Abstract
We show that the logarithmic derivative of the gauge coupling on the hadronic mass and the cosmological constant term of a gauge theory are related to the gluon condensate of the hadron and the vacuum respectively. These relations are akin to Feynman–Hellmann relations whose derivation for the case at hand is complicated by the construction of the gauge theory Hamiltonian. We bypass this problem by using a renormalisation group equation for composite operators and the trace anomaly. The relations serve as possible definitions of the gluon condensates themselves which are plagued in direct approaches by power divergences. In turn these results might help to determine the contribution of the QCD phase transition to the cosmological constant and test speculative ideas.
Highlights
We show that the logarithmic derivative of the gauge coupling on the hadronic mass and the cosmological constant term of a gauge theory are related to the gluon condensate of the hadron and the vacuum respectively
We outline the derivation of the standard RGE for local operator matrix elements on physical states which can be found in reference textbooks; e.g. [5, 6]
We begin by defining the relation between the bare operator Oi and the renormalized operator Oi
Summary
We outline the derivation of the standard RGE for local operator matrix elements on physical states which can be found in reference textbooks; e.g. [5, 6]. The symbol ∆ ̄ O ≡ dO + γO is, as usual, the scaling dimension of the operator O. Eq (6) can be solved by the method of characteristics by introducing a parameter which has the interpretation of a blocking variable. This is for instance used in Ref. [4] to identify the scaling corrections to correlators at a non-trivial IR fixed point. To this end we note that in this paper the Oi considered are physical quantities (no anomalous scaling) which in addition do not mix with other operators and (∆O)ij = dOiδij
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
