A comparative study of Jet-quenching Schemes

The four major approximation schemes devised to study the modification of jets in dense matter are outlined. The comparisons are restricted to basic assumptions and approximations made in each case and the calculation methodology used. Emergent underlying similarities between apparently disparate methods brought about by the approximation schemes are exposed. Parameterizations of the medium in each scheme are discussed in terms of the transport coefficient $\hat{q}$. Discrepancies between the estimates obtained from the four schemes are discussed. Recent developments in the basic theory and phenomenology of energy loss are highlighted.Comment: 12 pages, 10 figures, latex, plenary presentation at the 19th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions (QM2006), Shanghai, China Nov. 14-20, 200

Modified Fragmentation Function from Quark Recombination

Within the framework of the constituent quark model, it is shown that the single hadron fragmentation function of a parton can be expressed as a convolution of shower diquark or triquark distribution function and quark recombination probability, if the interference between amplitudes of quark recombination with different momenta is neglected. The recombination probability is determined by the hadron's wavefunction in the constituent quark model. The shower diquark or triquark distribution functions of a fragmenting jet are defined in terms of overlapping matrices of constituent quarks and parton field operators. They are similar in form to dihadron or trihadron fragmentation functions in terms of parton operator and hadron states. Extending the formalism to the field theory at finite temperature, we automatically derive contributions to the effective single hadron fragmentation function from the recombination of shower and thermal constituent quarks. Such contributions involve single or diquark distribution functions which in turn can be related to diquark or triquark distribution functions via sum rules. We also derive QCD evolution equations for quark distribution functions that in turn determine the evolution of the effective jet fragmentation functions in a thermal medium.Comment: 23 pages in RevTex with 8 postscript figure

Multiplicity distributions inside parton cascades developing in a medium

The explanation of the suppression of high-pT hadron yields at RHIC in terms of jet-quenching implies that the multiplicity distributions of particles inside a jet and jet-like particle correlations differ strongly in nucleus-nucleus collisions at RHIC or at the LHC from those observed at e+e- or hadron colliders. We present a framework for describing the medium-induced modification, which has a direct interpretation in terms of a probabilistic medium-modified parton cascade, and which treats leading and subleading partons on an equal footing. We show that our approach can account for the strong suppression of single inclusive hadron spectra measured in Au-Au collisions at RHIC, and that this implies a characteristic distortion of the single inclusive distribution of soft partons inside the jet. We determine, as a function of the jet energy, to what extent the soft fragments within a jet can be measured above some momentum cut.Comment: 5 pages, 4 eps-figures; talk given at Hot Quarks 2006, Villasimius (Sardinia, Italy), May 15-20, 200

N=1 Chern-Simons theories, orientifolds and Spin(7) cones

We construct three dimensional N=1 Chern-Simons theories living on M2 branes probing Spin(7) cones. We consider Spin(7) manifolds obtained as quotients of Calabi-Yau four-folds by an anti-holomorphic involution, following a construction by Joyce. The corresponding Chern-Simons theories can be obtained from N=2 theories by an orientifolding procedure. These theories are holographically dual to M theory solutions AdS_4 \times H, where the weak G_2 manifold H is the base of the Spin(7) cone.Comment: 26 pages, 3 figures, reference added

Medium-modified evolution of multiparticle production in jets in heavy-ion collisions

The energy evolution of medium-modified average multiplicities and multiplicity fluctuations in quark and gluon jets produced in heavy-ion collisions is investigated from a toy QCD-inspired model. In this model, we use modified splitting functions accounting for medium-enhanced radiation of gluons by a fast parton which propagates through the quark gluon plasma. The leading contribution of the standard production of soft hadrons is found to be enhanced by the factor $\sqrt{N_s}$ while next-to-leading order (NLO) corrections are suppressed by $1/\sqrt{N_s}$, where the nuclear parameter $N_s>1$ accounts for the induced-soft gluons in the hot medium. The role of next-to-next-to-leading order corrections (NNLO) is studied and the large amount of medium-induced soft gluons is found to drastically affect the convergence of the perturbative series. Our results for such global observables are cross-checked and compared with their limits in the vacuum and a new method for solving the second multiplicity correlator evolution equations is proposed.Comment: 21 pages and 8 figures, typo corrections, references adde

Evidence for the Gompertz Curve in the Income Distribution of Brazil 1978-2005

This work presents an empirical study of the evolution of the personal income distribution in Brazil. Yearly samples available from 1978 to 2005 were studied and evidence was found that the complementary cumulative distribution of personal income for 99% of the economically less favorable population is well represented by a Gompertz curve of the form $G(x)=\exp [\exp (A-Bx)]$, where $x$ is the normalized individual income. The complementary cumulative distribution of the remaining 1% richest part of the population is well represented by a Pareto power law distribution $P(x)= \beta x^{-\alpha}$. This result means that similarly to other countries, Brazil's income distribution is characterized by a well defined two class system. The parameters $A$, $B$, $\alpha$, $\beta$ were determined by a mixture of boundary conditions, normalization and fitting methods for every year in the time span of this study. Since the Gompertz curve is characteristic of growth models, its presence here suggests that these patterns in income distribution could be a consequence of the growth dynamics of the underlying economic system. In addition, we found out that the percentage share of both the Gompertzian and Paretian components relative to the total income shows an approximate cycling pattern with periods of about 4 years and whose maximum and minimum peaks in each component alternate at about every 2 years. This finding suggests that the growth dynamics of Brazil's economic system might possibly follow a Goodwin-type class model dynamics based on the application of the Lotka-Volterra equation to economic growth and cycle.Comment: 22 pages, 15 figures, 4 tables. LaTeX. Accepted for publication in "The European Physical Journal B