FROM QCD TO NUCLEI ASPECTS OF SYMMETRY

Wolfram Weise

Prof. Giulio Racah Memorial Lecture 2007 The Hebrew University of Jerusalem 13 March 2007

ünchen

Historical Prelude: Early Meson Theory of the Nuclear Force

Low-Energy QCD and Chiral Symmetry:

Pion in Lattice QCD

Chiral Effective Field Theory

Aspects of Chiral Symmetry in Modern Nuclear Theory:

Nuclear Chiral Dynamics

Pion as a Nambu-Goldstone Boson

Mass of the Nucleon

tem

perature

Tc

baryon chemical potential

!qq" #= 0

!qq" #= 0

quark ! gluon phase

µB1 GeV

nuclear

matter

0.2

T

[GeV] Nf = 2 (q = u,d)

critical point

hadron phase

CSC phasesuperconductor

(color)

matternuclear

QCD PHASE

DIAGRAM

. . . first orientation:

ATOMIC NUCLEUSNUCLEON

10 fm1 fm

density [fm!3]0.15

baryon chemical potential

0

0

1.

TheBeginnings

Fig. I. Three Regions of Nuclear Potential.*

Region I. Classi.cal region, r*\.irc-t, (r-t is the pion Comp'ton wave length) where the one-pion-exchange potential domi'nates and the quantitative behavior of the potential has beenestablished.

Region II. D.ynamical regi.on, 0.7{L!r{I.5rc-r, where thetwo-pion-exchange potential competes with and exceeds the one'pion-exchange potential. The recoil effect is also appreciablein this region. The qualitative behavior, however, has beenclarified.

Region III. Phenomenologi.cal region, r10.7rc-r, where existso many complicated effects, €.g., the relativistic effect, the isobareffect, the effect of new particles, etc., that at present we mayhave no means but some phenomenological treatment to fit withexperiments.

distance in the unit of the pion Compton wave length,x fi is the inter-nucleonE-r=L.4x10-13-cm](see p. 35).

!

!

!

NN

N N

N N

region 1I1short distance: unresolved

Nucleon-Nucleon Interaction M. Taketani, S. Nakamura, M. SasakiProg. Theor. Phys. 6 (1951) 581

region 1 long distance:

one-pion exchange

region 1I intermediate distance:

two-pion exchange

M. Taketani, Suppl. Prog. Theor. Phys. (1956)

Hierarchy of

SCALES

II. Understanding the

PION (and the NUCLEON)

in the context ofLow-Energy QCD

the 60’s and the 70’s :

Chiral Symmetry PCAC, Current Algebra

Quantum Chromo Dynamics

QUANTUM CHROMO DYNAMICS

GLUON

QUARK

GLUE

QUARKMASSES

LQCD = ! (i"µDµ! m) ! !

1

4Gµ!G

µ!

SU(3) Gauge Theory

9.Quantumchromodynamics17

0

0.1

0.2

0.3

110102

µ GeV

αs (µ)

Figure9.2:Summaryofthevaluesof!s(µ)atthevaluesofµwheretheyaremeasured.Thelinesshowthecentralvaluesandthe±1"limitsofouraverage.Thefigureclearlyshowsthedecreasein!s(µ)withincreasingµ.Thedataare,inincreasingorderofµ,#width,$decays,deepinelasticscattering,e+e!eventrateat25GeV,eventshapesatTRISTAN,Zwidth,e+e!eventshapesofMZ,135,and189GeV.

bysystematic,usuallytheoretical,errors.Onlysomeofthese,notablyfromthechoiceofscale,arecorrelated.Theaverageisnotdominatedbyasinglemeasurement;thereareseveralresultswithcomparablesmallerrors:thesearetheonesfrom#decay,latticegaugetheory,deepinelasticscattering,upsilondecayandtheZ0width.Wequoteouraveragevalueas!s(MZ)=0.1172±0.002,whichcorrespondsto!(5)=216+25

!24MeVusingEq.(9.5).Futureexperimentscanbeexpectedtoimprovethemeasurementsof!ssomewhat.Precisionatthe1%levelmaybeachievableifthesystematicandtheoreticalerrorscanbereduced[163].

Thevalueof!satanyscalecorrespondingtoouraveragecanbeobtainedfromhttp://www-theory.lbl.gov/!ianh/alpha/alpha.htmlwhichusesEq.(9.5)tointerpolate.

June18,200213:56

!s =g2s

4"

0.001 0.01 0.1

0.1

0.2

0.3

0

“Sliding” interaction strength

of QCD

distance [fm]

WEAK

STRONGPhysics 2004 http://nobelprize.org/physics/laureates/2004/index.html

1 of 1 12.10.2004 15:34

!"#$ %&'$(!$)* +,"-' %$+./!

)012(34567685("924:8;(<=(>??@ /4AB;6CD2(E(>??@('D8(F4:8G(H4IJ50264J

F",$) !"#$%&$ /!$#&%'.K #$L&/&F$ )&'$.+'-.$ *$+/$ $/"F"#&/%

'()*+(,+$ +.'&/)$% $L-/+'&"F+)

!"#$%&'#($)*+,#$+-$)"./+0/$1223

!"#$%&'(%)*+,#-($.%#"%/+.01&#&*,%"$(()#0%*2%&'(%&'(#$.%#"%&'(%+&$#23%*2&($/,&*#2!

(

-./01234256788 "42-./012!790:;<6 =6.>?2@09A;<?

(MNO(47(2D8(A;6P8 (MNO(47(2D8(A;6P8 (MNO(47(2D8(A;6P8

-%+ -%+ -%+

Q0RG6(&J1262I28(74;('D84;82690G(*DB1691=(-J6R8;162B(47(/0G674;J60(%0J20(,0;:0;0=(/+=(-%+

/0G674;J60(&J1262I28(47('89DJ4G4CB(*01058J0=(/+=(-%+

#01109DI18221(&J1262I28(47('89DJ4G4CB(S#&'T(/03:;65C8=(#+=(-%+

:U(MV@M :U(MV@V :U(MV<M

,B<2C7D<92!60;<20>2!BE80A82FGGH*;6P8(+JJ4IJ9838J2*;811(.8G8018+5R0J985(&J74;30264J&J74;30264J(74;(2D8(*I:G69

-./01234256788F4:8G()892I;8&J28;R68W"2D8;(.814I;981

"42-./012!790:;<6F4:8G()892I;8"2D8;(.814I;981

=6.>?2@09A;<?F4:8G()892I;8&J28;R68W"2D8;(.814I;981

(>??O (

'D8(>??@(*;6P8(6JX((*DB1691((/D83612;B((*DB164G4CB(4;(#85696J8(()628;02I;8((*8098(($94J4369(%968J981

H6J5(0()0I;8028X

!60;<2(>>7I>A<J<>:8'D8(G02812(6J74;30264J(6174IJ5(02(F4:8GA;6P8U4;C(Y

+KL976<2M2'<.6>Z0381(0J5(%63IG0264J1(Y

%&'$(H$$L,+/Q ( /"F'+/' ( '$))(+(H.&$FL

F038

4

Figure 3. Summary of measurements of !s(Q2). Results which are based on fits of !s(MZ0) to datain ranges of Q, assuming the QCD running of !s, are not shown here but are included in the overallsummary of !s(MZ0), see Figure 4 and Table 1.

agreement with the QCD prediction.Therefore it is appropriate to extrapolate all

results of !s(Q) to a common value of energy,which is usually the rest energy of the Z0 boson,MZ0 . As described in [1], the QCD evolution of !s

with energy, using the full 4-loop expression [29]with 3-loop matching [30] at the pole masses ofthe charm- and the bottom-quark, Mc = 1.7 GeVand Mb = 4.7 GeV , is applied to all results of!s(Q) which were obtained at energy scales Q !=MZ0 .

The corresponding values of !s(MZ0) are tab-ulated in the 4th column of Table 1; column 5and 6 indicate the contributions of the experi-

mental and the theoretical unceratinties to theoverall errors assigned to !s(MZ0). All values of!s(MZ0) are graphically displayed in Figure 4.Within their individual uncertainties, there isperfect agreement between all results. This jus-tifies to evaluate an overall world average value,!s(MZ0). As discussed e.g. in [1], however, thecombination of all these results to an overall aver-age, and even more so for the overall uncertaintyto be assigned to this average, is not trivial dueto the supposedly large but unknown correlationsbetween invidual results, especially through com-mon prejudices and biases within the theoreticalcalculations.

Running Coupling

S. Bethke, hep-ex/0606035

Experimental tests ofasymptotic freedom

in QCD

QCD : BASIC CONCEPTS and STRATEGIES

“HIGH - Q” ( several GeV)> SHORT DISTANCE ( 0.1 fm)<

Theory of WEAKLY INTERACTING QUARKS and GLUONS(Perturbative QCD)

“LOW - Q” ( 1 GeV)<< LONG DISTANCE ( 1 fm)

SPONTANEOUS (CHIRAL) SYMMETRY BREAKING

>

Effective Field Theory of WEAKLY INTERACTINGNAMBU-GOLDSTONE BOSONS (Pions)

LATTICE QCD

Large-scale computer simulations on

EUCLIDEAN SPACE-TIME Lattices

x

!

a

SPONTANEOUS SYMMETRY BREAKING

LOW T HIGH T

Ueff

< φ >

Ueff

< φ >

CHIRAL (QUARK) CONDENSATE

!qq" #= 0 !qq" = 0

(Nambu - Goldstone)

! !

QCD with (almost) MASSLESS u- and d-QUARKS (N = 2)

left - handed right - handed

momentumspinspin

Low-Energy QCD: CHIRAL SYMMETRY

SU(2)L ! SU(2)R

f

pseudoscalar - isovector

scalar - isoscalar

! = (u,d)

!a! " #5 t

a

"

σ ! ψ ψ

NAMBU - GOLDSTONE BOSON:

Spontaneously Broken CHIRAL SYMMETRY

f! = 92.4MeV

PION DECAY CONSTANTORDER PARAMETER:

PION

!0|Aaµ(0)|!b(p)" = i"ab pµ f!

!µ

!

SYMMETRY BREAKING SCALE MASS GAP

!! = 4! f" ! 1GeV

PCAC:

Gell-Mann - Oakes - Renner Relation

m2!f2!

= !mq "!!# + O(m2

q)

Axial current

Mmeson ! mQ ! mq

[GeV]

0

0.2

0.4

0.6

0.8

1.0

1.2

B!

B D!

D

K!

K

!

!

bd cd sd ud

Q Qq q[ ]1S0[ ]3S1

SCALES and SYMMETRY BREAKING PATTERN

HEAVY versus LIGHT

spontaneouschiral

symmetrybreaking

hyperfinesplitting

Q Qq q[ ]1S0[ ]3S1

perturbativeQCD

effective field theory of Goldstone

Bosons

mu,d ! 5MeV

MASS SPLITTINGS: SINGLET and TRIPLET quark-antiquark states

mb ! 4.3GeV mc ! 1.3GeV ms ! 0.1GeV

JP

= 1!

JP

= 0!

massgap

Interacting systems of PIONS coupled to NUCLEONS:

+ + ...

! !N N

LOW-ENERGY QCD: Effective Field Theory of weakly interacting GOLDSTONE BOSONS (PIONS)

+

! !

Leff = L!(U, !U) + LN (!N , U, ...)

higher orders

U(x) = exp[i!a"a(x)/f!]

(Weinberg; Gasser & Leutwyler; Ecker; ... + many others)

CHIRAL EFFECTIVE FIELD THEORY

Construction of Effective Lagrangian: Symmetries

+ + ...

! !N N

LN = !N [i!µ("µ ! iVµ) ! M0 + gA!µ!5Aµ] !N + ...

higher orders ! !N S !N + ...

Aµ =1

2f!

!" · #µ!$ + ... ; Vµ =

1

4f2!

!" · (!# ! $µ!#) + ... ; S = !N

!

1 !"#2

2f2!

+ ...

"

AXIAL VECTOR VECTOR SCALAR

f! = 92.4MeV gA = 1.267

PION-NUCLEON EFFECTIVE LAGRANGIAN

!N = !N |mu uu + md dd|N"! 50MeV

effects of ∆(1230)

short distance physics(low-energy constants)

pion decay constant nucleon axial vector

nucleon sigma term coupling constant

+

M0 ! 0.88GeV mass of the nucleon in the “chiral limit” (m! ! 0)

lattice(CP-PACS, JLQCD, QCDSF)

physical point

Masse des Nukleons[GeV]

25 50 75 100 150

Quarkmasse [MeV]

QCD and the ORIGIN of MASSHOW does the PROTON get its rest mass ?

answer: mostly GLUONS:

QCD

quark mass [MeV]

nucleon mass[GeV]

physical point

theory

(M. Procura et al. Phys. Rev. D (2004)) (D. Leinweber et al. 2004)

u + u + d = proton

mass : 3 + 3 + 6 != 938 !

mu ! 3MeV md ! 6MeV

CONFINEMENT

q

q

qglue

. . . brief digression:

small parameter:

Q

4!f!

energy / momentum / pion mass

mass gap of order 1 GeV

successfully applied to:

PION-PION scattering

PION-NUCLEON scattering

PION photoproduction and COMPTON scattering on the NUCLEON

long range NUCLEON-NUCLEON interaction

NUCLEAR MATTER and NUCLEI

Low-Energy Expansion: CHIRAL PERTURBATION THEORY

0.28 0.3 0.32 0.34 0.36 0.38

E(GeV)

0

5

10

15

20

δ 00 -δ 11 (degrees)

PSfrag replacements

0.180.220.26

Figure 3: Phase relevant for the decay K ! !!e". The three bands correspondto the three indicated values of the S–wave scattering length a0

0. The uncertaintiesare dominated by those from the experimental input used in the Roy equations.The triangles are the data points of Rosselet et al. [28], while the full circlesrepresent the preliminary E865 results [30].

narrow bands shown is obtained by fixing the value of a20 with the correlation

(13.2) and inserting the result in the numerical parametrization of the phaseshifts in appendix D of ref. [6]. At a given value of a0

0, the uncertainties in theresult for the phase di!erence #0

0(s) " #11(s) are dominated by the one in the

experimental input used for the I = 0 S–wave. Near threshold, the uncertaintiesare proportional to (s" 4M2

!)3/2 – in the range shown, they amount to less thana third of a degree. While the data of Rosselet et al. [28] are consistent with allthree of the indicated values of a0

0, the preliminary results of the E865 experimentat Brookhaven [29, 30] are not. Instead they beautifully confirm the prediction(11.2): The best fit to these data is obtained for a0

0 = 0.218, with $2 = 5.7 for 5degrees of freedom. As pointed out in ref. [46], the correlation (13.2) can be usedto convert data on the phase di!erence into data on the scattering lengths. Fora detailed discussion of the consequences for the value of a0

0, we refer to [46, 47].

14 Results for !1 and !2

The e!ective coupling constants of L4 enter the chiral perturbation theory repre-sentation of the scattering amplitude and of the scalar form factor only as correc-tions, so that our results for these are subject to significantly larger uncertainties

24

! !

S wave scattering lengths Next-to-leading order (NLO) one-loop analysis

Chiral Perturbation Theory

Accurate measurement of aI=0

0

aI=0

0

test of Gell-Mann - Oakes - Renner relation

G. Colangelo, J. Gasser, H. Leutwyler Nucl. Phys. B 603 (2001) 125

K ! !!e"

phase shifts low-energy from

!!

Tests of Chiral Symmetry Breaking Scenario:Pion-Pion Scattering

BNL E865.

m2!f2!

= !mq "!!# + O(m2

q)

Tests of Chiral Symmetry Breaking Scenario:Pion-Pion Scattering

confirmation of Nambu-Goldstone spontaneous chiral symmetry breaking scenario

ChiralPerturbation

Theory

Gell-Mann – Oakes – Renner relation

mu,d ! m! dependence according to Chiral Perturbation Theory:

m2! = 2

|"0|qq|0#|

f2!

m + O(m2, m2 ln m) m $ mu = md

0 0.01 0.02 0.03 am0

0.02

0.04

0.06

0.08

(amπ )2mπ∼676MeV

484

381

294

Lüscher @ Lattice 2005

Nucleon properties: from lattice QCD to the chiral limit – p.7/35

physical point

Tests of Chiral Symmetry Breaking Scenario:Lattice QCD

perfect consistency with leading-order Gell-Mann - Oakes - Renner relation

m2

! = !mu + md

f2

!

"qq# + O(m2

q)

O(m2

qlog mq)

M. LüscherProc. Lattice 2005

confirmation of “standard” (Nambu-Goldstone) spontaneous chiral symmetry breaking with Pions as Goldstone Bosons and large quark condensate:

|!qq"| # (0.23GeV)3 # 1.5 fm3

+

q

fm!3

III.

Chiral Thermodynamicsand

Goldstone Bosons in

Matter

0 0.05

0.1 0.15

0.2 0.25

0.3T[GeV]

0 0.1

0.2 0.3

0.4 0.5

0.6![fm-3]

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

f"[GeV]

0

20

40

60

80

f!(T, !) [MeV]

!0

!qq"T,!

!qq"0# 1 $

T 2

8f2"

$!N

m2" f2

"

" + ...f2!(T, !)

f2!(0)

!

f2!(T, !)

f2!(0)

!

!qq"T,!

!qq"0# 1 $

T 2

8f2"

$!N

m2" f2

"

" + ...

20

40

60

80

00.1

0.20.3

0.40.5

0.1

0.2

0

! [fm!3] T [GeV]

0 0.5 1 1.5 2 2.5T!Tc

0.2

0.4

0.6

0.8

1

!"##"$!!"##"$T%0

Nf%0 "Nt%8#Nf%0 "Nt%4#Nf%2 "Nt%4#

Nf%2&1 "Nt%4#Nf%4 "Nt%8#

CHIRAL ORDER PARAMETER

Pion decay constant and Chiral Condensate

dependence on temperature and baryon density

Lattice: G. Boyd et al.

Phys. Lett. B349 (1995)170

!!!"T!!!"T=0

S. Klimt, M. Lutz, W. W. Phys. Lett. B249 (1990) 386

C. Ratti, M. Thaler, W. W. Phys. Rev. D73 (2006) 014019

(!0 ! 0.16 fm!3)

f2! (T, !)

f2! (0)!

"qq#T,"

"qq#0= 1 $

T2

8 f2!$

"N

m2! f2!

! + ...

Experiment at GSI (Darmstadt)

... and Sn isotopes

“Fingerprints of

CHIRAL SYMMETRY RESTORATION ?”

GOLDSTONE BOSONS in MATTER

Deeply Bound States of Pionic Atoms

Ustrong =!n ! !p

4 f2!

+ ...

Chiral Symmetry:

f! ! f!

!(!)

DEEPLY BOUND STATES of PIONIC ATOMS

Experiment (GSI)Calculation:

K. Suzuki et al.Phys. Rev. Lett.

92 (2004) 072302

E. Kolomeitsev, N. Kaiser, W. W.

Phys. Rev. Lett. 90 (2003) 092501

Nucl. Phys. A721 (2003) 835

1s state

f!

!(!0) ! 0.8 f!

Energy Dependent Pion-Nucleus Potentialbased on

In-medium Chiral Perturbation Theory

! 1 "

!N

2m2! f2

!

"0

{ {

deduced from exp. theory pred.

(!N ! 50MeV)

Low-Energy Pion-Nucleus Scattering

Detailed analysis of isovector s-wave pion-nucleus interactioncompatible with

f!

!(medium) ! 0.83 f!(vacuum)

E. Friedman et al.Phys. Rev. Lett. (2004)Phys. Rev. C (2005)

E. Friedman, A. GalPhys. Lett.

B578 (2004) 85

IV.

Nuclear Chiral Dynamics:

Spontaneous Symmetry Breakingand the Pion in

Modern Nuclear Theory

7. Nuclei in the Universe 133

stable nucleiknown masses up to ‘95mass measurement s ‘95 - ’00mass measurement s ‘02

(on-line identification)unknown masses T > 1sunknown masses T < 1s

unknownmasses only

Neutron Number

Prot

onN

umbe

r

2028

50

82

8

8

20

28

50

82

126

Figure 7.6: The current knowledge of nuclear masses. Preliminary results obtained on-line from the frag-mentation or from the fission of a 238U beam are shown in yellow color. (Courtesy of Y. Litivinov)

significant impact on the r-process abundancepattern at the low-A wing of the peaks. Its firmverification, however, needs further experimen-tal study of the r-process progenitor nuclei inthe vicinity of the shell closure. In particular,major developments have to be started to pro-duce and study the refractory elements (Mo toPd) around N=82.

There are currently no data available for r-process nuclei in the region of the N=126 shellclosure, which is associated with the third r-process peak at around A ! 195. This is likelyto change, when this region can be reached bythe high-energy fragmentation of Pb or U beamsat GSI. These key experiments will then opena new era in nuclear structure and r-process re-search, in particular delivering the first measure-ments of halflives for N = 126 waiting points.Beyond N = 126, the r-process path reaches re-gions where nuclei start to fission, demandingan improved knowledge of fission barriers in ex-tremely neutron-rich nuclei to determine wherefission terminates the neutron capture flow andprevents the synthesis of superheavy elementswith Z>92. If the duration time of the r-process

is su!ciently long (as it could be found in neu-tron star mergers), the fission products can cap-ture again neutrons, ultimately initiating “fis-sion cycling” which can exhaust the r-processmatter below A = 130 and produce heavy nu-clei in the fission region. Fission can in partic-ular influence the r-process abundances of Thand U. This would change the Th/U r-processproduction ratio with strong consequences forthe age determination of our galaxy, which hasrecently been derived from the observation ofthese r-nuclides in old halo stars.

The direct measurement of neutron-capturecross sections on unstable nuclei is techni-cally not feasible. This goal can, however,be achieved indirectly by high resolution (d,p)-reaction, which are considered the key tool tostudy neutron capture cross sections of rare iso-topes at radioactive nuclear beam facilities. Forr-process nuclides, particular technical advance-ments need to be made to produce the requiredbeams of a few MeV/nucleon. Studies of betadelayed-neutron decays can help to determinethe existence of isolated resonances above theneutron-emission threshold in the daughter nu-

Z

N

... from QCD

via

CHIRAL EFFECTIVE FIELD THEORY ...

... to theNUCLEAR CHART ?

Two-Pion Exchange andSCALAR field of the NUCLEON

!

N

strongSCALAR

field

!

N

x

!

!

N,!

N

N

Van der Waals - type

NN interactionV(r) !

e!2m!r

r6P(m!r)

Scalar Form Factor of the Nucleon

5 10 15 200

0.5

1.0

1.5empirical

(Höhler et al.)

Born

ChPT(NNLO 2-loop)

t[m2

!]

(N)

(N + !)

!N(Q2) = !N ! Q2

!!

4m2!

dt"(t)

t(Q2 + t)

!(t)

t2N. Kaiser,

Phys. Rev. C(2003)

strongSPIN-ISOSPIN

polarizability of the Nucleon

CHIRAL DYNAMICS and the NUCLEAR MANY-BODY PROBLEM

PIONS and DELTA isobars as EXPLICIT degrees of freedom

pion exchange processes in the presence of a filled Fermi sea

Expansion of ENERGY DENSITY

!!

!

additional relevant scale: Fermi momentum

+ + ... “ in medium”

IN-MEDIUM CHIRAL PERTURBATION THEORY

N N

short-distance dynamics: contact interactions

F

N,!N N N N

kF ! 2m! ! M! " MN << 4! f2!

“small” scales:

in powers of Fermi momentum k

NUCLEAR THERMODYNAMICS

!

!

N N N N

+

NUCLEAR CHIRAL (PION) DYNAMICS (Yukawa + Van der Waals + Pauli)

... plus contact terms

Liquid - Gas Transition atCritical Temperature T = 15 MeVc

c

0 0.05 0.1 0.15 0.2

! [fm-3]-1

0

1

2

3

4

P [M

eV/fm

3 ]T=0MeV

T=5MeV

T=10MeV

T=15MeV

T=20MeVT=25MeV

S. Fritsch, N. Kaiser, W. W. Nucl. Phys. A 750 (2005) 259

(empirical: T = 16 - 18 MeV)

baryon density

pressure

nuclear matter: equation of state

FINITE NUCLEI: DENSITY FUNCTIONAL STRATEGIES

:

from in-medium Chiral Perturbation Theory (”Pionic fluctuations”)

:

strong SCALAR and VECTOR mean fields

E[!] = Ekin +

!d

3x [E(0)(!) + Eexc(!)] + Ecoul

Eexc(!)

E(0)(ρ)

... constrained by symmetry breaking pattern of low-energy QCD

generated by IN-MEDIUM changes of QCD CONDENSATES

RESULTS (part I)

P. Finelli, N. Kaiser, D. Vretenar, W. W. : Nucl. Phys. A735 (2004) 449, A770 (2006) 1

deviations (in %) between calculated and measured

-1

-0.5

0

0.5

1

E/A

(%

)

-1

-0.5

0

0.5

1

Rch(%

)

NL3

DD-ME1

FKVW_new

16

O

40

Ca48

Ca

72

Ni90

Zr

116

Sn124

Sn

132

Sn204

Pb

208

Pb214

Pb

210

Po

!E/A (%)

!!r2"1/2 (%)

Strategy :

Fix short distance constants (contact interactions) e.g. in Pb region

binding energies per nucleon ...

... and charge radii

Calculate physics at long and intermediate distances using nuclear chiral effective field theory

Predict systematics for all other nuclei

RESULTS (part II)

48charge density of Ca

0 0.5 1 1.5 2 2.5q (fm-1)

10-3

10-2

10-1

100

|F(q

)|

Exp. valuesFKVW_new

0 2 4 6ρ(fm-3)

0

0.02

0.04

0.06

0.08

ρ cgh(fm

-3)

48Ca

0 0.5 1 1.5 2 2.5q (fm-1)

10-3

10-2

10-1

100

|F(q

)|

Exp. valuesFKVW_new

0 2 4 6ρ(fm-3)

0

0.02

0.04

0.06

0.08

ρ cgh(fm

-3)

48Ca

r [fm]

!ch(r)

[fm!3]

Exp.Th.

P. Finelli, N. Kaiser, D. Vretenar, W. W. : Nucl. Phys. A735 (2004) 449, A770 (2006) 1

RESULTS (part III): DEFORMED NUCLEI

deviations (in %) between calculated and measured binding energies

130 140 150 160-0.5

0

0.5

140 150 160 170 150 160 170 180 190

140 150 160-0.5

0.0

0.5

!E

(%

)

150 160 170 170 180 190 200

140 150 160-0.5

0

0.5

150 160 170 180

A170 180 190 200

Nd

Sm

Gd

Dy

Er

Yb

Hf

Os

Pt

130 140 150 160

0

0.2

0.4

140 150 160 170 150 160 170 180 190

130 140 150 160

0

0.2

0.4

!2

150 160 170

Exp. data

FKVW [2005]

160 170 180 190 200

140 150 160 170

0

0.2

0.4

150 160 170 180

A160 170 180 190 200

Nd

Sm

Gd

Dy

Er

Yb

Hf

Os

Pt

P. Finelli, N. Kaiser, D. Vretenar, W. W. Nucl. Phys. A735 (2004) 449, A770 (2006) 1

Ground state deformations

Systematics through isotopic chains

governed by isospin dependent forces

from chiral pion dynamics

density

QUARKS & GLUONS

HADRONS

temperature

early universe

heavy-ioncollisions

confinementof quarks and gluonsin (composite) hadrons

vacuum structure : Condensation of quarks and gluon

spontaneous (chiral) symmetry breaking

Goldstone Bosons(pions)

Nuclear Masses and Forces temperatureTc0

QUARK

CONDENSATE

from Lattice QCD

Tc

precisionexperiments

Summary & Outlook: passing through PHASE BOUNDARIESte

mpe

ratu

re

NUCLEI