Conserved Charge Fluctuations And Correlations From .

8m ago
4 Views
0 Downloads
2.57 MB
38 Pages
Last View : 1m ago
Last Download : n/a
Upload by : Olive Grimm
Transcription

Conserved Charge Fluctuations and Correlationsfrom Lattice QCD and the Beam Energy ScanFrithjof KarschBrookhaven National Laboratory & Bielefeld UniversityOUTLINE– the QCD phase diagram– EoS at non-zero baryon chemical potential– cumulant ratios of conserved charge fluctuations– the QCD critical pointF. Karsch, RHIC&AGS,BNL 20151

Chiral critical point and QCD critical endpointLHC: mayestablish contactwith the QCDchiral PHASEtransitionRHIC: may establishevidence for theQCD critical end pointIs physics on the freeze-outline sensitive to criticalbehavior?F. Karsch, RHIC&AGS,BNL 20152

Exploring the QCD phase diagram2.0 1.3 0.7X. Luo (STAR Collaboration),PoS CPOD2014 (2014) 019observableconsequences:conserved charge fluctuationcontrolled by(.and)F. Karsch, RHIC&AGS,BNL 20153

Exploring the QCD phase diagram2.0 1.3 0.7equilibriumthermodynamics:Where is thecritical point?conserved charge fluctuationcontrolled byF. Karsch, RHIC&AGS,BNL 20154

LGT attempts to find the critical pointP. deForcrand, O. Philipsen, 2002Z. Fodor, S. Katz. 2001, 2004these calculations were possiblebecause(I) the lattices were coarse,(II) the discretization schemeswere crudecritical point or breakdown of thereweighting approach (loosing the overlap) ?S. Ejiri, PRD69, 094506 (2004)since 10 years no progress along this lineF. Karsch, RHIC&AGS,BNL 20155

Exploring the QCD phase diagramMore moderate questions:Can we understand the systematicsseen in cumulants of charge fluctuationsin terms of QCD thermodynamics ?How far do we get with low orderTaylor expansions of QCD in explainingthe obvious deviations from HRG modelbehavior ?2.0 1.3 0.7equilibriumthermodynamics:Where is thecritical point?conserved charge fluctuationcontrolled byF. Karsch, RHIC&AGS,BNL 20156

Exploring the QCD phase diagramMore moderate questions:preliminary answer (modulo wellknown details like proton vs baryonfluctuations, acceptance cuts, .)ForStructure of net-electric charge andnet-proton cumulants is inconsistentwith HRG thermodynamics, but caneventually be understood2.0 1.3 0.7equilibriumthermodynamics:Where is thecritical point?conserved charge fluctuationcontrolled byF. Karsch, RHIC&AGS,BNL 20157

Exploring the QCD phase diagramMore moderate questions:preliminary answer (modulo wellknown details like proton vs baryonfluctuations, acceptance cuts, .)?2.0 1.3 0.7equilibriumthermodynamics:ForStructure of net-electric charge andnet-proton cumulants is inconsistentwith HRG thermodynamics, but caneventually be understood in terms ofQCD thermodynamics in a 6th-orderTaylor expansionWhere is thecritical point?conserved charge fluctuationcontrolled byF. Karsch, RHIC&AGS,BNL 20158

Taylor expansion of the pressuregeneralized susceptibilities:conserved charge fluctuations:F. Karsch, RHIC&AGS,BNL 20159

Strong interaction matter in the crossover region (close to the freeze-out line) isnot a Hadron Resonance Gas – although HRG sometimes is a good approximationSome 4th and 6th order cumulantsF. Karsch, RHIC&AGS,BNL 201510

Equation of state of (2 1)-flavor QCD:for simplicity:F. Karsch, RHIC&AGS,BNL 201511

Equation of state of (2 1)-flavor QCDpressure,pressure entropy & energy densityA. Bazavov et al. (hotQCD) ,Phys. Rev. D90 (2014) 094503– improves over earlier hotQCD calculations:A. Bazavov et al., Phys. Rev. D80, 014504 (2009)– consistent with results from Budapest-Wuppertal(stout): S. Borsanyi et al., PL B730, 99 (2014)– up to the crossover region the QCD EoS agrees quite well with hadron resonance gas(HRG) model calculations; However,However QCD results are systematically above HRGF. Karsch, RHIC&AGS,BNL 201512

Equation of state of (2 1)-flavor QCD:variance of net-baryonnumber distributionleading order correction agrees wellwith HRG in crossover regionkurtosis*variance 20% deviations from HRG incrossover regionF. Karsch, RHIC&AGS,BNL 201513

Equation of state of (2 1)-flavor QCD:estimating thecorrection:The EoS is well controlled forF. Karsch, RHIC&AGS,BNL 201514

Conserved charge fluctuations and freeze-outTaylor coefficients control also leading termsin several ratios of conserved charge fluctuationsF. Karsch, RHIC&AGS,BNL 201515

Conserved charge fluctuations and freeze-outfor simplicity:freeze-out lineratio of cumulants on ''a line'' in theplane (NLO Taylor expansion)alleventually need tobe expanded in TF. Karsch, RHIC&AGS,BNL 201516

Conserved charge fluctuations and freeze-outfor simplicity:freeze-out lineratio of cumulants on ''a line'' in theplane (NLO Taylor expansion)for the purposeof this talk:alleventually need tobe expanded in TF. Karsch, RHIC&AGS,BNL 201517

QCD vs. HRG and simple scaling argumentsa simple question: How do cumulant ratios change when we increase the baryonchemical potential, in particularor?F. Karsch, RHIC&AGS,BNL 201518

QCD vs. HRG and simple scaling argumentsa simple question: How do cumulant ratios change when we increase the baryonchemical potential, in particular?ori) HRG:for allii) 3-d, Z(2) Ising universality,e.g. sigma models with a critical point:M. Stephanov, PRL 102 (2009) 032301;S. Mukherjee, R. Venugopalan, Y. Yin,arXiv:1506.00645correlation length diverges at the critical point,higher moments diverge with larger exponents200 62 39 27 20117.7F. Karsch, RHIC&AGS,BNL 201519

QCDa simple QCD prediction:for smallQCD:LO Taylor expansion:F. Karsch, RHIC&AGS,BNL 201520

QCDa simple QCD prediction:for smallQCD:LO Taylor expansion:atfit:caution: net-proton is only aproxy for net-baryonF. Karsch, RHIC&AGS,BNL 201521

QCDa simple QCD prediction:for smallQCD:LO Taylor expansion:– What does the curvature inthe data tell us?– Is it consistent with QCDexpectations?caution: net-proton is only aproxy for net-baryonF. Karsch, RHIC&AGS,BNL 201522

Skewness in Next-to-Leading OrderNLO Taylor expansioncurvature is negativeL.Chen (STAR Collaboration),Nucl. Phys. A904-905 (2013) 471c,F. Karsch, RHIC&AGS,BNL 201523

Consequences for the kurtosis on the freeze-out linein NLO Taylor expansionF. Karsch, RHIC&AGS,BNL 201524

Consequences for the kurtosis on the freeze-out linein NLO Taylor expansiontwice the curvature term ofF. Karsch, RHIC&AGS,BNL 201525

Consequences for the kurtosis on the freeze-out linein NLO Taylor expansionF. Karsch, RHIC&AGS,BNL 201526

Generic structure of 6th order cumulants6-th order net ''up-ness'' fluctuations – unlike baryon number fluctuationsstatistically under control;– qualitatively similar6th order cumulantschange rapidly in thecrossover region6th order fluctuations change sign in the transition region at– it is conceivable that they stay small on the freeze-out lineat small values of the chemical potential– they are expected to be large and positive close to the critical pointF. Karsch, RHIC&AGS,BNL 201527

Consequences for the kurtosis on the freeze-out lineintercept atquadratic fit:determines freeze-out temperaturesmaller ratio largerF. Karsch, RHIC&AGS,BNL 201528

Cumulant ratios of conserved net-charge fluctuationswhereare fixed through strangenessneutrality and charge/baryon numberconstraints realized in a HICF. Karsch, RHIC&AGS,BNL 201529

Freeze-out parameter from conserved charge fluctuationscumulant ratios of electric charge fluctuationsconstraints freeze-out temperaturedetermines freeze-out chemical potentialBI-BNL, PRL 109, 192302 (2012)S. Mukherjee, M. Wagner, PoS CPOD2013 (2013) 039F. Karsch, RHIC&AGS,BNL 201530

Mean net-charge over variance ratioslattice QCD (preliminary)NLO LQCD correction assumesnegligible contribution fromcurvature of the freeze-out linenet-proton fluctuations as a proxy for net-baryonfluctuations:systematic effects in some observables;may shift freeze-out temperature 5 MeVF. Karsch, RHIC&AGS,BNL 201531

Taylor expansion of the pressure and critical pointestimator for the radius of convergence:for simplicity :– radius of convergence correspondsto a critical point only, iffif not:– radius of convergencedoes not determinethe critical point– Taylor expansion can not beused close to the critical pointforcesandto be monotonically growing withatF. Karsch, RHIC&AGS,BNL 201532

Estimates of the radius of convergencea challenging prediction fromsusceptibility series forstandard staggered fermions:suggests large deviations fromHRG in the hadronic phasehuge deviationsfrom HRG inth6 order cumulants!HRGHRGS. Datta et al.,PoS Lattice2013 (2014) 202suggests a criticalpoint forat present, wecannot rule it out!BNL-Bielefeld-CCNUF. Karsch, RHIC&AGS,BNL 201533

Kurtosis*variance on the freeze-out linechanges sign incrossover region,can get large at lower T(larger)sketchconsistent treatment requiresknowledge of T-dependenceofon the freeze-out lineansatz:and control over NNLO correctionF. Karsch, RHIC&AGS,BNL 201534

Conclusionsin the rangethe pattern seen in the beam energy dependence ofup to 4th order cumulants of electric charge and proton (baryon)number fluctuations can be understood in terms ofQCD equilibrium thermodynamicsexperimental data atwith this patternmay still be consistentQCD equilibrium thermodynamics sets a baseline for thediscussion of systematic effects which, of course, need to betaken into account for a more quantitative comparison– in particular when one wants to understand thesystematic difference between STAR and PHENIX dataF. Karsch, RHIC&AGS,BNL 201535

preliminary PHENIX resultsF. Karsch, RHIC&AGS,BNL 201536

STAR net-proton data (preliminary)X. Luo (STAR Collaboration,PoS CPOD2014 (2014) 019,arXiv:1503.02558F. Karsch, RHIC&AGS,BNL 201537

decreases increases V. Skokov,Quark Matter 2012F. Karsch, RHIC&AGS,BNL 201538

– the QCD phase diagram – EoS at non-zero baryon chemical potential – cumulant ratios of conserved charge fluctuations – the QCD critical point Frithjof Karsch Brookhaven National Laboratory & Bielefeld University Conserved Charge Fluctuations and Correlations from Lattice QCD and the Beam Energy

Related Documents:

C) its momentum is not conserved, but its mechanical energy is conserved. D) its kinetic energy is conserved, but its momentum is not conserved. E) both its momentum and its mechanical energy are conserved. 12) 13) A fish weighing 16 N is weighed using two spring scales, each of negligible weight, as shown in the figure.

Table 3.4 shows inter-rater correlations; Cohen's (1992) standard for small/medium/large correlations are . r 0.10/0.30/0.50. As a rule of thumb, small and medium correlations are no bar to discriminant validity, but large positive correlations would be a concern. Table 3.4 Correlations Among Adult-Rated Process and Outcome Total Scores

The Princeton Review Practice SAT Physics Subject Test 1 431 GO ON TO THE NEXT PAGE 27. Four point charges are labeled Charge 1, Charge 2, Charge 3, and Charge 4. It is known that Charge 1 attracts Charge 2, Charge 2 repels Charge 3, and Charge 3 attracts Charge 4. Which

K-12 Curriculum &Activity Guide. Correlations to Florida State Standards (Correlations) Understanding and Using the Project Aquatic WILD K -12 Curriculum & Activity Guide (Guide) Standards Correlations . Focus: The standards listed in the Correlations are Florida Next Generation Sunshine State Standards (N

F K q 1q 2/r2 (Coulomb's Law) where K depends on the system of units K 8.99x10 9 Nm 2/C 2 (in MKS system) K 1/(4 πε0) where ε0 8.85x10-12 C 2/(Nm 2) Electric Charge : electron charge -e e 1.6x10-19 C proton charge e C Coulomb Electric charge is a conserved quantity (net electric charge is never created or destroyed !) q 1 q 2 r

Linear momentum is always conserved for an isolated system. Of course, we deal with components ix fx iy fy p p and p p I like to say that momentum is conserved in collisions and explosions. Note: The total momentum of the system is conserved. The momentum of an individual particle can change. Problem 18.

PAM vs BLOSUM PAM is based on closely related sequences, thus is biased for short evolutionary distances where number of mutations are scalable PAM is based on globally aligned sequences, thus includes conserved and non-conserved positions; BLOSUM is based on conserved positions only

Momentum is Conserved! Momentum is “Conserved” when there is no external impulse, meaning it cannot be created or destroyed Momentum can be transferred but if it is conserved, then P tot,i P tot,f. Thus P tot does not change with time absent external f

2 I. Binary Compounds A. Covalent Compounds B. Ionic Compounds 1. Metals with a single charge a. alkali metals (1 charge) b. alkaline earth metals (2 charge) c. Aluminum ion (3 charge), Silver ion (1 charge), Zinc ion (2 charge), and Cadmium ion (2 charge) 2. Metals with multiple charges I

Charge q C Linear charge density l C/m Surface charge density s C/m2 Volume charge density r C/m3 Table 22-2 Fig. 22-10 A ring of uniform positive charge.A differential element of charge occupies a length ds (greatly exaggerated for clarity).This element sets up an electric Þeld at point P.T

Mitigating Power Fluctuations in Electric Ship Propulsion With Hybrid Energy Storage System: Design and Analysis . system optimization. Power fluctuation mitigation and HESS loss . [10], and [11]. At the same time, for electrical sys-tems, power fluctuations, especially when the propeller is in and out of water, will cause unpredictable .

policy. Section 7 concludes. 2 International trade fluctuations: theory vs evidence In this section, we document salient features of international trade fluctuations and contrast them with the implications of standard models of

under the title Fluctuations of Glaciers, at fi rst by the Permanent Service on the Fluctuations of Glaciers (PSFG [Kasser 1970]) and then, after the merger of the PSFG with the Temporary Technical Secretariat for the World Glacier Inventory (TTS/WGI) in 1986, by the WGMS. An extensive overview of the corresponding lit-

Chapitre 4 - Crises et fluctuations économiques - 2018-2019 6 Lorsque le taux de chômage dépasse u*, les salaires réels diminuent, ce qui rétablit la part des profits et permet une reprise de l'investissement. Emmanuel Combe, Précis d'économie, Collection Major, PUF, 2012 Document 12 - Les limites des explications mécanistes des fluctuations économiques

Falsifying "inflation" We still need inflation to explain the flatness problem! (Homogeneity problem can be explained by a bubble nucleation.) However, the observed fluctuations may come from different sources. So, what I ask is, "can we rule out inflation as a mechanism for generating the observed fluctuations?" 8

Pearson’s (r) and Spearman’s (rs) correlations were calculated for the data. Knowledge and attitude had a weak correlation (r .220, rs .202). Attitude and behavior components demonstrated a moderate correlation (r .480, rs .494). These correlations substantiated my hypothesis that knowl

Laughlin-Jastrow factor, which leads to special, later intro-duced, Girvin-MacDonald GM! correlations in the bulk,2 and Wen’s correlations on the edge.3,4 The Laughlin-Jastrow factor is ever present in QHE states—it exists even in the compressible half-filled state,5 for which an explicit wave function has been proposed by Rezayi and Read .

generalized correlations are the highest correlations that can be achieved through linear orthogonal combinations of each of the two sets of factors.5 The four continuous industry factors (market, oil, finance and electricity) yield the very high generalized correlations of 1.00, 098, 0.95 and 0.80 with the four statistical continuous factors.

graphic correlations between wellbores in petroleum basins. Few publications, however, relate defined chemical stratigraphy to physical correlations, and none have been found that do so in flu-vial systems. Here, chemostratigraphy is applied to Permian flu-vial sediments within the Beaufort Group of the Karoo Basin in

T Readers series, a graded readers series for low-level learners of English. These free teacher’ s notes will help you and your classes get the most from your Shrek Popcorn EL T Reader. Level 1 Popcorn EL based on a 200 headword list. There are no past tenses at this level. T Readers level 1 is for students who are beginning to read in English, Shrek has a total story wor dcount of 546 wor .