Baryon femtoscopy in √sNN = 2.76 TeV
Pb-Pb collisions at ALICE
Jai Salzwedel
The Ohio State University
for the ALICE Collaboration
29th Winter Workshop on Nuclear Dynamics
Squaw Valley, CA, USA
February 6, 2012
This work has been supported by the National Science Foundation.
Overview
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Femtoscopic analyses of baryon-antibaryon (pp, pΛ, pΛ, ΛΛ)
and baryon-baryon (pp, pp) systems have been performed
(pΛ, pΛ, ΛΛ and ΛΛ underway)
Different sources of correlations:
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Quantum Statistics (QS)
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Coulomb Final State Interactions (FSI)
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Strong FSI
Complementary systems (pp vs. pp, pp vs. pp, pp vs. ΛΛ and
pΛ) for consistency check
Possibility to measure poorly known or unknown interactions
(pΛ, ΛΛ and, in future, ΛΛ)
6 Feb 2013, WWND 29
Jai Salzwedel – The Ohio State University
2/24
ALICE & analysis details
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Pb-Pb collisions at √sNN = 2.76 TeV
(~4·107 events from 2011).
Particle identification and tracking:
Time Projection Chamber,
Time-of-Flight detector.
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Correlation functions: C (qinv )=
A (qinv )
B (qinv )
A(q) – signal (both particles from save event)
B(q) – background (particles from two different events)
1D representation in qinv (for pp and ΛΛ)
and k* (pp and all pΛ systems)
6 Feb 2013, WWND 29
Single- and two-track effects taken
into account.
*
2
2
2
qinv =2k =∣q−P (m1 −m 2 )/ P ∣
q – pair relative momentum
P – pair total momentum
Jai Salzwedel – The Ohio State University
3/24
Baryon femtoscopy
C (⃗
q )=∫ S ( ⃗r )∣Ψ ( ⃗q , ⃗r )∣2 d 4 r
measured correlation
6 Feb 2013, WWND 29
emission function (radius)
cross-section
Jai Salzwedel – The Ohio State University
4/24
Baryon femtoscopy
C (⃗
q )=∫ S ( ⃗r )∣Ψ ( ⃗q , ⃗r )∣2 d 4 r
measured correlation
emission function (radius)
increase of (anti)correlation
=
decrease of the radius
or
increase of the interaction
cross-section
6 Feb 2013, WWND 29
cross-section
expected shape
of the signal (MC)
Jai Salzwedel – The Ohio State University
5/24
Baryon femtoscopy
C (⃗
q )=∫ S ( ⃗r )∣Ψ ( ⃗q , ⃗r )∣2 d 4 r
measured correlation
emission function (radius)
increase of (anti)correlation
=
decrease of the radius
or
increase of the interaction
cross-section
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●
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cross-section
expected shape
of the signal (MC)
For protons, the cross-sections are known, so only radius can be a free parameter.
For others (pΛ, ΛΛ, ΛΛ), neither the radius nor the cross-section are precisely
known → in fitting, we'd like only one to be a free parameter
Possible constraints on the radius can be taken from p femtoscopy.
6 Feb 2013, WWND 29
Jai Salzwedel – The Ohio State University
6/24
Analytical model
The Lednicky & Lyuboshitz analytical model can be
used to determine the interaction potential:
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[ ∣ ∣(
S
1 f (k *)
C (k *)=1+∑ ρS
2
R
S
2
1 1
f (k *)= S + d 0S k *2 −ik *
f0 2
S
(
f0 – scattering length
6 Feb 2013, WWND 29
S
Lednicky, Lyuboshitz,
Sov. J. Nucl. Phys.,
35, 770 (1982)
)
S
S
d0
2 ℜ f (k *)
ℑ f (k *)
1−
+
F 1(2k * R)−
F 2 (2k * R)
√π R
2√π R
R
]
−1
)
Spin (S) dependence neglected
f
singlet
=f
triplet
Assume Effective radius
=f
Jai Salzwedel – The Ohio State University
d 0 =0
7/24
Analytical model
The Lednicky & Lyuboshitz analytical model can be
used to determine the interaction potential:
●
[ ∣ ∣(
S
1 f (k *)
C (k *)=1+∑ ρS
2
R
S
2
1 1
f (k *)= S + d 0S k *2 −ik *
f0 2
S
(
f0 – scattering length
6 Feb 2013, WWND 29
S
Lednicky, Lyuboshitz,
Sov. J. Nucl. Phys.,
35, 770 (1982)
)
S
S
d0
2 ℜ f (k *)
ℑ f (k *)
1−
+
F 1(2k * R)−
F 2 (2k * R)
√π R
2√π R
R
]
−1
)
Spin (S) dependence neglected
f
singlet
=f
triplet
Assume Effective radius
=f
Jai Salzwedel – The Ohio State University
d 0 =0
8/24
Analytical model
Lednicky and Lyuboshitz analytical model
R=2.55 fm, Re(f0)=-1.75 fm, Im(f0)=0.00 fm
Lednicky and Lyuboshitz analytical model
R=2.55 fm, Re(f0)=-1.26 fm, Im(f0)=1.55 fm
pΛ theoretical CF
Real part
Imaginary part
pΛ theoretical CF
Real part
Imaginary part
The Lednicky & Lyuboshitz analytical model can be
used to determine the interaction potential:
●
[ ∣ ∣(
S
1 f (k *)
C (k *)=1+∑ ρS
2
R
S
2
1 1
f (k *)= S + d 0S k *2 −ik *
f0 2
S
(
f0 – scattering length
6 Feb 2013, WWND 29
S
Lednicky, Lyuboshitz,
Sov. J. Nucl. Phys.,
35, 770 (1982)
)
S
S
d0
2 ℜ f (k *)
ℑ f (k *)
1−
+
F 1(2k * R)−
F 2 (2k * R)
√π R
2√π R
R
]
−1
)
Spin (S) dependence neglected
f
singlet
=f
triplet
Assume Effective radius
=f
Jai Salzwedel – The Ohio State University
d 0 =0
9/24
Analytical model
Lednicky and Lyuboshitz analytical model
R=2.55 fm, Re(f0)=-1.75 fm, Im(f0)=0.00 fm
Lednicky and Lyuboshitz analytical model
R=2.55 fm, Re(f0)=-1.26 fm, Im(f0)=1.55 fm
pΛ theoretical CF
Real part
Imaginary part
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pΛ theoretical CF
Real part
Imaginary part
Contribution from Re{f(k*)} is either positive or negative but very narrow
(few tens of MeV) in k*.
The Im{f(k*)} accounts for the inelastic processes of baryon-antibaryon
annihilation.
Introducing a non-zero Im{f0} scattering length component – i.e.
annihilation – produces a wide (hundreds of MeV) negative correlation.
6 Feb 2013, WWND 29
Jai Salzwedel – The Ohio State University
10/24
Annihilation in baryon-antibaryon correlations
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Deviation of proton yields from thermal
models expectations.
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“Rescattering” phase should be taken into
account while determining yields:
–
Steinheimer, Aichelin, Bleicher;
arXiv:1203.5302
–
Werner et al.; Phys.Rev. C85 (2012) 064907
–
Karpenko, Sinyukov, Werner;
arXiv:1204.5351
(...)switching BB-annihilation on suppresses baryon yields,
in the same time increases pion yield, thus lowering p/π
ratio to the value 0.052, which is quite close to the one
measured by ALICE(...)
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if true → annihilation must be seen in
baryon-antibaryon correlations.
arXiv:1208.1974
6 Feb 2013, WWND 29
Jai Salzwedel – The Ohio State University
11/24
Experimental correlation
functions
6 Feb 2013, WWND 29
Jai Salzwedel – The Ohio State University
12/24
pp correlation functions
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Shape dominated by Coulomb and Strong FSI.
Correlation strength increases with decreasing multiplicity
(consistent with decrease of the system size).
Significant annihilation (from Strong FSI) expected and measured
(wide anticorrelation in k*).
6 Feb 2013, WWND 29
Jai Salzwedel – The Ohio State University
13/24
pΛ, pΛ, and ΛΛ correlations
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Wide negative correlation, consistent with annihilation in the strong FSI (and
qualitatively consistent with behavior seen in pp correlations)
Annihilation not limited to identical particle-antiparticle systems!
Quantitative analysis requires careful treatment of contaminations and residual
correlations
6 Feb 2013, WWND 29
Jai Salzwedel – The Ohio State University
14/24
pp and pp correlation functions
pp
pp
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QS, Coulomb and Strong FSI – all contribute to measured correlations.
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Expected maximum for qinv = 2k* ≈ 40 MeV/c.
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Correlation effect increases for more peripheral events - size decreases with
decreasing multiplicity.
6 Feb 2013, WWND 29
Jai Salzwedel – The Ohio State University
15/24
Study of residual correlations
6 Feb 2013, WWND 29
Jai Salzwedel – The Ohio State University
16/24
Study of residual correlations - pp
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While contributions from pp correlations describe
the maximum at k*≈ 0.02 GeV/c, they cannot explain
the broad excess from 0.05 to 0.1 GeV/c
Possible explanation: residual correlations
Main weak decay channel leading to protons:
Λ→ p+π −
6 Feb 2013, WWND 29
Jai Salzwedel – The Ohio State University
17/24
Study of residual correlations - pp
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While contributions from pp correlations describe
the maximum at k*≈ .02 GeV/c, they cannot explain
the broad excess from 0.05 to 0.1 GeV/c
Possible explanation: residual correlations
Main weak decay channel leading to protons:
Λ→ p+π −
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Fitting function calculated by quadratic interpolation
between theoretical pp and pΛ:
C meas (k ∗pp )=1+λ pp (C pp (k ∗pp ; R)−1)+λ p Λ (C p Λ (k ∗pp ; R)−1)
where
C p Λ (k ∗pp ; R)≡ ∑ C p Λ (k ∗pp )T (k ∗pp , k ∗pp )
∗
k pp
6 Feb 2013, WWND 29
Jai Salzwedel – The Ohio State University
18/24
Study of residual correlations - pp
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While contributions from pp correlations describe
the maximum at k*≈ .02 GeV/c, they cannot explain
the broad excess from 0.05 to 0.1 GeV/c
Possible explanation: residual correlations
Main weak decay channel leading to protons:
Λ→ p+π −
●
Fitting function calculated by quadratic interpolation
between theoretical pp and pΛ:
C meas (k ∗pp )=1+λ pp (C pp (k ∗pp ; R)−1)+λ p Λ (C p Λ (k ∗pp ; R)−1)
where
C p Λ (k ∗pp ; R)= ∑ C p Λ (k ∗pp )T (k ∗pp , k ∗pp )
∗
k pp
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Residual correlation details:
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Decay kinematics taken into account with
THERMINATOR transform matrix T
(k*pΛ converted to k*pp)
Assume a Gaussian source, with Rpp = RpΛ
6 Feb 2013, WWND 29
Jai Salzwedel – The Ohio State University
19/24
Study of residual correlations - pp
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Similar residual correlation
considerations are applicable for pp
data.
Instead of contribution from pΛ in pp
we have contribution from pΛ in pp:
∗
∗
∗
C meas (k )=1+λ p p (C p p (k ; R)−1)+λ p Λ (C p Λ (k ; R )−1)
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After taking into account the residual
correlations the shape of the
correlation function is very well
reproduced by the fit.
Residual correlation studies are in
progress for pΛ and ΛΛ systems.
6 Feb 2013, WWND 29
Jai Salzwedel – The Ohio State University
20/24
Fitting pp correlations for the
radius parameter
1D radius parameter, Rinv, is extracted
from Lednicky & Lyuboshitz fit
6 Feb 2013, WWND 29
Jai Salzwedel – The Ohio State University
21/24
Rinv from proton femtoscopy
Tendency for radii to increase with multiplicity, with higher kT giving
smaller radii.
6 Feb 2013, WWND 29
Jai Salzwedel – The Ohio State University
22/24
mT scaling with different masses
Approximate mT scaling after taking into account kinematics,
consistent with radial flow.
γ – Lorentz factor
6 Feb 2013, WWND 29
mt = √ k 2t +m20
Jai Salzwedel – The Ohio State University
23/24
Summary
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Presented baryon femtoscopy in Pb-Pb at √sNN=2.76 TeV
Annihilation is not limited to particle-antiparticle pairs. Baryon-antibaryon (pp ΛΛ, pΛ
and pΛ) correlations have significant annihilation contributions for all analyzed pairs.
Results are qualitatively consistent with the explanation of low proton yields at LHC
from final state rescattering
Measurement of annihilation cross-sections for poorly known systems (pΛ and
ΛΛ) with femtoscopic techniques underway. Will provide important new information for
rescattering codes
The residual correlations (e.g. pΛ feed-down in pp femtoscopy) must be studied and
taken into account in the fitting procedure in order to describe the data
A tendency is observed toward mT scaling for pions, kaons and protons with proper
Rinv scaling
6 Feb 2013, WWND 29
Jai Salzwedel – The Ohio State University
24/24