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Rudolph C. Hwa

Publications and source records attributed to Rudolph C. Hwa.

At least 37 records · Page 2Linked to original sources

Recombination in nuclear collisions

Recombination is a hadronization process that converts partons to hadrons at late time, but the description has no quantitative significance without some meaningful input on the parton distributions at earlier time. Thus observations of particle spectra and correlations have definitive implications on the partonic processes at all transverse momenta. After presenting a general review of the subject at the Workshop, I selected two topics in nuclear collisions for more detailed discussion, which are summarized here. One is on the azimuthal anisotropy at low $p_T$ due to hard or semihard scattering of partons that create ridges with or without triggers. The ridge particles are the products of recombination of thermal partons enhanced by the energy loss of hard or semihard partons. Their $ϕ$ dependence at midrapidity can be determined essentially from geometry. The other topic is on the scaling behavior in $ϕ$ and centrality at high $p_T$, where the hadronization process is dominated by TS and SS recombination. The relevant RHIC data are found to have the same scaling behavior. But at LHC such scaling is badly broken at $p_T \sim 10$ GeV/c if two-jet recombination is important. At the end of this article some comments are made to relate our study of the effects of semihard partons to the observation of minijets in the analyses of STAR data.

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Scaling Behavior of the Azimuthal and Centrality Dependencies of Jet Production in Heavy-ion Collisions

For heavy-ion collisions at RHIC a scaling behavior is found in the dependencies on azimuthal angle $ϕ$ and impact parameter $b$ for pion production at high $p_T$ essentially independent of the hadronization process. The scaling variable is in terms of a dynamical path length $ξ$ that takes into account detailed properties of geometry, medium density and probability of hard scattering. It is shown in the recombination model how the nuclear modification factor depends on the average $\barξ(ϕ,b)$. The data for $π^0$ production at $p_T=$ 4-5 and 7-8 GeV/c at RHIC are shown to exhibit the same scaling behavior as found in the model calculation. Extension to back-to-back dijet production has been carried out, showing the existence of $\barξ$ scaling also in the away-side yield per trigger. At LHC the hard-parton density can be high enough to realize the likelihood of recombination of shower partons arising from neighboring jets. It is shown that such 2-jet recombination can cause strong violation of $\barξ$ scaling. Furthermore, the large value of $R_{AA}$ that exceeds 1 can become a striking signature of such a hadronization process at high energy.

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Relationship Between the Azimuthal Dependencies of Nuclear Modification Factor and Ridge Yield

The azimuthal angular dependence of the nuclear modification factor R_{AA}(p_T, phi,N_{part}) recently obtained by PHENIX is related at low p_T to the trigger phi dependence of the ridge yield as measured by STAR in a framework in which the azimuthal anisotropy is driven by semihard scattering near the surface. Careful consideration of the initial geometry leads to the determination of a surface segment in which the production of semihard partons are responsible for the phi dependence of the inclusive distribution on the one hand, and for the angular correlation in ridge phenomenology on the other. With v_2 also being well reproduced along with R_{AA} and ridge yield, all relevant phi dependencies in heavy-ion collisions can now be understood in a unified description that emphasizes the ridge production whether or not a trigger is used.

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Hadron Correlations in Jets and Ridges through Parton Recombination

Hadron correlations in jets, ridges and opposite dijets at all $p_T$ above 2 GeV/c are discussed. Since abundant data are available from RHIC at intermediate $p_T$, a reliable hadronization scheme at that $p_T$ range is necessary in order to relate the semihard partonic processes to the observables. The recombination model is therefore first reviewed for that purpose. Final-state interaction is shown to be important for the Cronin effect, large B/M ratio and forward production. The effect of semihard partons on the medium is then discussed with particular emphasis on the formation of ridge with or without trigger. Azimuthal anisotropy can result from ridges without early thermalization. Dynamical path length distribution is derived for any centrality. Dihadron correlations in jets on the same or opposite side are shown to reveal detail properties of trigger and antitrigger biases with the inference that tangential jets dominate the dijets accessible to observation.

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Dependence of Ridge Formation on Trigger Azimuth: Correlated Emission Model

Ridge formation in near-side correlation in heavy-ion collisions is studied in the framework of a phenomenological model, called Correlated Emission Model (CEM). Successive soft emissions due to jet-medium interaction lead to the enhancement of thermal partons which follow the local flow directions. The correlation between the flow direction and the semihard parton direction is the major factor that causes the ridge formation to depend on the trigger direction relative to the reaction plane. With the use of a few parameters we have been able to reproduce the data on the ridge yields as functions of the trigger azimuthal angle for different centralities. An inside-outside asymmetry function is proposed to further probe the characteristics of the azimuthal correlation function. Insights are provided for the understanding of some detailed aspects of the centrality dependence.

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Hadron Correlation in Jets on the Near and Away Sides of High-p_T Triggers in Heavy-ion Collisions

Correlation between trigger and associated particles in jets produced on near and away sides of high-p_T triggers in heavy-ion collisions is studied. Hadronization of jets on both sides is treated by thermal-shower and shower-shower recombination. Energy loss of semihard and hard partons traversing the nuclear medium is parametrized in a way that renders good fit of the single-particle inclusive distributions at all centralities. The associated hadron distribution in the near-side jet can be determined showing weak dependence on system size because of trigger bias. The inverse slope increases with trigger momentum in agreement with data. The distribution of associated particle in the away-side jet is also studied with careful attention given to antitrigger bias that is due to the longer path length that the away-side jet recoiling against the trigger jet must propagate in the medium to reach the opposite side. Centrality dependence is taken into account after determining a realistic probability distribution of the dynamical path length of the parton trajectory within each class of centrality. For symmetric dijets with p_T^{trig}=p_T^{assoc}(away) it is shown that the per-trigger yield is dominated by tangential jets. The average parton momentum for the recoil jet is shown to be always larger than that of the trigger jet for fixed p_T^{trig} and centrality and for any measurable p_T^{assoc}(away). With the comprehensive treatment of dijet production described here it is possible to answer many questions regarding the behavior of partons in the medium under conditions that can be specified on measurable hadron momenta.

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Azimuthal Anisotropy: Ridges, Recombination and Breaking of Quark Number Scaling

Azimuthal anisotropy is studied by taking into account the ridges created by semi-hard scattering, which is sensitive to the initial spatial configuration in non-central heavy-ion collisions. No rapid thermalization is required. Although hydrodynamics is not used in this study, the validity of hydrodynamical expansion is not excluded at later time after equilibration is achieved. Phenomenological properties of the bulk and ridge behaviors are used as inputs to determine the elliptic flow of pion and proton at low p_T. At intermediate p_T the recombination of shower partons with thermal partons becomes more important. The phi dependence arises from the variation of the in-medium path length of the hard parton that generates the shower. The p_T dependence of v_2 is therefore very different at intermediate p_T compared to that at low p_T. Quark number scaling of v_2 is shown to be only approximately valid at low p_T, but is broken at intermediate p_T, even though recombination is the mechanism of hadronization in all p_T regions considered.

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Elliptic Flow arising from Ridges due to Semi-hard Scattering

Azimuthal anisotropy in heavy-ion collisions is studied by taking into account the ridges generated by semi-hard scattering of intermediate-momentum partons, which can be sensitive to the initial spatial configuration of the medium in non-central collisions. In a simple treatment of the problem where the recombination of only thermal partons is considered, analytical formulas can be derived that yield results in accord with the data on v_2 for p_T <1-2 GeV/c. Centrality dependence is described by a geometrical factor. Ridge phenomenology is used to determine the initial slopes of v_2 at low p_T for both pion and proton. For higher p_T, shower partons from high-p_T jets must be included, but they are not considered here.

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Forward Production of Protons and Pions in Heavy-ion Collisions

The problem of forward production of hadrons in heavy-ion collision at RHIC is revisited with modification of the theoretical treatment on the one hand and with the use of new data on the other. The basic formalism for hadronization remains the same as before, namely, recombination, but the details of momentum degradation and quark regeneration are improved. Recent data on the p/pi and pbar/p ratios are used to constrain the value of the degradation parameter. The p_T spectrum of the average charged particles is well reproduced. A prediction on the p_T dependence of the pbar/p ratio at eta=3.2 is made.

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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.

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Forward Production With Large p/πRatio and Without Jet Structure at Any p_T

Particle production in the forward region of heavy-ion collisions is shown to be due to parton recombination without shower partons. The regeneration of soft partons due to momentum degradation through the nuclear medium is considered. The degree of degradation is determined by fitting the $\bar p/p$ ratio. The data at $\sqrt s=62.4$ GeV and $η=3.2$ from BRAHMS on the $p_T$ distribution of average charged particles are well reproduced. Large proton-to-pion ratio is predicted. The particles produced at any $p_T$ should have no associated particles above background to manifest any jet structure.

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A Parton-Based Description of Forward-Backward Correlation in pp Collisions

Forward-backward correlation in pp collisions is studied in an approach that emphasizes the partonic scattering angles and circumvents the intractable problem related to the transverse momenta that are low. Assuming the back-to-back scattering of partons to be the origin of hadronic correlation, the properties of forward-backward multiplicity covariance can be derived essentially independent of details of hadronization. The range of correlation in pseudo-rapidity emerges from the study without any dynamical input, thus dispelling the notion that correlation length has any fundamental significance. An attempt is made to relate the results to the two-component structure seen in autocorrelation.

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Particles Associated with Omega Produced at Intermediate p_T

The dual observation of the Omega production in central Au+Au collisions having both an exponential p_T distribution and also associated particles above the background has been referred to as the Omega puzzle. We give a quantitative description of how that puzzle can be understood in terms of phantom jets, where only ridges without peaks are produced to give rise to both the Omega trigger and its associated particles. In the framework of recombination of thermal partons we are able to reproduce both the Δϕdistribution and the trigger-momentum dependence of the yield of the associated particles. We make predictions on other observables that can be checked by further analyses of the data.

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Production of strange particles at intermediate pT at RHIC

The recombination model is applied to the production of $K, ϕ, Λ$ and $Ω$ at all $p_T$ in central Au+Au collisions. The thermal-shower component of the recombination is found to be important for $K$ and $Λ$, but only in a minor way for $ϕ$ and $Ω$ in the intermediate to high $p_T$ region. The normalization and inverse slope of the thermal partons in the strange sector are determined by fitting the low-$p_T$ data. At higher $p_T$ the data of $K, ϕ, Λ$ and $Ω$ in the log scale are all well reproduced in our study that extends the thermal contribution and includes the shower contribution. The calculated result on the $Λ/K$ ratio rises to a maximum of around 2 at $p_T\approx 4$ GeV/c, arching over the data in linear scale. The production of $ϕ$ and $Ω$ are shown to arise mainly from the recombination of thermal partons, thus exhibiting exponential $p_T$ dependences in agreement with the data. Their ratio, $R_{Ω/ϕ}$, rises linearly to $p_T\approx 4$ GeV/c and develops a maximum at $p_T\approx 5.5$ GeV/c. It is argued that the $p_T$ spectra of $ϕ$ and $Ω$ reveal directly the partonic nature of the thermal source that characterizes quark-gluon plasma. Comments are made on the $Ω$ puzzle due to the simultaneous observation of both the exponential behavior of the $Ω$ spectrum in $p_T$ and the existence of low-$p_T$ particles associated with $Ω$ as trigger.

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Hadron Correlation in Jets

We review some recent experimental and theoretical work on the correlation among hadrons produced at intermediate $p_T$ at RHIC. The topics include: forward and backward asymmetry with and without trigger at mid-rapidity, associated-particle distribution on the near side, the $Ω$ puzzle and its solution, associated particles on the away side, and two-jet recombination at LHC.

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The Omega Puzzle

Recent data on particles associated with Omega trigger suggest that such events have jet structure. However, the exponential pT distribution of Omega suggests that no jets are involved. We resolve this puzzle by suggesting that the Omega is produced by the recombination of the enhanced thermal partons in the ridge that can have other hadrons in association with the trigger, all having exponential pT distributions.

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Away-side azimuthal distribution in a Markovian parton scattering model

An event generator is constructed on the basis of a model of multiple scattering of partons so that the trajectory of a parton traversing a dense and expanding medium can be tracked. The parameters in the code are adjusted to fit the Δϕazimuthal distribution on the far side when the trigger momentum is in the non-perturbative region, p_T(trigger)<4 GeV/c. The dip-bump structure for 1 8 GeV/c, the model reproduces the single-peak structure observed by STAR without invoking any new dynamical mechanism.

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