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Register a new userOn the Topic of Emergence from an Effective Field Theory Perspective
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Ulf-G. Mei{\\ss}ner
Publication date
2019
fields
Physics
and research's language is
English
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Effective Field Theories have been used successfully to provide a bottom-up description of phenomena whose intrinsic degrees of freedom behave at length scales far different from their effective degrees of freedom. An example is the emergent phenomenon of bound nuclei, whose constituents are neutrons and protons, which in turn are themselves composed of more fundamental particles called quarks and gluons. In going from a fundamental description that utilizes quarks and gluons to an effective field theory description of nuclei, the length scales traversed span at least two orders of magnitude. In this article we provide an Effective Field Theory viewpoint on the topic of emergence, arguing on the side of reductionism and weak emergence. We comment on Andersons interpretation of constructionism and its connection to strong emergence.
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In this paper we discuss two constructions of an effective field theory starting from a local interaction functional. One relies on the well-established graphical combinatorics of the BPHZ algorithm to renormalize divergent Feynman amplitudes. The other, more recent and due to Costello, relies on an inductive construction of local counterterms that uses no graphical combinatorics whatsoever. We show that these two constructions produce the same effective field theory.
We apply on-shell methods to the bottom-up construction of electroweak amplitudes, allowing for both renormalizable and non-renormalizable interactions. We use the little-group covariant massive-spinor formalism, and flesh out some of its details along the way. Thanks to the compact form of the resulting amplitudes, many of their properties, and in particular the constraints of perturbative unitarity, are easily seen in this formalism. Our approach is purely bottom-up, assuming just the standard-model electroweak spectrum as well as the conservation of electric charge and fermion number. The most general massive three-point amplitudes consistent with these symmetries are derived and studied in detail, as the primary building blocks for the construction of scattering amplitudes. We employ a simple argument, based on tree-level unitarity of four-point amplitudes, to identify the three-point amplitudes that are non-renormalizable at tree level. This bottom-up analysis remarkably reproduces many low-energy relations implied by electroweak symmetry through the standard-model Higgs mechanism and beyond it. We then discuss four-point amplitudes. The gluing of three-point amplitudes into four-point amplitudes in the massive spinor helicity formalism is clarified. As an example, we work out the $psi^c psi Zh$ amplitude, including also the non-factorizable part. The latter is an all-order expression in the effective-field-theory expansion. Further constraints on the couplings are obtained by requiring perturbative unitarity. In the $psi^c psi Zh$ example, one for instance obtains the renormalizable-level relations between vector and fermion masses and gauge and Yukawa couplings. We supplement our bottom-up derivations with a matching of three- and four-point amplitude coefficients onto the standard-model effective field theory (SMEFT) in the broken electroweak phase.
In an earlier paper~cite{Luu:2019jmb} we discussed emergence from the context of effective field theories, particularly as related to the fields of particle and nuclear physics. We argued on the side of reductionism and weak emergence. George Ellis has critiqued our exposition in~cite{Ellis:2020vij}, and here we provide our response to his critiques. Many of his critiques are based on incorrect assumptions related to the formalism of effective field theories and we attempt to correct these issues here. We also comment on other statements made in his paper. Important to note is that our response is to his critiques made in archi
The LHCb pentaquarks -- the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ -- have been theorized to be $Sigma_c bar{D}$ and $Sigma_c bar{D}^*$ S-wave molecules. Here we explore the possibility that two of these pentaquarks -- the $P_c(4440)$ and $P_c(4457)$ -- contain in addition a $Lambda_c(2595) bar{D}$ component in P-wave. We will analyze the effects of this extra channel within two effective field theories: the first one will be a standard contact-range effective field theory and the second one will include the non-diagonal pion dynamics connecting the $Sigma_c bar{D}^*$ and $Lambda_c(2595) bar{D}$ channels, which happens to be unusually long-ranged. The impact of the coupled-channel dynamics between the $Sigma_c bar{D}^*$ and $Lambda_c(2595) bar{D}$ components is modest at best for the $P_c(4440)$ and $P_c(4457)$, which will remain to be predominantly $Sigma_c bar{D}^*$ molecules. However, if the quantum numbers of the $P_c(4457)$ are $J^P = frac{1}{2}^-$, the coupled-channel dynamics is likely to induce the binding of a $Lambda_c(2595) bar{D}$ S-wave molecule (coupled to $Sigma_c bar{D}^*$ in P-wave) with $J^P = frac{1}{2}^+$ and a mass similar to the $P_c(4457)$. If this is the case, the $P_c(4457)$ could actually be a double peak containing two different pentaquark states.
We revisit several aspects of the interaction of self-gravitating, slowly varying sources with their own emitted radiation within the context of post-Newtonian approximation to General Relativity. We discuss and clarify the choice of boundary conditions of Greens functions used to determine conservative potentials, and the interplay between the so-called near and far zones, as well as the relation between far zone ultra-violet divergences and emitted power. Both near and far zone contributions are required for the computation of the conservative dynamics. Within a field-theory approach we rederive far-zone self-energy processes, known as tail and memory effects, generalising the calculation of their divergent part to arbitrary order in the post-Newtonian expansion.
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