# Haut PDF Jet evolution in a dense QCD medium

### Jet evolution in a dense QCD medium

Abstract Besides the emblematic studies of the Higgs boson and the search of new physics beyond the Standard Model, another goal of the LHC experimental program is the study of the quark- gluon plasma (QGP), a phase of nuclear matter that exists at high temperature or density, and in which the quarks and gluons are deconfined. This state of matter is now re-created in the laboratory in high-energy nucleus-nucleus collisions. To probe the properties of the QGP, a very useful class of observables refers to the propagation of energetic jets. A jet is a collimated spray of hadrons generated via successive parton branchings, starting with a highly energetic and highly virtual parton (quark or gluon) produced by the collision. When such a jet is produced in the dense environment of a nucleus-nucleus collision, its interactions with the surrounding medium lead to a modification of its physical properties, phenomenon known as jet quenching. In this thesis, we develop a new theory to describe jet quenching phenomena. Using a leading, double logarithmic approximation in perturbative QCD, we compute for the first time the effects of the medium on multiple vacuum-like emissions, that is emissions triggered by the virtuality of the initial parton. We show that, due to the scatterings off the plasma, the in- medium parton showers differ from the vacuum ones in two crucial aspects: their phase-space is reduced and the first emission outside the medium can violate angular ordering. A new physical picture emerges from these observations, with notably a factorisation in time between vacuum- like emissions and medium-induced parton branchings, the former constrained by the presence of the medium. This picture is Markovian, hence well suited for a Monte Carlo implementation. We develop then a Monte Carlo parton shower called JetMed which combines consistently both the vacuum-like shower and the medium-induced emissions.
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### Jet evolution in a dense medium: event-by-event fluctuations and multi-particle correlations

Abstract We study the gluon distribution produced via successive medium-induced branchings by an energetic jet propagating through a weakly-coupled quark-gluon plasma. We show that under suitable approximations, the jet evolution is a Markovian stochastic process, which is exactly solvable. For this process, we construct exact analytic solutions for all the n-point correlation functions describing the gluon distribution in the space of energy [1, 2]. Using these results, we study the event-by-event distribution of the energy lost by the jet at large angles and of the multiplicities of the soft particles which carry this energy. We ﬁnd that the event-by-event ﬂuctuations are huge: the standard deviation in the energy loss is parametrically as large as its mean value [1]. This has important consequences for the phenomenology of di-jet asymmetry in Pb +Pb collisions at the LHC: it implies that the ﬂuctuations in the branching process can contribute to the measured asymmetry on an equal footing with the geometry of the di-jet event (i.e. as the di ﬀerence between the in-medium path lengths of the two jets). We compute the higher moments of the multiplicity distribution and identify a remarkable regularity known as Koba-Nielsen-Olesen (KNO) scaling [2]. These predictions could be tested via event- by-event measurements of the di-jet asymmetry.
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### Dense-Medium Modifications to Di-Jet Hadron Pair Correlations in Au+Au Collisions at $\sqrt{s_{NN}}$ = 200 GeV

tributions and show that the dense medium formed in Au+Au collisions at RHIC modifies jet fragmentation. In central and mid-central collisions the away-side an- gular distribution is significantly broadened relative to peripheral and d+Au collisions, and appears to be non- Gaussian. The shapes of the away-side ∆φ distributions for non-peripheral collisions are apparently not consis- tent with purely stochastic broadening of the peripheral Au+Au away-side. However, the broadening and possi- ble changes in shape of the away-side jet are suggestive of recent theoretical predictions of dense medium effects on fragment distributions [14, 15, 16, 26]. The broad- ened shapes of the away-side distributions also imply that integration of the away-side peak in a narrow angular range around ∆φ = π yields fewer associated partners in central collisions than in peripheral/d+Au collisions, as seen elsewhere[8, 22]; but integrating over the entire broadened peak recovers the jet partners in the range 1.0 GeV/c < p B
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### Event-by-event fluctuations in the medium-induced jet evolution

This paper is organized as follows. In Sect. 2 we succinctly describe the physical picture of the medium-induced jet evolution and its mathematical formulation as a Markovian process. In particular, we present the transport equation ( 2.14 ) obeyed by the gluon pair density D (2) (x, x 0 ). More details on the formalism are deferred to App. A . In Sect. 3 we discuss the energy loss at large angles, operationally defined as the total energy transmitted, via successive branchings, to the very soft gluons with x → 0. Sect. 3.1 is devoted to the mean field picture, that is, the gluon spectrum D(x) and the average energy loss. Most of the results presented there were already known, but our physical discussion is more furnished, in line with our general purposes. In Sect. 3.2 , we present our main new results, which are both exact (within our theoretical framework): Eq. ( 3.9 ) for the gluon pair density D (2) (x, x 0 ) and Eq. ( 3.13 ) for the variance in the energy loss at large angles. The physical interpretation of these results is discussed at length, in Sect. 3.2 and the dedicated section 3.3 . Details on the calculations are presented in Appendices B and C . In Sect. 4 , we discuss the gluon number distribution, for gluons with energy fraction x ≥ x 0 . In Sect. 4.1 we compute the average multiplicity, while in Sect. 4.2 we present and discuss our results for the second factorial moment hN (N − 1)i and for the variance. The respective calculations are quite tedious (the details are deferred to App. D ), but in Sect. 4.2
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### Measurement of jet-medium interactions via direct photon-hadron correlations in Au$+$Au and $d$ $+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV

with lower momentum direct photons. Comparison to theoretical calculations suggests that the hadron excess arises from medium response to energy deposited by jets. I. INTRODUCTION Collisions of heavy nuclei at the Relativistic Heavy Ion Collider (RHIC) produce matter that is sufficiently hot and dense to form a plasma of quarks and gluons [1]. Bound hadronic states cannot exist in a quark gluon plasma, as the temperatures far exceed the transition temperature calculated by lattice quantum chromody- namics (QCD) [2]. Experimental measurements and the- oretical analyses have shown that this plasma exhibits remarkable properties, including opacity to traversing quarks and gluons [3, 4]. However, the exact mecha- nism for energy loss by these partons in quark gluon plasma and the transport of the deposited energy within the plasma is not yet understood.
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### Boson-Jet Correlations in a Hybrid Strong/Weak Coupling Model for Jet Quenching in Heavy Ion Collisions

d Physics Department, Theory Unit, CERN, CH-1211 Geneve 23, Switzerland Abstract We confront a hybrid strong /weak coupling model for jet quenching to data from LHC heavy ion collisions. The model combines the perturbative QCD physics at high momentum transfer and the strongly coupled dynamics of non- abelian gauge theories plasmas in a phenomenological way. By performing a full Monte Carlo simulation, and after fitting one single parameter, we successfully describe several jet observables at the LHC, including dijet and photon jet measurements. Within current theoretical and experimental uncertainties, we find that such observables show little sensitivity to the specifics of the microscopic energy loss mechanism. We also present a new observable, the ratio of the fragmentation function of inclusive jets to that of the associated jets in dijet pairs, which can discriminate among di fferent medium models. Finally, we discuss the importance of plasma response to jet passage in jet shapes.
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### Bending transition in the penetration of a flexible intruder in a two-dimensional dense granular medium

seeking. As shown by the blue curve in Fig. 13, this compu- tation now allows us to reasonably reproduce the full bending transition (regime II) of the fiber induced by the gradual compaction of grains upstream of the fiber. By tuning the value of A to a given value, it is possi- ble to reproduce the experimental evolution of deflection till its maximum value. The model does not allow to reproduce the behavior beyond (regime III), in particu- lar the plateau observed for this fiber length L=3 cm, as the elastica calculations are based on the same type of loading whatever the deflection, i.e. an orthogonal repar- tition of forces along the whole fiber length. This strong assumption is certainly no more valid in regime III when the fiber adopts a hook shape, that is when the angle θ( ξ = 1 ) exceeds π/2.
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### Constraint fitting of experimental data with a jet quenching model embedded in a hydrodynamical bulk medium

involved in calculations of radiative energy loss [2] are not yet known. Thus, the conclusion of the large strength remains, but caution is warranted on the precise interpretation of the actual magnitude obtained. These findings about the large partonic interaction strength in jet quenching and the hydrody- namical behavior of the bulk matter have led to the claim that the produced medium is strongly coupled [16]. Such a conclusion is of critical importance for our understanding of QCD. Therefore it must be substantiated by detailed studies which should consider: i) As many experimental ob- servables as available; ii) A detailed modeling of the medium compatible with experimental data on soft particle production; iii) A statistical analysis of the uncertainties in the constraints on the medium coming from both the experimental data and the theoretical implementation of energy loss and medium modeling.
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### Bending transition in the penetration of a flexible intruder in a 2D dense granular medium

seeking. As shown by the blue curve in Fig. 12, this compu- tation now allows us to reasonably reproduce the full bending transition (regime II) of the fiber induced by the gradual compaction of grains upstream of the fiber. By tuning the value of A to a given value, it is possi- ble to reproduce the experimental evolution of deflection till its maximum value. The model does not allow to reproduce the behavior beyond (regime III), in particu- lar the plateau observed for this fiber length L=3 cm, as the elastica calculations are based on the same type of loading whatever the deflection, i.e. an orthogonal repar- tition of forces along the whole fiber length. This strong assumption is certainly no more valid in regime III when the fiber adopts a hook shape, that is when the angle θ(s = L) exceeds π/2.
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### A Comprehensive Analysis of Jet Quenching via a Hybrid Strong/Weak Coupling Model for Jet-Medium Interactions

d Physics Department, Theory Unit, CERN, CH-1211 Geneve 23, Switzerland Abstract Within a hybrid strong/weak coupling model for jets in strongly coupled plasma, we explore jet modifications in ultra- relativistic heavy ion collisions. Our approach merges the perturbative dynamics of hard jet evolution with the strongly coupled dynamics which dominates the soft exchanges between the fast partons in the jet shower and the strongly coupled plasma itself. We implement this approach in a Monte Carlo, which supplements the DGLAP shower with the energy loss dynamics as dictated by holographic computations, up to a single free parameter that we fit to data. We then augment the model by incorporating the transverse momentum picked up by each parton in the shower as it propagates through the medium, at the expense of adding a second free parameter. We use this model to discuss the influence of the transverse broadening of the partons in a jet on intra-jet observables. In addition, we explore the sensitivity of such observables to the back-reaction of the plasma to the passage of the jet.
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### Medium-induced jet evolution: wave turbulence and energy loss

2 Typical scales and physical regimes We would like to study the gluon cascade generated via successive medium–induced gluon branchings by an original gluon — the ‘leading particle’ (LP) — with energy E which propagates through a dense QCD medium along a distance L. For the present purposes, the medium is solely characterized by a transport coefficient ˆ q, known as the ‘jet quenching parameter’, which measures the dispersion in transverse momentum acquired by a parton propagating through this medium per unit length (or time). Depending upon its energy, the leading particle can either escape the medium, or disappear inside it (in the sense of not being distinguishable from its products of fragmentation). The actual scenario depends upon the ratio between E and a characteristic medium scale ω c ≡ ˆqL 2 /2, which is
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### Probabilistic picture for medium-induced jet evolution

The goal of this paper is to complete the description of this cascade. It is organized as follows. In the next section we briefly recall the main results of Ref. [ 20 ] concerning the properties of the medium induced gluon splitting and of transverse momentum broadening within the BDMPSZ framework. Then, in Section 3, we construct a generating functional for the probabilities to observe n gluons in the cascade, at any given time. This is then used to derive the evolution equation for the inclusive one-gluon spectrum. This equation general- izes that studied in Ref. [ 21 ] in that it takes into account the dependence of the distribution function on the transverse momentum of the produced gluon, as generated via collisions in the medium. (The equation studied in [ 21 ] concerns only the energy distribution, that is, the integral of the one-gluon spectrum over the transverse momentum.) The kernel of this equation, however, is completely integrated over the transverse momenta and contains in- formation on these transverse momenta only in an average way: this follows from the fact that the transverse momentum broadening acquired during the branching processes can be neglected as compared to that accumulated via collisions in the medium in between successive branchings. Thus, to the accuracy of interest, the splittings can be effectively treated as be- ing collinear. By trying to improve the description and take into account more explicitly the transverse momentum dependence of the splitting kernel, we were led to identify large radia- tive corrections, which are formally infrared divergent, and are best interpreted as corrections to the transport coefficient ˆ q, which is a measure of the transverse momentum square acquired by the jet parton in the medium, per unit length. This will be discussed in Section 4. In particular, we recover the double logarithmic correction to transverse momentum broadening that has been calculated recently [ 22 ]. Technical material is gathered in three Appendices. The first one complements results obtained in [ 20 ], and gives an explicit expression for the splitting kernel in the harmonic approximation, with full dependence on transverse momenta. The contribution of the single scattering is emphasized. The second appendix is devoted to the calculation of the double logarithmic contribution to ˆ q. The third appendix presents an alternative form of the generating functional that may be more suitable for Monte-Carlo calculations.
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### Dimensional reduction in QCD: Lessons from lower dimensions

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### Baryon properties in meson mediums from lattice QCD

improved gauge action with m π ∼ 386 MeV and m K ∼ 543 MeV. The spatial lattice spacing for these ensembles is b s = 0.1227(8), and the anisotropy parameter ξ = b t /b s ∼ 3.5. We use en- sembles with a large volume, (32 3 ) to ensure that we are near the scattering threshold, and a large temporal extent (T = 256) to eliminate thermal effects. The quark propagators were computed by the NPLQCD collaboration (see Ref. [16]), and were generated using the same fermion action as was used for gauge field generation. Details of the analysis of the correlation functions and numerical values for the energy splittings may be found in Ref. [17].
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### QCD factorization in B decays into $\rho\pi$

C i ≡ C i( µ ) (in NDR), α s ≡ α s( µ ) (next to leading order), and CF = (N c 2 − 1)/2N c with N c = 3. 3. NUMERICAL RESULTS Assuming that all of the parameters involved in QCD factorization are constrained by independent studies where the input parameters related to factorization were fitted, we concentrate our efforts on the form factor F 1 B → π depending on the CKM matrix parameters ρ and η . In order to reach this aim, we have calculated the branching ratios for B decays such as B ± → ρ 0 π ± , B 0 → ρ ± π 0 , B 0 → ρ ± π ∓ , B 0 → ρ 0 π 0 and B ± → ωπ ± where the annihilation and ρ − ω mixing contributions were taken into account. All the results are shown in Figs. 3, 4 and 5, and the branching ratios are plotted as a function of the form factor F 1 B → π and as a function of the values of ρ and η as well.
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### Design evolution of medium gimbal scalable resistance dynamometer with user manual

The tow tank currently has a two axis adjustable tow post attached to the rear of the carriage that requires a line attachment to the model. Typically an eyebolt is fitted to the model at centerline of the hull on the deck or above waterline at the stern and attachment for the inline check pulls is accomplished through this. There is an in line comparison load cell linked by a shackle to the boat at the eye bolt and the other end of the Load cell is shackled to the pull line. The line is routed through a pulley system several meters aft of the boat to allow weight pan loading of the line from the carriage platform. The system requires connection and disconnection from a boat each time a load pull is required. A pre-load of the system is required to remove the catenary component of the pull caused by the weight of the line and the load cell hanging of the back of the boat. The pull line alignment is also an issue at initial setup ensuring that the tow post is
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### Homogenization of heat diffusion in a cracked medium

Received *****; accepted after revision +++++ Presented by Abstract We develop in this Note a homogenization method to tackle the problem of a diffusion process through a cracked medium. We assume that the cracks are orthogonal to the surface of the material, where an incoming heat flux is applied. The cracks are supposed to be of depth 1, of small width, and periodically arranged. We show that the cracked surface of the domain induces a volume source term in the homogenized equation.

### delta-baryon electromagnetic form factors in lattice QCD

A primary motivation for this work is to understand the role of deformation in baryon structure: whether any of the low-lying baryons have deformed intrinsic states and if so, why. Thus, a major achievement of this work is the devel- opment of lattice methods with sufficient precision to show, for the first time, that the electric quadrupole form factor is nonzero and hence the  has a nonvanishing quadrupole moment and an associated deformed shape. Unlike the , the spin-1=2 nucleon cannot have a quadru- pole moment, so the experiment of choice to explore its deformation has been measurement of the nucleon to  electric and Coulomb quadrupole transition form factors. Major experiments [ 5 – 7 ] have shown that these transition form factors are indeed nonzero, confirming the presence of deformation in either the nucleon , or both [ 8 , 9 ], and lattice QCD yields comparable nonzero results [ 10 , 11 ]. Our new calculation of the  quadrupole form factor, coupled with the nucleon to  transition form factors, should in turn shed light on the deformation of the nucleon. In order to evaluate the  electromagnetic (EM) form factors to the required accuracy, we isolate the two domi- nant form factors and the subdominant electric quadrupole form factor. This is particularly crucial for the latter since
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### Homogenization of heat diffusion in a cracked medium

Physically, the exchange surface between the optically thick medium and the energy source may be greatly modified by the fractures. This may have a significant impact on the energy balance of the considered system. In many situations, the intricacies of the cracked medium are such that it is almost impossible to carry out a direct calculation. Besides, many spatial scales may be involved simultaneously. Full numerical simulations of such multi-scaled media become hence infeasible.

### $\alpha_S$ from Lattice QCD: progresses and perspectives for a realistic full-QCD determination of the running Strong coupling

(black) [10] discussed in the text. The red points are for determinations using staggered fermions, the green for one using Wilson and the blue overlap fermions. The plot is taken from [9]. (b) α T from the lattice, after applying the appropriate lattice-artefacts curing procedure, confronted to the continuum formula obtained from PT and including OPE non-perturbative corrections. The solid line is for the complete non-perturbative expression, while dotted stands only for the perturbative four-loop one, α T pert . The momentum in the x-axis is expressed in lattice units of a ( β = 3.9) −1 . The plot is taken from ref. [7].
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