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