June 25, 2004 Jianwei Qiu, ISU 1 Introduction to Heavy Quark Production Jianwei Qiu Iowa State...

June 25, 2004 Jianwei Qiu, ISU 1

Introduction to Heavy Quark Production

Jianwei QiuIowa State University

CTEQ Summer School onQCD Analysis and Phenomenology

June 22 - 30, 2004University of Wisconsin, Madison, WI


Outline

Summary and outlook

Heavy quarks and heavy quark mesons

How heavy is a heavy quark?

Production of heavy flavors

Hidden heavy flavors - Quarkonia

Heavy quark distribution and intrinsic quark


Six quark flavors in SM

Quark families:

Quark masses:

Quark charges

Quark masses span a wide kinematical range:

Light quarks < GeV

Heavy quarks > GeV

Particle data book


How heavy is a heavy quark?

Heavy quarks are those that we can calculate their production rate perturbatively

A simple criterion:

QCD running coupling constant: Minimum pair production energy required ~ 2mQ

Reliable perturbative calculation in QCD requires

Renormalization scale order of the hard scale

Heavy quark mass > GeV

But, …


No free quarks floating around

QCD color confinement

Mesons and baryons in the detectors

Charmed mesons:

Charmed, strange mesons:

Bottom mesons:

Light quarks and nonperturbative binding are involved

Bottom, charmed mesons:

cc mesons:

bb mesons:

nonperturbative binding is involved

Nonperturbativephysics is alwaysinvolved in charm and bottom quarkproduction


Top quark is a better heavy quark

Charm and bottom quarks decay slowly and leave enough time to form charm and bottom mesons

Top quark decays very fast, likely before any top meson can be formed

Top quark should be a better candidate for studying heavy quark production, and heavy quark properties

Much more in Tim Tait’s lecture

mc and mb << MWCharm and bottom decay via a virtual W into light qq or ℓ

Semi-leptonic decay width: MeV

mt > MW + mb

t → W+ + b→ ℓ+ + or q + q )


Production of heavy flavors

Heavy flavor creation:

Heavy flavor is produced in a hard collision, and No heavy flavor in the initial-state

Heavy flavor excitation:

Hard collision librates (or excites) the Initial-state (or intrinsic) heavy flavor contents Q

Double counting:

Requires heavy flavor parton distributions

A part of the heavy flavor creation was includedIn the evolution of the heavy flavor distributions

Only relevant when energy exchange is much larger than heavy quark masses


Heavy flavor creation (pair production)

e+e- annihilation:

Lepton-hadron collision:

No machine had enough energy to produce the top/anti-top pairs

If the exchange energy is not too much larger than heavy quark masses,we are able to calculate productionrate with a set of the fixed flavor parton distributions without introducingthe heavy flavor parton distributions

No machine had enough energy to produce the top/anti-top pairs


Heavy flavor creation (pair production)

Hadron-hadron collision:

Dominates if 2mQ/√S >> 0.1

/

,/a A b BAB

a b

ab QQ

Discovery channel

light quark annihilation to heavy quarks:

gluon fusion to heavy quarks:

Dominates if 2mQ/√S << 0.1

Massive production channel


2 22242ˆ 1

9 3

41

ˆˆ ˆQ Qs

qq QQ

m

s ss

m

Lowest order pair productionLight quark annihilation: k1

p2 k2

p1

Partonic cross section:

22

ˆ 1ˆ ˆ16

| |q

Q

q

qq Q

d

dt sM

42 12 2

1 2

4 2 2 2 2 22

2 2 1 1Tr

ˆ9 2

Tr

2 2 ˆ ˆ ˆ = ( ) ( ) 2ˆ9

| |

Q Q

Q

q QQ

Q

q

Q

g p ps

k m k m

g m t m u m ss

M

21 2

21 1

22 1

ˆ ( )

ˆ ( )

ˆ ( )

s p p

t p k

u p k

Threshold constraint

/ 1 / 2

,

( ) ( )a A b BABa

b QQ

b

ax x

1 2

2

1 21 2ˆ , , , A B A Bs S p P p P S Px x x x P More see Ellis’ lecture


From heavy quark to heavy meson

Heavy quark fragmentation is different

2Tdk2

Tdk

2003 CTEQ SS - Cacciari

Massless limit Normal DGLAP

Heavy quark mass

Suppress radiation in acone of Θ < mQ/E

Dead cone effectNo collinear divergence


Consequences of the dead cone effect

Heavy quark mass cuts off the collinear divergence:

Heavy quark cross section are finite in fixed order pQCD

Large logarithmic high order corrections:

Collinear logs:

Soft logs:

2ˆln ( / )nQ

ns s m

2 1ln (1 )

1s

nn x

x

Resummation can improve the predictions for the production rate of heavy quarks

For production of charm and bottom hadrons, there is a need for non-perturbative fragmentation functions


Heavy quark fragmentation functions

A fast moving heavy quark of momentum P fragmentsinto a heavy hadron H=Qq of momentum zP:

Energy difference before and after the fragmentaton

Peterson function:

2 2

1 1 11 ( ) 1

1QH

Q H Q HH

ND z dz D z

z z z z E

Normalization condition

22 2 2 2 2 2 2

2 2

2

1

1 1

2 1

Q H q Q H q

QQ

Q q

Q

E E E E m P m z P m z P

m m

P z z m

Treated as a free parameter

This is just one of many possible models!

zP


Extraction of fragmentation functions

Heavy quarks in e+e- collisions:

ALEPH analysis (Phys. Lett. B512, 30 (2001)

BB

beam

Ex

E

1z z as well asthe others


b-quark at Tevatron

We cannot really measure b-quark momentum


b-mesons at Tevatron

Peterson fragmentation functions

More see Ellis’ lecture

Better fragmentation functionCacciari, Nason, PRL 89 (2002)


Heavy quark parton distributions Heavy flavor excitation:

Subtraction scheme to avoid double counting:

Total heavy quark cross section:

+ -

Heavy quark mass dependence here should be Consistent with DGLAP

Aivazis et alPhys. Rev. D50,3102 (1994)



Heavy quark pairs are produced locally:

A heavy quark pair is likely to become two open flavor heavy mesons if the invariant mass of the pair is larger than the total mass of the two mesons:

1 (for a charm-quark pair)

2

0.1 fm

0.025 fm (for a b-quark pair)

Q

rm

Heavy quark pairs areproduced at a distancescale much less than fm

A heavy quark pair needs to be coherently self-interacted and expanded before a heavy quarkonium can be formed

Q

Q

HA

B

meson

antimeson

Open flavor thresholdfor the quarkonium production



Quarkonium production:

( )2 2( )2

AB QQAB h QQ QQ h QQ

Q

states

statesstates Q

ddm F m

dm

Q

QH h

A

B

Production models:

Different assumptions on the non-perturbative transitionfrom the QQ pair to a quarkonium lead to different productionmodels

With2 not too much larger than mass of two heavy flavor mesonsQQm

maximum heavy quark velocity in QQ rest frame:

Charm: Bottom:22 2 1.87

11.4

0.89Q D c

Q c

v m

mc

k m

m

0.62v

c

Depend on choice of heavy quark mass


Color evaporation model

2

2

42

/ 2

4

/

D

c

m

AB ccAB J cc J cc

ccm

ddmF

dm


Non-relativistic QCD (NRQCD) model

2/ / [ ] /

[/

]

(0)AB J J AB O cc JO

JM m OM

Quantum states [O] separated by spin and color


NRQCD model vs CDF data


Color evaporation model vs data


Difficulties of these models


NRQCD model vs CDF data on polarization


Summary and outlook

Top quark is the only “true” heavy quark

Non-perturbative information are very important for understanding production of charm and bottom quarks from corresponding mesons

Need better information on heavy quark fragmentation functions

Need better understanding of heavy quarkonium production

See Lectures by Dr. Ellis and Dr. LeCompte in this school!

June 25, 2004 Jianwei Qiu, ISU 1 Introduction to Heavy Quark Production Jianwei Qiu Iowa State...

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