An Instanton Induced Interactionfafnir.phyast.pitt.edu/nstar/plenaryB/metsch.pdfAn Instanton Induced...

� ��

An Instanton Induced Interactionin a relativistic constituent quark model of baryons

Bernard Metsch

Helmholtz-Institut fur Strahlen– und Kernphysik

Universitat Bonn

Nußallee 14-16, D-53115 Bonn, GERMANY

e-mail: [email protected]

N*2002 Pittsburgh, 08-13.10.2002 – p.1

� ��

Outline

!

Instantons in QCD:! "SB! #%$ &' (

-problem!

instanton induced quark interaction:! ) *)-interaction: (pseudo)scalars! ) )-interaction: octet-decuplet-splitting!

a relativistic constituent quark model:!

basic assumptions and approximations: BSE + SE!

parameterisation of confinement!

results:!

mass spectra: Regge trajectories, parity doublets!

e.m properties; form factors and helicity amplitudes!

strong decays

N*2002 Pittsburgh, 08-13.10.2002 – p.2

� ��

Instantons

Yang-Mills lattice simulationsar

Xiv

:hep

-lat

/931

2071

v2

23

Dec

199

3ar

Xiv

:hep

-lat

/931

2071

v2

23

Dec

199

3

t

z

(a)

5

10

15

20

5

10

15

2

3

4

5

10

15

20

5

10

15

2

3

4

t

z

(b)

5

10

15

20

5

10

15

-0.05

0

0.05

5

10

15

20

5

10

15

-0.05

0

0.05

t

z

(c)

5

10

15

20

5

10

15

0

0.01

0.02

0.03

5

10

15

20

5

10

15

0

0.01

0.02

0.03

t

z

(d)

5

10

15

20

5

10

15

-0.001

0

0.001

0.002

5

10

15

20

5

10

15

-0.001

0

0.001

0.002

t

z

(e)

5

10

15

20

5

10

15

0

0.01

0.02

0.03

5

10

15

20

5

10

15

0

0.01

0.02

0.03

t

z

(f)

5

10

15

20

5

10

15

-0.001

0

0.001

0.002

5

10

15

20

5

10

15

-0.001

0

0.001

0.002

Action densityTopological

charge density

u

u

d_

d_

d_

uL

R

L

R

L

R

ππ

π I

A

!

Gas of instantons:,size

- . 0.3-0.4 fm;,separation

- . 0.9-1.0 fm;! /-symmetry breaking!

effective interaction! ,1032 2 - 465 7

!

constituent quark masses

N*2002 Pittsburgh, 08-13.10.2002 – p.3

� ��

effectivemassesand interaction

!

after normal ordering:89 :; <

eff

= 89 :> <

eff

= 89 :? <

eff

= 89 :@ <

effeffective masses effective interaction

dd

ud

s

ud

ss_

_uu

_uu

s

dd_

m(d)

m(s)

ds

g

g’

ss_

_

d

_ss_

uu

+ + +

uu_

η

η’

π

Κ∗ρ,ω

Mass

m(n)+m(s)

2m(n)

m(n)+m(s)

2m(s)Κ

2m(s)

2m(n)

N*2002 Pittsburgh, 08-13.10.2002 – p.4

� ��

(pseudo)scalarmesons

0

200

400

600

800

1000

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Mas

s M

[MeV

]

A

g[GeV^(-2)]

g’ = 0.0 GeV^(-2)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

g’[GeV^(-2)]

g = 1.73 GeV^(-2)

pionkaon

etaeta’

uu/dd_

ss_

_

g’g

_

dd_

uu

+

BDC C C mixes E * E%F G *GF H *H orIKJ F ' J for (pseudo)scalars

of’

aoKo

*Ko*of’

ao

fo fo

Mass [MeV]

1000

1500 1460

1350

1240nn

’1500’1450

1430

1470

1430

1320

980

ns

ss

’1000’

η’980

530

495

ηΚ

π140

Mass [MeV]

1000

500

0

910

810

690

ss

ns

nn

η’

495

ηΚ

π140

960

550

LNM = LPO O O Exp.

N*2002 Pittsburgh, 08-13.10.2002 – p.5

� ��

The instanton-induced Q Q-interaction

In 2 2SR T 5 0VU -channel W instantaneous potential:’t Hooft’s interaction (induced by instantons):

L :? <

’t Hooft

XZYV[ \ YV] ^ 5 _ :@ < XZYV[ \ YV] ^

` ab c

point-interaction

d

\ e fgih h j kml Xon n ^ = gh p j kml X nq ^ r

` a b c

flavour-dependent coupling

sut vw t v =yx z w x z{ j |~}%�� ;

G. ’t Hooft, Phys. Rev. D 14, 3432 (1976)

M. A. Shifman, A. I. Vainstein, V. I. Zakharov, Nucl. Phys. B 163, 46 (1980)

!

flavour-dependent:

j k�l: flavour-antisymmetric quark pairs.

!

spin-dependent:

j |}%� � �; : antisymmetric in spin

�> ? 5 7

.

!

point-interaction:

_ :@ < XZYy[ \ Y] ^ \ W [� �� exp

� \ ��

� does not act on: flavour-decuplet, spin-symmetric states;

� no

�� d ��

, no tensor forces.

N*2002 Pittsburgh, 08-13.10.2002 – p.6

� ��

a relativistic quark model: assumptions

Pretend to describe baryons in the framework of quantum fieldtheory: Basic quantities: Bethe-Salpeter amplitudes

/�� Xo� >R � ?R � @ ^�� 5 , 7 �� X � > ^ � Xo� ? ^ � Xo� @ ^ � 01� -(with

*y� � ¡¢ £ ¡¤ £ ¡¥ ;

*� ¤ � ¦ ¤

baryon mass;

§ &%¨© (

quark field operator)

which fulfill the Bethe-Salpeter Equation:

χ(3)- iK χΣ

zykl. Perm.1,2,3

+(2)

iK-χ =

Full quark propagators:

� ª Xo� \ � « ^ 5 , 7 � � � Xo� ^ 0 � Xo� « ^ � 7 -

++ + + ...=

Irreducible 2- and 3 -body interaction kernels:

+ + + + ...-iK(2) =

+ + + + ...=-iK(3)

N*2002 Pittsburgh, 08-13.10.2002 – p.7

� ��

momentumspace

From Poincaré invariance:

/� � Xo� >R � ?R � @ ^ 5 ¬ � ® �� ¯ °±²X³ ´ ^ °

¯ °±iµX³ ´ ^ ° ¬ � ¶· ² ¬ � ¶u¸ µ /�� X ±² R ± µ ^

� 8-dimensional integral equation

"¹º & ¡» F ¡½¼ ( � ¾J¢ & '¿ *� £ ¡» £ ' À ¡½¼ (�Á ¾J¤ & ' ¿ *Â�ÄÃ ¡» £ ' À ¡¼ (Á ¾J¥ & '¿ *Â� Ã ¡½¼ (

Å &Ã Æ ( G Ç ¡ È»& À½É ( ÇG Ç ¡ È¼& À½É ( Ç Ê & *� F ¡» F ¡Ë¼ F ¡ È» F ¡ È¼ ( " ¹º & ¡ È» F ¡ È¼ (

with integral kernel:

Ê� Ê Ì ¥ Í £ * Ê Ì ¤ Í,

* Ê Ì ¤ Í & *� F ¡» F ¡¼ F ¡ È» F ¡ È¼ (ÏÎ �(123)

Ê Ì ¤ Í & �¢ ¤ F ¡» F ¡ È» (�Á Ð ¾J¥ & ' ¿ *� Ã ¡½¼ (ÑÒ ¢ &À É ( ÇÔÓ Ì Ç Í & ¡½¼ Ã ¡ È¼ (

N*2002 Pittsburgh, 08-13.10.2002 – p.8

� ��

Bethe-SalpeterEquation, approximations...

Model assumptions (inspired by NonRelativistic Constituent Quark Model):

!

Free quark propagators replace full propagators:

� ª X ± ^ . Õ

x X ± ^ \ Ö = Õ ×

W Ö effective constituent quark masses

!

Instantaneous approximation: No dependence of interactionkernels on ± ;² und ± ;µ (in the restframe of the baryon):

Ø :@ < X 0Ô� R ±² R ± µ R ± «² R ± «µ ^ � � � � :ÙÛÚ Ü; < 5 L :@ < XÞÝ ² R Ý µ R Ý «² R Ý «µ ^

Ø :? < X � > ?R ±² R ± «² ^ � � � � :ÙÛÚ Ü; < 5 L :? < XÞÝ ² R Ý «² ^

ß ’Retardation effects are neglected’

� Salpeter amplitudeà Ù XÝ ² R Ý µ ^� 5 á d¶ â·? � d¶ â¸? � /��

� X ± ;² R Ý ² ^R X ± ;µ R Ý µ ^ � ãäãäãäã �� : ÙÚ å <

satisfies the Salpeter equation

æ à Ù 5 ç à Ù è , à Ù � à Ù - 5 ³ ç

N*2002 Pittsburgh, 08-13.10.2002 – p.9

� ��

SalpeterEquation, SalpeterHamiltonian

é é é approximate treatment of

L :? < é é é :

&ê ëKì ( & í » F í ¼ (�¥

© î ¢ï© ë ì & í » F í ¼ (

£ ð ñ ò¢ Á ñ ò¤ Á ñ ò¥ £ ñ Ò ¢ Á ñ Ò ¤ Á ñ Ò ¥ ó

ô õ Á ô õ Á ô õG¥ ¡ È»& À½É ( ¥G¥ ¡ È¼&À É ( ¥ B Ì ¥ Í & í » F í ¼ F í È» F í È¼ ( ë ì & í È» F í È¼ (

£ ð ñ ò¢ Á ñ ò¤ Á ñ ò¥ Ã ñ Ò ¢ Á ñ Ò ¤ Á ñ Ò ¥ ó

ô õ Á ô õ Á ' ö G¥ ¡ È»&À É ( ¥÷ B Ì ¤ Í & í » F í È» (Á ' ö ø ë ì & í È» F í ¼ (

£

cycl. perm. (123)

! ñ ù© & íú (Î � ûü ùý ü¤ ûü Energy projectors

! ï© & íú (Î � ô õ & þÿ íú £�� © (Dirac Hamiltonian

N*2002 Pittsburgh, 08-13.10.2002 – p.10

� ��

Confinement

Quark confinement is realized by a phenomenological string potentialfor 3 quarks (Ansatz similar to NRCQM):

L :@ <

Conf

XZY[ R Y] R Y � ^ 5 A � =

B �� Y � \ Y � �

3-Quark-String

In contrast to the nonrelativistic quark model the relativistic

quasi-potential

L :@ <�� depends on the Dirac structure for three quarks.We choose:A@ 5 � @ ° �t vw t vw t v = x ; w x ; w t v =yx ; w t vw x ; = t vw x ; w x ;

B@ 5 � >? � \ t vw t v w t v =yx ; w x ; w t v =yx ; w t vw x ; = t v w x ; w x ;

W Spin-orbit effects are small (compatible with exp.)

W Regge trajectories are quantitatively correct.

N*2002 Pittsburgh, 08-13.10.2002 – p.11

� ��

Model parameters

parameter value

quark- ’nonstrange’ � � 330 Mev

masses ’strange’ � � 670 Mev

confinement offset � -744 MeV

slope

�

470 MeV fmÒ ¢

’t Hooft’s nn-coupling � � � 136.0 MeV fm

¥

force ns-coupling � � � 94.0 MeV fm

¥

effective range�

0.4 fm

Parameters are fixed by

!

the

8

-Regge trajectory

\ W Confinement parameters �, �

and Öh

!

baryon ground-states (octet und decuplet)

\ W g�h h , gh p , �and Ö p

N*2002 Pittsburgh, 08-13.10.2002 – p.12

� ��

-Reggetrajectory

Model

�PDG 20008� �� X ³ �� 7 ^

8� � � �� X³ e³ 7 ^

8� � � �� X t �� 7 ^

8 � � � �� X t ³ U ³ ^

�

!" [GeV

" ]> z?#> >?#$? #@?#

10

8

6

4

2

0

N*2002 Pittsburgh, 08-13.10.2002 – p.13

� ��

-resonances

πP P33 S D31 F F D GH G II3 1135 37 39 H3 11 3 13 3 15 3 1333 35 37 3931KKL2T 2J

1232

20001950

1700

2150

1940 1930

2200

2750

1620

23502400

1900

2300

2420

2950

2390

19051920

1600

1750

1910

J 1/2+ 3/2+ 5/2+ 7/2+ 9/2+ 11/2+ 13/2+ 15/2+ 1/2- 3/2- 5/2- 7/2- 9/2- 11/2- 13/2- 15/2-

Mas

s [M

eV]

1000

1500

2000

2500

3000

*

********

*****

****

**

**

****

***

**

**

****

**

**

*

*

*

*

*******

***

N*2002 Pittsburgh, 08-13.10.2002 – p.14

%&' ()'* +,-./ 0. 12 - '.3 +45 6789 :; <= :>?@ ABC > D>E >

Instanton-inducedeffectsin the

F G

-spectrum

π

g [MeV fm ]nn3

conf

inem

ent o

nly

expe

rim

ent

+ ’

t Hoo

ft’s

for

ceco

nfin

emen

t

Roper-resonance

∆−Ν

split

ting

N

J 1/2+ 3/2+ 5/2+ 7/2+ 9/2+ 11/2+ 13/2+

Mas

s [M

eV]

1000

1500

2000

2500

3000

*

**

** **

**

S

****

****

*** **** ****

****

0 136 0 136 1360 1360 0 136 1360 0 136

N*2002 Pittsburgh, 08-13.10.2002 – p.15

%&' ()'* +,-./ 0. 12 - '.3 +45 6789 :; <= :>?@ ABC > D>E >

Instanton-inducedeffectsin the

FH -spectrum

π

conf

inem

ent o

nly

+ ’

t Hoo

ft’s

for

ceex

peri

men

t

conf

inem

ent

?

?

g [MeV fm ]nn3

J 1/2- 3/2- 5/2- 7/2- 9/2- 11/2- 13/2-

Mas

s [M

eV]

1000

1500

2000

2500

3000

*

***

**

**

***

****

****

S S

****

****

****

****

0 136 0 136 0 136 0 136 0 136 0 136 0 136

N*2002 Pittsburgh, 08-13.10.2002 – p.16

%&' ()'* +,-./ 0. 12 - '.3 +45 6789 :; <= :>?@ ABC > D>E >

-Reggetrajectory

Model

IPDG 2000

and ’t Hoofts forceConfinement

without ’t Hoofts forceonly Confinement,

J K K�LMN O PQ RS S T

J K K K KU N O PQ Q Q S T

J K K K KV N O PWX Y S T

J K K K KLN O PZ[ Z T

\]

^_ [GeV

_ ]`ab cdb ceb c`b c

10

8

6

4

2

0

H f ’t Hooft’s force produces a constant shift in

g b

Furthermore, parity doublets in the nucleon spectrum

N*2002 Pittsburgh, 08-13.10.2002 – p.17

%&' ()'* +,-./ 0. 12 - '.3 +45 6789 :; <= :>?@ ABC > D>E >

Parity doublets(high spin)

ω2 h ω2 h

ω3 h

ω4 h

ω5 h

ω

ω

ω

ω

1 h

3 h

4 h

5 h

?

?

g [MeV fm ]nn3

π

ω6 h

J

2000

2500

**

****

**

****

****

****

****

***

1360 1360 0 136 1360

**

0 136

7/2 9/25/2 11/2 13/2

+ + + -+ - - -+ -M

ass

[MeV

]0 1361360 0 136 0 1361360

3000

ω2 h ω2 h ω2 h

ω1 h ω1 h ω1 h

ω3 h ω3 h ω3 h

g [MeV fm ]nn3

π

J

Roper-resonance

∆−Ν

split

ting

N1000

1500

2000

Mas

s [M

eV]

5/21/2 3/2

*

S

****

****

***

0 136

+

*

****

****

S

-

**

****

0 136

+

***

**

S

****

-

**

****

1360

+

**

****

-0 136 0 136 0 136

N*2002 Pittsburgh, 08-13.10.2002 – p.18

%&' ()'* +,-./ 0. 12 - '.3 +45 6789 :; <= :>?@ ABC > D>E >

BSE NRCQM (

h

conf.

i hkj j j )

π 1/2+

�

3/2+

�

5/2+

�

7/2+

�

9/2+

�

11/2+

�

13/2+

�

1/2-

�

3/2-

�

5/2-

�

7/2-

�

9/2-

�

11/2-

�

13/2-

�

J

Mas

s [M

eV]

1000

1500

2000

2500

3000

****

****

***

*

*

****

**

****

** **

****

**

****

****

*

*

****

***

**

*

****

** ********

***

N*2002 Pittsburgh, 08-13.10.2002 – p.19

%&' ()'* +,-./ 0. 12 - '.3 +45 6789 :; <= :>?@ ABC > D>E >

Relativistic effects

Effects of ’t Hooft’s force in two different confinement models

h lm nopq r sutvxw tyxw tz { | }~ �� i�� icycl. perm.

�

Modell A (discussed so far)

i �� t� � t� � �� i�� i

cycl. perm.

�

h lm n op q r s tvxw ty w tz { |�

� }~ i � �� t� � t� � �� i� � � � � � � � i

cycl. perm.

�

Modell B (alternative)

Although both models give exactly the same results in thenonrelativistic limit, large differences appear in a fully relativistictreatment (Salpeter equation) !

Example: Roper resonance position � � �

N*2002 Pittsburgh, 08-13.10.2002 – p.20

%&' ()'* +,-./ 0. 12 - '.3 +45 6789 :; <= :>?@ ABC > D>E >

interplay of confinementand instanton effects...

2

2

8 [56]2

48 [70]

8 [70]

8 [20]

∆−Ν

split

ting

Roper-resonance

Roper-resonance

nn3g [MeV fm ]

∆−Ν

split

ting

11PN

21+

11PN

21+

nn3g [MeV fm ]

8 [56]2

228 [70]8 [56]

8 [56]

8 [56]

8 [70]

8 [56]8 [20]

8 [70]

8 [70]

2

2

4

22

2

2 8 [56]

8 [70]

8 [70]

8 [70]8 [56]

8 [56]

8 [20]

8 [56]

8 [56]

8 [70]

8 [70]

8 [20]

8 [56]

8 [70]

2

2

2

2

2

2

2

4

2

2

2

4

2

... ...

...

...

Exp.Exp.Confinement Confinement

N

only only+ ’t Hooft + ’t Hooft

N2

Model A Model B

*

S

****

****

***

*

S

****

****

***

Mas

s [M

eV]

1000

1500

2000

2500

89.601360

�

“Correct” masssplittings result froma specific interplayof relativistic effects,the Dirac structure ofthe confinementpotential and ’tHooft’s interaction�

A reliable test ofa residual interactionin fact requires a fullyrelativistic treatment

N*2002 Pittsburgh, 08-13.10.2002 – p.21

%&' ()'* +,-./ 0. 12 - '.3 +45 6789 :; <= :>?@ ABC > D>E >

Electromagneticand strongcoupling amplitudes

Mandelstam formalism: Matrix element in initial state rest frame (IA):

�� k� �� s� { � � �� | � } ¡ ¢¤£¥s �§¦ { ¢ ¡ ¢¨£ª©s �§¦ { ¢

«¬® s£ ¯¥w £ ¯© {° ±³² s£ ± { � ° ´² s£ ´ { � ° m ² µ£ ¯m ¶ ·¹¸� �° m ² s£ m { «kº s»£¥w »£x© {

�

Reconstruction of the vertex function in the rest frame

«kº s»£¥w »£x© { | � ¼ ¡m £ ¯¥s �¦ { m ¡m £ ¯©s �§¦ { ¢ h s»£¥w »£x©w »£ ¯¥w »£ ¯© {½ º s»£ ¯¥w »£ ¯© {

�

Boost

s�w » � {ª¾ s ¿� ´ i » � ´w » � {

�� k�w ¦ � �ÁÀ �° � � � � | � } ¡ ¢¤£¥s �§¦ { ¢ ¡ ¢ £©s �§¦ { ¢

«¬® s£ ¯¥w £ ¯© {° ±Â² s£ ± { � ° ´² s£ ´ { � ° m ² µ£ ¯m ¶ � « s£ {° m ² s£ m { «kº s»£¥w »£x© {

mesonic Bethe-Salpeter amplitudes from

(M.Koll et al., Eur. Phys. J. A 9, 73 (2000))

N*2002 Pittsburgh, 08-13.10.2002 – p.22

%&' ()'* +,-./ 0. 12 - '.3 +45 6789 :; <= :>?@ ABC > D>E >

Static electromagneticproperties

from

Ã b f S -limit of form factors:

Calc. Exp.ÄªÅ �ÇÆ È � ÄÉ �ÇÆ ÈÊ } ÄÉ (PDG)ÄxË � �Æ È� ÄÉ � �Æ Ê � } ÄÉ (PDG)�ÍÌ ´ ÅÏÎ � Æ Ð �

fm

� Æ Ð � È

fm (MMD)�ÍÌ ´ ËÎ � Æ � �

fm

´ � Æ � � } Ñ � Æ � � �fm

´(MMD)� Ì ´ Åº � Æ Ê �

fm

� Æ Ð }Òfm (MMD)� Ì ´ Ëº � Æ ÐÒ

fm

� Æ Ð Ð Êfm (MMD)

ÓÔ �ÇÆ � � �ÇÆ � Ò È� Ñ � Æ � � }Õ

(PDG)¿ �ÍÌ ´ Ô � Æ Ò �fm

� Æ Ò � Ñ � Æ � �

fm (Bernard)

MMD: Mergell, Meißner, DrechselBernard: Bernard, Elouadrhiri, Meißner

N*2002 Pittsburgh, 08-13.10.2002 – p.23

%&' ()'* +,-./ 0. 12 - '.3 +45 6789 :; <= :>?@ ABC > D>E >

Octet magneticmoments

from “expectation values” of local operators with S.A.:

ÖØ× Ö ÙÚÛ Ù

Û ×Û cnp

octet magnetic moments

1/N

ÜÜÝ

0.70.60.50.40.30.20.10

3

2

1

0

-1

-2

exp. Þ basis size (calc.)

N*2002 Pittsburgh, 08-13.10.2002 – p.24

%&' ()'* +,-./ 0. 12 - '.3 +45 6789 :; <= :>?@ ABC > D>E >

Electric form factor of proton and neutron

proton neutron

MMD

¸ ´ß

GeV

´à

á â ãäå æ

32.521.510.50

1

0.8

0.6

0.4

0.2

0

SchiavillaEden

PasschierHerberg, Ostrick

Argonne V18

¸ ´ß

GeV

´ à 32.521.510.50

0.14

0.12

0.1

0.08

0.06

0.04

0.02

0

MMD: Mergell, Meißner, Drechsel

N*2002 Pittsburgh, 08-13.10.2002 – p.25

%&' ()'* +,-./ 0. 12 - '.3 +45 6789 :; <= :>?@ ABC > D>E >

Electric form factor of proton and neutron

Isoscalar/isovector contributions withoutçéè è è

isovectorisoscalar

dipole

¸ ´ß

GeV

´ à

áê ëì âãäå æ

32.521.510.50

1

0.8

0.6

0.4

0.2

0

-0.2

íËÎíÅîÎdipole

¸ ´ß

GeV

´à

áï ëð âãäå æ

32.521.510.50

1

0.8

0.6

0.4

0.2

0

-0.2

Almost perfectdipole shape

wrong asymptotics ?

N*2002 Pittsburgh, 08-13.10.2002 – p.26

%&' ()'* +,-./ 0. 12 - '.3 +45 6789 :; <= :>?@ ABC > D>E >

Magnetic form factor of proton and neutron

proton neutron

MMD

¸ ´ß

GeV

´à

á ñ òóá ô

ãäåæ

10.10.01

1.4

1.2

1

0.8

0.6

0.4

0.2

0KubonAnklinMMD

¸ ´ß

GeV

´à 10.10.01

1.4

1.2

1

0.8

0.6

0.4

0.2

0

N*2002 Pittsburgh, 08-13.10.2002 – p.27

%&' ()'* +,-./ 0. 12 - '.3 +45 6789 :; <= :>?@ ABC > D>E >

Electroweaknucleonform factors

õÁö ÷ õÁø axial form factor

Jones

¸ ´ß

GeV

´à

ó ïáï âòá

ï ñãäå æ

32.521.510.50

1

0.8

0.6

0.4

0.2

0

BloomJoos

AmaldiBrauel

delGuerra¸ ´ß

GeV

´à

á ù ãäå æ

10.80.60.40.20

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

N*2002 Pittsburgh, 08-13.10.2002 – p.28

%&' ()'* +,-./ 0. 12 - '.3 +45 6789 :; <= :>?@ ABC > D>E >

Photoncouplings

úØû üH [ GeVH `b ý

state Calc PDG Calc PDG�m m s � � } � { þÉ ± ÿ ´ � Ð Ê � � }Õ Ñ ÒþÉm ÿ ´ � � Õ � � � Õ Õ Ñ Ð

° ± ± s � Õ }Õ { þÅ ± ÿ ´ � � } Ê � Ñ }� þ Ë ± ÿ ´ � ÈÕ � � Ò Ñ � È

° ± ± s � Ò Õ � { þÅ ± ÿ ´ Ò Õ } Ñ � Ò þ Ë ± ÿ ´ � � � � � Õ Ñ � �

� ± m s � Õ � � { þÅ ± ÿ ´ � Õ } � � � Ñ Ê þ Ë ± ÿ ´ � � Õ Ê Ñ ÊþÅm ÿ ´ Õ � � Ò Ò Ñ Õ þ Ëm ÿ ´ � Õ � � � } Ê Ñ � �

� ± m s � È� � { þÅ ± ÿ ´ � � Ð � � Ð Ñ � } þ Ë ± ÿ ´ � } � Ñ Õ �þÅm ÿ ´ � � � � � Ñ � � þ Ëm ÿ ´ � Ò � � } Ñ � �

� ±� s � Ò ÈÕ { þÅ ± ÿ ´ Õ � Ê Ñ Ð þ Ë ± ÿ ´ � }Õ � � } Ñ � �þÅm ÿ ´ È � Õ Ñ Ê þ Ëm ÿ ´ � � È � Õ Ð Ñ � }

� ± ± s � � � � { þÅ ± ÿ ´ � � Ð � Ò Õ Ñ � þ Ë ± ÿ ´ � È � � Ñ � �

° m ± s � Ò � � { þÉ ± ÿ ´ � Ð � È Ñ � �

�m m s � È� � { þÉ ± ÿ ´ Ò } � � � Ñ � ÕþÉm ÿ ´ Ò Ð ÐÕ Ñ � �

N*2002 Pittsburgh, 08-13.10.2002 – p.29

%&' ()'* +,-./ 0. 12 - '.3 +45 6789 :; <= :>?@ ABC > D>E >

Transition form factors

Nucleon Delta transition

FrolovStein

FosterBartel

¸ ´ß

GeV

´à

á� ñãäå æ

43.532.521.510.50

3

2.5

2

1.5

1

0.5

0

FrolovStein

FosterBartel

¸ ´ß

GeV

´à

á� ñòá� ñã� æ

á ô ãäå æ

43.532.521.510.50

1

0.8

0.6

0.4

0.2

0

N*2002 Pittsburgh, 08-13.10.2002 – p.30

%&' ()'* +,-./ 0. 12 - '.3 +45 6789 :; <= :>?@ ABC > D>E >

Helicity amplitudes

F15(1680) Nucleon transition D15(1675) Nucleon transition

þÅm ÿ ´þÅ ± ÿ ´

þÅm ÿ ´ Burkert

þÅ ± ÿ ´ Burkert

¸ ´ß

GeV

´ à

�ï �� GeV

� ëå �

32.521.510.50

150

100

50

0

-50

-100

þÅm ÿ ´þÅ ± ÿ ´

¸ ´ß

GeV

´à

�ï �� GeV

� ëå �

32.521.510.50

10

8

6

4

2

0

N*2002 Pittsburgh, 08-13.10.2002 – p.31

%&' ()'* +,-./ 0. 12 - '.3 +45 6789 :; <= :>?@ ABC > D>E >

Strongdecaywidths

J � decay widths

� �

MeV

� � � decay widths

� �

MeV�

Decay Calc

m � � PDG Decay Calc

m � � PDG° ± ± � � Õ }Õ { ¾ �¦ } } � � Ò � Ò Ð Ñ � Õ { � ¢�� ´m ¾ �¦ � � � �

° ± ± � � Ò Õ � { ¾ �¦ } � � Ê � � � Ê Ñ � Ò { � ´�� ¢ ¾ �¦ Õ � } � Ò Ñ Õ { � ´�

� ± m � � Õ � � { ¾ �¦ } Ð È � � Ò Ò Ñ Ò { � �� ¾ �¦ }Õ }Õ � � � Ñ Ò { �m� ´

� ± m � � È� � { ¾ �¦ � Æ � } � � � � Ñ Õ { �� ¾ �¦ Ð Ð È È Ð

seen

� ±� � � Ò ÈÕ { ¾ �¦ � � Ð � Ò Ð Ñ È { � ± ¢�� ¾ �¦ }� } � � Ð } Ñ È { � ± �� ± ± � � � � � { ¾ �¦ } Ð � � � � � � Ð Ñ � Ð { � ��

� �� ¾ �¦ }Õ � � � Ð Ð Ñ � Ð { � ´�� ´��m m � � � } � { ¾ �¦ Ò � � � Ð � � � Ê Ñ � { ��

��° m ± � � Ò � � { ¾ �¦ � � Ò � } Ð Ñ È { � �� ¾ �¦ È � � Ð � Ò Ð Ñ � } { � ± ¢� ± ¢

�m m � � È� � { ¾ �¦ � � � � � Õ Ñ � Õ { � ±�� ±� ¾ �¦ Õ � � Ò � � � }Õ Ñ � Õ { � ¢�� ¢�m � � : S. Capstick, W. Roberts, Phys.Rev. D49 (1994) 4570-4586

N*2002 Pittsburgh, 08-13.10.2002 – p.32

An Instanton Induced Interactionfafnir.phyast.pitt.edu/nstar/plenaryB/metsch.pdfAn Instanton Induced...

Documents

Transcript of An Instanton Induced Interactionfafnir.phyast.pitt.edu/nstar/plenaryB/metsch.pdfAn Instanton Induced...