A
bstract
We investigate a nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) with a non-trivial measure term in the path integral. We are motivated ...to revisit this older formulation of dynamical triangulations by hints from renormalization group approaches that gravity may be asymptotically safe and by the emergence of a semiclassical phase in causal dynamical triangulations (CDT).
We study the phase diagram of this model and identify the two phases that are well known from previous work: the branched polymer phase and the collapsed phase. We verify that the order of the phase transition dividing the branched polymer phase from the collapsed phase is almost certainly first-order. The nontrivial measure term enlarges the phase diagram, allowing us to explore a region of the phase diagram that has been dubbed the crinkled region. Although the collapsed and branched polymer phases have been studied extensively in the literature, the crinkled region has not received the same scrutiny. We find that the crinkled region is likely a part of the collapsed phase with particularly large finite-size effects. Intriguingly, the behavior of the spectral dimension in the crinkled region at small volumes is similar to that of CDT, as first reported in arXiv:1104.5505, but for sufficiently large volumes the crinkled region does not appear to have 4-dimensional semiclassical features. Thus, we find that the crinkled region of the EDT formulation does not share the good features of the extended phase of CDT, as we first suggested in arXiv:1104.5505. This agrees with the recent results of arXiv:1307.2270, in which the authors used a somewhat different discretization of EDT from the one presented here.
We review lattice results related to pion, kaon,
D
- and
B
-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the ...determination of the light-quark masses, the form factor
f
+
(
0
)
, arising in semileptonic
K
→
π
transition at zero momentum transfer, as well as the decay-constant ratio
f
K
/
f
π
of decay constants and its consequences for the CKM matrix elements
V
u
s
and
V
u
d
. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of
SU
(
2
)
L
×
SU
(
2
)
R
and
SU
(
3
)
L
×
SU
(
3
)
R
Chiral Perturbation Theory and review the determination of the
B
K
parameter of neutral kaon mixing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, we focus here on
D
- and
B
-meson decay constants, form factors, and mixing parameters, since these are most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. In addition we review the status of lattice determinations of the strong coupling constant
α
s
.
The rare decay B→πℓ^{+}ℓ^{-} arises from b→d flavor-changing neutral currents and could be sensitive to physics beyond the standard model. Here, we present the first ab initio QCD calculation of the ...B→π tensor form factor f_{T}. Together with the vector and scalar form factors f_{+} and f_{0} from our companion work J. A. Bailey et al., Phys. Rev. D 92, 014024 (2015), these parametrize the hadronic contribution to B→π semileptonic decays in any extension of the standard model. We obtain the total branching ratio BR(B^{+}→π^{+}μ^{+}μ^{-})=20.4(2.1)×10^{-9} in the standard model, which is the most precise theoretical determination to date, and agrees with the recent measurement from the LHCb experiment R. Aaij et al., J. High Energy Phys. 12 (2012) 125.
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