Multipoles and Coherent Gluon Radiation Plenary session

Transcription

1 Multipoles and Coherent Gluon Radiation Plenary session Lanny Ray, Univ. of Texas at Austin Higher-order harmonics? BFKL Pomeron diagrams and v On to the LHC Summary and Conclusions STAR Collaboration Meeting LBNL 0/7/03

2 Correlation measure Event ρ sibling (p,p ) ρ reference (p,p ) Fill D histograms ( -, - ), (p t,p t ) Event Number of correlated pairs per final-state particle ref dn ch dd sib mix FittingModel (, ), (, ) A 0 A D cos( ) A (Same side D Gaussian) " v Q cos( ) n " where : A Q dnch v d Relation between the quadrupole amplitude and v

3 What about higher harmonics, v n? Example: 00 GeV Au+Au 5-9% No additional model elements required Introduce a sextupole A S cos(3 ); maintain away-side fit: D Q D Q S D Q S D Q net sextupole contribution Same-side D peak = D ridge + reduced D Gaussian = Non-Gaussian D peak Issue is description of the same-side peak. (LR, Prindle, Trainor, arxiv: ) 3

4 Non-Gaussian models of same-side D peak 00 GeV Au+Au 8-38% scale x6 sextupole SS DG ridge NG exponents polynomial poly+ng quartic D D D / SSG exp Quartic: exp : exponent NG polynomialwith or without exp Non - Gaussian exponents : : -Side D Gaussian ridge Same A A A e A even k k s SS D peak model Non - Gaussian fit model Standard scale x6 Non-Gaussian models Slight leptokurtic shape at -3 significance. (LR, Prindle, Trainor, arxiv: , accepted Phys. Rev. C)

5 Sextupole (v 3 ) one example of a NG peak Reduction in c /DoF using sextupole and using the other NG models absolute c /DoF The net effect of the sextupole (v 3 ) is to allow a small non-gaussian shape for the same-side D peak. It is not unique in that regard; other NG models work as well or better. The only issue here is the small NG shape of the SS D peak. (LR, Prindle, Trainor, arxiv: , accepted Phys. Rev. C) 5

6 ATLAS Pb+Pb.76 TeV 0 %, p t = 3 GeV/c; (ATLAS, PRC 86, 0907 (0)) Data Fit Std. Fits with NG exponents, A Q < 0 ASG<0, no quad A Q,A S <0 ASG, A S <0 These data do not require a sextupole! v 3 >0 fits can be forced but give poor c. (LR, Prindle, Trainor, arxiv: , accepted Phys. Rev. C) 6

7 BFKL Pomerons - gluon interference E. Levin and A. H. Rezaeian, Phys. Rev. D 8, 0303 (0) N N Multiple gluon emission from or more Pomerons interfere producing azimuth anisotropy wrt momentum transfer Q T Two-BFKL Pomeron Exchange with two-gluon emission & interference Resulting correlation: cos( ) Random emission results in uniform dependence. This mechanism was proposed to explain the same-side ridge. However, it is a pqcd prediction for a quadrupole correlation, or v. (Balitsky, Fadin, Kuraev, Lipatov) 7

8 BFKL Pomerons & color-dipoles BFKL-saturation (glasma) model: Dusling and Venugopalan, arxiv: back-to-back di-gluons Quadrupole (v ) (from Raju) Color Dipole Model: Kopeliovich et al. Phys. Rev D78, 009 (008). v 8

9 MIT p+pb Workshop in honor of Wit Busza May 03 Many, very interesting talks: Miklos Gyulassy The Revenge of Wit : Will the Biblical Pillars of AA 003 be left Standing after the pa of 03? 9

10 0

11

12

13 3

14

15 But these questions have already been raised. Angular correlations jets, dijets (away-side) not dissipated Glauber superposition of minijets (transparency); large quadrupole (v ) Constituent v transverse rapidity boost, non-hydro (Romatschke) Quadrupole log(s)n bin scaling initial-state only; final-state effects? gluon-interference? ST All of this and much more were known before p+pb, BES, LHC. 5

16 BFKL Pomeron Application to 00 GeV p+p (work in progress) Two-gluon density for -Pomeron exchange: N IPh is the prob. for two parton showers in a N-N collision. d dyd p t p, Q q 3 d qt QT pt QT p t T t t 3 p t qt qt qt pt QT cos q t azimuthal anisotropy Construct correlations; estimate momentum integrals using the saturation limit (Q S ): n No. Pomeron showers/collision for p t Q S saturation: Q T ~ q t ~ Q S semi -saturated (Levin, Rezaeian PRD 8, 0303 (0)) Q T m /5 6

17 BFKL Pomeron Application to 00 GeV p+p Estimate Pomeron probabilities: Fit 00 GeV p+p frequency distribution assuming,, parton showers with probabilities P, P, Data (NBD) Mean N ch per parton shower equals the minbias mean.5 / N ch Poisson Each shower produces a Poisson distribution. P = 0.9, P = 0.09, P 3 = P ~ 0 P P n n n ch h h n n s s n n ch nch n h ch Pom Pom + hard &Pom + hard (fit), soft hard, per unit (STAR, PRD 7,03006) 7

18 BFKL Pomeron Application to 00 GeV p+p Estimate p+p minbias quadrupole, v : Probability weighted sum over & Pomeron diagrams; p t -integral correlation; Levin & Rezaeian Q S. N Q ch ref T Quad q /.5, Nch P P P t t / Q, saturated S 8 m /5QS, semi -sat p p 0.88 (GeV/c) Q T, Q S q 0.6 GeV cos A, m Prindle (STAR) ISMD-03 Q cos GeV Predicted Minimum-bias quadrupole amplitude: A Q = ; [semi-sat saturated] From D. Prindle (STAR) ISMD-03 poster: A Q = 0.00 for 00 GeV p-p NSD minbias; v = 0.07 A Q dnch v d STAR Preliminary 8

19 BFKL Pomeron Application to 00 GeV p-p N ch dependent quadrupole: ref nch # correl. Pom pairs total# pairs Prindle (STAR) ISMD-03 Q S =0.6 GeV P ( n nch ch ) n ch n ch n ch p t m 5Q 8 S cos Q S =0.8 GeV STAR Preliminary 9

20 BFKL Pomeron Application to 00 GeV p-p N ch dependent quadrupole: Prindle (STAR) ISMD-03 Or, find Q S for the three saturation assumptions in L & R: Fit Data: Solve for Q S n n ch s A Q ns ( nch ) STAR Preliminary Saturation limit Semi-saturated, m =.6 GeV Semi-saturated, m =0.8 GeV 0

21 7 TeV p+p from CMS CMS Collaboration, JHEP 009,09(00). Quadrupole Fits[Phys.Rev. D 8, 0300] obtain after converting to / A Q dnch, N 0, p at 8 at 7 TeV t d ref :

22 BFKL Pomerons for 7 TeV p+p (CMS, JHEP0, 079 (0)) Fit the CMS p+p NSD 7 TeV minbias multiplicity frequency distribution data; Mean n ch / = 6.0; assume ~ 0.0; minbias average probabilities: P - = {0.67, 0.7, 0.06, 0.0} Data, < 0.5 Fit with,,3 P + n h Pomeron Probabilities P P P 3 Illustrative only! Soft-hard decomposition remains to do., &,,&3 Pomerons, no hard scattering

23 BFKL Pomerons for 7 TeV p+p A N Q Q ch Nch T q n / 6.0, P n t n( n ) t 0. (GeV/c) T / Q, saturated S 8 m /5QS, semi -sat p p Q, Q S q 0.6 GeV, and 3 Pomeron showers included, m GeV Predicted range for A Q for 7 TeV p+p minbias: to 0.05 Compared to 00 GeV minbias p+p: to The increase is due to the larger pre-factor dn ch /d, larger -Pomeron probability, and the appearance of 3-Pomeron shower events. Illustrative only! Soft-hard decomposition remains to do; as well as Q S estimates. 3

24 5.0 TeV p+pb at the LHC Fit with quadrupole: A Q 0, at dnch d 3- x larger than the 7 TeV p p quadrupole (0.008) at similar N 5, ch. 30 ATLAS, PRL 0, 830 (03) N part [,0] at LHC In the BFKL-Pomeron model typical high multiplicity p+pb collisions will have a couple of multi-pomeron events producing quadrupoles. Those quad. correlations add; they do not cancel with random orientation of each N-N scattering plane: ( p A) ( p N) Quad N bin Quad Monotonic increase in same-side -extension, ~ inc. quadrupole amplitude

25 NN Superposition for 00 GeV p+au In Kopeliovich et al s color dipole model v in p+a is computed from the singles anisotropy wrt the p+a reaction plane. Random N-N orientation suppresses the net anisotropy and v. However, RP and EP are irrelevant for inclusive v measurements which equal the correlations on relative azimuth. In a Glauber superposition model quadrupoles from N+N add linearly in p+a and A+A. Naively we expect A Q (p+a) ~ A Q (NN,minbias) and A Q (A+A) ~ (N bin /N part )A Q (NN,minbias). Predicted N ch frequency distribution p+au Monte Carlo Glauber Sample b, find N bin Sample p+p NBD and get n ch (NN) Use A Q (n ch ) to calculate (NN) Sum to get (p+au), N ch (p+au) and A Q (p+au) A Q,p+p (n ch ) ~ parabolic ~ linear A Q (p+au) increases with multiplicity = constant 5

26 NN Superposition for 00 GeV p+au The naïve expectation A Q (p+a) ~ A Q (NN,minbias) ~ 0.00 was not realized. Why? To illustrate this I applied the MCG superposition model for larger numbers of N-N collisions. Eventually, we recover the naïve expectation, however large quadrupoles persist at higher N ch. The p+a quadrupole increases at the upper end of the frequency distribution because those events are biased toward higher n ch N+N collisions, with larger A Q. 6 0 A Q (NN,minbias) 0 6

27 Summary & Conclusions Higher-order harmonic (sextupole - v 3 ) descriptions of D angular correlations are actually describing small, non-gaussian structure in the same-side D (minijet) peak. The detailed structure of this peak is the real issue. Claims that these higher-order v n have been discovered in the data are questionable. Given the properties of angular correlations and the quadrupole in particular we may ask if there is a pqcd explanation for v. The BFKL-Pomeron model of Levin and Rezaeian was applied to 00 GeV and 7 TeV p+p frequency distributions and quadrupole correlations. Although there are large uncertainties due to saturation scale estimates (Q S ), the quadrupole predictions are consistent with recent data. Further study and application of pqcd (BFKL Pomerons, color-dipole) to the quadrupole correlations now observed in p+p, p+a and A+A at RHIC and LHC is warranted. 7