Investigating the low-energy structure of the nucleon with … · 2014. 1. 13. · J. M. Alarcón (JGU Mainz) •In 2012 I defended my thesis, entitled “Baryon Chiral Perturbation

Investigating the low-energy structure !of the nucleon with relativistic !

chiral effective field theory !

Jose Manuel AlarcónCluster of Excellence PRISMA, Institut für Kernphysik

Johannes Gutenberg Universität, Mainz

Biographical presentation

J. M. Alarcón (JGU Mainz)


•Born in 1983 in Cartagena in the Region of Murcia (Spain). •In 2001 I started my studies in Physics at the University of Murcia. •In 2005 I received the 1st prize in the physics contest “Celebrando la Física” organized by the University of Murcia. •In 2006 I finished them with the best grades, receiving a special prize for it (Premio extraordinario fin de carrera). •From 2006 to 2007 I did the “Master of Advanced Physics” specialized in theoretical physics at the University of Valencia. •In 2007 I defended my Master Thesis at the University of Valencia, receiving the maximum grade. •In 2007 I started to work on my thesis under the supervision of Prof. Jose Antonio Oller, at the University of Murcia. •Topic: Relativistic formulations of chiral EFT with baryons.

3/18


•In 2012 I defended my thesis, entitled “Baryon Chiral Perturbation Theory in its manifestly covariant forms and the study of the πΝ dynamics & On the Y(2175) resonance”. It was rated with the best mark (Sobresaliente Cum Laude). •Thesis awarded with the “Premio extraordinario de doctorado”, given to the best thesis in physics defended in the period 2012-2013 at the University of Murcia. •In July 2012 I started to work in the group of Prof. Marc Vanderhaeghen at the Johannes Gutenberg University, Mainz. •Working with Dr. Vladimir Pascalutsa applying the relativistic formalism used in my thesis to processes involving electromagnetic probes (Compton and pion photo- and electroproduction).

4/18


Research topics


Research topics

•Application of relativistic chiral EFT with baryons to fundamental nuclear reactions:

•Understanding of the chiral dynamics of the hadronic processes at low energies. •Insight into the internal structure of the nucleon.

•πΝ scattering. •Fundamental hadronic reaction involving one baryon. •Not completely understood in the context of chiral dynamics Disagreement with dispersive approaches [Becher and Leutwyler, JHEP (2001)] (is BChPT reliable?). •Information about the internal scalar structure of the nucleon

•Important hadronic uncertainty in direct detection of DM [Bottino, Donato,

Fornengo and Scopel, Astropart. Phys. 13, (2000); Astropart. Phys. 18, (2002)] [Ellis, Olive and Savage

PRD 77, (2008)]. •Formation of elements needed for life [Berengut et. al., PRD 87, (2013)].

6/18

�⇡N


Research topics

•The two manifest Lorentz invariant schemes were used: Infrared Regularization (IR) and Extended-On-Mass-Shell (EOMS). •Conclusions [Alarcón, Martin Camalich and Oller, Ann. of Phys. 336 (2013)]:

•At low energies above threshold IR, EOMS as well as Heavy Baryon ChPT give very similar results. •The inclusion of the Δ(1232) makes a difference in the prediction of the phenomenology at low energies EOMS is clearly the best.

7/18

�⇡N

-14-12-10

-8-6-4-2 0

1.08 1.1 1.12 1.14 1.16 1.18 1.2 2 3 4 5 6 7 8 9

10 11

1.08 1.1 1.12 1.14 1.16 1.18 1.2

-6-5-4-3-2-1 0 1

1.08 1.1 1.12 1.14 1.16 1.18 1.2-1.6-1.4-1.2

-1-0.8-0.6-0.4-0.2

0 0.2

1.08 1.1 1.12 1.14 1.16 1.18 1.2

0 10 20 30 40 50 60

1.08 1.1 1.12 1.14 1.16 1.18 1.2-4

-3.5-3

-2.5-2

-1.5-1

-0.5 0

0.5

1.08 1.1 1.12 1.14 1.16 1.18 1.2√s (GeV)

√s (GeV)

√s (GeV)

√s (GeV)

√s (GeV)

√s (GeV)

S11

S31

P11

P13

P31

P33

•EOMS + Δ(1232): •Convergence in all observables. •Agreement with the dispersive approaches

BChPT is reliable!•Phenomenological extraction of:

•Scattering lengths/volumes. •Pion-nucleon coupling ( ). •Pion-nucleon sigma term ( ).

g⇡N


Research topics

8/18

-30-25-20-15-10

-5 0

1.1 1.15 1.2 1.25 1.3 1.35 0 5

10 15 20 25 30 35 40

1.1 1.15 1.2 1.25 1.3 1.35

-14-12-10

-8-6-4-2 0

1.1 1.15 1.2 1.25 1.3 1.35-5 0 5

10 15 20 25 30 35 40

1.1 1.15 1.2 1.25 1.3 1.35

0 20 40 60 80

100 120 140 160 180

1.1 1.15 1.2 1.25 1.3 1.35-4.5

-4-3.5

-3-2.5

-2-1.5

-1-0.5

0 0.5

1.1 1.15 1.2 1.25 1.3 1.35√s (GeV)

√s (GeV)

√s (GeV)

√s (GeV)

√s (GeV)

√s (GeV)

S11

S31

P11

P13

P31

P33

IR + N/D

EOMS + N/D

HB + IAM

•Unitarization techniques are important in the extension to the strange-quark sector. •We showed in [Alarcón, Martin Camalich and Oller, Ann. of Phys. 336 (2013)] that EOMS gives the best results in SU(2).

•Improve the analysis of the meson-baryon spectroscopy in the SU(3) sector Accurate determination of the Λ(1405) poles.

[Alarcón, Martin Camalich, Oller and Alvarez-Ruso, PRC 83 (2011)]

[Alarcón, Martin Camalich and Oller, Ann. of Phys. 336 (2013)]

[Gomez Nicola, Nieves, Pelaez, Ruiz Arriola, PRD 69 (2004)]


Research topics

9/18

•Relativistic baryon chiral EFT with electromagnetic probes: •Forward VVCS. •Pion photo- and electroproduction.

•Learn about the internal electromagnetic structure of the nucleon.

0.00 0.05 0.10 0.15 0.20 0.25 0.30

!4

!2

0

2

4

Q2 !GeV2"

Γ0p !10!4 fm4"

0.00 0.05 0.10 0.15 0.20 0.25 0.300.0

0.5

1.0

1.5

2.0

2.5

Q2 !GeV2"

∆LTp !10"4 fm4"

Proton 0.00 0.05 0.10 0.15 0.20 0.25 0.30

!6!4!20246

Q2 !GeV2"

Γ0n !10!4 fm4"

Neu

tron

LO Rel. BChPT

BChPT+ΔMAID

LO HB

NLO HB

No puzzle!

�nLT

[Korchelev and Oh, PRD 85 (2012)]Δ contribution

too large!!!

0.00 0.05 0.10 0.15 0.20 0.25 0.300.0

0.5

1.0

1.5

2.0

2.5

3.0

Q2 !GeV2"

∆LTn !10"4 fm4"

IR-BChPT

LO HB

NLO HB

JLab future data Hall A and B [Karl Slifer, Mainz]


Research topics

10/18

•In forward VVCS only a combination of scalar and spin polarizabilities are accesible

•Scalar . •Spin .

•We are working on a set of sum rules to disentangle this combination [Alarcón, Lensky, Pascalutsa and Vanderhaeghen (Work on progress).]

• from the dependence of the photoabsorption cross sections. •For the spin polarizabilities is not clear yet. •The sum rules are being checked with relativistic baryon chiral EFT. •Only the relativistic approach can be used Preserves analytical properties

↵E1 + �M1

�0 ⌘ �(�E1E1 + �M1M1 + �M1E2 + �E1M2)

�M1 Q2


Research topics

11/18

•VVCS and LO electroproduction calculation was used to calculate the polarizabilities contribution to the μΗ Lamb shift. •Chiral EFT has the symmetries of QCD at low energies. •Predictive.

1

[1] K. Pachucki, Phys. Rev. A 60, 3593 (1999).[2] A. P. Martynenko, Phys. Atom. Nucl. 69, 1309 (2006).[3] D. Nevado and A. Pineda, Phys. Rev. C 77, 035202 (2008).[4] C. E. Carlson and M. Vanderhaeghen, Phys. Rev. A 84, 020102 (2011).[5] M. C. Birse and J. A. McGovern, Eur. Phys. J. A 48, 120 (2012).[6] M. Gorchtein, F. J. Llanes-Estrada and A. P. Szczepaniak, Phys. Rev. A 87, 052501 (2013).[7] R. J. Hill and G. Paz, Phys. Rev. Lett. 107, 160402 (2011).

Marty- Nevado & Carlson & Birse & Gorchtein

Pachucki nenko Pineda Vanderhaeghen McGovern et al. LO-B�PT

(µeV) [1] [2] [3] [4] [5] [6] [this work]

�E(subt)

2S 1.8 2.3 �� 5.3(1.9) 4.2(1.0) �2.3(4.6)a �3.0

�E(inel)

2S �13.9 �13.8 �� 12.7(5) �12.7(5)b �13.0(6) �5.2

�E(pol)

2S �12(2) �11.5 �18.5 �7.4(2.4) �8.5(1.1) �15.3(5.6) �8.2(+1.2�2.5)

aadjusted value; the original value of Ref. [6], +3.3, is based on a di↵erent decomposition into the ‘elastic’

and ‘polarizability’ contributions.btaken from Ref. [4].

TABLE I: Summary of available calculations of the ‘subtraction’ (second row), ‘inelastic’ (thirdrow), and their sum — polarizability (last row) e↵ects on the 2S level of µH. The last columnrepresents the �PT predictions obtained in this work; here the omitted e↵ect of the �(1232)-resonance excitation is missing in the first two (‘subtraction’ and ‘inelastic’) numbers, but it doesnot a↵ect the total polarizability contribution where it is to cancel out.

1

[1] K. Pachucki, Phys. Rev. A 60, 3593 (1999).[2] A. P. Martynenko, Phys. Atom. Nucl. 69, 1309 (2006).[3] D. Nevado and A. Pineda, Phys. Rev. C 77, 035202 (2008).[4] C. E. Carlson and M. Vanderhaeghen, Phys. Rev. A 84, 020102 (2011).[5] M. C. Birse and J. A. McGovern, Eur. Phys. J. A 48, 120 (2012).[6] M. Gorchtein, F. J. Llanes-Estrada and A. P. Szczepaniak, Phys. Rev. A 87, 052501 (2013).



(µeV) [1] [2] [3] [4] [5] [6] [this work]

�E(subt)

2S 1.8 2.3 �� 5.3(1.9) 4.2(1.0) �2.3(4.6)a �3.0

�E(inel)

2S �13.9 �13.8 �� 12.7(5) �12.7(5)b �13.0(6) �5.2

�E(pol)

2S �12(2) �11.5 �18.5 �7.4(2.4) �8.5(1.1) �15.3(5.6) �8.2(+1.2�2.5)




[Alarcón, Lensky and Pascalutsa, arXiv: 1312.1219. Submitted to EPJ C]

•Agreement with phenomenological extractions. •Understand the role of the Δ(1232) in μΗ Lamb shift. •Explain the HB result


Research topics

11/18

•VVCS and LO electroproduction calculation was used to calculate the polarizabilities contribution to the μΗ Lamb shift. •Chiral EFT has the symmetries of QCD at low energies. •Predictive.

1

[1] K. Pachucki, Phys. Rev. A 60, 3593 (1999).[2] A. P. Martynenko, Phys. Atom. Nucl. 69, 1309 (2006).[3] D. Nevado and A. Pineda, Phys. Rev. C 77, 035202 (2008).[4] C. E. Carlson and M. Vanderhaeghen, Phys. Rev. A 84, 020102 (2011).[5] M. C. Birse and J. A. McGovern, Eur. Phys. J. A 48, 120 (2012).[6] M. Gorchtein, F. J. Llanes-Estrada and A. P. Szczepaniak, Phys. Rev. A 87, 052501 (2013).[7] R. J. Hill and G. Paz, Phys. Rev. Lett. 107, 160402 (2011).



(µeV) [1] [2] [3] [4] [5] [6] [this work]

�E(subt)

2S 1.8 2.3 �� 5.3(1.9) 4.2(1.0) �2.3(4.6)a �3.0

�E(inel)

2S �13.9 �13.8 �� 12.7(5) �12.7(5)b �13.0(6) �5.2

�E(pol)

2S �12(2) �11.5 �18.5 �7.4(2.4) �8.5(1.1) �15.3(5.6) �8.2(+1.2�2.5)




1

[1] K. Pachucki, Phys. Rev. A 60, 3593 (1999).[2] A. P. Martynenko, Phys. Atom. Nucl. 69, 1309 (2006).[3] D. Nevado and A. Pineda, Phys. Rev. C 77, 035202 (2008).[4] C. E. Carlson and M. Vanderhaeghen, Phys. Rev. A 84, 020102 (2011).[5] M. C. Birse and J. A. McGovern, Eur. Phys. J. A 48, 120 (2012).[6] M. Gorchtein, F. J. Llanes-Estrada and A. P. Szczepaniak, Phys. Rev. A 87, 052501 (2013).



(µeV) [1] [2] [3] [4] [5] [6] [this work]

�E(subt)

2S 1.8 2.3 �� 5.3(1.9) 4.2(1.0) �2.3(4.6)a �3.0

�E(inel)

2S �13.9 �13.8 �� 12.7(5) �12.7(5)b �13.0(6) �5.2

�E(pol)

2S �12(2) �11.5 �18.5 �7.4(2.4) �8.5(1.1) �15.3(5.6) �8.2(+1.2�2.5)




[Alarcón, Lensky and Pascalutsa, arXiv: 1312.1219. Submitted to EPJ C]

•Agreement with phenomenological extractions. •Understand the role of the Δ(1232) in μΗ Lamb shift. •Explain the HB result


Research topics

12/18

•Pion photo- and electroproduction with Δ(1232). •Relativistic chiral EFT with the Δ(1232) gave important results in:

•Compton [Lensky and Pascalusta EPJ C 65, (2010)]. •πΝ scattering [Alarcón, Martin Camalich and Oller, Ann. of Phys. 336 (2013)].

•Breaking of the ChPT description of the too close to the production threshold [Fernandez-Ramirez and Bernstein, PLB 253 (2013)].

•Excellent test for the chiral dynamics of meson photoproduction. •Not understood in the context of chiral symmetry (yet).

!!!!!!

•We are including systematically the strong isospin breaking effects (for first time in the literature). •Work on progress. Planned to be finished within the next six months.

�p ! ⇡0p

and keeping the imaginary part of the P waves equal to zero, insummary1

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

0+

ω −mπ0

mπ+

+ iβqπ+

mπ+

, (9)

Pi/q =P (0)i

mπ+

+ P (1)i

ω −mπ0

m2π+

; i = 1, 2, 3 (10)

where E(0)0+ , E(1)

0+ , P (0)1 , P (1)

1 , P (0)2 , P (1)

2 , P (0)3 , and P (1)

3 arefree parameters that will be fitted to the experimental data. Wenote that this expansion goes to a lesser order in ω than HBChPT– i.e. Ect

0+ in equation (7) goes to order ω3– but entails moreparameters. We note that chiral symmetry is not imposed in thisapproach.

3. Results

Equipped with the HBChPT, U-HBChPT and empirical ap-proaches we perform fits to the experimental data in [4] upto different maximum photon energies Emax

γ within the range[158.72, 191.94] MeV and compute the χ2/dof as well as thecorresponding error bars of the extracted parameters (see Ap-pendix A). The energy bins of the data are approximately 2.4MeV wide, which is taken into account in the fitting and cal-culations. We do not employ the first two energy bins from[4], 146.95 and 149.35 MeV, because they are less reliable dueto systematic errors, starting the fits at Emin

γ = 151.68 MeV.The amount of data employed in each fit depends on up towhat energy we are fitting, — i.e. for our lowest-energy fit(Emax

γ = 158.72 MeV) we employ 100 experimental data (80differential cross sections and 20 photon beam asymmetries)and for our highest-energy fit (Emax

γ = 191.94 MeV) we em-ploy 514 experimental data (360 differential cross sections and154 photon beam asymmetries). The highest-energy fit hasbeen chosen high enough to obtain a χ2/dof that ensures thatthe three approaches no-longer hold and the lowest-energy fit toensure a reliable fit with enough experimental data. Systematicsare not included in the χ2 and this uncertainty can amount up to4% in the differential cross section and 5% in the photon asym-metry. The fits are performed employing a genetic algorithmwhose details can be found in [19].

3.1. Quality of the fitsFigure 1 shows the χ2/dof for every fit performed versus

the upper energy Emaxγ of the fit as well as the number of data.

It is shown that up to ∼170 MeV all the fits are equally goodproviding very low χ2/dof. Above 170 MeV the trend is differ-ent; while the empirical fit remains with a good and stable χ2/dof, both the HBChPT and the U-HBChPT with the fitted LECsstart rising, a trend that shows clearly how the theory fails to re-produce the experimental data above that energy. Because we

1The empirical parameterization in [4, 9] expands on the photon energy inthe laboratory frame Eγ while we prefer to expand in the pion energy in thecenter of mass frame ω in order to have direct comparison to HBChPT. Bothapproaches render equally good description of the observables and provide thesame multipoles.

1

2

3

4

155 160 165 170 175 180 185 190 195

χ2 /dof

Emaxγ (MeV)

EmpiricalHBChPT

U-HBChPT

100127

154181

208237

266297

328359

390421

452483

514

Amount of experimental data

Figure 1: (Color online.) χ2/dof energy dependence for the empirical (fullblack squares), HBChPT (full green circles), and U-HBChPT (open blue cir-cles) fits from a minimum photon energy of 151.68 MeV up to a variable maxi-mum energy Emax

γ . Each point represents a separate fit and the connecting linesare drawn to guide the eye. The points are plotted at the central energy of eachbin, although the calculations take the energy variation inside of each bin intoaccount. The value χ2/dof= 1 is highlighted with a solid line.

obtain very similar result for U-HBChPT and HBChPT, lack ofunitarity cannot be blamed for the disagreement between theoryand experiment. The HBChPT result contrasts with the empir-ical fit that up to 180 MeV provides a good description of thedata. Above 185 MeV the χ2/dof of the empirical fit starts torise showing the effects of higher orders in the partial wavesand the appearance of a non-negligible contribution from theimaginary part of the P waves.

3.2. LECs as a function of Emaxγ

An important test of the accuracy of the HBChPT expansionis the stability of the empirical LECs versus Emax

γ . The empir-ical fit provides a solid benchmark because the parameters arethe same (within errors) in the whole energy region [20]. Fig-ure 2 shows the Emax

γ (fit) dependence of the LECs for both theHBChPT (with errors) and U-HBChPT approaches. This in-cludes the S-wave LECs a+ and a− in Figures 2.(a) and 2.(b)respectively and P-wave LECs ξ1, ξ2, and bp in Figures 2.(c),2.(d), and 2.(e). Errors are larger for the fits with lowest Emax

γ

because of the smaller amount of data. The S-wave LECs arefairly stable in the whole energy range and both HBChPT andU-HBChPT are approximately constant within errors. On thecontrary, P-wave LECs show a non-stable pattern with a posi-tive slope for ξ1 and bp and a negative slope for ξ2. The large er-ror bars make the extracted LECs compatible up to Emax

γ ∼175MeV except for ξ1, whose value for the Emax

γ = 170.53 fit isalready incompatible with the lower energy fit Emax

γ = 161.08,confirming that ∼170 MeV above such energy the theory doesnot provide a good fit to the data. Besides, approximately at∼170 the U-HBChPT and HBChPT P-wave LECs start to be in-compatible. The U-HBChPT LECs are systematically smallerin absolute value than the ones obtained through HBChPT, thisis expected because the unitary β is larger than βHBChPT giv-

3

[Fernandez-Ramirez and Bernstein, PLB 253 (2013)]

Future Projects


Future projects

•Our VVCS and electroproduction calculations allow us to investigate: •Generalized GDH integrals and . •Spin structure functions , , and (measured in E08-027, Hall A). •Moments of the integrals of the structure functions ChPT is suited for higher moments at low .

14/18

IpA InAgp1gn1 gp2gn2

Q2


Future projects


•Example: Cornwall-Norton moment

14/18


Q2

[Courtesy of Karl Slifer]

ChPT

d2(Q2) = 2

Zx0

0dx x

2[g1(x,Q2) +

3

2g2(x,Q

2)]


Future projects



14/18


Q2


LO ChPT result (improvable through the inclusion of the Δ(1232))

ChPT

d2(Q2) = 2

Zx0

0dx x

2[g1(x,Q2) +

3

2g2(x,Q

2)]


Future projects



14/18


Q2


LO ChPT result (improvable through the inclusion of the Δ(1232))

Low will be accesible by JLab data

Q2 ChPT

d2(Q2) = 2

Zx0

0dx x

2[g1(x,Q2) +

3

2g2(x,Q

2)]


Future projects

•Extension of the relativistic approach to the strange-quark sector. •SU(3) meson-baryon in relativistic chiral EFT.

•Study of the baryonic spectrum (unitarized). •Pole properties of the Λ(1405). •Line-shape πΣ from the new CLAS data [Moriya et al. (CLAS Collaboration) PRC 87

(2013)].

•Strangeness photoproduction. •Unitarization plays a fundamental role.

Relativistic (EOMS) approach gives the best results Not explored yet!!!

15/18

Summary and Conclusions


Summary and Conclusions

•Relativistic chiral EFT with explicit Δ(1232) has become a new an promising approach to investigate the nuclear structure (MENU2013) [Lensky and Pascalusta EPJ C 65, (2010)], [Alarcón, Martin Camalich and Oller, Ann. of

Phys. 336 (2013)], [Bernard, Epelbaum, Krebs and Meissner, PRD 87 (2013)].

•Crucial to achieve a major progress in understanding the scalar and electromagnetic structure of the nucleon. •Much more possibilities to exploit.

•Further investigation of the electromagnetic structure. •Extension to the strange-quark sector.

•Interesting for experimental programs at JLab. •Many-body nuclear interactions (Nuclear Lattice EFT)

17/18

FIN

Spares


Future projects

•NN and many-body nuclear physics. •Relativistic NN, 3N and 4N interactions. •Nuclear Lattice EFT. Ab initio calculations of:

•Nuclear corrections to 2β decay. •Neutrino detection. •Properties of atomic nuclei. •Capture reactions. •Nuclear fusion. •Equation of state of neutron matter.


Research topics

•Thorough analysis of the phenomenology [Alarcón, Martin Camalich and

Oller, PRD 85 (2012)]. Big impact on direct detection of dark matter. �⇡N

[Gasser, Leutwyler & Sainio, PLB 253 (1991)]

[1] Baru, Hanhart, Hoferichter, Kubis, Nogga & Phillips, NPA 872 (2011)

�⇡N = 59(7) MeV

�-ChPT

a+0+(10�3M�1

⇡ )

⇡-atoms

(⇡+p,⇡�p)KA85

Compatible with updated

phenomenology!

-11(10) -1.2(3.3) 2.3(2.0) -1.0(9)

�-ChPT�-ChPTWI08 EM06

•The πΝ database was the origin of the different values of : •Old database •Modern database

�⇡N

�⇡N ⇠ 45 MeV

�⇡N ⇠ 60 MeV Favoured by phenomenology


Future projects

• dependence not satisfactory described by chiral EFT.

15/20

•[Bernard, Epelbaum, Krebs and

Meissner, PRD 87 (2013)]. • not understood

•Δ(1232) dominant and possitive Contradicts MAID model. •The problem seems to be in how the Δ(1232) is included.

�pLT

New data from Hall A and B at JLab [Karl Slifer, Mainz]

•Our work will help to solve this issue [Alarcón, Lensky and Pascalutsa (Work on

progress)].

0.00 0.05 0.10 0.15 0.20 0.25 0.30

!4

!2

0

2

4

Q2 !GeV2"

Γ0p !10!4 fm4"

0.00 0.05 0.10 0.15 0.20 0.25 0.300.0

0.5

1.0

1.5

2.0

2.5

Q2 !GeV2"

∆LTp !10"4 fm4"

0.00 0.05 0.10 0.15 0.20 0.25 0.30

!6!4!20246

Q2 !GeV2"

Γ0n !10!4 fm4"

0.00 0.05 0.10 0.15 0.20 0.25 0.300.0

0.5

1.0

1.5

2.0

2.5

3.0

Q2 !GeV2"

∆LTn !10"4 fm4"

Q2

Documents

Investigating the low-energy structure of the nucleon with … · 2014. 1. 13. · J. M. Alarcón (JGU Mainz) •In 2012 I defended my thesis, entitled “Baryon Chiral Perturbation