#### Confinement strings

The string hypothesis states that in the long-distance limit the quark-antiquark interaction can be described as a string joining both particles. At leading-order this hypothesis leads to a linear-rising confinement term in the quark-antiquark potential, where the proportionality constant can be identified as the string tension, this linear term has been present in most of the successful potential models used to describe the quarkonium spectrum.

With the development of pNRQCD the quark-antiquark potential could be obtained systematically from QCD order by order in the non-relativistic expansion in a model-independent way. The resulting expression, that is valid in the whole distance regime, is organized in powers of the inverse of the mass and depends on correlators that correspond to operators insertions in the expectation value of the rectangular Wilson loop. Assuming the string hypothesis at large distances, and considering the symmetries of the degrees of freedom of both theories, we are able to calculate these correlators in terms of string parameters.

Comparing the string potential with the available lattice evaluations of the QCD correlators we can test the validity of the string hypothesis. For instance, the non-trivial logarithmic dependence of the 1/m suppressed relativistic correction in the string potential fits the available lattice data for that correlator, confirming that at least at this order the string hypothesis gives the right potential shape. For most of the higher order relativistic corrections no lattice evaluation of the correlators is available yet, however, it would be interesting to see if data coming from these evaluations, once performed, can be fitted using the string potential.

In our research we also explore the use of the string potential in the study of quarkonium phenomenology, where the higher relativistic corrections of the potential are often necessary for a consistent evaluation of the observables.

#### Symmetries of Effective Field Theories

There are many classes of effective field theory (EFT) in the field of particle and nuclear physics or even cosmology nowadays, depending on what approach one adopts. In the top-down way of treating the EFT, non-relativistic QCD (NRQCD) or potential-NRQCD (pNRQCD) for instance, certain manifest symmetries of the underlying theory are seemingly lost. Lowering the energy scale of the theory does not mean that the theory loses its symmetry at all, but rather its manifestation is not there any more. We work on this topic on preservation of symmetries of the EFT, which enhances the predictability of the theory for its calculation of the observables.

**Lorentz (or Poincare) invariance** is clearly to be respected in any kind of relativistic field theories. However, in the non-relativistic regime, the corresponding theory loses its manifestation although it is to be preserved. We work on the manifest Lorentz (or Poincare) invariance of the several different EFTs, (such as NRQCD, pNRQCD, soft collinear EFT, etc), which sheds new insight on these well-established theories, as well as poses interesting questions on its symmetry properties.

**Diffeomorphism invariance** is another manifest symmetry in general relativity and field theories in curved spacetime. In the cosmological models, maximal symmetry of the spacetime is lost which then is reduced down to the maximally symmetric space, which preserves spatial diffeomorphisms. However, this is only an approximation to the realistic models of the universe we observe today, so it calls upon modifications of it, which requires a proper treatment in EFT methods.

*Written by H. Martinez and S. Hwang.*

#### People

*Nora Brambilla, Antonio Vairo, Hector Martinez, Matthias Berwein, Sungmin Hwang.*

#### Some related publications

Nora Brambilla, Michael Groher, Hector Martinez, Antonio Vairo

** Effective string theory and the long-range relativistic corrections to the quark-antiquark potential**

Phys.Rev. D90 (2014) 114032

arXiv:1407.7761 Inspire