Complete Lagrangian and set of Feynman rules for scalar leptoquarks

Leptoquarks (LQs) have attracted increasing attention within recent years, mainly since they can explain the flavor anomalies found in <math altimg="si1.svg"><mi>R</mi><mo stretchy="false">(</mo><msup><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">(</mo><mo>⁎</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo></math>, <math altimg="si12.svg"><mi>b</mi><mo stretchy="false">→</mo><mi>s</mi><msup><mrow><mi>ℓ</mi></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">+</mo></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">−</mo></mrow></msup></math> transitions and the anomalous magnetic moment of the muon. In this article, we lay the groundwork for further automated analyses by presenting the complete Lagrangian and the corresponding set of Feynman rules for scalar leptoquarks. This means we consider the five representations <math altimg="si3.svg"><msub><mrow><mi mathvariant="normal">Φ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi mathvariant="normal">Φ</mi></mrow><mrow><mover accent="true"><mrow><mn>1</mn></mrow><mrow><mo stretchy="false">˜</mo></mrow></mover></mrow></msub><mo>,</mo><msub><mrow><mi mathvariant="normal">Φ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi mathvariant="normal">Φ</mi></mrow><mrow><mover accent="true"><mrow><mn>2</mn></mrow><mrow><mo stretchy="false">˜</mo></mrow></mover></mrow></msub></math> and <math altimg="si4.svg"><msub><mrow><mi mathvariant="normal">Φ</mi></mrow><mrow><mn>3</mn></mrow></msub></math> and include the triple and quartic self-interactions, as well as couplings to the Standard Model (SM) fermions, gauge bosons and the Higgs. The calculations are performed using FeynRules and all model files are publicly available online at https://gitlab.com/lucschnell/SLQrules. Program Title: SLQrules CPC Library link to program files:https://doi.org/10.17632/sf8s89rhmv.1 Developer's repository link:https://gitlab.com/lucschnell/SLQrules Licensing provisions: CC By 4.0 Programming language: Mathematica, FeynRules Nature of problem: In order to explain the deviations from SM predictions in <math altimg="si1.svg"><mi>R</mi><mo stretchy="false">(</mo><msup><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">(</mo><mo>⁎</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo></math>, <math altimg="si5.svg"><mi>b</mi><mo stretchy="false">→</mo><msup><mrow><mi>ℓ</mi></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">+</mo></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">−</mo></mrow></msup></math> transitions and the muon AMM jointly, models involving multiple LQ representations are necessary. This significantly increases the number of possible interactions and creates the need for computational tools that allow for studying the phenomenology of these LQ models in an automated manner. While model files exist for each LQ representation individually [1], we are not aware of any publicly available model files that combine all scalar LQ representations as well as their self-interactions. Solution method: We implemented the complete scalar LQ Lagrangian in a FeynRules [2] model file and provide the corresponding MOD and UFO model files. These can be imported directly in FeynArts [3] and MadGraph [4] to obtain a versatile toolbox for the study of scalar LQs. [1]I. Doršner, A. Greljo, J. High Energy Phys. 05 (2018) 1-21.[2]A. Alloul, et al. Comput. Phys. Commun. 185 (2014) 2250-2300.[3]T. Hahn, Comput. Phys. Commun. 140 (2001) 418-431.[4]J. Alwall, et al., J. High Energy Phys. 07 (2014) 079.