Abstract
We study the structure of scalar, vector, and tensor currents for on-shell massive particles of any spin. When considering higher values for the spin of the particle, the number of form factors (FFs) involved in the decomposition of the matrix elements associated with these local currents increases. We identify all the fundamental structures that give rise to the independent FFs, systematically for any spin value. These structures can be conveniently organised using an expansion in covariant multipoles, built solely from the Lorentz generators. This approach allows one to uniquely identify the terms which are universal and those that arise because of spin. We derive counting rules which relate the number of FFs to the total spin $j$ of the state, showing explicitly that these rules match all the well-known cases up to spin 2.
Highlights
Matrix elements representing the interaction of quantum states with local currents are parametrized in terms of form factors (FFs)
In the spirit of Ref. [23] and with the aim of looking for the most general way to find the energy-momentum tensor (EMT) parametrization we present an alternative approach based on the covariant multipole expansion developed in Secs
The main disadvantage is that it is based on the direct inspection of the structures and on the explicit use of several on shell identities which are highly nontrivial. This is the reason why several former parametrizations proposed in the literature have been found either incomplete or overcomplete. We develop another technique based on covariant multipoles, complementary to the tensor product approach and confirming the number of FFs
Summary
Matrix elements representing the interaction of quantum states with local currents are parametrized in terms of form factors (FFs). Being formed by symmetrized products of Lorentz generators, the only nonvanishing 2j þ 1 multipoles are operators with given symmetry properties on each pair of Lorentz indices Starting from this basis of linearly independent multipoles, which is common to all operators (scalar, vector, tensor) for a given state of spin j, we build the coefficients of the expansion depending on the symmetry properties of the problem and on the relevant operator. This procedure leads to a systematic counting of FFs. Interestingly, we can show that the counting changes in a nontrivial way when going from lower to higher-rank operators. In the second one we derive a large set of exact and on shell identities, which are used to eliminate redundant Lorentz structures in the parametrizations
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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.
