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Strangeness and Heavy Flavour (Episode 1)

Strangeness and Heavy Flavour (Episode 1). Federico Antinori (INFN Padova & CERN). Tutorial: kinematic variables collision centrality invariant cross-section. Rapidity. Four-momentum : ( c = 1 , z coordinate along collision axis). Addition of velocities along z :. (Galileo).

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Strangeness and Heavy Flavour (Episode 1)

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  1. Strangeness and Heavy Flavour(Episode 1) Federico Antinori (INFN Padova & CERN)

  2. Tutorial:kinematic variablescollision centralityinvariant cross-section

  3. Rapidity Four-momentum: (c = 1 , z coordinate along collision axis) Addition of velocities along z: (Galileo) (relativistic) “rapidity” Federico Antinori - Trento - May 2008

  4. so under a Lorentz transformation to a frame moving with velocity b along z : (rapidities “add-up”) • therefore, rapidity distributions are boost-invariant: compare • e.g. at SPS: 0 1 2 3 4 5 6 ylab Federico Antinori - Trento - May 2008

  5. in the non-relativistic limit: Exercise: prove this • it can be shown that: Exercise: prove this Federico Antinori - Trento - May 2008

  6. Transverse variables • Transverse momentum: • Transverse mass: • Transverse energy: Exercise: prove these qi = angle w.r.t. beam direction Federico Antinori - Trento - May 2008

  7. Pseudorapidity rapidity pseudorapidity • in the ultrarelativistic limit: p ~ E  h ~ y • for the transverse variables: rapidity pseudorapidity Federico Antinori - Trento - May 2008

  8. it can be shown that: Exercise: prove this • so for ultra-relativistic particles (y ~ h) • rapidity only depends on emission angle Federico Antinori - Trento - May 2008

  9. Collision centrality participants spectators b y=0 spectators rapidity • How far do the centers of the two colliding nuclei pass one another? • Usually expressed in terms of: • b (impact parameter) • number of participants Npart(b) • [sometimes one speaks of “number of wounded nucleons”: NW(b) ] • cross section s(b) Federico Antinori - Trento - May 2008

  10. Experimentally, the centrality is evaluated by measuring one or more of these variables: • Nch: number of charged particles produced in a given rapidity interval (near mid-rapidity) • increases (~ linearly) with Npart • ET: transverse energy = SEi sin qi • increases (~ linearly) with Npart • EZDC: energy collected in a “zero degree” calorimeter • increases (~ linearly) with Nspectators Federico Antinori - Trento - May 2008

  11. e.g.: NA57 experiment: the centrality is evaluated from the charged particle multiplicity in the pseudorapidity range 2 < h < 4 Pb-Pb events are divided into multiplicity classes The distribution of the number of participants for the events in each class is evaluated Federico Antinori - Trento - May 2008

  12. Invariant cross-section • A + B  a1 + a2 + … + an • we may be interested only in the production of a specific type of particle e.g.: Pb + Pb W- + X • Differential cross section: • but is not Lorentz invariant; is used instead: • Lorentz-invariant for a boost along z Exercise: prove this Federico Antinori - Trento - May 2008

  13. Invariant cross-section: • in terms of pT: • integrating over j: Federico Antinori - Trento - May 2008

  14. End of tutorial

  15. Transverse Mass Spectra Apparent Temperature Thermal Freeze-out Federico Antinori - Trento - May 2008

  16. Transverse mass distributions Usually fitted to thermal distributions: T = “inverse slope” or “apparent temperature” or “mT slope” What does T mean? R.Stock Federico Antinori - Trento - May 2008

  17. Thermal freeze-out • In nucleus-nucleus collision we form a strongly interacting “fireball” which expands and cools down • When finally the system is so dilute (i.e. the mean free path is so large) that interactions among the collision products cease, we have “thermal freeze out” • From then on the collision products just stream out towards the detector Federico Antinori - Trento - May 2008

  18. Transverse flow • The temperature of the mT spectra is modified by the presence of a collective transverse flow FormT < 2m : apparent temperature transv. flow velocity freeze-out temperature In practice, it is a complicated business to disentangle the thermal and flow contributions. But additional information (e.g. from HBT interferometry) can be used Federico Antinori - Trento - May 2008

  19. Strangeness and Heavy Flavour(Episode 2) Federico Antinori (INFN Padova & CERN)

  20. Tutorial kinematic variables collision centrality invariant cross-section Transverse Mass Distributions transverse flow Summary of Episode 1 Federico Antinori - Trento - May 2008

  21. Strangeness Enhancement Federico Antinori - Trento - May 2008

  22. Historic QGP predictions K+ s s s s s s s s d d u u d X- u p- u d d d d d d d d d d d s u u u u u u u u s s u d d d d p+ u u s u u u u p u u d d d s W+ u s s u u d d u s d L • restoration of csymmetry -> increased production of s • mass of strange quark in QGP expected to go back to current value • mS ~ 150 MeV ~ Tc • copious production of ss pairs, mostly by gg fusion [Rafelski: Phys. Rep. 88 (1982) 331] [Rafelski-Müller: P. R. Lett. 48 (1982) 1066] • deconfinement  stronger effect for multi-strange • can be built recombining s quarks • strangeness enhancement increasing with strangeness content [Koch, Müller & Rafelski: Phys. Rep. 142 (1986) 167] Federico Antinori - Trento - May 2008

  23. E(W-) > E(X-) > E(L) (sss) (ssd) (sud) |s| = 3 |s| = 2 |s| = 1 • The QGP strangeness abundance is enhanced • As the QGP cools down, eventually the quarks recombine into hadrons (“hadronization”) • The abundance of strange hadrons should also be enhanced • The enhancement should be larger for particles of higher strangeness content, e.g.: Federico Antinori - Trento - May 2008

  24. Strangeness in a hadronic system E(W-) < E(X-) < E(L) (sss) (ssd) (sud) |s| = 3 |s| = 2 |s| = 1 • If a relatively long-lived strongly interacting hadronic system is formed in the collision, a certain amount of enhancement of the abundance of strange particles could be expected even in the absence of QGP • e.g.: • such processes are relatively easy (= fast on the collision timescale) for kaons and L, but are progressively harder (= slow on the collision timescale) for particles of higher strangeness • in this case, one expects: • The production of multistrange baryons such as X and W is therefore expected to be particularly sensitive to deconfinement Federico Antinori - Trento - May 2008

  25. Strange baryons (hyperons) beam p L p- • There are 35 strange baryons listed in the PDG summary tables • Only 6 decay weakly (ct ~ cm’s  separate decay vertex from event interaction vertex): L, S+, S- (sqq) X0, X-(ssq) W- (sss) • Only 3 of them can decay into final state with only charged particles Federico Antinori - Trento - May 2008

  26. Example: WA97 / NA57 • Aim: study the production of multi-strange particles in Pb-Pb collisions • Experimental technique: • high granularity silicon pixel tracker at central rapidity ycm ~ 0 • detect Ks0, L, X, W, by reconstructing weak decay topologies Federico Antinori - Trento - May 2008

  27. Hyperon signals • From NA57, Pb-Pb collisions at 158 A GeV/c Federico Antinori - Trento - May 2008

  28. Yield, Enhancement • Yield: multiplicity per event e.g.: # of W- / event in y1 < y < y2 : • Enhancement: yield per participant (i.e. wounded) nucleon relative to yield per participant nucleon in p-Be e.g.: W- enhancement: Federico Antinori - Trento - May 2008

  29. Strangeness enhancement pattern • Enhancement relative to pBe for pPb and 5 centrality classes in PbPb: (particles/event/participant) / (particles/event/participant) in pBe Federico Antinori - Trento - May 2008

  30. Strangeness enhancement pattern • Enhancement relative to p-Be Enhancement is larger for particles of higher strangeness content (QGP prediction!) up to a factor ~ 20 for W So far, no hadronic model has reproduced these observations (try harder!) Actually, the most reliable hadronic models predicted an opposite behaviour of enhancement vs strangeness Federico Antinori - Trento - May 2008

  31. Chemical Equilibrium Thermal Fits Chemical Freeze-out Federico Antinori - Trento - May 2008

  32. Chemical equilibrium [P.Braun-Munzinger, I.Heppe, J.Stachel, Phys. Lett. B465 (1999), 15] • The relative particle abundances measured in Pb-Pb collisions are close to the thermodynamical (chemical) equilibrium values (maximum entropy) corresponding to a temperature of ~ 170 MeV (“chemical freeze-out temperature”) this would be a natural outcome of statistical hadronization of uncorrelated quarks “chemical freeze out”: the moment when elastic interactions cease Federico Antinori - Trento - May 2008

  33. Hyperon enhancements @ RHIC • similar picture • open: NA57 @ SPS • closed: STAR @ RHIC Federico Antinori - Trento - May 2008

  34. Thermal fits again doing well Chemical equilibrium @ RHIC 200 GeV 62.4 GeV Jun Takahashi (STAR), SQM`07 Federico Antinori - Trento - May 2008

  35. remarkable regularity in freeze-out systematics Jean Cleymans, SQM`07 Federico Antinori - Trento - May 2008

  36. T vs µB systematics • the extracted freeze-out points at SPS and RHIC lay very close to the predicted QGP phase boundary

  37. A departure from equilibrium? The K+/π+ “horn”

  38. K abundance vs sNN • K+/p+ shows a sharp maximum at sNN ~8 GeV • K-/p- does not... • What’s this? • K+(us) very sensitive to baryon density, which decreases with energy • K+ peak indicates phase transition? (M.Gazdzicki) • new experiments under preparation Federico Antinori - Trento - May 2008

  39. More on strangeness from RHIC Nuclear modification factors Elliptic flow

  40. Participants Scaling vs Binary Scaling e.g.: Npart (or Nwound) = 7 “participants” Nbin (or Ncoll) = 12 “binary collisions” • “Soft”, large cross-section processes expected to scale like Npart • “Hard”, low cross-section processes expected to scale like Nbin Federico Antinori - Trento - May 2008

  41. Rcp, RAA, RdAu Yield/collision in central collisions Yield/collision in peripheral collisions Yield/collision in nucleus-nucleus Yield/collision in proton-proton Yield/collision in deuteron-nucleus Yield/collision in proton-proton Federico Antinori - Trento - May 2008

  42. High pT suppression • High pT particle production expected to scale with number of binary NN collisions if no medium effects • Clearly does not work for more central collisions • Interpreted as due to parton energy loss Federico Antinori - Trento - May 2008

  43. Baryon puzzle @ RHIC • Central Au-Au: as many p- (K-) as p (L) at pT ~ 1.5  2.5 GeV • e+e-jet (SLD) • very few baryons from fragmentation! p K p Federico Antinori - Trento - May 2008 H.Huang @ SQM 2004

  44. Rcp • strange particles come to rescue! • if loss is partonic, shouldn’t it affect p and p in the same way? Federico Antinori - Trento - May 2008

  45. Quark Recombination K+ s s s s s s s s d d u u d X- u p- u d d d d d d d d d d d s u u u u u u u u s s u d d d d p+ u u s u u u u p u u d d d s W+ u s s u u d d u s d L • if hadrons are formed by recombination, features of the parton spectrum are shifted to higher pT in the hadron spectrum, in a different way for mesons and baryons  constituent quark counting S.Bass @ SQM`04 Federico Antinori - Trento - May 2008

  46. Elliptic Flow • Non-central collisions are azimuthally asymmetric • The transfer of this asymmetry to momentum space provides a measure of the strength of collective phenomena • Large mean free path • particles stream out isotropically, no memory of the asymmetry • extreme: ideal gas (infinite mean free path) • Small mean free path • larger density gradient -> larger pressure gradient -> larger momentum • extreme: ideal liquid (zero mean free path, hydrodynamic limit)

  47. Azimuthal Asymmetry • at low pT: azimuthal asymmetry as large as expected at hydro limit! • very far from “ideal gas” picture of plasma Federico Antinori - Trento - May 2008

  48. elliptic flow v2 STAR Preliminary • Recombination also offers an explanation for the v2 baryon puzzle... scaled with n(quarks) Federico Antinori - Trento - May 2008

  49. A few hiccups... • Recombination provides a natural explanation for the hyperon enhancement pattern and for the RCP, v2 behaviours, but has a few theoretical problems... • it violates 2nd law of thermodynamics • reduction of the number of particles  lower disorder  entropy decreased • it actually also violates the 1st... • impossible to conserve energy and momentum simultaneously • what happens to gluons? • must break down at low pT (where hydrodynamical behaviour is expected to dominate) Federico Antinori - Trento - May 2008

  50. Kinetic Transverse Energy (KET) Scaling Phys. Rev Lett. 98, 162301 (2007) • impressive scaling also in softest region if KET used instead than pT (as expected in hydrodynamics-inspired models) Federico Antinori - Trento - May 2008

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