Perturbative QCD Kyle Lee Stony Brook University GRADTALK - PowerPoint PPT Presentation

Perturbative QCD Kyle Lee Stony Brook University GRADTALK 10/21/19 1

Introduction Physics at different scales 2

Introduction QCD and scales Jets Hadrons • QCD is complex theory that gives interesting structures due to its scale 
 dependent interactions • Physics at different energy scales are expected to decouple. 3

Introduction QCD and scales Jets Hadrons • Asymptotic freedom “only” allows us to compute interactions of quarks and gluons 
 at short-distance (partonic cross-sections). 
 • Detectors are long-distance away. Experiments can only see hadrons and not free partons. 4

Introduction IR safety and factorization IR-safe observables: • Observables which are independent of long-distance physics. 
 Asymptotic freedom is enough to guarantee a full theoretical (perturbative) calculation. e + e − → hadrons • One of the simplest observable: Hadrons 5

Introduction IR safety and factorization IR-safe observables: • Observables which are independent of long-distance physics. 
 Asymptotic freedom is enough to guarantee a full theoretical (perturbative) calculation. e + e − → hadrons • One of the simplest observable: 1-loop example: individually divergent, but finite sum! Real Virtual 6

Introduction IR safety and factorization • Asking a long-distance sensitive question will give sensitivity to non-perturbative physics! e + e − → h + X i.e. Hadron h 7

Introduction IR safety and factorization • Factorization to the rescue! pp → h + X Factorization Evolution d σ pp → hX Hadron µ d X X f a ⊗ f b ⊗ H c ab ⊗ D h dµD h P ji ⊗ D h = i = c j dp T d η a,b,c j Non-perturbative but universal Perturbatively computable Kang, Ringer, Vitev `16 8 8

Introduction IR safety and factorization • Factorization to the rescue! pp → h + X Factorization Evolution d σ pp → hX Hadron µ d X X f a ⊗ f b ⊗ H c ab ⊗ D h dµD h P ji ⊗ D h = i = c j dp T d η a,b,c j Non-perturbative but universal Perturbatively computable DGLAP evolution Kang, Ringer, Vitev `16 9 9

Introduction Hadron Structures Parton Distribution Functions (PDF) Electron-Ion Collider (EIC) • Many interesting hadron structures. • Important in testing idea of factorization. Answering questions related to hadron spin problem. 10

Introduction What are Jets? ✓ ◆ tan θ • Azimuthal angle and pseudorapidity φ η = − ln 2 11

Introduction What are Jets? ✓ ◆ tan θ • Azimuthal angle and pseudorapidity φ η = − ln 2 • We open the cylinder and plot observed particles’ and it’s angular distribution. P T 12

Introduction What are Jets? Dijet event ✓ ◆ tan θ • Azimuthal angle and pseudorapidity φ η = − ln 2 • We open the cylinder and plot observed particles’ and it’s angular distribution. P T • Jets = collimated spray of particles. 13

Introduction Why do we have jets? • Production of jet is consistent with the partonic picture of QCD. • High probability of collinear and soft splittings: with 
 p 2 1 = 0 , p 2 2 = 0 1 1 2 E 1 E 2 (1 − cos θ ) → ∞ when p 1 → 0 or or p 2 → 0 p 1 ∼ p 2 ( p 1 + p 2 ) 2 = (Of course, probability cannot be infinities. Should really think of it as degenerate states.) 14

Introduction Sterman-Weinberg Jets • Jet is another IR-safe observable! • IR safety tells us must be sufficiently inclusive to cancel IR divergences. Dijet events σ 2 → 2 = σ ( e + e − → q ¯ q ) + σ ( e + e − → q ¯ qg ) | δ , β ✓ ◆ 1 + α s C F = σ 0 ( − 16 ln δ ln β − 12 ln δ + c 0 ) 4 π • All energy must be inside narrow cones of half-angle 
 δ except for a small fraction of the center-of-mass energy Q. β / 2 E < β 2 Q δ 15


 
 
 
 
 
 Introduction No unique way to define a jet Cone-type algorithm Recombination-type algorithm 
 ( - type) k T 1.Begin with list of particles 2.Define metrics (a = -1, 0, 1 for , 
 k T Cambridge-Aachen(CA), anti- ) 
 k T ⇣ ⌘ p 2 a T i , p 2 a min T j [( η i − η j ) 2 + ( φ i − φ j ) 2 ] d ij = R 2 d i = p 2 a R T i d min = min { d ij , d i } 3.Merge particle i and j if . 
 d min = d ij Add i to list of jets if . d min = d i • Particles within some radius ‘R’ in 
 4.Back to 1 until only left with list of jets. - plane are defined as a jet. ( η , φ ) 16


 
 
 
 
 
 
 
 
 Introduction Jet substructures and characteristic scales Single prong observables 
 Hard p T • Jet angularities p T R Jet algorithm • Energy-energy correlations • Jet shape Energy profile p T r Multi-prong observables 
 m 2 • N-subjettiness J /p T Jet mass • D 2 z cut p T R Grooming IRC unsafe observables 
 • Hadron in jet . • Multiplicities . . • Jet charge Groomed observables Temperature T • All of the above • Observables characterizing 
 Hadronization Λ grooming (SD): z g , θ g = R g /R 17

Introduction “QCD is just a background” Statements that are often made to undermine the importance of studying QCD. Jets Hadrons QCD is inherently interesting - Gives rise to complicated structures like jets and hadrons 
 - Gives ways to really test our understanding of QFT, develop calculational methods. Even if one wants to attribute QCD as a mere “background” - Modern colliders rely on good understanding of QCD, and QCD background is complicated. 
 => allows us to develop methods to discover new physics. 18

Introduction QCD structures at the LHC • At the LHC, 60 - 70 % of ATLAS & CMS papers use jets in their analysis! • Complicated hadron structures 19

Introduction Some of my own works • Jet substructures - Jet angularity 1801.00790 - Jets at the EIC 1910.xxxxx - Groomed jet angularity / jet mass 1803.03645 and 1811.06983 - Groomed jet radius 1908.01783 - Background subtraction in jet substructures 1812.06977 etc… • Hadron structures -New process to measure hadron structure 1812.07549 -Higher “twist" hadron structures in heavy quarkonium production 19xx.xxxxx etc… 20

Introduction Some of my own works • Jet substructures - Jet angularity 1812.06977 } 1801.00790 - Jets at the EIC 1910.xxxxx - Groomed jet angularity / jet mass 1803.03645 and 1811.06983 - Groomed jet radius 1908.01783 -Hadron inside jet - Background subtraction in jet substructures 1906.07187 etc… • Hadron structures -New process to measure hadron structure 1812.07549 -Higher “twist" hadron structures in heavy quarkonium production 19xx.xxxxx etc… 21

Introduction Some of my own works • Jet substructures - Jet angularity Maybe only talk about these things 1812.06977 } 1801.00790 - Jets at the EIC 1910.xxxxx - Groomed jet angularity / jet mass 1803.03645 and 1811.06983 - Groomed jet radius 1908.01783 -Hadron inside jet - Background subtraction in jet substructures 1906.07187 etc… • Hadron structures -New process to measure hadron structure 1812.07549 -Higher “twist" hadron structures in heavy quarkonium production 19xx.xxxxx etc… 22

Introduction Application of jet studies at the LHC • Precision probe of QCD • Constrain BSM Models Fat jet from BSM signal • Probe of quark gluon plasma 23

Hadron-hadron QCD factorization J c Inclusive jet production pp → jet + X d σ pp → jet X X f a ⊗ f b ⊗ H c ab ⊗ J c = dp T d η p T R a,b,c Λ QCD p T Also exclusive processes and pp → Z/ γ + jet + X Dasgupta, Dreyer, Salam, Soyez `15 Kaufmann, Mukherjee, Vogelsang `15 Kang, Ringer, Vitev `16 Dai, Kim, Leibovich `16 24

Hadron-hadron QCD factorization G c ( τ ) Inclusive jet production pp → jet + X d σ pp → jet X X f a ⊗ f b ⊗ H c ab ⊗ J c = dp T d η p T R a,b,c Λ QCD p T Jet substructure τ d σ pp → jet( τ ) X X f a ⊗ f b ⊗ H c = ab ⊗ G c ( τ ) dp T d η d τ Λ QCD p T R p T a,b,c and other scale(s) depending on τ 25

Jet Angularity Jet angularity • A generalized class of IR safe observables ( ), angularity (applied to jet): −∞ < a < 2 = 1 X τ pp p T,i ( ∆ R iJ ) 2 − a τ a a p T i ∈ J Sterman et al. `03, `08, 
 Hornig, C. Lee, Ovanesyan `09, Ellis, Vermilion, Walsh, Hornig, C.Lee `10, 
 Chien, Hornig, C. Lee `15, Hornig, Makris, Mehen `16, Kang, KL, Ringer `18 • Varying sensitivity to collinear radiations as the parameter is varied. a = 0 = m 2 2 a = 1 τ pp + O (( τ pp J J 0 ) 2 ) + 0 p 2 T T g (girth) = 1 X p T,i ( ∆ R iJ ) p T i ∈ J 26


 
 
 Jet Angularity Factorization for the jet angularity • Replace 
 J c ( z, p T R, µ ) → G c ( z, p T R, τ a , µ ) G c • When , refactorize . 
 τ a ⌧ R 2 − a τ a ⌧ R 2 − a • The ungroomed case ( ) X G i ( z, p T R, τ a , µ ) = H i → j ( z, p T R, µ ) C j ( τ a , p T , µ ) ⊗ S j ( τ a , p T , R, µ ) j p T τ a 1 2 − a p T R p T τ a R 1 − a 27 Kang, KL, Ringer, arXiv:1801.00790

Substructure Measurements Quark and gluon discrimination • We can study how well angularity discriminates between quark and gluon jet 
 as a continuous function of ‘a’. 28