pdf file - Yale University

Transcription

Using Identified Particles to study
p+p Collisions at 200 GeV
Helen Caines - Yale University
Joint Workshop on Energy
Scaling of Hadron Collisions
Fermi Lab
April 27th - 29th 2009
Outline
• Why study p+p
• How PID is done
• Min-bias distributions
• Jets
• Summary
Modeling a collision - pQCD ansatz
Assume that the calculation is factorizable
Parton Distribution Function
(non-pert.)
LO parton processes
Fragmentation Function
(non-pert.)
Pions
K factor
NLO parton processes
RHIC
BKK, Phys Rev D (1995)
Helen Caines – Yale University
2
Modeling a collision - pQCD ansatz
Assume that the calculation is factorizable
Parton Distribution Function
(non-pert.)
LO parton processes
Fragmentation Function
(non-pert.)
Pions
K factor
NLO parton processes
RHIC
BKK, Phys Rev D (1995)
p+p collisions “messy”
Not all energy involved in the collision
2
Quark and gluon FF and PDFs
 Experimental data from different collisions systems have been fit with the
same fragmentation function (FF)
 The constraints on Gluon FF and PDF are much worse
Fragmentation function for Quarks
Fragmentation function for Gluons
Curves scaled by 1/100
ALEPH
all
uds-quark
b-quark
c-quark
OPAL
OPAL √s=91.2 GeV
KKP, Nucl.Phys.B582(2000)
AKK, Nucl.Phys.B725(2005)
3-jet events
3
Quark and gluon FF and PDFs
 Experimental data from different collisions systems have been fit with the
same fragmentation function (FF)
 The constraints on Gluon FF and PDF are much worse
Parton
Dist function
for Gluons
Fragmentation
function
for Quarks
Fragmentation function for Gluons
Curves scaled by 1/100
CTEQ6
ALEPH
CTEQ5
all
uds-quark
b-quark
c-quark
OPAL
OPAL √s=91.2 GeV
KKP, Nucl.Phys.B582(2000)
AKK, Nucl.Phys.B725(2005)
3-jet events
3
Uncertainties on the FF parameterization
Recent compilation and error analysis of available fragmentation functions by
(KKP,Kretzer, AKK) by Hirai et al. from e+e- data
K
π
p
1.5
gluon
1
2
2
Q = 2 GeV
0.5
0
KKP
AKK
-0.5
1.5
zD(!++!-)/2 (z)

HKNS
Kretzer
1.5
s quark
u quark
1
2
1
2
Q = 2 GeV
0.5
0.5
0
0
-0.5
1.5
-0.5
1.5
2
c quark
1
0.5
0.5
0
0
-0.5
0
0.2
0.4
0.6
z
0.8
b quark
1
Q2 = 10 GeV2
1
-0.5
2
Q = 2 GeV
2
2
Q = 100 GeV
0
0.2
0.4
0.6
0.8
1
z
Large uncertainties at low Q2
Different parameterizations give different fits
G. 13: (Color online) The NLO fragmentation functions
−
+
r the pion, z(Diπ + Diπ )/2, are compared with other

rametrizations
at Q2 =2 GeV2 , 10 GeV2 , and 100 GeV2 .
he solid, dashed, dash-dotted, and dotted curves indicate
KNS, KKP, AKK, and Kretzer parametrizations, respecvely, in the NLO MS scheme. The HKNS uncertainty bands
e shown by the shaded areas.
HKNS, PRD 75 (2007)
Need better constraints
4
RHIC: √s=200 GeV p+p
 Polarized p+p collisions at RHIC are used to investigate the spin
structure of the proton
 Unpolarized measurements are a crucial part of the RHIC program
 Inclusive hadron and jet cross section
measurements at RHIC add new results
to existing data from other accelerators
at different energies
√s=200 GeV
 Constrain fragmentation functions:
 Fits currently dominated by e+e- data
 Still large uncertainties, especially in
the gluon fragmentation functions
Significant contribution from gluons
in the RHIC regime
De Florian,Vogelsang, hep-ph 0704.1677
5
Baryons and mesons at RHIC
Contribution factor: Ng(i)/ (Ng(i) + Nq(i)); i = π, K, p…
At pT = 8 GeV/c: 50% for π
90% for p
AKK, NPB 725 (2005)
B. Mohanty(STAR), nucl-ex/0705.9053
6
Baryons and mesons at RHIC
Contribution factor: Ng(i)/ (Ng(i) + Nq(i)); i = π, K, p…
At pT = 8 GeV/c: 50% for π
90% for p
CTEQ6M PDF
AKK, NPB 725 (2005)
B. Mohanty(STAR), nucl-ex/0705.9053
Gluon jet contribution to baryon >> meson at high pT
6
Quark and gluon jets
Extensive studies into jet
properties have been done with
e+e- data
 Gluon jets fragmentation:
 produces higher multiplicities
7
e+e- data
 produces harder pT spectra
7
e+e- data
 produces harder pT spectra
 In p+p study:
 particle vs anti-particle
 different species
Vary gluon vs quark sensitivities:
constrain theory further
7
The STAR experiment at RHIC
 TPC and ToF: charged
particle contribution
 EMCal: neutral energy
contribution
Minbias:
Beam-Beam-Counter (BBC)
coincidence
High Tower:
BBC coincidence + one tower
(η x φ =0.05x0.05) above
threshold: ET >5.4 GeV
Jet-Patch:
BBC coincidence + EMCal JetPatch (Δη x Δφ = 1x1 above
threshold ET > 8 GeV)
8
The STAR experiment at RHIC
 TPC and ToF: charged
particle contribution
 EMCal: neutral energy
contribution
Minbias:
Beam-Beam-Counter (BBC)
coincidence
High Tower:
BBC coincidence + one tower
(η x φ =0.05x0.05) above
threshold: ET >5.4 GeV
High tower and Jet-Patch triggers
→ NEF FF bias → for jet studies
use non-triggered side
Jet-Patch:
BBC coincidence + EMCal JetPatch (Δη x Δφ = 1x1 above
threshold ET > 8 GeV)
8
Detectors used :
Time projection Chamber
(|η|<1.8, full φ and 4.2 m long)
Time-Of-Flight (–1.0 < η < 0
and π/30 in φ)
Efficiency high and ~const at hight pT
Log10(dE/dx)
Particle identification: stable particles
Low pT : Particle identification by
dE/dx and ToF ( pT < 2.5 GeV/c)
Log10(p)
High pT : Extend particle identification in
TPC by exploiting the relativistic rise in
ionization energy loss.
π, p separation up to p~10GeV/c
9
Particle Identification - weak decays
 Use charged decay channels to
identify secondary vertex
K0S → π- + π+
Λ →p +π-
Ξ- → π- + Λ
Ω- → K-+ Λ
 Invariant mass to identify parent
 Clean signals over large
kinematical range,
0.5<pT<10 GeV/c - limit statistics
 Low efficiency
K0s
10
Particle/Anti-particle ratios
STAR, Phys Lett B, 637 (2006) 161
STAR, PRC 75 (2007)
PYTHIA predicts:
 flat pT dependence for π−/π+
 slightly more prominent pT dependence for p/p
 even stronger dependence for Λ/Λ
Good agreement with current data
Data is consistent with gluon jet dominated production
- but does not allow strong conclusion
11
π cross-section - sensitivity to FF
 pT reach to 15 GeV/c
 NLO pQCD calculations
(factorization scale µ = pt) with
different fragmentation functions
AKK, PLB 725 (2005)
π
Kretzer vs
KKP
Phenix π0
AKK vs KKP
RHIC data now sufficiently precise to
be sensitive to different FF
Simon, SPIN2006,hep-ex/0612004
S. Kretzer, PRD 62 (2000)
12
π0 production at forward rapidity
Looking forward to probe the initial
gluon densities
 Inclusive forward π0 production in p
+p collisions at 200 GeV also
consistent with NLO pQCD
calculations
 Small η:
 data consistent with KKP
 Increasing η:
 data approaches cal. with
Kretzer set of FF
STAR, Phys.Rev.Lett.97,152302 (2006)
No one FF describes all data
13
(anti)proton cross-section
Baryons notoriously difficult to fit: limited knowledge of FF
Albino, Kramer, Kniehl
(AKK):
 use latest OPAL data to calculate
light flavor (u,d,s) separated
fragmentation functions for the first
time
AKK (arXiv:0803.2768)
_
 use BRAHMS p/p ratio as constraint
(y=2.95, pT<5GeV/c)
Z.Xu, QM 2008
(Phys. Rev. Lett. 98, 252001 (2007))
With improved FF baryon - data and theory in good agreement
14
Contributions from gluon vs. quark jet
Look closer at AKK calculation
 Compare:
Gluon contribution to cross-section
Total cross-section
• Should see affect for π
15
Contributions from gluon vs. quark jet
Look closer at AKK calculation
 Compare:
Gluon contribution to cross-section
Total cross-section
• Should see affect for π
At RHIC:
Protons dominated by gluon FF
π need both quark contribution
15
NLO calculations for strange particles
 First NLO predictions for RHIC energies K0s and Λ by W.Vogelsang (RIKEN)
K0s OK but Λ poor
 AKK (2005) NLO for K0s and Λ - better agreement:

constrained shape of Gluon FF to DgΛ = DgP/3
 constrained magnitude using by STAR data

KKP (2003) vs
AKK (2006)
DSV (WV) PRD57 (1998)
STAR, PRC 75 (2007)
16
Kaon FF at forward rapidities
STAR: K0s - mid rapidity
BRAHMS: K+/- - forward rapidity
DSS, PRD76 (2007)
Good description of kaons over large rapidity range
17
Extrapolating FF at higher energies
Fit to 200 GeV (STAR RHIC) and extrapolate to 630 GeV (UA1 SPS)
AKK Lines are for µ=2*pT, pT, pT/2
PLB 725 (2005), PLB 734 (2006)
 Gluon constrained fit for Λ gives
good extrapolation
Λ
UA1 (630GeV)
STAR (200GeV)
 AKK better fit to Λ
 KKP better fit to K
18
Extrapolating FF at higher energies
Fit to 200 GeV (STAR RHIC) and extrapolate to 630 GeV (UA1 SPS)
AKK Lines are for µ=2*pT, pT, pT/2
PLB 725 (2005), PLB 734 (2006)
 Gluon constrained fit for Λ gives
good extrapolation
Λ
K0s
UA1 (630GeV)
UA1 (630GeV)
STAR (200GeV)
STAR (200GeV)
 AKK better fit to Λ
 KKP better fit to K
Something still missing in strange hadron description
18
PYTHIA description of strange pT-spectra
 PYTHIA Version 6.3
 Incorporated parameter tunes from CDF
 New multiple scattering and shower algorithms
 Fails to describe baryons with default parameters
19
PYTHIA description of strange pT-spectra
 PYTHIA Version 6.3
 Incorporated parameter tunes from CDF
 New multiple scattering and shower algorithms
 Fails to describe baryons with default parameters
Necessary to tune: K-Factor (accounts for NLO contribution)
19
What about strange resonances ?
•
Compare PYTHIA 6.3 to published STAR data on φ, K*, Σ* (baryon resonance)
PYTHIA 6.3
PYTHIA 6.3
PYTHIA 6.3
PYTHIA 6.3,K=3
PYTHIA 6.3,K=3
PYTHIA 6.3,K=3
Resonance data also need K=3 for good description
20
K-factor in LO pQCD
How is the K-factor defined?
STAR
 Two definitions:
Kobs= σexp / σLO
Kth= σNLO / σLO
 Flavor dependence of K-factor,
differing NLO contributions ?
 For h- it decreases for collision
energy
•contribution
of NLO processes
smaller at higher energies
Eskola et al Nucl. Phys A 713 (2003)
K factor of 3 not unreasonable
21
What about non-strange particles ?
 Good agreement for π with K=1 but not for K=3
 proton with 1< K <3
• However only lower pT region measured
Need different K factors for different particles!
22
Baryon-meson ratios


Gluon jets produce a larger Baryon/Meson ratio than quark-jets
Cannot describe Baryon-Meson ratio at intermediate pT even
with tuned K-factors and/or di-quarks
STAR, Phys Lett B, 637 (2006) 161
√s=200 GeV
Our “tuned” PYTHIA under predicts B/M ratio at 200 and 630 GeV
also fails for p/π at ISR and FNAL: 19-53 GeV (not shown)
23
Baryon-meson ratios


Gluon jets produce a larger Baryon/Meson ratio than quark-jets
Cannot describe Baryon-Meson ratio at intermediate pT even
with tuned K-factors and/or di-quarks
STAR, Phys Lett B, 637 (2006) 161
UA1
√s=630 GeV
√s=200 GeV
Our “tuned” PYTHIA under predicts B/M ratio at 200 and 630 GeV
also fails for p/π at ISR and FNAL: 19-53 GeV (not shown)
23
Baryon-meson ratios
p/π
 Levai et al. discuss importance of RHIC p+p data for large-z part of FF
 Argue that kT smearing maybe a cause of poor agreement
→ assign a larger <kT> to proton than π
√s=27.4 GeV
Modified <kT>
Modified FF
p/π
Default
√s=62 GeV
pQCD 62 GeV
pQCD 130 GeV prediction
PRL 97, 152301 (2006) & Z.Xu, QM2008 (p+p Preliminary)
Fai, Levai & Zhang, PRL 89(2002)
24
<pT> vs particle mass
Measured particle spectra over large mass range

Mass dependence, but donʼt
expect flow in p+p (see Mike
on Wed)

Nice agreement with
phenomenological curve
established by ISR (23 GeV)
for lower masses

Strange baryons and
resonances are above the
curve
Bourquin and Gaillard
Nucl. Phys. B 114 (1976)
Linear dependence seems a better description at mid-rapidity
25
xT-scaling
xT = 2pT/√s
Works well in e+eat higher xT
π
K
p
Cross-section are multiplied
by (√sNN )2 factor
TPC, PRL 61(1988)
ALEPH,ZPC66(1995)
ARGUS,ZPC44(1989)
26
xT-scaling
xT = 2pT/√s
Works well in e+eat higher xT
p+p or p+p collisions
π
n~6.5
K
p
STAR, Phys Lett B, 637 (2006) 161
Cross-section are multiplied
by (√sNN )2 factor
TPC, PRL 61(1988)
ALEPH,ZPC66(1995)
ARGUS,ZPC44(1989)
n ~ 4 for basic scattering process
n ~ 5-8 depending on evolution of structure function and
fragmentation function (as seen in data)
Suggests transition from soft/hard processes ~pT=2 GeV/c
26
mT scaling of identified particles
 First studied at ISR - In Color Glass Condensate (CGC) picture mT-scaling
would be indicative of evidence of gluon saturation
 No absolute scaling (data shown are arbitrarily normalized)
 Baryon meson splitting above mT ~2 GeV/c
Scaled arbitrarily
STAR, PRC 75 (2007)
27
Scaled arbitrarily
PYTHIA 6.3
STAR, PRC 75 (2007)
PYTHIA and data show similar trends
27
Scaled arbitrarily
PYTHIA 6.3
STAR, PRC 75 (2007)
PYTHIA and data show similar trends - comes from gluon jets
27
K factor - charged multiplicity distribution
STAR prelim.
data
PYTHIA
6.3
STAR prelim.
data
PYTHIA 6.3,
K=3
 PYTHIA + simulated trigger and detector acceptance.
Probability of high multiplicity events very
sensitive to NLO corrections
28
Quick aside about Nch measurements
 How to define Multiplicity ?
Definition of Nch experiment dependent
(pseudo-rapidity acceptance coverage, correction factors)
29
PYTHIA <pT> vs Nch

More sensitive observable to compare models to (mini-jet and/or
multiple interaction implementations in models)
K factor tuned PYTHIA seems to do reasonable job for strange hadrons
30
PYTHIA <pT> vs Nch

More sensitive observable to compare models to (mini-jet and/or
multiple interaction implementations in models)

K-factor accounts for increase of <pT> with charged multiplicity
K factor tuned PYTHIA seems to do reasonable job for strange hadrons
30
Mini-jet production in p+p
Mini-jet - “Hardish” parton interaction (included in PYTHIA and HIJING)
 jets occur in higher multiplicity events

produce higher pT final states

measure higher <pT>
<pT>

Njet=2
Nch
XN.Wang et al (Phys Rev D45, 1992)
dNch/dη
Evidence of jet production in high mult. events
31
Mini-jet production in p+p
Mini-jet - “Hardish” parton interaction (included in PYTHIA and HIJING)
 jets occur in higher multiplicity events

produce higher pT final states

measure higher <pT>
<pT>

Njet=2
Nch
XN.Wang et al (Phys Rev D45, 1992)
dNch/dη
Evidence of jet production in high mult. events
31
Hadro-chemistry in p+p events
T
171 ± 9 MeV
γs
0.53 ± 0.04
r
3.49 ± 0.97 fm
ratio
p-p √s = 200 GeV
STAR Preliminary
 Statistical model fit OK but not
as good as in A+A
Canonical ensemble
32
p-p √s = 200 GeV
STAR Preliminary
171 ± 9 MeV
γs
0.53 ± 0.04
r
3.49 ± 0.97 fm
Canonical ensemble
pT>5 GeV/c
ratio
T
Z.Xu, QM 2008
as good as in A+A
 High-pT ratios first step to looking
at hadro-chemistry of jet FF
32
p-p √s = 200 GeV
STAR Preliminary
171 ± 9 MeV
γs
0.53 ± 0.04
r
3.49 ± 0.97 fm
Canonical ensemble
pT>5 GeV/c
ratio
T
Z.Xu, QM 2008
as good as in A+A
 High-pT ratios first step to looking
at hadro-chemistry of jet FF
Some ratios change significantly
32
Jet-Finding Algorithm
detector
Use 4 algorithms
• Midpoint-cone
• SISCone
• KT
• Anti-KT
GEANT
s
pythia
et
”j
particle
nt
ea
“g
Currently Pythia+GEANT+reco
compared to reconstructed real
data so data at “detector” level
ts
” je
ythia
parton
“p
Jet-Finder Algorithm cuts:
pT (track/tower) > 0.2 GeV
|vertex-z|<50 cm
|ηjet| < (1 –Rjet)
0.05 < Eneutral/Ejet (NEF) < 0.85
Seed-Cut: 0.5 GeV/c (for midpoint only)
Compare results from different algorithms - estimate of systematics
33
Fragmentation functions
MLLA Theory

No previous comparisons at
RHIC energies available.

Measurements at higher √s
agree well with theory.
CDF
Test energy scaling of
fragmentation functions.
Sapeta&Wiedemann, hep-ph/0707.3494
34
Fragmentation functions
MLLA Theory

No previous comparisons at
RHIC energies available.

Measurements at higher √s
agree well with theory.
CDF
Test energy scaling of
fragmentation functions.
Sapeta&Wiedemann, hep-ph/0707.3494

FF are particle species dependent.
Need to study composition
of jets and complete event.
34
•
1/N jet dN/d !
1/N jet dN/d !
ξ and z distributions for charged hadrons
2
1.6
SISCone
KT
Anti-K T
1.4
|ηjet|<1-R
1.8
Pythia 6.4
p-p data
Data not
corrected
to particle
level.
1
0.8
0.6
0.4
Preliminary
0.2
1.8
SISCone
KT
Anti-K T
Pythia 6.4
p-p data
|ηjet|<1-R
1.4
1.2
1
0.8
0.6
0.4
Preliminary
0.2
0
1
2
3
4
5
! (=ln(p Tjet /p TPart )
SISCone
KT
Anti-K T
10
p-p data
|ηjet|<1-R
“PYTHIA”
=
PYTHIA
+GEANT
-1
10
-2
Preliminary
10 0
0.1
0.2
0.3
0.4
1
R=0.4
Simulation
1
10
0
10
0.7
0.8
0.9
1
Z
4
5
Simulation
p-p data
|ηjet|<1-R
1
-1
10
Preliminary
-2
0.6
3
SISCone
KT
Anti-K T
10
0.5
2
30 <Jet pTreco< 40 GeV/c
1/N Jet dN/dZ
20 <Jet pTreco< 30 GeV/c
1/N Jet dN/dZ
2
1.6
1.2
-3
2.2
-3
10 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Helen
Caines – Yale University
Reasonable agreement
between
data and PYTHIA+GEANT. 35
1
Z
SISCone
KT
Anti-K T
1.8
1.6
Pythia 6.4
p-p data
R<0.4
1.4
1/N jet dN/d !
2
1.2
2.2
2
1.8
SISCone
KT
Anti-K T
Pythia 6.4
p-p data
1.6
1.4
1.2
1
1
0.8
|ηjet|<1-R
pTtrack > 0.2
0.6
0.4
Preliminary
0.2
0
1
2
3
2.2
2
0.8
0.6
0.4
Preliminary
0.2
4
20<pTreco<30 GeV/c
1/N jet dN/d !
1/N jet dN/d !
Charged hadrons ξ for different R and jet pT
SISCone
KT
Anti-K T
5
Pythia 6.4
Data not
corrected to
particle level.
0
1
2
3
4
30<pTreco<40 GeV/c
5
p-p data
1.8
“PYTHIA” =
PYTHIA
+GEANT
1.6
1.4
1.2
1
0.8
0.6
0.4
R<0.7
Preliminary
0.2
0
1
2
3
4
Preliminary
5
Agreement similar between PYTHIA and data for both radii.
36
ξ for K0s and Λ
Midpoint cone, pT hadron>0.5 GeV/c, K0s and Λ effic. corrected
10<Ejet<15
15<Ejet<20
20<Ejet<50
R<0.4
R<0.5
R<0.7
FF shapes different for h±, K0s and Λ
37
Mean of ξ distributions

PYTHIA
predicts particle
mass ordering
of mean ξ value
h± > K0s > Λ /p

PYTHIA
predicts particle
mass ordering
of mean ξ value
h± > K0s > Λ /p

Not observed
in STAR data
h± > Λ > K0s
(need to check
contamination)
R<0.4
[M. Heinz, Hard Probes 2008]

PYTHIA
predicts particle
mass ordering
of mean ξ value
h± > K0s > Λ /p

Not observed
in STAR data
h± > Λ > K0s
(need to check
contamination)

R<0.4
Nor BABAR
e+e- √s=10.54 GeV
(F. Anulli, Trento 2008
[arXiv:0804.2021v1] )
h± > K = p
[M. Heinz, Hard Probes 2008]
10
1
15<pTjet<20 GeV/c, |ηjet|<1-R (R=0.7)
10
Charged
particles
10
Jets
Transverse Max
Transverse Min
Min-Bias
-1
10
-2
10
All data raw
-2
1/N 1/p T dN/d "d! pT
1/N 1/p T dN/d "d! dp T
pT spectra in jet, UE, Min-Bias event
K0s
Jets
Transverse Max
-3
Transverse Min
Min-Bias
-4
10
Preliminary
-3
10
-4
-5
10
10
-5
10
-6
10
Preliminary
-6
10
-7
10
-8
10 0
2
4
6
8
Particle p
-2
T
10
(GeV/c)
2
4
6
Λ
Jets
Transverse Max
Transverse Min
-3
10
-4
10
(GeV/c)
⊼
Jets
Transverse Max
Transverse Min
-3
Min-Bias
-4
10
-5
-5
10
10
Preliminary
-6
T
-2
10
Min-Bias
10
10 0
8
Particle p
10
10
-7
10 0
2
4
6
8
Particle p
T
10
(GeV/c)
Preliminary
-6
10 0
2
4
6
8
Particle p
T
10
(GeV/c)
39
Summary
•
•
•
RHIC p+p data are extensive and can be used to constrain models
Although the (OPAL) light-flavor separated measurements in e+e- collisions
provided significant improvement of FF for baryons and strange particles there
is still more detail required
p+p data provides a unique tool for understanding gluon vs. quark jet
contributions
• Baryon to meson ratios
• Splitting of high baryon-meson mT
•
mT(xT)-scaling in show that hard processes (related to PDF and FF) dominate
over soft process for minbias collisions starts at pT ~ 2 GeV/c
•
PYTHIA
• Reproduces the rise in <pT> of strange hadrons with Nch
•
•
•
Describes the charged hadron ξ and z distributions at √s=200 GeV
Cannot describe all the p+p data with a common K-factor
Particle pT spectra are significantly softer out of jet cone compared to in jet
cone, those of UE are close to that of Min-Bias triggered events.
40

pdf file - Yale University

Transcription

Similar documents

Using hot quarks to examine the quark-gluon-plasma

Clockwise from above left: Mark Edward as `Angina` Pavlova in the

Early SUSY Discovery in Jets+MET with Low Jet

60s to the present, by the best of the best, s

bâÜ _twç Éy _ÉâÜwxá V{âÜv - Our Lady of Lourdes

May/June 2011 - Saint Anthony Greek Orthodox Church

September, 2003 - Association of Environmental Engineering and

this issue as a PDF - Yale Medicine

this issue as a PDF - Yale Medicine

Church of the Sacred Heart and Saint Mary Our Lady of Czestochowa

Inclusive charged hadron elliptic flow in Au+Au collisions at root s

2014.01 - January Observer - Annunciation Greek Orthodox Church

Psychoanalysis and Jurisprudence

[email protected]

File - Circle Masters Flying club

slide

Helen Keller