49 research outputs found
Analytic structure of scalar composites in the symmetric phase of the gauged Nambu-Jona-Lasinio model
The gauged Nambu-Jona-Lasinio model in the quenched-ladder approximation has
non-trivial dynamics near a critical scaling region (critical curve) separating
a chiral symmetric and a dynamically chiral symmetry broken phase. Scalar and
pseudoscalar composites corresponding to the four-fermion interaction become
relevant degrees of freedom at short distances, which is reflected in the
appearance of a large anomalous dimension of the four-fermion operators. A
method is introduced for solving the Schwinger-Dyson equation for the Yukawa
vertex in specific kinematic regimes. This allows one to derive an analytic
expression for the scalar propagator, which is valid along the entire critical
curve. The mass and width of the scalar composites in the critical scaling
region are reexamined and the conformal phase transition at the critical gauge
coupling is discussed.Comment: final version to appear in Phys. Rev.
Modelling galaxy stellar mass evolution from z~0.8 to today
We apply the empirical method built for z=0 in the previous work of Wang et
al. to a higher redshift, to link galaxy stellar mass directly with its hosting
dark matter halo mass at z~0.8. The relation of the galaxy stellar mass and the
host halo mass M_infall is constrained by fitting both the stellar mass
function and the correlation functions at different stellar mass intervals of
the VVDS observation, where M_infall is the mass of the hosting halo at the
time when the galaxy was last the central galaxy. We find that for low mass
haloes, their residing central galaxies are less massive at high redshift than
those at low redshift. For high mass haloes, central galaxies in these haloes
at high redshift are a bit more massive than the galaxies at low redshift.
Satellite galaxies are less massive at earlier times, for any given mass of
hosting haloes. Fitting both the SDSS and VVDS observations simultaneously, we
also propose a unified model of the M_stars-M_infall relation, which describes
the evolution of central galaxy mass as a function of time. The stellar mass of
a satellite galaxy is determined by the same M_stars-M_infall relation of
central galaxies at the time when the galaxy is accreted. With these models, we
study the amount of galaxy stellar mass increased from z~0.8 to the present day
through galaxy mergers and star formation. Low mass galaxies gain their stellar
masses from z~0.8 to z=0 mainly through star formation. For galaxies of higher
mass, the increase of stellar mass solely through mergers from z=0.8 can make
the massive galaxies a factor ~2 larger than observed at z=0. We can also
predict stellar mass functions of redshifts up to z~3, and the results are
consistent with the latest observations.Comment: 12 pages, 10 figures, accepted for publication in MNRA
Anomalous dimensions of gauge-invariant amplitudes in massless effective gauge theories of strongly correlated systems
We use the radial gauge to calculate the recently proposed ansatz for the
physical electron propagator in such effective models of strongly correlated
electron systems as the theory of the pseudogap phase of the cuprates.
The results of our analysis help to settle the recent dispute about the sign
and the magnitude of the anomalous dimension which characterizes the gauge
invariant amplitude in question and set the stage for computing other, more
physically relevant, ones.Comment: Latex, 11 pages, no figure
ONE LOOP QED VERTEX IN ANY COVARIANT GAUGE: ITS COMPLETE ANALYTIC FORM
The one loop vertex in QED is calculated in arbitrary covariant gauges as an
analytic function of its momenta. The vertex is decomposed into a longitudinal
part, that is fully responsible for ensuring the Ward and Ward-Takahashi
identities are satisfied, and a transverse part. The transverse part is
decomposed into 8 independent components each being separately free of
kinematic singularities in covariant gauge in a basis that modifies
that proposed by Ball and Chiu. Analytic expressions for all 11 components of
the vertex are given explicitly in terms of elementary functions
and one Spence function. These results greatly simplify in particular kinematic
regimes.Comment: 35 pages, latex, 2 figures, Complete postscript file available from:
ftp://cpt1.dur.ac.uk/pub/preprints/dtp95/dtp9506/dtp9406.p
Infrared cutoff dependence of the critical flavor number in three-dimensional QED
We solve, analytically and numerically, a gap equation in parity invariant
QED_3 in the presence of an infrared cutoff \mu and derive an expression for
the critical fermion number N_c as a function of \mu. We argue that this
dependence of N_c on the infrared scale might solve the discrepancy between
continuum Schwinger-Dyson equations studies and lattice simulations of QED_3.Comment: 5 pages, 1 figure (revtex4), final versio
Renormalization Flow of Bound States
A renormalization group flow equation with a scale-dependent transformation
of field variables gives a unified description of fundamental and composite
degrees of freedom. In the context of the effective average action, we study
the renormalization flow of scalar bound states which are formed out of
fundamental fermions. We use the gauged Nambu--Jona-Lasinio model at weak gauge
coupling as an example. Thereby, the notions of bound state or fundamental
particle become scale dependent, being classified by the fixed-point structure
of the flow of effective couplings.Comment: 25 pages, 3 figures, v2: minor corrections, version to appear in PR
N\'eel transition, spin fluctuations, and pseudogap in underdoped cuprates by a Lorentz invariant four-fermion model in 2+1 dimensions
We show that the N\'eel transition and spin fluctuations near the N\'eel
transition in planar cuprates can be described by an SU(2) invariant
relativistic four-fermion model in 2+1 dimensions. Features of the pseudogap
phenomenon are naturally described by the appearance of an anomalous dimension
for the spinon propagator.Comment: 5 pages, 2 figures (revtex4). Final revised and corrected versio
Towards a renormalizable standard model without fundamental Higgs scalar
We investigate the possibility of constructing a renormalizable standard
model with purely fermionic matter content. The Higgs scalar is replaced by
point-like fermionic self-interactions with couplings growing large at the
Fermi scale. An analysis of the UV behavior in the point-like approximation
reveals a variety of non-Gaussian fixed points for the fermion couplings. If
real, such fixed points would imply nonperturbative renormalizability and evade
triviality of the Higgs sector. For point-like fermionic self-interactions and
weak gauge couplings, one encounters a hierarchy problem similar to the one for
a fundamental Higgs scalar.Comment: 18 pages, 4 figure