Entropy at high E and μ B Peter Steinberg Brookhaven National Laboratory “Critical Point & Onset of Deconfinement” (deco) Workshop Galileo Galilei Institute, Florence, Italy, 5 July 2006

Brunelleschi’s dome: elegant & simple on the outside

Complicated inside

dN/dη vs. Beam Energy 5 years of RHIC PHOBOS, submitted to PRC-RC (in press)

Only 2 years until LHC...

e + e - annihilation → hadrons

Charged primaries + some secondaries (up to 8% correction) Modelling e+e- String model → Parton showers Resummed pQCD calculations (MLLA) pQCD evolution is primary dynamical component of the total multiplicity

minimum-bias p+p → hadrons

Modelling p+p Two component picture Soft component parametrized Hard component from PDFs & pQCD Various implementations PYTHIA, HERWIG, PHOJET, HIJING Different evolution I. Dawson, ATLAS

“leading” particles keep arbitrary fraction of √s w/ flat probability distribution: “effective energy” (a la Basile et al) p p The Leading Effect

e + e - & p+p vs. Models JETSET PYTHIA pQCD √s/2 p+p e+e- & e+e- overlap

pQCD vs. Landau pQCD evolution Landau evolution are quite close for available data... Landau hydro

Fermi-Landau Model Total Energy Total Volume Energy Density E/V (>3 TeV/fm RHIC!) Blackbody thermodynamics Cooper, Frye, Schonberg (1975) thermalization in overlap region

Relativistic Hydrodynamics z y dN/dy Cooper- Frye

What Landau is 3+1D Dynamics rapid local equilibration w/ no free parameters → Beam energy & T ch determine initial & final cond → Energy dep. of entropy No transparency No initial boost invariance Entire system is in thermal contact at t=0

What Landau is not No net baryons (or any conserved charges) No phase transitions (just p=ε/3) No hadronization per se (just T=T c ) No thermal freezeout No trivial mass dependence of dN/dy No resonance decays Caveats for all later results

P. Steinberg, nucl-ex/ Landau/Fermi multiplicity formula & Landau hydro dN/dy Longitudinal Scaling (a.k.a. Limiting Fragmentation) → “Extended Longitudinal Scaling”

Compiled in PHOBOS White Paper (2004)

pQCD “vs.” Landau MLLA pQCD shows “limiting fragmentation” & parametrically: pQCD ↔ Landau Hydro [?!] K. Tesima, Z. Phys. C (1989)

Parton distributions, Nuclear Geometry, Nuclear shadowing Parton production & reinteraction Chemical freezeout (Quark recombination) Jet fragmentation functions Hadron rescattering Thermal freezeout & Hadron decays Many dynamical stages, all in principle independent... p+p & e + e - → A+A

Limiting Fragmentation PHOBOS, submitted to PRC-RC (in press)

N part Scaling PHOBOS, submitted to PRC-RC (in press) Entropy scales linearly w/ volume (no centrality dependence) “one-component model” No simple extrapolation to p+p

Comparison with e + e - /p+p A+A appears “Suppressed” at low energy A+A same as e + e - and p+p above SPS Models diverge at high energy... (LHC?) /N part /2 (6% central) PHOBOS, submitted to PRC-RC (in press)

Comparison with e + e - /p+p PHOBOS, submitted to PRC-RC (in press)

Geometry of Stopping For most heavy ion events, ≥ 2-3. in p+p Maybe >1-2 collisions alleviates leading effect? PHOBOS, PRL (2006)

Total Multiplicity at Finite μ B (work with Cleymans, Wheaton, Stankiewicz, UCT)

Phase Diagram AGS SIS SPS RHIC As beam energy decreases, μ B ↑, T↓

Two Paths in T-μ B plane / = 1 GeV Thermal I: / =1 GeV Thermal II: Fit to data

Net Baryons Net momentum (-loss+gain) of net baryon number (not baryons!) “pile-up” at low energy, “transparency” at high energy?...

First collision typically not enough to stop baryons 2 nd + collision is displaced in original direction,

Fireball Sandwich bulk of baryon number near edge of reaction zone at t=t 0 ~1/ → net baryons are part of entropy generation process → hydro evolution pushes them to larger rapidity

Baryochemistry In equilibrium: Rearranges to: So chemical potential reduces entropy, and thus total multiplicity:

Phenomenology Need a “baryon free” N ch reference p+p and e+e- show same energy dependence p+p has leading baryons (complicated) choose e+e- as reference Two approaches Correct A+A data for presence of μ B Thermal model calculation of entropy density

“Correcting” Total Entropy Not yet applicable to N ch

“Correcting” Total Entropy Convert change in entropy to change part Convert change in entropy to change in multiplicity per N part /2 N B ≡N part α≡S/N=4 β≡N/N ch =3/2 αβ=6 is αβ=6 is “trivial estimate”. αβ=7.2 (15% diff.) THERMUS (Cleymans, et al) → αβ=7.2 (15% diff.)

Direct Calculation Convert √s to μ B (√s) & T(μ B (√s)) Use full thermal model to compute Predicts what data “should” show if V A+A = volume per participant pair vs.

Application to Data Direct calculation Corrected data (ΔN ch )

Application to Data Qualitative model of relationship between baryon density and entropy Cleymans, Wheaton, Stankiewicz, PAS, et al, nucl- th/ nucl- th/ Direct calculation Corrected data (ΔN ch )

Bottom Line 3 rules of thumb: 3. Use N ch : Don’t “choose” mesons vs. baryons as true entropy carriers Effective energy has a direct relationship to entropy (p+p vs. e+e-) 2. Suppression of entropy by net-baryon density (A+A vs. e+e-)

Baryons vs. Mesons As energy changes, s/T 3 (~degrees of freedom) remain constant if mesons AND baryons are included Tawfik et al (2004), Cleymans et al (2005) (x2)

~Landau variable... No baryons no accounting for leading effect NA49 Kink

Conclusions LHC will be exciting (what will N ch be?) RHIC½ & FAIR will be exciting (dynamical effects of μ B ) Much to learn from elementary reactions

What are the microscopic dynamics?

A (relatively) simple structure...