14,006 research outputs found
Hidden and explicit quantum scale invariance
There exist renormalisation schemes that explicitly preserve the scale
invariance of a theory at the quantum level. Imposing a scale invariant
renormalisation breaks renormalisability and induces new non-trivial operators
in the theory. In this work, we study the effects of such scale invariant
renormalisation procedures. On the one hand, an explicitly quantum scale
invariant theory can emerge from the scale invariant renormalisation of a scale
invariant Lagrangian. On the other hand, we show how a quantum scale invariant
theory can equally emerge from a Lagrangian visibly breaking scale invariance
renormalised with scale dependent renormalisation (such as the traditional
MS-bar scheme). In this last case, scale invariance is hidden in the theory, in
the sense that it only appears explicitly after renormalisation.Comment: Minor changes, updated references, matches published versio
Renormalisation group improvement of scalar field inflation
We study quantum corrections to Friedmann-Robertson-Walker cosmology with a
scalar field under the assumption that the dynamics are subject to
renormalisation group improvement. We use the Bianchi identity to relate the
renormalisation group scale to the scale factor and obtain the improved
cosmological evolution equations. We study the solutions of these equations in
the renormalisation group fixed point regime, obtaining the time-dependence of
the scalar field strength and the Hubble parameter in specific models with
monomial and trinomial quartic scalar field potentials. We find that power-law
inflation can be achieved in the renormalisation group fixed point regime with
the trinomial potential, but not with the monomial one. We study the transition
to the quasi-classical regime, where the quantum corrections to the couplings
become small, and find classical dynamics as an attractor solution for late
times. We show that the solution found in the renormalisation group fixed point
regime is also a cosmological fixed point in the autonomous phase space. We
derive the power spectrum of cosmological perturbations and find that the
scalar power spectrum is exactly scale-invariant and bounded up to arbitrarily
small times, while the tensor perturbations are tilted as appropriate for the
background power-law inflation. We specify conditions for the renormalisation
group fixed point values of the couplings under which the amplitudes of the
cosmological perturbations remain small.Comment: 17 pages; 2 figure
Flavour Mixing, Gauge Invariance and Wave-function Renormalisation
We clarify some aspects of the LSZ formalism and wave function
renormalisation for unstable particles in the presence of electroweak
interactions when mixing and CP violation are considered. We also analyse the
renormalisation of the CKM mixing matrix which is closely related to wave
function renormalisation. We critically review earlier attempts to define a set
of "on-shell" wave function renormalisation constants. With the aid of an
extensive use of the Nielsen identities complemented by explicit calculations
we corroborate that the counter term for the CKM mixing matrix must be
explicitly gauge independent and demonstrate that the commonly used
prescription for the wave function renormalisation constants leads to gauge
parameter dependent amplitudes, even if the CKM counter term is gauge invariant
as required. We show that a proper LSZ-compliant prescription leads to gauge
independent amplitudes. The resulting wave function renormalisation constants
necessarily possess absorptive parts, but we verify that they comply with the
expected requirements concerning CP and CPT. The results obtained using this
prescription are different (even at the level of the modulus squared of the
amplitude) from the ones neglecting the absorptive parts in the case of top
decay. The difference is numerically relevant.Comment: 19 pages, plain latex, one ps figur
Non-perturbative Renormalisation with Domain Wall Fermions
We present results from a study of the renormalisation of both quark bilinear
and four-quark operators for the domain wall fermion action, using the
non-perturbative renormalisation technique of the Rome-Southampton group. These
results are from a quenched simulation, on a 16^3 x 32 lattice, with beta=6.0
and L_s=16.Comment: 4 pages, 6 figures, Lattice 2000 (Improvement and Renormalisation),
RBC collaboration, Typos correcte
Current Renormalisation Constants with an O(a)-improved Fermion Action
Using chiral Ward identities, we determine the renormalisation constants of
bilinear quark operators for the Sheikholeslami-Wohlert action lattice at
beta=6.2. The results are obtained with a high degree of accuracy. For the
vector current renormalisation constant we obtain Z_V=0.817(2)(8), where the
first error is statistical and the second is due to mass dependence of Z_V.
This is close to the perturbative value of 0.83. For the axial current
renormalisation constant we obtain Z_A = 1.045(+10 -14), significantly higher
than the value obtained in perturbation theory. This is shown to reduce the
difference between lattice estimates and the experimental values for the
pseudoscalar meson decay constants, but a significant discrepancy remains. The
ratio of pseudoscalar to scalar renormalisation constants, Z_P/Z_S, is less
well determined, but seems to be slightly lower than the perturbative value.Comment: 8 pages uuencoded compressed postscript file. Article to be submitted
to Phys.Rev.
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