Fragmentation or Recombination at High p_T?

All hadronization processes, including fragmentation, are shown to proceed through recombination. The shower partons in a jet turn out to play an important role in describing the p_T spectra of hadrons produced in heavy-ion collisions. Due to the recombination of the shower partons with the soft thermal partons, the structure of jets produced in AA collisions is not the same as that of jets produced in pp collisions.Comment: Talk given at Quark Matter 200

Dihadron Correlation in Jets Produced in Heavy-Ion Collisions

The difference between the structures of jets produced in heavy-ion and hadronic collisions can best be exhibited in the correlations between particles within those jets. We study the dihadron correlations in jets in the framework of parton recombination. Two types of triggers, $\pi^+$ and proton, are considered. It is shown that the recombination of thermal and shower partons makes the most important contribution to the spectra of the associated particles at intermediate $p_T$. In $pp$ collisions the only significant contribution arises from shower-shower recombination, which is negligible in heavy-ion collisions. Moments of the associated-particle distributions are calculated to provide simple summary of the jet structures for easy comparison with experiments.Comment: 24 pages in Latex + 5 figure

The Role of Gluon Depletion in J/psi Suppression

The depletion of gluons as the parton flux traverses a nucleus in a heavy-ion collision can influence the production rate of heavy-quark states. Thus the suppression of $J/\psi$ can be due to gluon depletion in the initial state in addition to nuclear and hadronic absorption in the final state. A formalism is developed to describe the depletion effect. It is shown that, without constraints from other experimental facts beside the $J/\psi$ suppression data in $pA$ and $AB$ collisions, it is not possible to determine the relative importance of depletion vs absorption. Possible relevance to the enhanced suppression seen in the $Pb - Pb$ data is mentioned but not studied.Comment: 12 pages + 2 figures (in ps file), LaTex, Submitted to Phys. Rev.

Optimal transportation, topology and uniqueness

The Monge-Kantorovich transportation problem involves optimizing with respect to a given a cost function. Uniqueness is a fundamental open question about which little is known when the cost function is smooth and the landscapes containing the goods to be transported possess (non-trivial) topology. This question turns out to be closely linked to a delicate problem (# 111) of Birkhoff [14]: give a necessary and sufficient condition on the support of a joint probability to guarantee extremality among all measures which share its marginals. Fifty years of progress on Birkhoff's question culminate in Hestir and Williams' necessary condition which is nearly sufficient for extremality; we relax their subtle measurability hypotheses separating necessity from sufficiency slightly, yet demonstrate by example that to be sufficient certainly requires some measurability. Their condition amounts to the vanishing of the measure \gamma outside a countable alternating sequence of graphs and antigraphs in which no two graphs (or two antigraphs) have domains that overlap, and where the domain of each graph / antigraph in the sequence contains the range of the succeeding antigraph (respectively, graph). Such sequences are called numbered limb systems. We then explain how this characterization can be used to resolve the uniqueness of Kantorovich solutions for optimal transportation on a manifold with the topology of the sphere.Comment: 36 pages, 6 figure

Ridge Formation Induced by Jets in pppp Collisions at 7 TeV

An interpretation of the ridge phenomenon found in pp collisions at 7 TeV is given in terms of enhancement of soft partons due to energy loss of semihard jets. A description of ridge formation in nuclear collisions can directly be extended to pp collisions, since hydrodynamics is not used, and azimuthal anisotropy is generated by semihard scattering. Both the p_T and multiplicity dependencies are well reproduced. Some suggestions are made about other observables.Comment: Expanded version to be published in Phys. Rev.

Parton and Hadron Correlations in Jets

Correlation between shower partons is first studied in high $p_T$ jets. Then in the framework of parton recombination the correlation between pions in heavy-ion collisions is investigated. Since thermal partons play very different roles in central and peripheral collisions, it is found that the correlation functions of the produced hadrons behave very differently at different centralities, especially at intermediate $p_T$. The correlation function that can best exhibit the distinctive features is suggested. There is not a great deal of overlap between what we can calculate and what has been measured. Nevertheless, some aspects of our results compare favorably with experimental data.Comment: 28 pages in Latex + 13 figures. This is a revised version with extended discussions added without quantitative changes in the result

Critical Behavior of Hadronic Fluctuations and the Effect of Final-State Randomization

The critical behaviors of quark-hadron phase transition are explored by use of the Ising model adapted for hadron production. Various measures involving the fluctuations of the produced hadrons in bins of various sizes are examined with the aim of quantifying the clustering properties that are universal features of all critical phenomena. Some of the measures involve wavelet analysis. Two of the measures are found to exhibit the canonical power-law behavior near the critical temperature. The effect of final-state randomization is studied by requiring the produced particles to take random walks in the transverse plane. It is demonstrated that for the measures considered the dependence on the randomization process is weak. Since temperature is not a directly measurable variable, the average hadronic density of a portion of each event is used as the control variable that is measurable. The event-to-event fluctuations are taken into account in the study of the dependence of the chosen measures on that control variable. Phenomenologically verifiable critical behaviors are found and are proposed for use as a signature of quark-hadron phase transition in relativistic heavy-ion collisions.Comment: 17 pages (Latex) + 24 figures (ps file), submitted to Phys. Rev.

MARKET CONDUCT UNDER GOVERNMENT PRICE INTERVENTION IN THE U.S. DAIRY INDUSTRY

The degree of market power exercised by fluid and manufactured processors in the U.S. dairy industry is estimated. AppelbaumÂ’'s quantity-setting conjectural variation approach is cast into a switching regime framework to account for the two market regimes created by the existence of the dairy price support program: (a) government supported regime (market price is at the support price) and (b) market equilibrium regime (market price is above the support price). The model is also used to test whether government price intervention has a pro-competitive to anti-competitive influence on market conduct.Agricultural and Food Policy,

Centrality Scaling of the pTp_T Distribution of Pions

From the preliminary data of PHENIX on the centrality dependence of the $\pi^0$ spectrum in $p_T$ at midrapidity in heavy-ion collisions, we show that a scaling behavior exists that is independent of the centrality. It is then shown that $$ degrades with increasing $N_{\rm part}$ exponentially with a decay constant that can be quantified. A scaling distribution in terms of an intuitive scaling variable is derived that is analogous to the KNO scaling. No theoretical models are used in any part of this phenomenological analysis.Comment: 4 pages RevTex, 5 figures include

Physics Revealed at Intermediate p_T

A review is given on the subject of hadron production at intermediate $p_T$ in heavy-ion collisions. The underlying dynamical processes are inferred from interpreting the data in the framework of recombination. Ridge formation with or without triggers is found to play an important role in nearly all observables in that $p_T$ region. Correlation data would be hard to interpret without taking ridges into account. The semi-hard partons that create the ridges may even be able to drive elliptic flow without fast thermalization.Comment: 8 pages, plenary talk given at Quark Matter 2008, Jaipur, Indi