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Sanchis-Lozano, M. A., Barbero, J. F., & Navarro-Salas, J. (2012). Prime Numbers, Quantum Field Theory and the Goldbach Conjecture. Int. J. Mod. Phys. A, 27(23), 1250136–24pp.
Abstract: Motivated by the Goldbach conjecture in number theory and the Abelian bosonization mechanism on a cylindrical two-dimensional space-time, we study the reconstruction of a real scalar field as a product of two real fermion (so-called prime) fields whose Fourier expansion exclusively contains prime modes. We undertake the canonical quantization of such prime fields and construct the corresponding Fock space by introducing creation operators b(p)(dagger) – labeled by prime numbers p – acting on the vacuum. The analysis of our model, based on the standard rules of quantum field theory and the assumption of the Riemann hypothesis, allows us to prove that the theory is not renormalizable. We also comment on the potential consequences of this result concerning the validity or breakdown of the Goldbach conjecture for large integer numbers.
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Dhani, P. K., Rodrigo, G., & Sborlini, G. F. R. (2023). Triple-collinear splittings with massive particles. J. High Energy Phys., 12(12), 188–20pp.
Abstract: We analyze in detail the most singular behaviour of processes involving triple-collinear splittings with massive particles in the quasi-collinear limit, and present compact expressions for the splitting amplitudes and the corresponding splitting kernels at the squared-amplitude level. Our expressions fully agree with well-known triple-collinear splittings in the massless limit, which are used as a guide to achieve the final expressions. These results are important to quantify dominant mass effects in many observables, and constitute an essential ingredient of current high-precision computational frameworks for collider phenomenology.
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Bonilla, J., Brivio, I., Gavela, M. B., & Sanz, V. (2021). One-loop corrections to ALP couplings. J. High Energy Phys., 11(11), 168–57pp.
Abstract: The plethora of increasingly precise experiments which hunt for axion-like particles (ALPs), as well as their widely different energy reach, call for the theoretical understanding of ALP couplings at loop-level. We derive the one-loop contributions to ALP-SM effective couplings, including finite corrections. The complete leading-order – dimension five – effective linear Lagrangian is considered. The ALP is left off-shell, which is of particular impact on LHC and accelerator searches of ALP couplings to gamma gamma, ZZ, WW, Z gamma gluons and fermions. All results are obtained in the covariant Rg gauge. A few phenomenological consequences are also explored as illustration, with flavour diagonal channels in the case of fermions: in particular, we explore constraints on the coupling of the ALP to top quarks, that can be extracted from LHC data, from astrophysical sources and from Dark Matter direct detection experiments such as PandaX, LUX and XENONIT. Furthermore, we clarify the relation between alternative ALP bases, the role of gauge anomalous couplings and their interface with chirality-conserving and chirality-flip fermion interactions, and we briefly discuss renormalization group aspects.
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Du, M. L., Baru, V., Guo, F. K., Hanhart, C., Meissner, U. G., Oller, J. A., et al. (2021). Revisiting the nature of the P-c pentaquarks. J. High Energy Phys., 08(8), 157–50pp.
Abstract: The nature of the three narrow hidden-charm pentaquark P-c states, i.e., P-c (4312), P-c (4440) and P-c (4457), is under intense discussion since their discovery from the updated analysis of the process Lambda(0)(b) -> I ) J/psi pK(-) by LHCb. In this work we extend our previous coupled-channel approach [Phys. Rev. Lett. 124, 072001 (2020)], in which the Pc states are treated as Sigma(()(c)*()) (D) over bar (()*()) molecules, by including the Lambda(c)(D) over bar (()*()) and eta(c)p as explicit inelastic channels in addition to the J/psi p, as required by unitarity and heavy quark spin symmetry (HQSS), respectively. Since inelastic parameters are very badly constrained by the current data, three calculation schemes are considered: (a) scheme I with pure contact interactions between the elastic, i.e., Sigma(()(c)*()) (D) over bar (()*()), and inelastic channels and without the Lambda(c)(D) over bar (()*()) interactions, (b) scheme II, where the one-pion exchange (OPE) is added to scheme I, and (c) scheme III, where the Lambda(c)(D) over bar (()*()) interactions are included in addition. It is shown that to obtain cutoff independent results, OPE in the multichannel system is to be supplemented with S-wave-to-D-wave mixing contact terms. As a result, in line with our previous analysis, we demonstrate that the experimental data for the J/psi p invariant mass distribution are consistent with the interpretation of the P-c(4312) and P-c(4440)/P-c(4457) as Sigma(c)(D) over bar and Sigma(c)(D) over bar* hadronic molecules, respectively, and that the data show clear evidence for a new narrow state, P-c(4380), identified as a Sigma(c)*(D) over bar molecule, which should exist as a consequence of HQSS. While two statistically equally good solutions are found in scheme I, only one of these solutions with the quantum numbers of the P-c (4440) and P-c (4457) being J(P) = 3/2(-) and 1/2(-), respectively, survives the requirement of regulator independence once the OPE is included. Moreover, we predict the line shapes in the elastic and inelastic channels and demonstrate that those related to the P-c (4440) and the P-c (4457) in the Sigma(()(c)*())<(D)over ( )anf eta(c)p mass distributions from Lambda(0)(b) ->( )Sigma(()(c)*()) (D) over barK(-) and Lambda(0)(b) -> eta(c)pK(-) will shed light on the quantum numbers of those states, once the data are available. We also investigate possible pentaquark signals in the Lambda(c)(D) over bar (()*()) final states.
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Athron, P., Park, J. H., Stockinger, D., & Voigt, A. (2015). FlexibleSUSY-A spectrum generator generator for supersymmetric models. Comput. Phys. Commun., 190, 139–172.
Abstract: We introduce FlexibleSUSY, a Mathematica and C++ package, which generates a fast, precise C++ spectrum generator for any SUSY model specified by the user. The generated code is designed with both speed and modularity in mind, making it easy to adapt and extend with new features. The model is specified by supplying the superpotential, gauge structure and particle content in a SARAH model file; specific boundary conditions e.g. at the GUT, weak or intermediate scales are defined in a separate FlexibleSUSY model file. From these model files, FlexibleSUSY generates C++ code for self-energies, tadpole corrections, renormalization group equations (RGEs) and electroweak symmetry breaking (EWSB) conditions and combines them with numerical routines for solving the RGEs and EWSB conditions simultaneously. The resulting spectrum generator is then able to solve for the spectrum of the model, including loop-corrected pole masses, consistent with user specified boundary conditions. The modular structure of the generated code allows for individual components to be replaced with an alternative if available. FlexibleSUSY has been carefully designed to grow as alternative solvers and calculators are added. Predefined models include the MSSM, NMSSM, E6SSM, USSM, R-symmetric models and models with right-handed neutrinos. Program Summary Program title: FlexibleSUSY Catalogue identifier: AEVIv10 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEVIv10.html obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 129406 No. of bytes in distributed program, including test data, etc.: 854831 Distribution format: tar.gz Programming language: C++, Wolfram/Mathematica, FORTRAN, Bourne shell. Computer: Personal computer. Operating system: Tested on Linux 3.x, Mac OS X. Classification: 11.1, 11.6, 6.5. External routines: SARAH 4.0.4, Boost library, Eigen, LAPACK Nature of problem: Determining the mass spectrum and mixings for any supersymmetric model. The generated code must find simultaneous solutions to constraints which are specified at two or more different renormalization scales, which are connected by renormalization group equations forming a large set of coupled first-order differential equations. Solution method: Nested iterative algorithm and numerical minimization of the Higgs potential. Restrictions: The couplings must remain perturbative at all scales between the highest and the lowest boundary condition. FlexibleSUSY assumes that all couplings of the model are real (i.e. CP-conserving). Due to the modular nature of the generated code, adaption and extension to overcome restrictions in scope is quite straightforward. Running time: 0.06-0.2 seconds per parameter point.
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