175 research outputs found
Soft interactions in jet quenching
We study the collisional aspects of jet quenching in a high energy nuclear
collision, especially in the final state pion gas. The jet has a large energy,
and acquires momentum transverse to its axis more effectively by multiple soft
collisions than by few hard scatterings (as known from analogous systems such
as J/\psi production at Hera). Such regime of large E and small momentum
transfer corresponds to Regge kinematics and is characteristically dominated by
the pomeron. From this insight we estimate the jet quenching parameter in the
hadron medium (largely a pion gas) at the end of the collision, which is
naturally small and increases with temperature in line with the gas density.
The physics in the quark-gluon plasma/liquid phase is less obvious, and here we
revisit a couple of simple estimates that suggest indeed that the
pomeron-mediated interactions are very relevant and should be included in
analysis of the jet quenching parameter. Finally, the ocasional hard collisions
produce features characteristic of a L\`evy flight in the q_perp^2 plane
perpendicular to the jet axis. We suggest one- and two-particle q_perp
correlations as interesting experimental probes.Comment: 14 pages, 16 figure
X(3872) and its Partners in the Heavy Quark Limit of QCD
In this letter, we propose interpolating currents for the X(3872) resonance,
and show that, in the Heavy Quark limit of QCD, the X(3872) state should have
degenerate partners, independent of its internal structure. Magnitudes of
possible I=0 and I=1 components of the X(3872) are also discussed.Comment: 12 page
: what has been really seen?
The resonant structure has been experimentally
observed in the and decays. This structure is intriguing since it is a prominent candidate of
an exotic hadron. Yet, its nature is unclear so far. In this work, we
simultaneously describe the and invariant mass
distributions in which the peak is seen using amplitudes with exact
unitarity. Two different scenarios are statistically acceptable, where the
origin of the state is different. They correspond to using energy
dependent or independent -wave interaction. In the first one,
the peak is due to a resonance with a mass around the
threshold. In the second one, the peak is produced by a virtual state
which must have a hadronic molecular nature. In both cases the two
observations, and , are shown to have the same
common origin, and a bound state solution is not allowed. Precise
measurements of the line shapes around the threshold are called for
in order to understand the nature of this state.Comment: 6 pages, 6 figure
Drawing the Horton Set in an Integer Grid of Minimum Size
In 1978 Erd\H os asked if every sufficiently large set of points in general
position in the plane contains the vertices of a convex -gon, with the
additional property that no other point of the set lies in its interior.
Shortly after, Horton provided a construction---which is now called the Horton
set---with no such -gon. In this paper we show that the Horton set of
points can be realized with integer coordinates of absolute value at most
. We also show that any set of points
with integer coordinates combinatorially equivalent (with the same order type)
to the Horton set, contains a point with a coordinate of absolute value at
least , where is a positive constant
An upper bound on the k-modem illumination problem
A variation on the classical polygon illumination problem was introduced in
[Aichholzer et. al. EuroCG'09]. In this variant light sources are replaced by
wireless devices called k-modems, which can penetrate a fixed number k, of
"walls". A point in the interior of a polygon is "illuminated" by a k-modem if
the line segment joining them intersects at most k edges of the polygon. It is
easy to construct polygons of n vertices where the number of k-modems required
to illuminate all interior points is Omega(n/k). However, no non-trivial upper
bound is known. In this paper we prove that the number of k-modems required to
illuminate any polygon of n vertices is at most O(n/k). For the cases of
illuminating an orthogonal polygon or a set of disjoint orthogonal segments, we
give a tighter bound of 6n/k + 1. Moreover, we present an O(n log n) time
algorithm to achieve this bound.Comment: 9 pages, 4 figure
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