Transcript Document

Anomaly of p over  ratios in
Au+Au collision with jet quenching
Xiaofang Chen
IOPP, CCNU
Collaborator: Enke Wang
Hanzhong Zhang
Benwei Zhang
IOPP
Beijing Mar. 22-24
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Outline
The introduction of single hadron
spectrum in NLO PQCD
The anomaly of p /  and p /  ratios and the
two reasons for that


Summary and discussion
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Jet quenching:
Induced by multiple scattering in QGP medium, a parton
jet will radiate gluon and lose its energy.
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Invariant Cross Sections in pp collision
d
h
pp
dpT2 dy
CTEQ,MRS
Parton distribution function
 K   dxa dxb f a p ( xa , Q 2 ) f b p ( xb , Q 2 )
abcd
d

( ab  cd )
dtˆ
Dh0 c ( d ) ( zc ( d ) , Q 2 )
 zc ( d )
Parton fragmentation function
BKK,KKP,AKK
A factor K=1.5-2 was put
LO (Leading order) :
2→2 processes (tree level)
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A factor K is no longer needed
NLO (Next to Leading Order ) corrections:
One-loop corrections
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2→3 processes (tree level)
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 We use AKK fragmentation function
 Considering the shortage of fragmentation function,we introduce a
phenomenological multiplication factor to the production of proton.
X.F. Zhang and G. Fai, Phys. Rev. Lett. 89, 272301 (2002)
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Invariant Cross Sections in AA collision
Modified parton distribution function
Nuclear thick function
h
d AA
2
2
2
2

K
d
bd
rt
(
r
)
t
r

b

dx
dx
f
(
x
,
Q
,
r
)
f
(
x
,
Q
,r )

A
A
a
b a A
a
b A b
2


dpT dy
abcd


Dh c ( d ) ( zc ( d ) , Q 2 , Ec ( d ) )
d

(ab  cd )
ˆ
dt
 zc ( d )
Modified fragmentation functions
Due to jet quenching
t A (r ) 
3A
1  r 2 R2
2
2 R
Jet quenching in 2
2 and 2→3 processes
Z
 Z
2
2 
f a A ( x, Q , r )  S a / A ( x, r )  f a p ( x , Q )   1   f a n ( x , Q ) 
 A
A

2
S.Y. Li and X.N. Wang , Phys. Lett. B527,85(2002).
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'
z
 L/ c 0
2
D ( z , Q , E )  (1  e
)[ D ( z ' , Q 2 )  L / 
h/c c
c
z h/c c
c
 L/ 0
e
D ( zC , Q 2 )
h/c
Where,
z'
g 0
D
( z ' , Q 2 )]
z h/ g g
c
zc'  pT /( pTc  Ec ), z g'  L /  pT / Ec ,
The energy loss of final parton jet
the averaged scattering number,
L

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0 L

0
d
00
  
 g ( , b , r  n ),
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the gluon density distribution,
   0  0 RA2
 

 g ( , b , r ) 
[t A (r )  t A (| b  r |)],
 2A
In 1-demension expanding medium,
the total energy loss is written as a path integration:
dE
E 
dL
0 L
1d

0
  0
d
 g ( , b , r  n )
 0 0
The energy loss per unit length with detailed balance:
(Enke Wang and Xin-Nian Wang, PRL87 (2001) 142301)
dE
dL
  0 ( E / 0  1.6)1.2 /(7.5  E / 0 )
1d
An energy loss parameter proportional
to the initial gluon density
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 0  0
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h
h
d AA
(bmin , bmax )
dN AA
1
 AA
2
dpT dy  in  bmin , bmax 
dpT2 dy
 (bmin , bmax )   1  e

 inNN TAB ( b )
AB
in
d 2b

Nuclear Modification Factor:
RAB
d AB / dyd 2 pT

Nbinary d NN / dyd 2 pT

Nbin   db dr t A  r  t A r  b
2
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2
RAB  1
No Medium Effect
RAB  1
Medium Effect

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(     ) / 2 production rate is dominated by quark jets at high pT
and by gluon jet at low pT ;while ( p  p ) / 2 production
rate is dominated by gluon jets both in low and high pT .
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Data from STAR collaboration have indicated that p /  and p /  
ratios at high pT in central Au+Au collisions approach
those in p+p and d+Au collisions. These observations indicate that, at
high pT,fragmentation in central Au+Au and p+p events is similar and there
is no evidence of different energy loss for quarks and gluons in the medium.
ATAR Collaboration, J. Adams et al. Phys. Rev. Lett. 97, 152301 (2006)
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In order to differentiate p and p ,we think p come
from gluon and quark, p come from gluon and
antiquark .
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The energy loss is calculated in the state
of equilibrium ,but the QGP may be in non-equilibrium.
Recent studies have shown that elastic scattering of quark and gluon jets
in the QGP also leads to an appreciable loss of their energies.
S. Wicks, W. Horowitz, M. Djordjevic, and M. Gyulassy, Nucl. Phys. A784,426 (2007)
M.G. Mustafa, Phys. Rev. C 72, 014905 (2005)
Another forms of energy loss maybe exist in the process when parton jets
propagate through the QGP medium.
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Different
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p /   and p /   ratios due to equal energy losses of
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gluons and quarks
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Flavor conversion :
Inelastic scattering:
qq  gg
elastic scattering:
q  q  g  gq  q 
Quark and gluon jets traversing through a quark-gluon plasma not
only lose their energy but also can undergo flavor conversion.
X.N. Wang and X. Guo, Nucl. Phys. A696, 788(2001);
B.W. Zhang, X.N. Wang, and A. Schafer,ibid. A783551(2007)
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We find that conversions between quark and gluon jets
indeed lead to an increase in the final number of gluon jets
in central heavy ion collisions than in the case without conversions.
W. Liu , C.M. Ko, and B.W. Zhang PRC75, 051901(2007)
Jet flavor conversions reduce the number
of high transverse momentum quark jets by 30%.
Arxiv: 0801.0453v1 W. Liu and R. J Fries
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Different
p /   and p /  
ratios due to flavor conversion
The AKK fragmentation functions show that gluon fragmentation contribute to
40% of pion production at pT  10Gev while more than 80% of proton are from
gluon fragmentation. (S. Albino,B.A. Kniehl and G. Kramer. Nucl.Phys. B725,181(2005) )
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Summary and discussion
We investigate the consequence if gluons lose the same amount of
energy in QGP as quarks and demonstrate that it will enhance the
p /   and p /  ratios for central Au+Au collision.
We explore the effect of strong jet conversion where a net of
quark-to-gluon conversion also result in similar
ratios
p / 
pand
/ 
in central Au+Au and p+p collisions
The exploration presented here is a phenomenological one and
why the energy losses of quarks and gluons are equal or a strong jet
conversion happened in Au+Au collision still need further intense
theoretical investigate.
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Thank you!