Transcript Document
HEAVY QUARKONIUM
UPSILON
PRODUCTION IN HADRON COLLIDER
Yili Wang
Iowa State University
(in collaboration with E.L. Berger and J. Qiu)
Heavy Quarkonium Workshop
IHEP, Beijing, China, October 12 – 15, 2004
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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Production of heavy quarks and heavy quarkonia
Production Models: CEM, NRQCD, …
CSS b-space resummation formalism
Upsilon production at Tevatron
Conclusions
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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Motivation — New Data in Tevatron
QCD Perturbation Theory is very successful at high pT
New Data from Tevatron test QCD to a new level of accuracy.
pT ~ small, soft gluon radiation
2
dσ
1
Q
2 ln(
)
p 2T
dp 2T
pT
Need to be resumed
to all orders in s
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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Factorization of Hadron Production
fm
PA
Δr ~
1
2m b
0.025 fm
0.025 fm
PB
Heavy quark pairs are produced at
a distance scale much less than fm
σAB YX
ˆ
dx
φ
x
dx
φ
x
σ
a a/A a b b/B b ab YΧ
a,b
Heavy quark pairs are produced locally
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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Quarkonium production:
Q
a
H
b
H
b
Q
Q
a
Q
meson
antimeson
QQ has long life time. is produced at long distance.
A heavy quark pair must coherently self-interact and
expand before a heavy quarkonium is formed
Limit on invariant mass of heavy quark pair m2QQ 4mB2
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:
σˆ ab
ΥΧ
QQ
2
4mB
4m2
Q
dσˆ ab QQ Χ
dmQQ
F QQ
2
dmQQ
2
2
(m
ΥΧ
QQ )
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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Production models:
Different assumptions on F bb ΥΧ (m2bb )
different production models
Color evaporation model (CEM)
All bb pairs with invariant mass less than open bottom
threshold ( mbb mBB ) can become mesons.
Transition probability from bb pair to a meson is
independent of the pair’s color and its invariant mass.
σAB
Υ
Fbb Υ
2
4mB
2
4mb
dmbb
2
dσABbb
dmb2 b
Fqq
Approximation: Fb b Υis a constant.
CΥ
Fbb Υ (m bb )
0
2
m2Y mb2b 4mB2
otherwise
mqq
Independent
of color and spin
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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Non-relativistic QCD (NRQCD) model
All colored and uncolored pre- partonic states
can become color-singlet mesons.
Transition probability is proportional to
non-perturbative local matrix elements.
σAB Υ
bb
bb
σAB bb m
1,8
2
M
bb
1,8
1,8
S0 , S1 , P1
1
3
1
2
Υ
dm
2
bb
2
F bb Υ (m bb )
ˆ
O
b b
Quantum states [ bb ] separated
by spin and color
Fqq
dependent on
color and spin
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
mqq
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Upsilon production at low pT
Fixed-order pT – distribution
αs
dσ
Q 2 2 ) as p2 0
ln(
0
T
pT
dp 2T
p 2T
Events are dominated by low pT region
Initial-state gluon shower plays an important role
Resummed pT – distribution — double logarithms
DL
dσ
dp2T
σ0
αs
Q2 2 ) e
ln(
pT
p2T
2
C αsln2 (Q
)
p2
T
0 as p2T 0
CSS b-space resummation
dσpert dσ asym
dσ
dσresum
2
finite
as
p
0
T
2
2
2
2
dp T
dp T
dp T
dp T
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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CSS b-space resummation formalism
Fourier transformation:
The b-space distribution:
Perturbative b-space distribution (small-b only):
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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Sudakov exponentials:
All process independent terms for A and B are known
Perturbative hard parts:
The C and H depend on the resummation schemes:
Lowest order partonic parts depends on production models (CEM):
4m
2
b
Q2
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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Predictive power
Fourier transformation back to momentum space:
bW(b,Q)
bsp
bmax
Need nonperturbative input for b > bmax
Predictive power depends on the relative area for
b < bmax and b > bmax
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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The b-space distribution
Gluon-gluon dominates the production
Gluon initiated subprocesses should lead to smaller bsp
Dominated by perturbative contribution even at MΥ~10 GeV
Better predictive power for Upsilon production!
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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Upsilon production at Tevatron
CY
Y(1S)
0.044
Y(2S)
0.040
Y(3S)
0.041
p TM
~ 4.27 GeV,
κΥ 1.22 0.02
Phase space determines the
relative production rate for the
different S-states
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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Upsilon production at Tevatron - ll
CDF
S 1.8 TeV
S 1.96 TeV
Run — II
Resummed
Perturbative
Process independent
A and B only
Lowest order
C and H
No-free
parameters
No dependence
on C
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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Conclusions
At collider energies, low pT Upsilon production is
dominated by the resummable part (Sudakov logarithms)
of gluon shower.
Our calculation predicts the right shape for the low pT
spectrum of Upsilon (no –dependence on C).
O α
3
s
calculation is also consistent with high pT data
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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Backup transparencies
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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Matching between resum and pert
Matching:
dσ AB Υ(nS ) Χ
2
dp T dy
dσresum
AB Υ (nS ) Χ
dp
2
T
dy
p T p TM
dσpert
AB Υ (nS ) Χ
dp
2
T
dy
dσ
dp 2T
p T p TM
Avoid pert in low pT region.
e ~ 1 σ ~O α
resummation enhancement factor K
at matching point:
pT
p TM
S
resum
2
s
σ
pert
~ O α
(0)
(0)
(0)
(1) αs
(1) αs
(1) αs
(0)
(0)
C
C
C
C
H
H
KY C(0)
a i
b j
b j
ij
ij
a i Cb j Hij
a i
π
π
π
assuming K is constant
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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3
s
b-space resummation for upsilon
Existing calculation for colorless vector boson
( W, Z ) produced at the short distance.
is unlikely produced at short distance.
heavy bb pair can carry color
Final-state radiation lead to
1
2
pT
IR
NRQCD factorization breaks down as pT 0,
require a non-perturbative “shape-function”
Not resum the gluon radiation from the heavy quark pair
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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A new approach to the large b-region
In small-b region, CSS evolution equation
In large b-region, modified CSS evolution equation,
including leading power corrections,
Leading twist
Intrinsic power
corrections
Dynamical power
corrections
g1 and α are fixed by the continuity of W(b,Q) at
bmax
and have the natural √S-dependence
g2 g2 0
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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Production of heavy quark pairs
o gluon fusion to heavy quarks:
Dominates if 2mQ/√S << 0.1
Massive production channel
o light quark annihilation to heavy quarks:
Dominates if 2mQ/√S >> 0.1
Discovery channel
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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Both models work for S-state
Ψ production as function of PT
prompt
ψ
NRQCD
CEM
Our task: (nS) — S-state
expect small difference between models.
dσ AB Y nS X
dp2T dy
2
4MB
M 2Υ nS
dQ
2
dx φ x
a
a,b
a/A
a
dx b φb/B x b
dσˆ ab bb Q Χ
dQ 2 dp2T dy
FQ 2
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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Location of the saddle point
Using saddle point method:
d
d
~
ln (be S ( b ,Q ) )b b0
ln (WAB (Q, c , x A , xB )) b b0 0
b
db
db
~
If neglecting b-dependence in W , and keeping only
the A(1) term in S(b,Q), at QT = 0
With λ = 16/(49-2nf)
1 QCD
bsp
0.41 for nf = 5
QCD Q
~
b-dependence in W (b, c b , x A , xB ) is very important
d
1 d
~
ln (WAB (Q, c , x A , xB )) [
f g / A ( x A , )]
b
db
b dln
d
Evolution of d ln f ( x, ) is very steep
when x is far from x0 ~ 0.1
Evolution of
at x0 ~ 0.1
d
f ( x, )
d ln
change sign
Since x S , saddle point depends on S .
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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dσ
dp 2T
pT-double logarithms
pT2
Fixed-order
b-space
pT
pT
Yili Wang – Heavy Quarkonium Workshop, IHEP Beijing Oct. 12 - 15, 2004
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