Collective fields in the functional renormalization group for fermions, Ward identities, and the exact solution of the Tomonaga-Luttinger model

We develop a new formulation of the functional renormalization group (RG) for interacting fermions. Our approach unifies the purely fermionic formulation based on the Grassmannian functional integral, which has been used in recent years by many authors, with the traditional Wilsonian RG approach to quantum systems pioneered by Hertz [Phys. Rev. B 14, 1165 (1976)], which attempts to describe the infrared behavior of the system in terms of an effective bosonic theory associated with the soft modes of the underlying fermionic problem. In our approach, we decouple the interaction by means of a suitable Hubbard-Stratonovich transformation (following the Hertz-approach), but do not eliminate the fermions; instead, we derive an exact hierarchy of RG flow equations for the irreducible vertices of the resulting coupled field theory involving both fermionic and bosonic fields. The freedom of choosing a momentum transfer cutoff for the bosonic soft modes in addition to the usual band cutoff for the fermions opens the possibility of new RG schemes. In particular, we show how the exact solution of the Tomonaga-Luttinger model emerges from the functional RG if one works with a momentum transfer cutoff. Then the Ward identities associated with the local particle conservation at each Fermi point are valid at every stage of the RG flow and provide a solution of an infinite hierarchy of flow equations for the irreducible vertices. The RG flow equation for the irreducible single-particle self-energy can then be closed and can be reduced to a linear integro-differential equation, the solution of which yields the result familiar from bosonization. We suggest new truncation schemes of the exact hierarchy of flow equations, which might be useful even outside the weak coupling regime.Comment: 27 pages, 15 figures; published version, some typos correcte

Rare Top-quark Decays to Higgs boson in MSSM

In full one-loop generality and in next-to-leading order in QCD, we study rare top to Higgs boson flavour changing decay processes $t\to q h$ with $q=u,c$ quarks, in the general MSSM with R-parity conservation. Our primary goal is to search for enhanced effects on $Br(t\to q h)$ that could be visible at current and high luminosity LHC running. To this end, we perform an analytical expansion of the amplitude in terms of flavour changing squark mass insertions that treats both cases of hierarchical and degenerate squark masses in a unified way. We identify two enhanced effects allowed by various constraints: one from holomorphic trilinear soft SUSY breaking terms and/or right handed up squark mass insertions and another from non-holomorphic trilinear soft SUSY breaking terms and light Higgs boson masses. Interestingly, even with $\mathcal{O}(1)$ flavour violating effects in the, presently unconstrained, up-squark sector, SUSY effects on $Br(t\to q h)$ come out to be unobservable at LHC mainly due to leading order cancellations between penguin and self energy diagrams and the constraints from charge- and colour-breaking minima (CCB) of the MSSM vacuum. An exception to this conclusion may be effects arising from non-holomorphic soft SUSY breaking terms in the region where the CP-odd Higgs mass is smaller than the top-quark mass but this scenario is disfavoured by recent LHC searches. Our calculations for $t\to q h$ decay are made available in SUSY_FLAVOR numerical library.Comment: 32 pages, 6 figures; version accepted for publication in JHEP: additional comparison with literature added, minor misprints correcte

Lorentz breaking Effective Field Theory and observational tests

Analogue models of gravity have provided an experimentally realizable test field for our ideas on quantum field theory in curved spacetimes but they have also inspired the investigation of possible departures from exact Lorentz invariance at microscopic scales. In this role they have joined, and sometime anticipated, several quantum gravity models characterized by Lorentz breaking phenomenology. A crucial difference between these speculations and other ones associated to quantum gravity scenarios, is the possibility to carry out observational and experimental tests which have nowadays led to a broad range of constraints on departures from Lorentz invariance. We shall review here the effective field theory approach to Lorentz breaking in the matter sector, present the constraints provided by the available observations and finally discuss the implications of the persisting uncertainty on the composition of the ultra high energy cosmic rays for the constraints on the higher order, analogue gravity inspired, Lorentz violations.Comment: 47 pages, 4 figures. Lecture Notes for the IX SIGRAV School on "Analogue Gravity", Como (Italy), May 2011. V.3. Typo corrected, references adde