[PPT] - Using Kinematic Fitting in CLAS EG6: Beam-Spin Asymmetry of PowerPoint Presentation

SLIDE 1

Using Kinematic Fitting in CLAS EG6: Beam-Spin Asymmetry of Exclusive Nuclear DVMP

Frank Thanh Cao Advisor: K. Joo Co-Advisor: K. Hafidi

University of Connecticut

March 2018

SLIDE 2

Motivation

After particle identification, we are left with a set of particles and we want to know whether they are part of the same process of

interest. Usually, we rely on forming exclusivity variables from the

measured 4-momenta of the positively identified particles. We must confront the fact that 4-vectors coming from detectors are not perfect and it may be possible to do better. This presentation will outline kinematic fitting as an answer to this and some surprising results when applying it to the relatively rare process of DVπ0P off 4He in CLAS EG6.

SLIDE 3

Outline

◮ Kinematic Fitting in a Nutshell ◮ Kinematic Fitting Formalism

◮ Constructing Constraints and Covariance Matrix ◮ Obtaining Fitted Variables ◮ Quality of Fit

◮ Kinematic Fitting Applied to EG6

◮ 4C-fit on DVCS: Validation ◮ 4C-fit on DVπ0P: Case for Kinematic Fit ◮ 5C-fit on DVπ0P: Folding in π0 Decay

◮ Comparison to Previous Exclusivity Cuts ◮ Conclusion

SLIDE 4

Kinematic Fitting in a Nutshell

Kinematic fitting takes measure values and allows them to move within the measured values’ errors and are directed by a set of constraints. This is perfectly applicable for taking a set of measured 3-momenta and allowing each to move simultaneously, within detector resolutions, to satisfy energy and momentum conservation.

SLIDE 5

Formalism

Let # » η be a vector of n-measured variables. Then the true vector of the n-variables, # » y , will be displaced by n-variables, # » ε . They are related simply by: # » y = # » η + # » ε If there are, say m, unmeasured variables too, then they can be put in a vector, # » x . The two vectors, # » x and # » y , are then related by r constraint equations, indexed by k: fk (# » x , # » y ) = 0

SLIDE 6

Suppose # » x 0 and # » y 0 are our best guess (measurements) of the vectors # » x and # » y , respectively. Then Taylor expanding to first

rder each fk (#

» x , # » y ) about #» x0 and #» y0 gives: fk (# » x , # » y ) ≈ fk # » x 0, # » y 0 +

m

i=0

∂fk ∂xi

#»

x0, # » y 0

# » x − # » x 0

i

+

n

j=0

∂fk ∂yj

( #

» x 0, # » y 0)

# » y − # » y 0

j

(1) where # » x − # » x 0

i and

# » y − # » y 0

j denote the i-th and j-th

components of vector differences, respectively.

SLIDE 7

For convenience, let’s introduce Aij := ∂fi ∂xj

( #

» x 0, # » y 0)

Bij := ∂fi ∂yj

( #

» x 0, # » y 0)

ci := fi # » x 0, # » y 0 , (2) and # » ξ := # » x − # » x 0 # » δ := # » y − # » y 0 .

SLIDE 8

Then, since fk (# » x , # » y ) ≡ 0 ∀k, Eq. 1 can be written in matrix form as: # » 0 ≡ A# » ξ + B # » δ + # » c (3) where A and B are (r × n) and (r × m) matrices with components aij and bij, respectively, as defined by Eqn.’s 2.

SLIDE 9

Kinematic fitting can be done iteratively to get the best∗ value of # » y and # » x as possible. Let ν be the index that denotes the ν-th iteration. Then, we have # » ξ → # » ξ ν = # » x ν − # » x ν−1 # » δ → # » δ ν = # » x ν − # » x ν−1 and A → Aν B → Bν # » c → # » c ν Finally, we introduce the overall difference: # » ǫ ν := # » y ν − # » y 0 (4)

∗We can quantify best by introducing and minimizing χ2.

SLIDE 10

Constructing χ2

If we have a really good understanding of the correlations between

ur initial measured values, in #

» η ≡ # » y 0, then we can construct a covariance matrix, Cη: Cη = # » σηTρη # » ση where # » ση is a vector of the resolution errors of η and ρη is a symmetric correlation matrix whose components, ρij ∈ [−1, 1], house pairwise correlations coefficients, between ηi and ηj (⇒ ρii = 1).

SLIDE 11

Consider χ2, generalized to include correlations between measurements, to be:

χ2ν = (#

» ǫ ν)T C −1

η

# » ǫ ν (5) Then, if there are no correlations, ρη is the unit matrix and so the covariance matrix is just a diagonal matrix of the variances of η. In this case, the χ2 becomes the recognizable:

χ2ν =

m

i=0
yν

i − y0 i

2 (ση)i

2

=

m

i=0

(ǫν

i )2

(ση)i

2

SLIDE 12

Now that we have a χ2 to minimize, we can introduce a Lagrangian, L, with Lagrange multipliers # » µ such that: L = (# » ǫ ν)T C −1

η

# » ǫ ν + 2 (# » µν)T Aν # » ξ ν + Bν # » δ ν + # » c ν (6) is to be minimized. Minimization conditions are then: # » 0 ≡ 1 2 ∂L ∂ # » δ ν = C −1

η

# » ǫ ν + (Bν)T # » µν (7) # » 0 ≡ 1 2 ∂L ∂ # » µν = Aν # » ξ ν + Bν # » δ ν + # » c ν (8) # » 0 ≡ 1 2 ∂L ∂ # » ξ ν = (Aν)T # » µν . (9)

SLIDE 13

Solving for such # » ξ ν, # » µν, # » δ ν that satisfy these conditions result in: # » ξ ν = −C ν

x (Aν)T C ν B #

» r ν # » µν = C ν

B

Aν #

» ξ ν + # » r ν # » δ ν = −Cη (Bν)T # » µν − # » ǫ ν−1 . (10) where C ν

B is conveniently defined as

C ν

B :=

BνCη (Bν)T−1

C ν

x :=

(Aν)T C ν

BAν−1

# » r ν := # » c ν − Bν # » ǫ ν−1

SLIDE 14

With these new incremental vectors that satisfies the minimization condition, we can finally form our new fitted vectors # » x ν and # » y ν: # » x ν = # » x ν−1 + # » ξ ν # » y ν = # » y ν−1 + # » δ ν (11) with new covariance matrices: Cx = ∂ # » x ∂ # » η

Cη

∂ # » x ∂ # » η T =

ATCBA

−1 Cy = ∂ # » y ∂ # » η

Cη

∂ # » y ∂ # » η T = Cη − Cη

BTCBB
Cη + Cη
BTCB
ACxAT

CBB

Cη

.

SLIDE 15

Quality of Fit

To check on the quality of the fit, we look to two sets of distributions: The Confidence levels and the Pull distributions.

SLIDE 16

Confidence Levels

Since χ2 := # » ǫ TC −1

η

# » ǫ will produce an χ2 distribution for N degrees of freedom, let’s define the confidence level, CL as: CL := ∞

x=χ2 fN (x) dx,

where fN (x) is the χ2 distribution for N degrees of freedom. The fit is then referred to as a NC-fit.

◮

Characteristics

◮ If there is no background in the fit, the distribution is uniform

and flat.

confLevels Entries 1000 Mean 0.499 Std Dev 0.2882

Conf. Levels []

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 20 30 40 50 60 70 80 confLevels Entries 1000 Mean 0.499 Std Dev 0.2882

Confidence Levels

SLIDE 17

Confidence Levels

◮

Characteristics

◮ In the presence of background, there will be a sharp rise as

CL → 0.

confLevels Entries 2000 Mean 0.2545 Std Dev 0.3184

Conf. Levels []

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10

2

10

3

10 confLevels Entries 2000 Mean 0.2545 Std Dev 0.3184

Confidence Levels

confLevels Entries 2000 Mean 0.2544 Std Dev 0.3184

Conf. Levels []

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10

2

10

3

10 confLevels Entries 2000 Mean 0.2544 Std Dev 0.3184

Confidence Levels ( 977 events, est. SNR = 36.902261, sig. pct. = 97.361635% with conf. cut @ 0.04)

Cutting out the sharp rise as CL → 0 will cut out the much of the background while keeping much of the signal intact.

SLIDE 18

Pull Distributions

To see if the covariance matrix is correctly taking into account all pairwise correlations between the variables, we look to the pull

distributions. Let’s define #

» z to house the pulls, zi, defined as zi := yi − ηi

σ2

yi − σ2 ηi

SLIDE 19

Pull Distributions

◮

Characteristics Since these are normalized differences, the distributions should be normally distributed with

◮ mean 0 and ◮ width 1.

pulls

Entries 4000 Mean 0.4344 − Std Dev 2.543 pull [] 5 − 4 − 3 − 2 − 1 − 1 2 3 4 5 20 30 40 50 60

pulls

Entries 4000 Mean 0.4344 − Std Dev 2.543

Pulls

pulls_1 Entries 1000 Mean 0.006005 − Std Dev 0.9641 / ndf

2

χ 29.33 / 51 Constant 1.64 ± 41.06 Mean 0.03139 ± 0.01657 − Sigma 0.0237 ± 0.9488 pull [] 5 − 4 − 3 − 2 − 1 − 1 2 3 4 5 10 20 30 40 50 60 70 pulls_1 Entries 1000 Mean 0.006005 − Std Dev 0.9641 / ndf

2

χ 29.33 / 51 Constant 1.64 ± 41.06 Mean 0.03139 ± 0.01657 − Sigma 0.0237 ± 0.9488

Pulls After CLC

SLIDE 20

Kinematic Fit Applied to EG6: DVCS 4C-fit Validation

SLIDE 21

Exclusivity Variable Distributions

Measured values from: Red: Exclusivity Cuts Blue: Kinematic Fit Fitted values from: Green: Kinematic Fit

]

2

)

2

[(GeV/c

X 2

M 8 10 12 14 16 18 20 22 10 20 30 40 50 60

(After Conf. Lev. Cut)

X 2

M

]

2

)

2

[(GeV/c

1

X 2

M 1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1 10 20 30 40 50 60

(After Conf. Lev. Cut)

1

X 2

M

]

2

)

2

[(GeV/c

2

X 2

M 0.1 − 0.08 − 0.06 − 0.04 − 0.02 − 0.02 0.04 0.06 0.08 0.1 20 40 60 80 100 120 140 160 180 200 220

(After Conf. Lev. Cut)

2

X 2

M

[GeV/c]

x

P 0.2 − 0.15 − 0.1 − 0.05 − 0.05 0.1 0.15 0.2 10 20 30 40 50 60 70

(After Conf. Lev. Cut)

x

P

[GeV/c]

y

P 0.2 − 0.15 − 0.1 − 0.05 − 0.05 0.1 0.15 0.2 10 20 30 40 50 60 70 80

(After Conf. Lev. Cut)

y

P

[GeV/c]

t

P 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 10 20 30 40 50

(After Conf. Lev. Cut)

t

P

[GeV]

2

X

E 1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1 10 20 30 40 50

(After Conf. Lev. Cut)

2

X

E

[deg.] θ 0.5 1 1.5 2 2.5 3 3.5 10 20 30 40 50 60 70 80 90

(After Conf. Lev. Cut) θ

[deg.] φ ∆ 5 − 4 − 3 − 2 − 1 − 1 2 3 4 5 20 40 60 80 100 120 140

(After Conf. Lev. Cut) φ ∆

SLIDE 22

Beam-Spin Asymmetries

Measured values from: Red: Exclusivity Cuts Blue: Kinematic Fit

Bins in Q2

] ° [ φ 50 100 150 200 250 300 350

raw

A 0.5 − 0.4 − 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 0.4 0.5

/ ndf

2

χ 3.167 / 8 α 0.05485 ± 0.3592 / ndf

2

χ 3.167 / 8 α 0.05485 ± 0.3592 / ndf

2

χ 4.876 / 8 α 0.04851 ± 0.3122 / ndf

2

χ 4.876 / 8 α 0.04851 ± 0.3122

) 2 = 0.080654 GeV

t

= 0.131573 , x , 2 = 1.145889 GeV 2 Q (# events : 2404 )( φ vs. raw A ] ° [ φ 50 100 150 200 250 300 350 raw A 0.5 − 0.4 − 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 0.4 0.5

/ ndf

2

χ 3.409 / 8 α 0.05803 ± 0.3357 / ndf

2

χ 3.409 / 8 α 0.05803 ± 0.3357 / ndf

2

χ 6.659 / 8 α 0.04985 ± 0.4172 / ndf

2

χ 6.659 / 8 α 0.04985 ± 0.4172

) 2 = 0.094169 GeV

t

= 0.170550 , x , 2 = 1.423673 GeV 2 Q (# events : 2404 )( φ vs. raw A ] ° [ φ 50 100 150 200 250 300 350 raw A 0.5 − 0.4 − 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 0.4 0.5

/ ndf

2

χ 8.213 / 8 α 0.05627 ± 0.3708 / ndf

2

χ 8.213 / 8 α 0.05627 ± 0.3708 / ndf

2

χ 4.525 / 8 α 0.05018 ± 0.311 / ndf

2

χ 4.525 / 8 α 0.05018 ± 0.311

) 2 = 0.000000 GeV

t

= 0.000000 , x , 2 = 0.000000 GeV 2 Q (# events : 2404 )( φ vs. raw A

Bins in x

] ° [ φ 50 100 150 200 250 300 350

raw

A 0.5 − 0.4 − 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 0.4 0.5

/ ndf

2

χ 4.655 / 8 α 0.05115 ± 0.3419 / ndf

2

χ 4.655 / 8 α 0.05115 ± 0.3419 / ndf

2

χ 5.647 / 8 α 0.04461 ± 0.3188 / ndf

2

χ 5.647 / 8 α 0.04461 ± 0.3188

) 2 = 0.080654 GeV

t

= 0.131573 , x , 2 = 1.145889 GeV 2 Q (# events : 2404 )( φ vs. raw A ] ° [ φ 50 100 150 200 250 300 350 raw A 0.5 − 0.4 − 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 0.4 0.5

/ ndf

2

χ 4.134 / 8 α 0.06113 ± 0.2886 / ndf

2

χ 4.134 / 8 α 0.06113 ± 0.2886 / ndf

2

χ 8.089 / 8 α 0.05146 ± 0.3381 / ndf

2

χ 8.089 / 8 α 0.05146 ± 0.3381

) 2 = 0.094169 GeV

t

= 0.170550 , x , 2 = 1.423673 GeV 2 Q (# events : 2404 )( φ vs. raw A ] ° [ φ 50 100 150 200 250 300 350 raw A 0.5 − 0.4 − 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 0.4 0.5

/ ndf

2

χ 11.32 / 8 α 0.05778 ± 0.441 / ndf

2

χ 11.32 / 8 α 0.05778 ± 0.441 / ndf

2

χ 26.24 / 8 α 0.05491 ± 0.3781 / ndf

2

χ 26.24 / 8 α 0.05491 ± 0.3781

) 2 = 0.000000 GeV

t

= 0.000000 , x , 2 = 0.000000 GeV 2 Q (# events : 2404 )( φ vs. raw A

Bins in −t

] ° [ φ 50 100 150 200 250 300 350

raw

A 0.5 − 0.4 − 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 0.4 0.5

/ ndf

2

χ 4.756 / 8 α 0.05657 ± 0.4206 / ndf

2

χ 4.756 / 8 α 0.05657 ± 0.4206 / ndf

2

χ 3.324 / 8 α 0.04964 ± 0.3789 / ndf

2

χ 3.324 / 8 α 0.04964 ± 0.3789

) 2 = 0.080654 GeV

t

= 0.131573 , x , 2 = 1.145889 GeV 2 Q (# events : 2404 )( φ vs. raw A ] ° [ φ 50 100 150 200 250 300 350 raw A 0.5 − 0.4 − 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 0.4 0.5

/ ndf

2

χ 13.74 / 8 α 0.05617 ± 0.3475 / ndf

2

χ 13.74 / 8 α 0.05617 ± 0.3475 / ndf

2

χ 12.21 / 8 α 0.05026 ± 0.3195 / ndf

2

χ 12.21 / 8 α 0.05026 ± 0.3195

) 2 = 0.094169 GeV

t

= 0.170550 , x , 2 = 1.423673 GeV 2 Q (# events : 2404 )( φ vs. raw A ] ° [ φ 50 100 150 200 250 300 350 raw A 0.5 − 0.4 − 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 0.4 0.5

/ ndf

2

χ 9.053 / 8 α 0.05609 ± 0.3002 / ndf

2

χ 9.053 / 8 α 0.05609 ± 0.3002 / ndf

2

χ 14.21 / 8 α 0.04991 ± 0.3292 / ndf

2

χ 14.21 / 8 α 0.04991 ± 0.3292

) 2 = 0.000000 GeV

t

= 0.000000 , x , 2 = 0.000000 GeV 2 Q (# events : 2404 )( φ vs. raw A

SLIDE 23

Kinematic Fit Applied to EG6: 4C-fit on DVπ0P

SLIDE 24

Motivation

Even with the detected e in CLAS and 4He in the RTPC, we still have to sift all combinations of photon pairs formed from both the IC and EC:

h_M_pi0 Entries 796629 Mean 0.2775 Std Dev 0.1798 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 5000 10000 15000 20000 25000 30000 35000 40000 h_M_pi0 Entries 796629 Mean 0.2775 Std Dev 0.1798

Invariant Mass of Photon Pair (All)

SLIDE 25

Motivation

1Exc. Cuts

h_M_pi0 Entries 1291 Mean 0.2266 Std Dev 0.2064 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 50 100 150 200 250 h_M_pi0 Entries 1291 Mean 0.2266 Std Dev 0.2064

Invariant Mass of Photon Pair (All)

4C Kin. Fit

]

2

[GeV/c

γ γ

M 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 20 40 60 80 100 120 140 160 180 200 220 240

M_pi0_after

Entries 1122 Mean 0.285 Std Dev 0.2292 h_M_pi0_bayram Entries 802 Mean 0.1337 Std Dev 0.01044

After CLC

γ γ

M

M_pi0_fit_pass

Entries 1122 Mean 0.2853 Std Dev 0.2283

When applying the 4C kinematic fit, we see that the invariant mass distribution has a clear π0-peak with very little background (and maybe a broader, shallower η peak [Mη ≈ 0.55 GeV/c2]). Note: Nowhere in the implementation is the nominal value of Mπ0 used!

1For a fair comparison, additional π0 cuts includes a photon distance cut

(|∆xγγ − 5cm| < 2cm) and a momentum cut (pπ0 > 3GeV/c).

SLIDE 26

Kinematic Fit Applied to EG6: 5C-fit on DVπ0P

SLIDE 27

Setting up Kinematic Input Vectors

For convenience, let’s first introduce some 4-vectors before defining

ur input vectors for kinematic fitting:

PXπ0 :=

#

» p γ1 + # » p γ2 ,

#

» p γ1 + # » p γ22 + M2

π0

Pfin := Pe + P4He + PXπ0

Pinit := PBeam + PTarg and constraint 4-momentas for exclusivity and decay

PExc. := Pinit − Pfin

PDecay := PXπ0 − (Pγ1 + Pγ2) respectively.

SLIDE 28

Setting up Kinematic Inputs

Then, # » y 0 =                      pe θe φe p4He θ4He φ4He pγ1 θγ1 φγ1 pγ2 θγ2 φγ2                      , # » x 0 =   pπ0 θπ0 φπ0   , # » c 0 =              (PExc.)x (PExc.)y (PExc.)z (PExc.)E (PDecay)x (PDecay)y (PDecay)z (PDecay)E              , (12)

SLIDE 29

Setting up Kinematic Input Matrices

Before writing matrices A0 and B0 out, let’s define Dβ, where β represents the particle, β ∈

e, 4He, γ1, γ2, π0

: Dβ := (−1)     sin θβ cos φβ pβ cos θβ cos φβ −pβ sin θβ sin φβ sin θβ sin φβ pβ cos θβ sin φβ pβ sin θβ cos φβ cos θβ −pβ sin θβ

pβ Eβ

    . (13) The convention of the −1 emphasizes that these are final state

particles. Then,

B0 = De D4He Dγ1 Dγ2

,

A0 = Dπ0 −Dπ0

.

(14)

SLIDE 30

Setting up Covariance Matrix

Now, we set up the covariance matrix. Let’s start with a simple, uncorrelated matrix: Cη = diag

σ2

pe, σ2 θe, σ2 φe, . . . , σ2 pγ2, σ2 θγ2, σ2 φγ2

(15)

=             σ2

pe

. . . . . . . . . σ2

θe

... ... ... . . . . . . ... ... ... ... . . . . . . ... ... ... ... . . . . . . ... ... ... σ2

θγ2

. . . . . . . . . σ2

φγ2

            (16) where the σ’s are the widths extracted from previous Monte-Carlo studies that each depend on different combinations of measured p, θ, φ.

SLIDE 31

Fit Outputs

Confidence Level Distribution

confLevels Entries 796629 Mean 0.0003172 Std Dev 0.01431 / ndf

2

χ 41.52 / 25 p0 0.539 ± 7.557

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10

2

10

3

10

4

10

5

10

6

10

confLevels Entries 796629 Mean 0.0003172 Std Dev 0.01431 / ndf

2

χ 41.52 / 25 p0 0.539 ± 7.557 Confidence Levels ( 547 events, est. SNR = 1.767808, sig. pct. = 63.870325% with conf. cut @ 0.05)

CLC = 5 × 10−2% Pull Distributions

pull_0_1

Entries 547 Mean 0.177 Std Dev 0.9493 / ndf 2 χ 40.44 / 48 N (normalization) 1.29 ± 21.63 (mean) µ 0.0443 ± 0.1481 (width) σ 0.0408 ± 0.9468

5 − 4 − 3 − 2 − 1 − 1 2 3 4 5 5 10 15 20 25 pull_0_1

Entries 547 Mean 0.177 Std Dev 0.9493 / ndf 2 χ 40.44 / 48 N (normalization) 1.29 ± 21.63 (mean) µ 0.0443 ± 0.1481 (width) σ 0.0408 ± 0.9468

Pull (After Conf. Lev. Cut)

e'

p

pull_1_1

Entries 547 Mean 0.04221 Std Dev 0.9725 / ndf 2 χ 61.77 / 49 N (normalization) 1.24 ± 20.22 (mean) µ 0.04656 ± 0.04722 (width) σ 0.0439 ± 0.9738

5 − 4 − 3 − 2 − 1 − 1 2 3 4 5 5 10 15 20 25 30 pull_1_1

Entries 547 Mean 0.04221 Std Dev 0.9725 / ndf 2 χ 61.77 / 49 N (normalization) 1.24 ± 20.22 (mean) µ 0.04656 ± 0.04722 (width) σ 0.0439 ± 0.9738

Pull (After Conf. Lev. Cut)

e'

θ

pull_2_1

Entries 547 Mean 0.02611 − Std Dev 0.9931 / ndf 2 χ 48.16 / 50 N (normalization) 1.25 ± 21.29 (mean) µ 0.04512 ± 0.04792 − (width) σ 0.0384 ± 0.9465

5 − 4 − 3 − 2 − 1 − 1 2 3 4 5 5 10 15 20 25 30 pull_2_1

Entries 547 Mean 0.02611 − Std Dev 0.9931 / ndf 2 χ 48.16 / 50 N (normalization) 1.25 ± 21.29 (mean) µ 0.04512 ± 0.04792 − (width) σ 0.0384 ± 0.9465

Pull (After Conf. Lev. Cut)

e'

φ

pull_3_1

Entries 547 Mean 0.1862 Std Dev 1.083 / ndf 2 χ 59.77 / 53 N (normalization) 1.19 ± 19.25 (mean) µ 0.0480 ± 0.2187 (width) σ 0.045 ± 1.018

5 − 4 − 3 − 2 − 1 − 1 2 3 4 5 5 10 15 20 25 30 35 pull_3_1

Entries 547 Mean 0.1862 Std Dev 1.083 / ndf 2 χ 59.77 / 53 N (normalization) 1.19 ± 19.25 (mean) µ 0.0480 ± 0.2187 (width) σ 0.045 ± 1.018

Pull (After Conf. Lev. Cut)

he4'

p

pull_4_1

Entries 547 Mean 0.06834 Std Dev 0.9835 / ndf 2 χ 62.82 / 49 N (normalization) 1.17 ± 20.08 (mean) µ 0.04751 ± 0.06128 (width) σ 0.0383 ± 0.9713

5 − 4 − 3 − 2 − 1 − 1 2 3 4 5 5 10 15 20 25 30 pull_4_1

Entries 547 Mean 0.06834 Std Dev 0.9835 / ndf 2 χ 62.82 / 49 N (normalization) 1.17 ± 20.08 (mean) µ 0.04751 ± 0.06128 (width) σ 0.0383 ± 0.9713

Pull (After Conf. Lev. Cut)

he4'

θ

pull_5_1

Entries 547 Mean 0.2 Std Dev 0.9108 / ndf 2 χ 63.59 / 49 N (normalization) 1.30 ± 22.47 (mean) µ 0.0405 ± 0.1868 (width) σ 0.0326 ± 0.8657

5 − 4 − 3 − 2 − 1 − 1 2 3 4 5 5 10 15 20 25 30 pull_5_1

Entries 547 Mean 0.2 Std Dev 0.9108 / ndf 2 χ 63.59 / 49 N (normalization) 1.30 ± 22.47 (mean) µ 0.0405 ± 0.1868 (width) σ 0.0326 ± 0.8657

Pull (After Conf. Lev. Cut)

he4'

φ

pull_6_1

Entries 547 Mean 0.2031 Std Dev 1.1 / ndf 2 χ 60.66 / 54 N (normalization) 1.05 ± 18.15 (mean) µ 0.0517 ± 0.2567 (width) σ 0.04 ± 1.08

5 − 4 − 3 − 2 − 1 − 1 2 3 4 5 5 10 15 20 25 pull_6_1

Entries 547 Mean 0.2031 Std Dev 1.1 / ndf 2 χ 60.66 / 54 N (normalization) 1.05 ± 18.15 (mean) µ 0.0517 ± 0.2567 (width) σ 0.04 ± 1.08

Pull (After Conf. Lev. Cut)

1

γ

p

pull_7_1

Entries 547 Mean 0.1623 − Std Dev 0.9664 / ndf 2 χ 39.02 / 44 N (normalization) 1.25 ± 21.61 (mean) µ 0.046 ± 0.123 − (width) σ 0.0404 ± 0.9575

5 − 4 − 3 − 2 − 1 − 1 2 3 4 5 5 10 15 20 25 pull_7_1

Entries 547 Mean 0.1623 − Std Dev 0.9664 / ndf 2 χ 39.02 / 44 N (normalization) 1.25 ± 21.61 (mean) µ 0.046 ± 0.123 − (width) σ 0.0404 ± 0.9575

Pull (After Conf. Lev. Cut)

1

γ

θ

pull_8_1

Entries 547 Mean 0.03539 − Std Dev 1.026 / ndf 2 χ 50.79 / 50 N (normalization) 1.16 ± 19.68 (mean) µ 0.04879 ± 0.03714 − (width) σ 0.043 ± 1.025

5 − 4 − 3 − 2 − 1 − 1 2 3 4 5 5 10 15 20 25 pull_8_1

Entries 547 Mean 0.03539 − Std Dev 1.026 / ndf 2 χ 50.79 / 50 N (normalization) 1.16 ± 19.68 (mean) µ 0.04879 ± 0.03714 − (width) σ 0.043 ± 1.025

Pull (After Conf. Lev. Cut)

1

γ

φ

pull_9_1

Entries 547 Mean 0.1547 Std Dev 1.102 / ndf 2 χ 43.7 / 54 N (normalization) 1.07 ± 18.33 (mean) µ 0.052 ± 0.141 (width) σ 0.046 ± 1.114

5 − 4 − 3 − 2 − 1 − 1 2 3 4 5 5 10 15 20 25 pull_9_1

Entries 547 Mean 0.1547 Std Dev 1.102 / ndf 2 χ 43.7 / 54 N (normalization) 1.07 ± 18.33 (mean) µ 0.052 ± 0.141 (width) σ 0.046 ± 1.114

Pull (After Conf. Lev. Cut)

2

γ

p

pull_10_1

Entries 547 Mean 0.0003939 − Std Dev 0.9849 / ndf 2 χ 76.19 / 47 N (normalization) 1.26 ± 19.53 (mean) µ 0.04800 ± 0.06878 − (width) σ 0.0485 ± 0.9749

5 − 4 − 3 − 2 − 1 − 1 2 3 4 5 5 10 15 20 25 30 35 pull_10_1

Entries 547 Mean 0.0003939 − Std Dev 0.9849 / ndf 2 χ 76.19 / 47 N (normalization) 1.26 ± 19.53 (mean) µ 0.04800 ± 0.06878 − (width) σ 0.0485 ± 0.9749

Pull (After Conf. Lev. Cut)

2

γ

θ

pull_11_1

Entries 547 Mean 0.01672 Std Dev 1.038 / ndf 2 χ 38.24 / 53 N (normalization) 1.1 ± 19.5 (mean) µ 0.050846 ± 0.002969 − (width) σ 0.04 ± 1.06

5 − 4 − 3 − 2 − 1 − 1 2 3 4 5 5 10 15 20 25 30 pull_11_1

Entries 547 Mean 0.01672 Std Dev 1.038 / ndf 2 χ 38.24 / 53 N (normalization) 1.1 ± 19.5 (mean) µ 0.050846 ± 0.002969 − (width) σ 0.04 ± 1.06

Pull (After Conf. Lev. Cut)

2

γ

φ

SLIDE 32

Invariant Mass Distribution for γγ

Measured values from: Black: Exclusivity Cuts Blue: Kinematic Fit Fitted values from: Green: Kinematic Fit

]

2

[GeV/c

γ γ

M 0.05 0.1 0.15 0.2 0.25 0.3 10 20 30 40 50 60 70 80 90

M_pi0_after

Entries 547 Mean 0.1342 Std Dev 0.008738

h_M_pi0_bayram Entries 802 Mean 0.1337 Std Dev 0.01044

Distribution After

γ γ

M

M_pi0_fit_pass

Entries 547 Mean 0.135 Std Dev 0.0002981

SLIDE 33

Comparison to Exclusivity Cuts

SLIDE 34

Results

For the EG6 experiment, the BSA for the coherent DVMP process e 4He → e′4He

′π0

(17) is obtained from two different event selection methods: Exclusivity Cuts

[deg.] φ 50 100 150 200 250 300 []

Raw

A 0.2 − 0.1 − 0.1 0.2 0.3 / ndf

2

χ 4.455 / 7 α 0.0528 ± 0.08855 − / ndf

2

χ 4.455 / 7 α 0.0528 ± 0.08855 −

Exc. Fit All

)

2

< 3.500 (GeV/c)

2

(0.500 < Q φ vs

Raw

A

BSA = -8.9±5.3 % (800 events) Kinematic Fit

[deg.] φ 50 100 150 200 250 300 []

Raw

A 0.3 − 0.2 − 0.1 − 0.1 0.2

/ ndf

2

χ 3.477 / 7 α 0.06363 ± 0.005144 − / ndf

2

χ 3.477 / 7 α 0.06363 ± 0.005144 −

Kin. Fit All

)

2

< 3.500 (GeV/c)

2

(0.500 < Q φ vs

Raw

A

BSA = -0.5±6.3 % (537 events)

SLIDE 35

Datasets

Consider the Venn diagram of the datasets:

SLIDE 36

Beam Spin Asymmetries

Beam spin asymmetries for all 5C-fitted events : (537 Events)

[deg.] φ 50 100 150 200 250 300 []

Raw

A 0.3 − 0.2 − 0.1 − 0.1 0.2

/ ndf

2

χ 3.477 / 7 α 0.06363 ± 0.005144 − / ndf

2

χ 3.477 / 7 α 0.06363 ± 0.005144 −

Kin. Fit All

)

2

< 3.500 (GeV/c)

2

(0.500 < Q φ vs

Raw

A

( BSA = - 0.5±6.4 % )

SLIDE 37

Beam Spin Asymmetries

Beam spin asymmetries for all events passing exclusivity cuts : (800 events)

[deg.] φ 50 100 150 200 250 300 []

Raw

A 0.2 − 0.1 − 0.1 0.2 0.3 / ndf

2

χ 4.455 / 7 α 0.0528 ± 0.08855 − / ndf

2

χ 4.455 / 7 α 0.0528 ± 0.08855 −

Exc. Fit All

)

2

< 3.500 (GeV/c)

2

(0.500 < Q φ vs

Raw

A

( BSA = - 8.9±5.3 % )

SLIDE 38

Beam Spin Asymmetries

Beam spin asymmetries for events passing only 5C-fit : (488 Events)

[deg.] φ 50 100 150 200 250 300 []

Raw

A 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 / ndf

2

χ 4.662 / 7 α 0.06789 ± 0.03298 − / ndf

2

χ 4.662 / 7 α 0.06789 ± 0.03298 −

Intersection

)

2

< 3.500 (GeV/c)

2

(0.500 < Q φ vs

Raw

A

( BSA = - 3.3±6.8 % )

SLIDE 39

Beam Spin Asymmetries

Beam spin asymmetries for events only passing exclusivity cuts : (312 Events)

[deg.] φ 50 100 150 200 250 300 []

Raw

A 0.4 − 0.2 − 0.2 0.4 0.6 / ndf

2

χ 5.544 / 7 α 0.08549 ± 0.2029 − / ndf

2

χ 5.544 / 7 α 0.08549 ± 0.2029 −

Exc. Cut Only

)

2

< 3.500 (GeV/c)

2

(0.500 < Q φ vs

Raw

A

( BSA = - 20.3±8.5 % )

SLIDE 40

Exclusivity Variable Distributions

]

2

)

2

[ (GeV/c

X 2

M 5 10 15 20 25 30 10 20 30 40 50

) X π e → (

X 2

M

Intersection

Exc. Cut Only
Kin. Fit Only

]

2

)

2

[ (GeV/c

X 2

M 2 − 1.5 − 1 − 0.5 − 0.5 1 1.5 2 5 10 15 20 25 30 35

)

1

He X

4

e → (

1

X 2

M

Intersection

Exc. Cut Only
Kin. Fit Only

]

2

)

2

[ (GeV/c

X 2

M 0.1 − 0.08 − 0.06 − 0.04 − 0.02 − 0.02 0.04 0.06 0.08 0.1 10 20 30 40 50 60 70 80 90

)

2

X π He

4

e → (

2

X 2

M

Intersection

Exc. Cut Only
Kin. Fit Only

]

2

)

2

[ (GeV/c

X 2

M 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 5 10 15 20 25 30 35 40 45

)

2

X π He

4

e → (

X2

px

Intersection

Exc. Cut Only
Kin. Fit Only

]

2

)

2

[ (GeV/c

X 2

M 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 5 10 15 20 25 30 35 40

)

2

X π He

4

e → (

X2

py

Intersection

Exc. Cut Only
Kin. Fit Only

]

2

)

2

[ (GeV/c

X 2

M 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 5 10 15 20 25 30 35

)

2

X π He

4

e → (

X2

pt

Intersection

Exc. Cut Only
Kin. Fit Only

]

2

)

2

[ (GeV/c

X 2

M 1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1 5 10 15 20 25 30

)

2

X π He

4

e → (

X2

E

Intersection

Exc. Cut Only
Kin. Fit Only

]

2

)

2

[ (GeV/c

X 2

M 0.5 1 1.5 2 2.5 3 3.5 4 5 10 15 20 25 30 35

)

1

He X

4

e → (

π ,

1

X

θ

Intersection

Exc. Cut Only
Kin. Fit Only

]

2

)

2

[ (GeV/c

X 2

M 2 − 1.5 − 1 − 0.5 − 0.5 1 1.5 2 5 10 15 20 25

))

π

p ×

He

4

p ,

* γ

p ×

He

4

p ( ∠ ( φ ∆

Intersection

Exc. Cut Only
Kin. Fit Only

SLIDE 41

Beam Spin Asymmetries

Beam spin asymmetries summary:

(800 events, BSA = -8.9±5.3%)

[deg.] φ 50 100 150 200 250 300 []

Raw

A 0.2 − 0.1 − 0.1 0.2 0.3 / ndf

2 χ 4.455 / 7 α 0.0528 ± 0.08855 − / ndf 2 χ 4.455 / 7 α 0.0528 ± 0.08855 −

Exc. Fit All

)

2

< 3.500 (GeV/c)

2

(0.500 < Q φ vs

Raw

A

(488 events, BSA = -3.3±6.8%)

[deg.] φ 50 100 150 200 250 300 []

Raw

A 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 / ndf

2

χ 4.662 / 7 α 0.06789 ± 0.03298 − / ndf

2

χ 4.662 / 7 α 0.06789 ± 0.03298 − Intersection

)

2

< 3.500 (GeV/c)

2

(0.500 < Q φ vs

Raw

A

(312 events, BSA = -20.3±8.5%)

[deg.] φ 50 100 150 200 250 300 []

Raw

A 0.4 − 0.2 − 0.2 0.4 0.6 / ndf

2 χ 5.544 / 7 α 0.08549 ± 0.2029 − / ndf 2 χ 5.544 / 7 α 0.08549 ± 0.2029 −

Exc. Cut Only

)

2

< 3.500 (GeV/c)

2

(0.500 < Q φ vs

Raw

A

SLIDE 42

Sliding Down CLC to Match Statistics

SLIDE 43

Fit Outputs

Confidence Level Distribution CLC = 6 × 10−4 Pull Distributions

SLIDE 44

Exclusivity Variable Distributions

131 Events 669 Events 129 Events

SLIDE 45

Conclusion

The kinematic fit has a surprising effect of partitioning the previous 800 coherent π0 events into 312 events with asymmetry (≈20%) and 488 events without asymmetry (≈ 3%). Although it is not clear what this extra asymmetry is coming from, it is clear that events passing both the kinematic fit and the exclusivity cuts is diluting this larger asymmetry from seemingly background events. Kinematic Fitting allows to clean events using both detector resolutions and conservation law constraints. Some of these events cannot be accessed by any obvious series of cuts. Cuts for event selection require some extra insight and/or some cleverness.

SLIDE 46

Questions?

SLIDE 47

Backup Slides

SLIDE 48

Exclusivity Variables Definitions

Missing M2, E, p, etc. definitions corresponding to distributions: M2

X0

M2

X1

M2

X2

pxX2 pyX2 ptX2 EX2 θX0,π0 ∆φ where X0 : e 4He → e′4He

′X0

X1 : e 4He → e′π0X1 X2 : e 4He → e′4He

′π0X2

SLIDE 49

Sanity Check Distributions

SLIDE 50

Motivation: Vertex Coincidence

Before CLC

dVz Entries 796629 Mean 0.02084 − Std Dev 1.061 [cm.]

He

4

e,

vz ∆ 3 − 2 − 1 − 1 2 3 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 dVz Entries 796629 Mean 0.02084 − Std Dev 1.061

He

4

e,

vz ∆

After CLC

dVz_after Entries 547 Mean 0.008289 Std Dev 0.7514 [cm.]

He

4

e,

vz ∆ 3 − 2 − 1 − 1 2 3 5 10 15 20 25 dVz_after Entries 547 Mean 0.008289 Std Dev 0.7514

After CLC

He

4

e,

vz ∆ Line Distribution: All Measured Events Filled Distribution: Measured Events After CLC

SLIDE 51

Sanity Check: Photon Distance

Before CLC

DX Entries 166863 Mean 6.44 Std Dev 2.1 [cm.]

2

γ ,

1

γ

X ∆ 1 2 3 4 5 6 7 8 9 10 200 400 600 800 1000 1200 1400 DX Entries 166863 Mean 6.44 Std Dev 2.1

2

γ ,

1

γ

X ∆

After CLC

DX_after Entries 531 Mean 4.621 Std Dev 0.9666 [cm.]

2

γ ,

1

γ

X ∆ 1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 30 DX_after Entries 531 Mean 4.621 Std Dev 0.9666

After CLC

2

γ ,

1

γ

X ∆ Line Distribution: All Measured Events Filled Distribution: Measured Events After CLC

The 5C-fit has no knowledge of the vertex coincidence between the helium in the RTPC and the electron in CLAS but produces a clean distribution of their distance.

B. Torayev’s Cut : ∆X ∈ [3, 7] cm

SLIDE 52

Sanity Check: π0 Momentum Distribution

xs_0_0

Entries 547 Mean 4.459 Std Dev 0.5163

1 2 3 4 5 6 5 10 15 20 25 30 35

xs_0_0

Entries 547 Mean 4.459 Std Dev 0.5163

(fitted) (x's)

π

p

Red: Fitted After CLC Blue: Measured After CLC

The 5C-fit has no cut on the π0 momentum but the distribution shows that the minimum momentum is around 3GeV /c.

B. Torayev’s Cut : Pπ0 > 3 GeV/c

SLIDE 53

Sanity Check: γ2 Momentum Distribution

0.5 1 1.5 2 2.5 2 4 6 8 10 12 14

(fitted) (After Conf. Lev. Cut)

2

γ

p

Red: Fitted After CLC Blue: Measured After CLC

The 5C-fit has no cut on the γ2 but the distribution shows that the minimum momentum is around 0.3GeV /c.

B. Torayev’s Cut : Pγ2 > 0.4GeV /c

SLIDE 54

Detector Resolutions

Table: Detector Resolutions

δp (%) δθ (deg.) δφ (deg.) δx (cm) DC (Electron) 3.40 2.50 4.00 – IC (Photon) 1.33 – – 1.20 RTPC (Helium) 10.00 4.00 4.00 – δp (%) δθ (rad.) δφ (rad.) δx (cm) EC (Photon) – 0.004 0.004 –

Let ⊕ denote the square-root quadrature sum: a ⊕ b ⊕ c ⊕ . . . :=

a2 + b2 + c2 + . . .

Then with these resolutions, we can calculate the widths that were extracted from simulation particle-by-particle. The explicit forms of the widths are shown in the following subsections. For the following, all input momenta are in GeV/c, all input angles are in units denoted by the subscripts, and resolutions are in units given by Table 1.

SLIDE 55

Detector Errors: DC

Table: Parameters for DC widths

Parameter Index i Ai Bi Ci Di Ei p 3375 35 0.7 0.0033 0.0018 θ 1000 0.55 1.39 – – φ 1000 3.73 3.14 – –

σpe[GeV] = Ap Ibeam θdeg. Bp Cp pδp

(Dpp) ⊕ Ep

β

σθe[rad] = δθ

Aθ

Bθ ⊕ Cθ

pβ

σφe[rad] = δφ

Aφ

Bφ ⊕ Cφ

pβ

(18)

where Ibeam = 1900A, β = pc/E, and parameters Ai through Ei are listed in Table 2.

SLIDE 56

Detector Errors: IC

Table: Parameters for IC widths

Parameter Index i Ai Bi Ci p 0.024 0.0033 0.0019 θ 0.003 0.013 – φ 0.003 – – σpγ[GeV] = pδp

Ap ⊕ Bp

√p ⊕ Cp p

σθγ[rad] = δx

Aθ √p ⊕ (Bθθrad.)

σφγ[rad] = δx

Aφ √p

(19)

SLIDE 57

Detector Errors: EC

σpγ[GeV] = Ap √p σθγ[rad] = δθEC σφγ[rad] = δφEC (20) where the parameter Ap = 0.116.

SLIDE 58

Detector Errors: RTPC

σp4He[GeV] = pδp σθ4He[rad] = δθrad σφ4He[rad] = δφrad (21)

SLIDE 59

Sanity Check: Exclusivity Variable Distributions

]

2

)

2

[(GeV/c

X 2

M 8 10 12 14 16 18 20 22 5 10 15 20 25 30 35 40 45 ) (After Conf. Lev. Cut) X π (Final State: e

X 2 M

]

2

)

2

[(GeV/c

1 X 2

M 1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1 5 10 15 20 25 30 ) (After Conf. Lev. Cut)

1 He X 4 (Final State: e 1 X 2 M ] 2 ) 2 [(GeV/c 2 X 2

M 0.1 − 0.08 − 0.06 − 0.04 − 0.02 − 0.02 0.04 0.06 0.08 0.1 20 40 60 80 100 ) (After Conf. Lev. Cut)

2 X π He 4 (Final State: e 2 X 2 M

[GeV/c]

x

P 0.2 − 0.15 − 0.1 − 0.05 − 0.05 0.1 0.15 0.2 5 10 15 20 25 30 35

(After Conf. Lev. Cut)

x

P

[GeV/c]

y

P 0.2 − 0.15 − 0.1 − 0.05 − 0.05 0.1 0.15 0.2 5 10 15 20 25 30 35 40 45

(After Conf. Lev. Cut)

y

P

[GeV/c]

t

P 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 5 10 15 20 25 30

(After Conf. Lev. Cut)

t

P

[GeV]

2 X

E 1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1 5 10 15 20 25 30 35

(After Conf. Lev. Cut)

2

X

E

[deg.] θ 0.5 1 1.5 2 2.5 3 3.5 5 10 15 20 25 30 35

(After Conf. Lev. Cut) θ

[deg.] φ ∆ 5 − 4 − 3 − 2 − 1 − 1 2 3 4 5 10 20 30 40 50 60 70 80

(After Conf. Lev. Cut) φ ∆

Black: B. Torayev’s Distributions Blue: Measured After CLC Green: Fitted After CLC

B. Torayev’s Cuts:

|M2

X2 − 0.005| < 0.048

GeV/c22

|∆φ − 0.16| < 0.138 deg. |θπ0,X1 − 2.5| < 0.03 deg. |M2

X0 − 14.079| < 0.03

GeV/c22

The 5C-fit has no cuts on any of the exclusivity variables but they are essentially within the previous cuts.

SLIDE 60

Common Events’ BSA for Equally Statistic Events

800 Kin. Fit Events with CLC @ 6 × 10−4 overlap with 800 Exc. Cut events. The overlap is 669 events.

] ° [ φ 50 100 150 200 250 300 350

raw

A 0.5 − 0.4 − 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 0.4 0.5

/ ndf

2

χ 3.092 / 7 α 0.05759 ± 0.04887 − / ndf

2

χ 3.092 / 7 α 0.05759 ± 0.04887 − / ndf

2

χ 2.417 / 7 α 0.0573 ± 0.05174 − / ndf

2

χ 2.417 / 7 α 0.0573 ± 0.05174 − / ndf

2

χ 4.851 / 7 α 0.05258 ± 0.08983 − / ndf

2

χ 4.851 / 7 α 0.05258 ± 0.08983 −

)

2

= 0.174 GeV

t

= 0.113 , x ,

2

= 1.469 GeV

2

Q (# events : 669 )( φ vs.

raw

A

SLIDE 61

BSA vs. Conf. Level Cut: Full Dataset

Conf. Level Cut

18 −

10

16 −

10

14 −

10

12 −

10

10 −

10

8 −

10

6 −

10

4 −

10

2 −

10

events

n 500 1000 1500 2000 2500 3000

Conf. Level Cut

18 −

10

16 −

10

14 −

10

12 −

10

10 −

10

8 −

10

6 −

10

4 −

10

2 −

10 Beam Spin Asymmetry 0.1 − 0.05 − 0.05 0.1 0.15

SLIDE 62

BSA vs. Conf. Level Cut: Exclusivity Selected Events

Conf. Level Cut

18 −

10

16 −

10

14 −

10

12 −

10

10 −

10

8 −

10

6 −

10

4 −

10

2 −

10

events

n 200 300 400 500 600 700 800

Conf. Level Cut

18 −

10

16 −

10

14 −

10

12 −

10

10 −

10

8 −

10

6 −

10

4 −

10

2 −

10 Beam Spin Asymmetry 0.15 − 0.1 − 0.05 − 0.05 0.1 0.15

SLIDE 63

Invariant Mass Distributions

]

2

[ GeV/c 0.05 0.1 0.15 0.2 0.25 0.3 10 20 30 40 50 60

γ γ

M

Intersection (488 events)

Exc. Cut Only (312 events)
Kin. Fit Only (49 events)

SLIDE 64

Adding One Exclusivity Cut: E Cut

Exclusivity Variable Distributions

]

2

)

2

[(GeV/c

X 2

M 8 10 12 14 16 18 20 22 5 10 15 20 25 30 35 40 45

cart_0_1

Entries 692 Mean 13.97 Std Dev 1.17

) After CLC X π (Final State: e

X 2

M ]

2

)

2

[(GeV/c

1 X 2

M 1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1 5 10 15 20 25 30

cart_1_1

Entries 692 Mean 0.002705 − Std Dev 0.3302

) After CLC

1

He X

4

(Final State: e

1 X 2

M ]

2

)

2

[(GeV/c

2 X 2

M 0.1 − 0.08 − 0.06 − 0.04 − 0.02 − 0.02 0.04 0.06 0.08 0.1 20 40 60 80 100

cart_2_1

Entries 692 Mean 0.005629 − Std Dev 0.01412

) After CLC

2

X π He

4

(Final State: e

2 X 2

M [GeV/c]

x

P 0.2 − 0.15 − 0.1 − 0.05 − 0.05 0.1 0.15 0.2 5 10 15 20 25 30 35

cart_3_1

Entries 692 Mean 0.004173 − Std Dev 0.05381

After CLC

x

P

[GeV/c]

y

P 0.2 − 0.15 − 0.1 − 0.05 − 0.05 0.1 0.15 0.2 5 10 15 20 25 30 35 40 45

cart_4_1

Entries 692 Mean 0.003019 − Std Dev 0.0458

After CLC

y

P

[GeV/c]

t

P 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 5 10 15 20 25 30

cart_5_1

Entries 692 Mean 0.05839 Std Dev 0.03946

After CLC

t

P

[GeV]

2 X

E 1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1 5 10 15 20 25 30 35

cart_6_1

Entries 692 Mean 0.01007 Std Dev 0.1635

After CLC

2

X

E

[deg.] θ 0.5 1 1.5 2 2.5 3 3.5 5 10 15 20 25 30 35

cart_7_1

Entries 692 Mean 0.7109 Std Dev 0.5075

After CLC θ

[deg.] φ ∆ 5 − 4 − 3 − 2 − 1 − 1 2 3 4 5 10 20 30 40 50 60 70 80

cart_8_1

Entries 692 Mean 0.144 Std Dev 0.5354

After CLC φ ∆

Beam Spin Asymmetry

] ° [ φ 50 100 150 200 250 300 350

raw

A 0.5 − 0.4 − 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 0.4 0.5

/ ndf

2

χ 2.678 / 7 α 0.05634 ± 0.05976 − / ndf

2

χ 2.678 / 7 α 0.05634 ± 0.05976 − / ndf

2

χ 2.366 / 7 α 0.05625 ± 0.07229 − / ndf

2

χ 2.366 / 7 α 0.05625 ± 0.07229 − / ndf

2

χ 4.851 / 7 α 0.05258 ± 0.08983 − / ndf

2

χ 4.851 / 7 α 0.05258 ± 0.08983 −

)

2

= 0.176 GeV

t

= 0.111 , x ,

2

= 1.492 GeV

2

Q (# events : 692 )( φ vs.

raw

A

(692 events, BSA = -6.4±5.6%)

SLIDE 65

Likelihood of Selecting 488 out of 800 events having ARaw = −3.3%

asym Entries 10000 Mean 8.917 − Std Dev 3.879 / ndf

2

χ 88.45 / 97 Constant 2.2 ± 164.9 Mean 0.049 ± 8.902 − Sigma 0.046 ± 4.306

[%]

Raw

A 18 − 16 − 14 − 12 − 10 − 8 − 6 − 4 − 2 − 20 40 60 80 100 120 140 160 180

asym Entries 10000 Mean 8.917 − Std Dev 3.879 / ndf

2

χ 88.45 / 97 Constant 2.2 ± 164.9 Mean 0.049 ± 8.902 − Sigma 0.046 ± 4.306 Events) π (Choosing 488 Random Events Out of 800 Exc. Cut Coh.

Raw

A

SLIDE 66

Likelihood of Selecting 312 out of 800 events having ARaw = −20.3%

asym Entries 10000 Mean 9.309 − Std Dev 5.629 / ndf

2

χ 133.4 / 97 Constant 1.9 ± 137.6 Mean 0.090 ± 8.967 − Sigma 0.095 ± 6.856

[%]

Raw

A 20 − 15 − 10 − 5 − 20 40 60 80 100 120 140

asym Entries 10000 Mean 9.309 − Std Dev 5.629 / ndf

2

χ 133.4 / 97 Constant 1.9 ± 137.6 Mean 0.090 ± 8.967 − Sigma 0.095 ± 6.856 Events) π (Choosing 312 Random Events Out of 800 Exc. Cut Coh.

Raw

A

SLIDE 67

Adding One Exclusivity Cut: E Cut

Exclusivity Variable Distributions

]

2

)

2

[(GeV/c

X 2

M 8 10 12 14 16 18 20 22 5 10 15 20 25 30 35 40 45

cart_0_1

Entries 692 Mean 14.7 Std Dev 1.196

) After CLC X π (Final State: e

X 2

M ]

2

)

2

[(GeV/c

1 X 2

M 1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1 5 10 15 20 25 30

cart_1_1

Entries 692 Mean 0.02204 Std Dev 0.3215

) After CLC

1

He X

4

(Final State: e

1 X 2

M ]

2

)

2

[(GeV/c

2 X 2

M 0.1 − 0.08 − 0.06 − 0.04 − 0.02 − 0.02 0.04 0.06 0.08 0.1 20 40 60 80 100

cart_2_1

Entries 692 Mean 0.005613 − Std Dev 0.01505

) After CLC

2

X π He

4

(Final State: e

2 X 2

M [GeV/c]

x

P 0.2 − 0.15 − 0.1 − 0.05 − 0.05 0.1 0.15 0.2 5 10 15 20 25 30 35

cart_3_1

Entries 692 Mean 0.003616 − Std Dev 0.05389

After CLC

x

P

[GeV/c]

y

P 0.2 − 0.15 − 0.1 − 0.05 − 0.05 0.1 0.15 0.2 5 10 15 20 25 30 35 40 45

cart_4_1

Entries 692 Mean 0.001646 − Std Dev 0.0472

After CLC

y

P

[GeV/c]

t

P 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 5 10 15 20 25 30

cart_5_1

Entries 692 Mean 0.05935 Std Dev 0.03883

After CLC

t

P

[GeV]

2 X

E 1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1 5 10 15 20 25 30 35

cart_6_1

Entries 692 Mean 0.1131 Std Dev 0.1673

After CLC

2

X

E

[deg.] θ 0.5 1 1.5 2 2.5 3 3.5 5 10 15 20 25 30 35

cart_7_1

Entries 692 Mean 0.7385 Std Dev 0.5138

After CLC θ

[deg.] φ ∆ 5 − 4 − 3 − 2 − 1 − 1 2 3 4 5 10 20 30 40 50 60 70 80

cart_8_1

Entries 692 Mean 0.1526 Std Dev 0.5614

After CLC φ ∆

Beam Spin Asymmetry

] ° [ φ 50 100 150 200 250 300 350

raw

A 0.5 − 0.4 − 0.3 − 0.2 − 0.1 − 0.1 0.2 0.3 0.4 0.5

/ ndf

2

χ 8.174 / 7 α 0.05648 ± 0.07553 − / ndf

2

χ 8.174 / 7 α 0.05648 ± 0.07553 − / ndf

2

χ 5.357 / 7 α 0.05632 ± 0.08567 − / ndf

2

χ 5.357 / 7 α 0.05632 ± 0.08567 − / ndf

2

χ 4.851 / 7 α 0.05258 ± 0.08983 − / ndf

2

χ 4.851 / 7 α 0.05258 ± 0.08983 −

)

2

= 0.175 GeV

t

= 0.113 , x ,

2

= 1.490 GeV

2

Q (# events : 692 )( φ vs.

raw

A

(692 events, BSA = -7.8±5.6%)

SLIDE 68

Likelihood of 692/800 events having 33% Less Asymmetry

asym Entries 10000 Mean 8.866 − Std Dev 2.099 / ndf

2

χ 132.9 / 97 Constant 2.8 ± 223.1 Mean 0.022 ± 8.854 − Sigma 0.016 ± 2.116

A [%] 14 − 12 − 10 − 8 − 6 − 4 − 50 100 150 200 250

asym Entries 10000 Mean 8.866 − Std Dev 2.099 / ndf

2

χ 132.9 / 97 Constant 2.8 ± 223.1 Mean 0.022 ± 8.854 − Sigma 0.016 ± 2.116