Effective field theories for van der Waals interactions

Abstract

Van der Waals interactions between two neutral but polarizable systems at a separation R much larger than the typical size of the systems are at the core of a broad sweep of contemporary problems in settings ranging from atomic, molecular and condensed matter physics to strong interactions and gravity. In this paper, we reexamine the dispersive van der Waals interactions between two hydrogen atoms. The novelty of the analysis resides in the usage of nonrelativistic effective field theories of quantum electrodynamics. In this framework, the van der Waals potential acquires the meaning of a matching coefficient in an effective field theory, dubbed van der Waals effective field theory, suited to describe the low-energy dynamics of an atom pair. It may be computed systematically as a series in R times some typical atomic scale and in the fine-structure constant α. The van der Waals potential gets short-range contributions and radiative corrections, which we compute in dimensional regularization and renormalize here for the first time. Results are given in d space-time dimensions. One can distinguish among different regimes depending on the relative size between 1/R and the typical atomic bound-state energy, which is of order mα 2 . Each regime is characterized by a specific hierarchy of scales and a corresponding tower of effective field theories. The shortdistance regime is characterized by 1/R ≫ mα 2 and the leading-order van der Waals potential is the London potential. We compute also next-to-next-to-next-to-leading order corrections. In the long-distance regime we have 1/R ≪ mα 2 . In this regime, the van der Waals potential contains contact terms, which are parametrically larger than the Casimir-Polder potential that describes the potential at large distances. In the effective field theory, the Casimir-Polder potential counts as a next-to-next-to-next-to-leading-order effect. In the intermediate-distance regime, 1/R ∼ mα 2 , a significantly more complex potential is obtained. We compare this exact result with the two previous limiting cases. We conclude bz commenting on the van der Waals interactions in the hadronic case.

Nonlinear Regge trajectories with AdS/QCD

“…This motivated the idea that these states were made of a compact heavy quarkonium core surrounded by a light quark cloud [51]. This quarkonium core interacts with the light quark cloud through a colored Van der Waals-like force (similar as the one in molecular physics), allowing the decay of these states into the observed quarkonium core and the light quarks [52].…”

“…Following [52], we will suppose that the states ψð4260Þ, ψð4360Þ and ψð4660Þ with 0 þ ð1 −− Þ are possible hadrocharmonium states, forming a single vector trajectory. Holographically, the operator that creates these states has dimension six, i.e., Δ ¼ 6, implying that the bulk mass is M 2 5 R 2 ¼ 15, as in the case of the diquark-antidiquark pair configuration.…”

FeynOnium: using FeynCalc for automatic calculations in Nonrelativistic Effective Field Theories

“…Examples for such systems are nonrelativistic bound states (e.g. positronium, muonium [6], heavy quarkonia [7,8]) or systems made of nonrelativistic atoms [9] and molecules [10]. Even though NREFT methods are most commonly employed in nuclear and atomic physics, nowadays they are becoming increasingly popular for studying possible beyond the Standard Model scenarios such as nonrelativistic dark matter [11][12][13][14][15][16][17][18] or heavy neutrinos [19].…”

“…Switching to a different basis spanned by 3 independent vectors appearing in the calculation would be another possibility to deal with this problem 9. FeynArts does not support nonrelativistic theories, while QGRAF would require a separate interface toFeynCalc.…”

Effective field theory for the nucleon-quarkonium interaction

“…Van der Waals forces have been studied in an effective field theory (EFT) framework for QED in Ref. [36] and for quarkonium-quarkonium systems in Ref. [18].…”