23 research outputs found
Acceptance dependence of fluctuation measures near the QCD critical point
We argue that a crucial determinant of the acceptance dependence of
fluctuation measures in heavy-ion collisions is the range of correlations in
the momentum space, e.g., in rapidity, . The value of
for critical thermal fluctuations is determined by
the thermal rapidity spread of the particles at freezeout, and has little to do
with position space correlations, even near the critical point where the
spatial correlation length becomes as large as fm (this is in
contrast to the magnitudes of the cumulants, which are sensitive to ).
When the acceptance window is large, , the
cumulants of a given particle multiplicity, , scale linearly with
, or mean multiplicity in acceptance, , and
cumulant ratios are acceptance independent. While in the opposite regime,
, the factorial cumulants, ,
scale as , or . We demonstrate this general
behavior quantitatively in a model for critical point fluctuations, which also
shows that the dependence on transverse momentum acceptance is very
significant. We conclude that extension of rapidity coverage proposed by STAR
should significantly increase the magnitude of the critical point fluctuation
signatures.Comment: 9 pages, 4 figures, references adde
On spinodal points and Lee-Yang edge singularities
We address a number of outstanding questions associated with the analytic
properties of the universal equation of state of the theory, which
describes the critical behavior of the Ising model and ubiquitous critical
points of the liquid-gas type. We focus on the relation between spinodal points
that limit the domain of metastability for temperatures below the critical
temperature, i.e., , and Lee-Yang edge singularities that
restrict the domain of analyticity around the point of zero magnetic field
for . The extended analyticity conjecture (due to Fonseca and
Zamolodchikov) posits that, for , the Lee-Yang edge
singularities are the closest singularities to the real axis. This has
interesting implications, in particular, that the spinodal singularities must
lie off the real axis for , in contrast to the commonly known result
of the mean-field approximation. We find that the parametric representation of
the Ising equation of state obtained in the expansion, as
well as the equation of state of the -symmetric theory at
large , are both nontrivially consistent with the conjecture. We analyze the
reason for the difficulty of addressing this issue using the
expansion. It is related to the long-standing paradox associated with the fact
that the vicinity of the Lee-Yang edge singularity is described by Fisher's
theory, which remains nonperturbative even for , where the
equation of state of the theory is expected to approach the mean-field
result. We resolve this paradox by deriving the Ginzburg criterion that
determines the size of the region around the Lee-Yang edge singularity where
mean-field theory no longer applies.Comment: 26 pages, 8 figures; v2: shortened Sec. 4.1 and streamlined
arguments/notation in Sec. 4.2, details moved to appendix, added reference 1
Functional renormalization group approach to the Yang-Lee edge singularity
We determine the scaling properties of the Yang-Lee edge singularity as
described by a one-component scalar field theory with imaginary cubic coupling,
using the nonperturbative functional renormalization group in
Euclidean dimensions. We find very good agreement with high-temperature series
data in dimensions and compare our results to recent estimates of
critical exponents obtained with the four-loop expansion and
the conformal bootstrap. The relevance of operator insertions at the
corresponding fixed point of the RG functions is discussed and we
estimate the error associated with truncations of the
scale-dependent effective action.Comment: 10 pages, 4 figures, updated reference to supplementary materia
Conformality Lost
We consider zero-temperature transitions from conformal to non-conformal
phases in quantum theories. We argue that there are three generic mechanisms
for the loss of conformality in any number of dimensions: (i) fixed point goes
to zero coupling, (ii) fixed point runs off to infinite coupling, or (iii) an
IR fixed point annihilates with a UV fixed point and they both disappear into
the complex plane. We give both relativistic and non-relativistic examples of
the last case in various dimensions and show that the critical behavior of the
mass gap behaves similarly to the correlation length in the finite temperature
Berezinskii-Kosterlitz-Thouless (BKT) phase transition in two dimensions, xi ~
exp(c/|T-T_c|^{1/2}). We speculate that the chiral phase transition in QCD at
large number of fermion flavors belongs to this universality class, and attempt
to identify the UV fixed point that annihilates with the Banks-Zaks fixed point
at the lower end of the conformal window.Comment: 30 pages, 6 figures; v2: typos fixed, references adde
Lorentz Invariance in Chiral Kinetic Theory
We show that Lorentz invariance is realized nontrivially in the classical
action of a massless spin- particle with definite helicity. We find
that the ordinary Lorentz transformation is modified by a shift orthogonal to
the boost vector and the particle momentum. The shift ensures angular momentum
conservation in particle collisions and implies a nonlocality of the collision
term in the Lorentz-invariant kinetic theory due to side jumps. We show that
2/3 of the chiral-vortical effect for a uniformly rotating particle
distribution can be attributed to the magnetic moment coupling required by the
Lorentz invariance. We also show how the classical action can be obtained by
taking the classical limit of the path integral for a Weyl particle.Comment: 5 pages, 1 figur
Towards the Gravity Dual of Quarkonium in the Strongly Coupled QCD Plasma
We build a "bottom-up" holographic model of charmonium by matching the
essential spectral data. We argue that this data must include not only the
masses but also the decay constants of the J/psi and psi' mesons. Relative to
the "soft-wall" models for light mesons, such a matching requires two new
features in the holographic potential: an overall upward shift as well as a
narrow "dip" near the holographic boundary. We calculate the spectral function
as well as the position of the complex singularities (quasinormal frequencies)
of the retarded correlator of the charm current at finite temperatures. We
further extend this analysis by showing that the residues associated with these
singularities are given by the boundary derivative of the appropriately
normalized quasinormal mode. We find that the "melting" of the J/psi spectral
peak occurs at a temperature of about 540 MeV, or 2.8 T_c, in good agreement
with lattice results.Comment: 13 pages, 9 figure
Linear Confinement and AdS/QCD
In a theory with linear confinement, such as QCD, the masses squared m^2 of
mesons with high spin S or high radial excitation number n are expected, from
semiclassical arguments, to grow linearly with S and n. We show that this
behavior can be reproduced within a putative 5-dimensional theory
holographically dual to QCD (AdS/QCD). With the assumption that such a dual
theory exists and describes highly excited mesons as well, we show that
asymptotically linear m^2 spectrum translates into a strong constraint on the
INFRARED behavior of that theory. In the simplest model which obeys such a
constraint we find m^2 ~ (n+S).Comment: 14 pages, 1 figur
On the sign of the dilaton in the soft wall models
We elaborate on the existence of a spurious massless scalar mode in the
vector channel of soft-wall models with incorrectly chosen sign of the
exponential profile defining the wall. We re-iterate the point made in our
earlier paper and demonstrate that the presence of the mode is robust,
depending only on the infra-red asymptotics of the wall. We also re-emphasize
that desired confinement properties can be realized with the correct sign
choice.Comment: 10 page