We present a convex geometry perspective to the effective field theory (EFT) parameter space. We show that the second s derivatives of the forward EFT amplitudes form a convex cone, whose extremal ...rays are closely connected with states in the UV theory. For tree-level UV completions, these rays are simply theories with all UV particles living in at most one irreducible representation of the symmetries of the theory. In addition, all the extremal rays are determined by the symmetries and can be systematically identified via group theoretical considerations. The implications are twofold. First, geometric information encoded in the EFT space can help reconstruct the UV completion. In particular, we will show that the dim-8 operators are important in reverse engineering the UV physics from the standard model EFT and, thus, deserve more theoretical and experimental investigations. Second, theoretical bounds on the Wilson coefficients can be obtained by identifying the boundaries of the cone and are, in general, stronger than the current positivity bounds. We show explicit examples of these new bounds and demonstrate that they originate from the scattering amplitudes corresponding to entangled states.
Weak vector boson scattering (VBS) is a sensitive probe of new physics effects in the electroweak symmetry breaking. Currently, experimental results at the LHC are interpreted in the effective field ...theory approach, where possible deviations from the Standard Model in the quartic-gauge-boson couplings are often described by 18 dimension-eight operators. By assuming that an UV completion exists, we derive a new set of theoretical constraints on the coefficients of these operators; i.e., certain combinations of coefficients must be positive. These constraints imply that the current effective approach to VBS has a large redundancy: only about 2% of the full parameter space leads to an UV completion. By excluding the remaining unphysical region of the parameter space, these constraints provide guidance for future VBS studies and measurements.
A
bstract
Positivity bounds are powerful tools to constrain effective field theories. Utilizing the partial wave expansion in the dispersion relation and the full crossing symmetry of the scattering ...amplitude, we derive several sets of generically nonlinear positivity bounds for a generic scalar effective field theory: we refer to these as the
P Q
,
D
su
,
D
stu
and
D
¯
stu
bounds. While the
PQ
bounds and
D
su
bounds only make use of the
s
↔
u
dispersion relation, the
D
stu
and
D
¯
stu
bounds are obtained by further imposing the
s
↔
t
crossing symmetry. In contradistinction to the linear positivity for scalars, these inequalities can be applied to put upper and lower bounds on Wilson coefficients, and are much more constraining as shown in the lowest orders. In particular we are able to exclude theories with soft amplitude behaviour such as weakly broken Galileon theories from admitting a standard UV completion. We also apply these bounds to chiral perturbation theory and we find these bounds are stronger than the previous bounds in constraining its Wilson coefficients.
The most general action for a scalar field coupled to gravity that leads to second-order field equations for both the metric and the scalar--Horndeski's theory--is considered, with the extra ...assumption that the scalar satisfies shift symmetry. We show that in such theories, the scalar field is forced to have a nontrivial configuration in black hole spacetimes, unless one carefully tunes away a linear coupling with the Gauss-Bonnet invariant. Hence, black holes for generic theories in this class will have hair. This contradicts a recent no-hair theorem which seems to have overlooked the presence of this coupling.
A
bstract
We develop a formalism to extract triple crossing symmetric positivity bounds for effective field theories with multiple degrees of freedom, by making use of
su
symmetric dispersion ...relations supplemented with positivity of the partial waves,
st
null constraints and the generalized optical theorem. This generalizes the convex cone approach to constrain the
s
2
coefficient space to higher orders. Optimal positive bounds can be extracted by semi-definite programs with a continuous decision variable, compared with linear programs for the case of a single field. As an example, we explicitly compute the positivity constraints on bi-scalar theories, and find all the Wilson coefficients can be constrained in a finite region, including the coefficients with odd powers of
s
, which are absent in the single scalar case.
Psychological health problems, especially emotional disorders, are common among adolescents. The epidemiology of emotional disorders is greatly influenced by stressful events. This study sought to ...assess the prevalence rate and socio-demographic correlates of depressive and anxiety symptoms among Chinese adolescents affected by the outbreak of COVID-19. We conducted a cross-sectional study among Chinese students aged 12–18 years during the COVID-19 epidemic period. An online survey was used to conduct rapid assessment. A total of 8079 participants were involved in the study. An online survey was used to collect demographic data, assess students’ awareness of COVID-19, and assess depressive and anxiety symptoms with the Patient Health Questionnaire (PHQ-9) and the Generalized Anxiety Disorder (GAD-7) questionnaire, respectively. The prevalence of depressive symptoms, anxiety symptoms, and a combination of depressive and anxiety symptoms was 43.7%, 37.4%, and 31.3%, respectively, among Chinese high school students during the COVID-19 outbreak. Multivariable logistic regression analysis revealed that female gender was the higher risk factor for depressive and anxiety symptoms. In terms of grades, senior high school was a risk factor for depressive and anxiety symptoms; the higher the grade, the greater the prevalence of depressive and anxiety symptoms. Our findings show there is a high prevalence of psychological health problems among adolescents, which are negatively associated with the level of awareness of COVID-19. These findings suggest that the government needs to pay more attention to psychological health among adolescents while combating COVID-19.
A
bstract
Searching for deviations in quartic gauge boson couplings (QGCs) is one of the main goals of the electroweak program at the LHC. We consider positivity bounds adapted to the Standard Model, ...and show that a set of positivity constraints on 18 anomalous QGC couplings can be derived, by requiring that the vector boson scattering amplitudes of specific channels and polarisations satisfy the fundamental principles of quantum field theory. We explicitly solve the positivity inequalities to remove their dependence on the polarisations of the external particles, and obtain 19 linear inequalities, 3 quadratic inequalities, and 1 quartic inequality that only involve the QGC parameters and the weak angle. These inequalities constrain the possible directions in which deviations from the standard QGC can occur, and can be used to guide future experimental searches. We study the morphology of the positivity bounds in the parameter space, and find that the allowed parameter space is carved out by the intersection of pyramids, prisms, and (approximately) cones. Altogether, they reduce the volume of the allowed parameter space to only 2.1% of the total. We also show the bounds for some benchmark cases, where one, two, or three operators, respectively, are turned on at a time, so as to facilitate a quick comparison with the experimental results.
A
bstract
The positivity bounds, derived from the axiomatic principles of quantum field theory (QFT), constrain the signs of Wilson coefficients and their linear combinations in the Standard Model ...Effective Field Theory (SMEFT). The precise determination of these bounds, however, can become increasingly difficult as more and more SM modes and oper- ators are taken into account. We study two approaches that aim at obtaining the full set of bounds for a given set of SM fields: 1) the traditional elastic positivity approach, which exploits the elastic scattering amplitudes of states with arbitrarily superposed helicities as well as other quantum numbers, and 2) the newly proposed extremal positivity approach, which constructs the allowed coefficient space directly by using the extremal representation of convex cones. Considering the electroweak gauge-bosons as an example, we demonstrate how the best analytical and numerical positivity bounds can be obtained in several ways. We further compare the constraining power and the efficiency of various approaches, as well as their applicability to more complex problems. While the new extremal approach is more constraining by construction, we also find that it is analytically easier to use, nu- merically much faster than the elastic approach, and much more applicable when more SM particle states and operators are taken into account. As a byproduct, we provide the best positivity bounds on the transversal quartic-gauge-boson couplings, required by the axiomatic principles of QFT, and show that they exclude
≈
99
.
3% of the parameter space currently being searched at the LHC.
Graviton mass bounds de Rham, Claudia; Deskins, J. Tate; Tolley, Andrew J. ...
Reviews of modern physics,
05/2017, Letnik:
89, Številka:
2
Journal Article
PDF
