We derive the scale of unitarity violation from the geometry of Effective Field Theory (EFT) extensions of the Standard Model Higgs sector. The high-energy behavior of amplitudes with more than four scalar legs depends on derivatives of geometric inv
ariants with respect to the physical Higgs field $h$, such that higher-point amplitudes begin to reconstruct the scalar manifold away from our vacuum. In theories whose low-energy limit can be described by the Higgs EFT (HEFT) but not the Standard Model EFT (SMEFT), non-analyticities in the vicinity of our vacuum limit the radius of convergence of geometric invariants, leading to unitarity violation at energies below $4pi v$. Our results unify approaches to the HEFT/SMEFT dichotomy based on unitarity, analyticity, and geometry, and more broadly illustrate the sense in which observables probe the geometry of an EFT. Along the way, we provide novel basis-independent results for Goldstone/Higgs boson scattering amplitudes expressed in terms of geometric covariant quantities.
Motivated by FERCs recent direction and ever-growing interest in cloud adoption by power utilities, a Task Force was established to assist power system practitioners with secure, reliable and cost-effective adoption of cloud technology to meet variou
s business needs. This paper summarizes the business drivers, challenges, guidance, and best practices for cloud adoption in power systems from the Task Forces perspective, after extensive review and deliberation by its members that include grid operators, utility companies, software vendors and cloud providers. The paper begins by enumerating various business drivers for cloud adoption in the power industry. It follows with the discussion of challenges and risks of migrating power grid utility workloads to cloud. Next for each corresponding challenge or risk, the paper provides appropriate guidance. Importantly, the guidance is directed toward power industry professionals who are considering cloud solutions and are yet hesitant about the practical execution. Finally, to tie all the sections together, the paper documents various real-world use cases of cloud technology in the power system domain, which both the power industry practitioners and software vendors can look forward to design and select their own future cloud solutions. We hope that the information in this paper will serve as useful guidance for the development of NERC guidelines and standards relevant to cloud adoption in the industry.
This paper presents STrEAM (SuperTrace Evaluation Automated for Matching), a Mathematica package that calculates all functional supertraces which arise when matching a generic UV model onto a relativistic Effective Field Theory (EFT) at one loop and
to arbitrary order in the heavy mass expansion. STrEAM implements the covariant derivative expansion to automate the most tedious step of the streamlined functional matching prescription presented in arXiv:2011.02484 . The code and an example notebook are available at https://www.github.com/EFTMatching/STrEAM .
We simplify the one-loop functional matching formalism to develop a streamlined prescription. The functional approach is conceptually appealing: all calculations are performed within the UV theory at the matching scale, and no prior determination of
an Effective Field Theory (EFT) operator basis is required. Our prescription accommodates any relativistic UV theory that contains generic interactions (including derivative couplings) among scalar, fermion, and vector fields. As an example application, we match the singlet scalar extended Standard Model (SM) onto SMEFT.
We investigate precision observables sensitive to custodial symmetric/violating UV physics beyond the Standard Model. We use the SMEFT framework which in general includes non-oblique corrections that requires a generalization of the Peskin-Takeuchi $
T$ parameter to unambiguously detect custodial symmetry/violation. We take a first step towards constructing a SMEFT reparameterization-invariant replacement, that we call $mathscr{T}$, valid at least for tree-level custodial violating contributions. We utilize a new custodial basis of $ u$SMEFT (SMEFT augmented by right-handed neutrinos) which explicitly identifies the global $SU(2)_R$ symmetries of the Higgs and fermion sectors, that in turn permits easy identification of higher-dimensional operators that are custodial preserving or violating. We carefully consider equation-of-motion redundancies that cause custodial symmetric operators in one basis to be equivalent to a set of custodial symmetric and/or violating operators in another basis. Utilizing known results about tree/loop operator generation, we demonstrate that the basis-dependent appearance of custodial-violating operators does not invalidate our $mathscr{T}$ parameter at tree-level. We illustrate our results with several UV theory examples, demonstrating that $mathscr{T}$ faithfully identifies custodial symmetry violation, while $T$ can fail.
We apply Hilbert series techniques to the enumeration of operators in the mesonic QCD chiral Lagrangian. Existing Hilbert series technologies for non-linear realizations are extended to incorporate the external fields. The action of charge conjugatio
n is addressed by folding the $frak{su}(n)$ Dynkin diagrams, which we detail in an appendix that can be read separately as it has potential broader applications. New results include the enumeration of anomalous operators appearing in the chiral Lagrangian at order $p^8$, as well as enumeration of $CP$-even, $CP$-odd, $C$-odd, and $P$-odd terms beginning from order $p^6$. The method is extendable to very high orders, and we present results up to order $p^{16}$. (The title sequence is the number of independent $C$-even $P$-even operators in the mesonic QCD chiral Lagrangian with three light flavors of quarks, at chiral dimensions $p^2$, $p^4$, $p^6$, ...)
There are two canonical approaches to treating the Standard Model as an Effective Field Theory (EFT): Standard Model EFT (SMEFT), expressed in the electroweak symmetric phase utilizing the Higgs doublet, and Higgs EFT (HEFT), expressed in the broken
phase utilizing the physical Higgs boson and an independent set of Goldstone bosons. HEFT encompasses SMEFT, so understanding whether SMEFT is sufficient motivates identifying UV theories that require HEFT as their low energy limit. This distinction is complicated by field redefinitions that obscure the naive differences between the two EFTs. By reformulating the question in a geometric language, we derive concrete criteria that can be used to distinguish SMEFT from HEFT independent of the chosen field basis. We highlight two cases where perturbative new physics must be matched onto HEFT: (i) the new particles derive all of their mass from electroweak symmetry breaking, and (ii) there are additional sources of electroweak symmetry breaking. Additionally, HEFT has a broader practical application: it can provide a more convergent parametrization when new physics lies near the weak scale. The ubiquity of models requiring HEFT suggests that SMEFT is not enough.
Operating a modern power grid reliably in case of SCADA/EMS failure or amid difficult times like COVID-19 pandemic is a challenging task for grid operators. In [11], a PMU-based emergency generation dispatch scheme has been proposed to help the syste
m operators with the supply and demand balancing; however, its realization highly relies on the control center infrastructure for computing and communication. This work, rather than using the on-premises server and dispatch communication system, proposes and implements a cloud-centric serverless architecture to ensure the operation continuity regardless of local infrastructures availability and accessibility. Through its prototype implementation and evaluation at ISO New England, the solution has demonstrated two major advantages. Firstly, the cloud infrastructure is independent and fault-tolerant, providing grid monitoring and control capability even when EMS loses the corresponding functionality or when operators need to work remotely away from the control center. Secondly, the overall design is event-driven using serverless cloud services in response to the SCADA/EMS failure event. Thanks to serverless, the burden of the server provisioning and maintenance can be avoided from the user side. The cost of using public cloud services for this solution is extremely low since it is architected and implemented based on the event-driven Function-as-a-Service (FaaS) model. This work also develops a comprehensive cyber security mechanism to comply with critical infrastructure requirements for the power grid, which can serve as an exemplary framework for other grid operators to secure their cloud services.
General principles of quantum field theory imply that there exists an operator product expansion (OPE) for Wightman functions in Minkowski momentum space that converges for arbitrary kinematics. This convergence is guaranteed to hold in the sense of
a distribution, meaning that it holds for correlation functions smeared by smooth test functions. The conformal blocks for this OPE are conceptually extremely simple: they are products of 3-point functions. We construct the conformal blocks in 2-dimensional conformal field theory and show that the OPE in fact converges pointwise to an ordinary function in a specific kinematic region. Using microcausality, we also formulate a bootstrap equation directly in terms of momentum space Wightman functions.
4D CFTs have a scale anomaly characterized by the coefficient $c$, which appears as the coefficient of logarithmic terms in momentum space correlation functions of the energy-momentum tensor. By studying the CFT contribution to 4-point graviton scatt
ering amplitudes in Minkowski space we derive a sum rule for $c$ in terms of $TTmathcal{O}$ OPE coefficients. The sum rule can be thought of as a version of the optical theorem, and its validity depends on the existence of the massless and forward limits of the $langle TTTT rangle$ correlation functions that contribute. The finiteness of these limits is checked explicitly for free scalar, fermion, and vector CFTs. The sum rule gives $c$ as a sum of positive terms, and therefore implies a lower bound on $c$ given any lower bound on $TTmathcal{O}$ OPE coefficients. We compute the coefficients to the sum rule for arbitrary operators of spin 0 and 2, including the energy-momentum tensor.
