43 research outputs found
All order resummed leading and next-to-leading soft modes of dense QCD pressure
The cold and dense QCD equation of state (EoS) at high baryon chemical
potential involves at order an all-loop summation of the
soft mode contributions. Recently, the complete
soft contributions at order were calculated, using the hard
thermal loop (HTL) formalism. By identifying {\em massive} renormalization
group (RG) properties within HTL, we resum to all orders
the leading and next-to-leading logarithmic soft contributions. We obtain
compact analytical expressions, that show visible deviations from the
state-of-the art results, and noticeably reduced residual scale dependence. Our
results should help to reduce uncertainties in extending the EoS in the
intermediate regime, relevant in particular for the phenomenology of
neutron stars.Comment: 5 pages + appendices, 2 figures. Eq.(22) corrected, changes in Fig.2,
added content in appendices. To appear in PR
Renormalization Group Improved Optimized Perturbation Theory: Revisiting the Mass Gap of the O(2N) Gross-Neveu Model
We introduce an extension of a variationally optimized perturbation method,
by combining it with renormalization group properties in a straightforward
(perturbative) form. This leads to a very transparent and efficient procedure,
with a clear improvement of the non-perturbative results with respect to
previous similar variational approaches. This is illustrated here by deriving
optimized results for the mass gap of the O(2N) Gross-Neveu model, compared
with the exactly know results for arbitrary N. At large N, the exact result is
reproduced already at the very first order of the modified perturbation using
this procedure. For arbitrary values of N, using the original perturbative
information only known at two-loop order, we obtain a controllable percent
accuracy or less, for any N value, as compared with the exactly known result
for the mass gap from the thermodynamical Bethe Ansatz. The procedure is very
general and can be extended straightforwardly to any renormalizable Lagrangian
model, being systematically improvable provided that a knowledge of enough
perturbative orders of the relevant quantities is available.Comment: 18 pages, 1 figure, v2: Eq. (4.5) corrected, comments adde
Non-perturbative analysis of the spectrum of meson resonances in an ultraviolet-complete composite-Higgs model
We consider a vector-like gauge theory of fermions that confines at the
multi-TeV scale, and that realizes the Higgs particle as a composite Goldstone
boson. The weak interactions are embedded in the unbroken subgroup of a
spontaneously broken flavour group. The meson resonances appear as
poles in the two-point correlators of fermion bilinears, and include the
Goldstone bosons plus a massive pseudoscalar , as well as scalars,
vectors and axial vectors. We compute the mass spectrum of these mesons, as
well as their decay constants, in the chiral limit, in the approximation where
the hypercolour dynamics is described by four-fermion operators, \`a
la Nambu-Jona Lasinio. By resumming the leading diagrams in the
expansion, we find that the spin-one states lie beyond the LHC reach, while
spin-zero electroweak-singlet states may be as light as the Goldstone-boson
decay constant, TeV. We also confront our results with a set of
available spectral sum rules. In order to supply composite top-quark partners,
the theory contains additional fermions carrying both hypercolour and ordinary
colour, with an associated flavour symmetry-breaking pattern . We
identify and analyse several non-trivial features of the complete two-sector
gauge theory: the 't~Hooft anomaly matching conditions; the higher-dimension
operator which incorporates the effects of the hypercolour axial-singlet
anomaly; the coupled mass-gap equations; the mixing between the singlet mesons
of the two sectors, resulting in an extra Goldstone boson , and novel
spectral sum rules. Assuming that the strength of the four-fermion interaction
is the same in the two sectors, we find that the coloured vector and scalar
mesons have masses , while the masses of coloured pseudo-Goldstone
bosons, induced by gluon loops, are .Comment: v1: 65 pages, 25 figures. v2: 70 pages, 29 figures; several
references and clarifications included; two additional subsections on the
S-parameter and on the spectral sum rules for mixed meson
Revisiting No-Scale Supergravity Inspired Scenarios
We consider no-scale supergravity inspired scenarios, emphasizing the
possible dynamical determination of the soft supersymmetry-breaking parameters
as triggered by the radiative corrections that lift an essentially flat
tree-level potential in the hidden sector. We (re)emphasize the important role
played by the scale-dependent vacuum energy contribution to the effective
potential for the occurrence of consistent no-scale minima. The most relevant
input parameters are introduced as (the soft breaking mixing Higgs
parameter) and (the cosmological constant value at high energy)
instead of \mhalf and , the latter being determined through a
(generalized) potential minimization at electroweak scales. We examine the
theoretical and phenomenological viability of such a mechanism when confronted
with up-to-date calculations of the low energy sparticle spectrum and with
present constraints from the LHC and other observables. The tight dark matter
relic density constraint for a neutralino LSP scenario can be considerably
relaxed for a gravitino LSP scenario possible in this framework.Comment: Proceedings of the 2011 Europhysics Conference on High Energy
Physics, EPS-HEP 2011, July 21-27, 2011 Grenoble, Rh\^one-Alpes, Franc
Updating the Phase Diagram of the Gross-Neveu Model in 2+1 Dimensions
The method of optimized perturbation theory (OPT) is used to study the phase
diagram of the massless Gross-Neveu model in 2+1 dimensions. In the temperature
and chemical potential plane, our results give strong support to the existence
of a tricritical point and line of first order phase transition, previously
only suspected to exist from extensive lattice Monte Carlo simulations. In
addition of presenting these results we discuss how the OPT can be implemented
in conjunction with the Landau expansion in order to determine all the relevant
critical quantities.Comment: 7 pages, 2 eps figures. Replaced with the version that matches the
published one (PLB
Renormalization group improved pressure for hot and dense quark matter
We apply the renormalization group optimized perturbation theory (RGOPT) to
evaluate the quark contribution to the QCD pressure at finite temperatures and
baryonic densities, at next-to-leading order (NLO). Our results are compared to
NLO and state-of-the-art higher orders of standard perturbative QCD (pQCD) and
hard thermal loop perturbation theory (HTLpt). The RGOPT resummation provides a
nonperturbative approximation, exhibiting a drastically better remnant
renormalization scale dependence than pQCD, thanks to built-in renormalization
group invariance consistency. At NLO, upon simply adding to the RGOPT-resummed
quark contributions the purely perturbative NLO glue contribution, our results
show a remarkable agreement with ab initio lattice simulation data for
temperatures , with a remnant scale
dependence drastically reduced as compared to HTLpt.Comment: 24 pages, 17 figures. v2: some clarifications + 2 figures +
references added. To appear in Phys. Rev.
Vector-like contributions from Optimized Perturbation in the Abelian Nambu--Jona-Lasinio model for cold and dense quark matter
Two-loop corrections for the standard Abelian Nambu-Jona-Lasinio model are
obtained with the Optimized Perturbation Theory (OPT) method. These
contributions improve the usual mean-field and Hartree-Fock results by
generating a suppressed term, which only contributes at finite chemical
potential. We take the zero temperature limit observing that, within the OPT,
chiral symmetry is restored at a higher chemical potential , while the
resulting equation of state is stiffer than the one obtained when mean-field is
applied to the standard version of the model. In order to understand the
physical nature of these finite contributions, we perform a numerical
analysis to show that the OPT quantum corrections mimic effective repulsive
vector-vector interaction contributions. We also derive a simple analytical
approximation for the mass gap, accurate at the percent level, matching the
mean-field approximation extended by an extra vector channel to OPT. For the effective vector coupling matching OPT is numerically close
(for the Abelian model) to the Fierz-induced Hartree-Fock value ,
where is the scalar coupling, and then increases with in a
well-determined manner.Comment: 9 pages, 5 figures. In press Int. J. Mod. Phys. E (2012
Thermodynamics and Phase Structure of the Two-Flavor Nambu--Jona-Lasinio Model Beyond Large-N_c
The optimized perturbation theory (OPT) method is applied to the
version of the Nambu--Jona-Lasinio (NJL) model both at zero and at finite
temperature and/or density. At the first nontrivial order the OPT exhibits a
class of 1/N_c corrections which produce nonperturbative results that go beyond
the standard large-N_c, or mean-field approximation. The consistency of the OPT
method with the Goldstone theorem at this order is established, and appropriate
OPT values of the basic NJL (vacuum) parameters are obtained by matching the
pion mass and decay constant consistently. Deviations from standard large-N_c
relations induced by OPT at this order are derived, for example, for the
Gell--Mann-Oakes-Renner relation. Next, the results for the critical quantities
and the phase diagram of the model, as well as a number of other
thermodynamical quantities of interest, are obtained with OPT and then
contrasted with the corresponding results at large N_c.Comment: 29 pages, 20 figures, revtex. Minor corrections. In press Phys. Rev.
Exact 1/N and Optimized Perturbative Evaluation of mu_c for Homogeneous Interacting Bose Gases
In the framework of the O(N) three-dimensional effective scalar field model
for homogeneous dilute weakly interacting Bose gases we use the 1/N expansion
to evaluate, within the large N limit, the parameter r_c which is directly
related to the critical chemical potential mu_c. This quantity enters the
order-a^2 n^{2/3} coefficient contributing to the critical temperature shift
Delta T_c where a represents the s-wave scattering length and n represents the
density. Compared to the recent precise numerical lattice simulation results,
our calculation suggests that the large N approximation performs rather well
even for the physical case N=2. We then calculate the same quantity but using
different forms of the optimized perturbative (variational) method, showing
that these produce excellent results both for the finite N and large-N cases.Comment: 12 pages, 2 figures. We have performed a refined and extended
numerical analysis to take into account the very recent results of Ref. [15