parity non-conservation OR momentum & charge conservation Scott Pratt Michigan State University

Transcription

1 parity non-conservation OR momentum & charge conservation Scott Pratt Michigan State University

2 Parity Violation B B B E E E E a B a fluctuates randomly, but same sign with flux tube fluctuates as 1/Ntubes fluctuations span large rapidity range

3 Parity Violation (Fluctuation) (numerous papers by Kharzeev et al) B B B E E E E a B a couples to electromagnetic E B Inside flux tube, E and B fields can rotate into one another

4 Parity Fluctuations B fields add coherently E fields cancel in participant region Coupling to flux tubes generates non-zero Ey

5 Parity Fluctuations E y 0 positives negatives sinφ 1 sinφ 2 same sign sinφ 1 sinφ 2 opp sign > 0??? OR EQUIVALENTLY cos(φ 1 + φ 2 ) opp sign cos(φ 1 + φ 2 ) same sign > 0???

6 From STAR Same sign & opposite sign should have yielded opposite results STAR, PRL 2009

7 I. Correlations that separate charge Consider: γ p cos(φ i + φ j +- cos(φ i + φ j ) ss Parity Fluctuations Local Charge Conservation + Elliptic Flow Fluctuating Initial Conditions & E-Field HBT

8 Estimate Magnitude of Parity Signal Let E = B in each tube, γ p ~ Δp2 / p t 2 N tubes, Δp 40 MeV --> Signal of Correct Size E y 0 Only fraction of charges existent at τ=0.2 fm/c (reduce by 1/10) Particles absorbed and rethermalized (reduce by 1/20) E should be less by e/2π (reduce by 1000) Contribution 4-6 orders of magnitude too low positives negatives

9 Fluctuating IC E y 0 Monte-Carlo Calculations give contribution that is too small by 1/1000

10 Correlations from HBT Both Coulomb and Bose Differ between same- and opposite sign Since charge is conserved, must consider pair-wise correlations Messy calculation Appears to small by 1/100

11 Correlations from Local Charge Conservation Balancing Charge has similar y, pt, ϕ Charge Balance Functions B(Δy) N + (Δy) N ++ (Δy) N + Correlations Equally Feasible

12 Balance Functions DATA: STAR PRL, 2004 Blast-Wave: Cheng et al, PRC 65, 2004

13 B(Δφ) Dip from HBT

14 B(Δφ) Balance Function ave <cos( )> Run7, 0 < < Run4, 0 < < N part Radial flow more dominant for central collisions

15 Relation to B(Δφ) probability for charge observed at φ to have balancing particle emitted at φ +Δφ Three Contributions

16 v <c >! 2! b! more pairs in-plane than out-of-plane (elliptic flow)! v! 2c!

17 v!!"# balancing charge more likely to be found towards in-plane than out-of-plane (elliptic flow)!

18 Blast-Wave Calculation STAR parameterization (STAR, PRC 72, (2005)) Add Charge Conservation Te xt Correct for efficiency and acceptance (Cheng, et al., PRC (2004))

19 Normalizing B(Δφ) Multiply model B(Δφ) by 0.4 to reproduce experimental normalization (accounts for efficiency and percentage of balanced charge outside acceptance

20 RESULT % centrality Readily explains result perfect locality too extreme for peripheral collisions

21 More Differentially 0-5% centrality 20-30% centrality STAR Blast Wave 40-50% centrality

22 Charge Separation: Lessons Look at Differential Observables!!!! (Ghosts of Intermittencies Past) B(Δφ) Fluctuating Parity or IC Beware Non-Quantitative Predictions

23 II. Correlations not related to charge separation Consider: cos(φ i + φ j ) ss Momentum Conservation

24 Momentum Conservation cos(φ 1 +φ 2 ) = ( cosφ i cosφ j sinφ i sinφ j ) i<m, j<m,i j cosφ i = sinφ i 0 i cos(φ 1 +φ 2 ) cos(φ 1 +φ 2 ) same sign v 2 3M + i M 2 ( cos2φ i ) i<m, j<m,i j M 2 Assume all particles have same pt If v2 were weighted with pt 2, result would be model independent cos(φ 1 + φ 2 ) ʹ p t,i p t, j cos(φ i + φ j ) i j M p t 2 = v ʹ 2 M

25 Momentum Conservation (momentum "bath" from spectators) initial, uncorrelated & isotropic final momentum p i = k i + qi from local scatterings q i = 0 i Since k doesn't contribute to v2, result holds: cos(φ 1 + φ 2 ) same sign = v 2 M

26 Charge Conservation Magnifies Momentum For every positive particle with momentum px, there exists a negative particle with similar momentum Include (1/3) of momentum balance from neutrals -> nearly twice as much momentum to balance cos(φ 1 + φ 2 ) same sign = f P 2v 2 3M (1+ cosδφ balance )

27 Putting "knowns" to left 3M 2v 2 cos(φ 1 + φ 2 ) same sign (1+ cosδφ balance ) f P Overshoots crude estimate

28 To Reduce Model Dependence cos(φ 1 + φ 2 ) ʹ ss p t,i p t, j cos(φ i + φ j ) i j M p t 2 f P 2 ʹ v 2 3M 1+ cosδφ BAL ( ) Other contributions: Differential quenching, HBT...

29 Conclusions γ p cos(φ i + φ j +- cos(φ i + φ j ) ss explained by charge conservation + elliptic flow no evidence for parity fluctuations same-sign correlations are open question, but significant contribution comes from p- conservation charge/momentum conservation effects are interesting in their own right!!!

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