chiral dynamics: taming strong qcd...1 chiral dynamics: taming strong qcd ulf-g. meißner, univ....

1

Chiral Dynamics:Taming Strong QCD

Ulf-G. Meißner, Univ. Bonn & FZ Julich

Supported by DFG, SFB/TR-16 and by DFG, SFB/TR-110 and by CAS, PIFI and by BMBF 05P15PCFN1 and by HGF VIQCD VH-VI-417

Nuclear Astrophysics Virtual Institute

Chiral Dynamics - Taming Strong QCD – Ulf-G. Meißner – WW70 Fest, TUM, April 14, 2016 · ◦ C < ∧ O > B •

2

CONTENTS

• Short introduction to chiral dynamics

• The story of the Λ(1405)

• Chiral symmetry and the nucleon-nucleon interaction

• Strangeness nuclear physics

• Summary & outlook


3

Short Introduction


4CHIRAL DYNAMICS

• QCD with three light flavors: A theoretical paradise Leutwyler

LQCD = L0QCD − qMq , q =

uds

, M =

mu

md

ms

⇒ Exhibits spontaneuous and explicit chiral symmetry breaking

⇒ Can be analyzed systematically & precisely using EFT = chiral perturbation theoryWeinberg (1979) Gasser, Leutwyler (1984,1985)

⇒ Many intriguing results, but:

− often convergence problems in the presence of strange quarks

− limited by the appearance of resonances and bound states

• Discuss here such cases & methods that overcome these limitations

w/ particular emphasis on WW’s contribution [baryon spectrum & interactions]


5

The story of the Λ(1405)


6BASICS of the Λ(1405)

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��

EπΛ πΣ ΚΝ ηΛ

K nοK p−

π Σ+ −π Σ− +π Σο ο

Λ(1405)

• Quark model: uds excitation with JP = 12

−,

a few hundred MeV above the Λ(1116)m = 1405.1

+1.3−1.0 MeV , Γ = 50.5 ± 2.0 MeV [PDG 2015]

• Prediction as early as 1959 by Dalitz and Tuan:Resonance between the coupled πΣ and KN channelsDalitz, Tuan, Phys. Rev. Lett. 2 (1959) 425; J.K. Kim, PRL 14 (1965) 29

• Clearly seen in K−p→ Σ3π reactions at 4.2 GeV at CERNHemingway, Nucl.Phys. B 253 (1985) 742

• An enigma: Too low in mass for the quark model,but well described in models (hadron exchanges, cloudy bags, . . .)

many authors incl. some in the audience

• Problems:

? models are uncontrolled (theory like experiment must have errors!)

? connections to QCD?

Events(Σ+π− )


7

The MUNICH BREAKTHROUGH

• Great idea:Combine (leading-order) chiral SU(3) Lagrangian with coupled-channel dynamics

N. Kaiser, P. B. Siegel and W. Weise,“Chiral dynamics and the low-energy kaon - nucleon interaction,”

Nucl. Phys. A 594 (1995) 325519 citations

• Dominance of the Weinberg-Tomozawa term, excellent description of K−p dataand πΣ mass distribution, also inclusion of NLO terms with constrained fits

• Highly cited follow-ups from TUM group plus other groups, esp. “Spanish Mafia”Oset, Ramos (1997), . . .

• But: unpleasant regulator dependence (Yukawa-type, momentum cut-off)gauge invariance in photo-reactions?


8

A NEW TWIST

•With my excellent post-doc Jose Oller, we reanalyzed this problemOller, UGM Phys. Lett. B 500 (2001) 263, 537 cites

• Technical improvements:

− Subtracted meson-baryon loop with dim reg ↪→ standard method

− Coupled-channel approach to the πΣ mass distribution

− Matching formulas to any order in chiral perturbation theory established

• Most significant finding:

“Note that the Λ(1405) resonance is described bytwo poles on sheets II and III with rather differentimaginary parts indicating a clear departure fromthe Breit-Wigner situation...”

[pole 1: (1379.2 -i 27.6) MeV, pole 2: (1433.7 -i 11.0) MeV on RS II]

• Scrutinized through further calculations & group theory arguments 2 years laterJido, Oller, Oset, Ramos, UGM, Nucl. Phys. A 725 (2003) 181, 447 cites


9

SU(3) SYMMETRY CONSIDERATIONS

• Group theory: 8⊗ 8 = 1⊕ 8s ⊕ 8a︸︷︷︸binding at LO

⊕10⊕ 10⊕ 27

• Follow the pole movement from the SU(3) limit to the physical masses:'

&

$

%

250

200

150

100

50

0

Im z

R [M

eV

]

17001600150014001300

Re zR [MeV]

1390 (I=0) 1426

(I=0) 1680

(I=0)

1580 (I=1)

disappear (I=1)

Singlet Octet

x=0.5

x=1.0

x=0.5 x=1.0

x=1.0

x=0.5

x=0.5

x=1.0

x=0.5

x=0.6


10MUNICH-TOKYO RELOADED

• Improved calculation with all NLO terms and constraints from kaonic hydrogen

Y. Ikeda, T. Hyodo and W. Weise,“Chiral SU(3) theory of antikaon-nucleon interactions with

improved threshold constraints,”Nucl. Phys. A 881 (2012) 98

105 citations

→ Precise proton amplitudes

→ Predictions for neutron amps.

• — M. Bazzi et al. [SIDDHARTA Collaboration],

Phys. Lett. B 704 (2011) 113√

s [MeV]

Re

f(K

−p→

K−

p)

[fm

]

-1

-0.5

0

0.5

1

1.5

1340 1360 1380 1400 1420 1440√

s [MeV]

Imf(K

−p→

K−

p)

[fm

]

0

0.5

1

1.5

2

2.5

1340 1360 1380 1400 1420 1440

• Similar developments by the Bonn and Murcia groupsMai, UGM, Nucl. Phys. A 900 (2013) 51; Oller, Guo, Phys. Rev. C 87 (2013) 035202

-1

-0.5

0

0.5

1

1.5

1340 1360 1380 1400 1420 1440

Re[

T K- p

- K- p]

(fm

)

Ec.m. (MeV)

Re f(K!p ! K!p)

[fm]

!s [MeV]

0

0.5

1

1.5

2

2.5

1340 1360 1380 1400 1420 1440

Im[T

K- p-K- p]

(fm

)

Ec.m. (MeV)

[fm] Im f(K!p ! K!p)

!s [MeV]

!(1405)

!"##!"$#!""#!"%#&$#&"#&%#&'##($

#("

#(%

#('#($

#("

#(%

#('

!"#$%&

!"#$%&#'"(%

)*#$%&#'"(%

+,+&#-.'"(%

9

Pole structure in the complex energy planeResonance state ~ pole of the scattering amplitude

!

Tij(!

s) " gigj!s # MR + i!R/2

D. Jido, J.A. Oller, E. Oset, A. Ramos, U.G. Meissner, Nucl. Phys. A 723, 205 (2003)

Λ(1405) in meson-baryon scattering

T. Hyodo, D. Jido, arXiv:1104.4474

dominantly!!

dominantlyKN

Hyodo, Jido, Prog. Part. Nucl. Phys. 76 (2012) 55


11YET ANOTHER TWIST

•With my excellent post-doc Maxim Mai, we found yet another surprise:

⇒ at least 8 solutions of similar quality w/ different pairs of poles for the Λ(1405)Mai and UGM, EPJ A 51 (2015) 30

• Scattering data • Kaonic • Threshold

SIDDHARTA: M. Bazzi et al., Phys. Lett. B 704, 113 (2011)Scatt. data: Ciborowski et al., J. Phys. G 8, 13 (1982), Humphrey, Ross, Phys. Rev. 127, 1305 (1962)

Sakitt et al., Phys. Rev. B 139, 719 (1965), Watson et al., Phys.Rev. 131, 2248 (1963)

hydrogen ratios


12PHOTOPRODUCTION to the RESCUE

• Simple model for γp→ K+Σπ → CLAS dataCLAS, Phys. Rev. C 87, 035206 (2013)

• CLAS data prefer solution 4

• also good description of Σ+π− distributionfrom K−p→ Σ+π−π+π− (not fitted)

• solution 2 also acceptable

Events(Σ+π−)


13PRESENT STATUS of the TWO-POLE SCENARIO

• Two poles from scattering plus CLAS data:

→ PDG 2016: http://pdg.lbl.gov/2015/reviews/rpp2015-rev-lam-1405-pole-struct.pdf

POLE STRUCTURE OF THE Λ(1405) REGIONWritten November 2015 by Ulf-G. Meißner and Tetsuo Hyodo


14OPEN ENDS

• The story is not yet told to the end: Consider various NLO approaches

? precise location of the lighter pole

? subthreshold amplitudes not yet well determinedCieply, Mai, UGM, Smejkal, 1603.02531

ReFK−p ImFK−p ReFK−n ImFK−n

(MeV)1/2s

1400 1450 1500

(f

m)

p-K

Re

F

-1

0

1

2

(MeV)1/2s

1400 1450 1500

(f

m)

p-K

Im F

0

1

2

(MeV)1/2s

1400 1450 1500

(f

m)

n-K

Re

F

-1.0

-0.5

0.0

0.5

1.0

(MeV)1/2s

1400 1450 1500

(f

m)

n-K

Im F

0.0

0.5

Kyoto-Munich Bonn 2 Bonn 4 Murcia 1 Murcia 2 − · − PraguePrague: Cieply, Smejkal, Nucl. Phys. A 881 (2012) 115

• Conclusion on this section: Sorry Wolfram, no retirement yet!


15

Chiral symmetry and thenucleon-nucleon interaction


16NUCLEAR CHIRAL EFFECTIVE FIELD THEORY

• The silver jubilee of Weinberg’s work extending chiral EFTs to nuclear physics

S. Weinberg,“Nuclear forces from chiral Lagrangians,”Phys. Lett. B 251 (1990) 288 [submitted 14 August 1990].969 citations counted in INSPIRE as of 26 March 2016

S. Weinberg,“Effective chiral Lagrangians for nucleon - pion interactions and nuclear forces,”Nucl. Phys. B 363 (1991) 3 [submitted 02 April 1991].936 citations counted in INSPIRE as of 26 March 2016

• after 25 years, a mature field? Epelbaum, Hammer, UGM, Rev. Mod. Phys. 81 (2009) 1773

• yes and no→ let’s discuss some recent developments

• but first things first: The Munich work!

585 cites


17THE MUNICH BUILDING BLOCK• First field-theory calculation of OPE and TPE

→ basis of all precision studies thereafter!

N. Kaiser, R. Brockmann and W. Weise,“Peripheral nucleon-nucleon phase shifts and chiral symmetry,”


3H4

0.0

0.2

0.4

0.6

0.8

1.0

PH

AS

E S

HIF

T [d

eg]

0 50 100 150 200 250Tlab [MeV]

1H5

3H5 3H6

ε5

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

PH

AS

E S

HIF

T [d

eg]

0 50 100 150 200 250Tlab [MeV]

0 100 150 200 25050Tlab [MeV]

0.0

0.1

0.2

0.3

0.4

0.5

PH

AS

E S

HIF

T [d

eg]

0 50 100 200 250Tlab [MeV]

1500

1

2

3M

IXIN

G A

NG

LE [d

eg]

-2.0

-1.5

-1.0

-0.5

0.0

PH

AS

E S

HIF

T [d

eg]

0 50 100 150 200 250Tlab [MeV]

• Established the TPE in the peripheral waves

• Introduced spectral function representation↪→ coordinate space representation

1.0 1.2 1.4 1.6 1.8 2.0

r [fm]

-300

-200

-100

0

VC(r

) [M

eV

]

2π

σ + ω

σ

Isoscalar Central Potential

1 2 3 4

r [fm]

0

2

4

6

8

10

(mπr)

3 W

T(r

) [M

eV

]

1π

1π+2π

Isovector Tensor Potential

1π + 2πSAID1π


18NUCLEAR FORCES in CHIRAL NUCLEAR EFT• expansion of the potential in powers of Q [small parameter]

• explains observed hierarchy of the nuclear forces Weinberg, van Kolck

• most higher-order NN contributions calculated by Norbert Kaiser�Chiral expansion of nuclear forces [based on NDA]

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LO (Q0)

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N4LO (Q5)

— have been worked out and employed (recently, also parts of the N5LO NN force have been worked out )

— have been worked out but not employed yet [LENPIC, work in progress]— have not been completely worked out yet

worked out and applied worked out and to be applied calculations in progress


19

NN FORCES to FOURTH ORDEREpelbaum, Krebs, UGM, Eur. Phys. J. A 51: 53 (2015)

• new regularization of long-range physics [coordinate space cut-off]:

V reglong−range(~r ) = Vlong−range(~r )freg

(r

R

), freg =

[1− exp

(− r2

R2

)]6=⇒ No distortion of the long-range potential→ better at higher energies

=⇒ No additional spectral function regularization in the TPEP required

=⇒ Study of the chiral expansion of multi-pion exchanges: R = 0.8 · · · 1.2 fmBaru et al., EPJ A 48 (2012) 69

• new way of estimation the theoretical uncertainty [before: only cut-off variations]

=⇒ Expansion parameter depending on the region: Q = max

(Mπ

Λb,p

Λb

)=⇒ Breakdown scale Λb = 600 MeV for R = 0.8 · · · 1.0 fm


20CONVERGENCE of the CHIRAL SERIES

• phase shifts show expected convergence [large N2LO corrections understood]

0

20

40

60

� [d

eg] 1S0

-10

0

10

20 3P0

-30

-20

-10

0

101P1

-30

-20

-10

0 3P1

0

60

120

180

� [d

eg] 3S1 LO

NLON2LON3LO

-5

0

5

10�1

-30

-20

-10

03D1

0

5

10

151D2

0

10

20

30

0 100 200 300

� [d

eg]

Elab [MeV]

3D2

0

5

10

15

20

0 100 200 300

Elab [MeV]

3P2

-4

-3

-2

-1

0

0 100 200 300

Elab [MeV]

�2

-5

0

5

10

0 100 200 300

Elab [MeV]

3D3

=⇒ clear improvement comp. to earlier N3LO potentials [momentum space reg.]Entem, Machleidt (2003); Epelbaum, Glockle, UGM (2005)


21UNCERTAINTIES

• uncertainties show expected pattern

-20

0

20

40

60

� [d

eg]

1S0

-20

0

20

40

60

� [d

eg]

1S0

-10

0

10

20 3P0

-10

0

10

20 3P0

-40

-30

-20

-10

0

10

1P1

-40

-30

-20

-10

0

10

1P1

-30

-20

-10

03P1

-30

-20

-10

03P1

0

60

120

180

� [d

eg]

3S1

0

60

120

180

� [d

eg]

3S1

-5

0

5

10�1

-5

0

5

10�1

-30

-20

-10

0

3D1

-30

-20

-10

0

3D1

0

5

10

15

20

1D2

0

5

10

15

20

1D2

0

10

20

30

0 100 200 300

� [d

eg]

Elab [MeV]

3D2

0

10

20

30

0 100 200 300

� [d

eg]

Elab [MeV]

3D2

0

5

10

15

20

25

30

0 100 200 300

Elab [MeV]

3P2

0

5

10

15

20

25

30

0 100 200 300

Elab [MeV]

3P2

-4

-3

-2

-1

0

1

0 100 200 300

Elab [MeV]

�2

-4

-3

-2

-1

0

1

0 100 200 300

Elab [MeV]

�2

-10

-5

0

5

10

15

0 100 200 300

Elab [MeV]

3D3

-10

-5

0

5

10

15

0 100 200 300

Elab [MeV]

3D3

NLO N2LO N3LO


22NN FORCES to FIFTH ORDEREpelbaum, Krebs, UGM, Phys. Rev. Lett. 115 (2015) 122301

Entem, Kaiser, Machleidt, Nosyk, Phys. Rev. C 91 (2015) 014002

• No contact interactions at this order - odd in Q

• New contributions fixed from πN scattering, LECs ci, di, ei:Buttiker, Fettes, UGM, Steininger (1998-2000); Krebs, Gasparian, Epelbaum (2012), Hoferichter, Ruiz de Elvira, Kubis, UGM (2015)

LπN = L(1)πN + L(2)

πN(ci) + L(3)πN(di) + L(4)

πN(ei)

• Three-pion exchange can be neglected

→ explicit calculation of the dominant NLO contribution Kaiser (2001)

→ no influence on phase shifts or deuteron properties


23PHASE SHIFTS at N4LO

⇒ Precision phase shifts with small uncertainties up to Elab = 300 MeV

-20

0

20

40

60

� [d

eg]

1S0

-20

0

20

40

60

� [d

eg]

1S0

-10

0

10

20 3P0

-10

0

10

20 3P0

-40

-30

-20

-10

0

10

1P1

-40

-30

-20

-10

0

10

1P1

-30

-20

-10

03P1

-30

-20

-10

03P1

0

60

120

180

� [d

eg]

3S1

0

60

120

180

� [d

eg]

3S1

-5

0

5

10�1

-5

0

5

10�1

-30

-20

-10

0

3D1

-30

-20

-10

0

3D1

0

5

10

15

20

1D2

0

5

10

15

20

1D2

0

10

20

30

0 100 200 300

� [d

eg]

Elab [MeV]

3D2

0

10

20

30

0 100 200 300

� [d

eg]

Elab [MeV]

3D2

0

5

10

15

20

25

30

0 100 200 300

Elab [MeV]

3P2

0

5

10

15

20

25

30

0 100 200 300

Elab [MeV]

3P2

-4

-3

-2

-1

0

1

0 100 200 300

Elab [MeV]

�2

-4

-3

-2

-1

0

1

0 100 200 300

Elab [MeV]

�2

-10

-5

0

5

10

15

0 100 200 300

Elab [MeV]

3D3

-10

-5

0

5

10

15

0 100 200 300

Elab [MeV]

3D3

NLO N2LO N3LO N4LO


24FRONTIERS

• Three-nucleon forces→ LENPIC collaborationwww.lenpic.org

• Applications in nuclei:conventional many-body approaches/nuclear lattice simulations→Achim Schwenk’s talk [if I only had more time ...]

• Nuclear matter and the EoS, neutron stars→ again pioneering TUM work

N. Kaiser, S. Fritsch and W. Weise,“Chiral dynamics and nuclear matter,”


• nuclear matter/neutron matter√

• asymmetry energy√

• many interesting follow-ups 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

ρ [fm−3

]

−20

−15

−10

−5

0

5

10

15

20

25

30

E [

Me

V]

− chiral OPE+TPE

−− Friedman, Phandharipande (1981)

see alsoHammer, Nogga, Schwenk,Rev. Mod. Phys. 85 (2013) 197


25

Strangeness nuclear physics


26PUZZLES in HYPER-NUCLEAR PHYSICS

• The hyperon puzzle: EoS does notsupport 2 solar mass neutron starse.g. Li, Schulze (2008), ..., Bombaci, 1601.05339

→ need repulsion in the YN and YYinteractions (Y = Λ,Σ)

and/or repulsive YNN, . . ., forces8 10 12 14

R [km]

0

0.5

1

1.5

2

2.5

M/M

sun

0 0.5 1 1.5

central density [fm-3

]

0

0.5

1

1.5

2

2.5

M/M

sun

Av18+TNIAv18+TNI+ESC08b

Mmax

= 1.38 Msun

PSR J0348+0432

Mmax

= 2.28 Msun

VOLUME 86, NUMBER 19 P H Y S I C A L R E V I E W L E T T E R S 7 MAY 2001

E(1/2 )-E(3/2 ) = 152 54 keV+−- -

1 0 . 9

1 1 . 0

1 1 . 1

-1 .0 -0 .5 0 . 0 0 . 5 1 . 0

E (

MeV

)γ

R

FIG. 3. Peak positions obtained by fitting the g ray spectra areshown as a function of R.

we change the absolute cross section keeping the angulardistribution which is theoretically robust [18] to reproducethe yield. We then obtained 30 keV as the maximum devia-tion from the central value for the �s splitting. The fit withthe response function in Fig. 2 gave x2 � 0.87 1.27. Re-peating the analysis with different fitting functions gives,at most, a 19 keV change in the result for the �s splitting,as long as the same function is used for all three spectra.Correction of Doppler shift is found to be of negligibleimportance.

The observed �s splitting is quite small. The �s splittingfor the single-nucleon p states around this mass region is�3 5 MeV, thus the �s splitting for the single-pL state isabout 20–30 times smaller than that for the nucleon. Fur-thermore the p1�2�L� state appears higher than the p3�2�L�state, as is the case for nucleon.

Recently YN interactions have been refined in both anOBE model [24] and a quark model [25]. Hypernuclearstructure calculation with a cluster model shows that the�s splitting in 13

L C is 0.39–0.96 MeV for YN interactionsbased on an OBE model and it is �0.2 MeV for a YN in-teraction based on a quark model [26]. Systematic study oflight L hypernuclei shows that the YN interactions basedon an OBE model need to be modified so that a smaller�s splitting, as indicated by the present experiment, canbe accommodated [27]. A new mechanism will be re-quired for the unified understanding of the baryon-baryon(NN, YN, and YY ) interaction. In summary the �s splittingof single-L states has been directly observed. It is muchsmaller than that for the nucleon. The state-of-the-art cal-culation of the YN interaction based on OBE models isunable to reproduce the present result.

We thank the staff of the Brookhaven AGS for theirsupport in running the experiment. We thank ProfessorT. Motoba and Professor K. Itonaga for theoretical calcula-tion of angular distribution. We thank Mrs. Elinor Norton

of Chemistry Department of BNL for an evaluation of 13Cin our enriched benzene. We are grateful to ProfessorK. Imai for the continuous support of the experiment.Discussions with Dr. J. Millener and Dr. E. Hiyamaare greatly appreciated. This experiment is financiallysupported in part by the Grant-in-Aid for ScientificResearch in Priority Areas (Strangeness Nuclear Physics)08239205 and for International Scientific Research10044086 and in part by the U.S. Department of En-ergy under Contracts No. DE-AC02-98CH10886 andNo. DE-FG02-87ER40315.

[1] R. Chrien and C. Dover, Annu. Rev. Nucl. Part. Sci. 39,113 (1989), and references therein.

[2] P. H. Pile et al., Phys. Rev. Lett. 66, 2585 (1991).[3] T. Hasegawa et al., Phys. Rev. Lett. 74, 224 (1995);

T. Hasegawa et al., Phys. Rev. C 53, 1210 (1996).[4] W. Brückner et al., Phys. Lett. 79B, 157 (1978).[5] M. May et al., Phys. Rev. Lett. 47, 1106 (1981).[6] M. May et al., Phys. Rev. Lett. 51, 2085 (1983).[7] M. M. Nagels, T. A. Rijken, and J. J. de Swart, Phys. Rev.

D 12, 744 (1975); 15, 2547 (1977); 20, 1633 (1979).[8] C. Dover and A. Gal, in Progress in Particle and Nuclear

Physics, edited by D. Wilkinson (Pergamon, Oxford, 1984),Vol. 12, p. 171.

[9] Y. Yamamoto and H. Bando, Prog. Theor. Phys. Suppl. 81,42 (1985).

[10] K. Itonaga et al., Phys. Rev. C 49, 1045 (1994).[11] H. Pirner and B. Povh, Phys. Lett. 114B, 308 (1982).[12] O. Morimatsu, S. Ohta, K. Shimizu, and K. Yazaki, Nucl.

Phys. A420, 573 (1984).[13] A. Bouyssy, Phys. Lett. 91B, 15 (1980).[14] E. H. Auerbach et al., Phys. Rev. Lett. 47, 1110 (1981).[15] T. Nagae et al., in Proceedings of the International

INS Symposium on Nuclear and Particle Physics withthe Meson Beams in the 1 GeV�c Region, edited byS. Sugimoto and O. Hashimoto (Universal AcademicPress, Tokyo, 1995), p. 175; T. Motoba, ibid. p. 187.

[16] R. H. Dalitz, D. H. Davis, D. N. Tovee, and T. Motoba,Nucl. Phys. A625, 71 (1997).

[17] T. Motoba, Nucl. Phys. A 639, 135c (1998).[18] T. Motoba (private communication).[19] M. May et al., Phys. Rev. Lett. 78, 4343 (1998).[20] T. Kishimoto et al., AGS research proposal E929, 1996.[21] R. W. Stotzer et al., Phys. Rev. Lett. 78, 3646 (1997).[22] H. Kohri, Ph.D. thesis, Osaka University, 2000

(unpublished).[23] S. Ajimura et al., Nucl. Instrum. Methods Phys. Res., Sect.

A 459, 326 (2001).[24] T. A. Rijken, V. G. Stoks, and Y. Yamamoto, Phys. Rev. C

59, 21 (1999).[25] Y. Fujiwara, C. Nakamoto, and Y. Suzuki, Phys. Rev. Lett.

76, 2242 (1996).[26] E. Hiyama, M. Kamimura, T. Motoba, T. Yamada, and

Y. Yamamoto, Phys. Rev. Lett. 85, 270 (2000).[27] D. J. Millener (private communication).

4258

• Very small spin-orbit splitting inΛ single particle statese.g. Ajimura et al., PRL 86 (2001) 4255

• Λ-nucleus interaction is attractive

but Σ-nucleus interaction is repulsivee.g. Friedman, Gal, Phys. Rep. 452 (2007) 89


27HYPERON–NUCLEON INTERACTIONS

• LO chiral EFT for YN interaction pioneered at Bonn/JulichPolinder, Haidenbauer, UGM, Nucl. Phys. A 779 (2006) 244

• For NLO, teamed up with the TUM group

J. Haidenbauer, S. Petschauer, N. Kaiser,UGM, A. Nogga and W. Weise,“Hyperon-nucleon interaction at

next-to-leading orderin chiral effective field theory,”Nucl. Phys. A 915 (2013) 24

45 citations

→ good description of all scatt. data + 3ΛH BE

→ much needed repulsion found

→ error bands need to be refined

note: moderate attraction at low momentastrong repulsion at higher momenta

Author's personal copy

36 J. Haidenbauer et al. / Nuclear Physics A 915 (2013) 24–58

Fig. 2. “Total” cross section ! (as defined in Eq. (24)) as a function of plab. The experimental cross sections are takenfrom Refs. [54] (filled circles), [55] (open squares), [69] (open circles), and [70] (filled squares) ("p ! "p), from [56](#"p ! "n, #"p ! #0n) and from [57] (#"p ! #"p, #+p ! #+p). The red/dark band shows the chiral EFTresults to NLO for variations of the cutoff in the range " = 500, . . . ,650 MeV, while the green/light band are results toLO for " = 550, . . . ,700 MeV. The dashed curve is the result of the Jülich ’04 meson-exchange potential [37].

also for "p the NLO results are now well in line with the data even up to the #N threshold.Furthermore, one can see that the dependence on the cutoff mass is strongly reduced in the NLOcase. We also note that in some cases the LO and the NLO bands do not overlap. This is partlydue to the fact that the description at LO is not as precise as at NLO (cf. the total $2 values inTable 5). Also, the error bands are just given by the cutoff variation and thus can be consideredas lower limits.

A quantitative comparison with the experiments is provided in Table 5. There we list theobtained overall $2 but also separate values for each data set that was included in the fittingprocedure. Obviously the best results are achieved in the range " = 500–650 MeV. Here, inaddition, the $2 exhibits also a fairly weak cutoff dependence so that one can really speak ofa plateau region. For larger cutoff values the $2 increases smoothly while it grows dramatically

Author's personal copy

J. Haidenbauer et al. / Nuclear Physics A 915 (2013) 24–58 43

Fig. 6. The !p 1S0 and 1P1 phase shifts " as a function of plab. The red/dark band shows the chiral EFT results toNLO for variations of the cutoff in the range ! = 500, . . . ,650 MeV, while the green/light band shows results to LO for! = 550, . . . ,700 MeV. The dashed curve is the result of the Jülich ’04 meson-exchange potential [37].

Fig. 7. The !p phase shifts for the coupled 3S1–3D1 partial wave as a function of plab. Same description of curves asin Fig. 6.

state in the #N system. It should be said, however, that the majority of the meson-exchangepotentials [36,38,39] produce an unstable bound state, similar to our NLO interaction. The onlycharacteristic difference of the chiral EFT interactions to the meson-exchange potentials mightbe the mixing parameter $1 which is fairly large in the former case and close to 45! at the #N

threshold, see Fig. 7. It is a manifestation of the fact that the pertinent !p T -matrices (for the3S1 " 3S1, 3D1 " 3D1, and 3S1 # 3D1 transitions) are all of the same magnitude.

The strong variation of the 3S1–3D1 amplitudes around the #N threshold is reflected inan impressive increase in the !p cross section at the corresponding energy, as seen in Fig. 2.

LO

NLO

LO

NLO

repulsion

phase shift

Hyperon - Nucleon Interaction(contd.)

J. Haidenbauer, S. Petschauer, N. Kaiser,U.-G. Meißner, A. Nogga, W. W.

Nucl. Phys. A 915 (2013) 24

22

0.6 0.8 1.0 1.2 1.4 1.6kF (1/fm)

-60

-45

-30

-15

0

U! (M

eV)

0.6 0.8 1.0 1.2 1.4 1.6kF (1/fm)

-20

-15

-10

-5

0

5

10

S ! (M

eV fm

5 )

Figure 2: The ! s.p. potential U!(p! = 0) (left) and the Scheerbaum factor S! (right), as a function of the Fermi momentum kF . The red/darkband shows the chiral EFT results to NLO for variations of the cuto" in the range ! = 500,. . .,650 MeV, while the green/light band are results toLO for ! = 550,. . .,700 MeV. The hatched band is the NLO fit from [4] without antisymmetric spin-orbit force. The dashed curve is the result ofthe Julich ’04 meson-exchange potential [43].

also in Table 3 and denoted by NLO†(650). Clearly in this case S! is significantly larger. A closer inspection of therespective partial-wave contributions reveals what one expects anyway, namely that the main di"erence is due to theantisymmetric spin-orbit force whose contribution is given in the column labelled with 1P1!3P1. It is zero for the LOinteraction (because there is no antisymmetric spin-orbit force at that order) and also for the original NLO interaction,where it has been assumed to be zero. With the corresponding contact term included its strength can be used tocounterbalance the sizeable spin-orbit force generated by the basic interaction so that the small S! is then achievedby a cancellation between the spin-orbit and antisymmetric spin-orbit components of the G-matrix interaction. Note,however, that the results in Table 3 indicate that such a cancellation is not the only mechanism that can providea small spin-orbit force. For example, let us look at the predictions for the interaction (denoted by) NLO (600"),where all two-meson-exchange contributions involving the !- and/or K meson have been omitted. Here, a very smallS! is achieved without any antisymmetric spin-orbit force. It is simply due to overall more repulsive contributions,notably in the 3P0 and 3P2 partial waves. We want to emphasize that the interaction NLO (600") reproduces all !Nand #N scattering data with the same high quality as the other EFT interactions at NLO, see the results in Ref. [4].Finally, it is worthwhile to mention that also the Julich meson-exchange potentials predict rather small values for theScheerbaum factor. For both interactions there is a substantial contribution from the antisymmetric spin-orbit forcewhich is primarily due to vector-meson (") exchange [32]. The magnitude is comparable to the one of the chiral EFTinteraction at NLO.

The dependence of S! on kF can be seen in Fig. 2. Obviously, except for the LO interaction, the density de-pendence is fairly weak. A weak density dependence of S! was also observed in Ref. [20] in a calculaton of theScheerbaum factor for a YN interaction based on the quark model.

Let us now come to the # hyperon. In the course of constructing the NLO EFT interaction [4] it turned outthat the available YN scattering data can be fitted equally well with an attractive or a repulsive interaction in the3S 1 partial wave of the I = 3/2 #N channel. Indeed the underlying SU(3) structure as given in Table 1 of Ref. [4]suggests that there should be some freedom in choosing the interaction in this particular partial wave. From that tableone can see that the 3S 1 partial wave in the I = 3/2 #N channel belongs to the “isolated” 10 representation so that

9

LO

NLO!p1S0

WW, Hyperfine Interact. 233 (2015) 131


28HYPERONS in NUCLEAR MATTER• Consider hyperons in the medium→ Brueckner G-matrix

→ gap choice (only Re parts)Haidenbauer, UGM, Nucl. Phys. A 936 (2015) 29

→ continuous choice

J. Haidenbauer, S. Petschauer, N. Kaiser,UGM, and W. Weise,

“Hyperons in nuclear matter from SU(3)chiral effective field theory,”Eur. Phys. J. A 52 (2016) 15

→ reproduce small Λ s.o. force

→ predict sizeable Σ s.o. force (SΣ ' 5SΛ)

→ attractive UΛ(k = 0) & becoming repulsive

→ repulsive UΣ(k = 0) & staying repulsive

0 1 2 3k [fm−1]

−60

−50

−40

−30

−20

−10

0

10

20

30

ReU

Λ(k

)[M

eV]

χEFT NLOχEFT LOJulich ’04NSC97f

0 1 2 3k [fm−1]

−60

−40

−20

0

20

40

ReU

Σ(k

)[M

eV]

χEFT NLOχEFT LOJulich ’04NSC97f

[also thesis S. Petschauer]


29THREE–BODY FORCES• Phenomenological ΛNN forces can do the job

Lonardoni et al., Phys. Rev. Lett. 114 (2015) 092301Hell, Weise, Phys. Rev. C 90 (2014) 045801

• Need a more systematic approach tothese elusive forces

• A powerful team [also thesis S. Petschauer]

S. Petschauer, N. Kaiser, J. Haidenbauer,UGM, and W. Weise,

“Leading three-baryon forces from SU(3)chiral effective field theory,”

Phys. Rev. C 93 (2016) 014001

→ completely worked out & LECs to be estimated from decuplet excitations

↪→ let us see what these will give in hyper-nuclei and dense nuclear systems

4

been performed. In this case the additional repulsionprovided by the model (II) pushes ρth

Λ towards a densityregion where the contribution coming from the hyperon-nucleon potential cannot be compensated by the gain inkinetic energy. It has to be stressed that (I) and (II) givequalitatively similar results for hypernuclei. This clearlyshows that an EoS constrained on the available bindingenergies of light hypernuclei is not sufficient to draw anydefinite conclusion about the composition of the neutronstar core.

The mass-radius relations for PNM and HNM obtainedby solving the Tolman-Oppenheimer-Volkoff (TOV)equations [47] with the EoS of Fig. 1 are shown in Fig. 2.The onset of Λ particles in neutron matter sizably reducesthe predicted maximum mass with respect to the PNMcase. The attractive feature of the two-body ΛN interac-tion leads to the very low maximum mass of 0.66(2)M⊙,while the repulsive ΛNN potential increases the pre-dicted maximum mass to 1.36(5)M⊙. The latter resultis compatible with Hartree-Fock and Brueckner-Hartree-Fock calculations (see for instance Refs. [2–5]).

M [M

0]

R [km]

PNM

N

N + NN (I)

N + NN (II)

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

11 12 13 14 15

PSR J1614-2230

PSR J0348+0432

Figure 2. (Color online) Mass-radius relations. The key isthe same of Fig. 1. Full dots represent the predicted max-imum masses. Horizontal bands at ∼ 2M⊙ are the ob-served masses of the heavy pulsars PSR J1614-2230 [18] andPSR J0348+0432 [19]. The grey shaded region is the excludedpart of the plot due to causality.

The repulsion introduced by the three-body force playsa crucial role, substantially increasing the value of theΛ threshold density. In particular, when model (II) forthe ΛNN force is used, the energy balance never favorsthe onset of hyperons within the the density domain thathas been studied in the present work (ρ ≤ 0.56 fm−3).It is interesting to observe that the mass-radius relationfor PNM up to ρ = 3.5ρ0 already predicts a NS massof 2.09(1)M⊙ (black dot-dashed curve in Fig. 2). Evenif Λ particles would appear at higher baryon densities,the predicted maximum mass is consistent with present

astrophysical observations.

In this Letter we have reported on the first QuantumMonte Carlo calculations for hyperneutron matter, in-cluding neutrons and Λ particles. As already verifiedin hypernuclei, we found that the three-body hyperon-nucleon interaction dramatically affects the onset of hy-perons in neutron matter. When using a three-bodyΛNN force that overbinds hypernuclei, hyperons appeararound twice saturation density and the predicted max-imum mass is 1.36(5)M⊙. By employing a hyperon-nucleon-nucleon interaction that better reproduces theexperimental separation energies of medium-light hyper-nuclei, the presence of hyperons is disfavored in the neu-tron bulk at least until ρ = 0.56 fm−3 and the lowerlimit for the predicted maximum mass is 2.09(1)M⊙.Therefore, within the ΛN model that we have consid-ered, the presence of hyperons in the core of the neutronstars cannot be satisfactory established and thus there isno clear incompatibility with astrophysical observationswhen lambdas are included. We conclude that in order todiscuss the role of hyperons - at least lambdas - in neu-tron stars, the ΛNN interaction cannot be completelydetermined by fitting the available experimental energiesin Λ hypernuclei. In other words, the Λ-neutron-neutroncomponent of the ΛNN will need additional theoret-ical investigation and a substantial additional amountof experimental data. In particular, there are somefeatures of the hyperon-nucleon interaction (Λ-neutron-neutron channels, spin-orbit contributions) which mightbe efficiently constrained only by experiments involvinghighly asymmetric hypernuclei and/or excitation of thehyperon. We believe that our conclusions will not changequalitatively if other hyperons and/or a vΛΛ are includedin the calculation.

We would like to thank J. Carlson, S. C. Pieper, S.Reddy, A. W. Steiner, and R. B. Wiringa for stimulatingdiscussions. This research used resources of the NationalEnergy Research Scientific Computing Center (NERSC),which is supported by the Office of Science of the U.S.Department of Energy under Contract No. DE-AC02-05CH11231. The work of D.L. and S.G was supported bythe U.S. Department of Energy, Office of Nuclear Physics,under the NUCLEI SciDAC grant and A.L. by the De-partment of Energy, Office of Nuclear Physics, under con-tract No. DE-AC02-06CH11357. The work of S.G. wasalso supported by a Los Alamos LDRD grant. F.P. isalso member of LISC, the Interdisciplinary Laboratoryof Computational Science, a joint venture of the Univer-sity of Trento and the Bruno Kessler Foundation.

[1] V. A. Ambartsumyan and G. S. Saakyan, Sov. Astro. AJ4, 187 (1960).

[2] E. Massot, J. Margueron, and G. Chanfray, EuroPhys.

n ! matter

!N

!N

!N

!NN(1)

!NN(2)+

+

ChEFT

QMC

R [km]

M

MO.

WW, Hyperfine Interact. 233 (2015) 131�

�

�

�1 2 3


30

SUMMARY

Thank you Wolfram for all the insight

We owe you a lot!


31


chiral dynamics: taming strong qcd...1 chiral dynamics: taming strong qcd ulf-g. meißner, univ....

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