Scalar Dipole Dynamical Polarizabilities from proton Real Compton - - PowerPoint PPT Presentation

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Scalar Dipole Dynamical Polarizabilities from proton Real Compton - - PowerPoint PPT Presentation

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15th International Workshop on Meson Physics Krakv, Poland, June 7 th - 12 th 2018 Scalar Dipole Dynamical Polarizabilities from proton Real Compton Scattering data University of Pavia & INFN, Pavia (Italy) Stefano Sconfjetti 1 / 24

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SLIDE 1

15th International Workshop on Meson Physics Krakóv, Poland, June 7th - 12th 2018

Scalar Dipole Dynamical Polarizabilities from proton Real Compton Scattering data

Stefano Sconfjetti University of Pavia & INFN, Pavia (Italy) 1 / 24

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SLIDE 2

Outline

✔ RCS: theoretical framework ✔ Static polarizabilities ✔ Low Energy expansion ✔ Dynamical polarizabilities

MESON 2018, KRAKÓW 2 / 24

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SLIDE 3

Outline

✔ RCS: theoretical framework ✔ Static polarizabilities ✔ Low Energy expansion ✔ Dynamical polarizabilities ✔ Data set inconsistency ✔ Very high correlations ✔ T

  • o much parameters

✔ New approach: simplex + bootstrap

MESON 2018, KRAKÓW 2 / 24

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SLIDE 4

Outline

✔ RCS: theoretical framework ✔ Static polarizabilities ✔ Low Energy expansion ✔ Dynamical polarizabilities ✔ Data set inconsistency ✔ Very high correlations ✔ T

  • o much parameters

✔ New approach: simplex + bootstrap ✔ Static polarizabilities: cross check ✔ Systematical errors ✔ Dynamical polarizabilities from data ✔ Conclusions and future perspectives

MESON 2018, KRAKÓW 2 / 24

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SLIDE 5

RCS amplitudes and Dispersion Relations

  • D. Drechsel, M. Gorchtein, B. Pasquini, M. Vanderhaeghen, Phys.Rev. C61 (1999) 015204
  • B. Pasquini , D. Drechsel M. Vanderhaeghen, Phys.Rev. C76 (2007) 015203

3 / 24

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SLIDE 6

RCS amplitudes and Dispersion Relations

Subtracted Dispersion Relations (s-channel)

Ai(0,0) = ai Static polarizabilities

  • D. Drechsel, M. Gorchtein, B. Pasquini, M. Vanderhaeghen, Phys.Rev. C61 (1999) 015204
  • B. Pasquini , D. Drechsel M. Vanderhaeghen, Phys.Rev. C76 (2007) 015203

3 / 24

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SLIDE 7

s-CHANNEL t-CHANNEL

RCS amplitudes and Dispersion Relations

Subtracted Dispersion Relations (s-channel)

Ai(0,0) = ai Static polarizabilities

  • D. Drechsel, M. Gorchtein, B. Pasquini, M. Vanderhaeghen, Phys.Rev. C61 (1999) 015204
  • B. Pasquini , D. Drechsel M. Vanderhaeghen, Phys.Rev. C76 (2007) 015203

3 / 24

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SLIDE 8

Powell cross section: point-like nucleon with anomalous magnetic moment Static polarizabilities: response of the internal nucleon degrees of freedom to a static electric and magnetic fjeld

Static polarizabilities

A.I. L'vov, V.A. Petrun'kin, Martin Schumacher. Phys.Rev. C55 (1997) 359-377

  • D. Drechsel, B. Pasquini, M. Vanderhaeghen. Phys.Rept. 378 (2003) 99-205

4 / 24

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SLIDE 9

Powell cross section: point-like nucleon with anomalous magnetic moment Static polarizabilities: response of the internal nucleon degrees of freedom to a static electric and magnetic fjeld spin-independent dipole

Static polarizabilities

A.I. L'vov, V.A. Petrun'kin, Martin Schumacher. Phys.Rev. C55 (1997) 359-377

  • D. Drechsel, B. Pasquini, M. Vanderhaeghen. Phys.Rept. 378 (2003) 99-205

4 / 24

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SLIDE 10

Powell cross section: point-like nucleon with anomalous magnetic moment Static polarizabilities: response of the internal nucleon degrees of freedom to a static electric and magnetic fjeld spin-independent dipole spin-dependent dipole spin-dependent dipole- quadrupole

Static polarizabilities

A.I. L'vov, V.A. Petrun'kin, Martin Schumacher. Phys.Rev. C55 (1997) 359-377

  • D. Drechsel, B. Pasquini, M. Vanderhaeghen. Phys.Rept. 378 (2003) 99-205

4 / 24

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SLIDE 11

Powell cross section: point-like nucleon with anomalous magnetic moment Static polarizabilities: response of the internal nucleon degrees of freedom to a static electric and magnetic fjeld spin-independent dipole spin-dependent dipole spin-dependent dipole- quadrupole

Static polarizabilities

A.I. L'vov, V.A. Petrun'kin, Martin Schumacher. Phys.Rev. C55 (1997) 359-377

  • D. Drechsel, B. Pasquini, M. Vanderhaeghen. Phys.Rept. 378 (2003) 99-205

4 / 24

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SLIDE 12

Low Energy Expansion (LEX) (I)

  • D. Babusci, G. Giordano, A.I. L'vov, G. Matone, A.M. Nathan. Phys.Rev.C58 (1998) 1013-1041

5 / 24

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SLIDE 13

ν and t as independent variables Lorentz invariant amplitudes Need to choose a ref-frame: CM

Ri (Ai)

(ready for multipole expansion)

Low Energy Expansion (LEX) (I)

  • D. Babusci, G. Giordano, A.I. L'vov, G. Matone, A.M. Nathan. Phys.Rev.C58 (1998) 1013-1041

5 / 24

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SLIDE 14

Multipole expansion and DYNAMICAL polarizabilities

  • D. Babusci, G. Giordano, A.I. L'vov, G. Matone, A.M. Nathan.Phys.Rev. C58 (1998) 1013-1041
  • V. Lensky, J. McGovern, and V. Pascalutsa, Eur. Phys. J. C75, 604 (2015)

6 / 24

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SLIDE 15

DYNAMICAL POLARIZABILITIES

Multipole expansion and DYNAMICAL polarizabilities

  • D. Babusci, G. Giordano, A.I. L'vov, G. Matone, A.M. Nathan.Phys.Rev. C58 (1998) 1013-1041
  • V. Lensky, J. McGovern, and V. Pascalutsa, Eur. Phys. J. C75, 604 (2015)

6 / 24

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SLIDE 16

DYNAMICAL POLARIZABILITIES DIPOLE DYNAMICAL POLARIZABILITIES (DDPs) αE1(ω) βM1(ω)

Multipole expansion and DYNAMICAL polarizabilities

  • D. Babusci, G. Giordano, A.I. L'vov, G. Matone, A.M. Nathan.Phys.Rev. C58 (1998) 1013-1041
  • V. Lensky, J. McGovern, and V. Pascalutsa, Eur. Phys. J. C75, 604 (2015)

6 / 24

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SLIDE 17

DDPs: physical meaning

F . Hagelstein, R. Miskimen, V. Pascalutsa. Prog.Part.Nucl.Phys. 88 (2016) 29-97

7 / 24

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SLIDE 18

DDPs: physical meaning

F . Hagelstein, R. Miskimen, V. Pascalutsa. Prog.Part.Nucl.Phys. 88 (2016) 29-97

Pion cusp Delta resonance

DDPs: response of the internal nucleon degrees of freedom to an electric and magnetic fjeld with and explicit dependence on energy

7 / 24

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SLIDE 19

αE1(ω) = αE10 + αE11 ω + αE12 ω2 + αE13 ω3 + αE14 ω4 + αE15 ω5 βM1(ω) = βM10 + βM11 ω + βM12 ω2 + βM13 ω3 + βM14 ω4 + βM15 ω5

Low Energy Expansion (LEX) (II)

8 / 24

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SLIDE 20

αE1(ω) = αE10 + αE11 ω + αE12 ω2 + αE13 ω3 + αE14 ω4 + αE15 ω5 βM1(ω) = βM10 + βM11 ω + βM12 ω2 + βM13 ω3 + βM14 ω4 + βM15 ω5

αE1 (10-4 fm3) βM1 (10-4 fm3) ωcm (MeV) 130

Low Energy Expansion (LEX) (II)

ωcm (MeV) 130

LEX + fjt to DRs Full DRs calculation

8 / 24

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SLIDE 21

LEX + multipoles DRS calculation

LEX: up to ω5 multipoles: up to l=3

= 1 1 2 ° θ

DRs vs (LEX + multipoles)

9 / 24

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SLIDE 22

Extract scalar Dipole Dynamical Polarizabilites (DDPs) from RCS data

The GOAL

  • B. Pasquini, P

. Pedroni, S. S., arXiv:1711.07401v1

10 / 24

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SLIDE 23

Gradient method to fjnd the χ2 minimum VERY high correlations between parameters!

Complications

11 / 24

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MINUIT WARNING IN HESSE ============== MATRIX FORCED POS-DEF BY ADDING 0.13727E-01 TO DIAGONAL. Gradient method to fjnd the χ2 minimum VERY high correlations between parameters!

Complications

11 / 24

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SLIDE 25

MINUIT WARNING IN HESSE ============== MATRIX FORCED POS-DEF BY ADDING 0.13727E-01 TO DIAGONAL. Gradient method to fjnd the χ2 minimum VERY high correlations between parameters! VERY low sensitivity of the data to dynamical polarizabilities NO WAY to fjnd the “right” minimum and to defjne “right” errors on fjt parameters

Complications

11 / 24

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SLIDE 26

MINUIT WARNING IN HESSE ============== MATRIX FORCED POS-DEF BY ADDING 0.13727E-01 TO DIAGONAL. Gradient method to fjnd the χ2 minimum VERY high correlations between parameters! VERY low sensitivity of the data to dynamical polarizabilities NO WAY to fjnd the “right” minimum and to defjne “right” errors on fjt parameters Combination of SIMPLEX method and BOOTSTRAP technique

Complications

11 / 24

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SLIDE 27

Half of the Spartans that King Leonidas led to the Battle of Thermopylae...

The DATA set

12 / 24

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= 4 5 ° θ = 6 ° θ = 8 5 ° θ = 1 1 2 ° θ = 1 3 5 ° θ = 1 5 5 ° θ

Half of the Spartans that King Leonidas led to the Battle of Thermopylae...

The DATA set

12 / 24

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SLIDE 29

= 1 1 2 ° θ

FIRST cross check: comparison with LEX + multipoles and DRs

DRs vs (LEX + multipoles)

13 / 24

  • B. Pasquini, P

. Pedroni, S. S., arXiv:1711.07401v1

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SLIDE 30

αE1 (10-4 fm3) βM1 (10-4 fm3) DRs 11.9 ± 0.2 1.9 ± 0.2 LEX + MUL TIPOLES 11.8 ± 0.2 2.0 ± 0.2

= 1 1 2 ° θ

FIRST cross check: comparison with LEX + multipoles and DRs

DRs vs (LEX + multipoles)

13 / 24

  • B. Pasquini, P

. Pedroni, S. S., arXiv:1711.07401v1

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SLIDE 31

Si,exp

boot =Si,exp±γ σi,exp

Gaussian distributed

Bootstrap sampling and systematics

14 / 24

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SLIDE 32

Si,exp

boot =Si,exp±γ σi,exp

Gaussian distributed How can we include systematical errors? ...one normalization factor per data set is needed!

Bootstrap sampling and systematics

14 / 24

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SLIDE 33

Si,exp

boot =ξi [Si,exp±γ σi,exp]

Si,exp

boot =Si,exp±γ σi,exp

Gaussian distributed How can we include systematical errors? ...one normalization factor per data set is needed! At every bootstrap cycle the systematical errors for each set can vary independently!

Bootstrap sampling and systematics

14 / 24

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SLIDE 34

αE1 βM1

BOOTSTRAP

11.8 ± 0.2 2.0 ± 0.2

LEX + MUL TIPOLES

11.8 ± 0.2 2.0 ± 0.2

BOOTSTRAP SYS ON

11.8 ± 0.3 2.0 ± 0.3 Systematical errors enlarge the error band of polarizabilities!

Bootstrap vs Gradient: systematics ON

15 / 24

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SLIDE 35

“χ2” probability distribution in bootstrap framework (static pol.)

S y s t e ma t i c s O N S y s t e ma t i c s O F F

Work in collaboration with B.Pasquini, P . Pedroni, A. Rotondi (paper in preparation)

Not even more a “true”

χ2 distribution

(due to point correlations given by systematics)

16 / 24

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SLIDE 36

Expected Gaussian shape + systematics enlarging

The efgect of systematics (static spin- independent polarizabilities)

S y s t e ma t i c s O F F S y s t e ma t i c s O N

  • B. Pasquini, P

. Pedroni, S. S., in preparation

17 / 24

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SLIDE 37

Fit conditions

  • A. M. Baldin, Nucl. Phys. 18, 310 (1960)
  • V. Olmos de León, Eur. Phys. J. A 10, 207–215 (2001)

18 / 24

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Baldin’s sum rule Systematical errors ON FULL data set (150 data) TAPS data set (55 data)

Fit conditions

Errors on Baldin’s sum rule and γπ included in the procedure

  • A. M. Baldin, Nucl. Phys. 18, 310 (1960)
  • V. Olmos de León, Eur. Phys. J. A 10, 207–215 (2001)

18 / 24

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SLIDE 39

DRs calculation From FIT 95 % CL band 68% CL band FULL FULL TAPS TAPS

DDPs from the fjt (II)

  • B. Pasquini, P

. Pedroni, S. S., arXiv:1711.07401v1

19 / 24

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SLIDE 40

DDPs from the fjt: probability distributions

  • B. Pasquini, P

. Pedroni, S. S., arXiv:1711.07401v1

FULL data set TAPS data set

Probability distributions given by our technique (not a priori assumed)

20 / 24

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SLIDE 41

Global results: numerical values

  • B. Pasquini, P

. Pedroni, S. S., arXiv:1711.07401v1

21 / 24

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SLIDE 42

Very STRONG dependence on data set (maybe due to difgerent angular regions...) Very HIGH correlations among parameters

Global results: numerical values

  • B. Pasquini, P

. Pedroni, S. S., arXiv:1711.07401v1

21 / 24

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SLIDE 43
  • C. Patrignani et al. (Particle Data Group), Chin. Phys. C, 40, 100001 (2016) and 2017 update
  • V. Lensky, J. McGovern, and V. Pascalutsa, Eur. Phys. J. C75, 604 (2015)

Global results: αE1 and βM1

ChPT PDG TAPS set FULL set 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 - 1 1 2 3 4 5 6

αE

1

βM

1

(10-4 fm3) αE1 βM1

22 / 24

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SLIDE 44
  • C. Patrignani et al. (Particle Data Group), Chin. Phys. C, 40, 100001 (2016) and 2017 update
  • V. Lensky, J. McGovern, and V. Pascalutsa, Eur. Phys. J. C75, 604 (2015)

Global results: αE1 and βM1

ChPT PDG TAPS set FULL set 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 - 1 1 2 3 4 5 6

αE

1

βM

1

(10-4 fm3) αE1 βM1

DYNAMICAL STATIC FITTED 22 / 24

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SLIDE 45
  • B. R. Holstein, D. Drechsel, B. Pasquini, M. Vanderhaeghen. Phys.Rev. C61 (2000) 034316
  • B. Pasquini, D. Drechsel, M. Vanderhaeghen. Phys.Rev. C76 (2007) 015203
  • V. Lensky, J. McGovern, and V. Pascalutsa, Eur. Phys. J. C75, 604 (2015)

ChPT DRs(II) DRs TAPS set FULL set

  • 1

1 - 9 - 7 - 5 - 3

  • 1

1 3

αE

1 ν

βM

1 ν

2 4 6 8 1 1 2 1 4

Global results: αE1,ν and βM1,ν

(10-4 fm5) αE1,ν βM1,ν

23 / 24

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SLIDE 46
  • B. R. Holstein, D. Drechsel, B. Pasquini, M. Vanderhaeghen. Phys.Rev. C61 (2000) 034316
  • B. Pasquini, D. Drechsel, M. Vanderhaeghen. Phys.Rev. C76 (2007) 015203
  • V. Lensky, J. McGovern, and V. Pascalutsa, Eur. Phys. J. C75, 604 (2015)

ChPT DRs(II) DRs TAPS set FULL set

  • 1

1 - 9 - 7 - 5 - 3

  • 1

1 3

αE

1 ν

βM

1 ν

2 4 6 8 1 1 2 1 4

Global results: αE1,ν and βM1,ν

(10-4 fm5) αE1,ν βM1,ν

DYNAMICAL STATIC FITTED THEORY 23 / 24

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SLIDE 47

Conclusions & perspectives

Very useful and versatile technique for data analysis Efgect of systematic sources of uncertainties on the fjtted parameters Waiting for new data in order to reduce the uncertainties of the fjtted parameters (MAMI)

  • E. J. Downie et al., Proposal MAMI-A2/04-16 (2016)

24 / 24

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SLIDE 48

Conclusions & perspectives

Very useful and versatile technique for data analysis Fit of polarized observables in RCS with the same technique Efgect of systematic sources of uncertainties on the fjtted parameters Waiting for new data in order to reduce the uncertainties of the fjtted parameters (MAMI) DDPs without LEX (double subtraction in DRs)

  • E. J. Downie et al., Proposal MAMI-A2/04-16 (2016)

24 / 24

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SLIDE 49

BACKUP SLIDES

Some comments on the data set Difgerential cross section TAPS vs FULL data set LEX is very slow…

χ2 curvature close to its

minimum

Outliers identifjcations: rescaling of the errors

I / VII

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SLIDE 50

Some comments on the data set

Strong correlation between parameters Reduction of parameters number thanks to sum rules Identifjcations of the outliers (rescaling for statistic errors?) The χ2 is not the only quality indicator → no “defjnition” of data set Waiting for new data (MAMI)

  • E. J. Downie et al., Proposal MAMI-A2/04-16 (2016)

II / VII

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SLIDE 51

dσ/dΩ VS lab energy 100% error band from the bootstrap fjt

= 8 5 ° θ = 1 3 5 ° θ

Difgerential cross section

III / VII

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SLIDE 52

VERY small difgerence both in calculation and in error band

= 8 5 ° θ TAPS FULL TAPS 100% error band FULL 100% error band

TAPS vs FULL data set

IV / VII

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SLIDE 53

LEX is very slow ...

ωcm (MeV) 130 ωcm (MeV) 130 αE1 (10-4 fm3)

LEX (ω5 ) DR calculation

V / VII

βM1 (10-4 fm3)

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SLIDE 54

χ2 curvature close to its minimum

1 1 . 5 2 2 . 5 3 3 . 5 4 7 8 9 1 1 1 1 2 1 3 1 4 1 5 χ2 αE

1

( 1

  • 4

f m

3

) F U L L O P T I M T A P S

  • H. W. Grießhammer, J. A. McGovern, D. R. Phillips, and G. Feldman,Prog. Part. Nucl. Phys.

67, 841 (2012).

VI / VII

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SLIDE 55

Outliers identifjcation: rescaling of the errors

  • O. Behnke, K. Kröninger, G. Schott and T. Schörner-Sadenius, Data Analysis in High Energy

Physics: A Practical Guide to Statistical Methods, Wiley-VCH, 2013

Outliers → rescaling of all the statistic uncertainties by a factor

√χ

2

Efgect: enlarging of errors on fjtted parameters (~20%) NOT scaled Scaled

α+β

α−β

χ2≈1.00 χ

2≈1.40

VII / VII