1 / 18
EVA status report
Nobuo SatoUniversity of ConnecticutCLAS Collaboration Meeting, Jefferson Lab, Oct, 2017
EVA workflow
2 / 18
SimulationEvent Generators
X-sectionAsymmetries
18-StructureFuncs in grids
18-Structure Funcs
Input TMDs
ExtractionDetector
Simulations
EventReconstruction
Extracted X-sectionAsymmetries
Extracted Struc-ture Funcs
TMD Analysis validation
validation
validation
(x,Q2, z, P hT ,φ) (x,Q2, z, P h
T)
(x,Q2, z, P hT ,φ)
(x,Q2, z, P hT) (x,Q2, z, P h
T)
EX
PT
HY
EX
PT
HY
How to approach the problem?
3 / 18
Simulation stageUse EVA to validate the dataanalysis framework
“physics” does not need to beperfect, only approximatedversion is required
Questions to be solved:Is the input and output“physics” consistent?
Which regions of kinematics(x, z,Q2, PhT ) need be coveredin order to “unveil” the physics?
Physics analysis on real dataStudy PhT integrated SIDISusing the JAM framework
Use the approximated “physics”to interpret PhT dependentSIDIS data.
Repeat the analysis with thestate-of-the-art QCD theory:CSS with W + Y (at least forFUU).
Perform global analysis and test“universality”
Comments on approximated “physics”
4 / 18
Use WW approximation to cast twist 3 observables interms of LT correlators.(S. Bastami et al. arxiv-(in preparation))
It allows to “describe” most of the 18 SF in SIDIS
Use gaussian ansatz to factorize the x, z, PhTdependence on each SF.
New global analysis to tune the framework is needed toproceed to event simulation
SIDIS cross section WW+gaussian ansatz
5 / 18
dσ
dx dy dΨ dz dφh dP2hT
= α2
xyQ2y2
2(1− ε)
(1 + γ2
2x
) 18∑i=1
Fi(x, z,Q2, P 2hT )βi
Fi Standard label βiF1 FUU,T 1F2 FUU,L ε
F3 FLL S||λe√
1− ε2
F4 Fsin(φh+φS)UT |~S⊥|ε sin(φh + φS)
F5 Fsin(φh−φS)UT,T |~S⊥|sin(φh − φS)
F6 Fsin(φh−φS)UT,L |~S⊥|ε sin(φh − φS)
F7 F cos 2φhUU ε cos(2φh)
F8 Fsin(3φh−ψS)UT |~S⊥|ε sin(3φh − φS)
F9 Fcos(φh−φS)LT |~S⊥|λe
√1− ε2 cos(φh − φS)
F10 F sin 2φhUL S||ε sin(2φh)
F11 F cosφSLT |~S⊥|λe
√2ε(1− ε) cosφS
F12 F cosφhLL S||λe
√2ε(1− ε) cosφh
F13 Fcos(2φh−φS)LT |~S⊥|λe
√2ε(1− ε) cos(2φh − φS)
F14 F sinφhUL S||
√2ε(1 + ε) sinφh
F15 F sinφhLU λe
√2ε(1− ε) sinφh
F16 F cosφhUU
√2ε(1 + ε) cosφh
F17 F sinφSUT |~S⊥|
√2ε(1 + ε) sinφS
F18 Fsin(2φh−φS)UT |~S⊥|
√2ε(1 + ε) sin(2φh − φS)
Kq Fq(x) Dq(z)F1 FUU,T x f q1 Dq
1F2 FUU,L 0F3 FLL x gq1 Dq
1F4 F
sin(φh+φS)UT
2xzPhTmhwq
hq1 H⊥(1)q1
F5 Fsin(φh−φS)UT,T −2xzMPhT
wqf⊥(1)q1T Dq
1
F6 Fsin(φh−φS)UT,L 0
F7 Fcos(2φh)UU
4xz2MP 2hTmh
w2q
h⊥(1)q1 H
⊥(1)q1
F8 Fsin(3φh−φS)UT
2xz3P 3hTmh〈k2
⊥〉qw3
qh⊥(1)q1T H
⊥(1)q1
F9 Fcos(φh−φS)LT
2xzMPhTwq
g⊥q1T Dq1
F10 Fsin(2φh)UL
4xz2MP 2hTmh
w2q
h⊥q1L H⊥(1)q1
F11 F cosφSLT −2M
Q xz2〈k2
⊥〉q[P 2hT +〈P 2
⊥〉q]+〈P 2⊥〉
2
w2q
g⊥q1T Dq1
F12 F cosφhLL −2xzPhT
Q
〈k2⊥〉qwq
gq1 Dq1
F13 Fcos(2φh−φS)LT −2xz2MP 2
hTQ
〈k2⊥〉qw2
qg⊥q1T Dq
1
F14 F sinφhUL −8M3
Q xz2〈k2
⊥〉q(P 2hT−z
2〈k2⊥〉q)+〈P 2
⊥〉2q
w3q
h⊥q1L H⊥(1)q1
F15 F sinφhLU 0
F16 F cosφhUU (i) −8M
Q xzPhTmh[〈P 2
⊥〉2q+z2〈k2
⊥〉q(P 2hT−z
2〈k2⊥〉q)]
w3q
h⊥(1)q1 H
⊥(1)q1
F16 F cosφhUU (ii) −2M
QxzPhTM
〈k2⊥〉qwq
f q1 Dq1
F17 F sinφSUT (i) −2M
Q xz2〈k2
⊥〉q(P 2hT +〈P 2
⊥〉q)+〈P 2⊥〉
2q
w2q
f⊥(1)q1T Dq
1
F17 F sinφSUT (ii) 4xz2mh
Q
〈k2⊥〉q(−P 2
hT +wq)w2
qhq1 H
⊥(1)q1
F18 Fsin(2φh−φS)UT (i) −2M2
Q x〈k2
⊥〉qMw2
qf⊥(1)q1T Dq
1
F18 Fsin(2φh−φS)UT (ii) −2M2
Q x4z2P 2
hTmh
w2q
h⊥(1)q1T H
⊥(1)q1
Details
6 / 18
Basic building blocks of WWansatz
type Name Kq CqFq upol. PDF 1 f q1Fq pol. PDF 1 gq1Fq Transversity 1 hq1Fq Sivers 2M2
ωqf⊥(1)q1T
Fq Boer-Mulders 2M2
ωqh⊥(1)q1
Fq Pretzelosity 2M2
ωqh⊥(1)q1T
Cq FF 1 Dq1
Cq Collins 2z2m2h
ωqH⊥(1)q1
ready , in progress , TODO
Factorization ansatz for partonsin nucleon
Fq(x, p⊥) = Kq Cq(x)exp
(−k2
⊥/ωq
)πωq
Factorization ansatz for partonsto hadrons
Dq(z, p⊥) = Kq Cq(z)exp
(−P 2
⊥/ωq
)πωq
Collinear distributions areparametrized as:
Cq(ξ) = N ξa (1− ξ)b (1 + cξ + dξ2)
N, a, b, c, d are fitted to existingdata
Extraction methodology: Bayesian perspective
7 / 18
The goal is to estimate:
E[O] =∫dnaP(a|data)O(a)
V[O] =∫dnaP(a|data)[O(a)− E[O]]2
Use Bayes theorem:
P(a|data) = 1ZL(data|a)π(a)
Z =∫dnaL(data|a)π(a)
Gaussian likelihood:
L(data|a) = exp(−1
2χ2(a)
)= exp
(−1
2∑i
(di − ti(a)
σi
)2)
O(a) = f1(x,Q2, kT ,a), d1(z,Q2, kT ,a), g1(x,Q2, kT ,a), h1(x,Q2, kT ,a), ...
Example
← typically n is large O(10− 100)
Theory of fitting from Bayesian perspective
8 / 18
The goal is to estimate:
E[O] =∫dna P(a|data) O(a)
V[O] =∫dna P(a|data) [O(a)− E[O]]2
Monte Carlo methods
P(a|data)→{ak, wk}
E[O] ≈∑k wk O(ak)
V[O] ≈∑k wk [O(ak)− E[O]]2
Maximum Likelihood
Maximize P(a|data)→a0
E[O] ≈ O (a0)
V[O] ≈ Hessian, Lagrange
Monte Carlo sampling: Nested Sampling
9 / 18
Its is a relatively recent technique used in astrophysics. See
- arXiv:astro-ph/0508461v2- arXiv:astro-ph/0701867v2- arxiv.org/abs/1703.09701
The basic idea → convert n-dim integral into 1-dim integral:
Z =∫dna L(data|a)π(a) =
∫dXL(X)
X(λ) =∫L(a)>λ
dna π(a)
It is more efficient and accurate than VEGAS at very large dimensions
HERMES multiplicities
10 / 18
Fit the gaussian widths of PDF and FF (π,K) TMDsx and z dependence is assumed to be the same as collineardistributionsThis is a 6–dimensional problem
10−7 10−6 10−5 10−4 10−3
wcut
10−7
10−6
10−5
10−4
10−3
10−2
10−1
100
∑kwkθ(w
cut−wk)
10−16 10−15 10−14 10−13 10−12 10−11 10−10 10−9 10−8
X
10−158
10−157
10−156
10−155
10−154
10−153
10−152
10−151
10−150
L(X
)
400 500 600 700 800 900 1000 1100 1200
iterations
−750
−700
−650
−600
−550
−500
−450
−400
logZ
HERMES multiplicities
11 / 18
Distribution of parameters
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
pdf-widths0 valence
0.0 0.2 0.4 0.6 0.8 1.00.0
0.1
0.2
0.3
pdf-widths0 sea
0.0 0.2 0.4 0.6 0.8 1.00.0
0.1
0.2
0.3
ff-widths0 pi+ fav
0.0 0.2 0.4 0.6 0.8 1.00.0
0.1
0.2
ff-widths0 pi+ unfav
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
ff-widths0 k+ fav
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
ff-widths0 k+ unfav
Data vs. theory
0.2 0.3 0.4 0.5 0.6 0.7
pT
100
101
102
103
M(H
ER
ME
S)×
4i
pi+(1000)pi+(1000)pi+(1000)pi+(1000)pi+(1000)pi+(1000)
Q2=1.80 x=0.10
z=[0.00,0.19]z=[0.20,0.25]z=[0.26,0.29]
z=[0.30,0.35]z=[0.40,0.50]z=[0.50,1.00]
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
pT
10−1
100
101
102
103
pi+(1000)pi+(1000)pi+(1000)pi+(1000)pi+(1000)pi+(1000)
Q2=2.90 x=0.15
z=[0.00,0.19]z=[0.20,0.25]z=[0.26,0.29]
z=[0.30,0.35]z=[0.40,0.50]z=[0.50,1.00]
0.2 0.3 0.4 0.5 0.6 0.7 0.8
pT
10−1
100
101
102
103
pi+(1000)pi+(1000)pi+(1000)pi+(1000)pi+(1000)pi+(1000)
Q2=5.20 x=0.25
z=[0.00,0.19]z=[0.20,0.25]z=[0.26,0.29]
z=[0.30,0.35]z=[0.40,0.50]z=[0.50,1.00]
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
pT
10−1
100
101
102
103
pi+(1000)pi+(1000)pi+(1000)pi+(1000)pi+(1000)pi+(1000)
Q2=9.20 x=0.41
z=[0.00,0.19]z=[0.20,0.25]z=[0.26,0.29]
z=[0.30,0.35]z=[0.40,0.50]z=[0.50,1.00]
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
pT
10−1
100
101
102
M(H
ER
ME
S)×
4i
pi-(1001)pi-(1001)pi-(1001)pi-(1001)pi-(1001)pi-(1001)
Q2=1.80 x=0.10
z=[0.00,0.19]z=[0.20,0.25]z=[0.26,0.29]
z=[0.30,0.35]z=[0.40,0.50]z=[0.50,1.00]
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
pT
10−1
100
101
102
pi-(1001)pi-(1001)pi-(1001)pi-(1001)pi-(1001)pi-(1001)
Q2=2.90 x=0.15
z=[0.00,0.19]z=[0.20,0.25]z=[0.26,0.29]
z=[0.30,0.35]z=[0.40,0.50]z=[0.50,1.00]
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
pT
10−1
100
101
102
pi-(1001)pi-(1001)pi-(1001)pi-(1001)pi-(1001)pi-(1001)
Q2=5.20 x=0.25
z=[0.00,0.19]z=[0.20,0.25]z=[0.26,0.29]
z=[0.30,0.35]z=[0.40,0.50]z=[0.50,1.00]
0.2 0.3 0.4 0.5 0.6 0.7
pT
100
101
102
pi-(1001)pi-(1001)pi-(1001)pi-(1001)pi-(1001)pi-(1001)
Q2=9.20 x=0.41
z=[0.00,0.19]z=[0.20,0.25]z=[0.26,0.29]
z=[0.30,0.35]z=[0.40,0.50]z=[0.50,1.00]
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
pT
10−1
100
101
102M
(HE
RM
ES
)×4i
k+(1002)k+(1002)k+(1002)k+(1002)k+(1002)k+(1002)
Q2=1.80 x=0.10
z=[0.00,0.19]z=[0.20,0.25]z=[0.26,0.29]
z=[0.30,0.35]z=[0.40,0.50]z=[0.50,1.00]
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
pT
10−4
10−3
10−2
10−1
100
101
102
k+(1002)k+(1002)k+(1002)k+(1002)k+(1002)k+(1002)
Q2=2.90 x=0.15
z=[0.00,0.19]z=[0.20,0.25]z=[0.26,0.29]
z=[0.30,0.35]z=[0.40,0.50]z=[0.50,1.00]
0.2 0.3 0.4 0.5 0.6 0.7 0.8
pT
10−1
100
101
102
k+(1002)k+(1002)k+(1002)k+(1002)k+(1002)k+(1002)
Q2=5.20 x=0.25
z=[0.00,0.19]z=[0.20,0.25]z=[0.26,0.29]
z=[0.30,0.35]z=[0.40,0.50]z=[0.50,1.00]
0.2 0.3 0.4 0.5 0.6 0.7 0.8
pT
100
101
102
k+(1002)k+(1002)k+(1002)k+(1002)k+(1002)k+(1002)
Q2=9.20 x=0.41
z=[0.00,0.19]z=[0.20,0.25]z=[0.26,0.29]
z=[0.30,0.35]z=[0.40,0.50]z=[0.50,1.00]
0.2 0.3 0.4 0.5 0.6 0.7 0.8
pT
10−2
10−1
100
101
102
M(H
ER
ME
S)×
4i
k-(1003)k-(1003)k-(1003)k-(1003)k-(1003)k-(1003)
Q2=1.80 x=0.10
z=[0.00,0.19]z=[0.20,0.25]z=[0.26,0.29]
z=[0.30,0.35]z=[0.40,0.50]z=[0.50,1.00]
0.2 0.3 0.4 0.5 0.6 0.7 0.8
pT
10−2
10−1
100
101
k-(1003)k-(1003)k-(1003)k-(1003)k-(1003)k-(1003)
Q2=2.90 x=0.15
z=[0.00,0.19]z=[0.20,0.25]z=[0.26,0.29]
z=[0.30,0.35]z=[0.40,0.50]z=[0.50,1.00]
0.2 0.3 0.4 0.5 0.6 0.7
pT
10−1
100
101
k-(1003)k-(1003)k-(1003)k-(1003)k-(1003)k-(1003)
Q2=5.20 x=0.25
z=[0.00,0.19]z=[0.20,0.25]z=[0.26,0.29]
z=[0.30,0.35]z=[0.40,0.50]z=[0.50,1.00]
0.2 0.3 0.4 0.5 0.6 0.7 0.8
pT
100
101
102
k-(1003)k-(1003)k-(1003)k-(1003)k-(1003)k-(1003)
Q2=9.20 x=0.41
z=[0.00,0.19]z=[0.20,0.25]z=[0.26,0.29]
z=[0.30,0.35]z=[0.40,0.50]z=[0.50,1.00]
Transversity and Collins functions (π)
12 / 18
Fits to transversity and collins (π) distributions.x, z PhT dependence are fittedThis is a 19–dimensional problemNeed to run nested sampling several times to check convergence
10−7 10−6 10−5 10−4 10−3
wcut
10−7
10−6
10−5
10−4
10−3
10−2
10−1
100
∑kwkθ(w
cut−wk)
10−17 10−15 10−13 10−11 10−9 10−7
X
102
104
106
108
1010
1012
L(X
)
200 400 600 800 1000 1200 1400 1600
iterations
−60
−40
−20
0
20
40
logZ
Transversity parameters
13 / 18
0.0 0.5 1.0 1.5 2.00.0
0.1
0.2
0.3
transversity-widths0 valence
0.0 0.5 1.0 1.5 2.00.0
0.1
0.2
transversity-widths0 sea
−10 −5 0 5 100.0
0.2
0.4
transversity-u N
0.0 2.5 5.0 7.5 10.00.0
0.5
1.0
transversity-u a
0 2 4 6 8 100.0
0.1
0.2
0.3
transversity-u b
−20 −10 0 10 200.0
0.1
0.2
0.3
transversity-d N
0 2 40.00
0.25
0.50
0.75
transversity-d a
0 5 10 15 200.0
0.2
0.4transversity-d b
−10 −5 0 5 100.0
0.1
0.2
0.3
transversity-s N
0 2 40.0
0.2
0.4
transversity-s a
0 2 4 6 8 100.0
0.1
0.2
transversity-s b
The distributionsseems to beconvergent
is a run withthe median ZSome outlierswhere present,they gave muchsmaller χ2 →signal ofover-fitting
Collins π parameters
14 / 18
0.0 0.2 0.4 0.6 0.8 1.00.00
0.25
0.50
0.75
collins-widths0 pi+ fav
0.0 0.5 1.0 1.5 2.00.0
0.5
1.0
collins-widths0 pi+ unfav
0 5 10 15 200.0
0.1
0.2
collins-pi+ u N
0 2 40.0
0.2
0.4
collins-pi+ u a
0 2 4 6 8 100.0
0.2
0.4collins-pi+ u b
−20 −15 −10 −5 00.0
0.1
0.2
collins-pi+ d N
0 2 40.0
0.1
0.2
0.3
0.4collins-pi+ d a
0 2 4 6 8 100.0
0.2
0.4
collins-pi+ d b
Similar behavior as in transversity
Data vs. Theory (χ2/Npts = 69/106)
15 / 18
0.1 0.2 x
−0.05
0.00
AC UT
(p,π
)
HERMESHERMES
0.3 0.4 0.5 z−0.050
−0.025
0.000
0.025
0.050
HERMESHERMES
0.2 0.4 0.6 pT−0.04
−0.02
0.00
0.02
HERMESHERMES
0.1 0.2 x
−0.05
0.00
0.05
AC UT
(p,π
)
COMPASSCOMPASS
0.3 0.4 0.5 z
−0.02
0.00
0.02
COMPASSCOMPASS
0.2 0.4 0.6 pT
−0.02
0.00
0.02
COMPASSCOMPASS
0.1 0.2 x−0.050
−0.025
0.000
0.025
0.050
AC UT
(d,π
)
COMPASSCOMPASS
0.3 0.4 0.5 z
−0.02
0.00
0.02
COMPASSCOMPASS
0.2 0.4 0.6 pT
−0.04
−0.02
0.00
0.02
COMPASSCOMPASS
SIDIS (π+) (π−)
Transversity and Collins function
16 / 18
0.0 0.2 0.4 0.6 0.8 x0.0
0.5
1.0hq 1(x
)
u0.0 0.2 0.4 0.6 0.8 x
−2
0
d0.0 0.2 0.4 0.6 0.8 x
−0.2
0.0
0.2
s
0.0 0.2 0.4 0.6 0.8 z0.0
0.5
1.0
1.5
2.0
H⊥π/q
1(x
)
u0.0 0.2 0.4 0.6 0.8 z
−1.00
−0.75
−0.50
−0.25
0.00
d
data coverage
Kaon analysis is in progress. Some tensions with pions needs to beresolvedInclusion of SIA data sets are in progress (E. Moffat, A. Prokudin)The current analysis is been combined with lattice gT , Lin,Melnitchouk, Prokudin, Sato, Shows (in preparation)
Summary
17 / 18
Dedicated numerical framework to study TMDs in SIDIS
To be used as event generator for detector simulations
It uses state-of-the-art Monte Carlo fitting techniques
Current implementation is based on standard gaussian ansatz. It willbe extend to include CSS formalism in future
At present, the simulator is been tunned to describe existing data
A first combined TMD analysis will be presented in upcomingpublication
Next steps
18 / 18
After completion of the tunning, we construct the event-generator(using VEGAS)
Store the samples in JSON format and perform detector studies
Redo the data analysis with simulated SIDIS asymmetries andcompare with input TMDs
Check that the validation loop works