Sitting in the Interphase: Connecting Experiment and

Theory in Nuclear and Hadronic Physics

César Fernández-RamírezNuclear Physics Group, Universidad Complutense de Madrid

Indiana-JLab Interview, 11th January 2013

Biographical Presentation

Biography (I)

• Born in Madrid, Spain on March 13, 1978• 1996-2001 ‘Licenciado’ (5yr) in Physics (Theoretical)

Universidad Complutense de Madrid (UCM)• 2001-2003 MSc in Atomic and Nuclear Physics

UCM• 2003 Fellow of the Marie Curie Training program on Nuclear

Structure at ECT* (Trento)• 2002-2006 PhD

Structure of Matter Institute (Spanish Council for Scientific Research)defended at UCMTitle: Electormagnetic Production of Light MesonsSupervisors: Prof. E. Moya de Guerra and Prof. J.M. Udías

Biography (II)

• 2007 Researcher associated to a projectNuclear Physics Group, UCMElectron scattering and kinematics calculations for planned experiments at FAIR/GSI (ELISe and EXL collaborations) with Prof. J.M. Udías

• 2007-2009 Spanish Ministry of Science and Technology Postdoctoral FellowCTP and LNS, MITwith Prof. T.W. Donnelly and Prof. A.M. Bernstein working onnear-threshold pion photoproduction and HBChPT

• 2009-2011 Postdoc Research AssociateECT* (Director: Prof. Achim Richter)Independent researcher, pion photoproduction and hadron spectroscopy

• 2011-? Spanish Government “Juan de la Cierva” Research FellowNuclear Physics Group, UCMIndependent researcher, pion photoproduction and hadron spectroscopy

Teaching Experience

• UCM, Master Erasmus Mundus in Nuclear Fusion Science and Engineering Physics: Computational Physics: 10/11, 11/12, & 12/13

• UCM, Degree in Physics: Physics Lab: 10/11, 11/12Nuclear and Particle Physics: 04/05

• UCM, Degree in Chemistry:General Physics: 12/13

• UCM, One Master thesis supervised within the Inter-University Nuclear Physics Master Program. Chaos in Hadrons 11/12

Research

Research

• Pion photoproduction from the Nucleon in the Resonance Region

• Pion Production from Nuclei

• Near-Threshold Pion Photoproduction

• Quantum Chaos in Hadrons

• Experimental Physics

0

5

10

15

20

Re[

E 0+p ]

(m

F)

-40-30-20-10

010203040

R

e[M

1+3/2 ]

(mF)

-2

0

2

4

6

8

0.0 0.2 0.4 0.6 0.8 1.0

Im[E

0+p ] (

mF)

E (GeV)

0

10

20

30

40

50

0.0 0.2 0.4 0.6 0.8 1.0

Im[M

1+3/2 ]

(mF)

E (GeV)

Pion Photoproduction from the Nucleon in the Resonance Region

Pion Photoproduction Model in the Resonance Region

• PhD thesis• Up to 1.8 GeV of invariant mass• Effective Lagrangian Approach• 8 Resonances, Spin 1/2 and 3/2• Consistent Spin-3/2 treatment• Crossing symmetric• Straightforward extension to nuclei• Full model published in Ann. Phys. (N.Y.) 321

(2006) 1408-1456

20

15

10

5

0

E 0+p (

mF)

Real partImaginary part

4

2

0

-2

M1-p (

mF)

60

40

20

0

-20

M1+3/

2 (m

F)

4

2

0

-2

-4

1.21.00.80.60.40.2

E 1+3/2 (

mF)

E (GeV)

Pion Photoproduction from the Nucleon

Examples of the isospin-3/2 and Isospin-1/2 proton channels

Highlights

• Development of Lagrangians for D33, D13 and P13 resonances[Ann. Phys. (NY) 321 (2006) 1408]

• Study of the Δ(1232) electromagnetic deformation within a consistent spin-3/2 framework [Phys. Rev. C 73 (2006) 042201(R), Eur. Phys. J. A 31 (2007) 572]

• Impact of crossing symmetry in phenomenological models [Phys. Lett. B 660 (2008) 188]

• Reliability of resonance inclusion and parameter assessment employing novel fitting techniques (genetic algorithms) [Phys. Rev. C 77 (2008) 065212]

• Testing SU(3) chiral symmetry through pseudovector-pseudoscalar mixing in eta photoproduction [Phys. Lett. B 651 (2007) 369]

Ejected pion

Electromagnetic probe

Nucleus

Nucleons

Pion Production from Nuclei

16O(γ,π-p) Reaction in the Δ region: Previous Analysis

• Pion photoproduction model SAID: Factorization

• Nuclear model: Harmonic oscillator

• Conclusion: Medium modifications

1.0

0.6

0.2

-0.2

-0.6

-1.0

=36o

=44o

=52o

1.0

0.6

0.2

-0.2

-0.6

-1.0

=60o

=68o

=76o

1.0

0.6

0.2

-0.2

-0.6

-1.0

=84o

=92o

=100o

1.0

0.6

0.2

-0.2

-0.6

-1.0

=108o

=116o

9075604530

p (deg)

=124o

1.0

0.6

0.2

-0.2

-0.6

-1.09075604530

p (deg)

=132o

9075604530

p (deg)

=140o

16O(γ,π-p) Reaction in the Δ region: Improved Analysis

• Pion photoproduction model: Effective Lagrangian ⇒ No Factorization and consistent Δ

• Nuclear model: Relativistic Mean Field

• Conclusion: No medium modifications needed for this observable

[Phys. Lett. B 664 (2008) 57]

Currently working on Reaction Model for Primakoff Effect

• 208Pb(γ,π0) and 12C(γ,π0)• “High-energy” pion photoproduction• Forward angle• Full pion rescattering• Lagrangian approach• No factorization• Nuclear transitions (arbitrary nuclear model)

Why?

• Pion lifetime

• Chiral symmetry breaking

• Very important to count with a reliable and accurate reaction model

• Once the model is built, adapt to other processes is straightforward

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5 3 3.5 4

d/d

(!b/

rad)

(deg)

E =5.2 GeV, 12C, elastic

I. Sick1s1/21p3/2

1s1/2+1p3/2

Why Nuclear Physics Matters

• Although the photon energy is high...• ...the momentum exchange is low• And nuclear effects show up through:

• Ground state (elastic channel)• Excited states (inelastic channels)

-20

-10

0

10

20

30

4 5 6 7 8 9

a - (G

eV-4

)

a+ (GeV-4)

Bernard et al.

xSP

SPD70%

90%

Near-Threshold Pion Photoproduction

Why Near-Threshold Pion Photoproduction?

• Chiral Symmetry in the Baryon sector• Unitarity (testing against Compton and

Pion-Nucleon Scattering)• Chiral Perturbation Theory• Important research programs at MAMI

and JLab (electroproduction)

partial waves

• In most of hadronic processes• First S wave contributes• Then P waves and the rest of partial waves add

up orderly• Neutral pion photoproduction

• S wave is very weak• P waves are strong due to Δ(1232) appearance• D waves contribute due to the weakness of the

S wave

D waves Impact in CHPT

• No impact in P waves extraction

• Up to a 20% impact at the cusp in the S wave extraction

• Besides, the S wave is the most interesting partial wave regarding chiral symmetry breaking

D waves Impact in CHPT

• No impact in P waves extraction

• Up to a 20% impact at the cusp in the S wave extraction

• Besides, the S wave is the most interesting partial wave regarding chiral symmetry breaking

-20

-10

0

10

20

30

4 5 6 7 8 9a -

(GeV

-4)

a+ (GeV-4)

Bernard et al.

xSP

SPD70%

90%

D waves Impact in CHPT

• No impact in P waves extraction

• Up to a 20% impact at the cusp in the S wave extraction

• Besides, the S wave is the most interesting partial wave regarding chiral symmetry breaking

-1.1

-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

0.14 0.145 0.15 0.155 0.16 0.165 0.17

Re

E 0+

(10-3

/M+ )

E (GeV)

0

5

10

15

20

25

30

35

40

45

0.145 0.15 0.155 0.16 0.165

102 |

1- S

PD/S

P | (

%)

E (GeV)

D waves Impact in CHPT

• No impact in P waves extraction

• Up to a 20% impact at the cusp in the S wave extraction

• Besides, the S wave is the most interesting partial wave regarding chiral symmetry breaking

Full analysis

• We provided a full analysis of the observables structure in the near-threshold region and the impact of D waves within different theoretical approaches

• We studied what could be measured and suggested new observables to measure

[Phys. Rev. C 80 (2009) 065201]

• We also proved that you could ignore partial waves higher than D

Working with the A2 Collaboration at Mainz

• Energy dependence of the photon asymmetry in the near-threshold region was measured for the first time, providing an unprecedented insight on chiral symmetry

• Dr. L. Tiator and I made the energy-independent PWA

• I made the energy-dependent PWA employing empirical approach and HBChPT

Observable expansion

σT (W, θ) ≡ qπkγ

WT (W, θ)

Σ (W, θ) ≡ − WS (W, θ)

WT (W, θ)

WT (W, θ) ≡ T0 (W ) + T1 (W )P1 (θ) + T2 (W )P2 (θ) + T3 (W )P3 (θ) + T4 (W )P4 (θ)

WS (W, θ) ≡ [S0 (W ) + S1 (W )P1 (θ) + S2 (W )P2 (θ) ] sin2 θ

0

10

20

30

40

50

60

70

80

90

150 160 170 180 190

T 0 (1

0-6/M

2 + )

E (MeV)

(a)

-22

-18

-14

-10

-6

-2

T 1 (1

0-6/M

2 + )

(b)

-20

-16

-12

-8

-4

0

S 0 (1

0-6/M

2 + )

(d)

-24

-20

-16

-12

-8

-4

0

150 160 170 180 190

T 2 (1

0-6/M

2 + )

E (MeV)

(c)

-6

-4

-2

0

2

4

150 160 170 180 190

S 1 (1

0-6/M

2 + )

E (MeV)

(e)

Extracting t0, t1, t2, s0, s1

Restricts us to 4 single-energy partial wavesRe E0+, Re E1+, Re M1+, Re M1-

(Re E0+, Re P1, Re P2, Re P3)

Multipole Description

• EmpiricalF-R, Bernstein, Donnelly, PRC80, 065201 (2012)

• HBChPTBernard, Kaiser, Meiβner, Z. Phys. C70, 483 (1996); EPJA11, 209 (2001)

• Unitary HBChPTF-R, Bernstein, submitted, arXiv:1212.3237 [nucl-th]

• BChPTHilt, Scherer, Tiator, to be submitted (2013)

1

1.5

2

2.5

3

3.5

4

155 160 165 170 175 180 185 190 195Emax (MeV)

2/dof

EmpiricalHBChPT

U-HBChPTBChPT

100127

154181

208237

266297

328359

390421

452483

514

Amount of experimental data

Fits

-1.4

-1

-0.6

-0.2

Re

E 0+

(10-3

/m+ )

(a)

9

9.5

10

10.5

11

Re

P 1/q

(10-3

/m2 + )

(b)

-13

-12

-11

-10

Re

P 2/q

(10-3

/m2 + )

(c)

9

11

13

15

140 150 160 170 180 190

Re

P 3/q

(10-3

/m2 + )

E (MeV)

(d)

Results

• Successfully extracted S an P waves

• Chiral Perturbation Theory without Δ works up to 170 MeV (Both Relativistic and Heavy Baryon)

• While empirical fits work up to 185 MeV

Ongoing research

• New MAMI data on pion photoproduction data in the delta region

• New MAMI data for the F and T asymmetries both in the near-threshold and delta regions

• Involved in both PWA

0 0.5 1 1.5 2 2.5 3 3.5 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

s

P(s)

Data

D Wigner

D Poisson

D Berry Robnik

Quantum Chaos in Hadrons

Quantum Chaos in Hadrons

• In 2003 V. Pascalutsa studied the experimental hadron spectrum and found traces of chaotic behavior

• Started this research line in 2006 by combining hadronic physics with spectral-statistics analyses inherited from Quantum Chaos

• Very low statistics, so new techniques had to be developed (distorted distributions)

• 1st publication PRL 98, 062001 (2007)

to the absence of some baryons which are not observed butare predicted by quark models, and if we assume thatmissing resonances are randomly distributed [18], the ex-perimental spectrum should be less correlated than thetheoretical ones.

Prior to any statistical analysis we have to accomplishtwo preliminary tasks. First of all, it is necessary to identifythe different symmetries involved in the spectra. If a se-quence of levels involves more than one symmetry, itsspectral statistics are deflected towards a Poisson distribu-tion (see [13,20] for generic reviews and [19] for a recentwork where the effects of both mixing symmetries andmissing levels in the same sequence are surveyed). Hence,it is necessary to extract from the full spectrum sequencesof levels involving the same symmetries (quantum num-bers) to proceed with the spectral analysis.

In the spectra considered in this Letter, we can identifythe following symmetries associated to the baryons: spin,isospin, parity, and strangeness. Strangeness can bedropped due to the assumption of flavor SU!3" invariance.Therefore, for every statistical analysis, we split all thespectra in sequences where all the levels present the samevalues of spin, isospin, and parity. For reasons stated belowwe only account for sequences with three or more levels.

The second preliminary task is the unfolding procedure.In any energy-level spectrum, we can split the level density!!E" into a smooth part !!!E" and a fluctuating part ~!!E",with !!E" # !!!E" $ ~!!E". The unfolding procedure al-lows one to extract the fluctuating part from the leveldensity, removing the smooth component of the spectrum.There are several ways to unfold a spectrum and we choosethe simplest one. First, we compute the distance betweentwo consecutive levels, Si # Ei$1 % Ei, and then we re-scale Si using its average value si # Si=hSi [21]. Theresulting quantities are called nearest neighbor spacings(NNS). This procedure undergoes some problems, espe-cially in the long-range correlation analysis [22], but it issuitable for the kind of analysis of our concern in thisLetter.

From the NNS we obtain one of the most relevantquantities in spectral statistical analysis: the nearest neigh-bor spacing distribution (NNSD). The NNSD follows thePoisson distribution P!s" # exp!%s" if the spectrum isintegrable (noncorrelated) [14], but it follows the Wignersurmise P!s" # "s

2 exp!% "s24 ", which stems from RMT, for

a chaotic (correlated) spectrum [15]. For our purpose here,it is enough to consider that the less (more) correlated thesequence of levels is, the closer to the Poisson (Wigner)distribution the NNSD is.

In order to obtain a significative result we have calcu-lated the NNSD, P!s", for each one of the four differentspectra we survey: EXP, CI, L1, and L2. We account for allthe sequences fsigX, where X stands for the quantum num-bers which identify each sequence [23]. Set EXP has 70energy levels distributed in 15 sequences; set CI, 145 levels

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5 3 3.5 4

P(s)

s

-4

-2

0

0 0.5 1 1.5 2

Log 10

F(x

)

x

(a) Experimental values from PDG (set EXP).

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5 3 3.5 4

P(s)

s

-6

-4

-2

0

0 1 2

Log 10

F(x

)

x

(b) Model by Capstick and Isgur (set CI).

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5 3 3.5 4

P(s)

s

-6

-4

-2

0

0 1 2

Log 10

F(x

)

x

¨Model by Loring(c) et al. (set L1).

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5 3 3.5 4

P(s)

s

-6

-4

-2

0

0 1 2

Log 10

F(x

)

x

(d) (set L2).Model by Loring et al.¨

FIG. 1. NNSD for the experimental spectrum provided by thePDG data, the model by Capstick and Isgur, and two parame-trizations of the model by Loring et al. The histogram representsthe spacings; the solid line, the Wigner surmise; and the dashedline, the Poisson distribution. The inset shows the function F!x"in logarithmic scale.

PRL 98, 062001 (2007) P H Y S I C A L R E V I E W L E T T E R S week ending9 FEBRUARY 2007

062001-2

First Results

• Baryon spectrum is Wigner-like

• Constituent quark models for baryons are Poisson-like

• CQMs for baryons are incompatible with experiment

Ongoing Research

• We have improved the statistical techniques

• Now, we have very robust techniques• Expanded the analysis to the meson

sector (which is also Wigner-like)[Phys. Lett. B 710 (2012) 139]

• Long paper on the hadron spectrum and the techniques is in the works

0 1 2 3 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

s

P(s)

0 1 2 3 4s

Mesons

• Experimental spectrum is closer to a Wigner distribution

• Quark model by Vijande et al. is the only one that is close to experiment

• Lattice is closer to a Poisson distribution

0 0.5 1 1.5 2 2.5 3 3.5 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

s

P(s)

What for?

• Agreement between theory and experiment• Problem of missing states

• Insight on the properties of the strong interaction in the low-energy regime

• Help to guide effective interactions• Collaborating with quark-model researchers in order to

assess which interactions rise right properties• Vijande et al. 2005 →Poisson

2011→ (almost) Wigner

• The difference is the confinement interaction

Experimental Physics

Physics at FAIR/GSI

• Member of the ELISe and EXL collaborations• Listed in the EXL technical report [M.

Chartier et al. (2005)]• For the ELISe collaboration, co-author in the

conceptual design study: [Nucl. Inst. Meth. A 637 (2011) 60]

• So far, provided kinematical analysis input for the experiments

Physics at JLab

• Member of the Hall A collaboration since 2005

• Involved in theoretical support to experiments and in actual experiments

[Phys. Rev. Lett. 105 (2010) 262302]

• E02-013, Neutron form factor measurement

• E04-007, π0 electroproduction as a test of chiral symmetry

• E05-110, Coulomb Sum Rule

• E06-007, Impulse approximation in Lead

And That’s It, so Far

César Fernández-RamírezNuclear Physics Group, Universidad Complutense de Madrid

Indiana-JLab Interview, 11th January 2013

Backup

1.025

1.020

1.015

1.010

1.005

1.000-0.118-0.119-0.120-0.121

2 /2 m

in

A1/2 (GeV-1/2)1.025

1.020

1.015

1.010

1.005

1.000-0.22-0.23-0.24

2 /2 m

in

A3/2 (GeV-1/2)

-0.118

-0.119

-0.120

-0.121-0.220-0.225-0.23-0.235-0.240

A 1/2 (

GeV

-1/2

)A3/2 (GeV-1/2)

(1232)

Assessing the Δ(1232) parameters with a genetic algorithm

multipoles

Tn (s) =�

ij

Re{M∗i (s) T ij

n Mj (s) }

Sn (s) =�

ij

Re{M∗i (s) Sij

n Mj (s) }

Mj (s) = E0+, E1+, E2+, E2−,M1+,M1−,M2+,M2−.

multipole structure

T0 =S × S + P × P +D ×D + F × F + . . .

T1 =S × P + P ×D +D × F + F ×G+ . . .

T2 =S ×D + P × P +D ×D + P × F + . . .

T3 =P ×D + . . .

T4 =D ×D + . . .S0 =P × P + S ×D + . . .

S1 =P ×D + . . .

S2 =D ×D + . . .

Example: t1

T1 E∗0+ E∗

1+ E∗2+ E∗

2− M∗1+ M∗

1− M∗2+ M∗

2−E0+ 3 1 −1E1+ 3 72/5 −3/5 9/5 −9/5E2+ 72/5E2− −3/5 1 −1M1+ 1 1 27/5 3/5M1− −1 −1 3M2+ 9/5 27/5M2− −9/5 3/5 3

-1.4

-1

-0.6

-0.2

Re

E 0+

(10-3

/m+ )

(a)

9

9.5

10

10.5

11

Re

P 1/q

(10-3

/m2 + )

(b)

-13

-12

-11

-10

Re

P 2/q

(10-3

/m2 + )

(c)

9

11

13

15

140 150 160 170 180 190

Re

P 3/q

(10-3

/m2 + )

E (MeV)

(d)

Single-Energy Multipoles

• Single-energy extraction

• “Almost” model independent

• Im E0+ fixed through unitarity (next slides)

• Im Pi = 0

• D waves = Born Terms

E0+ =eiδ0 [A0 + iβq+/mπ+ ] ; W > Wthr(π+n)

E0+ =eiδ0 [A0 − β |q+| /mπ+ ] ; W < Wthr(π+n)

Unitary Cusp

β = E0+(γp → π+n)× a(π+n → π0p)

ReE0+(γp → π+n) = (28.06± 0.27± 0.45)× 10−3/mπ+

a(π−p → π0n) = −(0.122± 0.002)/mπ+

a(π+n → π0p) = −a(π−p → π0n)

a(π+p → π0p) = −(0.1195± 0.0016)/mπ+

0

0.5

1

1.5

2

2.5

3

145 155 165 175 185 E (MeV)

Im E0+ (10-3/M +)

HBCHPTBCHPT

UNITARY

Unitarity

BChPT: Hilt, Scherer, Tiator, private communication

β = (3.44± 0.08)× 10−3/mπ+ Unitary IS

β = (3.35± 0.08)× 10−3/mπ+ Unitary ISB

β = 2.72× 10−3/mπ+ HBChPT

β = 3.10× 10−3/mπ+ BChPT

Im E0+ (W ) = βqπ+ (W )

mπ+

empirical Fit

E0+ = E(0)0+ + E(1)

0+

ω −mπ0

mπ+

+ iβqπ+

mπ+

Pi/q =P (0)i

mπ+

+ P (1)i

ω −mπ0

m2π+

; i = 1, 2, 3

• Taylor expansion in the partial waves + S wave cusp

• Unitarity is respected in the S wave• 8 parameters (2 per partial wave)• P waves are real• D waves: Born terms

empirical Fit

E0+ = E(0)0+ + E(1)

0+

ω −mπ0

mπ+

+ iβqπ+

mπ+

• Chiral symmetry is not incorporated in this approach

• v.g. exact chiral symmetry in the S wave

E(0)0+ = β

qthrπ+

mπ+

LECs (HBChPT)

6.8

7

7.2

7.4

7.6

7.8

8

155 160 165 170 175 180

a + (G

eV-4

)

Emax (MeV)

(a)

5

10

15

20

25

30

155 160 165 170 175 180

a - (G

eV-4

)

Emax (MeV)

(b)

33

34

35

36

37

38

155 160 165 170 175 180

1 (a

dim

ensi

onal

)

Emax (MeV)

(c)

-36

-35

-34

-33

-32

155 160 165 170 175 180

2 (a

dim

ensi

onal

)

Emax (MeV)

(d)

20.4

20.6

20.8

21

155 160 165 170 175 180b p

(GeV

-3)

Emax (MeV)

(e)