Selected topics in High-energy QCD physics

Size: px

Start display at page:

Download "Selected topics in High-energy QCD physics"

Shavonne Pierce
5 years ago
Views:

1 1 Selected topics in High-energy QCD physics

2 Outline 2 Recent results in highenergy QCD physics q q q QCD - Theoretical Foundation QCD Features e e + Summary and Outlook

QCD Features 3 QCD - Features L QCD = ψ [iγ µ µ m] ψ g s ψγ µ G a µ λ a 2 ψ 1 4 Ga µνg µν a G a µν = µ G a ν ν G a µ g s f a bcg b µg c ν Interactions arise from fundamental symmetry principles:

3 QCD Features 3 QCD - Features L QCD = ψ [iγ µ µ m] ψ g s ψγ µ G a µ λ a 2 ψ 1 4 Ga µνg µν a G a µν = µ G a ν ν G a µ g s f a bcg b µg c ν Interactions arise from fundamental symmetry principles: SU(3) c Visible phenomena (e.g. proton) emerge through complex structure of the vacuum (e.g formation of Hadrons from quarks/gluons) Fundamental differences to QED: Self-interacting: highly nonlinear Interaction increases at large distances: Confinement Interaction decreases at small distances: Asymptotic freedom Strong coupling: α s >>α em Topological excitations QCD

4 QCD Features 4 QCD - Profound differences between hadrons and other many-body systems Atoms, molecules, nuclei,...: Constituents can be removed Exchanged boson generating interaction may be subsumed into static potential (e.g. photon into Coulomb potential) Most of mass from fermion constituents Nucleons: Quarks are confined Gluons are essential degrees of freedom Most of mass generated by interactions (~99%) Forcedominated matter matters Exploration of QCD: Analytical (e.g. perturbative) / non-perturbative (e.g. Lattice QCD - Numerical solution on space-time lattice) methods in comparison to experimental results

5 QCD Features 5 QCD - Perturbative Side Discovery of asymptotic freedom in the theory of strong interaction (Quantum Chromo Dynamics): Nobel prize in physics 24 α s α s large at large distances (low energy) α s small at small distances (high energy) TASSO Collaboration, R. Brandelik et al., Phys. Lett. B 86 (1979) 243.

QCD Features 6 QCD - Non-Perturbative Side Lattice QCD: Numerical solution of path integrals on space-time lattice Successful description of various hadron properties (e.g. mass spectrum in the context of lattice QCD calculations) For a large class of problems (e.

6 QCD Features 6 QCD - Non-Perturbative Side Lattice QCD: Numerical solution of path integrals on space-time lattice Successful description of various hadron properties (e.g. mass spectrum in the context of lattice QCD calculations) For a large class of problems (e.g. hadron formation from quarks), phenomenological methods and modeling are indispensable Y. Kuramashi, Lattice 27, PACS-CS Collaboration

7 QCD Features 7 QCD - Questions (The Frontiers of Nuclear Science - Long Range Plane 27) What is the internal landscape of the nucleons? What does QCD predict for the properties of strongly interacting matter? What governs the transition of quarks and gluons into hadrons? What is the role of gluons and gluon selfinteractions in nucleons and nuclei? What are the phases of strongly interacting matter? What determines the key features of QCD? Nuclear-Science.Low-Res.pdf

8 QCD Features 8 Exploring the proton structure and dynamics Lattice QCD GPDs Hadron Structure (JLAB 12 GeV, RHIC-Spin) Valence Sea ab initio QCD Calculations & Computational Development Physics of Strong Color Fields Condensed Matter Physics Bose-Einstein Condensate Spin Glasses Graphene QCD Theory Non-linearity, Confinement, AdS/QCD QCD EIC Saturation Models Color Glass Condensate QCD Background High Energy Physics (LHC, LHeC, Cosmic Rays) Understanding of Initial Conditions, Saturation, Energy Loss CP Violation? New Generation of Instrumentation Relativistic Heavy Ion Physics Fundamental Symmetries (RHIC, LHC & FAIR) Technology Frontier Examples: beam cooling, energy recovery linac, polarized electron source, superconducting RF cavities Structure and dynamics of proton (mass) ( visible universe) originates from QCD-interactions! What about spin as another fundamental quantum number? Synergy of experimental progress and theory (Lattice QCD / Phenomenology incl. phenomenological fits / Modeling) critical!

9 QCD Features 9 Mass in QCD Quote from Nobel prize lecture in physics, 24, given by Professor Frank Wilczek (MIT): Stated as m=e/c 2 : Possibility of explaining mass in terms of energy. Einstein s original paper does not contain the equation E=mc 2, but rather m=e/c 2 : Does the Inertia of a Body Depend Upon its Energy Content? (A. Einstein, Annalen der Physik, 18 (195) 639.) Modern QCD: Mass of ordinary matter derives almost entirely from energy - the energy of massless gluons and nearly massless quarks, which are the ingredients from which protons, neutrons, and atomic nuclei are made.

QCD Features 1 Spin in QCD Traditional way to introduce spin in QM textbooks: Stern-Gerlach experiment (1922) Concept of spin: Long and tedious battle to understand splitting patters and

10 QCD Features 1 Spin in QCD Traditional way to introduce spin in QM textbooks: Stern-Gerlach experiment (1922) Concept of spin: Long and tedious battle to understand splitting patters and separations in line spectra Anomalous magnetic moment of proton by Stern et al. (1933) Proposal of self-rotating electron by Goudsmit and Uhlenbeck (1925): Quark Model QCD QCD + Orbital motion

11 QCD - Theoretical foundation 11 How do we probe the structure and dynamics of matter in ep / pp scattering? e p x Q 2 e dσ ep F 2 = xe 2 qf q (x) q X Universality p p x 1 x 2 p T dσ pp f 1 f 2 σ h D h f Factorization W 2 Q 2 /x f(x) = f(x) = Momentum contribution + f + (x) + f (x) f + (x) f (x) contribution Spin

12 QCD - Theoretical foundation 12 Fundamental QCD ingredients e (k µ /) Asymptotic freedom: e (k µ ) α s at short distances: perturbative QCD γ (Q 2 ) σ h (x,q 2 ) α s large at long distances: non-perturbative QCD P (p µ ) xp f j (x,q 2 ) X (p µ /) Evolution: Factorization: hard scale Q 2, m c, m b σ ep = γ(x, Q 2 ) f j (x, Q 2 ) ˆσ(x, Q 2 ) non-perturbative part Beyond Quark-Parton model, Parton densities become functions of Q 2 Predict Q 2 dependence of parton distribution functions (DGLAP evolution equations)

13 QCD - Theoretical foundation 13 Evolution The presence of QCD related diagrams leads to a modification of F 2 + F 2 = νw 2 ν = p q m p F 2 (x, Q 2 ) x = i Q 2 i 1 ( dy y ) q(y) ( ( δ 1 x ) ( αs ) ( ) ) x + P qq log Q2 y 2π y µ 2 Logarithmic violation of scaling F 2 (x, Q 2 ) x q(y) f q (y) = i Quark densities depend on x and Q 2 : i Q 2 i Q 2 i 1 ( dy y Parton model ) (q(y)+ q(y, Q 2 ) ) ( δ 1 x ) y ( q(x)+ q(x, Q 2 ) ) q(x, Q 2 )= Gluon radiation = Splitting function ( αs ) ( ) Q 2 1 ( ) ( ) dy x log 2π µ 2 q(y)p qq x y y

14 QCD - Theoretical foundation 14 Evolution of parton distribution functions (1) Consider the change of the quark density Q 2 Q 2 Q 2 Δq(x,Q 2 ) over an interval of ΔlogQ 2 General including other types of splitting functions: d d log Q 2 q(x, Q2 )= ( αs ) 1 ( ) ( ) dy x q(y, Q 2 )P qq 2π y y Probability of finding a parton of type i with momentum fraction x which originated from parton j having momentum fraction y! Singlet distribution Σ(x, Q 2 )= n f [ qi (x, Q 2 ) + q i (x, Q 2 ) ] Gluon distribution g(x, Q 2 ) i=1 P ij ( x y )

15 QCD - Theoretical foundation Evolution of parton distribution functions (2) Types of splitting functions 15 q(x,q 2 ) g(x,q 2 ) q(x,q 2 ) g(x,q 2 ) Probability of finding a parton of type i with q(y,q 2 ) q(y,q 2 ) g(y,q 2 ) g(y,q 2 ) momentum fraction x which originated from P qq P gq P qg P gg p a r t o n j h a v i n g momentum fraction y! dσ(x, Q 2 ) d ln Q 2 = α s 2π 1 x dz z [ ( x ) ( x ) ] P qq Σ(z, Q 2 )+P qg g(z, Q 2 ) z z dg(x, Q 2 ) d ln Q 2 = α s 2π 1 x dz z [ ( x ) ( x ) ] P gq Σ(z, Q 2 )+P gg g(z, Q 2 ) z z DGLAP evolution equations: G. Altarelli and G. Parisi, Nucl. Phys. B 126 (1977) 298; V. Gribov and L.N. Lipatov, Soc. J. Nucl. Phys. 15 (1972) P ij ( x y ) 438; L.N. Lipatov, Soc. J. Nucl. Phys. 2 (1975) 96; Y.L. Dokshitzer, Soc. Phys. JETP 46 (1977) 641.

F (x) Minimize χ 2 QCD data in terms of F 2 and F 2 by adjusting parameters in xf i (x,q 2 ) Net result: QCD

16 QCD - Theoretical foundation 16 Global fits QCD Determine F 2 in terms of parton distribution functions QCD Evolve F 2 through parton distribution functions based on evolution equations xf i (x, Q 2 )=A i x λ i (1 x) η i F (x) Minimize χ 2 QCD data in terms of F 2 and F 2 by adjusting parameters in xf i (x,q 2 ) Net result: QCD prediction for xf i (x,q 2 ) and therefore F 2 (x,q 2 ) Various global pdf analysis: GRV CTEQ MRST Low x: λ i High x: η i

17 QCD - Theoretical foundation 17 Factorization f(x) = Unpolarized proton structure: + f + (x) + f (x) Three step process: Partons (quarks/gluons) in initial state: Long distance (non-perturbative QCD domain) Parton (quarks/gluons) distribution functions Hard interaction: Small distances (high energies) (perturbative QCD domain) Cross-section prediction (LO,NLO,NNLO) long-range short-range long-range σ pp πx = f 1,f 2 f 1 f 2 ˆσ D π f Quarks in final state: Long distance (non-perturbative QCD domain): Quarks fragment into observable hadrons described by fragmentation functions

18 Recent results in high-energy QCD physics 18 Overview Collider programs: Hadron-Hadron: Tevatron/ RHIC Electron-Hadron: HERA Electron/Positron: LEP q q QCD topics QCD factorization Parton-distribution functions / Fragmentation functions Strong-coupling constant Jet algorithms QCD matrix elements in LO, NLO, NNLO Multi-leg final states Low-x physics e e + Soft processes: Underlying event / Hadronization / Diffraction

3km Measurement of α s DESY Fragmentation functions Extraction of parton

19 Recent results in high-energy QCD physics 19 Experimental QCD tests in ep Circumference: 6.3km Measurement of α s DESY Fragmentation functions Extraction of parton distribution functions Color/spin dynamics E e = 27.5 GeV E p = 92 GeV Quark-Gluon jet properties Event shape variables (Sphericity, thrust, ) Diffraction

20 Recent results in high-energy QCD physics 2 Experimental QCD tests in ee Measurement of α s Fragmentation functions Color/spin dynamics Quark-Gluon jet properties CERN Event shape variables (Sphericity, thrust, ) LEP: Centre-of-mass energy (e + e - ) up to 25GeV

$(Sphericity, thrust, ) BNL Diffraction RHIC: Centre-of-mass energy 2-5GeV$

21 Recent results in high-energy QCD physics 21 Experimental QCD tests in pp Measurement of α s Fragmentation functions Extraction of parton distribution FNAL functions Color/spin dynamics Quark-Gluon jet properties Event shape variables (Sphericity, thrust, ) BNL Diffraction RHIC: Centre-of-mass energy 2-5GeV (polarized protons)

22 Recent results in high-energy QCD physics 22 Precision measurements (e.g. F 2 ) Precision on quark/gluon structure Strong violation e (k / ) of scaling at low x e (k µ ) and high Q 2 γ * (q µ ) xg ( df2 ) d ln Q 2 P (p µ ) X (p µ /) In contrast to: Evolution Low Q 2 high x!

$Large uncertainties for all distribution functions at large momentum fractions: Impact of W/Z program at LHC Impact of high-e T jet$

23 Recent results in high-energy QCD physics 23 Precision on quark/gluon structure Enormous precision reached over a wide kinematic region Large uncertainties for all distribution functions at large momentum fractions: Impact of W/Z program at LHC Impact of high-e T jet production

24 Recent results in high-energy QCD physics 24 Cross Section Results - RHIC (Hadrons) Good agreement between data and NLO calculations for neutral pion production at forward and central rapidity

25 Recent results in high-energy QCD physics 25 Cross Section Results - RHIC (Jets / Photons) Good agreement between data and NLO calculations for jet production and prompt photon production at central rapidity

26 Recent results in high-energy QCD physics 26 What do we know about the polarized quark and gluon distributions? Spin carried by quarks is very small (ΔΣ.4)! 1 2 Σ 1 2 = S q + S g + L q + L g G Σ = u + ū + d + d + s + s x!u x!d x(!u+!u ) DSSV x(!d+!d ) DNS KRE DNS KKP x!s x!u DSSV!" 2 =1 DSSV!" 2 =2% x!u v x!d v x!g x!d GRSV maxg GRSV ming x -2 x Bj x x Bj.4 x!g x!s 1-2 x Bj KRE (NLO).4 KKP (NLO) unpolarized KRE " 2 min +1.2 KRE " 2 min +2% u/d sea-quarks undetermined! Substantial improvement for.5<x<.2 Large uncertainties at low x q i (Q 2 ) = 1 q i (x, Q 2 )dx G(Q 2 ) = 1 g(x, Q 2 )dx D. de Florian et al., Phys. hep-ph/ Rev. D71, 9418 (25).

27 Recent results in high-energy QCD physics 27 Gluon polarization - Extraction G(Q 2 ) = 1 g(x, Q 2 )dx f 1 σ h a LL qg qg qq qq q q q q gg gg f Extract Δg(x,Q 2 ) through Global Fit (Higher Order QCD analysis)! long-range short-range long-range gg q q cosθ * A LL = d σ dσ f 1 f 2 f 1 f 2 σ h a LL D h f f 1 f 2 σ h D h f a LL = σ h σ h Input

Jet production (2GeV: Solid line / 5GeV: Dashed line).7.6.

28 Recent results in high-energy QCD physics 28 Gluon polarization - Inclusive Measurements Jet π + π g parton particle detector σ ij /σ tot σ ij /σ tot Δg Inclusive Jet production (2GeV: Solid line / 5GeV: Dashed line) <η<1 gg qg qq p T -1<η<1 gg qg qq Δq.4 q x T =2p T / s X T

29 Recent results in high-energy QCD physics 29 Gluon polarization - Correlation Measurements Correlation measurements provide access to partonic kinematics through Di-Jet/Hadron production and Photon-Jet production x 1 (2) = 1 s ( p T3 e η 3( η 3 ) + p T4 e η 4( η 4 ) ) p gg, qg, qq x 1 x 2 p T p Di-Jet production / Photon-Jet production Di-Jet production Di-Jets: All three (LO) QCD-type processes contribute: gg, qg and qq with relative contribution dependent on topological coverage Photon-Jet: One dominant underlying (LO) process with large partonic a LL at forward rapidity p x 1 p T Larger cross-section for di-jet production compared to photon qg related measurements Photon reconstruction more challenging than jet reconstruction p x 2 Full NLO framework exists Input to Global analysis Photon-Jet production

30 Recent results in high-energy QCD physics 3 x!g(x,q 2 ) ΔG frac Gluon polarization - Inclusive Measurements Q 2 = 1 GeV GRSV-STD!g =!g std GRSV-MAX!g = g GRSV-ZERO!g = GRSV-MIN!g = -g Q 2 =1GeV 2 Q 2 =1GeV 2 Q 2 =1GeV 2 G(Q 2 =1GeV 2 ) 1.8 G(Q 2 =1GeV 2 ) x Examine wide range in Δg: g < g < +g GRSV-STD: Higher order QCD analysis of polarized DIS experiments!.5 < x <.2 G(Q 2 ) = 1 A LL A LL -1<"<2 Inclusive # production GRSV-STD!g = g std -.2 GRSV-MAX!g = g max p T (GeV) <"<2 Inclusive jet production g(x, Q 2 )dx GRSV-MIN!g = -g max GRSV-ZERO!g = p T (GeV) A LL A LL -1<"<1 - Inclusive # + / # GRSV # GRSV # p T (GeV) <"<2 Inclusive $ production p T (GeV) x parton 2p T / s

31 Recent results in high-energy QCD physics 31 STAR Inclusive Jet production - RUN 6: A LL Gluon spin contribution -.7 < η <.9 frac G Q =1GeV /c a) p = 5.6 GeV/c T -2 1 x parton 2p T / s X gluon p =28 GeV/c T x dn / d(log x) RUN 6 results: GRSV-MAX / GRSV-MIN ruled out - A LL result favor a gluon polarization in the measured x-region which falls in-between GRSV-STD and GRSV-ZERO Consistent with RUN 5 result (Factor 3-4 improved statistical precision for p T >13GeV/c)

32 Recent results in high-energy QCD physics 32 41! Global analysis incl. RHIC pp data all data sets x-range: , [.5-.2 ] "g (a) PHENIX STAR SIDIS DIS , [.5-.2 ] "g Strong constraint on the size of Δg from RHIC data for.5<x<.2 Evidence for a small gluon polarization over a limited region of momentum fraction (b) 15 "! 2 i x"g GRSV max. "g GRSV min. "g Q =1GeV /c FIG. 2: Our polarized sea and.6.75 gluon a) densities compared to.4.5 previous fits [4, 6]. The shaded bands correspond to alternative fits with χ 2 = 1 and χ 2 p =.2 /χ GeV/c T.25 = 2% (see text). Important: Mapping of x-dependence and extension of x-coverage needed! frac G D. de Florian et al. PRL 11 (28) X gluon x p =28 GeV/c T x STAR Collaboration, PRL 1 (28) dn / d(log x)

Recent results in high-energy QCD physics 33 Run 9 STAR Beam-Use Request: Di-Jet projections Substantial improvement in from Di-Jet production: 5pb -1 and 6% beam

33 Recent results in high-energy QCD physics 33 Run 9 STAR Beam-Use Request: Di-Jet projections Substantial improvement in from Di-Jet production: 5pb -1 and 6% beam polarization Good agreement between LO MC evaluation and full NLO calculations M = x 1 x 2 s η 3 + η 4 = ln x 1 x 2 x 1 (2) = 1 s ( p T3 e η 3( η 3 ) + p T4 e η 4( η 4 ) )

$momentum fractions - Impact for LHC program Higher-order QCD calculations needed (Beyond NLO) for precision pdf extraction and α s$ Generally large uncertainties and model dependence on soft processes such as underlying event and hadronization Evidence for a small

Generally large uncertainties and model dependence on soft processes such as underlying event and hadronization Evidence for a small

34 Summary and Outlook 34 Summary Enormous precision reached for unpolarized distribution functions - Large uncertainties remain at larger momentum fractions - Impact for LHC program Higher-order QCD calculations needed (Beyond NLO) for precision pdf extraction and α s Generally large uncertainties and model dependence on soft processes such as underlying event and hadronization Evidence for a small gluon polarization Renaissance of constituent quark model! Outlook Electron-Ion Collider: Precision measurement of polarized ep and ea scattering

Topics on QCD and Spin Physics

Topics on QCD and Spin Physics (sixth lecture) Rodolfo Sassot Universidad de Buenos Aires HUGS 21, JLAB June 21 Spin (revisited)? naive quark spin parton spin QCD parton spin polarized DIS:? EMC experiment: