152 research outputs found
Global Wilson-Fisher fixed points
The Wilson-Fisher fixed point with universality in three dimensions is
studied using the renormalisation group. It is shown how a combination of
analytical and numerical techniques determine global fixed point solutions to
leading order in the derivative expansion for real or purely imaginary fields
with moderate numerical effort. Universal and non-universal quantitites such as
scaling exponents and mass ratios are computed, for all , together with
local fixed point coordinates, radii of convergence, and parameters which
control the asymptotic behaviour of the effective action. We also explain when
and why finite- results do not converge pointwise towards the exact
infinite- limit. In the regime of purely imaginary fields, a new link
between singularities of fixed point effective actions and singularities of
their counterparts by Polchinski are established. Implications for other
theories are indicated.Comment: 28 pages, 10 figures, v2: explanations and refs added, to appear
(NPB
Lattice calculations of the leading hadronic contribution to (g-2)_mu
We report on our ongoing project to calculate the leading hadronic
contribution to the anomalous magnetic moment of the muon a_mu^HLO using two
dynamical flavours of non-perturbatively O(a) improved Wilson fermions. In this
study, we changed the vacuum polarisation tensor to a combination of local and
point-split currents which significantly reduces the numerical effort.
Partially twisted boundary conditions allow us to improve the momentum
resolution of the vacuum polarisation tensor and therefore the determination of
the leading hadronic contribution to (g-2)_mu. We also extended the range of
ensembles to include a pion mass below 200 MeV which allows us to check the
non-trivial chiral behaviour of a_mu^HLO.Comment: 7 pages, 3 figures, 1 table, talk presented at the 30th International
Symposium on Lattice Field Theory (Lattice2012), Cairns, Australi
Hadronic form factors for rare semileptonic decays
We discuss first results for the computation of short distance contributions
to semileptonic form factors for the rare decays
and . Our simulations are based on RBC/UKQCD's
ensembles with domain wall light quarks and the Iwasaki gauge action.
For the valence -quark we chose the relativistic heavy quark action.Comment: 7 pages, 1 table, 3 figures, presented at the 33rd International
Symposium on Lattice Field Theory (Lattice2015), July 14-18, 2015, Kobe,
Japa
Theoretical aspects of quantum electrodynamics in a finite volume with periodic boundary conditions
First-principles studies of strongly-interacting hadronic systems using
lattice quantum chromodynamics (QCD) have been complemented in recent years
with the inclusion of quantum electrodynamics (QED). The aim is to confront
experimental results with more precise theoretical determinations, e.g. for the
anomalous magnetic moment of the muon and the CP-violating parameters in the
decay of mesons. Quantifying the effects arising from enclosing QED in a finite
volume remains a primary target of investigations. To this end, finite-volume
corrections to hadron masses in the presence of QED have been carefully studied
in recent years. This paper extends such studies to the self-energy of moving
charged hadrons, both on and away from their mass shell. In particular, we
present analytical results for leading finite-volume corrections to the
self-energy of spin-0 and spin- particles in the presence of QED
on a periodic hypercubic lattice, once the spatial zero mode of the photon is
removed, a framework that is called . By altering
modes beyond the zero mode, an improvement scheme is introduced to eliminate
the leading finite-volume corrections to masses, with potential applications to
other hadronic quantities. Our analytical results are verified by a dedicated
numerical study of a lattice scalar field theory coupled to
. Further, this paper offers new perspectives on the
subtleties involved in applying low-energy effective field theories in the
presence of , a theory that is rendered non-local
with the exclusion of the spatial zero mode of the photon, clarifying recent
discussions on this matter.Comment: 57 pages, 10 figures, version accepted for publication in Phys. Rev.
Complex dynamics in adaptive phase oscillator networks
Networks of coupled dynamical units give rise to collective dynamics such as
the synchronization of oscillators or neurons in the brain. The ability of the
network to adjust coupling strengths between units in accordance with their
activity arises naturally in a variety of contexts, including neural plasticity
in the brain, and adds an additional layer of complexity: the dynamics on the
nodes influence the dynamics of the network and vice versa. We study a model of
Kuramoto phase oscillators with a general adaptive learning rule with three
parameters (strength of adaptivity, adaptivity offset, adaptivity shift). This
rule includes as special cases learning paradigms such as (anti-)Hebbian
learning and spike time dependent plasticity (STDP). Importantly, the
adaptivity parameter allows to study the impact of adaptation on the collective
dynamics as we move away from the non-adaptive case given by stationary
coupling. First, we carry out a detailed bifurcation analysis for N = 2
oscillators with (un-)directed coupling strengths. Adaptation dynamics in terms
of nontrivial bifurcations arises only when the strength of adaptation exceeds
a critical threshold. Whereas the paradigms of (anti-)Hebbian learning and STDP
result in non-trivial multi-stability and bifurcation scenarios, mixed-type
learning rules exhibit even more complicated and rich dynamics including a
period doubling cascade to chaotic dynamics as well as oscillations displaying
features of both librational and rotational character. Second, we numerically
investigate a larger system with N = 50 oscillators and explore dynamic
similarities with the case of N = 2 oscillators
Computing the Adler function from the vacuum polarization function
We use a lattice determination of the hadronic vacuum polarization tensor to
study the associated Ward identities and compute the Adler function. The vacuum
polarization tensor is computed from a combination of point-split and local
vector currents, using two flavours of O()-improved Wilson fermions.
Partially twisted boundary conditions are employed to obtain a fine momentum
resolution. The modifications of the Ward identities by lattice artifacts and
by the use of twisted boundary conditions are monitored. We determine the Adler
function from the derivative of the vacuum polarization function over a large
region of momentum transfer . As a first account of systematic effects, a
continuum limit scaling analysis is performed in the large regime.Comment: 7 pages, 4 figures, presented at the 31st International Symposium on
Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German
Isospin Breaking Corrections to the HVP with Domain Wall Fermions
We present results for the QED and strong isospin breaking corrections to the
hadronic vacuum polarization using Domain Wall fermions. QED is
included in an electro-quenched setup using two different methods, a stochastic
and a perturbative approach. Results and statistical errors from both methods
are directly compared with each other.Comment: 8 pages, 6 figures, presented at the 35th International Symposium on
Lattice Field Theory (Lattice 2017), Granada, Spain, June 18-24, 201
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