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A bstract We obtain the complete and independent bases of effective operators at mass dimension 5, 6, 7, 8, 9 in both standard model effective field theory with light sterile right-handed neutrinos ( ν SMEFT) and low energy effective field theory with light sterile neutrinos ( ν LEFT). These theories provide systematical parametrizations on all possible Lorentz-invariant physical effects involving in the Majorana/Dirac neutrinos, with/without the lepton number violations. In the ν SMEFT, we find that there are 2 (18), 29 (1614), 80 (4206), 323 (20400), 1358 (243944) independent operators with sterile neutrinos included at the dimension 5, 6, 7, 8, 9 for one (three) generation of fermions, while 24, 5223, 3966, 25425, 789426 independent operators in the ν LEFT for two generations of up-type quarks and three generations of all other fermions.

A bstract We consider extended scalar sectors of the Standard Model as ultraviolet complete motivations for studying the effective Higgs self-interaction operators of the Standard Model effective field theory. We investigate all motivated heavy scalar models which generate the dimension-six effective operator, | H | 6 , at tree level and proceed to identify the full set of tree-level dimension-six operators by integrating out the heavy scalars. Of seven models which generate | H | 6 at tree level only two, quadruplets of hypercharge Y = 3 Y H and Y = Y H , generate only this operator. Next we perform global fits to constrain relevant Wilson coefficients from the LHC single Higgs measurements as well as the electroweak oblique parameters S and T . We find that the T parameter puts very strong constraints on the Wilson coefficient of the | H | 6 operator in the triplet and quadruplet models, while the singlet and doublet models could still have Higgs self-couplings which deviate significantly from the standard model prediction. To determine the extent to which the | H | 6 operator could be constrained, we study the di-Higgs signatures at the future 100 TeV collider and explore future sensitivity of this operator. Projected onto the Higgs potential parameters of the extended scalar sectors, with 30 ab −1 luminosity data we will be able to explore the Higgs potential parameters in all seven models.

We uncover a negative relation between herding behavior and skill in the mutual fund industry. Our new, dynamic measure of fund-level herding captures the tendency of fund managers to follow the trades of the institutional crowd. We find that herding funds underperform their antiherding peers by over 2% per year. Differences in skill drive this performance gap: Antiherding funds make superior investment decisions even on stocks not heavily traded by institutions, and can anticipate the trades of the crowd; furthermore, the herding-antiherding performance gap is persistent, wider when skill is more valuable, and larger among managers with stronger career concerns.

A bstract We obtain the complete operator bases at mass dimensions 5, 6, 7, 8, 9 for the low energy effective field theory (LEFT), which parametrize various physics effects between the QCD scale and the electroweak scale. The independence of the operator basis regarding the equation of motion, integration by parts and flavor relations, is guaranteed by our algorithm [1, 2], whose validity for the LEFT with massive fermions involved is proved by a generalization of the amplitude-operator correspondence. At dimension 8 and 9, we list the 35058 (756) and 704584 (3686) operators for three (one) generations of fermions categorized by their baryon and lepton number violations (∆ B , ∆ L ), as these operators are of most phenomenological relevance.

A bstract We describe a general procedure to construct the independent and complete operator bases for generic Lorentz invariant effective field theories, given any kind of gauge symmetry and field content, up to any mass dimension. By considering the operator as contact on-shell amplitude, the so-called amplitude operator correspondence, we provide a unified construction of the Lorentz and gauge and flavor structures by Young Tableau tensor. Several bases are constructed to emphasize different aspects: independence (y-basis and m-basis), repeated fields with flavors (p-basis and f-basis), and conserved quantum numbers (j-basis). We also provide new algorithms for finding the m-basis by defining inner products for group factors and the p-basis by constructing the matrix representations of the Young symmetrizers from group generators. The on-shell amplitude basis gives us a systematic way to convert any operator into such basis, so that the conversions between any other operator bases can be easily done by linear algebra. All of these are implemented in a Mathematica package: ABC4EFT ( A mplitude B asis C onstruction for E ffective F ield T heories).

Kinetic energy density (KED) plays a fundamental role in density functional theory, chemical bonding, etc. As a basic quantity, its definition is ambiguous, which will inevitably exert unpredictable adverse effects on application. We derive another form of local total energy density (ED) and KED based on the perturbation theory. Contrary to popular belief, our study reveals that energy is only distributed inside the potential well and exactly fills the entire potential well. It seems that the ambiguity of the quantum definition of total ED is eliminable by the stability of energy distribution, and there is a one-to-one correspondence between this form of KED and total ED. As a result, the ambiguity of the KED is also eliminable. Moreover, this new form of local KED 'selectively' agrees well with the key regions of other commonly used ones. However, it is much less localized than other forms. Its locality features imply that it may provide a native way to describe the strong correlation and the van der Waals interactions.

A bstract We enumerate the complete and independent sets of operators at the next-to-leading order (NLO) in the Higgs effective field theory (HEFT), based on the Young tensor technique on the Lorentz, gauge, and flavor structures. The operator-amplitude correspondence tells a type of operator forms the on-shell amplitude basis, and for operators involved in Nambu-Goldstone bosons, the amplitude basis is further reduced to the subspace satisfying the Adler zero condition in the soft momentum limit. Different from dynamical fields, the spurion should not enter into the Lorentz sector, instead, it only plays the role of forming the SU(2) invariant together with other dynamical fields. With these new treatments, for the first time, we could obtain the 224 (7704) operators for one (three) generation fermions, 295 (11307) with right-handed neutrinos, and find there were 8 (11) terms of operators missing and many redundant operators can be removed in the effective theory without (with) right-handed neutrinos.

A bstract The standard model can be extended to include weakly-interacting light particle (WILP): real or complex singlet scalar with a conserved U(1) charge, Majorana or Dirac neutral fermion, neutral or hidden-charged vector boson, etc. Imposing the Z 2 symmetry, these particles can be lifted as the weakly-interacting massive particle (WIMP), the candidate of dark matter. Instead, imposing the shift symmetry on the scalar components gives rise to the axion-like particle, dark photon, etc. Utilizing these light degrees of freedom along with the standard model particles and imposing different symmetries, we construct the complete and independent sets of effective operators up to dimension eight with the Young tensor technique, consistent with counting from the Hilbert series.