June 25, 2004 Jianwei Qiu, ISU 1 Introduction to Heavy Quark Production Jianwei Qiu Iowa State University CTEQ Summer School on QCD Analysis and Phenomenology June 22 - 30, 2004 University of Wisconsin, Madison, WI
Dec 30, 2015
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
June 25, 2004 Jianwei Qiu, ISU 2
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
June 25, 2004 Jianwei Qiu, ISU 3
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
June 25, 2004 Jianwei Qiu, ISU 4
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, …
June 25, 2004 Jianwei Qiu, ISU 5
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
June 25, 2004 Jianwei Qiu, ISU 6
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 )
June 25, 2004 Jianwei Qiu, ISU 7
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
June 25, 2004 Jianwei Qiu, ISU 8
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
June 25, 2004 Jianwei Qiu, ISU 9
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
June 25, 2004 Jianwei Qiu, ISU 10
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
June 25, 2004 Jianwei Qiu, ISU 11
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
June 25, 2004 Jianwei Qiu, ISU 12
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
June 25, 2004 Jianwei Qiu, ISU 13
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
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
June 25, 2004 Jianwei Qiu, ISU 14
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
June 25, 2004 Jianwei Qiu, ISU 15
b-quark at Tevatron
We cannot really measure b-quark momentum
June 25, 2004 Jianwei Qiu, ISU 16
b-mesons at Tevatron
Peterson fragmentation functions
More see Ellis’ lecture
Better fragmentation functionCacciari, Nason, PRL 89 (2002)
June 25, 2004 Jianwei Qiu, ISU 17
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)
June 25, 2004 Jianwei Qiu, ISU 18
Hidden heavy flavors - Quarkonia
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
June 25, 2004 Jianwei Qiu, ISU 19
Hidden heavy flavors - Quarkonia
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
June 25, 2004 Jianwei Qiu, ISU 20
Color evaporation model
2
2
42
/ 2
4
/
D
c
m
AB ccAB J cc J cc
ccm
ddmF
dm
June 25, 2004 Jianwei Qiu, ISU 21
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
June 25, 2004 Jianwei Qiu, ISU 22
NRQCD model vs CDF data
June 25, 2004 Jianwei Qiu, ISU 23
June 25, 2004 Jianwei Qiu, ISU 24
Color evaporation model vs data
June 25, 2004 Jianwei Qiu, ISU 25
June 25, 2004 Jianwei Qiu, ISU 26
Difficulties of these models
June 25, 2004 Jianwei Qiu, ISU 27
NRQCD model vs CDF data on polarization
June 25, 2004 Jianwei Qiu, ISU 28
June 25, 2004 Jianwei Qiu, ISU 29
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!