Four-dimensional random geometries can be generated by statistical models with rank-4 tensors as random variables. These are dual to discrete building blocks of random geometries. We discover a potential candidate for a continuum limit in such a model by employing background-independent coarse-graining techniques where the tensor size serves as a pre-geometric notion of scale. A fixed point candidate which features two relevant directions is found. The possible relevance of this result in view of universal results for quantum gravity and a potential connection to the asymptotic-safety program is discussed. I. THE CASE FOR UNIVERSAL, BACKGROUND-INDEPENDENT QUANTUM GRAVITYTo describe physically relevant spacetimes, such as black holes or Friedmann-Lemaitre-Robertson-Walker spacetimes, it is necessary to go beyond General Relativity, where these spacetimes feature singularities. Such singularities are expected to be resolved once quantum fluctuations of spacetime are properly accounted for. Yet, this is a particularly challenging task if it is to be compatible with the background-independence at the heart of our modern understanding of gravity. Backgroundindependence implies that no configuration of spacetime should be singled out a priori from all configurations that enter the path integral. This is incompatible with perturbative techniques around a fixed spacetime, which single out a special background to perturb around, and which do not provide a predictive quantum field theory of gravity. Instead, one is led to introduce an infinite number of independent local counterterms to cancel divergences at each loop order [1][2][3]. This motivates that background independence should be taken seriously in the search for an ultraviolet complete definition of the gravitational path integral. Thus, we aim at an implementation of the path integral without auxiliary geometric background structures 1 . A promising route to construct a background independent path integral consists of making a transition to discrete building blocks, as in dynamical triangulations [5], Regge calculus [6], matrix/tensor models [7-9], spin foams [10] and causal sets [11]. This allows to construct a discrete approximation of all random geometries (and potentially additional configurations with no interpreta- * eichhorn@cp3.sdu.dk † j.lumma@thphys.uni-heidelberg.de ‡ adpjunior@id.uff.br § a.sikandar@thphys.uni-heidelberg.de 1 An alternative route makes use of an auxiliary background structure at the technical level while ensuring the independence of physical results from this background structure, see, e.g., [4].tion as a spacetime geometry) that enter the path integral for quantum gravity. These discrete building blocks are typically not viewed as physical, "fundamental" building blocks of spacetime. Rather, they are auxiliary, unphysical entities, allowing to define a regularized path integral in analogy to lattice gauge theories for non-gravitational quantum field theories. One might object that quantum spacetime might be fundamentally discrete, wh...

The rare decay B → Aγ, with A representing axial-vector mesons such as K 1(1270), K 1(1400), b 1(1300), a 1(1260), is studied at next-to-leading order (NLO) in soft collinear effective theory (SCET). The large outgoing meson energy encourages the study of the decay with an appropriate factorization scheme that separates the factorizable and non-factorizable parts systematically. We have analyzed the leading-power and O ( α s ) diagrams that contribute to matching to SCETI. The new intermediate theory is matched onto SCETII and the running of SCETI operators is performed to sum large perturbative logarithms. The values of soft-overlap function ζ ⊥ for K 1(1270, 1400), a 1 and b 1 mesons are estimated from the light cone-sum-rules, and later using it the corresponding branching fractions for B → K 1 ( 1270 , 1400 ) , a 1 , b 1 γ decays are calculated. We find that in case of B → K 1(1270, 1400)γ decays the results are in good agreement with their experimental measurements. Also the estimated values of the branching ratios of the B → (b 1, a 1)γ decays are potentially large to be measured at the LHCb and future B-factories.

The symmetries arise due to heavy quark and large energy limit help us to reduce the number of independent form factors in the heavy-to-light B-meson decays. It is expected that these symmetry relations are not exact and are broken by the perturbative effects, namely, the vertex corrections and the hard-spectator scatterings. The former are included in the form factors via vertex renormalization whereas the later are calculated through lightcone distribution amplitudes. We first calculate these symmetry breaking corrections to the form factors involved in semileptonic B-meson to an axial-vector (K 1 )-meson decay. Later, by using these form factors we see their effect on the physical observables such as the zero-position of the forward-backward (A F B ) asymmetry and the longitudinal lepton polarization (P L ) asymmetry in B → K 1 (1270)µ + µ − decay. We find that as a result of these corrections to the form factors, the zero-position of the forward-backward asymmetry is shifted by 10% from its SM value while the effects on P L are rather insignificant.