Introduction to the Physics of Saturation

Saturation Physics in Heavy Ion Collisions

We discuss expectations of saturation physics for various observables in heavy ion collisions. We show how simple saturation-inspired assumptions about particle production in heavy ion collisions lead to Kharzeev-Levin-Nardi model. Comparing this model to RHIC data on particle multiplicities we conclude that saturation effects may play an important role in particle production and dynamics at the early stages of Au-Au collisions already at RHIC energies. We then estimate the contribution of the initial state two-particle azimuthal correlations to elliptic flow observable v_2 in Au-Au collisions…

Small-x Physics, High Parton Densities and Parton Saturation in QCD

Partons are defined as the quanta in a Fock space description of a hadron. Gluon saturation is described in the Weizsäcker-Williams approximation for a large nucleus. The elements of DGLAP and BFKL evolution are given with the BFKL equation derived in a large-$N_c$ dipole formalism. A more general discussion of saturation is given in terms of a dipole scattering on a nucleon or nucleus. Possible evidence for saturation at HERA is discussed.

Low $x$ physics as an infinite twist (G)TMD framework: unravelling the origins of saturation

We show how the formulations of low $x$ physics involving Wilson line operators can be fully rewritten into an infinite twist TMD or GTMD framework, respectively for inclusive and exclusive observables. This leads to a perfect match between low $x$ physics and moderate $x$ formulations of QCD in terms of GTMDs, TMDs, GPDs or PDFs. We derive the BFKL limit as a kinematic limit and argue that beyond the Wandzura-Wilczek approximation, 3-body and 4-body unintegrated PDFs should be taken into account even in this regime. Finally, we analyze how saturation should be understood as three distinct eff…

Saturation Physics on the Energy Frontier

Saturation physics is expected to be relevant at sufficiently small parton momentum fractions $x$ in high-energy proton- (or deuteron-)ion collisions at RHIC and the LHC. Accordingly, these collisions provide the best available testing ground for the saturation model. However, producing precise numerical predictions from the model is a complicated task; the state of the art in this area involves next-to-leading order QCD calculations, which are difficult to do numerically. Here I'll review recent progress in extracting numerical predictions from saturation models and matching them to experimen…

The QCD shockwave approach at NLO: towards precision physics in gluonic saturation

We review the recent developments of the QCD shockwave approach at Next-to-Leading Order. The general method of this effective action is sketched, and illustrated by the case of diffractive processes.

Has saturation physics been observed in deuteron-gold collisions at RHIC?

We have addressed the question of whether saturation (CGC) has been observed in deuteron-gold collisions at RHIC. We have made a detailed analysis of the Cronin peak characteristic of the nuclear modification factor measured for d-Au collisions at mid-rapidity. The Cronin peak which is obtained around $p_t\simeq 3$ GeV may be reproduced at the proper height only by boosting the saturation momentum by a huge non-perturbative additional component. At forward rapidity, we get a quantitative agreement with data, reproducing hadron production spectra and the $R_{CP}$ ratio using a recently develope…

Saturation Physics and Deuteron--Gold Collisions at RHIC

We present a review of parton saturation/Color Glass Condensate physics in the context of deuteron-gold ($d+Au$) collisions at RHIC. Color Glass Condensate physics is a universal description of all high energy hadronic and nuclear interactions. It comprises classical (McLerran-Venugopalan model and Glauber-Mueller rescatterings) and quantum evolution (JIMWLK and BK equations) effects both in small-$x$ hadronic and nuclear wave functions and in the high energy scattering processes. Proton-nucleus (or $d+A$) collisions present a unique opportunity to study Color Glass Condensate predictions, sin…

Paving the Way Towards Precision Physics in Saturation Studies Through Exclusive Diffractive Light Neutral Vector Meson Production

We perform the first next-to-leading order computation of the $γ^{(*)} \to V$ ($ρ, ϕ, ω$) impact factor in the QCD shockwave approach and in the most general kinematics. This paves the way to the very first quantitative study of high-energy nucleon and nucleus saturation beyond the leading order, in various processes to be measured in $ep$, $eA$, $pp$ and $pA$ collisions at existing and future colliders.

Saturation model for 2-gamma physics

We introduce a saturation model for photon-photon interactions, based on a QCD dipole picture of high energy scattering. The two-dipole cross-section is assumed to satisfy the saturation property. This pomeron-like contribution is supplemented with QPM and non-pomeron reggeon contributions. The model gives a very good description of the data on the gamma-gamma total cross-section, on the photon structure function F_2^gamma(x,Q^2) at low x and on the gamma*-gamma* cross-section.

Small-x physics near the saturation regime

We consider the T-matrix near the unitarity limit and the energy dependence of the saturation momentum. We discuss the solution to the Kovchegov equation, or equivalently, to the BFKL evolution in the presence of a single saturation boundary. We include some of the correlations missed in the Kovchegov equation by solving the BFKL equation in the presence of two boundaries. The T-matrix now turns out to be frame-independent, which was not the case for the solution in the case of a single boundary, and it doesn't show the scaling behavior of the solution to the Kovchegov equation. We find for th…

Towards the Test of Saturation Physics Beyond Leading Logarithm

We present results from the first next-to-leading order (NLO) numerical analysis of forward hadron production in pA collisions in the small-x saturation formalism. Using parton distributions and fragmentation functions at NLO, as well as the dipole amplitude from the solution to the Balitsky-Kovchegov equation with running coupling, together with the NLO corrections to the hard coefficients, we obtain a good description of the available RHIC data in dAu collisions. We also comment on the results in the large p_T region beyond the saturation scale. Furthermore, we make predictions for forward h…

Saturation physics at HERA and RHIC: An unified description

One of the frontiers of QCD which are intensely investigated in high energy experiments is the high energy (small $x$) regime, where we expect to observe the non-linear behavior of the theory. In this regime, the growth of the parton distribution should saturate, forming a Color Glass Condensate (CGC). In fact, signals of parton saturation have already been observed both in $ep$ deep inelastic scattering at HERA and in deuteron-gold collisions at RHIC. Currently, the description of the experimental data of these experiments is possible considering different phenomenological saturation models f…

Forward physics hard processes and saturation: theory and phenomenology review

Selected aspects of the theory and phenomenology of production of forward jets at the LHC and RHIC are overviewed. In the theory part we discuss basics of frameworks originating from the BFKL dynamics while in the phenomenology part we present results for forward-central jet correlations at the LHC and forward di-jet production at RHIC.

Baryon stopping and saturation physics in relativistic collisions

We investigate baryon transport in relativistic heavy-ion collisions at energies reached at the CERN Super Proton Synchrotron, BNL Relativistic Heavy-Ion Collider (RHIC), and CERN LHC in the model of saturation. An analytical scaling law is derived within the color glass condensate framework based on small-coupling QCD. Transverse momentum spectra, net-baryon rapidity distributions and their energy, mass and centrality dependences are well described. In a comparison with RHIC data in Au + Au collisions at sqrt (s_NN) = 62.4 GeV and 200 GeV, the gradual approach to the gluon saturation regime i…

Has saturation physics been observed in deuteron-gold collisions at RHIC?

In the framework of the recently proposed saturation picture, we examine in a systematic way whether the nuclear modification factor measured for d-Au collisions at RHIC may be simply explained. The Cronin peak which is obtained at mid-rapidity around $k_{\bot}\simeq 3$ GeV may be reproduced at the proper height only by boosting the saturation momentum by an additional nuclear component as already shown in the literature. In this respect, mid-rapidity RHIC data cannot necessarily be seen as a probe of the saturation picture. The large rapidity ($η\simeq 3$) region allows us to test the shape o…

Particle Multiplicities in Nuclear Collisions at the LHC from Saturation Physics

The inclusion of running coupling effects in the BK-JIMWLK evolution equations considerably reduces the energy dependence of the saturation scale with respect to previous estimates based on fits to HERA data. We discuss how such slowdown affects the expectations for particle multiplicities in Pb-Pb collisions at LHC energies. Our prediction is based on the use of k_t-factorization and on the use of unintegrated gluon distributions taken from the numerical solutions of the BK equation with running coupling. We obtain a central value dN/dη(sqrt{s}=5.5 TeV)(η=0)~1390.

DIS data and the problem of saturation in small-x physics

New experimental data from HERA explore the region of very small x and small and moderate $Q^2$. We study the role of unitarity corrections in the description of these data. For that, we propose a model separating the small and large components of the $q\bar q$ fluctuation. This model gives a unified description of total and diffractive production in $γ^*p$ interactions. In this model unitarity corrections are controlled by diffraction data.

From Parton Saturation to Proton Spin: the Impact of BFKL Equation and Reggeon Evolution

Lev Lipatov was a giant in the field of strong interactions and a dominant force in high-energy QCD for many decades. His work deeply influenced both how we think about QCD and how we perform calculations in the theory. Below we describe the work in two related research directions: the physics of parton saturation and proton spin at small $x$. Both developments would have been impossible without Lipatov's groundbreaking work. Saturation physics would not have happened without the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation. The recent progress in our theoretical understanding of the proton s…

Probing Saturation Physics in the Real Compton Scattering at Ultraperipheral $pPb$ Collisions

The Real Compton Scattering in ultraperipheral $pPb$ collisions at RHIC and LHC energies is investigated and predictions for the squared transverse momentum ($t$) and rapidity ($Y$) distributions are presented. The scattering amplitude is assumed to be given by the sum of the Reggeon and Pomeron contributions and the Pomeron one is described by the Color Dipole formalism taking into account the non - linear (saturation) effects in the QCD dynamics. We demonstrate that the behaviour of the cross sections at large -- $t$ and/or $Y$ is dominated by the Pomeron contribution and is strongly affecte…

CGC/saturation approach for high energy soft interactions: $\mathbf{v_2}$ in proton-proton collisions

In this paper we continue our program to construct a model for high energy soft interactions, based on the CGC/saturation approach. We demonstrate that in our model which describes diffractive physics as well as multi-particle production at high energy, the density variation mechanism leads to the value of $v_2$ which is about $60\% ÷70\%$ of the measured $v_2$. Bearing in mind that in CGC/saturation approach there are two other mechanisms present: Bose enhancement in the wave function and local anisotropy, we believe that the azimuthal long range rapidity correlations in proton-proton collisi…

Deep Inelastic Scattering Data and the Problem of Saturation in Small-x Physics

We investigate the role of unitarization effects in virtual photon-proton (γ^*p) interactions at small x. The q\bar{q}-fluctuation of the initial photon is separated into a small distance and a large distance component and a model for the unitarization of each component is proposed. The Born approximation for the small size component is calculated using QCD perturbation theory. Reggeon diagram technique is used in order to obtain a self-consistent scheme for both total γ^*p cross section and diffractive production. The model gives a good description of HERA data in the small-x region, with a s…

Saturation in diffractive deep inelastic eA scattering

In this paper we investigate the saturation physics in diffractive deep inelastic electron-ion scattering. We estimate the energy and nuclear dependence of the ratio $σ^{diff}/σ^{tot}$ and predict the $x_{\pom}$ and $β$ behavior of the nuclear diffractive structure function $F_{2,A}^{D(3)}(Q^2, β, x_{IP})$. Moreover, we analyze the ratio $R^{diff}_{A1,A2}(Q^2, β, x_{IP}) = F_{2,A1} ^{D(3)}/F_{2,A2} ^{D(3)}$, which probes the nuclear dependence of the structure of the Pomeron. We show that saturation physics predicts that approximately 37 % of the events observed at eRHIC should be diffractive.

EIC 中轻子-喷注关联内部分子饱和的谐波

Harmonics of Parton Saturation in Lepton-Jet Correlations at the EIC

本文提出利用 EIC 深度非弹性散射中的轻子-喷注方位角各向异性探测部分子饱和，并表明 e+p 与 e+Au 系统的谐波系数差异可提供定量证据。

White Paper on Forward Physics, BFKL, Saturation Physics and Diffraction

The goal of this whitepaper is to give a comprehensive overview of the rich field of forward physics. We discuss the occurrences of BFKL resummation effects in special final states, such as Mueller-Navelet jets, jet gap jets, and heavy quarkonium production. It further addresses TMD factorization at low x and the manifestation of a semi-hard saturation scale in (generalized) TMD PDFs. More theoretical aspects of low x physics, probes of the quark gluon plasma, as well as the possibility to use photon-hadron collisions at the LHC to constrain hadronic structure at low x, and the resulting compl…

Phenomenology of neutrino oscillation ---Brief overview and its relevance to tau physics---

Status of neutrino oscillation study is briefly reviewed. Some aspects relevant to tau physics are also described.

High energy pA collisions in the Color Glass Condensate approach

We present a brief review of phenomenological applications of the gluon saturation approach to the proton-nucleus collisions at high energies.

The Color Glass Condensate and some applications

We give an elementary discussion of parton saturation and its description by the effective theory of the Color Glass Condensate. We report on progress in calculating multi-gluon correlators. The latter are necessary for many phenomenological applications, upon some of which we briefly touch.

Color Glass Condensate and its relation to HERA physics

I give a brief overview of the effective theory for the Color Glass Condensate, which is the high-density gluonic matter which controls high-energy scattering in QCD in the vicinity of the unitarity limit. I concentrate on fundamental phenomena, like gluon saturation, unitarization, and geometric scaling, and the way how these are encoded in the formalism. I emphasize the importance of the next-to-leading order corrections, especially the running of the coupling, for both conceptual and phenomenological issues. I survey the implications of the CGC theory for the HERA physics and its phenomenol…

Saturation Physics in Ultra High Energy Cosmic Rays: Heavy Quark Production

In this work we estimate the heavy quark production in the interaction of ultra high energy cosmic rays in the atmosphere, considering that the primary cosmic ray is a proton or a photon. At these energies the saturation momentum Q_{sat}^2 stays above the hard scale μ_c^2=4m_c^2, implying charm production probing the saturation regime. In particular, we show that the ep HERA data presents a scaling on τ_c = (Q^2+μ_c^2)/Q_{sat}^2. We derive our results considering the dipole picture and the Color Glass Condensate formalism, which one shows to be able to describe the heavy quark production in ph…

饱和框架中NLO阶的衍射单强子与双强子产生

Diffractive single and di-hadron production at the NLO in a saturation framework

本文在冲击波形式体系中计算了NLO阶衍射单强子与双强子产生截面，旨在提高LHC和EIC上检验饱和物理的理论预测精度。

Parton Saturation at Small x and in Large Nuclei

Quark and gluon distributions in the light-cone wavefunction of a high energy hadron or nucleus are calculated in the saturation regime. One loop calculations are performed explicitly using the equivalence between the parton distribution in the light-cone wavefunction and the production distribution of that parton in a current-nucleon (nucleus) scattering. We argue that, except for some overall numerical factors, the Weizsacker- Williams wavefunction correctly gives the physics of the gluon distribution in a light-cone wavefunction.

Brief introduction to viscosity in hadron physics

We introduce the concept of viscosity (both shear and bulk) in the context of hadron physics and in particular the meson gas, highlighting the current theoretical efforts to connect possible measurements of the viscosities to underlying physics such as a phase transition or the trace anomaly.

A brief theory overview of Higgs physics at the LHC

This is a brief review of the theoretical status of Higgs production at the LHC in the Standard Model, with an emphasis on the recent developments and computations. In particular, I focus on both inclusive and differential cross sections for the dominant production mode in the Standard Model, where the theoretical uncertainties induced by the different interplays between top- and bottom-quark effects in the gluon-fusion scattering amplitude are discussed.

小x深非弹性散射中饱和的幂次计数

Power Counting to Saturation

本文基于从QCD推导的有效理论中的幂次计数，描述了小x深非弹性散射中的饱和现象，通过因子化公式分离出原子核的普适物理，并识别出一种新的辐射模式以区分饱和标度的出现与向非线性演化的转变。

CGC-py：用于胶子饱和物理的蒙特卡洛事例产生器

CGC-py: A Monte Carlo Event Generator for Gluon Saturation Physics

该研究开发了CGC-py蒙特卡洛事例产生器，结合CGC截面与PYTHIA 8处理相关过程，验证后用于研究胶子饱和物理，揭示核效应及不同动力学对双强子远离侧宽度的贡献。

Parton Cascades, Small x, and Saturation in High Energy Collisions

These lecture notes are a combination of two lectures and a contribution to the celebration of Andrzej Białas' birthday at the LI Cracow School of Theoretical Physics in June 2011. I here discuss the dynamics of particle production in high energy reactions. It includes parton cascades and hadronization in e+e--ann., small x evolution including the Double Leading Log approximation and the BFKL equation, saturation at high densities and the BK equation, and finally the Lund Dipole Cascade model for high energy collisions, which is implemented in the DIPSY MC.

超边缘碰撞中作为可能饱和信号的新截面比

Novel Cross Section Ratios as Possible Signals of Saturation in UPCs

本文提出在超边缘碰撞中测量弹性矢量介子与单举强子或喷注光生截面的新比值，通过构建双重比值并计算小$x$演化，发现其在饱和区域内外对核原子数依赖性显著不同，有助于实验寻找饱和物理证据。

饱和框架下通过衍射过程的胶子层析成像

Gluon tomography through diffractive processes in a saturation framework

本研究通过对四类衍射过程进行NLO及超出领头扭度的处理，将饱和物理与胶子层析成像推向精准时代，为胶子饱和动力学精准研究提供新途径，有望在EIC、LHC的UPC实验中开展唯象研究。

Brief Neutrino Physics Update

The discovery of neutrino mass establishes the need for physics beyond the Standard Model. I summarize the status of two- and three-neutrino oscillation parameters from current solar, atmospheric, reactor and accelerator data. Future neutrinoless double beta decay experiments will probe the nature of neutrinos, as well as the absolute scale of neutrino mass, also tested by tritium beta decay spectra and cosmological observations. Sterile neutrinos do not provide a good way to account for the LSND hint, which needs further confirmation. Finally I sketch the main theoretical ideas for generating…

在相干粲偶素电产生于原子核的动量转移依赖中寻找胶子饱和效应

Searching for gluon saturation effects in the momentum transfer dependence of coherent charmonium electroproduction off nuclei

本文首次在QCD色偶极格林函数框架下研究原子核相干粲偶素电产生的横向动量转移分布，系统纳入色透明与高阶及前导扭度遮蔽修正，预测非单调能量依赖并揭示可能的胶子饱和信号。

Brief Introduction to Flavor Physics

We consider the standard model (SM) quark flavor sector. We study its structure in a spurionic, symmetry oriented approach. The SM picture of flavor and CP violation is now experimentally verified, hence strong bounds on beyond the SM flavor structure follow. We show how to parametrically derive such bounds, in a model independent manner, via minimal flavor violation power counting. This min-review summarizes lectures given at the ISSCSMB '08 international school. It aims to give basic tools to understand how flavor and CP violation occur in the SM and its extensions. It should be particularly…

Low x Physics

This is a talk, given at Diffraction'2000, Sept. 2 - 7, Centraro, Italy. In this talk, we present the arguments, that a new QCD regime - gluon saturation, has been reached at HERA.

Brief Review of Charm Physics

Charm physics has attracted increased attention after first evidence for charm mixing was observed in 2007. The level of attention has risen sharply after LHCb reported first evidence for CP violation in the charm sector. Neither mixing nor CP violation have been established by a single unambiguous measurement to date. This review covers the status of mixing and CP violation measurements and comments on the challenges on the road ahead, both on the experimental and theoretical side, and on ways to tackle them.

Practicing carpe diem in the journey of studying physics: A brief review of the scientific contribution of Ru-Keng Su

We briefly review the scientific contributions of the late Prof. Ru-Keng Su in his academic life. In the area of intermediate and high-energy nuclear physics, Su explored various topics in high-energy nuclear physics and particle physics, inclusively about the finite temperature field theory, effective models for nuclear and quark matter, soliton, and quasiparticle models, among others. In gravity and cosmology, Su's research primarily embraces black hole thermodynamics, quasinormal modes, cosmological microwave background radiation, modified theories of gravity, and AdS/CFT correspondence and…