Risk and Intellectual Property in Technical Standard Competition： A Game Theory Perspective

Technical standard is typically characterized by network effect.The key point for a technical standard is the consumers' choice,which is based on consumers' maximum benefits.When a technical standard becomes a national standard,its interests have been integrated into the national interests.National interests are divided into economic profits and security factors.From the perspective of consumers' choice,this paper deals with the main factors which affect the result of technical standard competition- the risk and profits of intellectual property based on the assumption of bounded rationality and dynamic game theory.

On capped Higgs positivity cone

The Wilson coefficients of the standard model effective field theory are subject to a series of positivity bounds.It has been shown that while the positivity part of the ultraviolet(UV)partial wave unitarity leads to the Wilson coefficients living in a convex cone,further including the nonpositivity part caps the cone from above.For Higgs scattering,a capped positivity cone was obtained using a simplified,linear unitarity condition without utilizing the full internal symmetries of Higgs scattering.Here,we further implement stronger nonlinear unitarity conditions from the UV,which generically gives rise to better bounds.We show that,for the Higgs case in particular,while the nonlinear unitarity conditions per se do not enhance the bounds,the fuller use of the internal symmetries do shrink the capped positivity cone significantly.

Perturbative Power Counting,Lowest-Index Operators and Their Renormalization in Standard Model Effective Field Theory

We study two aspects of higher dimensional operators in standard model effective field theory.We first introduce a perturbative power counting rule for the entries in the anomalous dimension matrix of operators with equal mass dimension.The power counting is determined by the number of loops and the difference of the indices of the two operators involved,which in turn is defined by assuming that all terms in the standard model Lagrangian have an equal perturbative power.Then we show that the operators with the lowest index are unique at each mass dimension d,i.e.,(H^(†)H)^(d/2)for even d≥4,and(L^(T)εH)C(L^(T)εH)^(T)(H^(†)H)^((d-5)/2)for odd d≥5.Here H,L are the Higgs and lepton doublet,andε,C the antisymmetric matrix of rank two and the charge conjugation matrix,respectively.The renormalization group running of these operators can be studied separately from other operators of equal mass dimension at the leading order in power counting.We compute their anomalous dimensions at one loop for general d and find that they are enhanced quadratically in d due to combinatorics.We also make connections with classification of operators in terms of their holomorphic and anti-holomorphic weights.

Positivity in electron-positron scattering:testing the axiomatic quantum field theory principles and probing the existence of UV states

We consider the positivity bounds on dimension-8 four-electron operators and study two related phenomenological aspects at future lepton colliders.First,if positivity is violated,probing such violations will revolutionize our understanding of the fundamental pillars of quantum field theory and the S-matrix theory.We observe that positivity violation at scales of 1-10 TeV can potentially be probed at future lepton colliders even if one assumes that dimension-6 operators are also present.Second,the positive nature of the dimension-8 parameter space often allows us to either directly infer the existence of UV-scale particles together with their quantum numbers or exclude them up to certain scales in a model-independent way.In particular,dimension-8 positivity plays an important role in the test of the Standard Model.If no deviations from the Standard Model are observed,it allows for simultaneous exclusion limits on all kinds of potential UV-complete models.Unlike the dimension-6 case,these limits apply regardless of the UV model setup and cannot be removed by possible cancellations among various UV contributions.This thus consists of a novel and universal test to confirm the Standard Model.We demonstrate with realistic examples how all the previously mentioned possibilities,including the test of positivity violation,can be achieved.Hence,we provide an important motivation for studying dimension-8 operators more comprehensively.

Constraints on anomalous quartic gauge couplings via Wγjj production at the LHC

Vector boson scattering at the Large Hadron Collider(LHC)is sensitive to anomalous quartic gauge couplings(aQGCs).In this study,we investigate the aQGC contribution to Wγjj production at the LHC with√s=13 TeV in the context of an effective field theory(EFT).The unitarity bound is applied as a cut on the energy scale of this production process,which is found to have significant suppressive effects on signals.To enhance the statistical significance,we analyze the kinematic and polarization features of the aQGC signals in detail.We find that the polarization effects induced by aQGCs are unique and can discriminate the signals from the SM backgrounds well.With the proposed event selection strategy,we obtain the constraints on the coefficients of dimension-8 operators with current luminosity.The results indicate that the process pp→Wγjj is powerful for searching for the OM2,3,4,5 and OT5,6,7 operators.