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Building on our automated framework that uses ring diagrams for classifying CP basis invariants [1], this paper broadens the application of the methodology with more extensive examples and a wider scope of theoretical frameworks. Here, we showcase its versatility through detailed analyses in the Standard Model Effective Field Theory (SMEFT) up to dim-2n, and SMEFT with sterile neutrinos ({\nu}SMEFT) up to dimension-7. By integrating the ring-diagram technique with the Cayley-Hamilton theorem, we have developed a system that not only simplifies the process of identifying basic and joint invariants but also enables the automatic differentiation between CP-even and CP-odd invariants from the lowest orders. Additionally, this work presents a comparison of our results with those derived using the traditional Hilbert-Poincar\'e series and its Plethystic logarithm. While these conventional approaches primarily yield the numerical count of invariants, our framework provides a complete structure of invariants, thereby surpassing the limitations of these traditional methods., Comment: 42 pages

The Two-Higgs Doublet Model (2HDM) is a well-motivated theoretical framework that provides additional sources of CP Violation (CPV) beyond the Standard Model (SM). After studying the vacuum topology of a general (convex) 2HDM potential, we unambiguously identify three origins of CPV: (I) Spontaneous CPV (SCPV), where the vacuum manifold has at least two degenerate CPV minima disconnected by domain walls, (ii) Explicit CPV (ECPV) with one single CPV ground state, and (iii) Mixed Spontaneous and Explicit CPV (MCPV), where the theory possesses more than one $non$-degenerate CPV local minimum. Most importantly, we define a novel complex parameter $r_{\rm CP}$ whose norm and phase control the three different realisations of CPV, at least at the tree level. In all these scenarios, only two CPV phases can be made independent, as any third CPV parameter will always be constrained via the CP-odd tadpole condition. Since ECPV vanishes in 2HDMs where SM Higgs alignment is achieved naturally through accidental continuous symmetries, we analyse the possibility of maximising CPV through soft and explicit breaking of these symmetries. We derive upper limits on key CPV parameters that quantify the degree of SM misalignment from constraints due to the non-observation of an electron Electric Dipole Moment (EDM). Finally, we delineate the CP-violating parameter space of the so-constrained naturally aligned 2HDMs that can further be probed at the CERN Large Hadron Collider (LHC)., Comment: 38 pages, 6 figures and 4 tables

In this study, we introduce a transformative, automated framework for classifying basis invariants in generic field theories. Utilising a novel ring-diagram methodology accompanied by the well-known Cayley-Hamilton theorem, our approach uniquely enables the identification of basic invariants and their CP-property characterisation. Critically, our framework also unveils previously concealed attributes of established techniques reliant on the Hilbert-Poincar\'e series and its associated Plethystic logarithm. This paradigm shift has broad implications for the deeper understanding and more accurate classification of CP invariants in generic field theories., Comment: 14 pages, 4 figures and 4 tables

Fabrication of superconducting nanomechanical resonators for quantum research, detectors and devices traditionally relies on a lithographic process, resulting in oscillators with sharp edges and a suspended length limited to a few 100 micrometres. We report a low-investment top-down approach to fabricating NbTi nanowire resonators with suspended lengths up to several millimetres and diameters down to 100 nanometres. The nanowires possess high critical currents and fields, making them a natural choice for magnetomotive actuation and sensing. This fabrication technique is independent of the substrate material, dimensions and layout and can readily be adapted to fabricate nanowire resonators from any metal or alloy with suitable ductility and yield strength. Our work thus opens access to a new class of nanomechanical devices with applications including microscopic and mesoscopic investigations of quantum fluids, detecting dark matter and fundamental materials research in one-dimensional superconductors in vacuum., Comment: 19 pages, 4 figures

The wealth of experimental data collected at laboratory experiments suggests that there is some scale separation between the Standard Model (SM) and phenomena beyond the SM (BSM). New phenomena can manifest itself as small corrections to SM predictions, or as signals in processes where the SM predictions vanish or are exceedingly small. This makes precise calculations of the SM expectations essential, in order to maximize the sensitivity of current and forthcoming experiments to BSM physics. This topical group report highlights some past and forthcoming theory developments critical for maximizing the sensitivity of the experimental program to understanding Nature at the shortest distances., Comment: 36 pages, 2 figures. Report of the TF06 topical group for Snowmass 2021. V2: minor updates

While it is usually stated that dimensional regularization (DR) has no direct physical interpretation, consensus has recently grown on the idea that it might be endowed with special physical properties that would provide the mechanism that solves the naturalness/hierarchy problem. Comparing direct Wilsonian calculations with the corresponding DR ones, we find that DR indeed has a well-defined physical meaning, and we point out its limitations. In particular, our results show that DR cannot provide the solution to the naturalness/hierarchy problem. The absence of too large corrections to the Higgs boson mass is due to a secretly realized fine-tuning, rather than special physical properties of DR. We also investigate these issues within the Wilsonian RG framework and, by comparison with the usual perturbative RG analysis, we show that several popular proposals for the resolution of the problem, commonly considered as physical mechanisms free of fine-tuning, again secretly implement the tuning., Comment: 29 pages, 1 figure

We consider an explicitly CP-violating model with two Higgs doublets and one complex singlet scalar. The singlet $S$ is charged under a global $\rm U(1)$ symmetry which is softly broken by a mass term $\mu^2 S^2+\hc$. Imaginary part of $S$ is a stable dark matter candidate which at the tree level, in the limit of zero momentum transfer, decouples from nucleons naturally satisfying all existing direct detection limits on dark matter scattering cross-section. It is explicitly shown that within this framework in the alignment limit CP-violation is still present in contrast to a popular version of a 2-Higgs doublet model with softly broken $Z_2$ symmetry. In this context, we investigate dark matter implications of the model both with and without CP violation in the scalar sector. In particular, dark matter relic abundance is calculated and the possibility for its indirect detection is discussed., Comment: 41 pages, 16 figures and 2 tables

In this brief Snowmass White Paper for the Theory Frontier, we argue that there have been important recent developments in the algorithms used to generate a simulated parton shower and that further progress can be achieved in the coming decade. A much more detailed exposition can be found in a corresponding White Paper of the Energy Frontier., Comment: Contribution to Snowmass 2021. Revised version has a revised author list, slightly revised text, and a few added references

High energy collisions at the High-Luminosity Large Hadron Collider (LHC) produce a large number of particles along the beam collision axis, outside of the acceptance of existing LHC experiments. The proposed Forward Physics Facility (FPF), to be located several hundred meters from the ATLAS interaction point and shielded by concrete and rock, will host a suite of experiments to probe Standard Model (SM) processes and search for physics beyond the Standard Model (BSM). In this report, we review the status of the civil engineering plans and the experiments to explore the diverse physics signals that can be uniquely probed in the forward region. FPF experiments will be sensitive to a broad range of BSM physics through searches for new particle scattering or decay signatures and deviations from SM expectations in high statistics analyses with TeV neutrinos in this low-background environment. High statistics neutrino detection will also provide valuable data for fundamental topics in perturbative and non-perturbative QCD and in weak interactions. Experiments at the FPF will enable synergies between forward particle production at the LHC and astroparticle physics to be exploited. We report here on these physics topics, on infrastructure, detector, and simulation studies, and on future directions to realize the FPF's physics potential., Comment: 429 pages, contribution to Snowmass 2021

Maximally Symmetric $n$-Higgs Doublet Models (MS-$n$HDMs)define very economic settings that enable sharp Higgs-sector predictions beyond the Standard Model (SM) potentially testable at high-energy colliders. The scalar potential of a MS-$n$HDM obeys an $\mathrm{Sp(2}n)$ symmetry, which is softly broken by bilinear scalar masses and explicitly by hypercharge and Yukawa couplings through renormalisation-group effects. The $\mathrm{Sp(2}n)$ also ensures natural SM alignment and allows for quartic coupling unification up to the Planck scale. As typical examples, we consider maximally symmetric realisations of the Type-II 2HDM and the Type-V 3HDM. We show how in terms of a few input parameters, definite predictions for the entire scalar mass spectrum of the MS-2HDM and MS-3HDM are obtained, including the SM-like Higgs-boson couplings to the gauge bosons and fermions., Comment: DISCRETE 2020-2021 Proceeding, 10 pages and 6 figures

We calculate the fiducial and differential $W^{\pm}/Z^0+jet(s)$ production cross-sections in the presence of electroweak (EW) corrections through virtual loop contributions to the matrix elements (MEs) of the processes and real partonic cascade emissions. The calculations are carried out for proton-proton collisions at $\sqrt{s} = 13$ TeV, using Herwig 7 general-purpose Monte-Carlo event generator with leading-order or next-to-leading-order MEs that are interfaced with different parton-shower configurations. The results are compared with precision experimental measurements from ATLAS collaboration and with similar predictions within the $k_t$-factorisation framework, providing a test for the validity of the newly-implemented QCD$\oplus$QED$\oplus$EW parton shower in Herwig 7. It is shown that the inclusion of EW radiations in the parton shower simulations improves Herwig 7's predictions in describing the experimental data. Additionally, the inclusion of parton shower-induced real EW emissions can take precedence over the incorporation of virtual EW corrections for the simulation of EW-sensitive events., Comment: 21 pages, 9 figures and 1 table

We consider the general Three-Higgs Doublet Model (3HDM) and identify all limits that lead to exact SM alignment. After discussing the underlying symmetries that can naturally enforce such an alignment, we focus on the most economic setting, called here the Maximally Symmetric Three-Higgs Doublet Model (MS-3HDM). The potential of the MS-3HDM obeys an $\mathrm{Sp(6)}$ symmetry, softly broken by bilinear masses and explicitly by hypercharge and Yukawa couplings through renormalisation-group effects, whilst the theory allows for quartic coupling unification up to the Planck scale. Besides the two ratios of vacuum expectation values, $\tan\beta_{1,2}$, the MS-3HDM is predominantly governed by only three input parameters: the masses of the two charged Higgs bosons, $M_{h_{1,2}^{\pm}}$, and their mixing angle $\sigma$. Most remarkably, with these input parameters, we obtain definite predictions for the entire scalar mass spectrum of the theory, as well as for the SM-like Higgs-boson couplings to the gauge bosons and fermions. The predicted deviations of these couplings from their SM values might be probed at future precision high-energy colliders. The new phenomenological aspects of the MS-3HDM with respect to the earlier studied MS-2HDM are discussed., Comment: 45 pages and 6 figures

We construct accidentally symmetric potentials in the framework of Two Higgs Model Effective Field Theory (2HDMEFT) including higher-order operators of dimension 6 and dimension 8. Our construction is facilitated by an earlier developed technique based on prime invariants. In addition, we employ an alternative method that utilises the generators of each symmetry in the bi-adjoint representation and show how this method can be used to identify operators of any higher dimension. The accidentally symmetric 2HDMEFT potentials exhibit two classes of symmetries: (i) continuous symmetries and (ii) discrete symmetries. The number of continuous symmetries in the 2HDMEFT remains the same as in the 2HDM. However, the introduction of higher-order operators allows additional higher-order discrete symmetries, such as $Z_n$ and CP$n$. We classify the full list of the 17 accidental symmetries in the 2HDMEFT including dimension-6 and dimension-8 operators, and derive the relations that govern the theoretical parameters of the corresponding effective potentials., Comment: 22 pages, 4 tables, references added

We present the complete set of continuous maximal symmetries that the potential of an $n$-Higgs Doublet Model ($n$HDM) should satisfy for natural Standard Model (SM) alignment. As a result, no large mass scales or fine-tuning is required for such alignment, which still persists even if these symmetries were broken softly by bilinear mass terms. In particular, the Maximal Symmetric $n$HDM (MS-$n$HDM) can provide both natural SM alignment and quartic coupling unification up to the Planck scale. Most remarkably, we show that the MS-2HDM is a very predictive extension of the SM governed by two only additional parameters: (i) the charged Higgs mass $M_{h^{\pm}}$ (or $m^2_{12}$) and (ii) $\tan\beta$, whilst the quartic coupling unification scale $\mu_X$ is predicted to assume two discrete values. With these two input parameters, the entire Higgs-mass spectrum of the model can be determined. Moreover, we obtain definite predictions of misalignment for the SM-like Higgs-boson couplings to the gauge bosons and to the quarks, which might be testable at future precision high-energy colliders., Comment: CORFU2019 Proceeding, 21 pages, 6 figures and 2 tables

The potential of $n$-Higgs Doublet Models ($n$HDMs) contains a large number of SU(2)$_L$-preserving accidental symmetries as subgroups of the symplectic group Sp(2$n)$. To classify these, we introduce prime invariants and irreducible representations in bilinear field space that enable us to explicitly construct accidentally symmetric $n$HDM potentials. We showcase the classifications of symmetries and present the relationship among the theoretical parameters of the scalar potential for; (i) the Two Higgs Doublet Model (2HDM) and (ii) the Three Higgs Doublet Model (3HDM). We recover the maximum number of $13$ accidental symmetries for the 2HDM potential and for the first time, we present the complete list of $40$ accidental symmetries for the 3HDM potential., Comment: 33 pages and 2 tables

We consider the Maximally Symmetric Two-Higgs Doublet Model (MS-2HDM) in which the so-called Standard Model (SM) alignment can be naturally realised as a consequence of an accidental SO(5) symmetry in the Higgs sector. This symmetry is broken (i) explicitly by renormalization-group (RG) effects and (ii) softly by the bilinear scalar mass term $m^2_{12}$. We find that in the MS-2HDM all quartic couplings can unify at large RG scales $\mu_X \sim 10^{11}\,$-$\,10^{20}$ GeV. In particular, we show that quartic coupling unification can take place in two different conformally invariant points, where all quartic couplings vanish. We perform a vacuum stability analysis of the model in order to ensure that the electro-weak vacuum is sufficiently long-lived. The MS-2HDM is a minimal and very predictive extension of the SM governed by only three additional parameters: the unification scale $\mu_X$, the charged Higgs mass $M_{h^{\pm}}$ (or $m^2_{12}$) and $\tan\beta$, which allow one to determine the entire Higgs sector of the model. In terms of these input parameters, we present illustrative predictions of misalignment for the SM-like Higgs-boson couplings to the $W^\pm$ and $Z$ bosons and, for the first time, to the top and bottom quarks., Comment: Minor typo corrected

With the aim of exploring the Higgs sector of the Two Higgs Doublet Model (2HDM), we have chosen the exact and soft $Z_2$ symmetry breaking versions of the 2HDM with non-zero vacuum expectation values for both Higgs doublets (Mixed Model). We consider two SM-like scenarios: with 125 GeV $h$ and 125 GeV $H$. We have applied the condition for cancellation of quadratic divergences in the type II 2HDM in order to derive masses of the heavy scalars. Solutions of two relevant conditions were found in the considered SM-like scenarios. After applying the current LHC data for the observed 125 GeV Higgs boson, the precision electroweak data test and lower limits on the mass of $H^+$, the allowed region of parameters shrink strongly.

In the present work, we intend to predict the production rates of the Higgs bosons in the simplest extension of the Standard Model (SM) by a neutral complex singlet (cSMCS). This model has an additional source of CP violation and provides strong enough first-order electroweak phase transition to generate the baryon asymmetry of universe (BAU). The scalar spectrum of the cSMCS includes three neutral Higgs particles with the lightest one considered to be the 125 GeV Higgs boson found at LHC. The SM-like Higgs boson comes mostly from the SM-like SU(2) doublet, with a small correction from the singlet. To predict the production rates of the Higgs bosons, we use a conventional effective LO QCD framework and the unintegrated parton distribution functions (UPDF) of Kimber-Martin-Ryskin (KMR). We first compute the SM Higgs production cross-section and compare the results to the existing theoretical calculations from different frameworks as well as the experimental data from the CMS and ATLAS collaborations. It is shown that our framework is capable of producing sound predictions for these high-energy QCD events in the SM. Afterwards we present our predictions for the Higgs boson production in the cSMCS., Comment: Fitted by the published version, 1 figure and 2 benchmarks have been omitted, additional comparisons have been added and several misprints have been corrected

CP violation of the SM is insufficient to explain the baryon asymmetry in the universe and therefore an additional source of CP violation is needed. Here the extension of the SM by a neutral complex scalar singlet with a nonzero vacuum expectation value (cSMCS) plus a heavy vector quark pair is considered. This model offers the spontaneous CP violation and proper description in the baryogenesis, it leads strong enough first-order electro-weak phase transition to suppress the baryon-violating sphaleron process., Comment: Typos in the caption Fig. 2 and Eq.(26) are corrected and acknowledgment has been added

We consider the simplest extension of the SM with a complex singlet and a pair of heavy doublet vector quarks, the so-called cSMCS model. In this model, the CP violation can emerge spontaneously as a consequence of the time-dependent phase of the complex singlet vacuum expectation value and the mass mixing of the SM and heavy vector quarks. In our model, the CP-violating time-dependent phase depends on the Higgs field within the bubble-wall via the Higgs-singlet coupling that can directly explain the observed baryon-to-entropy ratio $\sim 9\times 10^{-11}$. Additionally, as a result of the mixing between vector quarks and SM quarks, the tree level Flavour Changing Neutral Currents and the charged-current decay channels $t' \to Wb, \, Zt, \, h_{i} t$ and $b' \to Wt, \, Zb, \, h_{i} b$ would arise that are well constrained by experimental data. We investigate the implications of these constraints on the total cross-section for the production of heavy vector quark pairs via $pp \to t'\bar{t'}$ and $pp \to b'\bar{b'}$ channels and obtain the bounds on the heavy quark masses for this model. Accordingly, we show the contribution of these heavy quarks in the Higgs bosons signal strength, $\mathcal{R}_{\gamma\gamma}$, as well as corrections to the gauge boson propagators., Comment: 25 pages and 8 figures, matches NPB published version

The Inert Doublet Model and its extension with an additional complex singlet is considered. The CP violation aspects are analysed in the simplified case, with one SM-like Higgs doublet and a complex singlet., Comment: Presented at Zakopane School 2015 by M. Krawczyk and N. Darvishi; v2: Updated references

Within the Inert Doublet Model (IDM) there is a viable dark matter candidate. This simple model can provide a strong enough first order phase transition, which is required in order to account for the matter-antimatter asymmetry in the Universe (BAU). However, another necessary ingredient is missing, as there is no additional source of CP violation in the IDM, besides the standard CKM phase from the Standard Model. Additional CP violating phase can appear if a complex singlet of $SU(3)_C \times SU(2)_W \times U(1)_Y$ with a non-zero vacuum expectation value is added to the scalar sector of the IDM. We construct the scalar potential of the inert doublet plus singlet model (IDMS), assuming an exact $Z_2$ symmetry, with singlet being $Z_2$-even. To simplify the model we use a softly broken $U(1)$ symmetry, which allows a reduction of the number of free parameters in the potential. We study the masses and interactions of scalar particles for a few benchmark scenarios. Constraints from collider physics, in particular from the Higgs signal observed at LHC with $M_h\approx 125$ GeV are discussed, as well as constraints from the dark matter experiments., Comment: v3: updated references, extended discussion about parameter space, updated experimental constraints, results and conclusions unchanged. To appear in Journal of Physics G: Nuclear and Particle Physics