristic of the complex link of a Whitney stratum.

math-ph↗

arXiv2024

The two-loop Amplituhedron

The loop-Amplituhedron $\mathcal{A}^{(L)}_{n}$ is a semialgebraic set in the product of Grassmannians $\mathrm{Gr}_{\mathbb{R}}(2,4)^L$. Recently, many aspects of this geometry for the case of $L=1$ have been elucidated, such as its algebraic and face stratification, its residual arrangement and the existence and uniqueness of the adjoint. This paper extends this analysis to the simplest higher loop case given by the two-loop four-point Amplituhedron $\mathcal{A}^{(2)}_4$.

hep-th↗

arXiv2024

Landau Singularities from Whitney Stratifications

We demonstrate that the complete and non-redundant set of Landau singularities of Feynman integrals may be explicitly obtained from the Whitney stratification of a certain map. As a proof of concept, we leverage recent theoretical and algorithmic advances in their computation in order to determine this set for nontrivial examples of two-loop integrals. Interestingly, different strata of the Whitney stratification describe not only the singularities of a given integral, but also those of integrals obtained from kinematic limits, e.g. by setting some of its masses or momenta to zero.

hep-th↗

arXiv2023

UV-complete Gauged Anomaly-free U(1) Froggatt-Nielsen Model

We investigate the possibility of understanding all fermion masses and mixings within a gauged Froggatt-Nielsen framework. Continuing the work from [J. Rathsman and F. Tellander, Phys. Rev. D \textbf{100}, 055032 (2019)] we especially focus on a UV completion of this type of models. Independent of the UV completion, we construct an anomaly-free two Higgs doublet model with a gauged $U(1)_F$ flavor symmetry and three right-handed neutrinos explaining all observed masses and mixings in the fermion sector. We then investigate two different UV completions: one through fermions and one through scalars. The fermion completion has low lying Landau poles in the gague couplings while the scalar completion is viable up to the gravity scale.

hep-ph↗

arXiv2023

Tropical Feynman integration in the physical region

The software feyntrop for direct numerical evaluation of Feynman integrals is presented. We focus on the underlying combinatorics and polytopal geometries facilitating these methods. Especially matroids, generalized permutohedra and normality are discussed in detail.

hep-th↗

arXiv2023

Symbol Alphabets from the Landau Singular Locus

We provide evidence through two loops, that rational letters of polylogarithmic Feynman integrals are captured by the Landau equations, when the latter are recast as a polynomial of the kinematic variables of the integral, known as the principal $A$-determinant. Focusing on one loop, we further show that all square-root letters may also be obtained, by re-factorizing the principal $A$-determinant with the help of Jacobi identities. We verify our findings by explicitly constructing canonical differential equations for the one-loop integrals in both odd and even dimensions of loop momenta, also finding agreement with earlier results in the literature for the latter case. We provide a computer implementation of our results for the principal $A$-determinants, symbol alphabets and canonical differential equations in an accompanying Mathematica file. Finally, we study the question of when a one-loop integral satisfies the Cohen-Macaulay property and show that for almost all choices of kinematics the Cohen-Macaulay property holds. Throughout, in our approach to Feynman integrals, we make extensive use of the Gel'fand, Graev, Kapranov and Zelevinski\u{\i} theory on what are now commonly called GKZ-hypergeometric systems whose singularities are described by the principal $A$-determinant.

hep-th↗

arXiv2023

Tropical Feynman integration in the Minkowski regime

We present a new computer program, $\texttt{feyntrop}$, which uses the tropical geometric approach to evaluate Feynman integrals numerically. In order to apply this approach in the physical regime, we introduce a new parametric representation of Feynman integrals that implements the causal $i\varepsilon$ prescription concretely while retaining projective invariance. $\texttt{feyntrop}$ can efficiently evaluate dimensionally regulated, quasi-finite Feynman integrals, with not too exceptional kinematics in the physical regime, with a relatively large number of propagators and with arbitrarily many kinematic scales. We give a systematic classification of all relevant kinematic regimes, review the necessary mathematical details of the tropical Monte Carlo approach, give fast algorithms to evaluate (deformed) Feynman integrands, describe the usage of $\texttt{feyntrop}$ and discuss many explicit examples of evaluated Feynman integrals.

hep-ph↗

arXiv2021

Cohen-Macaulay Property of Feynman Integrals

The connection between Feynman integrals and GKZ $A$-hypergeometric systems has been a topic of recent interest with advances in mathematical techniques and computational tools opening new possibilities; in this paper we continue to explore this connection. To each such hypergeometric system there is an associated toric ideal, we prove that the latter has the Cohen-Macaulay property for two large families of Feynman integrals. This implies, for example, that both the number of independent solutions and dynamical singularities are independent of space-time dimension and generalized propagator powers. Furthermore, in particular, it means that the process of finding a series representation of these integrals is fully algorithmic.

hep-th↗

arXiv2020

On the Uniqueness Problem for Quadrature Domains

We study questions of existence and uniqueness of quadrature domains using computational tools from real algebraic geometry. These problems are transformed into questions about the number of solutions to an associated real semi-algebraic system, which is analyzed using the method of real comprehensive triangular decomposition.

math.CV↗

arXiv2019

Anomaly-free Model Building with Algebraic Geometry

We present a method to find anomaly-free gauged Froggatt-Nielsen type models using results from algebraic geometry. These methods should be of general interest for model building beyond the Standard Model (SM) when rational charges are required. We consider models with a gauged $U(1)$ flavor symmetry with one flavon and two Higgs doublets and three right-handed SM singlets to provide three model examples based on different physical assumptions. The models we study are: anomaly-free with no SM neutral heavy chiral fermions, anomaly-free with SM neutral heavy chiral fermions, and supersymmetric with SM neutral heavy chiral fermions where the anomalies cancel via the Green-Schwarz mechanism. With these different models we show how algebraic methods may be used in model building; both to reduce the charge constraints by calculation of Gr\"obner bases, and to find rational solutions to cubic equations using Mordell-Weil generators. Using these tools we find three phenomenologically viable models explaining the observed flavor structure.

hep-ph↗

arXiv2016

Tertiary particle production and target optimization of the H2 beam line in the SPS North Area

In this note, the tertiary particle yield from secondary targets of different materials placed at the 'filter' position of the H2 beam line of SPS North Area are presented. The production is studied for secondary beams of different momenta in the range of 50-250 GeV/c. More specifically, we studied six different targets: two copper cylinders with a radius of 40 mm and lengths of 100 and 300 mm, one solid tungsten cylinder with a radius of 40 mm and a length of 150 mm and three polyethylene cylinders with radius of 40 mm and lengths of 550, 700 and 1000 mm. Eight different momenta of the secondary beam (50, 60, 70, 100, 120, 150, 200 and 250 GeV/c) as well as two different physics lists (QGSP_BIC and FTFP_BERT) have been extensively studied. The purpose of this study is (a) to optimize (using the appropriate filter target) the particle production from the secondary targets as demanded by the experiments (b) investigate the proton production (with respect to the pion production) in the produced tertiary beams, a fact interesting for cross-section measuring experiments (e.g. NA61), (c) provide an expected beam-composition database for each target and energy that will act as a reference for the test-beam users of the North Area and (d) demonstrate the differences between the different GEANT-4 physics lists. Moreover this work constitutes a starting point for a more detailed benchmark of the different available Monte-Carlo models and codes in this momentum range.

physics.acc-ph↗