Scott Pratt Michigan State University Resonances, from a Correlations Perspective Scott Pratt, Michigan State University THEORY: ● Production Rates ● Density of States ● Wave-Function Formalism COMPETING CORRELATIONS: ● Charge Conservation ● Jets ● Flow

Scott Pratt Michigan State University THEORY: PRODUCTION RATES ● Typically used for dilepton production ● Can incorporate collision broadening ● Time duration uncertain ● Not valid for sudden breakup ● Inconsistent with density of states ● Ignores finite-size effects Reasonable for dilepton production, questionable for final-state hadrons R.Rapp, NPA725 (2003)

Scott Pratt Michigan State University Theory: Two-particle density of states Spectral function (also wrong): Ignores alteration of scattered wave function Breit-Wigner Form (wrong):

Scott Pratt Michigan State University Theory: Two-particle density of states W. Broniowski, W. Florkowski & B. Hiller, PRC68 (2003) S.P. & W.Bauer, nucl-th/ Phase shift approach (correct): R

Scott Pratt Michigan State University Density of states for  +  - in  channel ( l =1) Breit-Wigner, rises as q 6 Spectral Function, rises as q 3 Phase Shift expression, rises as q

Scott Pratt Michigan State University Inv. Mass Dist. for  +  - Spectral function (  only), Phase shift expression (  only) Phase shift expression (s,p and d)

Scott Pratt Michigan State University Bose Effects = d  /dE for with no Bose Bose modification

Scott Pratt Michigan State University Bose Effects With Bose No Bose Peak position not strongly affected

Scott Pratt Michigan State University Wave-Function Formalism (Finite-Size Effects) Standard HBT: If   is localized, reproduces thermal expression

Scott Pratt Michigan State University Wave-Function Formalism (Finite-Size Effects) Phase-shift expression good when: qR >> 1 Coulomb not important

Scott Pratt Michigan State University Like-Sign Subtraction In the real world, Contributions: Resonances Coulomb Correlations Other Strong-interaction correlations Charge Conservation (same as numerator in charge balance function) Non-contributors: Jets Collective flow

Scott Pratt Michigan State University Equivalence to Balance Function M could be replaced by Q inv or  y Challenges Include all effects in thermal model: Resonances Coulomb Correlations Other Strong-interaction correlations Charge Conservation (same as numerator in charge balance function)

Scott Pratt Michigan State University Canonical Blast-Wave Correlations within domain (charge conservation / resonances) 1.Generate particles from domains (T  =175,V  =64 fm 3 ) Conserve Q, B and S in each domain Include all resonances Monte Carlo consistent with canonical ensemble 2.Choose v and r (T k =120, v max =0.7c) Reset momenta according to T k Boost according to v max and r. 3. Perform like-sign subtraction for particles within same domain.

Scott Pratt Michigan State University Canonical Blast-Wave Inter-domain correlations (HBT, Coulomb, strong interaction) 1.Generate 2 domains, A & B 2.Calculate weight for particle a in A due to presence of B 3.Perform like-sign subtraction with weights 4.Scale to account for multiplicity

Scott Pratt Michigan State University Canonical Blast-Wave In order of importance: 1.Charge conservation 2.Resonances 3.Coulomb (more important for large sources) 4.Other strong interactions direct pions only +resonances +interpair corr.s +resonances +interpair correlations

Scott Pratt Michigan State University STAR vs. Canonical Blast-Wave S.P., S.Cheng, S.Petriconi, M.Skoby, C.Gale, S.Jeon, V.Topor Pop and Q-H. Zhang, in prep. Suggestive of delayed hadronization S.Bass,P.Danielewicz and S.P. PRL 2001

Scott Pratt Michigan State University CONCLUSIONS Important to use correct density of states Wave-function formalism important for qR ~ 1 or for Coulomb Like-sign subtraction DOMINATED by charge conservation effects