Zhong-Bo Kang Los Alamos National Laboratory
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1 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
2 Selected references on QCD! QCD and Collider Physics: Ellis-Stirling-Webber! Foundations of Perturbative QCD: J. Collins! Applications of Perturbative QCD: R. Field! Quantum Chromodynamics: Greiner-Schramm-Stein! CTEQ collaboration: QCD Resource Letter: arxiv: by Kronfeld-Quigg! Particle Data Group: Jun 19, 014
3 We explore the structure of matter (normal and/or QGP)! The exploration on the structure of matter has a really long history! Dalton 1803 (atom)! Rutherford 1911 (nucleus)! Chadwic 193 (neutron)! Gell-Mann and Zweig 1964 (quar model)! Feynman 1969 (parton),... Our Universe strong interaction Jun 19, 014 3
4 Collider experiments to study hadron structure! How to study the hadron structure! send a high energy probe to collide with the hadron, loo for the outcome of the collisions! from these out-coming particles, using perturbative QCD, one could trace bac to see what s inside the hadron (E, p ) e (E, p) " * q N u u d h!!! Key: perturbative QCD and QCD factorization! + Jun 19, 014 4
5 QED: the fundamental theory of electro-magnetic interaction! QED Lagrangian:! Feynman rule: photon has no charge, thus does not self-interact Jun 19, 014 5
6 QCD: the fundamental theory of the strong interaction! As the fundamental theory, QCD describes the interaction between quars and gluons (not hadrons directly)! Feynman rules: gluon carries the color, thus can self-interact Jun 19, 014 6
7 Experimental verification about the color! The color does exist: color of quars Nc=3 (low energy R=/3.vs. ) R e + e = σ(e+ e q q) e + e µ + µ = N c q e q Jun 19, 014 7
8 Understanding QCD: the running coupling (Asymptotic freedom)! Rough qualitative picture: due to gluon carrying color charges! Value of the strong coupling!s depends on the distance (i.e., energy) Screening: α em (r) as r Anti-screening: α s (r) as r Jun 19, 014 8
9 Why does the coupling constant run?! Leading order calculation is simple: tree diagrams -- always finite! Study a higher order Feynman diagram: one-loop, the diagram is divergent as q " q! Mae sense of the result: redefine the coupling constant to be physical Jun 19, 014 9
10 Renormalization (Redefine the coupling constant)! Renormalization Jun 19,
11 Beta-function can be calculated perturbatively! Since scale µ is an artificial scale we introduced to regulate our calculation, the physical observable (cross section) should be independent of µ, thus study the divergence behavior of the cross section, we could derive how the coupling constant running with the energy scale! Leading order result Jun 19,
12 Simple study of Deep Inelastic Scattering: parton model! DIS has been used a lot in extracting hadron structure (E, p ) e (E, p) " * q N u u d h!!! Leptonic and hadronic tensor! + Jun 19, 014 1
13 Structure functions! Hadronic tensor: Lorentz decomposition+parity invariance (for photon case)+time-reversal invariance+gauge invariance! All the information about hadron structure is contained in the em F -log10 (x) 5 x=6.3e-5 x= x= x= x= x= x= x= ZEUS NLO QCD fit tot. error ZEUS 96/97 structure functions 4 x= x=0.001 x=0.003 BCDMS E665 NMC x=0.005 x= x=0.013 x=0.01 x=0.03 x=0.05 x=0.08 x= x=0.18 x=0.5 x=0.4 x=0.65 Jun 19, Q (GeV ) 13
14 Parton model picture! Photon interact with parton: deep inelastic scattering e+p e+x e e q ˆσ parton P xp parton X φ parton/hadron Parton Distribution Functions (PDFs): probability density for finding a parton in a hadron with longitudinal momentum fraction x σ Hadron (Q) =φ parton/hadron (Λ QCD ) ˆσ parton (Q) Universal (measured) calculable! Hadron structure: encoded in PDFs! QCD dynamics at short-distance: partonic cross section, perturbatively calculable Jun 19,
15 ering :! -' 0 d " ep #ex 4 $% e.m. y * y = 1& y + F (x,q ) & F (x,q ) / Parton distribution functions ), L 4 dxdq xq.( + 1 By measuring the structure functions (crosssections) in DIS, one violation: df/dlnq and Scaling could trace bac to find the parton distribution functions inside the linear DGLAP Evolution! proton by comparing the data with the theoretical formalism G(x,Q)! Gluons dominate low-x wave function xg (! 1 0 xu v ) xd v xs (! 1 Jun 19, ) 15
16 What about higher order?! pqcd calculations: understand and mae sense of all inds of divergences! Ultraviolet (UV) divergence : renormalization (redefine coupling constant)! Collinear divergence //P : redefine the PDFs and FFs! Soft divergence 0 : usually cancel between real and virtual diagram for collinear PDFs/FFs; do not cancel for t-dependent PDFs/FFs, leads to new evolution equations! If going beyond the leading order of the DIS, we face another divergence W µν = + q q! 1 q q! P P Jun 19,
17 QCD dynamics beyond tree level! Going beyond leading order calculation A!? 1 B! P d 4 1 q i 1 +i q Collinear divergence!!! (from ) 1 0 i 1 i " 1 0 intermediate quar is on-shell 1 q t AB " gluon radiation taes place long before the photon-quar interaction a part of PDF q! P 1 =( + g ) =EE g (1 cos θ) Partonic diagram has both long- and short-distance physics Jun 19,
18 QCD factorization: beyond parton model! Systematic remove all the long-distance physics into PDFs Q 0 d 1 P 1 q C (0) φ (1) LO + evolution q! µ 1 q q! = + = 0 d 1 P q q! 1 0 Q µ d 1 µ 0 d 1 P P 1 q 1 q! C (1) φ (0) NLO + Q µ d 1 1 q q! 1 0 d P Jun 19,
19 Scale-dependence of PDFs! Logarithmic contributions into parton distributions q q! C(Q /µ ) P P φ(x, µ ) ! Going to even higher orders: QCD resummation of single logs... P 1 φ(x, µ ) = P α s ln µ Λ P α s ln µ Λ Jun 19,
20 DGLAP evolution = resummation of single logs! Evolution = Resum all the gluon radiation P P P 1 φ(x, µ ) = φ(x, µ ) - P ln µ φ i(x, µ ) = j DGLAP Equation = P Evolution ernel splitting function P ij ( x x ) φ j(x, µ ) P ! By solving the evolution equation, one resums all the single n logarithms of α s ln µ Λ Jun 19, 014 0
21 Parton distribution also depends on the scale of the probe! Increase the energy scale, one sees parton picture differently em F -log10 (x) 5 x=6.3e-5 x= x= x= x= x= x= x= ZEUS NLO QCD fit tot. error ZEUS 96/97 x= BCDMS Q 0 Q > Q 0 4 x=0.001 x=0.003 E665 NMC x=0.005 x= x=0.013 x=0.01 x=0.03 x=0.05 x=0.08 x= x=0.18 x=0.5 x=0.4 x= Q (GeV ) Jun 19, 014 1
22 Evolutions of parton distribution functions! Perturbative change: Q 0 Q > Q 0! Feynman diagrams for unpolarized PDF (non-singlet case): q(x, µ F ) ln µ F = α s π 1 x dξ ξ P qq (z) q(ξ, µ F ) 1 + z P qq (z) = C F + 3 δ(1 z) (1 z) + Jun 19, 014
23 Success of QCD factorization! Universality of PDFs: mapped in one process (say DIS), used in other process ( ) p+p!jet+x DIS em F -log10 (x) 5 x=6.3e-5 x= x= x= x= x= x= x= ZEUS NLO QCD fit tot. error ZEUS 96/97 x= BCDMS 4 x=0.001 x=0.003 E665 NMC x= x=0.008 x=0.013 x=0.01 x=0.03 x=0.05 x=0.08 x= x=0.18 x=0.5 x=0.4 x= Q (GeV ) Jun 19, 014 3
24 -' 0 d " ep #ex 4 $% e.m. y * y Deep Inelastic Scattering : = Success of QCD factorization /)1& y +, F (x,q ) & FL (x,q ) 4 dxdq xq.( + 1! Universality of PDFs: mapped in one process (say DIS), used in other and Scaling violation: df /dlnq process ( p+p!jet+x ) linear DGLAP Evolution! G(x,Q) DIS em F -log10(x) ZEUS x=6.3e-5 x= x= x= x= x= x= x= ZEUS NLO QCD fit tot. error ZEUS 96/97 x= BCDMS E665 x=0.001 NMC 4 x=0.003! x=0.005 Gluons dominate low-x wave function xu v x= xg (! 1 x=0.013 x= ) xd v x=0.03 x=0.05 xs (! 1 x= ) x=0.13 x= x=0.5 x=0.4 3 x= Jun 19, Q(GeV ) 5 3
25 Success of QCD factorization! Universality of PDFs: mapped in one process (say DIS), used in other process ( ) p+p!jet+x DIS RHIC 00 GeV em F -log10 (x) 5 x=6.3e-5 x= x= x= x= x= x= x= ZEUS NLO QCD fit tot. error ZEUS 96/97 x= BCDMS 4 x=0.001 x=0.003 E665 NMC x= x=0.008 x=0.013 x=0.01 x=0.03 x=0.05 x=0.08 x= x=0.18 x=0.5 x=0.4 x= Q (GeV ) Jun 19, 014 3
26 Success of QCD factorization! Universality of PDFs: mapped in one process (say DIS), used in other process ( ) p+p!jet+x DIS Tevatron 1.96 TeV em F -log10 (x) 5 x=6.3e-5 x= x= x= x= x= x= x= ZEUS NLO QCD fit tot. error ZEUS 96/97 x= BCDMS 4 x=0.001 x=0.003 E665 NMC x= x=0.008 x=0.013 x=0.01 x=0.03 x=0.05 x=0.08 x= x=0.18 x=0.5 x=0.4 x= Q (GeV ) Jun 19, 014 3
27 Success of QCD factorization! Universality of PDFs: mapped in one process (say DIS), used in other process ( ) p+p!jet+x DIS LHC 7 TeV em F -log10 (x) 5 x=6.3e-5 x= x= x= x= x= x= x= ZEUS NLO QCD fit tot. error ZEUS 96/97 x= BCDMS 4 x=0.001 x=0.003 E665 NMC x= x=0.008 x=0.013 x=0.01 x=0.03 x=0.05 x=0.08 x= x=0.18 x=0.5 x=0.4 x= Q (GeV ) Jun 19, 014 3
28 An explicit example: SIDIS (detailed note for your convenience)! Semi-inclusive deep inelastic scattering! Connection to high energy nuclear physics (heavy ion physics) Higher-twist approach to energy loss, Wang-Guo, PRL,000 Energy loss at HERMES, Wang-Wang, PRL, 00 Jun 19, 014 4
29 Summary! pqcd provides a way to extract information on hadron structure! Asymptotic freedom: allow one to calculate partonic cross sections! Parton distribution functions! Renormalization scale and factorization scale Jun 19, 014 5
30 Summary! pqcd provides a way to extract information on hadron structure! Asymptotic freedom: allow one to calculate partonic cross sections! Parton distribution functions! Renormalization scale and factorization scale Than you Jun 19, 014 5
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Zhong-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
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