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
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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 
dmQQ  
  F QQ  
2
 dmQQ  
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 (m2bb )
 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
dσABbb
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
FQ 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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