The energy dependence of saturation scale at next-to-leading order

Slides:



Advertisements
Similar presentations
Quarkonia: theoretical overview Marzia Nardi INFN Torino III Convegno Nazionale sulla Fisica di ALICE Frascati, Novembre 2007.
Advertisements

1.  Motivation  Theoretical framework  Perturbative QCD Approach  Numerical Results  Summary 2.
The Color Glass Condensate and RHIC Phenomenology Outstanding questions: What is the high energy limit of QCD? How do gluons and quarks arise in hadrons?
Perturbative Odderon in the Color Glass Condensate
Triumvirate of Running Couplings in Small-x Evolution Yuri Kovchegov The Ohio State University Based on work done in collaboration with Heribert Weigert,
1 D. Kharzeev Nuclear Theory BNL Alice Club, CERN TH, May 14, 2007 Non-linear evolution in QCD and hadron multiplicity predictions for the LHC.
Jet substructures of boosted Higgs Hsiang-nan Li ( 李湘楠 ) Academia Sinica Presented at PPCHP Oct. 08, 2014 Collaborated with J. Isaacson, Z. Li, CP Yuan.
Running Coupling in Small-x Evolution Yuri Kovchegov The Ohio State University Based on work done in collaboration with Heribert Weigert, hep-ph/
Outline of Lectures Lecture I: EFT approach to high energy QCD-The Color Glass Condensate; multi-particle production in the CGC Lecture II: Hadronic scattering.
Lecture II. 3. Growth of the gluon distribution and unitarity violation.
Introduction to the Physics of Saturation Introduction to the Physics of Saturation Yuri Kovchegov The Ohio State University.
First correction to JIMWLK evolution from the classical EOMs N. Armesto 19th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions.
As one evolves the gluon density, the density of gluons becomes large: Gluons are described by a stochastic ensemble of classical fields, and JKMMW argue.
The Color glass COndensate A classical effective theory of high energy QCD Raju Venugopalan Brookhaven National Laboratory ICPAQGP, Feb. 8th-12th, 2005.
SSAs at small x and the the anomalous magnetic moment Jian Zhou Regensburg University Based on: Phys.Rev. D89 (2014) ZJ arXiV: A. Schafer.
J/ψ Production in pPb Collisions at the LHC Zhang, Hong-Fei Third Military Medical University.
Testing saturation with diffractive jet production in DIS Cyrille Marquet SPhT, Saclay Elastic and Diffractive Scattering 2005, Blois, France based on.
Cronin Effect and High-p T Suppression in pA Collisions Yuri Kovchegov University of Washington Based on work done in collaboration with Based on work.
Zhongbo Kang Los Alamos National Laboratory QCD structure of the nucleon and spin physics Lecture 5 & 6: TMD factorization and phenomenology HUGS 2015,
Small-x physics 2- The saturation regime of QCD and the Color Glass Condensate Cyrille Marquet Columbia University.
Jet energy loss at RHIC and LHC including collisional and radiative and geometric fluctuations Simon Wicks, QM2006 Work done with Miklos Gyulassy, William.
Overview of saturation Yoshitaka Hatta (Saclay) Low-x meeting, 2007, Helsinki.
11/28/20151 QCD resummation in Higgs Boson Plus Jet Production Feng Yuan Lawrence Berkeley National Laboratory Ref: Peng Sun, C.-P. Yuan, Feng Yuan, PRL.
Transverse Momentum Broadening of a Fast Quark in a N=4 Yang Mills Plasma Jorge Casalderrey-Solana LBNL Work in collaboration with Derek Teany.
Forward particle production in d+Au collisions in the CGC framework Cyrille Marquet Institut de Physique Théorique, CEA/Saclay.
Color Glass Condensate HIM MEETING( 광주 ) Dec. 4, 2004.
Recent advances in High-Energy QCD evolution equations Javier L. Albacete High Energy QCD: From RHIC to LHC. ECT, Trento, January 2007.
Status of the theory of saturation of partonic densities Cyrille Marquet Theory Division - CERN.
The Color Glass Condensate and Glasma What is the high energy limit of QCD? What are the possible form of high energy density matter? How do quarks and.
Color Glass Condensate in High Energy QCD Kazunori Itakura SPhT, CEA/Saclay 32 nd ICHEP at Beijing China 16 Aug
STAR azimuthal correlations of forward di-pions in d+Au collisions in the Color Glass Condensate Cyrille Marquet Institut de Physique Théorique, CEA/Saclay.
Overview of low-x and diffraction at HERA Henri Kowalski DESY Rencontres de Moriond La Thuile, March 2006.
Mean Field Effect on J/psi Production in Heavy Ion Collisions Baoyi Chen Physics Department Tsinghua University Cooperators: Kai Zhou Yunpeng Liu Pengfei.
Forward di-jet production in p+Pb collisions Centre de Physique Théorique Ecole Polytechnique & CNRS Cyrille Marquet A. van Hameren, P. Kotko, K. Kutak,
Distribution of linearly polarized gluons inside a large nucleus Jian Zhou Regensburg University Based on: Phys.Rev. D84 (2011) A. Metz and ZJ.
L. Apolinário, N. Armesto, J. G. Milhano, C. Salgado TOWARDS JET CALCULUS IN A QCD MEDIUM.
Long-Range Rapidity Correlations in Heavy-Light Ion Collisions Yuri V. Kovchegov The Ohio State University based on arXiv: [hep-ph] with Douglas.
Lecture III. 5. The Balitsky-Kovchegov equation Properties of the BK equation The basic equation of the Color Glass Condensate - Rapid growth of the.
Yan-Qing Ma ( 马滟青 ) Peking University The Second Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Central China Normal University,
Azimuthal correlations of forward di-hadrons in d+Au collisions at RHIC Cyrille Marquet Theory Division - CERN Based on :C.M., Nucl. Phys. A796 (2007)
Theory at the RIKEN/BNL Research Center initial state "Glasma" "Quark-Gluon Plasma" hadrons Cartoon of heavy ion collisions at high energy: (Now: RHIC.
Production, energy loss and elliptic flow of heavy quarks at RHIC and LHC Jan Uphoff with O. Fochler, Z. Xu and C. Greiner Hard Probes 2010, Eilat October.
Running Coupling Corrections to Nonlinear Evolution for Diffractive Dissociation Yuri Kovchegov The Ohio State University.
Heavy quarks and charmonium at RHIC and LHC within a partonic transport model Jan Uphoff with O. Fochler, Z. Xu and C. Greiner XLIX International Winter.
Quark Pair Production in the Color Glass Condensate Raju Venugopalan Brookhaven National Laboratory AGS users-Quarkonium workshop, June 6th, 2006.
Quark Pair Production in the Color Glass Condensate Raju Venugopalan Brookhaven National Laboratory RBRC Heavy Flavor Workshop, Dec. 12th-14th, 2005.
1 Proton Structure Functions and HERA QCD Fit HERA+Experiments F 2 Charged Current+xF 3 HERA QCD Fit for the H1 and ZEUS Collaborations Andrew Mehta (Liverpool.
From Lagrangian Density to Observable
Introduction to pQCD and TMD physics
Jet shape & jet cross section: from hadrons to nuclei
Computing gluon TMDs at small-x in the Color Glass Condensate
Lecture 2 Evolution and resummation
Multiple parton interactions in heavy-ion collisions
Running coupling corrections to inclusive gluon production
Semi-inclusive DIS at Small-x
Color Glass Condensate : Theory and Phenomenology
Forward particle production in the presence of saturation
Computing gluon TMDs at small-x in the Color Glass Condensate
Feng Yuan Lawrence Berkeley National Laboratory
Kenji Fukushima (RIKEN BNL Research Center)
Electron ion collisions and the Color Glass Condensate
New d+Au RHIC data show evidence for parton saturation
A prediction of unintegrated parton distribution
Heavy-to-light transitions on the light cone
“Min-Bias” and the “Underlying Event”
Hadron Multiplicity from Color Glass Condensate at LHC
QCD at very high density
Calculation of Pure Annihilation Type B Decay in PQCD Approach
Before the HERA measurements most of the predictions for low-x behaviour of the structure functions and the gluon PDF were wrong Now it seems that the.
Presentation transcript:

The energy dependence of saturation scale at next-to-leading order Mengliang WANG Guizhou University of Finance and Economic

Outline Motivation The BK equation and the corrections BK equation in NLO The BK equation and the corrections The higher order correction The initial conditions The numerical calculation Summary and outlook 现代金融理论 <2000年 QTP2017, Xi'an, July 21-23 Mengliang WANG

The BK equation At high energy, dipole-hadron scattering perturbative QCD (pQCD) predict non-linear phenomena: gluon saturation multiple scattering   𝒓 2 The non-linear solutions: Balitsky-JIMWLK* hierarchy + mean field approximation: Balitsky-Kovchegov (BK) equation * Jalilian-Marian–Iancu–McLerran–Weigert–Leonidov–Kovner At high energy, dipole-hadron scattering perturbative QCD (pQCD) predicts a rapid growth of the gluon density with increasing energy, which leads to non-linear phenomena:   The BK evolve equation of leading order: QTP2017, Xi'an, July 21-23 Mengliang WANG

The BK equation of NLO Insufficient for leading logarithmic accuracy compare with data: structure functions in DIS at HERA particle production in heavy ion collisions at LHC A further corrections are needed to explain data: BK equation of Full NLO reads: QTP2017, Xi'an, July 21-23 Mengliang WANG

The higher order corrections Beside the long full NLO-BK equation, simpler corrections can be used as to neglect the contribution from the high order of 𝛼 𝑠 However, the NLO BK equation suffers from a severe lack of stability: solution can be negative with increasing rapidity (no-physically meaningful evolution) The origin of this instability can be traced back to the large double transverse logarithmic NLO correction: Several way of corrections have been developed to overcome the problem. QTP2017, Xi'an, July 21-23 Mengliang WANG

The higher order corrections (1) 𝜕𝒩(𝑟,𝑥) 𝜕𝑌 = 𝑑 2 𝑟 1 𝓚 𝒓, 𝒓 𝟏 ,𝒙 𝒩 𝑟 1 ,𝑥 +𝒩 𝑟 2 ,𝑥 −𝒩 𝑟,𝑥 −𝒩( 𝑟 1 ,𝑥)𝒩( 𝑟 2 ,𝑥) Leading order 𝒦 𝐿𝑂 𝑟, 𝑟 1 ,𝑥 = 𝛼 𝑠 2𝜋 𝑟 2 𝑟 2 2 𝑟 1 2 Running coupling (including quark loop) 𝒦 𝑅𝐶 𝑟, 𝑟 1 ,𝑥 = 𝛼 𝑠 2𝜋 𝑟 2 𝑟 2 2 𝑟 1 2 + 1 𝑟 1 2 𝛼 𝑠 ( 𝑟 1 2 ) 𝛼 𝑠 ( 𝑟 2 2 ) −1 + 1 𝑟 2 2 𝛼 𝑠 ( 𝑟 2 2 ) 𝛼 𝑠 ( 𝑟 1 2 ) −1 The propagator of the emitted gluon can be understand as a pair of quark-antiquark, contract to the fix–coupling. The quark-antiquark pair which added to the evolved wave function, not only can modify the BK kernel, but also can change the interaction structure of the evolution equation. QTP2017, Xi'an, July 21-23 Mengliang WANG

The higher order corrections (2) 𝜕𝒩(𝑟,𝑥) 𝜕𝑌 = 𝑑 2 𝑟 1 𝓚 𝒓, 𝒓 𝟏 ,𝒙 𝒩 𝑟 1 ,𝑥 +𝒩 𝑟 2 ,𝑥 −𝒩 𝑟,𝑥 −𝒩( 𝑟 1 ,𝑥)𝒩( 𝑟 2 ,𝑥) NLL (next-to-leading logarithmic) correction:     Double Logarithmic Approbation (DLA): Resummation of large double logarithmic term from light-cone perturbative theory Next-to-leading logarithmic (NLL): Promoting this method to NLO-BK equation: To avoid the disaster of the double logarithmic term, a effective method of resummation of large double logarithmic correction (DLA), by promoting this method to NLO-BK equation, established from light-cone perturbation theory. s to all orders QTP2017, Xi'an, July 21-23 Mengliang WANG

Initial Condition To solve these BK equations, the initial condition (Y=0) is necessary. Typical methods are GBW and MV (the results of with MV are shown in these slides):   Golec-Biernat and Wusthoff (GBW) model   McLerran-Venugopalan (MV) model QTP2017, Xi'an, July 21-23 Mengliang WANG

Solutions from the BK equation Results of several Y (=8, 16, 24): The initial condition (Y=0) is shown in black dash line. LO are in orange RC are in green NLL are in violate QTP2017, Xi'an, July 21-23 Mengliang WANG

Saturation scale: 𝑌, 𝑟 𝐿𝑂 𝑌, 𝑟 𝑁𝐿𝐿 𝑌, 𝑟 RC In order to show the energy dependence of the saturation scale, we extract the values of 𝑄 𝑠 from the numerical solutions in previous figure, via define 𝑁(𝑟=1/ 𝑄 𝑠 , 𝑌) =𝜅, we used 𝜅=0.5 in this slides. 𝑌, 𝑟 𝑁𝐿𝐿 𝑌, 𝑟 RC 𝑌, 𝑟 𝐿𝑂 QTP2017, Xi'an, July 21-23 Mengliang WANG

The energy/rapidity dependence For the saturation 𝒩 𝑟,𝑌 =0.5 region, the different saturation scale 𝑄 𝑠 (=1/𝑟) are abstracted for the corresponding rapidity Y(0 ~ 25) LO are in orange RC are in green NLL are in violate Reasonable results for different experiment: 𝑸 𝒔 =0.5 ~ 2 from HERA, RHIC and LHC, which agrees with NLL and RC results QTP2017, Xi'an, July 21-23 Mengliang WANG

Thank you ! Summary and outlook With the MV initial condition, different approaches (LO, RC, NLL) are used of solving the BK equation in coordinates space. The corresponding energy (rapidity) dependence are calculated. The study of other approaches (DLA-rc, STL+DLA) are on going, together with the GBW Initial conditions. Thank you ! QTP2017, Xi'an, July 21-23 Mengliang WANG

backup QTP2017, Xi'an, July 21-23 Mengliang WANG

The higher order corrections   Leading order: Running coupling (including quark loop): NLL (next-to-leading logarithmic) correction:       QTP2017, Xi'an, July 21-23 Mengliang WANG

  𝒓 2 QTP2017, Xi'an, July 21-23 Mengliang WANG