Zhong-Bo Kang - Jetjetsummer14.ucdavis.edu/lectures/kang_talk_1.pdfIntroduction to pQCD and Jets: lecture 1 Jet Collaboration Summer School University of California, Davis July 19–21,

Introduction to pQCD and Jets: lecture 1

Jet Collaboration Summer SchoolUniversity of California, DavisJuly 19–21, 2014

Zhong-Bo KangLos Alamos National Laboratory

Jun 19, 2014 Zhongbo Kang, LANL

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: http://www.phys.psu.edu/~cteq! QCD Resource Letter: arXiv:1002.5032 by Kronfeld-Quigg! Particle Data Group: http://pdg.lbl.gov

2

http://www.phys.psu.edu/~cteq

http://www.phys.psu.edu/~cteq

http://pdg.lbl.gov

http://pdg.lbl.gov


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)! Chadwick 1932 (neutron) ! Gell-Mann and Zweig 1964 (quark model)! Feynman 1969 (parton), ...

3

Our Universe

stronginteraction


Collider experiments to study hadron structure

! How to study the hadron structure! send a high energy probe to collide with the hadron, look for the outcome of

the collisions! from these out-coming particles, using perturbative QCD, one could trace back

to see what’s inside the hadron

! Key: perturbative QCD and QCD factorization

4

N

(E, p)

h!

!

q

e

+

(E, p )’ ’

!

u

du

*"


QED: the fundamental theory of electro-magnetic interaction

! QED Lagrangian:

! Feynman rule: photon has no charge, thus does not self-interact

5


QCD: the fundamental theory of the strong interaction

! As the fundamental theory, QCD describes the interaction between quarks and gluons (not hadrons directly)

! Feynman rules: gluon carries the color, thus can self-interact

6


Experimental verification about the color

! The color does exist: color of quarks Nc=3 (low energy R=2/3 .vs. 2)

7

Re+e− =σ(e+e− → qq̄)

e+e− → µ+µ− = Nc

�

q

e2q


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)

8

Screening: Anti-screening: αs(r) ↓ as r ↓αem(r) ↑ as r ↓


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→"

! Make sense of the result: redefine the coupling constant to be physical

9

q


Renormalization (Redefine the coupling constant)

! Renormalization

10


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

11

N

(E, p)

h!

!

q

e

+

(E, p )’ ’

!

u

du

*"


Simple study of Deep Inelastic Scattering: parton model

! DIS has been used a lot in extracting hadron structure

! Leptonic and hadronic tensor

12


Structure functions

! Hadronic tensor: Lorentz decomposition+parity invariance (for photon case)+time-reversal invariance+gauge invariance

! All the information about hadron

13

ZEUS

0

1

2

3

4

5

1 10 102

103

104

105

F2

em-l

og

10(x

)

Q2(GeV

2)

ZEUS NLO QCD fit

tot. error

ZEUS 96/97

BCDMS

E665

NMC

x=6.32E-5x=0.000102

x=0.000161x=0.000253

x=0.0004x=0.0005

x=0.000632x=0.0008

x=0.0013

x=0.0021

x=0.0032

x=0.005

x=0.008

x=0.013

x=0.021

x=0.032

x=0.05

x=0.08

x=0.13

x=0.18

x=0.25

x=0.4

x=0.65

structure is contained in the

structure functions

! Photon interact with parton: deep inelastic scattering e+p→e+X

! Hadron structure: encoded in PDFs! QCD dynamics at short-distance: partonic cross section, perturbatively

calculable


Parton model picture

14

Universal (measured) calculable

σHadron(Q) = φparton/Hadron(ΛQCD)⊗ σ̂parton(Q)

xP

ee

X

q

P

parton

σ̂parton

φparton/Hadron

Parton Distribution Functions (PDFs): probability density for finding a parton in a hadron with longitudinal momentum fraction x


Parton distribution functions

! By measuring the structure functions (cross sections) in DIS, one could trace back to find the parton distribution functions inside the proton by comparing the data with the theoretical formalism

15

3

What Do We Know About Glue in Matter?

• Scaling violation: dF2/dlnQ2 and

linear DGLAP Evolution !

G(x,Q2)!

Deep Inelastic Scattering : d

2" ep#eX

dxdQ2

=4$%e.m.

2

xQ4

1& y +y

2

2

'

( )

*

+ , F2(x,Q2) &

y2

2FL (x,Q2)

-

. /

0

1 2

Gluons dominate low-x wave function

)20

1( !xG

)20

1( !xS

vxu

vxd

!


What about higher order?

! pQCD calculations: understand and make sense of all kinds of divergences! Ultraviolet (UV) divergence : renormalization (redefine coupling

constant)! Collinear divergence : redefine the PDFs and FFs! Soft divergence : usually cancel between real and virtual diagram for

collinear PDFs/FFs; do not cancel for kt-dependent PDFs/FFs, leads to new evolution equations

! If going beyond the leading order of the DIS, we face another divergence

16

= +Wµν

q

k1

!

P

qk

P

q q

k

!

k → ∞

k → 0

k//P


QCD dynamics beyond tree level

! Going beyond leading order calculation

17

" intermediate quark is on-shell

" gluon radiation takes place long before the photon-quark interaction a part of PDF

tAB → ∞k21 ∼ 0

Partonic diagram has both long- and short-distance physics

⇒�

d4k1i

k21+i�

−i

k21−i�

⇒∞

?

Collinear divergence!!! (from )k21 ∼ 0

A

B

P

kq

1!

qk

q

k1

!

P

qk

!

k21 = (k + kg)2 = 2EEg(1− cos θ)


QCD factorization: beyond parton model

! Systematic remove all the long-distance physics into PDFs

18

LO + evolution

NLO

q

k1

!

P

qk

q

k1

!

P

qk

q

k1

!

P

qk

q q!

q1

!q

k

P

k

k1k

P

� ∼Q2

0dk2

1

� ∼Q2

µ2dk2

1

� µ2

0dk2

1

� µ2

0dk2

1

k21 ≈ 0

� ∼Q2

µ2dk2

1

� k21

0dk2

C(0)⊗φ(1)

C(1)⊗φ(0)

= +

=

+


Scale-dependence of PDFs

! Logarithmic contributions into parton distributions

! Going to even higher orders: QCD resummation of single logs

19

P

kk1

k

P

q q!

φ(x, µ2)C(Q2/µ2)

+ + ...

...

αs lnµ2

Λ2

�αs ln

µ2

Λ2

�2P

kk1

k

P

kP

= + + + ...φ(x, µ2)


DGLAP evolution = resummation of single logs

! Evolution = Resum all the gluon radiation

! By solving the evolution equation, one resums all the single logarithms of

20

P

kk1

k

P

kP

= + + + ...φ(x, µ2)

DGLAP Equation

P

k-P

kk1

k

P+ + ...=φ(x, µ2)

∂

∂ lnµ2φi(x, µ2) =

�

j

Pij(x

x� )⊗ φj(x�, µ2)

Evolution kernel splitting function

�αs ln

µ2

Λ2

�n


Parton distribution also depends on the scale of the probe

! Increase the energy scale, one sees parton picture differently

21

ZEUS

0

1

2

3

4

5

1 10 102

103

104

105

F2

em-l

og

10(x

)

Q2(GeV

2)

ZEUS NLO QCD fit

tot. error

ZEUS 96/97

BCDMS

E665

NMC

x=6.32E-5x=0.000102

x=0.000161x=0.000253

x=0.0004x=0.0005

x=0.000632x=0.0008

x=0.0013

x=0.0021

x=0.0032

x=0.005

x=0.008

x=0.013

x=0.021

x=0.032

x=0.05

x=0.08

x=0.13

x=0.18

x=0.25

x=0.4

x=0.65

Q20 Q2 > Q2

0


Evolutions of parton distribution functions

! Perturbative change:

! Feynman diagrams for unpolarized PDF (non-singlet case):

22

Q20 Q2 > Q2

0

q(x, µF )∂lnµ2

F

=αs

2π

� 1

x

dξ

ξ

�Pqq(z) q(ξ, µF )

�

Pqq(z) = CF

�1 + z2

(1− z)++

32δ(1− z)

�


Success of QCD factorization! Universality of PDFs: mapped in one process (say DIS), used in other

process ( )

23

ZEUS

0

1

2

3

4

5

1 10 102

103

104

105

F2

em-l

og

10(x

)

Q2(GeV

2)

ZEUS NLO QCD fit

tot. error

ZEUS 96/97

BCDMS

E665

NMC

x=6.32E-5x=0.000102

x=0.000161x=0.000253

x=0.0004x=0.0005

x=0.000632x=0.0008

x=0.0013

x=0.0021

x=0.0032

x=0.005

x=0.008

x=0.013

x=0.021

x=0.032

x=0.05

x=0.08

x=0.13

x=0.18

x=0.25

x=0.4

x=0.65

DISp+p!jet+X



process ( )

23

ZEUS

0

1

2

3

4

5

1 10 102

103

104

105

F2

em-l

og

10(x

)

Q2(GeV

2)

ZEUS NLO QCD fit

tot. error

ZEUS 96/97

BCDMS

E665

NMC

x=6.32E-5x=0.000102

x=0.000161x=0.000253

x=0.0004x=0.0005

x=0.000632x=0.0008

x=0.0013

x=0.0021

x=0.0032

x=0.005

x=0.008

x=0.013

x=0.021

x=0.032

x=0.05

x=0.08

x=0.13

x=0.18

x=0.25

x=0.4

x=0.65

3

What Do We Know About Glue in Matter?

• Scaling violation: dF2/dlnQ2 and

linear DGLAP Evolution !

G(x,Q2)!

Deep Inelastic Scattering : d

2" ep#eX

dxdQ2

=4$%e.m.

2

xQ4

1& y +y

2

2

'

( )

*

+ , F2(x,Q2) &

y2

2FL (x,Q2)

-

. /

0

1 2

Gluons dominate low-x wave function

)20

1( !xG

)20

1( !xS

vxu

vxd

!

DISp+p!jet+X



process ( )

23

ZEUS

0

1

2

3

4

5

1 10 102

103

104

105

F2

em-l

og

10(x

)

Q2(GeV

2)

ZEUS NLO QCD fit

tot. error

ZEUS 96/97

BCDMS

E665

NMC

x=6.32E-5x=0.000102

x=0.000161x=0.000253

x=0.0004x=0.0005

x=0.000632x=0.0008

x=0.0013

x=0.0021

x=0.0032

x=0.005

x=0.008

x=0.013

x=0.021

x=0.032

x=0.05

x=0.08

x=0.13

x=0.18

x=0.25

x=0.4

x=0.65

DISp+p!jet+X

RHIC 200 GeV



process ( )

23

ZEUS

0

1

2

3

4

5

1 10 102

103

104

105

F2

em-l

og

10(x

)

Q2(GeV

2)

ZEUS NLO QCD fit

tot. error

ZEUS 96/97

BCDMS

E665

NMC

x=6.32E-5x=0.000102

x=0.000161x=0.000253

x=0.0004x=0.0005

x=0.000632x=0.0008

x=0.0013

x=0.0021

x=0.0032

x=0.005

x=0.008

x=0.013

x=0.021

x=0.032

x=0.05

x=0.08

x=0.13

x=0.18

x=0.25

x=0.4

x=0.65

DISp+p!jet+X Tevatron 1.96 TeV



process ( )

23

ZEUS

0

1

2

3

4

5

1 10 102

103

104

105

F2

em-l

og

10(x

)

Q2(GeV

2)

ZEUS NLO QCD fit

tot. error

ZEUS 96/97

BCDMS

E665

NMC

x=6.32E-5x=0.000102

x=0.000161x=0.000253

x=0.0004x=0.0005

x=0.000632x=0.0008

x=0.0013

x=0.0021

x=0.0032

x=0.005

x=0.008

x=0.013

x=0.021

x=0.032

x=0.05

x=0.08

x=0.13

x=0.18

x=0.25

x=0.4

x=0.65

DISp+p!jet+X LHC 7 TeV


An explicit example: SIDIS (detailed note for your convenience)

! Semi-inclusive deep inelastic scattering

! Connection to high energy nuclear physics (heavy ion physics)

24

Higher-twist approach to energy loss, Wang-Guo, PRL,2000Energy loss at HERMES, Wang-Wang, PRL, 2002

! 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


Summary

25

! 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


Summary

25

Thank you

Kang

Documents

Zhong-Bo Kang - Jetjetsummer14.ucdavis.edu/lectures/kang_talk_1.pdfIntroduction to pQCD and Jets: lecture 1 Jet Collaboration Summer School University of California, Davis July 19–21,