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The 9th Workshop on Hadron physics in China and Opportunities Worldwide
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2017年7月24-28日，南京 Hadron2017
The 9th Workshop on Hadron physics in China and Opportunities Worldwide
Globally Polarized Quark Gluon Plasma in Non-Central A+A Collisions - - PowerPoint PPT Presentation
Globally Polarized Quark Gluon Plasma in Non-Central A+A Collisions - - PowerPoint PPT Presentation
The 9th Workshop on Hadron physics in China and Opportunities Worldwide Globally Polarized Quark Gluon Plasma in Non-Central A+A Collisions at High Energies (Liang Zuo-tang) (School of physics, Shandong
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Outline
Ø Introduction Ø Orbital angular momentum of QGP in non-central AA collisions Ø Global polarization of QGP in non-central AA collisions Ø Direct consequences: Hyperon polarization & vector meson spin alignment Ø Measurements and results Ø Further discussions and developments Ø Summary and out look
ZTL & Xin-Nian Wang, PRL 94 (2005), Phys. Lett. B629 (2005); Jian-Hua Gao, Shou-Wan Chen, Wei-Tian Deng, ZTL, Qun Wang, Xin-Nian Wang, PRC77 (2008). ZTL, plenary talk at the 19th Inter. Conf. on Ultra-Relativistic Nucleus-Nucleus Collisions (QM2006).
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Introduction
Nuclear physics: Nuclear shell model and L-S-coupling Condensed matter physics: Spintronics High energy physics: proton’s spin crisis
Spin effects usually provide us with useful information and often surprises.
Much more …....... Examples:
p+ p/ A→ Λ+ X
p(↑)+ p→ p+ p
Ø Since 1970s: Transverse polarization of hyperon in unpolarized pp or pA collisions; Ø Since 1970s: Single-spin left-right asymmetry in inclusive production Ø Since 1970s: Spin analyzing power in pp elastic scattering
p(↑)+ p→π + X p(↑)+ p→ p+ p
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Introduction
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Introduction
Do spin physics in AA collisions without polarizing A ?
heavy ion collider polarized pp collider heavy ion physics spin physics spin physics in heavy ion collisions ? RHIC
two important aspects in QCD physics Nuclear dependence Spin dependence
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Global Orbital Angular Momentum
Y b
- Huge orbital angular momentum of the colliding system.
reaction plane: can be determined by measuring v2 and v1.
normal of the reaction plane impact parameter
| | b p b p n
in in re
- ×
× =
- Ly in unit of 105
b/RA
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Global orbital angular momentum
Gradient in pz-distribution along the x-direction
x z impact parameter b
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Gradient in pz-distribution along x-direction
GeV s c s p 22 . 2 ) ( 2 / ≈ = Au+Au at 200AGeV pz(x,b) in unit of p0
ZTL & X.N. Wang, PRL 94, 102301(2005), PLB 629, 20(2005); J.H. Gao, S.W. Chen, W.T. Deng, ZTL, Q. Wang, X.N. Wang, PRC77, 044902 (2008). GeV/fm 68 . / 2 ≈
A
R p
dpz\dx in unit of 2p0\RA
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Local Orbital Angular Momentum
x Δ
x dx dp p
z z
Δ = Δ 7 . 1 − ≈ Δ Δ − = Δ x p L
z y
for b =RA, Δx=1fm
impact parameter of the two partons
T
x
- T
x has a preferred direction ( ) !
b
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Question
Can such a local orbital angular momentum be transferred to the polarization of quark or anti-quark through the interactions between the partons in a strongly interacting QGP?
take a collision as an example.
q1 +q2 → q1 +q2
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average over the preferred directions
T
x
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Quark scattering with fixed reaction plane
Scattering amplitude in momentum space
) , (
,
E q M
T
i
- λ
λ
spin independent part
Differential cross section w.r.t. the impact parameter
spin dependent part
T
x
- =
=
∑ ∫
⋅ −
) , ( ) , ( 2 1 ) 2 ( ) 2 (
* , , ) ( 2 2 2 2 2
E q M E k M e k d q d x d d
T T x q k i T T T
i i i T T T
- λ
λ λ λ λ λ
π π σ
+λ dΔσ d2xT
dσ unp d2xT
Quark polarization after the scattering:
unp q
P σ σ / Δ ≡
a 2-dimensional Fourier transformation to impact parameter space
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Qualitative results
), ( 4
2 2 2 T D s T T unp
x K c x d d µ α σ =
- Static potential model with “small angle approximation”
Both have exactly the same form !
) ( ) ( 4 ) ( ) (
1 2 2 T D T D s T q D T T
x K x K c m E E p x p n x d d µ µ α µ σ
λ
+ × ⋅ − = Δ
- Bessel functions
) (
2 2 2 2 T s qq T T T unp
x F c x d d x d d x d d α σ σ σ = + ≡
− +
- QCD at finite temperature with HTL(hard thermal loop) gluon propagator
) ( ) (
2 2 2 2 T s qq T T T T
x F c x p n x d d x d d x d d Δ × ⋅ − = − ≡ Δ
− +
α σ σ σ
λ
- scalar functions of xT
spin direction of the quark after the scattering
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Qualitative results
dΔσ d2xT ∝−! nλ ⋅(! p× ! xT )
has a preferred direction
! xT
! b
has a preferred direction
! p× ! xT
−! nre ∝ ! pin × ! b
a polarization of quark in the direction opposite to the normal of the reaction plane!
normal of the AA-reaction plane
dΔσ d2xT = dΔσ d2xT ⎛ ⎝ ⎜ ⎞ ⎠ ⎟
max
at ! nλ = −! nre
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Quantitative results with QCD at finite temperature
Δp/T
- Quark polarization
Pq T: temperature
ZTL & X.N. Wang, PRL 94, 102301(2005), PLB 629, 20(2005); J.H. Gao, S.W. Chen, W.T. Deng, ZTL, Q. Wang, X.N. Wang, PRC77, 044902 (2008).
P
q ∼0.02−0.25
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A new picture of QGP in non-central AA collisions
f
p
- p
- T
x
- re
n
- The scattered quark acquires a
negative polarization in the normal direction of the reaction plane!
“global polarization”
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Direct consequences
e+e− → Z 0 → ! q + ! q → H(or V)+ X
Compare to: global polarization of quarks & anti-quarks polarization
- f hadrons
hadronization
ρ00 : probability for the third component of the spin of K*0 to take zero.
In a non-central AA collision:
OPAL e+e− → K *0 + X ρ00=1/3: unpolarized Vector meson spin alignment Lambda polarization
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Consequence I: Hyperon polarization
Recombination scenario
P
u = P d = P u = P d = P s = P s
Hyperon Λ Σ Ξ Ω PH Ps PH in the case that Pq = Ps Pq Pq Pq Pq
We expect
P
u = P d = P u = P d ≡ P q, P s = P s .
P
H = P q for all H's and H 's.
In the case that
4P
q − P s −3P sP q 2
3−4P
qP s + P q 2
4P
s − P q −3P sP q 2
3−4P
qP s + P s 2
P
s(5+ P s 2)
3(1+ P
s 2)
q1
↑ +q2 ↑ +q3 ↑ → H↑
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Consequence I: Hyperon polarization
Fragmentation scenario
Hyperon Λ Σ Ξ Ω PH PH in the case of Pq =Ps PH in the case of Pq =Ps and ns =fs
nsP
s
ns +2fs
4 fsP
q −nsP s
3(ns +2fs) 4nsP
s − fsP q
3(2ns + fs) P
s
3 ns ns +2fs P
q
4 fs −ns 3(ns +2fs)P
q
4ns − fs 3(2ns + fs)P
q
P
s
3 3
q
P
Nu :Nd :Ns =1:1:ns for quarks in QGP Nu :Nd :Ns =1:1: fs for quarks produced in fragmentation
3
q
P 3
q
P 3
q
P
q↑ → H + X
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Consequence I: Hyperon polarization
Some of the expected qualitative features
n The same for hyperons and anti-hyperons. n (Approximately) the same for different hyperons. n No polarization at b=0, increases approximately linearly with b.
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Consequence II: Vector meson spin alignment
q↑ →V + X or q ↑ →V + X
ρV( frag) >1/3 for q↑ →V + X or q ↑ →V + X
ρ00
ρ( frag) =
1+ βP
q 2
3− βP
q 2 ,
ρ00
K*(rec) =
fs ns + fs 1+ βP
q 2
3− βP
q 2 +
ns ns + fs 1+ βP
s 2
3− βP
s 2 ,
In analog to (parameterization)
e+e− → Z 0 → ! q + ! q → K *+ + X
β ≈0.5
ρ00
V(rec) <1/3 for q↑ +q ↑ →V
ρ00
ρ(rec) =
1− P
q 2
3+ P
q 2 ,
ρ00
K*(rec) =
1− P
qP s
3+ P
qP s
,
Fragmentation scenario Recombination scenario q1
↑ +q2 ↑ →V
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Measurements
dN dΩ* = N 4π (1+αP
H cosθ *)
Hyperon: Spin self-analyzing parity violating decay
dN dΩ* = 3N 4π [(1− ρ00
V )+(3ρ00 V −1)cos2θ *].
Vector meson: Strong decay H → N + M
V → M1 + M2
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Earlier Measurements by STAR on global polarization STAR Collaboration
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Results of STAR beam energy scan
STAR Collaboration, arXiv:1701.06657 [nucl-exp] (2017).
l At each energy, a polarization is
- bserved at 1.1-3.6σ level
l The polarization decreases with
increasing energy
l Averaged over energy l (Electro)magnetic field leads to
difference between and
P
Λ =(1.08±0.15)%
P
Λ =(1.38±0.30)%
P
Λ
P
Λ
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Further theoretical discussions/developments
Other directly measurable quantities:
(1) Spin alignment of vector meson
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“Lambda polarization and phi spin alignment Measurements at RHIC”, Aihong Tang (BNL), talk to be presented in workshop on “QCD physics and ‘973’-project annual exchange meeting”, August 1-5, Weihai, China.
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Further theoretical discussions/developments
Other directly measurable quantities:
Influence from hyperon decay on Λ polarization is very large!
E.g.: take only (1/2)+ baryons into account.
P
Λ final = P Λ direct 2+3λ(1+γ )
6(1+ λ) = 0.33P
Λ direct for λ →0
0.44P
Λ direct for λ =1
⎧ ⎨ ⎪ ⎩ ⎪
(2) Polarization of other JP=(1/2)+ hypeons and anti-hyperons
t
Λ,Σ0 D
= −1/3; tΛ,Ξ
D =(1+γ )/2, γ = 0.87
Σ0 → Λ+γ Ξ→ Λ+π
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Decay spin transfer factor for a parity conserving decay if M is a JP=0- meson.
Hi → H j + M
Other (1/2)+ hypeons and anti-hyperons are more sensitive.
Decay spin transfer factor:
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Further theoretical discussions/developments
Other directly measurable quantities:
(3) Spin correlation of hyperon(s) and/or anti-hyperon(s)
CNN
H1H2 ≡ σ(↑↑)+σ(↓↓)−σ(↑↓)−σ(↓↑)
σ(↑↑)+σ(↓↓)+σ(↑↓)+σ(↓↑) = P
H1 ⋅P H2
dN1 dΩ1
* = 1
4π (1+α1 ! P
H1 ⋅ !
ncosθ1
*)
dN2 dΩ2
* = 1
4π (1+α2 ! P
H2⋅ !
ncosθ2
*)
dN12 dΩ1
*dΩ2 * =
1 (4π)2(1+α1 ! P
H1 ⋅ !
ncosθ1
* +α2
! P
H2⋅ !
ncosθ2
* +α1α2
! P
H1 ⋅ !
n ! P
H2⋅ !
ncosθ1
*cosθ2 *)
〈cosθ1
*cosθ2 *〉 =α1α2(
! P
H1 ⋅ !
n)( ! P
H2⋅ !
n)=α1α2CNN
H1H2
Independent of the direction of reaction plane!
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Further theoretical discussions/developments
The essence: spin-orbital coupling Dirac equation
i ∂ ∂tψ = ˆ Hψ ˆ H = ! α ⋅ ! ˆ p+ βm [ ˆ H, ! ˆ L]= −i " α × " ˆ p ≠ 0 [ ˆ H, ! Σ]= 2i ! α × ! ˆ p ≠ 0 [ ˆ H, ! ˆ J]= 0 ! ˆ J = ! ˆ L + ! Σ /2 [ ˆ H, ! ˆ L2]= 2" α ⋅ " ˆ p ≠ 0
Spin-orbital coupling is intrinsic in relativistic Quantum Dynamics!
〈ψ | ! ˆ M|ψ 〉 → 〈ϕ| e 2m( ! ˆ L + ! σ )|ϕ〉 ! ˆ M = e 2 ! r × ! α ψ = ϕ χ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ˆ Hψ = Eψ
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Further theoretical discussions/developments
Thermal equilibrium?
l solar surface flow: 10-7 sec-1 l large-scale terrestrial atmospheric patterns: 10-7-10-5 sec-1 l supercell tornado core: 10-1 sec-1 l the Great Red Spot of Jupiter: up to 10-4 sec-1 l rotating, heated soap bubbles: 100 sec-1 l turbulent flow in bulk superfluid He-II: 150 sec-1 l superfluid nanodroplet: 107 sec-1
Betz, Gyulassy, Torrieri, PRC (2007); …....................... Becattini, Piccinini, Rizzo, PRC(2008); Becattini, Karpenko, Lisa, Upsal, Voloshin, PRC(2017).
A single collision multiple collisions equilibration
ω ~2P
ΛT ~(9±1)×1021sec−1
STAR data implies the most vortical fluid STAR Collaboration: arXiv:1701.06657[nucl-exp]. ! P
H = 1
2tanh ω 2T ε m ˆ ω − ˆ ω ⋅ ! p m(ε +m) ! p ⎡ ⎣ ⎢ ⎤ ⎦ ⎥~ ω 2T ˆ ω
Relativistic ideal (vortical) gas
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Further theoretical discussions/developments
QGP as a vortical fluid
spin transport in strongly interacting medium Spintronics in strong interaction ?
Huge orbital angular momentum
statistical-hydrodynamic approach quantum kinetic approach hydro-dynamical model chiral kinetic approach holographic description chiral magnetic effects local polarization …...........
“Global and local spin polarization in heavy ion collisions: a brief overview”, Qun Wang (USTC), plenary talk at 26th International Conference on Ultrarelativistic Nucleus-Nucleus Collisions (Quark Matter 2017), arXiv:1704.04022 [nucl-th].
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Summary
n A great advantage to study spin effects in non-central
AA-collisions is: the reaction plane can be determined experimentally by measuring v1 and v2.
n There exists a huge orbital angular momentum of the colliding
system w.r.t. the reaction plane.
n Quarks and anti-quarks are “globally polarized” in the
- pposite direction as the normal of the reaction plane due to
spin-orbital interaction in QCD.
n Many consequences, many open questions ……
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Outlook
………………………
Ø A possible method to study the role of orbital angular
momentum in high energy spin physics.
Ø An effective way to study spin-orbital interaction in QCD ? Ø A new window to look at the properties of QGP ?
Thanks for your attention!
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Description of polarization of particles with different spins
Spin 1/2 hadrons: Spin 1 hadrons: The spin density matrix is 3x3:
ρ = ρ11 ρ10 ρ1−1 ρ01 ρ00 ρ0−1 ρ−11 ρ−10 ρ−1−1 ⎛ ⎝ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ = 1 3 (1 + 3 2 ! S ⋅ ! Σ + 3T ijΣij )
Vector polarization: Sµ = (0,
! ST,λ)
Tensor polarization:
SLT
µ = (0,SLT x ,SLT y ,0),
STT
xµ = (0,STT xx ,STT xy ,0)
SLL,
8 The spin density matrix is 2x2: Vector polarization: Sµ = (0,
! ST,λ)
ρ = ρ++ ρ+− ρ−+ ρ−− ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = 1 2 (1 + ! S ⋅ ! σ )
See e.g. A. Bacchetta, & P.J. Mulders, PRD62, 114004 (2000).
transverse plane
independent components. 3 5