Factorization and Fully Unintegrated Factorization
|
|
- Antonia Hood
- 5 years ago
- Views:
Transcription
1 Factorization and Fully Unintegrated Factorization Ted C. Rogers Vrije Universiteit Amsterdam Factorization and unintegrated PDFs: open problems Fully unintegrated factorization INT 09 - September, 2009
2 Perturbative QCD Asymptotic freedom: Strong coupling becomes small over short time/distance scales! α s (Q 2 )<<1; Q>>Λ QCD Hard scale Use standard Feynman perturbation theory to make accurate first principles calculations. 2
3 pqcd and Factorization The Real World: Always involves both long and short time/distance scales. Factorization Theorem: Systematic separation of long and short distance scales in QFT. Short distance part: Well-defined perturbation series in small coupling. Long distance parts: Universal correlation functions. Access quark/gluon degrees of freedom. 3
4 DIS: Standard Approximations LO DIS: Before approximations: q k P l J(l) Φ(k, P) P = q= ( P +, M2 p 2P +,0 t ) ( xp +, ) Q 2 2xP,0 + t Parton model kinematics: k=(k +,k,k ) k + =xp + + M2 J +k2 t 2(q +k ) l=k+q=(k + xp +,q +k,k ) l 2 0 k + xp + x B P + 4
5 Standard Approximations (cont.) Unapproximated structure tensor: W µν (q,p)= e2 j d 4 k 4π (2π) 4Tr[γµ J(k+q)γ ν Φ(k,P)] l 5
6 Standard Approximations (cont.) Unapproximated structure tensor: W µν (q,p)= e2 j d 4 k 4π (2π) 4Tr[γµ J(k+q)γ ν Φ(k,P)] l Approximate momentum inside subgraphs: k (xp +,k,k ); k+q (l +,q,0 ) Inside target subgraph Inside jet subgraph 6
7 Standard Approximations (cont.) Unapproximated structure tensor: W µν (q,p)= e2 j d 4 k 4π (2π) 4Tr[γµ J(k+q)γ ν Φ(k,P)] l Approximate momentum inside subgraphs: k (xp +,k,k ); k+q (l +,q,0 ) Inside target subgraph Inside jet subgraph Use parton model approximation inside hard part. k ˆk=(xP +,0,0 ); l ˆl=(0,q,0 ) 7
8 Standard Approximations (cont.) Unapproximated structure tensor: W µν (q,p)= e2 j d 4 k 4π (2π) 4Tr[γµ J(k+q)γ ν Φ(k,P)] l Approximate momentum inside subgraphs: k (xp +,k,k ); k+q (l +,q,0 ) Inside target subgraph Inside jet subgraph Use parton model approximation inside hard part. k ˆk=(xP +,0,0 ); l ˆl=(0,q,0 ) Project out largest Dirac components. 8
9 Factorized Graph 2 = Parton Distribution??? LO partonic structure functions. Note shift in kinematics!! 9
10 Varieties of parton correlation functions Standard Integrated PCFs: All small momentum components are integrated in definitions. 10
11 Factorized Graph 2 = Parton Distribution??? LO partonic structure functions. Note shift in kinematics!! 11
12 Varieties of parton correlation functions Standard Integrated PCFs: All small momentum components are integrated in definitions. Transverse momentum dependent (TMD) PCFs. Only the minus component (smallest) is integrated in definition. Sivers, etc 12
13 Factorized Graph 2 = Parton Distribution??? LO partonic structure functions. Note shift in kinematics!! 13
14 Varieties of parton correlation functions Standard Integrated PCFs: All small momentum components are integrated in definitions. Transverse momentum dependent (TMD) PCFs. Only the minus component (smallest) is integrated in definition. Sivers, etc Fully unintegrated PCFs. Explicit dependence on exact parton momentum. 14
15 Varieties of parton correlation functions Standard Integrated PCFs: All small momentum components are integrated in definitions. Transverse momentum dependent (TMD) PCFs. Only the minus component (smallest) is integrated in definition. Sivers, etc Fully unintegrated PCFs. Explicit dependence on exact parton momentum. How to set up factorization that treats kinematics more accurately? 15
16 Hadron Kinematics Explicit sample: cc photoproduction Try: Parton model kinematics. Keeping k T dependence, but approximating minus component. (TMD PDFs) Exact kinematics. (Fully unintegrated PDFs) 16
17 Errors in final state kinematics Cascade Compare: Parton model kinematics TMD kinematics (From Collins and Jung, 2005) 17
18 Errors in final state kinematics Cascade Compare: TMD kinematics Fully Unintegrated kinematics (From Collins and Jung, 2005) 18
19 Errors in final state kinematics Cascade Compare: TMD kinematics Fully Unintegrated kinematics Fully Unintegrated TMD (From Collins and Jung, 2005) 19
20 Large-x (SI)DIS But k T runs to order Q in the def. of the integrated PDF! Definition of standard PDF becomes inconsistent. Sensitive to remnant mass. Fully unintegrated PDFs needed. (Accardi, Qiu, JHEP 0807:090,2008)
21 Wilson lines Ward identity: Target collinear gluons decouple from hard part. Ward identity collinear lines extracted into overall factor. Wilson line becomes trivial in light-cone gauge. 21
22 Standard (Integrated) PDF Operator definition: f(x,µ)= dw 4π e ixp+ w p ψ(0,w,0 t )V w(u J )γ + V 0 (u J )ψ(0) p u J =(0,1,0 t ) Light-like Wilson lines enforce gauge invariance. 22
23 TMD PDFs: Generally accepted definition: P(x,k t,µ)= Link at infinity dw dw t 16π 3 e ixp+ w +ik t w t p ψ(0,w,w t )V w(n)i n;w,0 γ + V 0 (n)ψ(0) p n=u J =(0,1,0 t ) Fields are no longer evaluated along light-like separation. Connection at infinity needed for closed Wilson line / gauge invariance. 23
24 Complications with K T - Factorization: Uncanceled light-cone divergences corresponding to gluons moving with infinite rapidity in minus direction. + Use non-light-like Wilson lines. Introduces new arbitrary parameter. Predictability recovered with new evolution equations (e.g. CSS). 24
25 TMD PDFs: Wilson Lines Paths of Wilson lines: + + w w,w t Standard (Integrated) Unintegrated First Try _ w,w t + Same issues arise in treating fully unintegrated PCFs Unintegrated tilted Wilson line directions 25
26 Hadron-Hadron Scattering: Modified Universality? Unintegrated-factorization generally fails in hadroproduction of high-p T hadrons. No simple Wilson line structure in PDFs. (Bomhof et al., Phys.Lett.B596: ,2004) (Collins and Qiu, PRD75:114014,2007) Recall Piet Mulders talk + 26
27 Modified Universality? Consider one correlator at a time. Wilson line structure emerges. (Bomhof et al, Eur.Phys.J.C47: , 2006, Bomhof, Mulders Nucl.Phys.B795: ,2008) Φ [,( )] q Φ [+] q 27
28 Modified Universality? (Mulders et al, Eur.Phys.J.C47: , 2006) Consider one correlator at a time. Wilson line structure emerges. Φ [,( )] q Φ [+] q σ N2 N 2 1 H 2 Φ [,( )] q Φ [+][ ] g [ ] q 1 N 2 1 H 2 Φ [+] q Φ [+][ ] g [ ] (Boer et al, Phys.Lett.B660: , 2008) q 28
29 Modified Universality? Complex Wilson Lines:?? σ C Φ [WL 1] q Φ [WL 2] g [WL 3] q + Sum over color structures
30 Modified Universality? P B 0 P A?? σ Φ [+( )] Φ [+( )] One gluon contribution gives zero! 30
31 Modified Universality? Open questions: Can a generalization of K T -factorization be formulated with well-defined but non-standard Wilson lines??? σ C P A F1 WL 1 F 1 P A P B F2 WL 2 F 2 P B + Or,?? σ C P A P B F1 F2 WL 1 WL 2 F 1 F 2 P A P B + After P T weighting? 31
32 Summary So Far Details of kinematic approximations in standard factorization. 32
33 Summary So Far Details of kinematic approximations in standard factorization. Motivation for more exact formalism. 33
34 Summary So Far Details of kinematic approximations in standard factorization. Motivation for more exact formalism. Emphasis on need for well-defined operator definition. Problems 34
35 Summary So Far Details of kinematic approximations in standard factorization. Motivation for more exact formalism. Emphasis on need for well-defined operator definition. Problems Basic Problem: In standard treatment, factorization works after integrations, but final states are changed! 35
36 Fully Unintegrated Factorization Back to Deep Inelastic Scattering Proposal: Set up a factorization formalism with exact kinematics for initial and final states. (Collins, TCR, Stasto, PRD77:085009,2008) 36
37 Fully Unintegrated Factorization Back to Deep Inelastic Scattering Proposal: Set up a factorization formalism with exact kinematics for initial and final states. (Collins, TCR, Stasto, PRD77:085009,2008) Factorization should work point-by-point in phase space. (correct of up to power suppressed terms.) 37
38 Fully Unintegrated Factorization Back to Deep Inelastic Scattering Proposal: Set up a factorization formalism with exact kinematics for initial and final states. (Collins, TCR, Stasto, PRD77:085009,2008) Factorization should work point-by-point in phase space. (correct of up to power suppressed terms.) To obtain factorization, only apply approximations to the hard part. 38
39 Fully Unintegrated Factorization Back to Deep Inelastic Scattering Proposal: Set up a factorization formalism with exact kinematics for initial and final states. (Collins, TCR, Stasto, PRD77:085009,2008) Factorization should work point-by-point in phase space. (correct of up to power suppressed terms.) To obtain factorization, only apply approximations to the hard part. Hard scattering should involve ordinary functions. 39
40 Fully Unintegrated Factorization Back to Deep Inelastic Scattering Proposal: Set up a factorization formalism with exact kinematics for initial and final states. (Collins, TCR, Stasto, PRD77:085009,2008) Factorization should work point-by-point in phase space. (correct of up to power suppressed terms.) To obtain factorization, only apply approximations to the hard part. Hard scattering should involve ordinary functions. Need well-defined fully unintegrated parton correlation functions. 40
41 Factorization Strategy Consider general unapproximated Feynman diagrams. Classify leading regions. 41
42 Factorization Strategy Consider general unapproximated Feynman diagrams. Classify leading regions. Apply approximations appropriate for each region starting with the smallest (but never changing final state momentum!). 42
43 Factorization Strategy Consider general unapproximated Feynman diagrams. Classify leading regions. Apply approximations appropriate for each region starting with the smallest (but never changing final state momentum!). Obtain contribution from larger regions by subtracting smaller regions. 43
44 Factorization Strategy Consider general unapproximated Feynman diagrams. Classify leading regions. Apply approximations appropriate for each region starting with the smallest (but never changing final state momentum!). Obtain contribution from larger regions by subtracting smaller regions. Use Ward identities to disentangle soft and collinear gluons from hard part in sum over graphs. 44
45 Factorization Strategy Consider general unapproximated Feynman diagrams. Classify leading regions. Apply approximations appropriate for each region starting with the smallest (but never changing final state momentum!). Obtain contribution from larger regions by subtracting smaller regions. Use Ward identities to disentangle soft and collinear gluons from hard part in sum over graphs. Identify well-defined operator definitions for the PCFs. 45
46 General Graphical Structure Should start with: Must disentangle soft and collinear gluons to get factorization 46
47 Graphical Example: Single extra gluon: real emission Jet Collinear Soft Target Collinear y J y Q y p 47
48 Soft Region: Factorized Structure 48
49 Graphical Example (Cont.): Subtractions Consider target-collinear region After applying Ward identities. The contribution to the PDF (target PCF) requires double counting subtractions. 49
50 Recall the starting point: Factorization After steps outlined above, this becomes (Ward identities + subtractions) 50
51 Topological Factorization: A formula of this type is the goal. Also need double counting subtractions. 51
52 Full Factorization 52
53 Next-to-Leading Order (TCR, PRD78:074018,2008) Wide angle jets: Non-trivial hard scattering matrix element. + Cross terms Relies on details of LO treatment. 53
54 Next-to-Leading Order (Cont.) NLO hard scattering overlaps with LO. Factorization requires double counting subtractions. Standard integrated factorization: Hard scattering involves generalized functions (distributions)! Exactly analogous subtractive formalism used in fully unintegrated case. (Collins, Zu, JHEP 03 (2005) 059) Double counting subtractions give factorized expression with power suppressed errors point-by-point in phase. 54
55 Fully Unintegrated Approach: Full factorization for scalar theory. Collins, Zu, JHEP 03 (2005) 059 Abelian Gauge Theory: Detailed treatment of factorization for case of a single outgoing jet in DIS (SIDIS). (Collins, TCR, Stasto, PRD77:085009,2008) Suggestive of complete all-orders treatment in QCD Simplest NLO wide-angle hard scattering calculation in DIS. LO + NLO consistent with factorization point-by-point in phase space (TCR, PRD78:074018,2008) 55
56 Outlook Practical Issues: Fully Unintegrated PDFs: Need to finish calculation of NLO hard scattering. Simplifications? Implementation in MCEGs. Open problems in unintegrated formalism: Hadron-hadron scattering? Definitions of TMD/Fully Unintegrated PDFs. Do we have consistent definitions? Other UV divergences? (Cherednikov et al., arxiv: ) Evolution equations (CSS formalism??). Relationship to other approaches? Full extension to non-abelian case. 56
Factorization and Factorization Breaking with TMD PDFs
Factorization and Factorization Breaking with TMD PDFs Ted C. Rogers Vrije Universiteit Amsterdam trogers@few.vu.nl Standard PDFs, Gauge Links and TMD PDFs in DIS. TMD factorization breaking in pp hadrons.
More informationToward the QCD Theory for SSA
Toward the QCD Theory for SSA Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory 5/6/2009 1 Outline Introduction Great progress has been made recently Transverse momentum
More informationFactorization, Evolution and Soft factors
Factorization, Evolution and Soft factors Jianwei Qiu Brookhaven National Laboratory INT Workshop: Perturbative and nonperturbative aspects of QCD at collider energies University of Washington, Seattle,
More informationWhat are the Low-Q and Large-x Boundaries of Collinear QCD Factorization Theorems?
What are the Low-Q and Large-x Boundaries of Collinear QCD Factorization Theorems? Presented by Eric Moffat Paper written in collaboration with Wally Melnitchouk, Ted Rogers, and Nobuo Sato arxiv:1702.03955
More informationQCD Collinear Factorization for Single Transverse Spin Asymmetries
INT workshop on 3D parton structure of nucleon encoded in GPD s and TMD s September 14 18, 2009 QCD Collinear Factorization for Single Transverse Spin Asymmetries Iowa State University Based on work with
More informationNLO weighted Sivers asymmetry in SIDIS and Drell-Yan: three-gluon correlator
NLO weighted Sivers asymmetry in SIDIS and Drell-Yan: three-gluon correlator Lingyun Dai Indiana University Based on the work done with Kang, Prokudin, Vitev arxiv:1409.5851, and in preparation 1 2 Outlines
More informationWhat are the Low-Q and Large-x Boundaries of Collinear QCD Factorization Theorems?
What are the Low-Q and Large-x Boundaries of Collinear QCD Factorization Theorems? Presented by Eric Moffat Old Dominion University Paper written in collaboration with Wally Melnitchouk, Ted Rogers, and
More informationEvolution of 3D-PDFs at Large-x B and Generalized Loop Space
Evolution of 3D-PDFs at Large-x B and Generalized Loop Space Igor O. Cherednikov Universiteit Antwerpen QCD Evolution Workshop Santa Fe (NM), 12-16 May 2014 What we can learn from the study of Wilson loops?
More informationQCD and Rescattering in Nuclear Targets Lecture 2
QCD and Rescattering in Nuclear Targets Lecture Jianwei Qiu Iowa State University The 1 st Annual Hampton University Graduate Studies Program (HUGS 006) June 5-3, 006 Jefferson Lab, Newport News, Virginia
More informationGluonic Spin Orbit Correlations
Gluonic Spin Orbit Correlations Marc Schlegel University of Tuebingen in collaboration with W. Vogelsang, J.-W. Qiu; D. Boer, C. Pisano, W. den Dunnen Orbital Angular Momentum in QCD INT, Seattle, Feb.
More informationScale dependence of Twist-3 correlation functions
Scale dependence of Twist-3 correlation functions Jianwei Qiu Brookhaven National Laboratory Based on work with Z. Kang QCD Evolution Workshop: from collinear to non collinear case Thomas Jefferson National
More informationIntroduction to Perturbative QCD
Introduction to Perturbative QCD Lecture 3 Jianwei Qiu Iowa State University/Argonne National Laboratory PHENIX Spinfest at RIKEN 007 June 11 - July 7, 007 RIKEN Wako Campus, Wako, Japan June 6, 007 1
More informationWhy Glauber Gluons Are Relevant?
Why Glauber Gluons Are Relevant? Ahmad Idilbi MIT, March 09 A.I and A. Majumder, arxiv:0808.1087 [hep-ph] Semi-Inclusive Deep-Inelastic Scattering (SIDIS) and Transverse Momentum Parton Distribution (TMDPDF)
More informationProbing nucleon structure by using a polarized proton beam
Workshop on Hadron Physics in China and Opportunities with 12 GeV Jlab July 31 August 1, 2009 Physics Department, Lanzhou University, Lanzhou, China Probing nucleon structure by using a polarized proton
More informationIntroduction to High Energy Nuclear Collisions I (QCD at high gluon density) Jamal Jalilian-Marian Baruch College, City University of New York
Introduction to High Energy Nuclear Collisions I (QCD at high gluon density) Jamal Jalilian-Marian Baruch College, City University of New York Many thanks to my colleagues, A. Deshpande, F. Gelis, B. Surrow
More informationQCD Factorization and Transverse Single-Spin Asymmetry in ep collisions
QCD Factorization and Transverse Single-Spin Asymmetry in ep collisions Jianwei Qiu Brookhaven National Laboratory Theory seminar at Jefferson Lab, November 7, 2011 Jefferson Lab, Newport News, VA Based
More informationQCD Factorization and PDFs from Lattice QCD Calculation
QCD Evolution 2014 Workshop at Santa Fe, NM (May 12 16, 2014) QCD Factorization and PDFs from Lattice QCD Calculation Yan-Qing Ma / Jianwei Qiu Brookhaven National Laboratory ² Observation + Motivation
More informationKinematics and Parton Correlation Functions in the Parton Model. Paul McCullough Supervisors: Piet Mulders and Ted Rogers
Kinematics and Parton Correlation Functions in the Parton Model Paul McCullough Supervisors: Piet Mulders and Ted Rogers August 30, 2009 Abstract In the Standard Model of Particle Physics, QCD is the
More informationThe transverse spin and momentum structure of hadrons. 03/26/10 talk #3 Parton Model Gauge Links T-odd TMDs. Leonard Gamberg Penn State University
The transverse spin and momentum structure of hadrons 03/26/10 talk #3 Parton Model Gauge Links T-odd TMDs Leonard Gamberg Penn State University T-Odd Effects From Color Gauge Inv. via Wilson Line Gauge
More informationGluon TMDs and Heavy Quark Production at an EIC
Gluon TMDs and Heavy Quark Production at an EIC Cristian Pisano INT-7-3 Workshop Hadron imaging at Jefferson Lab and at a future EIC September 25-29 27 Seattle (USA) Quark TMDs Angeles-Martinez et al.,
More informationThe transverse spin and momentum structure of hadrons. 03/26/10 talk #2 Parton Model, SIDIS & TMDs. Leonard Gamberg Penn State University
The transverse spin and momentum structure of hadrons 03/26/10 talk #2 Parton Model, SIDIS & TMDs Leonard Gamberg Penn State University The Transverse Spin and Momentum Structure of Hadrons Details TMDs
More informationlight-cone (LC) variables
light-cone (LC) variables 4-vector a µ scalar product metric LC basis : transverse metric 24-Apr-13 1 hadron target at rest inclusive DIS target absorbes momentum from γ * ; for example, if q z P z =0
More informationZhong-Bo Kang Los Alamos National Laboratory
Introduction to pqcd and Jets: lecture 1 Zhong-Bo Kang Los Alamos National Laboratory Jet Collaboration Summer School University of California, Davis July 19 1, 014 Selected references on QCD! QCD and
More informationZhongbo Kang. QCD evolution and resummation for transverse momentum distribution. Theoretical Division, Group T-2 Los Alamos National Laboratory
QCD evolution and resummation for transverse momentum distribution Zhongbo Kang Theoretical Division, Group T-2 Los Alamos National Laboratory QCD Evolution Worshop Jefferson Lab, Newport News, VA Outline:
More informationContribution of the twist-3 fragmentation function to single transverse-spin asymmetry in SIDIS
Contribution of the twist-3 fragmentation function to single transverse-spin asymmetry in SIDIS Graduate School of Science and Technology, Niigata University, Ikarashi -8050, Niigata 950-8, Japan Department
More informationTransverse Momentum Dependent Distribution Functions of Definite Rank
QCD204: QCD Evolution 204 Workshop Santa Fe, 2-6 May 204 ransverse Momentum Dependent Distribution Functions of Definite Rank Piet Mulders mulders@few.vu.nl ABSRAC MDs of definite rank Piet Mulders (Nikhef/VU
More informationTed Conant Rogers curriculum vitae
Ted Conant Rogers curriculum vitae C.N. Yang Institute for Theoretical Physics Stony Brook University Math Tower, Rm: 5-105, Stony Brook, New York 11794-3840, USA Phone: 646-532-8443, E-mail: rogers@insti.physics.sunysb.edu
More information季向东 (Xiangdong Ji) Shanghai Jiao Tong University University of Maryland
季向东 (Xiangdong Ji) Shanghai Jiao Tong University University of Maryland 1. Gauge symmetry and Feynman parton distributions 2. TMDs in light of gauge symmetry 3. Wigner distributions and angular momentum
More informationPhysics at LHC. lecture one. Sven-Olaf Moch. DESY, Zeuthen. in collaboration with Martin zur Nedden
Physics at LHC lecture one Sven-Olaf Moch Sven-Olaf.Moch@desy.de DESY, Zeuthen in collaboration with Martin zur Nedden Humboldt-Universität, October 22, 2007, Berlin Sven-Olaf Moch Physics at LHC p.1 LHC
More informationFactorisation in Double Parton Scattering: Glauber Gluons
Factorisation in Double Parton Scattering: Glauber Gluons Jonathan Gaunt, Nikhef & VU Amsterdam MPI@LHC 2015, ICTP Trieste, Italy, 24/11/2015 Based on [arxiv:1510.08696], Markus Diehl, JG, Daniel Ostermeier,
More informationCOMPASS Measurements of Asymmetry Amplitudes in the Drell-Yan Process Observed from Scattering Pions off a Transversely Polarized Proton Target
COMPASS Measurements of Asymmetry Amplitudes in the Drell-Yan Process Observed from Scattering Pions off a Transversely Polarized Proton Target University of Illinois E-mail: rsheitz2@illinois.edu On behalf
More informationFOUNDATIONS OF PERTURBATIVE QCD
FOUNDATIONS OF PERTURBATIVE QCD The most non-trivial of the established microscopic theories of physics is QCD: the theory of the strong interaction. A critical link between theory and experiment is provided
More informationHadron Tomography. Matthias Burkardt. New Mexico State University Las Cruces, NM, 88003, U.S.A. Hadron Tomography p.
Hadron Tomography Matthias Burkardt burkardt@nmsu.edu New Mexico State University Las Cruces, NM, 88003, U.S.A. Hadron Tomography p.1/24 Outline GPDs: probabilistic interpretation as Fourier transforms
More informationIntroduction to Perturbative QCD
Introduction to Perturbative QCD Lecture Jianwei Qiu Iowa State University/Argonne National Laboratory PHENIX Spinfest at RIKEN 007 June 11 - July 7, 007 RIKEN Wako Campus, Wako, Japan June 5, 007 1 Infrared
More informationTransverse momentum-dependent parton distributions from lattice QCD. Michael Engelhardt New Mexico State University
Transverse momentum-dependent parton distributions from lattice QCD Michael Engelhardt New Mexico State University In collaboration with: B. Musch P. Hägler J. Negele A. Schäfer Lattice theorists go shopping...
More informationRecent QCD results from ATLAS
Recent QCD results from ATLAS PASCOS 2013 Vojtech Pleskot Charles University in Prague 21.11.2013 Introduction / Outline Soft QCD: Underlying event in jet events @7TeV (2010 data) Hard double parton interactions
More informationFOLLOWING PINO - THROUGH THE CUSPS AND BEYOND THE PLANAR LANDS. Lorenzo Magnea. University of Torino - INFN Torino. Pino Day, Cortona, 29/05/12
FOLLOWING PINO - THROUGH THE CUSPS AND BEYOND THE PLANAR LANDS Lorenzo Magnea University of Torino - INFN Torino Pino Day, Cortona, 29/05/12 Outline Crossing paths with Pino Cusps, Wilson lines and Factorization
More informationCancellation of Glauber gluon exchange in the double Drell-Yan process arxiv: v1 [hep-ph] 29 Oct 2015
Prepared for submission to JHEP DESY 15-187 Cancellation of Glauber gluon exchange in the double Drell-Yan process arxiv:1510.08696v1 [hep-ph] 29 Oct 2015 Markus Diehl, a Jonathan R. Gaunt, a,1 Daniel
More informationarxiv: v1 [hep-ph] 4 Aug 2010
1 RUB-TPII-06/2010 arxiv:1008.0725v1 [hep-ph] 4 Aug 2010 TRANSVERSE-MOMENTUM PARTON DENSITIES: GAUGE LINKS, DIVERGENCES AND SOFT FACTOR I. O. CHEREDNIKOV INFN Cosenza, Università della Calabria I-87036
More informationDouble-Longitudinal Spin Asymmetry in Single- Inclusive Lepton Scattering
QCD Evolution 2017, JLab, May 22-26, 2017 Double-Longitudinal Spin Asymmetry in Single- Inclusive Lepton Scattering Marc Schlegel Institute for Theoretical Physics University of Tübingen in collaboration
More informationParton-hadron duality and PDF fits
Parton-hadron duality and PDF fits Alberto Accardi Hampton U. and Jefferson Lab Topical Meeting on Parton Hadron Duality University of Virginia, 13 March 2015 Why PDFs at large x? Accardi, Mod.Phys.Lett.
More informationTransverse Momentum Dependent Parton Distributions
Transverse Momentum Dependent Parton Distributions Feng Yuan Lawrence Berkeley National Laboratory 8/14/2012 1 Feynman Parton: one-dimension Inclusive cross sections probe the momentum (longitudinal) distributions
More informationTransverse Momentum Distributions: Matches and Mismatches
Transverse Momentum Distributions: Matches and Mismatches Ahmad Idilbi ECT* M.G. Echevarría, Ahmad Idilbi, Ignazio Scimemi. [arxiv:.947] MGE, AI, Andreas Schäfer, IS. [arxiv: 08.8] MGE, AI, IS. JHEP 07
More informationTransverse SSA Measured at RHIC
May 21-24, 2007 Jefferson Lab Transverse SSA Measured at RHIC Jan Balewski, IUCF Exclusive Reactions Where does the proton s spin come from? p is made of 2 u and 1d quark S = ½ = Σ S q u u Explains magnetic
More informationTransverse Spin Effects and k T -dependent Functions
Transverse Spin Effects and k T -dependent Functions Daniël Boer Free University, Amsterdam Outline Left-right single spin asymmetries Azimuthal spin asymmetries; Sivers and Collins effects Transversity
More informationContributions to our Understanding of TMDs from Polarized Proton Collisions at STAR
Contributions to our Understanding of TMDs from Polarized Proton Collisions at STAR Stephen Trentalange University of California at Los Angeles, for the STAR Collaboration QCD-N16 Bilbao, Spain July 15,
More informationLOOP-TREE DUALITY AND QUANTUM FIELD THEORY IN 4D
LOOP-TREE DUALITY AND QUANTUM FIELD THEORY IN 4D Germán F. R. Sborlini in collaboration with R. Hernández-Pinto and G. Rodrigo Institut de Física Corpuscular, UV- CSIC (Spain) and Departamento de Física,
More informationQuantum Chromodynamics at LHC
Quantum Chromodynamics at LHC Zouina Belghobsi LPTh, Université de Jijel EPAM-2011, TAZA 26 Mars 03 Avril Today s high energy colliders past, present and future proton/antiproton colliders Tevatron (1987
More informationAsmita Mukherjee Indian Institute of Technology Bombay, Mumbai, India
. p.1/26 Sivers Asymmetry in e + p e + J/ψ + X Asmita Mukherjee Indian Institute of Technology Bombay, Mumbai, India Single spin asymmetry Model for J/ψ production Formalism for calculating the asymmetry
More information2. HEAVY QUARK PRODUCTION
2. HEAVY QUARK PRODUCTION In this chapter a brief overview of the theoretical and experimental knowledge of heavy quark production is given. In particular the production of open beauty and J/ψ in hadronic
More informationHadron Tomography. Matthias Burkardt. New Mexico State University Las Cruces, NM, 88003, U.S.A. Hadron Tomography p.
Hadron Tomography Matthias Burkardt burkardt@nmsu.edu New Mexico State University Las Cruces, NM, 88003, U.S.A. Hadron Tomography p.1/27 Outline GPDs: probabilistic interpretation as Fourier transforms
More informationZhongbo Kang UCLA. The 7 th Workshop of the APS Topical Group on Hadronic Physics
Probing collinear and TMD fragmentation functions through hadron distribution inside the jet Zhongbo Kang UCLA The 7 th Workshop of the APS Topical Group on Hadronic Physics February 1-3, 2017 Jets are
More informationHadron Mass Effects on Kaon Multiplicities: HERMES vs. COMPASS
Hadron Mass Effects on Kaon Multiplicities: HERMES vs. COMPASS Juan Guerrero Hampton University & Jefferson Lab QCD evolution 2017 May 26, 2017 Based on: J. G., J. Ethier, A. Accardi, S. Casper,W. Melnitchouk,
More informationAN INTRODUCTION TO QCD
AN INTRODUCTION TO QCD Frank Petriello Northwestern U. & ANL TASI 2013: The Higgs Boson and Beyond June 3-7, 2013 1 Outline We ll begin with motivation for the continued study of QCD, especially in the
More informationQuark/gluon orbital motion and nucleon spin. Alexei Prokudin. JLab December 8, Alexei Prokudin,
Quark/gluon orbital motion and nucleon spin Alexei Prokudin JLab December 8, 20 EIC Golden Topic # 2 talk Bob McKeown @ INT workshop Map the spin and spatial quark-gluon structure of nucleons Image the
More informationMeasurement of photon production cross sections also in association with jets with the ATLAS detector
Nuclear and Particle Physics Proceedings 00 (07) 6 Nuclear and Particle Physics Proceedings Measurement of photon production cross sections also in association with jets with the detector Sebastien Prince
More informationA complete NLO calculation of the J/ψ production at Tevatron and LHC In collaboration with Wang Kai and Chao Kuang-Ta
A complete NLO calculation of the J/ψ production at Tevatron and LHC Ma Yan-Qing ( 马滟青 ) Department of physics, Peking University yqma.cn@gmail.com In collaboration with Wang Kai and Chao Kuang-Ta p.1
More informationTMDs at small-x: an Operator Treatment
TMDs at small-x: an Operator Treatment Yuri Kovchegov The Ohio State University work with Dan Pitonyak and Matt Sievert, arxiv:76.436 [nucl-th] and 5 other papers + papers in preparation Outline Goal:
More informationIntroduction to Jets. Hsiang nan Li ( 李湘楠 ) Academia Sinica, Taipei. July. 11, 2014
Introduction to Jets Hsiang nan Li ( 李湘楠 ) Academia Sinica, Taipei at CTEQ School, Beijing July. 11, 2014 1 Outlines Introduction e+e annihilation and jets Jets in experiment Jets in theory Summary 2 Introduction
More informationIntroduction to Quantum Chromodynamics (QCD)
Introduction to Quantum Chromodynamics (QCD) Jianwei Qiu Theory Center, Jefferson Lab May 29 June 15, 2018 Lecture One The plan for my four lectures q The Goal: To understand the strong interaction dynamics
More informationUniversality of Perturbative QCD Soft Radiation in ee, ep andjanuary pp Collisions 13, / 2
Universality of Perturbative QCD Soft Radiation in ee,ep and pp Collisions Ou Zhang University of Arizona, IPN-Orsay Collabration with Christopher Lee and Deakyoung Kang, Los Alamos National Lab, U.S.A.
More informationIntroduction to Quantum ChromoDynamics and the parton model
Introduction to Quantum ChromoDynamics and the parton model Pavel Nadolsky Southern Methodist University Dallas, TX, USA TMD Collaboration Summer School June 22, 2017 Objectives of the lectures Review
More informationJuly 8, 2015, Pittsburgh. Jets. Zoltan Nagy DESY
July 8, 2015, Pittsburgh Jets Zoltan Nagy DESY What are Jets? A di-jet ATLAS event A multi-jet (6-jet) event What are Jets? What are Jets? The pt is concentrated in a few narrow sprays of particles These
More informationElementary Particle Physics
Yorikiyo Nagashima Elementary Particle Physics Volume 2: Foundations of the Standard Model WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA Contents Preface XI Acknowledgments XV Color Plates XVII Part One
More informationSingle inclusive jet production at very forward rapidity in proton-proton collisions with s = 7 and 13 TeV
production at very forward rapidity in proton-proton collisions with s = 7 and ev Instytut izyki Jadrowej, Radzikowskiego, - Krakow, Poland E-mail: krzysztof.kutak@ifj.edu.pl Hans Van Haevermaet Particle
More informationFactorisation in diffractive ep interactions. Alice Valkárová Charles University, Prague
Factorisation in diffractive ep interactions Alice Valkárová Charles University, Prague 8th International Workshop on Multiple Partonic Interactions at the LHC, San Cristóbal de las Casas, 2016 HERA collider
More informationImproving the kinematics in BK/BFKL to resum the dominant part of higher orders
Improving the kinematics in BK/BFKL to resum the dominant part of higher orders Guillaume Beuf Brookhaven National Laboratory QCD Evolution Workshop: from collinear to non collinear case Jefferson Lab,
More informationTMDs in covariant approach
TMDs in covariant approach Petr Zavada Institute of Physics AS CR, Prague, Czech Rep. (based on collaboration and discussions with A.Efremov, P.Schweitzer and O.Teryaev) Newport News, VA, May, 16-19, 2016
More informationMeasurements of unpolarized azimuthal asymmetries. in SIDIS at COMPASS
Measurements of unpolarized azimuthal asymmetries in SIDIS at COMPASS Trieste University and INFN on behalf of the COMPASS Collaboration Measurements of unpolarized azimuthal asymmetries in SIDIS at COMPASS
More informationThe three colors of nature
The three colors of nature This talk will be about the strong force and the three colors of nature Motivation: QCD is the strongest force If there would be infinitely many colors calculations would be
More informationarxiv: v1 [hep-ph] 15 May 2014
arxiv:1405.4017v1 [hep-ph] 15 May 2014 Evolution anynamics of cusped light-like Wilson loops University of Antwerp E-mail: frederik.vanderveken@ua.ac.be We address a connection between the energy evolution
More informationTMD Fragmentation Function at NNLO
TMD Fragmentation Function at NNLO Institut für Theoretische Physik, Universität Regensburg, D-9040 Regensburg, Germany E-mail: vladimirov.aleksey@gmail.com The calculation of the unpolarized non-singlet
More informationExperimental Aspects of Deep-Inelastic Scattering. Kinematics, Techniques and Detectors
1 Experimental Aspects of Deep-Inelastic Scattering Kinematics, Techniques and Detectors 2 Outline DIS Structure Function Measurements DIS Kinematics DIS Collider Detectors DIS process description Dirac
More informationCoulomb gluons and colour evolution
Coulomb gluons and colour evolution René Ángeles-Martínez in collaboration with Jeff Forshaw Mike Seymour JHEP 1512 (2015) 091 & arxiv:1602.00623 (accepted for publication) DPyC, BUAP 2016 In this talk:
More informationCoulomb gluons and colour evolution
Coulomb gluons and colour evolution René Ángeles-Martínez in collaboration with Jeff Forshaw Mike Seymour JHEP 1512 (2015) 091 & arxiv:1602.00623 (accepted for publication) 1 DPyC, BUAP 2016 In this talk:
More informationSpin physics at Electron-Ion Collider
Spin physics at Electron-Ion Collider Jianwei Qiu Brookhaven National Laboratory Workshop on The Science Case for an EIC November 16-19, 2010; INT, University of Washington, Seattle, WA Outline of my talk
More informationOne-loop amplitudes with off-shell gluons
Institute of Nuclear Physics Polish Academy of Sciences, PL-31342 Kraków, Poland E-mail: hameren@ifj.edu.pl I report on recent progress in the calculation of cross sections within factorization prescriptions
More informationUnitarity, Dispersion Relations, Cutkosky s Cutting Rules
Unitarity, Dispersion Relations, Cutkosky s Cutting Rules 04.06.0 For more information about unitarity, dispersion relations, and Cutkosky s cutting rules, consult Peskin& Schröder, or rather Le Bellac.
More informationBessel Weighted Asymmetries Alexei Prokudin
Bessel Weighted Asymmetries May 29, 2015 Unified View of Nucleon Structure Wigner WignerDistribution Distribution 5D Transverse Momentum Distributions Generalized Parton Distributions 3D GPDs DVCS TMDs
More informationJAMboree. Theory Center Jamboree Jefferson Lab, Dec 13, Pedro Jimenez Delgado
JAMboree Theory Center Jamboree Jefferson Lab, Dec 13, 2013 Introduction Hadrons composed of quarks and gluons scattering off partons Parton distribution functions Plausible at high energies (from GeV):
More informationTwo Photon Exchange in Inclusive and Semi Inclusive DIS
Two Photon Exchange in Inclusive and Semi Inclusive DIS Marc Schlegel Theory Center, Jefferson Lab In collaboration with Christian Weiss, Andrei Afanasev, Andreas Metz Two Photon Exchange in elastic scattering
More informationMatching collinear and small x factorization calculations for inclusive hadron production in pa collisions
Matching collinear and small x factorization calculations for inclusive hadron production in pa collisions The Pennsylvania State University, Physics Department, University Park, PA 16802 H. Niewodniczański
More informationHigh Energy Transverse Single-Spin Asymmetry Past, Present and Future
High Energy Transverse Single-Spin Asymmetry Past, Present and Future Jianwei Qiu Brookhaven National Laboratory Stony Brook University Transverse single-spin asymmetry (TSSA) q Consistently observed for
More informationPoS(Confinement X)133
Endpoint Logarithms in e + e J/ψ + η c Geoffrey T. Bodwin HEP Division, Argonne National Laboratory E-mail: gtb@hep.anl.gov Department of Physics, Korea University E-mail: neville@korea.ac.kr Jungil Lee
More informationNon-perturbative momentum dependence of the coupling constant and hadronic models
Non-perturbative momentum dependence of the coupling constant and hadronic models Pre-DIS Wokshop QCD Evolution Workshop: from collinear to non collinear case April 8-9, 2011 JLab Aurore Courtoy INFN-Pavia
More informationMeasuring the gluon Sivers function at a future Electron-Ion Collider
Measuring the gluon Sivers function at a future Electron-Ion Collider Speaker: Liang Zheng Central China Normal University In collaboration with: E.C. Aschenauer (BNL) J.H.Lee (BNL) Bo-wen Xiao (CCNU)
More informationPARTON OAM: EXPERIMENTAL LEADS
PARTON OAM: EXPERIMENTAL LEADS 7 TH GHP WORKSHOP FEBRUARY 1-3, 2017 WASHINGTON, DC Simonetta Liuti University of Virginia 2/1/17 2 and A. Rajan et al., soon to be posted 2/1/17 3 Outline 1. Definitions
More informationInternal structure of the pion inspired by the AdS/QCD correspondence
Internal structure of the pion inspired by the AdS/QCD correspondence Sabrina Cotogno Vrije Universiteit and Nikhef, Amsterdam Supervisor: Prof. P.J.G. Mulders In collaboration with Prof. Alessandro Bacchetta
More informationTMDs and the Drell-Yan process
TMDs and the Drell-Yan process Marc Schlegel Theory Center Jefferson Lab Jefferson Lab upgrade at 12 GeV, INT Kinematics (less intuitive than DIS): The Drell Yan process d¾ d 4 l d 4 l 0 = d¾ d 4 q d 4
More informationIntroduction to perturbative QCD and factorization
Introduction to perturbative QCD and factorization Part 1 M. Diehl Deutsches Elektronen-Synchroton DESY Ecole Joliot Curie 2018 DESY Plan of lectures 0. Brief introduction 1. Renormalisation, running coupling,
More informationQuasi-PDFs and Pseudo-PDFs
s and s A.V. Radyushkin Physics Department, Old Dominion University & Theory Center, Jefferson Lab 2017 May 23, 2017 Densities and Experimentally, one works with hadrons Theoretically, we work with quarks
More informationResearch in QCD factorization
Research in QCD factorization Bowen Wang Southern Methodist University (Dallas TX) Jefferson Lab Newport News VA 1/1/015 My research at SMU in 011-015 Ph. D. advisor: Pavel Nadolsky Ph. D. thesis: The
More informationThe Strong Interaction and LHC phenomenology
The Strong Interaction and LHC phenomenology Juan Rojo STFC Rutherford Fellow University of Oxford Theoretical Physics Graduate School course Lecture 2: The QCD Lagrangian, Symmetries and Feynman Rules
More informationLattice QCD investigations of quark transverse momentum in hadrons. Michael Engelhardt New Mexico State University
Lattice QCD investigations of quark transverse momentum in hadrons Michael Engelhardt New Mexico State University In collaboration with: B. Musch, P. Hägler, J. Negele, A. Schäfer J. R. Green, S. Meinel,
More informationZhong-Bo Kang Los Alamos National Laboratory
Introduction to pqcd and Jets: lecture 3 Zhong-Bo Kang Los Alamos National Laboratory Jet Collaboration Summer School University of California, Davis July 19 21, 2014 Selected references on QCD QCD and
More informationTMDs at Electron Ion Collider Alexei Prokudin
TMDs at Electron Ion Collider Alexei Prokudin 2 3 Why Electron Ion Collider? Eur. Phys. J. A (2016) 52: 268 DOI 10.1140/epja/i2016-16268-9 THE EUROPEAN PHYSICAL JOURNAL A Review Electron-Ion Collider:
More informationQCD at the LHC Joey Huston Michigan State University
QCD at the LHC Joey Huston Michigan State University Some references CHS over 1500 downloads so far arxiv:07122447 Dec 14, 2007 goal is to provide a reasonably global picture of LHC calculations (with
More informationStandard Model of Particle Physics SS 2012
Lecture: Standard Model of Particle Physics Heidelberg SS 2012 W- and Z-Bosons 1 2 Contents Discovery of real W- and Z-bosons Intermezzo: QCD at Hadron Colliders LEP + Detectors W- and Z- Physics at LEP
More informationPoS(LHC07)034. Dijet correlations in pp collisions at RHIC
Institute of Nuclear Physics, PL-31-342 Cracow, Poland and University of Rzeszów, PL-35-959 Rzeszów, Poland E-mail: Antoni.Szczurek@ifj.edu.pl Anna Rybarska Institute of Nuclear Physics, PL-31-342 Cracow,
More informationTransverse Momentum Dependent distributions:theory...phenomenology, future
Transverse Momentum Dependent distributions:theory...phenomenology, future Umberto D Alesio Physics Department and INFN University of Cagliari, Italy QCD-N6, 2 nd Workshop on the QCD structure of the nucleon
More information