1. NA61/SHINE search for the critical point
of strongly interacting matter
- Basic ideas
- NA49 pilot results
- NA61/SHINE systematic search
M. Gazdzicki
Frankfurt,Kielce

2. Observation of the onset of deconfinement implies that:
- Basic ideas
Observation of the onset of deconfinement implies that:
there are two phases of strongly interacting matter
(popular nicknames are hadron gas and quark-gluon plasma)
and thus there is a transition line/region between them
The next goals are to study properties of
- QGP (LHC),
- hadron gas (SIS, Nuklotron) and
- the transition line (SPS, RHIC, NICA)
In particular, a possibility to discover a hypothetical
critical end point of strong interacting matter attracts
a significant attention.

3. Phase diagrams of strongly interacting matter
The most popular one
and an example of
a less popular one
Asakawa, Yazaki, NP A504, 668 (89)
within the Nambu, Jona-Lasinio model
Gorenstein, M.G., Greiner,
PR C72, (05)
within the quark-gluon bag model

4. The SPS and RHIC experimental programs are
mostly based on the most popular phase diagram
cross-over
1st order PT
End point

5. Properties of the end point of the 1st order line are believed
to resemble the properties of the 2nd order phase transition
1st order phase transition:
discontinuity of energy
and entropy density at TC
The two phases are very
different. For small
fluctuations of energy
density there are
only small fluctuations
of the phase composition.
2nd order phase transition:
energy and entropy densities
are continuous at TC
The two phases are similar
For small fluctuations of
energy density
there are large fluctuations
of the phase composition.

6. in the vicinity of the End point large volume
fluctuations of matter droplets are expected.
Fluctuations in the vicinity of the critical point:
micro-state 1
micro-state 2
micro-state 3
Fluctuations in the mixed phase (1st order PT):
micro-state 1
micro-state 2
micro-state 3

7. specific heat capacity: c ≡ dε /dT
Maximum of c at T < TC
appears for the 3rd and
higher order PT
as well as the cross-over
Infinite c for T → TC
is typical for the 2nd order PT

8. Temperature fluctuations in A+A collisions:
Stodolsky, PRL 75, 1044 (95),
Shuryak, PL B423, 9 (98)
(MCE with fixed E)
Particle number fluctuations in A+A collisions:
Mrowczynski, PL B430, 9 (98)
(GCE with fixed T)
Energy fluctuations in A+A collisions:
Stephanov, Rajagopal, Shuryak
PR D60, (99)
(GCE with fixed T)

9. Anomaly in fluctuations in a narrow domain
of the phase diagram is considered as
the main signal of the critical end point
but predictions what and how should
strongly fluctuate are model-dependent
Search for the critical end point in heavy ion
collisions implies a scan in the parameters
controlled in laboratory (collision energy and
centrality, system size). By changing them
we change freeze-out conditions (T, µB).
In the case they are close to the critical end
point anomaly in fluctuations should be observed.

10. E Schematic dependance of freeze-out
and early stage (T, µB) on collision energy
Early stage E
freeze-out

11. Freeze-out (T, µB) dependence on the laboratory controlled parameters
Collision energy dependence for central Pb+Pb (Au+Au)

12. NA49: System size dependence at 158A GeV
p+p
C+C
Si+Si
central Pb+Pb
Becattini, MG, Manninen, PR C73, (06)
Kraus, JP G31, S147 (05)

13. T µB Summary on freeze-out (T, µB) dependence on
the laboratory controlled parameters T
energy A µB
Search for the critical point makes
sense only at energies larger than
the onset one (30A GeV)

14. and expected signals: hills of fluctuations
Critical Point:
freeze-out close to critical point,
and system large enough,
expected signal: a hill in fluctuations
and local power-law fluctuations
Pb+Pb
Be+Be 13

15. - NA49 pilot results

16. NA49 pT and multiplicity fluctuations
inelastic p+p and central C+C, Si+Si, Pb+Pb collisions
(cms rapidity yπ > 1.1)
system size at 158A GeV energy dependence for Pb+Pb
fluctuations of PT, N
(5% most central collisions)
fluctuations of multiplicity
(1% most central collisions)

17. NA49 PT and multiplicity fluctuations
p+p
Pb+Pb
Pb+Pb
p+p
Pb+Pb
system size at 158A GeV
energy for central Pb+Pb
First hint of the
fluctuation hill?
NA49, PR C78:034914
NA49 PR D60:114028

18. NA49 intermittency analysis
intermittency in particle production as signal of the critical point
Antoniou et al., NPA693,799(2001); PRL97,032002(2006)
at the critical point local density fluctuations with power-law
singularity expected both in configuration and momentum space
- σ field: density of σ particles, related to low-mass π+π- pairs
- baryonic density: related to net baryon density ( ≈ protons)
experimental observation via factorial moments in pT space:
(subdivided into M bins in px and py )
estimate the background by mixed events and subtract
predicted intermittency index ϕ low-mass π+ π- pairs 2/3
- protons /6 ~

19. σ→ π+π- intermittency analysis
pions identified by dE/dx measured in the TPCs
study π+π- pairs near threshold to reduce combinatorial background
exclude Coulomb correlation region at very small Qinv
NA49 results for central collisions at 158A GeV:
T.Anticic et al, PRC81,064907(2010) M2
Combinatorial background
too large

20. power law fit to ΔF2 in central “Si”+Si collisions
Φ2 ≈ ± ± ± 0.09 M2
π+π- intermittency seen in
central Si+Si collisions
at 158A GeV

21. proton intermittency analysis (arXiv:1208.5292)
protons identified by dE/dx measured in the TPCs
selection by cuts in dE/dx such that purity > 80 %
cms rapidity |ycms | < 0.75

22. power law fits to background corrected factorial moments ΔF2
12 % most central collisions at 158A GeV
suggestive of maximum in
p intermittency for central
Si+Si collisions at 158A GeV

23. - NA61/SHINE systematic search

24. Advances related to the NA61/SHINE search:
- precise measurements of the number of projectile
spectators thanks to the Projectile Spectator Detector
- 2D scan with central collisions of similar mass nuclei
possible thanks to an increase of the event rate
- use of strongly intensive quantities to
remove bias due to volume fluctuations
- reduction of delta electron and secondary interaction
background thanks to the new He beam pipes
- use of the identity method to correct data for
an incomplete particle identification (PID)
- use of a new method to correct fluctuation results
for experimental biases other than PID

25. - precise measurements of the number of projectile
spectators thanks to the Projectile Spectator Detector

26. Projectile Spectator Detector
spectators
Projectile Spectator Detector p
target
central
peripheral K- p- p+
produced particles
Projectile Spectator Detector:
- 44 module,
- 440 MAPD read-out channels
- 17 tons
→ single nucleon resolution

27. - 2D scan with central collisions of similar mass nuclei
possible thanks to an increase of the event rate

28. Central collisions of light and medium size nuclei
cannot be replaced by peripheral Pb+Pb collisions
The fluctuations of the number of projectile participants are suppressed by selecting collisions with fixed number of projectile spectators
(in NA61/SHINE measured by PSD)
The fluctuations of the number of target participants can be suppressed only by selection of very central collisions
peripheral
central
Number of projectile participants
Fluctuations of target participants

30. - use of strongly intensive quantities to
remove bias due to volume fluctuations

31. Multiplicity Fluctuations: the second moments
( [x]  Var[x]/<x>, Var[x] = <(x-<x>)2> )
WNM:
[N] = *[N] + <N>/<W> [W]
SM(GCE):
[N] = *[N] + <N>/<V> [V]
where *[N] is the scaled variance
calculated for any fixed value of W or V
Properly weighted sums of second moments
of joint multiplicity distribution of two hadrons is
independent of system size and its fluctuations
( P(W) and P(V) )
(it is strongly intensive)

32. Properly weighted sums of second moments:
Δ[A,B] = (<B>[A] - <A>[B])/(<B> - <A>)
Σ[A,B] = (<B>[A] + <A>[B] –
- 2(<AB> - <A><B>))/(<B> + <A>)
(Σ is a reincarnation of the Φ fluctuation measure)
are independent of P(W) in WNM
and of P(V) in SM(GCE)
MG, Mrowczynski 1992
Gorenstein, MG, 2011

33. - reduction of delta electron and secondary interaction
background thanks to the new He beam pipes

34. He beam pipes:
reduces number of δ-electrons and beam/spectator interactions
in VTPC-1 and VTPC-2 by a factor of about 10
Position of the reconstructed interaction
point along the beam direction
He beam pipe installed
In the VTPC-1 gas volume
(extremely light-weight,
low Z materials used)

35. - use of the identity method to correct data for
an incomplete particle identification

39. - use the new method to correct fluctuation results
for experimental biases other than PID

40. The new method to correct experimental results on
fluctuations for experimental biases other than PID:
- prepare joint distribution of relevant event quantities
measured in an experiment with the inserted target
→ JD1
- subtract from it the corresponding distribution obtained
with the removed target – the correction for non-target
interactions
→ JD2
- correct JD2 for the remaining biases using Monte Carlo
simulation/reconstruction chain:
physics MC event → raw MC data → reconstructed MC data
→ JD3
- from JD3 calculate the relevant fluctuation measures, e.g.,
strongly intensive quantities: Δ[A,B] and Σ[A,B]

41. NA61/SHINE first results

42. NA61/SHINE and NA49: no anomalies in fluctuations in
p+p and central Pb+Pb collisions
NA49: an indication of increased fluctuations in
Si+Si interactions at 158A GeV/c
NA61/SHINE: energy scan with Ar+Ca and Xe+La may
lead to the discovery of the critical point

44. Additional slides

45. +Z detector, +A detector
NA61/SHINE at CERN SPS
top view, not to scale
PSD
+Z detector, +A detector

46. NA61/SHINE at CERN SPS BPDs: for each beam particle:
top view, not to scale
PSD
BPDs
BPDs: for each beam particle:
straight line trajectory
TPCs: for each charged particle:
charge, momentum, mass (dE/dx)
TOFs: for each charged particle:
mass (tof)
PSD: for all particles:
total energy

48. x measure (ZP C54, 127 (1992)) of fluctuations (x=pT, f, Q)
Fluctuation measures (NA49 and/or NA61):
sdyn measure of dynamical particle
ration fluctuations (K/p, p/p, K/p)
E-by-e fit of particle multiplicities required in NA49
Mixed events used as reference
s2dyn ∝ 1/NW (PR C81, (2010), arXiv: )
Scaled variance w of multiplicity distribution
Intensive measure
For Poissonian multiplicity distribution w=1
In wounded nucleon model (superposition) w(A+A) = w(N+N) + <n>wW
<n> - mean multiplicity of hadrons from a single N+N; wW - fluctuations in NW w is strongly dependent on NW fluctuations
relative width (of K/π, p/π, K/p) σ= 𝑅𝑀𝑆 𝑀𝑒𝑎𝑛 ⋅100 % σ 𝑑𝑦𝑛 =𝑠𝑖𝑔𝑛 σ 𝑑𝑎𝑡𝑎 2 − σ 𝑚𝑖𝑥𝑒𝑑 ∣ σ 𝑑𝑎𝑡𝑎 2 − σ 𝑚𝑖𝑥𝑒𝑑 2 ∣ σ 𝑑𝑦𝑛 2 ≈∣ ν 𝑑𝑦𝑛 ∣
ω= 𝑁 2 − 𝑁 2 𝑁
x measure (ZP C54, 127 (1992)) of fluctuations (x=pT, f, Q)
In superposition model x(A+A) = x(N+N)
For independent particle emission x=0
In superposition model x is independent of NW and NW
fluctuations (strongly intensive)
𝑧 𝑥 =𝑥− 𝑥 ˉ ; 𝑥 ˉ − inclusive average event variable 𝑍 𝑥 = 𝑖=1 𝑁 𝑥 𝑖 − 𝑥 ˉ Φ 𝑥 = 𝑍 𝑥 2 𝑁 − 𝑧 𝑥 2 ˉ

49. 3rd moment of pT measure (pT(3))
Strongly intensive (PL B465, 8 (1999))
Intermittency in low mass p+p- pair
density fluctuations in pT space
Proper mass window and multiplicity required
Mixed events used as reference
Power-law behavior from s mode expected:
Critical QCD prediction f2 = 2/3
Φ 𝑝 𝑇 3 =  𝑍 𝑝 𝑇 𝑁  −  𝑧 𝑝 𝑇 3 ˉ  1 3
2D transv. momentum factorial moments: 𝐹 𝑝 𝑀 = 1 𝑀 2 𝑖=1 𝑀 2 𝑛 𝑖 𝑛 𝑖 − 𝑛 𝑖 −𝑝 𝑀 2 𝑖=1 𝑀 2 𝑛 𝑖 𝑝 𝑀 2 − number of cells in 𝑝 𝑇 space of di−pion 𝑝 𝑇,ππ = 𝑝 𝑇, π 𝑝 𝑇, π − 𝑛 𝑖 − number of reconstruc. di−pions in𝑖−th cell Δ 𝐹 2 𝑀 − combinatorial background subtracted (by use of mixed events) second factorial moment
Δ 𝐹 2 ~ 𝑀 2 φ 2