Steffen A. Bass Dynamics of Hadronization #1 Steffen A. Bass Duke University & RIKEN-BNL Research Center • The baryon puzzle at RHIC • Recombination + Fragmentation Model • Results and Predictions Dynamics of Hadronization: Interplay of Fragmentation and Recombination R.J. Fries, C. Nonaka, B. Mueller & S.A. Bass, PRL 90 202303 (2003) R.J. Fries, C. Nonaka, B. Mueller & S.A. Bass, PRC 68 044902 (2003)
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Steffen A. BassDynamics of Hadronization #1 Steffen A. Bass Duke University & RIKEN-BNL Research Center The baryon puzzle at RHIC Recombination + Fragmentation.
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Steffen A. Bass Dynamics of Hadronization #1
Steffen A. Bass
Duke University& RIKEN-BNL Research Center
• The baryon puzzle at RHIC• Recombination + Fragmentation Model• Results and Predictions
Dynamics of Hadronization: Interplay of Fragmentation and
Recombination
Dynamics of Hadronization: Interplay of Fragmentation and
Recombination
R.J. Fries, C. Nonaka, B. Mueller & S.A. Bass, PRL 90 202303 (2003) R.J. Fries, C. Nonaka, B. Mueller & S.A. Bass, PRC 68 044902 (2003)
Steffen A. Bass Dynamics of Hadronization #2
The baryon puzzle @ RHIC
The baryon puzzle @ RHIC• where does the large proton over pion ratio at high pt come from?
• why do protons not exhibit the same suppression as pions? fragmentation yields Np/Nπ<<1 fragmentation starts with a single fast parton: energy loss affects pions and protons in the same way!
ratio of KKP fragmentation functions for p and π from u quarks
Steffen A. Bass Dynamics of Hadronization #3
Species dependent saturation of elliptic flow
Species dependent saturation of elliptic flow
• hyperon v2 saturates later and higher than kaon v2.
• same effect observed for protons and pions.
• at low pT the phenomenology seems better described in mT – m0 than pT , indicating hydro scaling, yet scaling breaks down for high pT
• what drives the different pT scales for KS and Λ v2?
novel mechanism of baryon formation?
Steffen A. Bass Dynamics of Hadronization #4
Recombination+Fragmentation Model
Recombination+Fragmentation Model
basic assumptions:• at low pt, the quarks and antiquark spectrum is
thermal and they recombine into hadrons locally “at an instant”:
features of the parton spectrum are shifted to higher pt in the hadron spectrum
• at high pt, the parton spectrum is given by a pQCD power law, partons suffer jet energy loss and hadrons are formed via fragmentation of quarks and gluons
qq M qqq B
Steffen A. Bass Dynamics of Hadronization #5
Recombination: Pro’s & Con’s
Recombination: Pro’s & Con’s
Pro’s:• for exponential parton spectrum, recombination is more effective than fragmentation• baryons are shifted to higher pt than mesons, for same quark distribution understand behavior of protons!Con’s:
• simple recombination violates entropy conservation• gluons at hadronization need to be converted
recombining partons:p1+p2=ph
fragmenting parton:ph = z p, z<1
Steffen A. Bass Dynamics of Hadronization #6
Recombination: new life for an old idea
Recombination: new life for an old idea
High Energy Physics Phenomenology:• K.P. Das & R.C. Hwa, Phys. Lett. B68, 459 (1977)
Quark-Antiquark Recombination in the Fragmentation Region description of leading particle effect• T. Ochiai, Prog. Theo. Phys. 75, 1184 (1986)• E. Braaten, Y. Jia & T. Mehen, Phys. Rev. Lett. 89, 122002 (2002)• R. Rapp & E.V. Shuryak, Phys. Rev. D67, 074036 (2003)
Heavy-Ion Phenomenology:• T. S. Biro, P. Levai & J. Zimanyi, Phys. Lett. B347, 6 (1995)
ALCOR: a dynamical model for hadronization yields and ratios via counting of constituent quarks• R.C. Hwa & C.B. Yang, Phys. Rev. C66, 025205 (2002) • R. Fries, B. Mueller, C. Nonaka & S.A. Bass, Phys. Rev. Lett. 90• V. Greco, C.M. Ko and P. Levai, Phys. Rev. Lett. 90
Anisotropic flow:• S. Voloshin, QM2002, nucl-ex/020014• Z.W. Lin & C.M. Ko, Phys. Rev. Lett 89, 202302 (2002)• D. Molnar & S. Voloshin, nucl-th/0302014
Steffen A. Bass Dynamics of Hadronization #7
Recombination: nonrelativistic formalism
Recombination: nonrelativistic formalism
3
3 31 12 2
212
3
2
3
2
(2 ) (2 )
21
(
ˆ ( )
2 )
MM
M
MM
dN V d qC w P q w P q
d P
VC
PP
Tw
q
• use thermal quark spectrum given by: w(p) = exp(-p/T)
• for a Gaussian meson wave function with momentum width ΛM, the meson spectrum is obtained as:
• similarly for baryons:
313
23 3
1 ( / )(2 )
BB Bw
dN VC O TP
d PP
Steffen A. Bass Dynamics of Hadronization #8
Recombination vs. Fragmentation
Recombination vs. Fragmentation
1h 1
h3 3 20
( , ) ( )(2 ) z
dN P u dzE d w R P D zd P z
Fragmentation…
frag bdN P rec 2bdN P
… but it wins out at large pT, when the spectrum is a power law ~ (pT)-b :
… never competes with recombination for a thermal (exponential) spectrum:
/ ex expp( / ) ( / ) /n
w P n P u T P u zT w P z
Steffen A. Bass Dynamics of Hadronization #9
Hadron Spectra Hadron Spectra
Steffen A. Bass Dynamics of Hadronization #10
Hadron Ratios vs. pt
Hadron Ratios vs. pt
Steffen A. Bass Dynamics of Hadronization #11
Flavor Dependence of high-pt Suppression
Flavor Dependence of high-pt Suppression
•R+F model describes different RAA behavior of protons and pions
•in the fragmentation region all hadron flavors exhibit jet-quenching
Steffen A. Bass Dynamics of Hadronization #12
• anisotropic or “elliptic” flow is sensitive to initial geometry
Elliptic FlowElliptic Flow
more flow in collision plane than perpendicular to it
Force P
less absorption in collision plane than perpendicular to it
E L
low pt domain: high pt domain:
r fecomb g222ra1t t ttt v pv r p v pr pp
•total elliptic flow is the sum of both contributions:
r(pt): relative weight of the fragmentation contribution in spectra
Steffen A. Bass Dynamics of Hadronization #13
2
2
2 2
3
2 2
2 2
2
2
2
3
2
1 2
and
1 6
33
3
3
p t
p t
p pt t
p t
M
Bt
t
pv
pv
p p
v p
p
v
pv
v
v
Parton Number Scaling of v2Parton Number Scaling of v2
• Recombination approach allows for two particle correlations, provided they are contained in the parton source distributions
• Three distinct types are conceivable: F-F, SH-F and SS-SS
• Ansatz for SS-SS: for two mesons, use product of correlated parton distributions:
Which results in a correlated two hadron yield:
21234 1 3 4 1 iji j
wW w Cw w
1234
6
3 3 A A BBA
BA
B
ABC d
dd
N
d P d PW
Steffen A. Bass Dynamics of Hadronization #15
Summary & Outlook
Summary & Outlook
The Recombination + Fragmentation Model:• provides a natural solution to the baryon puzzle at RHIC
• describes the intermediate and high pt range of hadron ratios & spectra jet-quenching phenomena elliptic flow leading / next-to-leading particle correlations
• provides a microscopic basis for the Statistical Model
issues to be addressed in the future:• entropy production• treatment of gluons• realistic space-time dynamics of parton source• need improved data of identified hadrons at high pt
Steffen A. Bass Dynamics of Hadronization #16
The End
Steffen A. Bass Dynamics of Hadronization #17
transv
ers
e m
om
entu
m p
t
time
Connecting the dots …
Connecting the dots …
initial state
pre-equilibrium
QGP andhydrodynamic expansion
hadronization
hadronic phaseand freeze-out
shattered
color-glas
jetproductio
n
hydrodynamicevolution
jetquenching
partonrecombination
fragmentation
reco/SM?radialflow
HBT?!
Steffen A. Bass Dynamics of Hadronization #18
Parton Number Scaling of Elliptic Flow
Parton Number Scaling of Elliptic Flow
•in the recombination regime, meson and baryon v2 can be obtained from the parton v2 in the following way:
3
2
2
2
2
2 2
2
2
2
3 322
1
an
2
d
3
12
3
63
p pt tp t
Mt
p pt t
Bt
p pp v vv
p pv
p pv v
v
neglecting quadratic and cubic terms, one finds a simple scaling law: