286 Read more

Apprehending the dynamics of nonadiabatic processes **in** atomic and molecular physics is not an easy task. The initial and final states have generally complex fine struc- tures and even **in** the case of well-defined boundary con- ditions, multiple pathways can drive the dynamics from the beginning to the end of the process. Beyond the iden- tification of the reaction routes, their relative coherence must explicitely be considered since it monitors the even- tual occurence of interferences and determines the final outcome of the reaction. The degree of coherence, that our (basically classical) intuition cannot easily grasp, is generally revealed by quantum mechanical or semiclas- sical calculations. However continuous advances **in** co- incidence and probe techniques have opened the way to ’quantum mechanical complete’ coherence experiments [1] which are able to measure not only the reaction prob- abilities but also the relative phase of the transition am- plitudes. Such experiments have been performed for low- **energy** ion-atom **collisions** [2–7], electron impact excita- tion of helium [8, 9] and photon-induced ionization of krypton atoms [10]. Nevertheless, **in** most of the cases involving heavy **particle** impact, the experimental reso- lution did not allow to scrutinize the details of the scat- tering patterns predicted theoretically.

Show more
Abstract
First results on K/π, p/π and K/p **fluctuations** are obtained with the ALICE detector at the CERN LHC as a function of centrality **in** Pb–Pb **collisions** at √ s NN = 2.76 TeV. The observable ν dyn ,
which is defined **in** terms of the moments of **particle** multiplicity distributions, is used to quantify the magnitude of dynamical **fluctuations** of relative **particle** yields and also provides insight into the correlation between **particle** pairs. This study is based on a novel experimental technique, called the Identity Method, which allows one to measure the moments of multiplicity distributions **in** case of incomplete **particle** identification. The results for p/π show a change of sign **in** ν dyn from positive

Show more
19 Read more

Further, one has to take into account the fact that the damping behavior **in** Eq. (A8) is caused only by the spatial inhomogeneity of the system at a fixed tempera- ture. **In** realistic **collisions** and event samples there is no single relevant temperature. For instance, finite central- ity binning adds together a range of **fluctuations** origi- nating from **collisions** with different N part . However, **in** principle these centrality-correlated **fluctuations** are **in**- dependent of the thermally-induced spatial **fluctuations**. **In** addition, although the self correlation at the zero dis- tance between two sub-volumes **in** Eq. (A6) was excluded, the self correlation cannot be excluded **in** the integrated two **particle** correlation function contained **in** Eq. (3). We have tried various kind of functional forms for C 2 which contained power terms and also plural correlation lengths. However, we found empirically that just adding the constant term **in** Eq. (7) produced the best fit results to all data points.

Show more
32 Read more

Jet quenching has been observed at RHIC [12, 13, 14, 15] and at the LHC [16] via the measurement of **high** p t hadron inclusive production and correlations, which are observed to be strongly suppressed **in**
central A–A **collisions** compared to a scaled pp reference. These **high** p t hadron observables have been
the major tool for measuring the **energy** loss of hard scattered partons and thereby the properties of the medium, but they provide only indirect and biased information on the parton evolution **in** the medium. The aim of full jet reconstruction is to measure jet modifications due to **energy** loss **in** an unbiased way [17, 18]. Already first measurements of reconstructed jets **in** heavy-ion **collisions** at the LHC showed an **energy** imbalance between back-to-back dijets, which is attributed to jet quenching [9, 19].

Show more
21 Read more

2.4. LOOKING AT A PROTON, SECOND PART 23 simplistic: it is **in** fact only valid when the proton is at rest. When the proton is moving at almost the speed of light, the picture is drastically changed. There are indeed other partons (a generic term regrouping the gluons and the quarks) that appear inside the proton. They are the sea quarks 3 and the gluons, which are the mediators of the strong interaction, as the photons are the mediators of the electromagnetic force. Why is it so? This is related to one of the most important principles **in** quantum theory called the Heisenberg uncertainty principle. What this principle essentially states is that it is not possible to know exactly at the same time the position and the speed of a **particle**, nor is it possible to know exactly its **energy** at a given time. This last uncertainty implies that on sufficiently small time scales - and **in** a heavy ion **collisions**, we are talking about a few times 10 − 24 seconds - the uncertainty on the **energy** triggers incredibly **high** **fluctuations** of its intensity at any point of space so that sometimes, the vacuum can acquire sufficiently **high** **energy** so that a pair of particles is created. This is called vacuum **fluctuations**, and is one of the explanation for such a rich content of a proton at **high** **energy**. Figure 2.7 illustrates the part of momentum which is carried by the different constituents of the protons **in** function of the momentum scale.

Show more
200 Read more

The excess mass spectra for all 4 multiplicity bins, resulting from subtraction of the conservative hadron de- cay cocktail from the measured data, are shown **in** Fig. 3. The cocktail and the level of charm decays, found **in** the 3 upper centrality bins to be about 1=3 of the measured yield **in** the mass interval 1:2 < M < 1:4 GeV=c 2 [15], are shown for comparison. The qualitative features of the spectra are striking: a peaked structure is seen **in** all cases, broadening strongly with centrality, but remaining essen- tially centered around the position of the nominal pole. At the same time, the total yield increases relative to the cocktail , their ratio reaching values above 4 for M < 0:9 GeV=c 2 **in** the most central bin. Such values are con- sistent with the results found by CERES [12], if the latter are also referred to the cocktail and rescaled according to the different multiplicity density. The errors shown are purely statistical. The dominant sources of systematic er- rors are connected to the uncertainties **in** the levels of the combinatorial background (1%) and fake matches (5%). On the basis of these values and the signal-to-background ratios, the systematic errors **in** the broad continuum region 0:4 < M < 0:6 and 0:8 < M < 1:0 GeV=c 2 are estimated

Show more
5
Chapter 3 is the rst one dealing with new results. Especially the di-gluon production cross-section is the main result of our paper [38] with Edmond Iancu. Many physical ideas introduced **in** the previous chapter are used **in** this one. I spent some pages to motivate why the di-gluon production has a special importance **in** p-A **collisions** at the LHC for nding quantitative evidences of saturation physics. To get the formal background, I rst deal with the simplest case : the single quark production. Indeed it shows the emergence of color operators and playing with it enables us to introduce almost everything we will need for the di-gluon production. Then when I discuss the di-gluon case, I will not have to set plenty of denitions all along the discussion. Appendices C and D will be used **in** this chapter for cross-sections and Feynman rules respectively. These appendices are the derivation of results which are intuitive **in** the sense that the structure of the cross-sections and the Feynman rules can be more or less guessed by a familiar reader who is more interested by an overall understanding rather than a careful check of prefactors. Chapter 4 is more theoretical. It deals with the small x evolution **in** nucleus-nucleus **collisions** that shows a universal character encoded into the factorization property. I fully detail calculations leading to the LO to NLO recursion relations both for gluons and quarks. The former is the new result, mentioned **in** our paper with Francois Gelis [39]. The starting point of this chapter will make use of the Schwinger-Keldysh formalism treated **in** appendix E. There are also gauge xing questions whose deep existence are justied **in** appendix F.

Show more
145 Read more

(Dated: September 25, 2018)
Elliptic flow **in** ultrarelativistic heavy-ion **collisions** results from the hydrodynamic response to the spatial anisotropy of the initial density profile. A long-standing problem **in** the interpretation of flow data is that uncertainties **in** the initial anisotropy are mingled with uncertainties **in** the response. We argue that the non-Gaussianity of flow **fluctuations** **in** small systems with large **fluctuations** can be used to disentangle the initial state from the response. We apply this method to recent measurements of anisotropic flow **in** Pb+Pb and p+Pb **collisions** at the LHC, assuming linear response to the initial anisotropy. The response coefficient is found to decrease as the system becomes smaller and is consistent with a low value of the ratio of viscosity over entropy of η/s ' 0.19. Deviations from linear response are studied. While they significantly change the value of the response coefficient they do not change the rate of decrease with centrality. Thus, we argue that the estimate of η/s is robust against non-linear effects.

Show more
V \.. singular multiparticle distributions in 3D momentum space [48]. They have observed that the effect of the dimensional projection depends on the range of the transverse momentum, ov[r]

87 Read more

There are some useful limits that can be used to compensate this growth. First, I will look at the operator B when two arguments are set to the same value. This will naturally lead to the pointlike limit where a pair **in** the amplitude (and the conjugate pair **in** the conjugate amplitude) is set to have a vanishing transverse separation. Within this pointlike limit of B, one is able to find how the distribution f simplifies into simpler distributions involving less partons. Another approach is to consider a system with a large number of partons but an observable that requires to observe only a few of them. **In** such a situation, the complicated evolution of the 2m-parton system **in** the medium relates to the simpler 2n-parton system evolution (with n < m). This evolution is described by a thus a convolution **in** momentum space of an initial distribution h with a broadening distribution f n encoding the evolution **in** the medium.

Show more
147 Read more

a signature of the CP. Certainly, within both approaches, pre- cision measurements are needed **in** order to reach conclusive results.
Acknowledgments This work was supported by the US Department of **Energy** Grant DE-FG03-97ER41020/A000, the Bundesministerium fur Bildung und Forschung (06F 137), Germany, the German Research Foundation (Grant GA 1480/2-2), the National Science Centre, Poland (Grants DEC-2011/03/B/ST2/02617 and 2014/14/E/ST2/00018), the Hungarian Scientific Research Foundation (Grants OTKA 68506, 71989, A08-77719 and A08-77815), the Bolyai Research Grant, the Bulgarian National Science Fund (Ph-09/05), the Croatian Ministry of Science, Education and Sport (Project 098-0982887-2878), Stichting FOM, the Netherlands and the “Demokritos” National Center for Sci- entific Research, Greece.

Show more
11 Read more

INTRODUCTION
Relativistic heavy-ion **collisions** are performed at the BNL Relativistic Heavy Ion Collider (RHIC) and at the CERN Large Hadron Collider (LHC) with the aim of creating the quark-gluon plasma, the **high**-temperature state of strongly-interacting matter. The nuclear-sized droplet of quark-gluon plasma formed **in** a collision ex- pands like a low-viscosity fluid [1], whose properties are studied through characteristic azimuthal anisotropies generated during the expansion [2–6]. **In** a hydrodynamic framework, azimuthal anisotropy **in** the final state is en- gendered by the spatial anisotropy that characterizes the **energy**-density profile at the onset of the hydrodynamic evolution [1, 7]. This primordial spatial anisotropy has, **in** a heavy-ion collision, a twofold origin: First, it is due to the almond shape of the overlap area between two nuclei for noncentral **collisions**, that generates elliptic flow [8]; Second, it originates from event-to-event density **fluctuations** [9], that yield an elliptic deformation even **in** central **collisions** [10], and a triangular anisotropy [11]. The role of primordial **fluctuations** for heavy-ion phe- nomenology draws, hence, an interesting parallel [12] with the physics of primordial **fluctuations** **in** cosmology, where the observed anisotropies of the Cosmic Microwave Background [13] originate from quantum **fluctuations** **in** the early Universe [14].

Show more
1.4 Summary Of Chapter 1
Our goal is to reduce uncertainties **in** wind resource assessment. We claim that, based on the state of the art **in** wind **energy**, poor approximations to the **high**- number of degrees of freedom that arise **in** a bounded, turbulent, atmosphere are the main cause of uncertainty. Numerical attempts to model these complex and highly non-linear processes typically require a truncation of scales and more often than not complex parameterisations. Even if all of the scales were resolved (i.e., if we were given an infinitely powerful computer so that we could resolve all scales down to the dissipation scale) this will not prevent the uncertainties that would occur from the upscaled initial/boundary conditions at infinitely small scales. A statistical understanding of the corresponding simulations of the Navier-Stokes equations is therefore still required. We argue that due to the symmetries of the governing equations of fluid motion for a **high**-Reynolds number flow, the statistics of the wind are scaling and multifractal. It is therefore unnecessary to truncate the scales of the process.

Show more
343 Read more

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.

Show more
radial flow [ 44 ], and the Cronin effect [ 45 ]. At higher p T , parton **energy** loss also becomes a
significant effect. Generally, R AA and R ∗ AA agree with each other **in** the range p T < 4 GeV.
However, the data may indicate a slight difference **in** suppression levels at higher p T . As the
centrality range examined becomes more peripheral, the oscillating shape of R AA ∗ becomes less pronounced. **In** the most peripheral **collisions** examined, the XeXe data are relatively flat, indicating that the spectral shape for peripheral centrality ranges is similar to that of pp **collisions**. Although there is a large normalization uncertainty, the R ∗ AA is significantly below unity **in** this centrality range. Such a suppression **in** peripheral events is not expected to be caused by strong **energy** loss effects, but might be related to correlations between the charged-**particle** yields **in** the mid-rapidity region with event activity **in** the range 3 < |η| < 5.2 that is used to determine the event centrality [ 46 ]. Recent measurements of R AA **in** peripheral PbPb **collisions** by the ALICE Collaboration show a similar effect

Show more
43 Read more

nature. Fig. 1(a) shows the scattering angle θ c.m. as a
function of the angular momentum L. For L ≥ 90, the trajectories are close to Rutherford scattering (dashed line) and correspond to quasi-elastic reactions with small total kinetic **energy** loss (TKEL) as shown by the solid line **in** Fig. 1(b). At lower L, deviations from the Ruther- ford formula occur because of nuclear attraction, lead- ing to rotation of the di-nuclear system formed by the two fragments **in** contact. For instance, L ≤ 72 de- fines (arbitrarily) the orbiting region where the fragments have crossed their incoming trajectory, i.e., with n ≥ 4 crossings of the x (collision axis) or y−axis [see inset **in** Fig. 1(a)]. Following [24], damped events are defined by a TKEL≥ 30 MeV, corresponding to L < 82 **in** Fig. 1. We see that a wide range of scattering angles may oc- cur for these damped events, which is a known feature of DIC. For L ≤ 66, capture occurs. It corresponds to a fusion cross section of ∼ 1140 mb with the sharp cut- off formula [13], **in** good agreement with a fit on fusion- evaporation measurements at lower energies [26].

Show more
Keywords: Collinear factorization, fracture functions, Drell-Yan process
I. INTRODUCTION
The description of **particle** production **in** hadronic **collisions** is interesting and challenging **in** many aspects. Perturbation theory can be applied whenever a sufficiently hard scale characterizes the scattering process. The comparison of early LHC charged **particle** spectra with next-to-leading order perturbative QCD predictions [1] shows that the theory offers a rather good description of data at sufficiently **high** hadronic transverse momentum, of the order of a few GeV. For inelastic scattering processes at even lower transverse momentum, the theoretical description **in** terms of perturbative QCD breaks down since both the coupling and partonic matrix elements diverge as the transverse momenta of final state parton vanish. **In** this paper we will study the semi-inclusive version of the Drell-Yan process, H 1 + H 2 → H + γ ∗ + X, **in** which one **particle** is tagged **in** the final

Show more
15 Read more

1 Introduction
The multiplicity distribution of particles produced **in** proton-proton (pp) **collisions** and the multiplicity dependence of other global event characteristics represent fundamental observables reflecting the prop- erties of the underlying **particle** production mechanisms. **In** the Feynman picture, the strongly interacting hadrons can be seen as bunches of point-like partons producing particles **in** interactions with small (soft) and large (hard) momentum transfer. As expected from Feynman scaling [1], at low centre-of-mass ener- gies ( √ s), where **particle** production is dominated by soft interactions, the mean number of particles hMi was found to rise logarithmically with √ s. Moreover, the evolution of the charged **particle** multiplicity distribution P(M) as a function of √ s follows the Koba-Nielsen-Oleson (KNO) scaling [2] with scaling variable z = M/hMi and P(M)hMi = ψ (z), where ψ (z) is an **energy** independent function. Experimen- tally one finds that KNO scaling is violated for √ s > 200 GeV [3]. This scaling violation which increases with √ s has been interpreted as a consequence of **particle** production through multiple parton-parton **in**- teractions (MPI) [4, 5]. Further, at the LHC, already at a transverse momentum transfer of a few GeV/c the cross section for leading order (LO) parton-parton scatterings exceeds the total pp inelastic cross sec- tion. This apparent inconsistency can be resolved by aggregating several quasi independent scatterings **in** the same pp collision [6, 7]. If multiple semi-hard scatterings play a dominant role **in** the production of **high** multiplicity events, this should lead to distinct experimentally observable effects. The search for these is the aim of the present analysis of pp **collisions** recorded with the ALICE detector at the LHC. Each parton-parton scattering produces partons almost back-to-back **in** azimuth, ϕ . They fragment pro- ducing two correlated bundles of particles. With increasing multiplicity we expect that both the number of sources of correlated particles and the number of correlated particles per source increase. Thus, we have designed our analysis methods **in** a way that the two effects can be separated as much as possible. Since many of the bundles of particles (low transverse-momentum jets) overlap **in** the same event, they can not be identified and separated event-by-event. An alternative method, pursued **in** this analysis, is to study two-**particle** angular correlations as a function of the event multiplicity [8].

Show more
36 Read more