1. Run 12 Sea Quark Polarization:
Data analysis by using W → μ
Chong Kim
Korea University 1 / RIKEN 2
1 Department of Physics, Korea University, Seoul , South Korea
2 RIKEN, 2-1 Hirosawa, Wako, Saitama , Japan
for the PHENIX collaboration
Japan-Korea PHENIX Collaboration Workshop 2013

2. Outline PHENIX Muon Arms W → μ analysis Summary and Perspectives
W physics
Detectors and Recent Runs
W → μ analysis
Preselection
W likelihood
Composing PDFs
S/BG ratio estimation
Single spin asymmetry (AL)
Summary and Perspectives

3. 1. PHENIX Muon Arms – a. W physics
ALW+ = Δ𝑢 𝑥 1 𝑑 𝑥 2 − Δ 𝑑 𝑥 1 𝑢( 𝑥 2 ) 𝑢 𝑥 1 𝑑 𝑥 𝑑 𝑥 1 𝑢( 𝑥 2 )
~ Δ𝑢 𝑥 1 𝑢 𝑥 1 ( 𝑥 1 ≫ 𝑥 2 ) or ~ − Δ 𝑑 𝑥 1 𝑑 𝑥 1 ( 𝑥 2 ≫ 𝑥 1 )
* Swap u and d for W－case
ALW = 1 𝑃 × 𝑁 − 𝑊 − 𝑁 + 𝑊 𝑁 − 𝑊 + 𝑁 + 𝑊
ALW : Single spin asymmetry
P : Beam polarization
𝑁 −(+) (W) : # of events contains leptons decayed from W
with corresponding helicity (negative/positive)
in real experiment,
* un-polarized: integrated for certain beam
W physics in RHIC/PHENIX
Target maximal parity-violating W bosons produced via polarized p – unpolarized p collision
Measure the Single spin asymmetry (AL) of the quark, by using leptons directly decayed from W bosons
Advantages:
Fixed flavor combination: full flavor separated measurements
No dependence on fragmentation functions: direct and clean signal

4. 1. PHENIX Muon Arms – b. Detectors and Recent Runsμ
D. Florian and W. Vogelsang
PRD81,
Recent longitudinally polarized pp runs
Year √s
L (pb-1)
P (%)
FoM (P2L)
2009
500
8.6 39
1.3
2011
16.7 48
3.8
2012
510
31.5
51.9
8.5
2013
146.0 55
44.2
* Int. L under condition of |Vertex z| < 30 cm
* Previous/Current speaker related Run
PHENIX Muon Arms (2013)
Acceptance: 1.2 < |η| < 2.2 (S) / 2.4 (N) and Δφ = 2π
Tracking: FVTX, MuTR
Triggering and PID: MuID and RPCs
Radial B field: 0.72 (T·m) at θ = 15˚

5. 2. W → μ analysis – a. Preselection
Preselection of μ candidates from data:
by using Basic cut to several signal-sensitive Kinematic variables
Kinematic variables: χ2, DCAr , Rpc1DCA, Rpc3DCA, DG0, DDG0
Basic cut: requirements for rough μ identification
Apply loose requirements to χ2, DG0, and DDG0
16 < pT < 60 (GeV)
Last recorded hit in the MuID gap = 4 (5th and last) x y
Track
MuTR
St 1
DCAr 1 2 3 4
RPC1
MuTR
MuID
RPC3
Track z
DDG0
DG0
Rpc3DCA
Rpc1DCA

6. 2. W → μ analysis – a. Preselection
Total data
composition
- Size: surviving events
- Green: W events
- Violet: μ BG
- Cyan: Hadronic BG
Before
preselection
After
data
μ backgrounds
W signal
MC simulation
(PYTHIA + PISA)
Hadron backgrounds
Samples
MC simulation (PYTHIA + PISA):
Signal: W → μ and Z → μ
μ backgrounds: Direct γ, Quarkonium, Opencharm, Openbottom,
W → hadron/tau, and Z → hadron/tau
Hadronic BG MC is not available for now
data (pp510 Run 12):
Sampled luminosity: 42 pb-1
Still background dominant after preselection

7. 2. W → μ analysis – b. W likelihood
χ2, DCAr, Rpc1DCA, Rpc3DCA, DG0, DDG0
(preselected signal-sensitive kinematic variables)
data
μ backgrounds
W signal
MC simulation
(PYTHIA + PISA)
Compose 1st PDFs (Probability Density Function):
λ = p(χ2) · p(DCAr) · p(Rpc1DCA) · p(Rpc3DCA) · p(DG0, DDG0)
W likelihood
= 𝜆 𝑠𝑖𝑔𝑛𝑎𝑙 ( 𝑥 𝑖 ) 𝜆 𝑠𝑖𝑔𝑛𝑎𝑙 ( 𝑥 𝑖 )+ 𝜆 𝐵𝐺 ( 𝑥 𝑖 )
South Arm, W - → μ-
Data
Signal (PYTHIA + PISA)
Signal + μ backgrounds (PYTHIA + PISA)
Hadronic backgrounds (fakes)

8. 2. W → μ analysis – c. Composing PDFs
Define variables for fit: η and dw23
Scale each sample by luminosity
Preselected kinematic variables
data
μ BG W MC
1st PDFs by each variables
W likelihood
* dw23 (reduced azimuthal bending) ≡ pT × sin θ × dφ23 x y
MuTR
St 2
St 3 z θ
dφ23
W MC, South Arm, W - → μ- η
dw23
A.U
Projection to η
Projection to dw23
W likelihood > 0.92

9. 2. W → μ analysis – c. Composing PDFs
Preselected kinematic variables
data
μ BG W MC
1st PDFs by each variables
W likelihood
Define variables for fit: η and dw23
then collect samples satisfying W likelihood cut (ex. > 0.92)
Scale each sample by luminosity
Compose 2nd PDFs by using η and dw23:
λ signal (η, dw23)
by W MC
λ μ BG (η, dw23)
by μ background MC
λ Hadronic BG (η, dw23)
by driven from data
Total data
composition
- Size: surviving events
- Green: W events
- Violet: μ BG
- Cyan: Hadronic BG
Compose final combined PDF: λ final
→ perform unbinned maximum likelihood fit

10. 2. W → μ analysis – c. Composing PDFs
Data-driven Hadron backgrounds distribution in region of interest
Unlike η, shape of dw23 sensitively varies by W likelihood
Extrapolate expected HBG distribution on ROI:
perform 2D fit by using pol4 (W likelihood) and coaxial double Gaussian (dw23)

11. 2. W → μ analysis – d. S/BG ratio estimation
2D unbinned max. likelihood fit:
← 1D projections onto each variable
Signal (fit): W → μ and Z → μ
μ backgrounds (fixed):
sum of various channels of μ BG
(L scaled & total efficiency corrected)
Hadronic backgrounds (fit)
Estimated S/BG ratio (preliminary)

12. 2. W → μ analysis – e. Single spin asymmetry (AL)
ALW+ = Δ𝑢 𝑥 1 𝑑 𝑥 2 − Δ 𝑑 𝑥 1 𝑢( 𝑥 2 ) 𝑢 𝑥 1 𝑑 𝑥 𝑑 𝑥 1 𝑢( 𝑥 2 )
~ Δ𝑢 𝑥 1 𝑢 𝑥 1 ( 𝑥 1 ≫ 𝑥 2 ) or ~ − Δ 𝑑 𝑥 1 𝑑 𝑥 1 ( 𝑥 2 ≫ 𝑥 1 )
* Swap u and d for W－case
Sampled Luminosity (pb-1):
Run 12: 42
Run 13: 228
Run 12 preliminary
Beam combined asymmetries for mid / forward rapidity WRT η mean
Shows optimistic agreement with theoretic expectation

13. 3. Summary and Perspectives
W physics in RHIC/PHENIX:
target better constraint on flavor-decomposed sea quark polarization
Longitudinally polarized pp in PHENIX:
Total achieved int. L: ~ 200 pb-1
Avg. beam polarization: > 50 %
W → μ in PHENIX Muon Arms:
Main analysis method:
Backgrounds dominant in region of interest: estimation of direct S/BG ratio is impossible
Estimation of S/BG ratio by using unbinned maximum likelihood fit
Major challenge: separation of Hadronic backgrounds from in-flight decay
Estimated S/BG ratio: ~ 0.2 to ~ 0.4, varies by side and charge
Single spin asymmetry: shows optimistic agreement to the theoretic expectation

14. 3. Summary and Perspectives
Refine current using factors: efficiency tune, various cross checks…
Inclusion of FVTX matching variables:
3 additional high-precision variables available
Looking forward enhanced statistics in region of interest as well as reduced error
Major update required for the proper integration: now ongoing
χ2, DCAr, Rpc1DCA, Rpc3DCA, DG0, DDG0
+ FVTX_dr, FVTX_dφ, FVTX_dθ
data
μ backgrounds
W signal
MC simulation
(PYTHIA + PISA) …
FVTX event display

15. Backup u d Spin crisis: Proton spin sum rule: Polarized DIS/SIDIS:
D. de Florian et al,
PRD (2009) d u
Spin crisis:
proton spin is not a simple sum of its constituent quarks
(quark spin contribution to the total: < 40 %)
Proton spin sum rule:
1 2 = ΔΣ + ΔG + Lz , where
ΔΣ (quark spin contribution) = (Δu + Δ u ) + (Δd + Δ d ) + (Δs + Δ s )
ΔG (gluon spin contribution) = 0 1 Δg x, Q2 dx
Lz (orbital angular momenta) = Lq + Lg
Polarized DIS/SIDIS:
Flavor-combined PDFs (ex. Δu + Δ u )) is well known,
while their flavor-separated PDF is only known with
large uncertainties
Still better constraint on sea quark polarization
is required

16. Backup – W measurement in PHENIX
If W pdoruction processed only through (a),
If processed only through (b),
In general, the asymmetry is a
superposition of two cases:
* To obtain the asymmetry for W-,
swap u and d

17. Backup – Forward μ trigger upgrade
MuTRG
ADTX
MRG
Level 1
Trigger
Board
MuTr
FEE
Resistive Plate Chamber
(RPC) (φ segmented) B
2 planes 5%
95%
Interaction Region
Rack Room
Optical
1.2Gbps
Amp/Discri.
Transmit
Data
Merge
RPC
Trigger events with straight track
(e.g. Dstrip <= 1)
RPC / MuTRG data are
also recorded on disk

18. Backup – Central Arm W analysis
𝐸𝑐𝑜𝑛𝑒− 𝐸𝑐𝑎𝑛𝑑𝑖𝑎𝑡𝑒 𝐸𝑐𝑎𝑛𝑑𝑖𝑎𝑡𝑒 <10 (%)

19. Backup – μ backgrounds

20. Backup – μ backgrounds

21. Backup – W likelihood distribution

22. Backup – MC Production statistics and Luminosity
Ref (low)
pytune100
k factor
# of gen events (M)
x-section (mb)
luminosity (pb-1)
data (common)
1.5
N/A 43
dy (direct photon)
11600
5.32E-002
218.0
light
311.1
5.94E+001
0.0
onium
32910
1.35E-001
243.8
openbottom
1552
7.30E-003
212.6
opencharm
145940
5.71E-001
255.6 w
65.1
1.66E-006
whad
120
wjet
11.9
1.20E-006
9916.7
wtau
118 z
81.5
1.59E-005
5125.8
zjet
1.02E-006
zonly
1.33E-007
Ref (mid)
48510
911.8
152
0.003
69790
517.0
4489
614.9
250830
439.3
451.2
335
13.3
346
253.7
13.2
136.8
Ref (high)
6400
120.3
193.6
55470
410.9
4003
548.4
134220
235.1
173.4 81
8.2
6833.3 82
245.2
8039.2
106.5

23. Backup – η vs. dw23, by W MC

24. Backup – η vs. dw23, by μ BG MC

25. Backup – η vs. dw23, by data (≒ μ BG + Hadronic BG)

26. Backup – Fit results (preliminary)

27. Backup – Fit results (preliminary)

28. Backup – Beam separated/Run11 and 12 AL