early experimental tests of qcdrfield/cdf/qcd2_rickfield_9-6-16.pdf · 9/6/2016 · outgoing...

BND Summer School Antwerp, September 6, 2016

Rick Field – Florida

Rick FieldUniversity of Florida

Lecture 3

BND Summer School in BND Summer School in Particle Physics 2016Particle Physics 2016

Proton Proton

PT(hard)

Outgoing Parton

Outgoing Parton

Underlying Event Underlying Event

Initial-State Radiation

Final-State Radiation

University of Antwerp August 26 – September 9, 2016

Early Experimental Tests of QCD

�Collider Coordinates.

�Drell-Yan Muon-Pair Production.

�My talk at ICHEP 1978 in Tokyo and my lectures in Boulder in 1979.

�Parton Intrinsic (Primordial) Transverse Momentum.

�The QCD Improved Parton Model.

�Large Transverse Meson Production in Hadron-Hadron Collisions.

�Large Transverse “Jet” Production in Hadron-Hadron Collisions.

�The Invariant Differential.



My Story of QCDMy Story of QCD

Proton

momentum P Partons

The Quark ModelThe Eightfold Way

Iz

Y

SU(3)flavor Triplet

s

d u 3

The Parton Model The Naïve Parton Model

Proton momentum

P

u u

d

s

s Quarks

& Anti-quarks

The QCD Improved Parton Model

Proton Proton

PT(hard)

Outgoing Parton

Outgoing Parton

Underlying Event Underlying Event

Initial-State Radiation

Final-State Radiation

g0

q q

q

g0 + + …

q q q

q q

g0 g0 g0 g0

qbar

q

+ g

g

g g0 g0 g0 g0

q

q q

q

Before we knew the partonswere quarks and gluons!Non-interacting partons!

Partons = quarks, anti-quarks, and glue!Still non-interacting partons!

Parton Model + Perturbative QCD!Interacting quarks, anti-quarks, and gluons!

QCD Theory!



“Feynman-Field Jet Model”

The FeynmanThe Feynman--Field Field DaysDays

� FF1: “Quark Elastic Scattering as a Source of High Transverse MomentumMesons”, R. D. Field and R. P. Feynman, Phys. Rev. D15, 2590-2616 (1977).

� FFF1: “Correlations Among Particles and Jets Produced with Large Transverse Momenta” , R. P. Feynman, R. D. Field and G. C. Fox, Nucl. Phys. B128, 1-65 (1977).

� FF2: “A Parameterization of the properties of Quark Jets”, R. D. Field and R. P. Feynman, Nucl. Phys. B136, 1-76 (1978).

� F1: “Can Existing High Transverse Momentum Hadron Experiments be Interpreted by Contemporary Quantum Chromodynamics Ideas?”, R. D. Field, Phys. Rev. Letters 40, 997-1000 (1978).

� FFF2: “A Quantum Chromodynamic Approach for the Larg e Transverse Momentum Production of Particles and Jets”, R. P. Feynman, R. D. Field and G. C. Fox, Phys. Rev. D18, 3320-3343 (1978).

1973-1983

� FW1: “A QCD Model for e +e- Annihilation” , R. D. Field and S. Wolfram, Nucl. Phys. B213, 65-84 (1983).

My 1st graduate student!



“Feynman-Field Jet Model”

The FeynmanThe Feynman--Field Field DaysDays

� FF1: “Quark Elastic Scattering as a Source of High Transverse MomentumMesons”, R. D. Field and R. P. Feynman, Phys. Rev. D15, 2590-2616 (1977).

� FFF1: “Correlations Among Particles and Jets Produced with Large Transverse Momenta” , R. P. Feynman, R. D. Field and G. C. Fox, Nucl. Phys. B128, 1-65 (1977).

� FF2: “A Parameterization of the properties of Quark Jets”, R. D. Field and R. P. Feynman, Nucl. Phys. B136, 1-76 (1978).

� F1: “Can Existing High Transverse Momentum Hadron Experiments be Interpreted by Contemporary Quantum Chromodynamics Ideas?”, R. D. Field, Phys. Rev. Letters 40, 997-1000 (1978).

� FFF2: “A Quantum Chromodynamic Approach for the Larg e Transverse Momentum Production of Particles and Jets”, R. P. Feynman, R. D. Field and G. C. Fox, Phys. Rev. D18, 3320-3343 (1978).

1973-1983

� FW1: “A QCD Model for e +e- Annihilation” , R. D. Field and S. Wolfram, Nucl. Phys. B213, 65-84 (1983).

My 1st graduate student!

The Naïve Parton Model



QCD Improved Parton Model





ICHEP 1978 TokyoICHEP 1978 Tokyo

� The Effective Strong Interaction Coupling Constant, ααααs(Q2), and the Mass Scale ΛΛΛΛ.

� Quark and Gluon Distributions within Hadrons: Scale Breaking.

�Analysis of ep and µp Data.

�Analysis of F2 and xF3 in Neutrino Processes.

� Muon-Pair Production in pp Collisions.�QCD Factorization – “Constant” Pieces.

� Large pT Muon-Pair Production.

� “Scaling” in pp → µ+µ- +X.

Dynamics of High Energy ReactionsRick Field

California Institute of Technology(Plenary talk presented at the XIX International Conference on High Energy Physics, Tokyo, Japan)

The QCD Parton Model Approach - Outline of Talk

� Quark and Gluon Fragmentation Functions: Scale Breaking.

�Gluon Jets.

� Large pT Production of Mesons and Jets in pp Collisions.

�Scale Breaking Effects: Edσ/d3p.

�Correlations – Evidence for Gluons.

� The Jet Cross Section..

� A Look to the Future.� pp → π0 +X at W = 500 GeV.

� Large pT Charm Production.

� γγ→ Jet + Jet and e+e- → e+e-+Jet+Jet.

� Three Jets: e+e- → q+qbar+Jet and pp→Jet+Jet+Jet+X..

R. D. Field ICHEP78



Boulder 1979Boulder 1979� The NATO Advanced Institute on Quantum Flavordynamics, Quantum Chromodynamics,

and Unified Theories, held at the University of Colorado, Boulder, Colorado, July 9 – 27, 1979. (NATO Advanced Institute Series B: Physics, Volume 24, Plenum Press, 1980)

Lecturers

G. Altarelli

A. J. Buras

C. De Tar

S. Ellis

R. D. Field

D. Gross

C. H. Llewellyn Smith

J. Wess

Rick Field Boulder 1979 Jimmie Field Boulder 1979



My QCD BookMy QCD Book� Applications of Perturbative QCD, Addison-Wesley

Publishing Company, The Advanced Book Program, Frontiers in Physics (Volume No. 77), 1989.





Out of Print





http://www.phys.ufl.edu/~rfield/cdf/RDF_QCD_Book.pdf

Thanks to the DESY Theory Group, there is a scanned version on-line!

Out of Print





http://www.phys.ufl.edu/~rfield/cdf/RDF_QCD_Book.pdf

Thanks to the DESY Theory Group, there is a scanned version on-line!

Out of Print

I am sorry for the many typing

mistakes in the book! And in these

lectures?



Collider CoordinatesCollider Coordinates

� The z-axis is defined to be the beam axis. Let the xz-plane be the plane of the scattering with the xy-plane being the “transverse” plane.

� θθθθcm is the center-of-mass scattering angle and φφφφ is the azimuthal angle. The “transverse” momentum of a particle is given by pT = p cos(θθθθcm) = px. The “longitudinal” momentum of a particle is given by pL = p sin(θθθθcm) = pz.

2o4

6o3

15o2

40o1

90o0

θθθθcmηηηη

� The “rapidity” y of a particle with mass m is

A+B→h+X Center-of-Mass Frame

A B

h

z-axis

x-axis

y-axis

Beam Axis

A B

h

z-axis

x-axis

ph

Scattering Plane xz-plane

θθθθcm pT

pL

Scattering Angle

h

x-axis

y-axis Transverse Plane xy-plane

φφφφ (pT)y

pT

(pT)x

Azimuthal Angle

222

sin

cos

mppE

pp

pp

TL

cmL

cmT

++===

θθ

η→

−++

+++=

−+≡ =0222

222

log2

1log

2

1m

LTL

LTL

L

L

pmpp

pmpp

pE

pEy

� The “pseudo-rapidity” ηηηη of a particle is ( ))2/tan(log cmθη −≡



NaNaïïve Parton Modelve Parton Model

q A B

q

µµµµ+

µµµµ-

z-axis

x-axis

Drell-Yan Process (1970): A+B→µµµµ+µµµµ- + X

Born Term =

qγγγγ∗∗∗∗ γγγγ∗∗∗∗

q, pq

µµµµ+, pµµµµ+

q, pq

µµµµ-, pµµµµ-

2

22

31

3

4)(

)(ˆ

µµ

παµµγσ

M

e

qq

qem=

+→→+ −+∗

Bbq

Aaq

Pxp

Pxp~~

~~

==

2222 4)(2~~

2)~~

( CMCMCMBABA PPPPPPPs =+=⋅=+=

=

CM

CM

CMA

P

P

P0

0~

−

=

CM

CM

CMB

P

P

P0

0~

sPCM 21= sM /2

µµτ =

sxxMpps

sxxpppps

ba

baqqqq

==+==⋅=+=

−+22

2

)~~(ˆ

~~2)~~(ˆ

µµµµ

qqzL ppppP −=+= −+ )( µµµµ rr

222222 )()()( µµµµ

µµµµµµ

µµ MPMPPE LTL +=++=

baLL xxsPx −== /2

sExE /2 µµ= τ422 += LE xx

)(ˆ)()( )0()0( −+∗+→+ +→→+=→→

−+

µµγσσ µµ qqdxxGdxxGd bbaaXBA

qBqA

),()(

1

9

4),,( )0(

2

22

baqqBAba

emL

L

ABDY xxP

xxMxMs

dxd

d→++

=µµ

µµπα

τσ

[ ]∑=

→→→→→+ +=nf

ibqBaqAbqBaqAqbaqqBA xGxGxGxGexxP

iiiii1

)0()0()0()0(2)0( )()()()(),(

)()( 21

21

LEbLEa xxxxxx −=+=

0)( =+= −+ TT ppP µµµµ rr

0

)( ba

Lba xx

dxddxdx

+= τ

τ=baxx

Transverse Momentum of the Muon-Pair

Assume incoming partons have no transverse momentum!

Longitudinal Momentum of the Muon-Pair

)()0(bqB xG →)()0(

aqA xG →



NaNaïïve Parton Modelve Parton ModelDrell-Yan Process (1970): A+B→µµµµ+µµµµ- + X

)()( 21

21

LEbLEa xxxxxx −=+=

sM /2µµτ =

Lba xxx =−

τ422 += LE xx

=

−+=

−+

≡b

a

LE

LE

L

L

x

x

xx

xx

pE

pEy log

2

1log

2

1log

2

1µµ

µµ

µµµµ

µµ

τ=baxx

µµ

µµ

ττ

yLEb

yLEa

exxx

exxx−

+

=−==+=

)(

)(

21

21

),(9

4),,( )0(

2

22

baqqBAem

ABDY xxP

MyMs

dyd

d→+=

µµµµµµ

µµ

πατσ

Rapidity of Muon-Pair

),(),(9

4),,( )0()0(

222

µµµµµµµµ

µµ τπατσ

yFxxPyMsdyd

dM baqqBA

emABDY == →+

Parton Model Scaling


)(ˆ)()( )0()0( −+∗+→+ +→→+=→→

−+

µµγσσ µµ qqdxxGdxxGd bbaaXBA

qBqA

µµτdyddxdx ba =

q A B

q

µµµµ+

µµµµ-

z-axis

x-axis

)()0(bqB xG →)()0(

aqA xG →

τµµ

4

)()( 2

22

22 LE

LE

LE

LE

LEy xx

xx

xx

xx

xxe

+=−+=

−+=

τµµ

4

)()( 2

22

22 LE

LE

LE

LE

LEy xx

xx

xx

xx

xxe

−=−−=

+−=−

= Constant at fixed ττττ and yµµµµµµµµ!(provided the PDF’s scale)

Born Term

),(2),,( )0(23µµµµµµ

µµµµµµ ττσ

yFyMsdydM

dM

ABDY =



QCD Improved Parton ModelQCD Improved Parton ModelDrell-Yan Muon-Pair Production

q Proton

q

µµµµ+

µµµµ-

Proton

Xpp +→+ −+µµ

γγγγ∗∗∗∗

quark

µµµµ+

anti-quark

µµµµ-

s

t ̂

^

Born Term =

−+ +→+ µµqq


q q s ^

A0 =

∗→+ γqq

Include Leading Order QCD Corrections (Order ααααs)


q q

AR =

gluon

gs

s ^

t ^


q q

+

gluon

gs

s ^

t ̂


q

q

CR =

gluon

gs

s ^

t ^


q

q

+ gluon

gs

s ^

t ^


q q

AV = gluon

gs gs


q q

+ gluon

gs gs


q q

+ gluon

gs

gs

gqq +∗→+ γ

qgq +∗→+ γ

Born Amplitude =

“Annihilation”

“Compton”

q Proton

q

µµµµ+ µµµµ-

Proton γγγγ*

gluon

q

Proton q

µµµµ+ µµµµ-

Proton γγγγ*

gluon

“Born”

“Annihilation”

“Compton”

Virtual Corrections



R. Field ICHEP78R. Field ICHEP78

� Leading order QCD prediction of the di-muon mass spectrum at y = 0 and W = 27.4 GeV using the “renormalization group” improved quark and antiquark distributions.

The data are from D. C. Horn et al., Phys. Rev. Letters 36, 1239 (1976) and 37, 1374 (1976); S. W. Herb et al., Phys. Rev. Letters 39, 352 (1977); W. R. Innes et al., Phys. Rev. Letters 39, 1240 (1977); also see the talk by L. Lederman at this conference.

[ ]∑=

→→→→→+ +=nf

ib

DISqBa

DISqAb

DISqBa

DISqAqba

DISqqBA QxGQxGQxGQxGeQxxP

iiiii1

222222 ),(),(),(),(),,(

QCD Improved Parton ModelUse the “renormalization group

improved” PDF’s from DIS!

),0,(2

)0,,( 22

QyFMW

yMWdydM

d DISAB

LODY ===−µµ

µµµµµµ

µµµµ

τσ

sM /2µµτ =

ττττ

µµ

µµ

µµ

µµ

→=−=

→=+=

=−

=+

021

021

)(

)(

y

yLEb

y

yLEa

exxx

exxx

µµMQ =

Use Q = Mµµµµµµµµas the scale!

18.0≈τ 55.0≈τ

Rick Field 1978

M µµµµµµµµ = 15 GeV!




� Leading order QCD prediction of the di-muon mass spectrum at y = 0 and W = 27.4 GeV using the “renormalization group” improved quark and antiquark distributions.


[ ]∑=

→→→→→+ +=nf

ib

DISqBa

DISqAb

DISqBa

DISqAqba

DISqqBA QxGQxGQxGQxGeQxxP

iiiii1

222222 ),(),(),(),(),,(

QCD Improved Parton ModelUse the “renormalization group

improved” PDF’s from DIS!

),0,(2

)0,,( 22

QyFMW

yMWdydM

d DISAB

LODY ===−µµ

µµµµµµ

µµµµ

τσ

sM /2µµτ =

ττττ

µµ

µµ

µµ

µµ

→=−=

→=+=

=−

=+

021

021

)(

)(

y

yLEb

y

yLEa

exxx

exxx

µµMQ =


18.0≈τ 55.0≈τ

Rick Field 1978

M µµµµµµµµ = 15 GeV!

Drell-Yan Muon-Pair Production Today

Xpp +→+ −+µµ

M µµµµµµµµ = 2,000 GeV!



Center-of-Mass Frame

b, pb

γγγγ*, pγγγγ*

d, pd

θθθθCM pT ^

pT θθθθCM

^

^ ^

a, pa ~ ~

~

~ x-axis

z-axis

Kinematics (1)Kinematics (1)

2ˆˆˆ ∗=++ γMuts

2-to-2 Scattering

s

t ̂

^ a, pa ~ b, pb

γγγγ*, pγγγγ* d, pd

~

~ ~

a+b→γγγγ*+d(neglect the mass of a, b, and d)

)ˆcos1('ˆˆ2~~2)~~()~~(ˆ

)ˆcos1('ˆˆ2~~2)~~()~~(ˆˆ4~~2)~~(ˆ

22

22

22

CMCMCMdadab

CMCMCMdbdba

CMbaba

ppppppppu

ppppppppt

ppppps

θθ

γ

γ

+−=⋅−=−=−=−−=⋅−=−=−=

=⋅=+=

∗

∗

s

utpT ˆ

ˆˆˆ 2 =

spx TT ˆ/ˆ2ˆ ≡

=

CM

CM

CMa

p

p

p

ˆ

0

0

ˆ

~

−

=

CM

CM

CMb

p

p

p

ˆ

0

0

ˆ

~

+

=

∗

∗

CMCM

CMCM

CM

CM

p

p

Mp

p

θ

θγ

γ

ˆcos'ˆ

0

ˆsin'ˆ

'ˆ

~

32

−

−=

CMCM

CMCM

CM

CMd

p

p

p

p

θ

θ

ˆcos'ˆ

0

ˆsin'ˆ

'ˆ

~

CMCMT pp θ̂sin'ˆˆ =

spCM ˆˆ21=

)2/ˆcot(ˆˆˆsin

)ˆcos1(ˆˆ2)ˆcos1('2ˆ

)2/ˆtan(ˆˆˆsin

)ˆcos1(ˆˆ2)ˆcos1('2ˆ

21

21

CMT

CM

CMTCMCMCMCM

CMT

CM

CMTCMCMCMCM

xsppppu

xsppppt

θθ

θθ

θθ

θθ

−=+−=+−=

−=−−=−−=

s

MspCM ˆ2

)ˆ('ˆ

2∗−

= γ

CMd

CMCMb

CMa pppp ~~~~ +=+ ∗γ



Kinematics (2)Kinematics (2)A+B→(γγγγ*→µµµµ+µµµµ-)+X (neglect the mass of A and B)


B, PB X

θθθθCM pT

A, PA ~

~

x-axis

z-axis

γ∗γ∗γ∗γ∗

µµµµ+ µµµµ-

=

CM

CM

CMA

p

p

P0

0~

−

=

CM

CM

CMB

p

p

P0

0~

)(2~~

2)~~

(

)(2~~

2)~~

(

4~~

2)~~

(

222

222

22

µµµµµµµµµµµµ

µµµµµµµµµµµµ

LCMBB

LCMAA

CMBABA

PEpMPPMPPu

PEpMPPMPPt

pPPPPs

+−=⋅−=−=−−=⋅−=−=

=⋅=+=spCM 2

1=

s

tupT =2

=

−+=

−+

≡2

1log2

1log

2

1log

2

1

x

x

xx

xx

pE

pEy

LE

LE

L

L

µµµµ

µµµµ

µµ


τ4222 ++= LTE xxx

spx

spx

sM

LL

TT

/2

/2

/2

µµ

µµµµτ

===

µµ

µµ

ττ

yTLE

yTLE

exxxsMtx

exxxsMux−

+

+=−=−−≡+=+=−−≡

4)(/)(

4)(/)(2

21

212

2

221

212

1

Lxxx =− 21

=

µµ

µµµµ

µµ

L

TCM

p

p

E

P0

~

2222 )()( µµµµµµ

µµ MppE LT ++=

τµµ

4

)()(2

2

22

22

++=

−+=

−+=

T

LE

LE

LE

LE

LEy

x

xx

xx

xx

xx

xxe

τµµ

4

)()(2

2

22

22

+−=

−−=

+−=−

E

LE

LE

LE

LE

LEy

x

xx

xx

xx

xx

xxe

τ+= 241

21 Txxx




2ˆˆˆ µµMuts =++

External Variables (neglect the mass of A and B)

2-to-2 Scattering

s

t ̂

^ a, pa ~ b, pb

γγγγ∗∗∗∗, pγ∗γ∗γ∗γ∗ d, pd

~

~ ~

a+b→γγγγ∗∗∗∗+dInternal Variables (neglect the mass of a, b, and d)

)()~~

2(~~2)~~(ˆ

)()~~

2(~~2)~~(ˆ)

~~2(~~2)~~(ˆ

22222

22222

2

µµµµµµµµµµγ

µµµµµµµµγµµγ

MuxMPPxMppMppu

MtxMPPxMppMppt

sxxPPxxpppps

bBbbcb

aAaaa

baBAbababa

−+=⋅−=⋅−=−=−+=⋅−=⋅−=−=

=⋅=⋅=+=

∗

∗∗

Bbb

Aaa

Pxp

Pxp~~

~~

==

Internal-External Connection

sxxMuxMu

sxxMtxMt

bb

aa

122

222

)(ˆ

)(ˆ

−=−=−−=−=−

µµµµ

µµµµ s

utpT ˆ

ˆˆ2 =

A+B→γγγγ*+X

BB

AA

CMBABA

PPMPPu

PPMPPt

pPPPPs

~~2)

~~(

~~2)

~~(

4~~

2)~~

(

22

22

22

⋅−=−=⋅−=−=

=⋅=+=

µµµµµµ

µµµµµµ

b A B

a


d

pT

µµµµ+ µµµµ-

=

2

1log2

1

x

xyµµ


µµ

µµ

ττ

yT

yT

exsMtx

exsMux−

+

+=−−≡+=−−≡

4/)(

4/)(2

212

2

2212

1

21 xxxL −=

222 )ˆ()ˆ(ˆ µµµµµµ MMuMts −=−+−+

τ−=−− 12 xxxxxx baba

1

2

xx

xxx

a

ab −

−= τ

2

1

xx

xxx

b

ba −

−= τ

spx

spx

sM

LL

TT

/2

/2

/2

µµ

µµµµτ

===

τ4222 ++= LTE xxx



b A B

a


d

pT

µµµµ+ µµµµ-

NaNaïïve Parton Modelve Parton ModelLarge Transverse Momentum Muon-Pair Production (Order ααααs) XBA +→+ −+µµ

1

2

xx

xxx

a

ab −

−= τ

)()0(aaA xG →

tdtstddM

ddxxGdxxGpyMs

dM

d dba

bbbBaaaAT

XBA

ˆ)ˆ,ˆ(ˆ

ˆ)()(),,,(

2)0()0(2

2

=

+→+

→→

+→+ ∗∗

µµ

γ

µµµµµµ

γ σσ

)()0(bbB xG →

−=

+→+

→→

∗

∫ )ˆ,ˆ(ˆ

ˆ)()(),,,(

21

)0()0(0.1

222

min

tstddM

d

xx

xxxGxGdxpyMs

dpdydM

d dba

a

babbBaaA

x

aTT

ABDY

aµµ

γ

µµµµµµµµ

σσ

2

1

2

1

41

211

ˆT

a

baT

a

ba

a

bab dpdy

xx

xxdxdy

xx

xsxdxdx

xx

xsxtddx µµµµ

−=

−=

−=

µµ

µµ

ττ

yT

yT

exx

exx−

+

+=+=

4

42

21

2

221

1

2

1min

1 x

xxa −

−= τ

241

21 Tdxdydxdx µµ=

2

1

xx

xxx

b

ba −

−= τ

=

2

1log2

1

x

xyµµ τ44 21

2 += xxxT

sxxMt a 22ˆ −= µµ

1

2

xx

xxx

a

ab −

−= τ

xb = 1




QCD Differential CrossQCD Differential Cross--SectionsSectionsLarge Transverse Momentum Muon-Pair Production (Order ααααs)


q q

AR =

gluon

gs

s ^

t ^


q q

+

gluon

gs

s ^

t ̂

gqq +∗→+ γ

++=

+→+ ∗

ut

tusM

sM

ets

tddM

d qemsgqq

ˆˆ

ˆˆˆ2

ˆ27

8)ˆ,ˆ(

ˆˆ 222

22

22

2

µµ

µµµµ

γ αασ“Annihilation”


q

q

CR =

gluon

gs

s ^

t ^


q

q

+ gluon

gs

s ^

t ^

qgq +∗→+ γ“Compton”

−++

=+→+ ∗

ts

tsuM

sM

ets

tddM

d qemsqgq

ˆˆ

ˆˆˆ2

ˆ9

1)ˆ,ˆ(

ˆˆ 222

22

22

2

µµ

µµµµ

γ αασ

2ˆˆˆ µµMuts =++

)ˆ,ˆ(ˆ

ˆ)ˆ,ˆ(

ˆˆ

22

2ts

tddM

dets

tddM

d Aq

gqq

µµµµ

γ σσ =+→+ ∗

)ˆ,ˆ(ˆ

ˆ)ˆ,ˆ(

ˆˆ

22

2ts

tddM

dets

tddM

d Cq

qgq

µµµµ

γ σσ =+→+ ∗

s

utpT ˆ

ˆˆ2 =



b A B

a


d

pT

µµµµ+ µµµµ-


1

2

xx

xxx

a

ab −

−= τ

)()0(aaA xG → )()0(

bbB xG →

−= ∫ )ˆ,ˆ(

ˆˆ

),(),,,(2

1

)0(0.1

222

min

tstddM

d

xx

xxxxPdxpyMs

dpdydM

d A

a

babaA

x

aTT

DYA

aµµ

µµµµµµµµ

σσ

µµ

µµ

ττ

yT

yT

exx

exx−

+

+=+=

4

42

21

2

221

1

[ ]∑=

→→→→ +=nf

ibqBaqAbqBaqAqbaA xGxGxGxGexxP

iiiii1

)0()0()0()0(2)0( )()()()(),(

[ ]∑=

→→→→ +=nf

ibqBagAbgBaqAqbaC xGxGxGxGexxP

iii

2

1

)0()0()0()0(2)0( )()()()(),(

−= ∫ )ˆ,ˆ(

ˆˆ

),(),,,(2

1

)0(0.1

222

min

tstddM

d

xx

xxxxPdxpyMs

dpdydM

d C

a

babaC

x

aTT

DYC

aµµ

µµµµµµµµ

σσ

2

1min

1 x

xxa −

−= τ

Parton Flux



QCD Differential CrossQCD Differential Cross--SectionsSectionsLarge Transverse Momentum Muon-Pair Production (Order ααααs) XBA +→+ −+µµ


q q

AR =

gluon

gs

s ^

t ^


q q

+

gluon

gs

s ^

t ̂

gqq +∗→+ γ

++=

ut

tusM

sMts

tddM

d emsA

ˆˆ

ˆˆˆ2

ˆ27

8)ˆ,ˆ(

ˆˆ 222

22

2

2

µµ

µµµµ

αασ“Annihilation”

{ }{ }sp

su

sps

t

T

T

ˆ/4)ˆ1()ˆ1(2

ˆˆ

ˆ/4)ˆ1()ˆ1(2

ˆˆ

22

22

−−+−−=

−−−−−=

ττ

ττ

2ˆˆˆ µµMuts =++s

utpT ˆ

ˆˆ2 =

)ˆ1(ˆ

ˆ

ˆ

ˆτ−−=+

s

u

s

t

−−−

=

=

s

t

s

t

s

u

s

t

s

pT

ˆ

ˆ)ˆ1(

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

2

τ

sM ˆ/ˆ 2µµτ =

−+=

s

p

spMts

tddM

d T

T

emsA

ˆ2

ˆ1ˆ27

8)ˆ,ˆ(

ˆˆ 2

222

2

2ταασ

µµµµsxxs ba=ˆ

−+

−=

− ba

T

baTa

emsA

a

ba

xx

x

xxpMxxts

tddM

d

xx

xx

2)(1

)(

1

27

8)ˆ,ˆ(

ˆˆ 2

2

2

241

2

21

τταασµµµµ

baxx

ττ =ˆ

sM /2µµτ = spx TT /2=



b A B

a


d

pT

µµµµ+ µµµµ-


1

2

xx

xxx

a

ab −

−= τ

)()0(aaA xG → )()0(

bbB xG →

),,(),,,( )0(222

24TAsT

T

DYA

T xyFpyMsdpdydM

dpM µµµµµµ

µµµµµµ τασ =

µµ

µµ

ττ

yT

yT

exx

exx−

+

+=+=

4

42

21

2

221

1

[ ]∑=

→→→→ +=nf

ibqBaqAbqBaqAqbaA xGxGxGxGexxP

iiiii1

)0()0()0()0(2)0( )()()()(),(

[ ]∑=

→→→→ +=nf

ibqBagAbgBaqAqbaC xGxGxGxGexxP

iiii

2

1

)0()0()0()0(2)0( )()()()(),(

2

1min

1 x

xxa −

−= τ

Parton Flux

−+

−= ∫

ba

T

baabaA

x

aem

TA xx

x

xxxxxxPdxxyF

a2)(

1)(

),(27

8),,(

2

2

2

1

)0(0.12

)0(

min

ττατ µµ

),,(),,,( )0(222

24TCsT

T

DYC

T xyFpyMsdpdydM

dpM µµµµµµ



= Constant at fixed ττττ, yµµµµµµµµ, and xT!(provided the PDF’s scale and ααααs is constant)



b A B

a


d

pT

µµµµ+ µµµµ-

Parton Model ScalingParton Model ScalingLarge Transverse Momentum Muon-Pair Production (Order ααααs) XBA +→+ −+µµ

),,(),,,( )0(222

24TsT

T

DY

T xyFpyMsdpdydM

dpM µµµµµµ



),,(),,,( )0(222

24TsT

T

DY

T xyFpyMspddydM

dpM µµµµµµ

µµµµµµ τπασ =

),,(2),,,( )0(2

23TsT

T

DY

T xyFpyMspddydM

dpM µµµµµµ

µµµµµµ τπασ =

222 // WMsM µµµµτ ==

sW=

Wpx TT /2= 25412

21323 2

3

)()( TTT xWWxWpM ττµµ ==

),,(8

),,,( )0(

225

23 T

T

sT

T

DY

xyFx

pyMWpddydM

dW µµµµµµ

µµµµ

ττπασ = = Constant at fixed ττττ, yµµµµµµµµ, and xT!

(provided the PDF’s scale and ααααs is constant)



QCD Improved Parton ModelQCD Improved Parton ModelLarge Transverse Momentum Muon-Pair Production (Order ααααs) XBA +→+ −+µµ

1

2

xx

xxx

a

ab −

−= τ

),,,()(),,,( 22222

24 QxyFQpyMsdpdydM

dpM T

DISAsT

T

XBAA

T µµµµµµµµµµ

γ

µµ τασ =+→+ ∗

µµ

µµ

ττ

yT

yT

exx

exx−

+

+=+=

4

42

21

2

221

1

[ ]∑=

→→→→ +=nf

ib

DISqBa

DISqAb

DISqBa

DISqAqba

DISA QxGQxGQxGQxGeQxxP

iiiii1

222222 ),(),(),(),(),,(

[ ]∑=

→→→→ +=nf

ib

DISqBa

DISgAb

DISgBa

DISqAqba

DISC QxGQxGQxGQxGeQxxP

iiii

2

1

222222 ),(),(),(),(),,(

2

1min

1 x

xxa −

−= τ

Parton Flux

−+

−= ∫

ba

T

baaba

DISA

x

aem

TDISA xx

x

xxxxQxxPdxQxyF

a2)(

1)(

),,(27

8),,,(

2

2

2

1

20.12

2

min

ττατ µµ

),,,()(),,,( 22222

24 QxyFQpyMsdpdydM

dpM T

DISCsT

T

XBAC


γ

µµ τασ =+→+ ∗


Naïve parton model scaling is now broken!

Use the “renormalization group improved” PDF’s from DIS and

the running QCD coupling!

µµMQ =




QCD Improved Parton ModelQCD Improved Parton ModelLarge Transverse Momentum Muon-Pair Production (Order ααααs) XBA +→+ −+µµ

1

2

xx

xxx

a

ab −

−= τ

),,,()(),,,( 22222

24 QxyFQpyMsdpdydM

dpM T

DISAsT

T

XBAA


γ

µµ τασ =+→+ ∗

µµ

µµ

ττ

yT

yT

exx

exx−

+

+=+=

4

42

21

2

221

1

[ ]∑=

→→→→ +=nf

ib

DISqBa

DISqAb

DISqBa

DISqAqba

DISA QxGQxGQxGQxGeQxxP

iiiii1

222222 ),(),(),(),(),,(

[ ]∑=

→→→→ +=nf

ib

DISqBa

DISgAb

DISgBa

DISqAqba

DISC QxGQxGQxGQxGeQxxP

iiii

2

1

222222 ),(),(),(),(),,(

2

1min

1 x

xxa −

−= τ

Parton Flux

−+

−= ∫

ba

T

baaba

DISA

x

aem

TDISA xx

x

xxxxQxxPdxQxyF

a2)(

1)(

),,(27

8),,,(

2

2

2

1

20.12

2

min

ττατ µµ

),,,()(),,,( 22222

24 QxyFQpyMsdpdydM

dpM T

DISCsT

T

XBAC


γ

µµ τασ =+→+ ∗



Use the “renormalization group improved” PDF’s from DIS and

the running QCD coupling!

µµMQ =


Renormalization Group Improved PDF’s! Running QCD Effective Coupling!




� The distribution in transverse momentum, pT, of the µµµµ+µµµµ- pair produced in pp collisions at W = 27.4 GeVtogether with the QCD perturbative predictions. The “Compton” and “annihilation” contributions are given by the dashed and dotted curves, respectively.

R. D. Field ICHEP78

Rick Field 1978



QCD Improved Parton ModelQCD Improved Parton ModelReal Gluon Emissions Order ααααs

),,,(),,,(),,,( 222

222

2T

T

XBAC

TT

XBAA

TDYR pyMs

dpdydM

dpyMs

dpdydM

dpyMs µµµµ

µµµµ

γ

µµµµµµµµ

γ

µµµµσσσ

+→++→+ ∗∗

+≡

Born Term Plus Virtual Gluon Emissions Order ααααs

),,(),,( 22

2µµµµ

µµµµ

γ

µµµµσσ yMs

dydM

dyMs

XBAVBDY

V

+→++

∗

≡

Total Cross-Section Order ααααs

∫+≡+→+

+

∗

22222

2 ),,,(),,(),,( TTDYR

XBAVBDY

tot dppyMsyMsdydM

dyMs µµµµµµµµ

µµµµ

γ

µµµµ σσσ

),,(9

4),,(),,( 2

2

22

22

µµµµ

µµµµµµµµ

µµµµπασσ MxxP

sMyMs

dydM

dyMs ba

DISqq

emDY

LOtotDYLOtot == −

−

Finite = Infinite + Infinite

[ ]∑=

→→→→ +=nf

ib

DISqBa

DISqAb

DISqBa

DISqAqba

DISqq MxGMxGMxGMxGeMxxP

iiiii1

222222 ),(),(),(),(),,( µµµµµµµµµµ

Total Cross-Section Leading Order



Intrinsic Parton Intrinsic Parton kkTT

Proton momentum

u

u

d

s s

kT

From the uncertainty principle one expects that the partons will have some intrinsic (primordial) transverse momentum.

Parton Intrinsic (Primordial) Transverse Momentum:

MeVfm

fmMeV

x

cpc x 200

1

3.197 ≈⋅=∆

≈∆ h

Transverse size of the proton.

Expect intrinsic kT(P→q) ≈ 200 – 300 MeV/c!

Also expect that the hadrons within a jet will have some intrinsic transverse momentom.Jet Size:

γγγγ*

qbar q Short time – Small distance

Two Jet Final State: e+e- to Jet + Jet

Hadronic Jet

Hadronic Jet kT

Expect intrinsic kT(q→h) ≈ 200 – 300 MeV/c!



Primordial Primordial kkTT SmearingSmearing

kT x-axis

qT y-axis

pT 2

2

4

22

4

1)( primordial

Tk

primordialT ekf σ

πσ

−

=

TTT kpqrrr −=

[ ] TTDYVT

DYRTprimordialT

DYsmear kdqyMsqyMskfpyMs 2222222 )(),,(),,,()(),,,,( ∫ += δσσσσ µµµµµµµµµµµµ

[ ] ),,()()()(),,,(

),,,,(

2222222

2

µµµµµµµµ

µµµµ

σσ

σσ

yMspfkdpfkfqyMs

pyMs

DYtotTTTTT

DYR

TDYsmear

+−

=

∫

22 primordialprimordialTk σ=><

Intrinsic Primordial transverse momentum!

[ ][ ]∫

∫++

−=

TTDYVT

DYRT

TTTTDYRprimordialT

DYsmear

qdqyMsqyMspf

kdpfkfqyMspyMs

222222

222222

)(),,(),,,()(

)()(),,,(),,,,(

δσσ

σσσ

µµµµµµµµ

µµµµµµµµ

Finite Finite




� The distribution in transverse momentum, pT, of the µµµµ+µµµµ- pair produced in pp collisions at W = 27.4 GeV together with the QCD perturbative prediction folded with a Gaussian primordial parton momentum spectrum with <k T> = 600 MeV(solid curve). The dashed curve results from the partonprimordial motion only with no perturbative QCD term s.

R. D. Field ICHEP78

Rick Field 1978




� The distribution in transverse momentum, pT, of the µµµµ+µµµµ- pair produced in pp collisions at W = 27.4 GeV together with the QCD perturbative prediction folded with a Gaussian primordial parton momentum spectrum with <k T> = 600 MeV(solid curve). The dashed curve results from the partonprimordial motion only with no perturbative QCD term s.

R. D. Field ICHEP78

Large primordial k T!

Early Experimental Test of QCD

Rick Field 1978




� Energy dependence of the large pT tail expected for pp -> µµµµ+µµµµ- + X from the QCD perturbativeprediction folded with a Gaussian primordial parton momentum spectrum with <kT> = 600 MeV.





� Data on the energy dependence of the <pT> of the µµµµ+µµµµ- pair in proton-nucleon collisions which indicate that the pTdistribution is becoming broader as the energy increases.






� Data on the energy dependence of the <pT> of the µµµµ+µµµµ- pair in proton-nucleon collisions which indicate that the pTdistribution is becoming broader as the energy increases.


W = 19.4 GeV

W = 27.4 GeV





� Expected “scale breaking” of the quantity W5dσσσσ/dMdyd2pT for pp->µµµµ+µµµµ- +X at y = 0 and xT = 0.2 from QCD with ΛΛΛΛ = 0.4 GeV/c. The solid (dashed) curves are the results after (before) smearing with a parton primordial transverse momentun with <k T> = 600 MeV. The dotted curves would be expected if primordial motion alone were responsible for the muon pair pT. Scaling would predict this quantity to be independent of W at fixed ττττ and xT.

R. D. Field ICHEP78

TpdMdyddW 25 /σ

R. FieldICHEP78




� Expected “scale breaking” of the quantity W5dσσσσ/dMdyd2pT for pp->µµµµ+µµµµ- +X at y = 0 and xT = 0.2 from QCD with ΛΛΛΛ = 0.4 GeV/c. The solid (dashed) curves are the results after (before) smearing with a parton primordial transverse momentun with <k T> = 600 MeV. The dotted curves would be expected if primordial motion alone were responsible for the muon pair pT. Scaling would predict this quantity to be independent of W at fixed ττττ and xT.

R. D. Field ICHEP78

TpdMdyddW 25 /σ

R. FieldICHEP78

Early QCD Predictions

Smearing breaks naïve parton model scaling!



The Invariant DifferentialThe Invariant DifferentialA+B→h+X Center-of-Mass Frame

A B

h

z-axis

x-axis

ph

Scattering Plane xz-plane

θθθθcm pT

pL

Scattering Angle

h

x-axis

y-axis Transverse Plane xy-plane

φφφφ (pT)y

pT

(pT)x

Azimuthal Angle 222

sin

cos

mppE

pp

pp

TL

cmL

cmT

++===

θθ

E

pddp

E

pd TL23

=

Invariant Differential

22212

),(

),(TTTTT

T

Ty

TxT

yTxT dpddpddppddp

p

ppdpdppd πφφφ

φ===

∂∂

==

Integrate over φφφφ

E

p

dp

dE L

L

=

−+≡

L

L

pE

pEy log

2

1

EpEE

p

pEE

p

dp

dy

L

L

L

L

L

111

2

1 =

−

−−

+

+= dy

E

dpL =

24122

3

TTT sdydxdydppdydE

pd ππ === spx

spx

TT

TT

/4

/222 =

=

φφ

sin

cos

TT

TTx

pp

pp

y==

TTT

Ty

Tx

TTyT

Tx

T

Ty

Tx p

pppp

pppp

p

pp=

−=

∂∂∂∂∂∂∂∂

=∂

∂φφ

φφφφφ cossin

sincos

//

//

),(

),(

Jacobian



Kinematics (1)Kinematics (1)A+B→h+X

2XMuts =++

b A B

h

a

c

d

pT

(neglect the mass of A, B, and h)


B, PB

h, Ph

X

θθθθCM pT

A, PA ~

~

~ x-axis

z-axis

=

CM

CM

CMA

p

p

P0

0~

−

=

CM

CM

CMB

p

p

P0

0~

′

′′

=

CMCM

CMCM

CM

CMh

p

p

p

P

θ

θ

ˆcos

0

ˆsin~

)cos1(2~~

2)~~

(

)cos1(2~~

2)~~

(

4~~

2)~~

(

2

2

22

CMCMCMBhBh

CMCMCMAhAh

CMBABA

ppPPPPu

ppPPPPt

pPPPPs

θθ

+′−=⋅−=−=−′−=⋅−=−=

=⋅=+=

spx TT /2≡

CMCMT pp θsin′=

spCM 21=

s

Msp X

CM2

2−=′

s

tupT =2

)2/cot(sin

)cos1(2)ˆcos1(2

)2/tan(sin

)cos1(2)ˆcos1(2

21

21

CMTCM

CMTCMCMCMCM

CMTCM

CMTCMCMCMCM

sxppppu

sxppppt

θθ

θθ

θθ

θθ

−=+−=+′−=

−=−−=−′−=



Kinematics (2)Kinematics (2)A+B→h+X

b A B

h

a

c

d

pT

(neglect the mass of A, B, and h)


B, PB

h, Ph

X

θθθθCM pT

A, PA ~

~

~ x-axis

z-axis

=

CM

CM

CMA

p

p

P0

0~

−

=

CM

CM

CMB

p

p

P0

0~

=

L

TCMh

p

p

E

P0

~

)()(2~~

2)~~

(

)()(2~~

2)~~

(

212212

LELCMBhBh

LELCMAhAh

xxspEpPPPPu

xxspEpPPPPt

+−=+−=⋅−=−=−−=−−=⋅−=−=

spx

spx

spx

EE

LL

TT

/2

/2

/2

≡≡≡

CMCMT pp θsin′=spCM 2

1=

yTLE

yTLE

exxxstx

exxxsux−

+

=−=−≡=+=−≡

21

21

2

21

21

1

)(/

)(/

=

−+=

−+≡

2

1log2

1log

2

1log

2

1

x

x

xx

xx

pE

pEy

LE

LE

L

L

Rapidity of h

CMCML pp θcos′=222TL ppE +=

2

2

22

22 )()(

T

LE

LE

LE

LE

LEy

x

xx

xx

xx

xx

xxe

+=−+=

−+=+

2

2

22

22 )()(

T

LE

LE

LE

LE

LEy

x

xx

xx

xx

xx

xxe

−=−−=

+−=−

222TLE xxx +=

)2/cot(

)2/tan(

21

21

1

21

21

2

CMTy

T

CMTy

T

sxesxsxu

sxesxsxt

θθ

−=−=−=−=−=−=

+

−

( ))2/tan(log cmy θη −==



22--toto--2 Kinematics2 Kinematics

0ˆˆˆ =++ uts

2-to-2 Scattering

s

t ̂

^ a, pa ~ b, pb

c, pc d, pd

~

~ ~

a+b→c+d (neglect masses)

)ˆcos1(ˆ2~~2)~~(ˆ

)ˆcos1(ˆ2~~2)~~(ˆˆ4~~2)~~(ˆ

22

22

22

CMCMbcbc

CMCMacac

CMbaba

pppppu

pppppt

ppppps

θθ

+−=⋅−=−=−−=⋅−=−=

=⋅=+=

s

utpT ˆ

ˆˆˆ 2 =

spx TT ˆ/ˆ2ˆ ≡


b, pb

c, pc

d, pd

θθθθCM pT ^

pT θθθθCM

^

^ ^

a, pa ~ ~

~

~ x-axis

z-axis

=

CM

CM

CMa

p

p

p

ˆ

0

0

ˆ

~

−

=

CM

CM

CMb

p

p

p

ˆ

0

0

ˆ

~

=

CMCM

CMCM

CM

CMc

p

p

p

p

θ

θ

ˆcosˆ

0

ˆsinˆ

ˆ

~

−

−=

CMCM

CMCM

CM

CMd

p

p

p

p

θ

θ

ˆcosˆ

0

ˆsinˆ

ˆ

~

CMCMCMT spp θθ ˆsinˆˆsinˆˆ21==spCM ˆˆ

21=

)2/ˆcot(ˆˆˆsin

)ˆcos1(ˆˆ2)ˆcos1(ˆ2ˆ

)2/ˆtan(ˆˆˆsin

)ˆcos1(ˆˆ2)ˆcos1(ˆ2ˆ

212

212

CMT

CM

CMTCMCMCM

CMT

CM

CMTCMCMCM

xspppu

xspppt

θθ

θθ

θθ

θθ

−=+−=+−=

−=−−=−−=




0ˆˆˆ =++ uts

BhBh

AhAh

BABA

PPPPu

PPPPt

PPPPs

~~2)

~~(

~~2)

~~(

~~2)

~~(

2

2

2

⋅−=−=⋅−=−=⋅=+=A+B→h+X

External Variables (neglect the mass of A, B, and h)

2-to-2 Scattering

s

t ̂

^ a, pa ~ b, pb

c, pc d, pd

~

~ ~

a+b→c+dInternal Variables (neglect masses)

cbcBhbbcbc

cacAhaacac

baBAbababa

zuxzPPxppppu

ztxzPPxppppt

sxxPPxxpppps

//)~~

(2~~2)~~(ˆ

//)~~

(2~~2)~~(ˆ)

~~(2~~2)~~(ˆ

2

2

2

=⋅−=⋅−=−==⋅−==⋅−=−=

=⋅=⋅=+=

cch

Bbb

Aaa

pzP

Pxp

Pxp

~~

~~

~~

===

Internal-External Connection

bac x

x

x

xz 21 +=

stx

sux

/

/

2

1

−=−=

Wpx TT /2=

b A B

h

a

c

d

pT

2

2

22 1

ˆ

ˆˆˆ

c

T

cT z

p

s

tu

zs

utp ===

cTT zpp /ˆ =012 =−−

c

b

c

aba z

xx

z

xxxx

2

1

xxz

xxx

bc

ba −

=1

2

xxz

xxx

ac

ab −

=



b A B

h

a

c

d

pT

NaNaïïve Parton Modelve Parton ModelA+B→h+X External Variables

)()0(aaA xG →

Wpx TT /2=sEW cm ==

cchc

dcba

bbbBaaaAXhBA dzzDtdts

td

ddxxGdxxGtsd )(ˆ)ˆ,̂(

ˆˆ

)()(),( )0()0()0(→

+→+

→→+→+

= σσ

)()0(bbB xG →

)()0(chc zD →

0ˆˆˆ =++ uts

Internal Variables

cbcb

caca

ba

zsxxzuxu

zsxxztxt

sxxs

//ˆ

//ˆˆ

1

2

−==−==

=

bac x

x

x

xz 21 +=

E

pd

ztddz

cc

31ˆπ

=

1

2min

xx

xxx

a

ab −

=2

1min

1 x

xxa −

=

cTT zpp /ˆ =

)ˆ,̂(ˆ

ˆ1)()()(

1),,(

,

0.1 0.1)0()0()0(

3min min

tstd

d

zzDxGxGdxdxps

pd

dE

dcba

ba x x cchcbbBaaAbacmT

XhBA

a b

+→+

→→→

+→+

∑ ∫ ∫= σπ

θσ

2

1

xxz

xxx

bc

ba −

=1

2

xxz

xxx

ac

ab −

=xb = 1zc = 1

zc = 1

yTLE

yTLE

exxxstx

exxxsux−

+

=−=−≡=+=−≡

21

21

2

21

21

1

)(/

)(/

yT

yT

esxsxu

esxsxt+

−

−=−=−=−=

21

1

21

2

212121 ),(

),ˆ(ˆ dxdxz

sdxdx

xx

ztdztd

c

cc =

∂∂= TTT

T

dydxxdydxxy

xxdxdx 2

12121 ),(

),( =∂∂=



QCD PartonQCD Parton--Parton ScatteringParton ScatteringLarge Transverse Meson Production in Hadron-Hadron Collisions

XhBA +→+

2

2

22

)ˆ,ˆ(ˆ

)()ˆ,ˆ(

ˆˆ

tsAs

Qts

td

d dcbasdcba

+→++→+

= πασ

Include All The QCD 2-to-2 Parton-Parton Processes (Order ααααs2)

Parton = quark, anti-quark, & gluon

b A B

h

a

c

d

pT

jijiji qqqq +→+ ≠


iiii qqqq +→+

iiii qqqq +→+

ggqq ii +→+

ii qqgg +→gqgq ii +→+

gqgq ii +→+

gggg +→+

(1)

(2)

(3)

(4)

(5)

QCD effective coupling

(6)

(7)

(8)

(9)



Parton Model ScalingParton Model ScalingQuark-Quark Elastic Scattering

qi qj

qi qj

s

t ̂

^

gluon gs gs =+→+ )ˆ,ˆ( tsA

jiji qqqq

2

222

ˆˆˆ

9

4)(

t

usqqqqA jiji

+

=+→+

Sum over final-state spins and color.Average over initial-state spins and color.

0ˆˆˆ =++ utss

utpT ˆ

ˆˆˆ 2 = spx TT ˆ/ˆ2ˆ = 22 ˆ/4ˆ TT xps=

( )221 ˆ11ˆˆ

Txst −−−= ( )221 ˆ11ˆˆ Txsu −+−=

)ˆ(ˆ

ˆ1

ˆˆ

9

ˆˆˆ

ˆ

ˆˆˆ

9

ˆˆ

ˆˆ

ˆ

ˆˆ

9

ˆ1

2222

2

22

2

2

TTTT xf

s

u

t

ux

t

u

s

u

t

ux

t

us

s

utx =

+

=

+

=+

+

=

+=2

22

2

2

4

2

2

22

2

2

ˆˆˆ

ˆ

ˆˆ

9

ˆ

ˆˆˆˆ

ˆ9

4)ˆ,ˆ(

ˆˆ

t

us

s

utx

pt

us

sts

td

d T

T

ss παπασ

bac x

x

x

xz 21 +=

1

2min

xx

xxx

a

ab −

=

2

1min

1 x

xxa −

=

),(),,(),,(),,( 1

0.1

1

0.1 2)0(

1314

min min

cmT

x

Tba

x c

scbabacmT

XhBA

T xFxxxfz

zxxPdxdxpspd

dEp

a b

θαθσ == ∫ ∫+→+

1

2

xxz

xxx

ac

ab −

=

∑≠

→→→=ji

chqbqBaqAcba zDxGxGzxxPiji

)()()(),,( )0()0()0()0(1

)2/tan(

)2/tan(/

21

2

21

1

cmT

cmT

xx

xx

θθ

==


Constant at fixed θθθθcm and xT!(provided the PDF’s and the fragmentation

functions scale and ααααs is constant)

spx TT /2=



Parton Model ScalingParton Model Scaling

bac x

x

x

xz 21 +=

1

2min

xx

xxx

a

ab −

=

2

1min

1 x

xxa −

=

∑=

+→+

=9

13

4 ),(),,(k

cmTkcmT

XhBAall

T xFpspd

dEp θθσ

1

2

xxz

xxx

ac

ab −

=)2/tan(

)2/tan(/

21

2

21

1

cmT

cmT

xx

xx

θθ

==

k = 1 to 9

= Constant at fixed θθθθcm and xT!(provided the PDF’s and the fragmentation

functions scale and ααααs is constant)



iiii qqqq +→+

iiii qqqq +→+

(1)

(2)

(3)

(4)

ggqq ii +→+


gqgq ii +→+

gggg +→+

(5)

(6)

(7)

(8)

(9)


)ˆ(ˆ

)ˆ,ˆ(ˆˆ

4

2

TkT

sk xfp

tstd

d πασ =

Large Transverse Meson Production in Hadron-Hadron Collisions

spx TT /2=




High High ppTT ππππππππ--Meson ProductionMeson Production

High pT Data 1977

spx TT /2=

pdEd 3/σ

pdEdpT38 /σ

Wxp TT 21=sW=

2.0=Tx

W = 19.4 GeV xT = 0.2cGeVGeVpT /92.1)2.19)(2.0(2

1 ==W = 53 GeV xT = 0.2

cGeVGeVpT /3.5)53)(2.0(21 ==

o90=θ

The FNAL data (open squares) are from J. W. Cronin et al. (CP Collaboration), Phys. Rev. D11(1975); D. Antreasyanet al., Phys. Rev. Letters 38(1977); Phys. Rev. Letters 38(1977).

The FNAL data at W = 19.4 GeV (solid triangles) are from G. Donaldson et al., Phys Rev. Letters 36(1976).

The FNAL data (open circles) are from D. C. Carey et al., Fermilab Report FNAL-PUB-75120-EXP (1975).

The ISR data (solid dots) are from B. Alperet al. (BS Collaboration), Nucl. Phys. B100(1975).

The ISR data (crosses) are from F. W. Busseret al., Nucl. Phys. B106(1976).



High High ppTT ππππππππ--Meson ProductionMeson Production

High pT Data 1977

spx TT /2=

pdEd 3/σ

pdEdpT38 /σ

Wxp TT 21=sW=

2.0=Tx

W = 19.4 GeV xT = 0.2cGeVGeVpT /92.1)2.19)(2.0(2

1 ==W = 53 GeV xT = 0.2

cGeVGeVpT /3.5)53)(2.0(21 ==

o90=θ

The FNAL data (open squares) are from J. W. Cronin et al. (CP Collaboration), Phys. Rev. D11(1975); D. Antreasyanet al., Phys. Rev. Letters 38(1977); Phys. Rev. Letters 38(1977).

The FNAL data at W = 19.4 GeV (solid triangles) are from G. Donaldson et al., Phys Rev. Letters 36(1976).

The FNAL data (open circles) are from D. C. Carey et al., Fermilab Report FNAL-PUB-75120-EXP (1975).

The ISR data (solid dots) are from B. Alperet al. (BS Collaboration), Nucl. Phys. B100(1975).

The ISR data (crosses) are from F. W. Busseret al., Nucl. Phys. B106(1976).

Yikes!! The data is behaving like 1/pT

8 not 1/pT4 at fixed xT.



FF1: BlackFF1: Black--Box ModelBox Model

)ˆ/ˆ(ˆ

)ˆ,ˆ(ˆ

ˆutf

s

Ats

td

dN

BoxBlack

=−σ

)ˆ,̂(ˆ

ˆ1)()()(

1

),,(

,

0.1 0.1)0()0()0(

3

min min

tstd

d

zzDxGxGdxdx

pspd

dE

BoxBlack

ba x x cchcbbBaaAba

cmT

XhBA

a b

−

→→→

+→+

∑ ∫ ∫

=

σπ

θσ

Naïve Parton-Parton Black-Box Model

ts

A

t

s

s

Ats

td

d BoxBlackFF

ˆˆˆˆ

ˆ)ˆ,ˆ(

ˆˆ

3

41

−=

−=

−σ

661 103.2 GeVbAFF ⋅×= µ

),(),,(23 cmTNT

cmT

XhBA

xFp

Aps

pd

dE θθσ =

+→+

),()103.2(

),,(8

66

31

cmTT

cmT

XhBAFF xF

p

GeVbps

pd

dE θµθσ ⋅×=

+→+

FF1 (1977)sdusduba ,,,,,, =



FF1: BlackFF1: Black--Box ModelBox Model

)ˆ/ˆ(ˆ

)ˆ,ˆ(ˆ

ˆutf

s

Ats

td

dN

BoxBlack

=−σ

QCD N = 2FF1 N = 4CIM N = 4

)ˆ,̂(ˆ

ˆ1)()()(

1

),,(

,

0.1 0.1)0()0()0(

3

min min

tstd

d

zzDxGxGdxdx

pspd

dE

BoxBlack

ba x x cchcbbBaaAba

cmT

XhBA

a b

−

→→→

+→+

∑ ∫ ∫

=

σπ

θσ

Naïve Parton-Parton Black-Box Model

ts

A

t

s

s

Ats

td

d BoxBlackFF

ˆˆˆˆ

ˆ)ˆ,ˆ(

ˆˆ

3

41

−=

−=

−σ

661 103.2 GeVbAFF ⋅×= µ

),(),,(23 cmTNT

cmT

XhBA

xFp

Aps

pd

dE θθσ =

+→+

),()103.2(

),,(8

66

31

cmTT

cmT

XhBAFF xF

p

GeVbps

pd

dE θµθσ ⋅×=

+→+

FF1 (1977)sdusduba ,,,,,, =



CIM ModelCIM Model

Proton Proton

ππππ+

ππππ+

u-quark

u-quark

ππππ+

ππππ+

u-quark

u-quark d-quark

Constituent Interchange Model (CIM)

),(1

),,(83 cmTCIMT

cmT

XppCIM xF

pps

pd

dE θθσ π

=+→+

Meson-Quark Scattering

D. Sivers, S. J. Brodsky, and R. Blankenbecler, Phys. Reports 23C, 1 (1976); R. Blankenbecler, S. J. Brodsky, and J. F. Gunion, “The Magnitudes of Large Transverse Momentum Cross Sections”, SLAC-PUB-2057 (1977)

Meson within the proton!



QCD Improved Parton ModelQCD Improved Parton ModelLarge Transverse Meson Production in Hadron-Hadron Collisions

XhBA +→+

2

2

2

)(ˆ

)ˆ,ˆ(ˆ

ˆdcbaA

sts

td

d sdcba

+→+=+→+ πασ

Quark-Quark Elastic Scattering

Include Leading Order QCD 2-to-2 Parton-Parton Processes (Order ααααs

2)

qi qi

qi qi

s

t ̂

^

gluon gs gs

qi

+

qi

qi qi

s

t ^

^

gluon gs gs

qi qj

qi qj

s

t ̂

^

gluon gs gs =+→+ )ˆ,ˆ( tsA

jiji qqqq

=+→+ )ˆ,ˆ( tsAiiii qqqq

2

222

ˆˆˆ

9

4)(

t

usqqqqA jiji

+

=+→+

tu

s

t

us

t

usqqqqA iiii ˆˆ

ˆ

27

8ˆ

ˆˆˆ

ˆˆ

9

4)(

2

2

22

2

222

−

+++

=+→+

qqqq

qqqq

qqqq

+→++→++→+

ggqq

qgqg

qgqg

+→++→++→+

gggg

qqgg

+→++→+

Parton = quark, anti-quark, & gluon

Sum over final-state spins and color.Average over initial-state spins and color.

q A B

h

q

q

q

pT



b A B

h

a

c

d

pT

QCD Improved Parton ModelQCD Improved Parton Model

A+B→h+X

),( 2QxG aDIS

aA→ ),( 2QxG bDIS

bB→

),( 2QzD ceehc

−+

→

abc x

x

x

xz 21 +=

)2/tan(

)2/tan(/

21

2

21

1

cmT

cmT

xx

xx

θθ

==

1

2min

xx

xxx

a

ab −

=2

1min

1 x

xxa −

=

)/,(ˆ

ˆ1),(),(),(

1

),,(

,

0.1 0.1222

3

min min

cbba

dcba

ba x x cc

eehcb

DISbBa

DISaAba

cmT

XhBA

ztxsxxtd

d

zQzDQxGQxGdxdx

pspd

dE

a b

+→+

→→→

+→+

∑ ∫ ∫−+

= σπ

θσ

2

2

22

)ˆ,ˆ(ˆ

)()ˆ,ˆ(

ˆˆ

tsAs

Qts

td

d dcbasdcba

+→++→+

= πασ


Use the “renormalization group improved”PDF’s from DIS and “renormalization group improved” fragmentation functions from e+e-

annihilations and the running QCD coupling!

Q2 dependent PDF’s!

Wpx TT /2=

sEW cm ==

Q2 dependent fragmentation!



b A B

h

a

c

d

pT


A+B→h+X

),( 2QxG aDIS

aA→ ),( 2QxG bDIS

bB→

),( 2QzD ceehc

−+

→

abc x

x

x

xz 21 +=

)2/tan(

)2/tan(/

21

2

21

1

cmT

cmT

xx

xx

θθ

==

1

2min

xx

xxx

a

ab −

=2

1min

1 x

xxa −

=

)/,(ˆ

ˆ1),(),(),(

1

),,(

,

0.1 0.1222

3

min min

cbba

dcba

ba x x cc

eehcb

DISbBa

DISaAba

cmT

XhBA

ztxsxxtd

d

zQzDQxGQxGdxdx

pspd

dE

a b

+→+

→→→

+→+

∑ ∫ ∫−+

= σπ

θσ

2

2

22

)ˆ,ˆ(ˆ

)()ˆ,ˆ(

ˆˆ

tsAs

Qts

td

d dcbasdcba

+→++→+

= πασ




Q2 dependent PDF’s!

Wpx TT /2=

sEW cm ==

Q2 dependent fragmentation!

Renormalization Group Improved Fragmentation! Renormalization Group Improved PDF’s!

Running QCD Effective Coupling!




bac x

x

x

xz 21 +=

1

2min

xx

xxx

a

ab −

=

2

1min

1 x

xxa −

=

∑=

+→+

=9

13

4 ),,(),,(k

cmTkcmT

XhBAall

T psFpspd

dEp θθσ

1

2

xxz

xxx

ac

ab −

=)2/tan(

)2/tan(/

21

2

21

1

cmT

cmT

xx

xx

θθ

==

k = 1 to 9jijiji qqqq +→+ ≠


iiii qqqq +→+

iiii qqqq +→+

(1)

(2)

(3)

(4)

ggqq ii +→+


gqgq ii +→+

gggg +→+

(5)

(6)

(7)

(8)

(9)


)ˆ(ˆ

)()ˆ,ˆ(

ˆˆ

4

22

TkT

sk xfp

Qts

td

d πασ =

Large Transverse Meson Production in Hadron-Hadron Collisions





Possible Choices for the Scale

22 ˆ4 TpQ =

2222

ˆˆˆ

ˆˆˆ2

uts

utsQ

++=


spx TT /2=




� Comparison of a QCD model (normalized absolutely) with data on large pT pion production in proton-proton collisions at W = 19.4 and 53 GeVwith θθθθcm = 90o. The dot-dashed and solid curves are the results before and after smearing, respectively, with ΛΛΛΛ = 0.4 GeV/c and <kT>primordial = 848 MeV/cand the dashed curves are with ΛΛΛΛ = 0.6 GeV/c. The contributions from quark-quark, quark-antiquark, and antiquark-antiquark ( i.e.no gluons) is shown by the dotted curves.

pdEd 3/σ


F1 (1978)

FFF2 (1978)R. D. Field ICHEP78





� Comparison of a QCD model (normalized absolutely) with data on large pT pion production in proton-proton collisions at W = 19.4 and 53 GeVwith θθθθcm = 90o. The dot-dashed and solid curves are the results before and after smearing, respectively, with ΛΛΛΛ = 0.4 GeV/c and <kT>primordial = 848 MeV/cand the dashed curves are with ΛΛΛΛ = 0.6 GeV/c. The contributions from quark-quark, quark-antiquark, and antiquark-antiquark ( i.e.no gluons) is shown by the dotted curves.

pdEd 3/σ


F1 (1978)

FFF2 (1978)R. D. Field ICHEP78


Primordial k T has a big effect at low pT and low W where the cross section is very steep!

Large primordial k T!




� Data on pT4 times Edσσσσ/d3p for large pT pion production at θθθθcm =

90o and fixed xT = 0.2 versus pT compared with the predictions (with absolute normalization) of a model that incorporates all the features expected from QCD. The dot-dashed and solid curves are the results before and after smearing with <kT>primordial = 848 MeV, respectively, with ΛΛΛΛ = 0.4 GeV/c and the dashed curves are the results of using ΛΛΛΛ = 0.6 GeV/c (after smearing). The dotted curve is pT

4(1/pT8).

pdEdpT34 /σ


F1 (1978)R. D. Field ICHEP78






4(1/pT8).

pdEdpT34 /σ

pT4(1/pT

8)








4(1/pT8).

pdEdpT34 /σ

pT4(1/pT

8)

Approaches a constant at large pT!







90o and fixed xT = 0.2, 0.35, and 0.5 versus pT compared with the predictions (with absolute normalization) of a model that incorporates all the features expected from QCD. The dot-dashed and solid curves are the results before and after smearing with <kT>primordial = 848 MeV, respectively, with ΛΛΛΛ = 0.4 GeV/c and the dashed curves are the results of using ΛΛΛΛ = 0.6 GeV/c (after smearing). Recent data from ISR (triangles, open circles) show a deviation from a horizontal straight line (1/pT

8) behavior as expected from QCD.

pdEdpT38 /σ


FFF2 (1978)

R. D. Field ICHEP78





90o and fixed xT = 0.2, 0.35, and 0.5 versus pT compared with the predictions (with absolute normalization) of a model that incorporates all the features expected from QCD. The dot-dashed and solid curves are the results before and after smearing with <kT>primordial = 848 MeV, respectively, with ΛΛΛΛ = 0.4 GeV/c and the dashed curves are the results of using ΛΛΛΛ = 0.6 GeV/c (after smearing). Recent data from ISR (triangles, open circles) show a deviation from a horizontal straight line (1/pT

8) behavior as expected from QCD.

pdEdpT38 /σ


FFF2 (1978) Approaches a pT4

behavior at large pT!R. D. Field ICHEP78

The ISR data (open circles) are from A. G. Clark et al., Phys Letters 74B (1978) 267. Also, talk presented by A. G. Clark at this conference.

The ISR data (triangles) are from CERN-Columbia-Oxford-Rockefeller Experiment (CCOR), reported by L. Di Lellain the Workshop on Future ISR Experiments, September 14-21, 1977.





� The behavior of pT8 times the 90o single ππππ0 cross

section, Edσσσσ/d3p, at xT = 0.05 versus pT calculated from the QCD approach with ΛΛΛΛ = 0.4 GeV/c (solid curves) and ΛΛΛΛ = 0.6 GeV/c (dashed curves). The two low pT data points are at 53 and 63 GeV. The predictions are a factor of 100 (1000) times larger than the flat horizontal (1/pT

8) extrapolation to W = 500 GeV (1000 GeV).

pdEdpT38 /σ


R. FieldICHEP78

R. D. Field ICHEP78

Early QCD Predictions



CDF Run 2 DataCDF Run 2 Data

)/( φσ dyddppd TT

Charged Particle Production

Xhpp +→+ ±

Measurement of Particle Production and Inclusive Differential Cross Sections in Proton-Antiproton Collisions at 1.96 TeV,

CDF Collaboration, Phys. Rev. D79, 112005 (2009)



CDF Run 2 DataCDF Run 2 Data

)/( φσ dyddppd TT

Charged Particle Production

W = 1.96 TeV xT = 0.05

cGeVGeVpT /49)1960)(05.0(21 ==

29 )//(10)/49,05.0(

cGeVmbdyddpp

cGeVpxd

TT

TTh

−≈==±

φσ

φσσσ

ddpyp

d

pyd

d

pd

dE

TTT

==23

67

298

38

)/(1066.1

)//(10)/49)(5.0(

)/49,05.0(0

cGeVb

cGeVmbcGeV

pd

cGeVpxdEp TT

T

⋅×≈

×≈

==

−

µ

σπ

5.00

≈+ −+ hh

π

Xhpp +→+ ±

Measurement of Particle Production and Inclusive Differential Cross Sections in Proton-Antiproton Collisions at 1.96 TeV,

CDF Collaboration, Phys. Rev. D79, 112005 (2009)



R. Field BND 2016R. Field BND 2016



R. Field BND 2016R. Field BND 2016108

50

W = 1960

factor of≈ 10,000

Amazing! I was right!



R. Field Boulder 1979R. Field Boulder 1979

At low xT the dominate QCD sub-process is gluon production which fragments equally into ππππ+ and ππππ-!

ππππ- p

ππππ±

gluon

pT gluon

gluon

gluon

ππππ-+p→ππππ± + X

),( 2QxG aDIS

g→−π),( 2QxG b

DISgp→

),( 2QzD cee

g

−+

±→πCIM versus the QCD Improved Parton Model

Proton

ππππ-

ππππ-

d-quark

d-quark

ππππ-

ππππ-

d-quark

d-quark u-quark

Direct CIM Contribution ππππ-+ d-quark → ππππ- + d-quark

To produce an outgoing ππππ+ in the CIM approach one must find a ππππ+ within the incoming

ππππ- or the incoming proton (with small probability)!



R. Field Boulder 1979R. Field Boulder 1979

At low xT the dominate QCD sub-process is gluon production which fragments equally into ππππ+ and ππππ-!

ππππ- p

ππππ±

gluon

pT gluon

gluon

gluon

ππππ-+p→ππππ± + X

),( 2QxG aDIS

g→−π),( 2QxG b

DISgp→

),( 2QzD cee

g

−+

±→πCIM versus the QCD Improved Parton Model

Proton

ππππ-

ππππ-

d-quark

d-quark

ππππ-

ππππ-

d-quark

d-quark u-quark

Direct CIM Contribution ππππ-+ d-quark → ππππ- + d-quark

To produce an outgoing ππππ+ in the CIM approach one must find a ππππ+ within the incoming

ππππ- or the incoming proton (with small probability)!

The data are from H. J. Frisch, Precise Measurement of the High pT Single Particle Spectra in ππππ-p Collisions at Fermilab

(E258), talk presented at the XIV Moriond Conference (1979)..



b A B

a

c

d

pT

QCD QCD ““ JetJet”” ProductionProductionA+B→c+X

),( 2QxG aDIS

aA→ ),( 2QxG bDIS

bB→

)1(),( 2cc

eehc zQzD −=−+

→ δ

bac x

x

x

xz 21 +=

1

2

xx

xxx

a

ab −

=2

1min

1 x

xxa −

=

)ˆ,̂(ˆ

ˆ1)1(),(),(

1),,(

,

0.1 0.122

3min min

tstd

d

zzQxGQxGdxdxps

pd

dE

dcba

ba x x ccb

DISbBa

DISaAbacmT

XcBA

a b

+→+

→→

+→+

∑ ∫ ∫ −= σδπ

θσ

Large Transverse Momentum Parton Production

2

1

xxz

xxx

bc

ba −

=1

2

xxz

xxx

ac

ab −

=

),(ˆ

ˆ),(),(

1),,(

,

0.122

2

2

3min

txsxxtd

dQxGQxG

x

xdxps

pd

dE bba

dcba

ba x

bDIS

bBaDIS

aAb

acmT

XcBA

a

+→+

→→

+→+

∑ ∫= σπ

θσ


22

bb

c

x

x

dx

dz −=

)ˆ,̂(ˆ

ˆ)1(),(),(

1),,(

,

0.1 0.1

2

222

3min min

tstd

d

zx

xzQxGQxGdzdxps

pd

dE

dcba

ba x z c

bcb

DISbBa

DISaAcacmT

XcBA

a c

+→+

→→

+→+

∑ ∫ ∫ −= σδπ

θσ




� Comparison of the jet and single ππππ0 cross sections measured at 200 GeV (W = 19.4 GeV) and θθθθcm = 90o. The jet data are from two FNAL experiments, E260 and E395, where a jet is defined as the sum of all the particles into their respective detectors.Also shown is the QCD prediction for the cross section of producing a parton (quark, antiquark, or gluon) at W = 19.4 GeV and θθθθcm = 90o.

The FNAL data (E260) are from C. Bromberg et al., Phys Rev Letters 38(1977); C. Bromberg et al., CALT-68-613 (to be published in Nucl. Phys.).

The FNAL data (E395) are from the Fermilab-Lehigh-Pennsylvania-Wisconsin Collaboration, talk given by W. Selove at this conference.


FFF2 (1978)

R. D. Field ICHEP78





� Comparison of the jet and single ππππ0 cross sections measured at 200 GeV (W = 19.4 GeV) and θθθθcm = 90o. The jet data are from two FNAL experiments, E260 and E395, where a jet is defined as the sum of all the particles into their respective detectors.Also shown is the QCD prediction for the cross section of producing a parton (quark, antiquark, or gluon) at W = 19.4 GeV and θθθθcm = 90o.

The FNAL data (E260) are from C. Bromberg et al., Phys Rev Letters 38(1977); C. Bromberg et al., CALT-68-613 (to be published in Nucl. Phys.).

The FNAL data (E395) are from the Fermilab-Lehigh-Pennsylvania-Wisconsin Collaboration, talk given by W. Selove at this conference.


FFF2 (1978)

R. D. Field ICHEP78


6 GeV/c Jets!




� Comparison of the results on the 90o ππππ0 cross section, Edσσσσ/d3p, from the QCD approach with ΛΛΛΛ = 0.4 GeV/c(solid curves) and the quark-quark “black-box” partonmodel of FF1 (dotted curves). Both models agree with the data at W = 53 GeV. The QCD approach results in much larger cross sections than the FF1 model at W = 500 and 1000 GeV. The FF1 results at 1000 GeV (not shown) are only slightly larger than at 500 GeV. Also shown are the cross sections for producing a jet at 90o

(divided by 1000) as predicted by the QCD approach (dashed curves) and the FF1 model (dot-dashed curve)

R. D. Field ICHEP78

Early QCD PredictionsQCD Improved Parton Model




� Comparison of the results on the 90o ππππ0 cross section, Edσσσσ/d3p, from the QCD approach with ΛΛΛΛ = 0.4 GeV/c(solid curves) and the quark-quark “black-box” partonmodel of FF1 (dotted curves). Both models agree with the data at W = 53 GeV. The QCD approach results in much larger cross sections than the FF1 model at W = 500 and 1000 GeV. The FF1 results at 1000 GeV (not shown) are only slightly larger than at 500 GeV. Also shown are the cross sections for producing a jet at 90o

(divided by 1000) as predicted by the QCD approach (dashed curves) and the FF1 model (dot-dashed curve)

R. D. Field ICHEP78

30 GeV/c Jets!

Early QCD PredictionsQCD Improved Parton Model



Boulder 1979Boulder 1979

30 GeV/c Jets!

R. Field Boulder 1979

400 GeV/c Jets!

2 TeV

40 TeV

�The NATO Advanced Institute on Quantum Flavordynamics, Quantum Chromodynamics, and Unified Theories, held at the University of Colorado, Boulder, Colorado, July 9 – 27, 1979.



R. Field BND 2016R. Field BND 2016CDF (2006)

400 GeV/c Jets!

1.96 TeV





400 GeV/c Jets!

1.96 TeV


)/(10)( 2143

GeVbXJetpppd

dE µσ −≈+→

=

pd

dEp

dydp

dT

T3

2

2σπσ




400 GeV/c Jets!

1.96 TeV

27 Years!


2 TeV

)/(10)( 2143

GeVbXJetpppd

dE µσ −≈+→

)/(1051.2)( 52

GeVnbXJetppdydp

d

T

−×≈+→σ

=

pd

dEp

dydp

dT

T3

2

2σπσ




400 GeV/c Jets!

1.96 TeV

27 Years!


2 TeV

)/(10)( 2143

GeVbXJetpppd

dE µσ −≈+→

)/(1051.2)( 52

GeVnbXJetppdydp

d

T

−×≈+→σ

=

pd

dEp

dydp

dT

T3

2

2σπσ

Amazing! I was right!



QCD QCD ““ JetJet”” ProductionProduction

High pT “Jet” Production Today

CMS at the LHC

2,000 GeV/c Jets!




� No evidence against the (perturbative) QCD parton model approach.

� Lots of qualitative support for the approach:� ep→e + X, µp→µ + X, νp→µ- + X.

� pp→µ+µ- + X, pp→π + X, pp→Jet + X.

� e+e-→Jet+Jet + X, νp→µ-+Jet + X.

� The applications of the theory are still quite crude and should be considered as qualitative first quesses.

Rick Field(Plenary talk presented at the XIX International Conference on High Energy Physics, Tokyo, Japan)

The QCD Parton Model Approach – Summary & Conclusions

� Many of the most dramatic and definitive predictions of the theory have not yet been observed experimentally.

� Our knoweledge of what the theory predicts is improving and soon (two years) we should have a more quantative picture (i.e. predictions to say 20% level).

� Care must be taken in using the (perturbative) aspects of the theory only where they apply (i.e. large Q2). There are in many cases large corrections to the asymptotic forms at low Q2 (i.e. 1/Q2 effects, non-perturbative effects) which cannot at present be calculated.

R. D. Field ICHEP78

� This is a very exciting and fun time. We have a theory and it is up to all of us to confirm that it is indeed the correcttheory of strong interactions.




� No evidence against the (perturbative) QCD parton model approach.

� Lots of qualitative support for the approach:� ep→e + X, µp→µ + X, νp→µ- + X.

� pp→µ+µ- + X, pp→π + X, pp→Jet + X.

� e+e-→Jet+Jet + X, νp→µ-+Jet + X.

� The applications of the theory are still quite crude and should be considered as qualitative first quesses.

Rick Field(Plenary talk presented at the XIX International Conference on High Energy Physics, Tokyo, Japan)

The QCD Parton Model Approach – Summary & Conclusions

� Many of the most dramatic and definitive predictions of the theory have not yet been observed experimentally.

� Our knoweledge of what the theory predicts is improving and soon (two years) we should have a more quantative picture (i.e. predictions to say 20% level).

� Care must be taken in using the (perturbative) aspects of the theory only where they apply (i.e. large Q2). There are in many cases large corrections to the asymptotic forms at low Q2 (i.e. 1/Q2 effects, non-perturbative effects) which cannot at present be calculated.

R. D. Field ICHEP78

� This is a very exciting and fun time. We have a theory and it is up to all of us to confirm that it is indeed the correcttheory of strong interactions.

QCD is not just “another theory”. If it is not the correct description of nature,

then it will be quite some time before another candidate theory emerges.

- R. Field, ICHEP78

early experimental tests of qcdrfield/cdf/qcd2_rickfield_9-6-16.pdf · 9/6/2016 · outgoing...

Documents