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Register a new userFrom Jacobi off-shell currents to integral relations
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William Javier Torres Bobadilla Dr.
Publication date
2017
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English
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In this paper, we study off-shell currents built from the Jacobi identity of the kinematic numerators of $ggto X$ with $X=ss,qbar{q},gg$. We find that these currents can be schematically written in terms of three-point interaction Feynman rules. This representation allows for a straightforward understanding of the Colour-Kinematics duality as well as for the construction of the building blocks for the generation of higher-multiplicity tree-level and multi-loop numerators. We also provide one-loop integral relations through the Loop-Tree duality formalism with potential applications and advantages for the computation of relevant physical processes at the Large Hadron Collider. We illustrate these integral relations with the explicit examples of QCD one-loop numerators of $ggto ss$.
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Examining the Higgs sector at high energy scales through off-shell Higgs production can potentially shed light on the naturalness problem of the Higgs mass. We propose such a study at the LHC by utilizing a representative model with a new scalar field ($S$) coupled to the Standard Model Higgs doublet ($H$) in a form $ |S|^2 |H|^2$. In the process $p p rightarrow h^* rightarrow ZZ$, the dominant momentum-dependent part of the one-loop scalar singlet corrections, especially above the new threshold at $2m_S$, leads to a measurable deviation in the differential distribution of the $Z$-pair invariant mass, in accordance with the quadratic divergence cancellation to the Higgs mass. We find that it is conceivable to probe such new physics at the $5sigma$ level at the high-luminosity LHC, improving further with the upgraded $27$ TeV LHC, without requiring the precise measurement of the Higgs boson total width. The discovery of such a Higgs portal could also have important implications for thermal dark matter as well as for electroweak baryogenesis.
In this note, we investigate relations between tree-level off-shell currents in nonlinear sigma model. Under Cayley parametrization, all odd-point currents vanish. We propose and prove a generalized $U(1)$ identity for even-point currents. The off-shell $U(1)$ identity given in [1] is a special case of the generalized identity studied in this note. The on-shell limit of this identity is equivalent with the on-shell KK relation. Thus this relation provides the full off-shell correspondence of tree-level KK relation in nonlinear sigma model.
One of the methods to calculate tree-level multi-gluon scattering amplitudes is to use the Berends-Giele recursion relation involving off-shell currents or off-shell amplitudes, if working in the light cone gauge. As shown in recent works using the light-front perturbation theory, solutions to these recursions naturally collapse into gauge invariant and gauge-dependent components, at least for some helicity configurations. In this work, we show that such structure is helicity independent and emerges from analytic properties of matrix elements of Wilson line operators, where the slope of the straight gauge path is shifted in a certain complex direction. This is similar to the procedure leading to the Britto-Cachazo-Feng-Witten (BCFW) recursion, however we apply a complex shift to the Wilson line slope instead of the external momenta. While in the original BCFW procedure the boundary integrals over the complex shift vanish for certain deformations, here they are non-zero and are equal to the off-shell amplitudes. The main result can thus be summarized as follows: we derive a decomposition of a helicity-fixed off-shell current into gauge invariant component given by a matrix element of a straight Wilson line plus a reminder given by a sum of products of gauge invariant and gauge dependent quantities. We give several examples realizing this relation, including the five-point next-to-MHV helicity configuration.
We construct an unfolded system for off-shell fields of arbitrary integer spin in 4d anti-de Sitter space. To this end we couple an on-shell system, encoding Fronsdal equations, to external Fronsdal currents for which we find an unfolded formulation. We present a reduction of the Fronsdal current system which brings it to the unfolded Fierz-Pauli system describing massive fields of arbitrary integer spin. Reformulating off-shell higher-spin system as the set of Schwinger-Dyson equations we compute propagators of higher-spin fields in the de Donder gauge directly from the unfolded equations. We discover operators that significantly simplify this computation, allowing a straightforward extraction of wave equations from an unfolded system.
The consistent recursive subtraction of UV divergences order by order in the loop expansion for spontaneously broken effective field theories with dimension-6 derivative operators is presented for an Abelian gauge group. We solve the Slavnov-Taylor identity to all orders in the loop expansion by homotopy techniques and a suitable choice of invariant field coordinates (named bleached variables) for the linearly realized gauge group. This allows one to disentangle the gauge-invariant contributions to off-shell 1-PI amplitudes from those associated with the gauge-fixing and (generalized) non-polynomial field redefinitions (that do appear already at one loop). The tools presented can be easily generalized to the non-Abelian case.
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