Measurement of Transverse Spin Transfer of Λ and Λ
in Transversely Polarized Proton+Proton Collisions
at RHIC-STAR
Jincheng Mei
(for STAR Collaboration)
Shandong University
DIS17, Jincheng Mei
1
Outline
✦
Motivation
✦
Experiment Setup
✦
¯ ) Reconstruction
⇤(⇤
✦
Measurement Method
✦
DTT Measurement Results
✦
Summary
DIS17, Jincheng Mei
2
Motivation
Transversely polarized cross section of hyperons could be parameterized into
three parts:
✦
Xu, Liang, Sichtermann.
Phys.Rev. D73 (2006) 077503
transversity
distribution
pQCD
calculation
transversely polarized
fragmentation function
Crucial elements for the study of nucleon spin structure:
transversity distribution and transversely polarized fragmentation
✦
The transverse spin transfer is defined as:
✦
The transverse spin transfer provides insights into transversely polarized
fragmentation function and transversity distribution function.
DIS17, Jincheng Mei
3
Frames and Azimuthal Distributions
¯ ) polarization can be extracted from the ⇤ (⇤
angular distribution of its decay product in its rest
frame.
✦
S
θ*
π-
α: decay parameter
¯
0.642 for ⇤ and -0.642 for ⇤
¯)
P𝛬: polarization of ⇤(⇤
p
𝛬 rest frame
θ* : the angle between decay particle (proton) momentum in 𝛬’s rest frame and the direction of 𝛬 polarization
In transverse case, azimuthal angle of polarization needs
to be determined which is not needed in longitudinal case.
DTT : the spin transfer along the polarization of
outgoing quark considering the rotation in scattering
plane.
✦
DTT
In this analysis, reconstructed jet axis is used as substitute of the outgoing quark momentum direction
J.Collins et al, NPB420 (1994)565
DIS17, Jincheng Mei
4
RHIC - Relativistic Heavy Ion Collider
✦
The Relativistic Heavy Ion Collider (RHIC) is the first and only polarized proton
collider in the world.
✦
Data sample: transversely polarized p+p collisions at 200GeV taken with STAR
detector in 2012.
✦
RHIC Beam polarization: blue beam: 64%, yellow beam: 58%.
DIS17, Jincheng Mei
5
STAR Detectors
BEMC
STAR experiment detectors
TPC
Sub detectors involved in this analysis:
✦
✦
TPC : Time Projection Chamber 𝞰 ~ (-1.2, 1.2)
Track reconstruction of charged particles and charged particle identification.
BEMC: Barrel Electromagnetic Calorimeter 𝞰 ~ (-1.0, 1.0)
For triggering.
DIS17, Jincheng Mei
6
¯
and
Reconstruction
⇤
⇤
5 GeV
7 GeV
15
1.16
ss[GeV]
55 GeV
0 GeV
22
GeV
47GeV
.15
1.16
15
1.16
ss[GeV]
ss[GeV]
61 GeV
34 GeV
40
100
0
1.08
✦
60
200
20
1.09
1.1
1.11
1.12
1.13
1.14
1.15
1.16
mass[GeV]
0
1.08
¯ ! p̄⇡ +
¯ via their decay channels: ⇤ ! p⇡ and ⇤
Applied topological cuts to reconstruct ⇤ and ⇤
200
×10
180
3
Central :
Width
:
Bkg Frac. :
Λ , p :2~3 GeV/c
T
1.1157 GeV
0.0021 GeV
0.0716
50000
Λ , p :4~5
16000 GeV/c
Λ , p :3~4
T
T
Central :
GeV/c
Width
:
Bkg Frac. :
CentralGeV:
1.1158
Width GeV:
0.0028
Bkg Frac. :
0.0683
1.1160 GeV
0.0034 GeV
0.0660
140
Λ , p :5~6
T
4000
12000
40000
120
10000
3000
30000
100
8000
80
2000
6000
20000
60
4000
40
1000
10000
2000
20
0
1.08
180
5000
160
5000
14000
160
200
1.09
1.09
×10
1.1
1.11
1.12
1.13
1.14
1.15
1.16
mass[GeV]
0
1.08
1.09
0
1.08
1.1
1.09
1.11
1.1
1.12
1.11
1.13
1.12
1.14
1.13
1.16
1.15 1.14
1.16 1.15
mass[GeV]
mass[GeV]
0
1.08
1.09
3
Central :
Central
:
Width
Bkg Frac. ::
Width
Bkg Frac. :
Λ , p :2~3 GeV/c
Λ , p T:5~6 GeV/c
T
1.1157 GeV
1.1162
GeV
0.0020 GeV
0.0812
0.0042 GeV
0.0731
140
4000
50000
2500
Central : 1.1158 GeV
Central : : 0.0025
1.1166GeV
GeV
Width
Bkg
Frac. :: 0.0751
Width
0.0051 GeV
Bkg Frac. : 0.0896
Λ , p :3~4 GeV/c
Λ , pT :6~8 GeV/c
T
40000
2000
120
30000
1500
100
3000
80
20000
1000
2000
60
40
10000
500
1000
20
0
1.08
0
1.08
4000
1.09
1.09
1.1
1.1
1.11
1.11
Λ , p :5~6 GeV/c
1.12
1.12
1.13
1.13
Central
Width
1.14
1.15
1.16
1.14 mass[GeV]
1.15
1.16
mass[GeV]
:
:
1.1163 GeV
0.0041 GeV
0
1.08
0
1.08
1.09
1.09
1.1
1.1
DIS17,
Jincheng Mei
1800
1.11
1.11
Λ , p :6~8 GeV/c
1.12
1.12
1.13
1.13
Central
Width
1.14
1.15
1.16
1.14 mass[GeV]
1.15
1.16
mass[GeV]
:
:
1.1168 GeV
0.0052 GeV
7
¯
and
Reconstruction
⇤
⇤
✦
5 GeV
7 GeV
15
1.16
ss[GeV]
55 GeV
0 GeV
22
GeV
47GeV
.15
1.16
15
1.16
ss[GeV]
ss[GeV]
61 GeV
34 GeV
¯ ! p̄⇡ +
¯ via their decay channels: ⇤ ! p⇡ and ⇤
Applied topological cuts to reconstruct ⇤ and ⇤
200
×10
180
¯ after selection
Raw yields of ⇤and ⇤
3
Central :
Width
:
Bkg Frac. :
Λ , p :2~3 GeV/c
T
1.1157 GeV
0.0021 GeV
0.0716
50000
Λ , p :3~4 GeV/c
PTT [GeV/c]
Central :
Width
:
Bkg Frac. :
1~2
490 k
544 k
2~3
323 k
382 k
3~4
183 k
201 k
4~5
78 k
74 k
5~6
32 k
26 k
6~8
20 k
14 k
Total
1126 k
1242 k
160
140
40000
120
30000
100
80
20000
60
40
10000
20
0
1.08
200
180
5000
160
1.09
×10
1.1
1.11
1.12
1.13
1.14
1.15
1.16
mass[GeV]
0
1.08
1.09
1.1
1.11
⇤
1.12
1.13
1.1158 GeV
0.0028 GeV
0.0683
1.14
¯
⇤
1.15
1.16
mass[GeV]
3
Central :
Central
:
Width
Bkg Frac. ::
Width
Bkg Frac. :
Λ , p :2~3 GeV/c
Λ , p T:5~6 GeV/c
T
1.1157 GeV
1.1162
GeV
0.0020 GeV
0.0812
0.0042 GeV
0.0731
140
4000
50000
2500
Central : 1.1158 GeV
Central : : 0.0025
1.1166GeV
GeV
Width
Bkg
Frac. :: 0.0751
Width
0.0051 GeV
Bkg Frac. : 0.0896
Λ , p :3~4 GeV/c
Λ , pT :6~8 GeV/c
T
40000
2000
120
30000
1500
100
3000
80
20000
1000
2000
60
40
10000
500
1000
20
0
1.08
0
1.08
4000
1.09
1.09
1.1
1.1
1.11
1.11
Λ , p :5~6 GeV/c
1.12
1.12
1.13
1.13
Central
Width
1.14
1.15
1.16
1.14 mass[GeV]
1.15
1.16
mass[GeV]
:
:
1.1163 GeV
0.0041 GeV
0
1.08
0
1.08
1.09
1.09
1.1
1.1
DIS17,
Jincheng Mei
1800
1.11
1.11
Λ , p :6~8 GeV/c
1.12
1.12
1.13
1.13
Central
Width
1.14
1.15
1.16
1.14 mass[GeV]
1.15
1.16
mass[GeV]
:
:
1.1168 GeV
0.0052 GeV
8
¯
and
Reconstruction
⇤
⇤
✦
5 GeV
7 GeV
15
1.16
ss[GeV]
55 GeV
0 GeV
22
GeV
47GeV
.15
1.16
15
1.16
ss[GeV]
ss[GeV]
61 GeV
34 GeV
¯ ! p̄⇡ +
¯ via their decay channels: ⇤ ! p⇡ and ⇤
Applied topological cuts to reconstruct ⇤ and ⇤
200
×10
180
¯ after selection
Raw yields of ⇤ and ⇤
3
Central :
Width
:
Bkg Frac. :
Λ , p :2~3 GeV/c
T
1.1157 GeV
0.0021 GeV
0.0716
50000
Λ , p :3~4 GeV/c
PTT [GeV/c]
Central :
Width
:
Bkg Frac. :
1~2
490 k
544 k
2~3
323 k
382 k
3~4
183 k
201 k
4~5
78 k
74 k
5~6
32 k
26 k
6~8
20 k
14 k
Total
1126 k
1242 k
160
Draw
140
120
100
40000
30000
Dbkg
80
20000
60
40
10000
20
0
1.08
200
180
5000
160
1.09
×10
1.1
1.11
1.12
1.13
1.14
1.15
1.16
mass[GeV]
3
Central :
Central
:
Width
Bkg Frac. ::
Width
Bkg Frac. :
Λ , p :2~3 GeV/c
Λ , p T:5~6 GeV/c
T
1.1157 GeV
1.1162
GeV
0.0020 GeV
0.0812
0.0042 GeV
0.0731
140
4000
0
1.08
1.09
1.1
⇤
1.11
1.12
1.13
1.14
¯
⇤
1.15
1.16
mass[GeV]
Central
: 1.1158 GeV
Background fraction is
estimated
by side bands.
Central
1.1166GeV
GeV
Width
: : 0.0025
Λ , p :3~4 GeV/c
Frac. :: 0.0751
Width
0.0051 GeV
Λ , p :6~8 GeV/craw
50000
The
D andBkg
their
uncertainties
T
2500 obtained
Bkg
Frac. : statistical
0.0896
were corrected for the residual background:
40000
T
2000
120
DT T
30000
1500
100
3000
80
20000
1000
2000
60
40
0
1.08
0
1.08
1.09
1.09
1.1
1.1
1.11
1.11
Λ , p :5~6 GeV/c
1.12
1.12
1.13
1.13
Central
Width
1.14
1.15
1.16
1.14 mass[GeV]
1.15
1.16
mass[GeV]
:
:
1.1163 GeV
0.0041 GeV
DTraw
T
=
1
r
(
DT T =
10000
500
1000
20
4000
1.1158 GeV
0.0028 GeV
0.0683
0
1.08
0
1.08
1.09
1.09
2
DTraw
T )
rDTbkg
T
r
⇣
+ r
1
r
DTbkg
T
⌘2
1.12 background
1.13
1.14
1.15fraction
1.16
r : 1.11
residual
1.1
1.1
DIS17,
Jincheng Mei
1800
1.11
Λ , p :6~8 GeV/c
1.12
1.13
Central
Width
1.14 mass[GeV]
1.15
1.16
mass[GeV]
:
:
1.1168 GeV
0.0052 GeV
9
Jet Correlation
✦
✦
¯)by calculating 𝛥R.
Use anti-Kt algorithm to reconstruct jet then make correlation to a ⇤ (⇤
Request ηjet ~ (-0.7, 0.9), PT > 5.0 GeV/c, neutral fraction of Jet < 0.95.
If 𝛥R < 0.6 (near side), we use the jet momentum direction as outgoing quark direction to
obtain quark’s polarization direction.
Λ :PT 2~3 GeV/c
Λ :PT 4~5 GeV/c
DIS17, Jincheng Mei
10
Measurement Method
✦
✦
¯ ) and the angular distribution
Based on the relationship between polarization of ⇤ (⇤
of its decay product in its rest frame.
In this analysis, DTT is extracted from the asymmetry of 𝛬 counts with opposite beam
polarization in a small cosθ* bin:
DT T =
✦
↵Pbeam
1
N"
RN #
< cos ✓⇤ > N " + RN #
Pbeam : polarization of beam
<cosθ*> : mean in each cosθ* bin
¯ ) counts with positive beam polarization
N " : ⇤ (⇤
¯ ) counts with negative beam polarization
N # : ⇤ (⇤
R: relative luminosity
Acceptance of reverse beam polarization is expected to be the same in each cosθ*
bin, and thus cancelled.
DIS17, Jincheng Mei
11
Extraction of Spin Transfer DTT
N#
N"
⇤ counts versus cosθ* with opposite beam polarization.
Separate the whole range of cosθ* into 20 bins.
Λ : pT 1~2 GeV/c, 𝜂 > 0
positive beam polarization
Λ : pT 1~2 GeV/c, 𝜂 > 0
negative beam polarization
statistical uncertainty only
DTT extraction in each cosθ*
↵Pbeam
#
1
N
RN
< cos ✓⇤ > N " + RN #
( L |P :1~2GeV|phy. η>0|ALL )
DTTD for
Λ :PT 1~2 GeV/c
TT
T
D TT
DT T =
"
statistical uncertainty only
0.6
χ2 / ndf
p0
21.91 / 19
−0.008204 ± 0.008131
0.4
0.2
0
Fit the 20 DTT with a constant.
Fitted result as the DTT in the pT bin.
−0.2
−0.4
The method passed the null check with
statistical uncertainty only
−1
DIS17, Jincheng Mei
−0.5
0
0.5
1
cosθ*
12
Systematic Uncertainty
✦
✦
3.4% scale uncertainty from RHIC beam polarization measurement. —obtained from the polarimetry group of RHIC
2% from decay parameter (0.642 ± 0.013). —PDG
✦
0.012 from relative luminosity measurement.
✦
Residual background fraction estimation.
—Compare two methods of residual background fraction ( fit and side-band )
✦
Trigger bias estimated from MC simulation.
✦
Pileup effect.
✦
The sum of systematic uncertainty is range of 0.012 ~ 0.026
DIS17, Jincheng Mei
13
Results of DTT
¯ in p+p collision at 200 GeV.
Results of transverse spin transfer DTT of ⇤ and ⇤
✦
𝜂>0
STAR Preliminary
3.4% beam polarization uncertainty included
feed-down contribution included
✦
✦
✦
𝜂<0
STAR Preliminary
3.4% beam polarization uncertainty included
feed-down contribution included
¯ ) polarization in p+p collision at RHIC, which reach pT
Most precise measurement on ⇤ (⇤
~8 GeV/c with statistical uncertainty of 0.04 .
The dominant source of systematic uncertainty is from relative luminosity in low pT.
¯ are consistent with each other and consistent with zero at the current
DTT of ⇤ and ⇤
precision.
DIS17, Jincheng Mei
14
Summary
✦
¯ ) in p+p
First measurement on transverse spin transfer of ⇤( ⇤
collisions, which can provide insights into transversely polarized
fragmentation function and nucleon transversity distribution.
✦
¯ ) sample is the largest so far in p+p collision at RHIC and
The ⇤ (⇤
¯)
the precision of DTT is ~0.04 at pT ~8 GeV/c for ⇤ (⇤
✦
¯ are consistent with each other and consistent with
DTT of ⇤ and ⇤
zero at the presently available precision.
DIS17, Jincheng Mei
15
Thanks for Your Attention!
16
Backup
DIS17, Jincheng Mei
17
Previous Results
Previous measurement of transverse spin transfer.
-Only DNN spin transfer w.r.t. production plane (Fermilab E704 Collaboration,1997).
✦
DNN : spin transfer along normal direction of
Λ production plane.
Significant spin transfer was found at
large xF.
DIS17, Jincheng Mei
18
DTT comparison two axises
DTT for Λ , physical η > 0
DTT
DTT
DTT for Λ , physical η > 0
0.2
0.2
0.1
0.1
0
0
−0.1
−0.1
−0.2
−0.3
1
−0.2
Jet Axis
Λ(Λ) Axis
2
3
4
5
6
7
8
pT /[GeV]
−0.3
1
Jet Axis
Λ(Λ) Axis
2
3
4
5
6
7
8
pT /[GeV]
Comparison for different substitutes of outgoing quark momentum direction:
1, jet direction
2, hyperon direction
DIS17, Jincheng Mei
19
Theory Prediction
¯ polarization for
Transverse ⇤
transverse momentum
pT ≧ 8 GeV/c in PP collisions
at 200 GeV with one
transversely polarized beam
¯
versus pseudorapidity 𝞰 of the ⇤
Positive 𝞰 is taken along the
polarized beam direction.
Xu, Qing-hua et al.
Phys.Rev. D73 (2006) 077503
DIS17, Jincheng Mei
20
δ TT
Check
0.8
(c) K
η>0 δ TT -0.0018 ± 0.0050
0
S
χ2 /ndf = 20.0/19
0.6
η<0 δ TT -0.0074 ± 0.0051
0.4
χ2 /ndf = 18.9/19
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
−1.2
−1
2.0 < P T <3.0 GeV/c
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
cosθ*
The spin asymmetry for
was also extracted, which is used as a null check (
zero), and the results are consistent with zero as expected.
It is also a good check for acceptance assumption.
DIS17, Jincheng Mei
is spin
21
Pileup Effect Estimation
Four beam polarization
sets in RHIC p+p collision:
++, +-, -+, --.
Yield/Event
Plot of Lambda yield vs.
collision rate.
h_L_spin0
Pileup(20kHz): -0.062 ± 0.010
0.025
Line Fit
Weighted Mean
χ 2 /ndf 397.05 / 389
χ 2 /ndf 434.94 / 390
p0 0.0085 ± 0.0001
p0 0.0080 ± 0.0000
p1 -8.53e-10 ± 1.39e-10
0.02
0.015
0.01
The factor (u for each set is
the difference between
linear fit and constant fit at
collision rate = 20kHz
0.005
0
300
400
500
600
700
800
900
×10
1000
1100
BBCrate[Hz]
3
The uncertainty of DTT from pileup effect is estimated by :
TT
TT
DIS17, Jincheng Mei
TT
22