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

Perturbative QCD

Kyle Lee Stony Brook University

1

GRADTALK 10/21/19

Introduction

2

Physics at different scales

Introduction

QCD and scales

3

• QCD is complex theory that gives interesting structures due to its scale 


dependent interactions Jets Hadrons

• Physics at different energy scales are expected to decouple.

Introduction

QCD and scales

4

• 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.

Jets Hadrons

Introduction

5

• One of the simplest observable:

Hadrons

• Observables which are independent of long-distance physics.


Asymptotic freedom is enough to guarantee a full theoretical (perturbative) calculation.

IR safety and factorization

IR-safe observables:

e+e− → hadrons

Introduction

6

• One of the simplest observable:
• Observables which are independent of long-distance physics.


Asymptotic freedom is enough to guarantee a full theoretical (perturbative) calculation. 1-loop example: Virtual Real individually divergent, but finite sum!

IR safety and factorization

IR-safe observables:

e+e− → hadrons

Introduction

7

• Asking a long-distance sensitive question will give sensitivity to non-perturbative physics!

Hadron h

IR safety and factorization

e+e− → h + X

i.e.

Introduction

8 dσpp→hX dpT dη = X

a,b,c

fa ⊗ fb ⊗ Hc

ab ⊗ Dh c

µ d dµDh

i =

X

j

Pji ⊗ Dh

j

Evolution Factorization Hadron

Kang, Ringer, Vitev `16 8

Perturbatively computable Non-perturbative but universal

IR safety and factorization

• Factorization to the rescue!

pp → h + X

Introduction

9 dσpp→hX dpT dη = X

a,b,c

fa ⊗ fb ⊗ Hc

ab ⊗ Dh c

µ d dµDh

i =

X

j

Pji ⊗ Dh

j

Evolution Factorization Hadron

Kang, Ringer, Vitev `16 9

Perturbatively computable

IR safety and factorization

• Factorization to the rescue!

DGLAP evolution

pp → h + X

Non-perturbative but universal

Introduction

Hadron Structures

10

• Many interesting hadron structures.
• Important in testing idea of factorization. Answering questions related to hadron spin problem.

Electron-Ion Collider (EIC) Parton Distribution Functions (PDF)

Introduction

What are Jets?

11

• Azimuthal angle and pseudorapidity

η = − ln ✓ tan θ 2 ◆

φ

Introduction

What are Jets?

12

• Azimuthal angle and pseudorapidity

η = − ln ✓ tan θ 2 ◆

φ

• We open the cylinder and plot observed particles’ and it’s angular distribution.

PT

Introduction

What are Jets?

13

• We open the cylinder and plot observed particles’ and it’s angular distribution.
• Azimuthal angle and pseudorapidity

η = − ln ✓ tan θ 2 ◆

φ

PT

• Jets = collimated spray of particles.

Dijet event

Introduction

Why do we have jets?

14

• Production of jet is consistent with the partonic picture of QCD.
• High probability of collinear and soft splittings: with


p2

1 = 0, p2 2 = 0

1 (p1 + p2)2 = 1 2E1E2(1 − cos θ) → ∞ when p1 → 0

p2 → 0

• r
• r

p1 ∼ p2

(Of course, probability cannot be infinities. Should really think of it as degenerate states.)

Introduction

Sterman-Weinberg Jets

15

Dijet events

σ2→2 = σ(e+e− → q¯ q) + σ(e+e− → q¯ qg)|δ,β = σ0 ✓ 1 + αsCF 4π (−16 ln δ ln β − 12 ln δ + c0) ◆

• IR safety tells us must be sufficiently inclusive to cancel IR divergences.
• All energy must be inside narrow cones of half-angle 


except for a small fraction of the center-of-mass energy Q.

δ

β/2

δ

E < β 2 Q

• Jet is another IR-safe observable!

Introduction

No unique way to define a jet

16

Cone-type algorithm Recombination-type algorithm
 ( - type)

kT

R

• Particles within some radius ‘R’ in 

• plane are defined as a jet.

(η, φ)

1.Begin with list of particles 2.Define metrics (a = -1, 0, 1 for ,
 Cambridge-Aachen(CA), anti- )
 
 
 
 
 
 
 3.Merge particle i and j if . 
 Add i to list of jets if . 4.Back to 1 until only left with list of jets.

kT kT

dij = min ⇣ p2a

Ti, p2a Tj

⌘ R2 [(ηi − ηj)2 + (φi − φj)2] di = p2a

Ti

dmin = min{dij, di}

dmin = dij

dmin = di

Introduction

Jet substructures and characteristic scales

17

Single prong observables
 
 
 
 
 Multi-prong observables
 
 
 IRC unsafe observables
 
 
 
 Groomed observables

• Jet angularities
• Energy-energy correlations
• Jet shape
• N-subjettiness
• D2
• Hadron in jet
• Multiplicities
• Jet charge
• All of the above
• Observables characterizing 


grooming (SD): zg,

θg = Rg/R

pT pT R pT r m2

J/pT

zcutpT R Λ T

. . .

Hard Jet algorithm Energy profile Jet mass Grooming Temperature Hadronization

Introduction

“QCD is just a background”

18

Statements that are often made to undermine the importance of studying QCD. 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.

Jets Hadrons

• Modern colliders rely on good understanding of QCD, and QCD background is complicated.


=> allows us to develop methods to discover new physics. Even if one wants to attribute QCD as a mere “background”

Introduction

19

• At the LHC, 60 - 70 % of ATLAS & CMS

papers use jets in their analysis!

QCD structures at the LHC

• Complicated hadron structures

Introduction

Some of my own works

20

• Jet substructures
• Hadron structures
• Higher “twist" hadron structures in heavy quarkonium production
• Jet angularity
• Groomed jet angularity / jet mass
• Groomed jet radius
• New process to measure hadron structure
• Jets at the EIC

etc… 1801.00790 1910.xxxxx 1803.03645 and 1811.06983 1908.01783 1812.07549 19xx.xxxxx

• Background subtraction in jet substructures

1812.06977 etc…

Introduction

Some of my own works

21

• Jet substructures
• Hadron structures
• Higher “twist" hadron structures in heavy quarkonium production
• Jet angularity
• Groomed jet angularity / jet mass
• Groomed jet radius
• New process to measure hadron structure
• Jets at the EIC

etc… 1801.00790 1910.xxxxx 1803.03645 and 1811.06983 1908.01783 1812.07549 19xx.xxxxx

• Background subtraction in jet substructures

1812.06977 }

• Hadron inside jet

1906.07187 etc…

Introduction

Some of my own works

22

• Jet substructures
• Hadron structures
• Higher “twist" hadron structures in heavy quarkonium production
• Jet angularity
• Groomed jet angularity / jet mass
• Groomed jet radius
• New process to measure hadron structure
• Jets at the EIC

etc… 1801.00790 1910.xxxxx 1803.03645 and 1811.06983 1908.01783 1812.07549 19xx.xxxxx

• Background subtraction in jet substructures

1812.06977 }

• Hadron inside jet

1906.07187 etc… Maybe only talk about these things

Introduction

Application of jet studies at the LHC

23

• Precision probe of QCD
• Constrain BSM Models
• Probe of quark gluon plasma

Fat jet from BSM signal

Hadron-hadron

QCD factorization

24

dσpp→jetX dpT dη = X

a,b,c

fa ⊗ fb ⊗ Hc

ab ⊗ Jc

Jc

ΛQCD

pT pT R

Inclusive jet production pp → jet + X

Dasgupta, Dreyer, Salam, Soyez `15 Kaufmann, Mukherjee, Vogelsang `15 Kang, Ringer, Vitev `16 Dai, Kim, Leibovich `16

Also exclusive processes and pp → Z/γ + jet + X

Hadron-hadron

QCD factorization

25

Inclusive jet production pp → jet + X

dσpp→jetX dpT dη = X

a,b,c

fa ⊗ fb ⊗ Hc

ab ⊗ Jc

Gc(τ)

dσpp→jet(τ)X dpT dη = X

a,b,c

fa ⊗ fb ⊗ Hc

ab ⊗ Gc(τ)

Jet substructure τ

ΛQCD

pT pT R

ΛQCD

pT pT R

and other scale(s) depending on τ

dτ

Jet Angularity

Jet angularity

26

τa

• A generalized class of IR safe observables ( ), angularity (applied to jet):

τ pp

a

= 1 pT X

i∈J

pT,i(∆RiJ)2−a

τ pp = m2

J

p2

T

+

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

−∞ < a < 2

• Varying sensitivity to collinear radiations as the parameter is varied.

g(girth) = 1 pT X

i∈J

pT,i (∆RiJ)

a = 1

a = 0

2 J T

+ O((τ pp

0 )2)

Jet Angularity

27

Factorization for the jet angularity

• Replace 

• When , refactorize . 


Jc(z, pT R, µ) → Gc(z, pT R, τa, µ)

Gc

Kang, KL, Ringer, arXiv:1801.00790

τa ⌧ R2−a

• The ungroomed case ( )

τa ⌧ R2−a

Gi(z, pT R, τa, µ) = X

j

Hi→j(z, pT R, µ)Cj(τa, pT , µ) ⊗ Sj(τa, pT , R, µ)

pT R

pT τ

1 2−a

a

pT τa R1−a

Substructure Measurements

Quark and gluon discrimination

28

• We can study how well angularity discriminates between quark and gluon jet 


as a continuous function of ‘a’.

Substructure Measurements

Quark and gluon discrimination

29

0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 Gluon Background Rejection Quark Signal Efficiency ROC curve

a = 0.8 a = 0.5 a = 0 a = −0.5

20 40 60 80 100 120 0.002 0.004 0.006 0.008 0.01 0.012 0.014

a = 0, R = 0.4, √s = 7 TeV 200 GeV < pT < 250 GeV, |η| < 1.2

F(τa; η, pT , R) τa

q g q + g

• We can study how well angularity discriminates between quark and gluon jet 


as a continuous function of ‘a’.

• As 'a’ increases, better discrimination but more sensitive to non-perturbative effects.

Non-perturbative Effects

Non-perturbative Effects

30

• Non-perturbative effects:

Figs from P . Bartalini et al. `11 soft soft

• Multi-Parton Interactions (MPI)

(Underlying Events (UE)) Multiple secondary scatterings of partons within the protons may enter and contaminate jet.

Non-perturbative Effects

31

• Non-perturbative effects:

soft soft soft soft Figs from P . Bartalini et al. `11

• Pileups

Secondary proton collisions in a bunch may enter and contaminate jet.

• Multi-Parton Interactions (MPI)

(Underlying Events (UE)) Multiple secondary scatterings of partons within the protons may enter and contaminate jet.

Non-perturbative Effects

Non-perturbative Effects

• Non-perturbative effects:

Hadrons

• Hadronization

Partons forming the jet eventually hadronizes.

32

Non-perturbative Effects

Non-perturbative Effects

Appearance of the NGLs

33

Inclusive

Dasgupta, Salam `01 Banfi, Marchesini, Smye `02 Larkoski, Moult, Neill `15 Becher, Neubert, Rothen, Shao `15, `16 …

• Non-global logarithms (NGLs):


arises from the correlation between 
 the in-jet and the out-of-jet radiation.

θs ∼ R

Dasgupta, Salam `01

θH ∼ R

αn

s lnn(τa/R2−a)

Jet Angularity

34

Large non-perturbative effects:

dσ dpT dηdτa = dσpert dpT dηdτa ⊗ FNP

µS ∼ pT τa R1−a

0.00 0.05 0.10 0.15 0.20 0.25 0.30 5 10 15 20 25

0.005 0.01 0.015 0.02 0.025 50 100 150 20

400 < pT < 500 GeV

5

1 σ dσ dmJ

mJ (GeV)

200

Non-perturbative Effects

Non-perturbative Effects

35

• Single parameter NP shape function :
• Both hadronization and MPI effects in jet angularity is well-represented by 


shifting first-moments.

Lee, Sterman `07, Stewart, Tackmann, Waalewijn `15

Fκ(k) = ✓ 4k Ω2

κ

◆ exp ✓ − 2k Ωκ ◆

dσ dηdpT dτ = Z dkFκ(k) dσpert dηdpT dτ ✓ τ − R pT k ◆

• Ωκ =

Z dk k F(k)

Ωκ = Ωhad

κ

+ ΩMPI

κ

is universal up to calculable coefficient.

Ωhad

κ

= Ωhad,(0)

κ

+ Ωhad,(2)

κ

R2 + · · ·

Stewart, Tackmann, Waalewijn `15

Non-perturbative Model

Ωhad,(0)

κ

= 1 1 ah0|O|0i ⇠ 1 1 aΛQCD

Soft Drop Grooming

Soft Drop Grooming

36

• Soft drop grooming algorithms:
• 1. Reorder emissions in the identified jet according to their 


relative angle using C/A jet algorithm.


• 2. Recursively remove soft branches until soft drop condition is met:

Larkoski, Marzani, Soyez, Thaler `14 Frye, Larkoski, Schwartz, Yan `16 z

1 − z

min[pT,1, pT,2] pT,1 + pT,2 > zcut ✓∆R12 R ◆β

Groom jets to reduce sensitivity to the wide-angle soft radiation.

• Taming wide angle soft radiations, giving sensitivity to UE, PU, and NGLs directly changing

distribution.

Soft Drop Grooming

Factorization for the groomed jet angularity

37

θ/

∈gr ∼ R

• The groomed case ( )

τa,gr/R2−a ⌧ zcut ⌧ 1

• The ungroomed case ( )

τa ⌧ R2−a

θH ∼ R

Gi(z, pT R, τa, µ) = X

j

Hi→j(z, pT R, µ)Cj(τa, pT , µ) ⊗ Sj(τa, pT , R, µ)

Gi(z, pT R, τa, zcut, β, µ) = X

j

Hi→j(z, pT R, µ)S /

∈gr j

(pT , R, zcut, β, µ)Cj(τa, pT , µ) ⊗ S∈gr

j

(τa, pT , R, zcut, β, µ)

Kang, KL, Liu, Ringer `18

Jc → Gc

Soft Drop Grooming

Factorization for the groomed jet angularity

38

αn

s lnn(zcut)

n ≥ 2 n ≥ 2

• Non-global logs directly affect the jet angularity spectrum.
• Non-global logs only indirectly affects the


jet angularity spectrum through normalization.

θs ∼ R

θ/

∈gr ∼ R

• The groomed case ( )

τa,gr/R2−a ⌧ zcut ⌧ 1

• The ungroomed case ( )

τa ⌧ R2−a

θH ∼ R θH ∼ R

αn

s lnn(τa/R2−a)

Gi(z, pT R, τa, µ) = X

j

Hi→j(z, pT R, µ)Cj(τa, pT , µ) ⊗ Sj(τa, pT , R, µ)

Gi(z, pT R, τa, zcut, β, µ) = X

j

Hi→j(z, pT R, µ)S /

∈gr j

(pT , R, zcut, β, µ)Cj(τa, pT , µ) ⊗ S∈gr

j

(τa, pT , R, zcut, β, µ)

Kang, KL, Liu, Ringer `18

Jc → Gc

Grooming

Phenomenology (groomed jet mass)

39

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 −4 −3 −2 −1

√s = 13 TeV, anti-kT, R = 0.8 pT > 600 GeV, |η| < 1.5 soft drop, zcut = 0.1, β = 0

−4 −3 −2 −1

Groomed inclusive di-jet β = 1

−4 −3 −2 −1

β = 2 1 σresum dσ/d log10(m2 J,gr/p2 T)

log10(m2

J,gr/p2 T) NLL NLL + NP(Ω = 1) ATLAS

log10(m2

J,gr/p2 T)

log10(m2

J,gr/p2 T)

• Developed the formalism for single inclusive groomed jet mass cross-section.

• Shows very good agreement with the data.


Reduced contamination as expected.
 NP effects mostly from hadronization.

See also ATLAS, arXiv:1711.08341 Larkoski, Marzani, Soyez, Thaler `14 Frye, Larkoski, Schwartz, Yan `16

Ωk = 1 GeV =

⇒

• Kang, KL, Liu, Ringer `18

Soft Drop Grooming

40 0.2 0.4 0.6 0.8

√s = 13 TeV, anti-kT, R = 0.8 pT > 600 GeV, |η| < 1.5 soft drop, zcut = 0.1, β = 0 Single inclusive groomed jet β = 1, a = −0.5 β = 2

0.2 0.4 0.6 −8 −6 −4 −2

β = 0

−8 −6 −4 −2

β = 1, a = −1

−8 −6 −4 −2

β = 2 1 σincldσ/d log10(τa) NLL NLL + NP(Ωa = 1 GeV

1−a )

Pythia 1 σincldσ/d log10(τa)

log10(τa) log10(τa) log10(τa)

Phenomenology

Kang, KL, Liu, Ringer `18

• General angularities show decent agreement with Pythia 


with reduced contamination from UE/PU

Groomed Angularity

41

extraction

αs

• Complimentary study to extractions.

e+e−

• Most precise input: lattice determination
• World Average with 0.9% total uncertainty
• Most numerous input: event shape determination:


thrust and C-parameter. Using pp-extractions:

• High-quality of data pouring out of the LHC.

Les Houches 2017 I. Moult, B. Nachman, G. Soyez, J. Thaler (section coordinators)

• Currently feasible to determine with 10% uncertainty.

e+e−

3 − 4σ

• tension with lattice.

αs(mZ) = 0.1181 ± 0.0011

Groomed Angularity

42

extraction

αs

leading shift of the first moment shown to be universal

• Key challenges in extraction is the degeneracy with non-perturbative effects.

αs

Groomed Angularity

extraction

αs

• Extend range of validity by two orders for 1 TeV jet.

pT τ R

pT τ R ✓zcutR2 τ 2 ◆

1 2+β

Ungroomed:

µS ∼ µS ∼

SD Groomed: µS = ΛQCD ∼ 1 GeV with ,

τgr = τungr ✓ ΛQCD pT Rzcut ◆

1 1+β

• Reduced robustness to NP effects and increased sensitivity to αs
• Currently feasible to determine with 10% uncertainty.

Les Houches 2017 I. Moult, B. Nachman, G. Soyez, J. Thaler (section coordinators)

• Groomed angularities or energy-energy correlations provide 


additional independent handles with `a’. Onset of NP physics