ATLAS measurement of dipolar flow (v 1 ) in Pb-Pb collisions Jiangyong Jia for the ATLAS Collaboration WWND 2012 April 7 th - 14 rd Based on results in (v 1 -v 6 summary)

Motivation 2 22 33 44 Initial geometry has multi-pole shape due to fluctuations. ~400 nucleons>20000 particles Probe shape of initial geometry and transport properties Alver, Roland etc Fourier expansion of azimuthal distribution in momentum space Also measure with two-particle correlation (2PC)

Eccentricity from Glauber model Sizable eccentricities for all order v n ~ε n in linearized hydro, but Complicated by dynamic mixing during expansion, especially for n>3. Higher order v n damped more by viscosity. ε 1 is smaller, but v 1 is not affected by dynamic mixing and less affected by viscosity. 3

Two-particle correlation (2PC) method Long range structure (“ridge”, “double-hump”) well described by v 1,1 -v 6,6. Factorization works for n=2-6 Soumya Mohapatra’s talk Not for n=1. 4 |Δη|>2

v 1 physics v 1 (η) dependence has a rapidity-odd and a rapidity-even component rapidity-odd v 1 reflect sideward bounce off, small at mid-rapidity rapidity-even v 1 is associated with the dipole asymmetry in initial geometry v 1 also affected by global momentum conservation Balance of p T of one particle by all other particles: N. Borghini nucl-th/ Inversely proportional to multiplicity M, linear in p T. 5 Odd component: vanish at η=0 Even component: ~boost invariant in η Fig from P. Stankus

Dipole in Cosmic Microwave Background The CMB is dominated by a dipole, representing the Doppler shift of observer (600km/s) 6

Rapidity-even v 1 and expected trend in v 1,1 Values inferred from STAR 2PC data by estimating the second term. 7 Expected v 1,1 contribution from rapidity-even v 1 a,b both at high p T  positive and increase with p T a,b (convex shape) a,b both at vey low p T  positive a at low p T, b at high p T  negative, more negative at higher p T b (concave shape) Luzum et.al Do we see these trends in the data?

Δη dependence of v 1,1 Peripheral collisions(GMC dominated): v 1,1 is always negative at large Δη. More negative at higher p T. Magnitude decrease at large Δη Influence of jets and dijets Central collisions(flow dominated): v 1,1 is negative at low p T, become positive at large p T. Magnitude flat in Δη. Consistent with a rapidity-even v 1. Integrate over 2<|Δη|<5 and look at the p T dependence 8

p T dependence of v 1,1 data Peripheral collisions (GMC dominated): v 1,1 negative, linear in p T a,p T b. Central collisions (flow dominated): v 1,1 becomes positive at GeV range, but on top of a negative momentum conservation component Cross each other at low p T  where flow driven v 1,1 ~ zero. 9 Can we account for both with a two-component fit?

Two-component fit Simultaneous fit of v 1,1 data of each centrality with a function Simple χ 2 minimization v 1 Fit (p T ) defined at 15 p T, and interpolate in between. Total 16 parameters Systematic checks: Interpolation form: Linear or cubic spline. Number of interpolation points (vary within 9-21 points) Vary p T range of fitting (0-5 to 0-10 GeV) Account for correlations between data points and fitting parameters. 10 Similar fit in arXiv:

Fit for 0-5% centrality Agrees with data within 1σ at p T <6 GeV. Slightly more deviation ~ 2σ in some higher p T bin. 11

Understanding v 1,1 = in 2PC (0-5%) Correlation function well described by v 2 -v 6 and v 1,1 12 Most of v 1,1 is due to momentum conservation ~1.5 : 1~3:1 Most of v 1,1 is due to dipolar flow

Fit for 40-50% centrality Despite that the v 1,1 is always negative, significant positive v 1 can still exist. 13

Fit result vs p T and centrality v 1 Fit (p T ) peaks around 4-5 GeV, peak-value increases with centrality by about 20%. Less viscosity damping, reflecting the increase in ε 1 ? 14 Glauber

Compare with v 2 and v 3 v 1 comparable to v 3 but peak at higher p T. High p T v 1 seems drop slower than v 2,v 3. Limitation of two-component assumption? Both L dependent eloss become important? v 1 >v 2 in jet absorption model calculation in central collisions L3L3

About momentum conservation component The system that conserves momentum may only be a subset of the event c dN/dη but decrease toward peripheral by 20-30% For =1 GeV 2, M=5000 in 0- 5% events, about 3 units in rapidity Increases for peripheral collisions, about ~4 unit for 40-50% centrality 16 ? M. Lisa

Comparison with AMPT model: arxiv: AMPT=HIJING +F.S scattering. Interaction strength controlled by α s and μ. HIJING only need momentum conservation, while AMPT need both The complex p T dependence of v 1,1 can naturally be generated from final state interaction 17 v 1,1 calculated for pairs with |Δη|>1.5 Arxiv

Centrality and energy dependence p T dependence is qualitatively similar to what is seen in data and hydro predictions Weak dependence on centrality Increases from RHIC to LHC 18

Dependence on the strength of interaction More sensitive to changing α s than changing screening mass μ Values from a larger screening mass and smaller coupling constant is closer to the data from ATLAS: α s =0.33, σ=1.5mb 19

Summary The cos(Δ ϕ ) component of the 2PC data suggests contributions from rapidity-even dipolar flow and global momentum conservation. A two-component fit is used to extract the individual contribution from these two components Extracted v 1 cross zero at p T ~1 GeV, reaches a value of 0.1 (comparable to v 3 ), and decreases at higher p T. The p T at which it reaches maximum is 1 GeV higher than other v n. Extracted v 1 shows a mild increase with centrality (~20%) The system conserving momentum only involves a subset of the event AMPT transport model calculation confirmed qualitative trend at low p T. Dipolar flow is indeed associated with final state interaction Flow magnitude is sensitive to the strength of the interaction 20

Backup 21

Extracting the η dependence: Extend the procedure to study rapidity dependence by using a simultaneous fit of the 4-D v 1,1 data. Only v 1,1 data satisfying a certain η gap is used (|Δη|>2) The number of independent c values can be restricted by symmetry Impose the constraint v 1 (η) = v 1 (−η) 22

η dependence of v 1 and c from AMPT Weak η dependence at RHIC energies but has a dip at mid-rapidity at LHC energy  strong longitudinal flow? c is not constant: contribution from momentum conservation is not constant across whole η and |∆η| range and shows a strong dependence on |∆η| 23

24

25

26