Chiral dynamics in hard processesM.V.Polyakovhttp://www.tp2.rub.de/~maximp

Ruhr-University Bochum

Chiral symmetry breaking - the phenomenon shaping our World

New soft pion theorems in hard processes– how ChSB works for colour clusters

Data: present & possibilities to discover new chiral phenomena @ PANDA

QCD & chiral symmetry

235 QCDUm const

4 1 ( )4

a a a aQCD f f f

f

S d x G G i g t m

p QCDm const 235

2

1( ) ( )QCDtot

QCD

p U fE

2

28( )bg Mcut

QCD cutM e

11 23 3c fb N N

Contains all strong interaction phenomena

Symmetries:

0 ( ) ( )d d L f R fm m U N U N

But:1

770 1300

940 1535A

N N

m MeV m MeV

m MeV m MeV

Transmutation of dimension: scaleis given not by quark masses but

Chiral symmetry is broken spontaneosly

30 0 (250 )

350

Goldstone bosons pions

Order parameters MeV

dynamical quark massM MeV

One of puzzles: Why nucleon looks like

not like

? ?1Q Hidden small parameW y tR erh M

Nambu, Nobel Prize 2008

To solve this and other puzzles one has to understand mechanisms of ChSB in QCD.As important as understanding of confinement!

Due to spontaneous chiral symmetry breakdown: 95% mass of the nucleon is generated 95 % mass of visible Universe!

Chiral symmetry is broken spontaneously that is why:

Protons and neutrons exist and are massive

Nuclei exist

Pions are light

... We are here and can study strong interactions @ FAIR

Spontaneous breakdown of chiral symmetry really shapes our world!

Up to now ChSB phenomenon has been studied only in soft processes and it was never studied at the level of quark and gluon degrees of freedom.

generator of broken subgroup

0state i Q

Main idea of soft pion theorems is in the following equation:

5 5

. .

,a a

e g

Q x

computable by symmetry transformation

0lim ( )a B A

5 , ...ai B Q Af

Pion production near threshold*( )q

Pion is a (pseudo) Nambu-Goldstone Boson of SBChS => soft pion theorem

/Nambu, Lurie ’62Nambu, Shraumer

’62/

N

2W

N

2 2q Q

thW W m

th NW M m

These ideas created a new direction:ChPT. Note however that the fundamental d.o.f. Of QCD are not involved!

- chirally rotated e.m. current => related to axial FF

x

22 2

2

1 ( ) ( )22 A A Mn

N

QG Q g G QQ Mf

*( )thW WA p n

mO

Example:

5 5

. .

,a a

e g

Q x

Would be breakthrough if here we would have a well defined cluster of quarks and gluons! Would allow to connect ChSB with fundamendal d.o.f. of QCD! Big potential for discovery of new phenomena and understanding of mechanisms of “world shaping phenomenon” in QCD.

0lim ( )a B A

5 , ...ai B Q Af

In the limit of Nucleon FF‘s are described in terms of partons-clusters of quarks

Nucleon

2Q

2

24 (( ) ( ) (, ))S

N H NQF Q dx dy x T y

Qx y

Light-cone WF

Filtering out the lowest Fock component of the hadron‘s WF

2

4Sg

/S. Brodsky, P. Lepage/

/Efremov, Radyushkin/

*hard interactions=>pQCD

N

LC WF of nucleon

LC WF of πN system

�*

N

N

2

*4 ( ) ,HS

th NNA N N dx T xdQ

yy x y

For NS theorem to work the pion should soft relative to all hadrons!

2 0Let us take first Q and then m

thWe need this for W W m

23 / !/NW m Q show this

the pion is not soft relative to initial nucleon

32for Q

m

*

'N

N

Higher twists (1/Q2 supressed) –suppression of initial Nambu-Goldstone immision!

32For Q one has prove SPTh

m

N�*

N

N

N Lowmass system For LC WF of

What are πN WF’s when π is near threshold?

Connected by chiral rotation

0 S 6p U d U U U d d U Uf

Simple algebra!

N N

S 26

p U d U U U d d U U

a U U d d U U

a

2 2U U d d U U

f

/Pobylitsa, Strikman,MVP , PRL 2001/

New theorem = “1/2”of NS theorem

For new SPTh important that QCD is a gauge theory!

Comparison

2" " Qm

Nambu Shrauner window

* 12th A A MnA p n G g Gf

* 1 5 43 32th Mp MnA p n G G

f

/Pobylitsa, Strikman,MVP , PRL 2001/

2" " m

Our window Q

What about data?

2 2 22

136

( , ) & 9Pth

E SLAC experiment

F w Q at W W m Q GeV

/P.Bosted etal. ’94/

2

22 6

1( , )P

QF W Q for both theorems

Q

but the coefficient is given by different combinations of FF’s of nucleon

E136 experiment /Bosted et al ‘94/

22

2 2

( )( , ) *16

P Q wF W Q

22 ( , ) thF W Q at W W m

2 29Q GeV

0

2 2 2 2 2 4*

2 2 2 2

3 ( ) ( )* ( ) ( )

4( )A Mp

x p Nn

g G Q w w mA p x

w M m

2 2

2 2

( ) ( )( ) 1 1N NM m M mw

W W

*

2

2

1,42 6

2 ( , )th

GeVP

W

dw Q F W Q

0.20

0.15

0.10

0.05

5 10 15 20 25 30 Q2

2

2

1,42 6 2 8

2 ( , ) 0,1 0,02th

GeV

W

dw Q F W Q GeV

2 29136

For Q GeVE gives

80,11 0,02

New soft pion theorem

GeV

80,03 0,01

Nambu Shrauner theorem

GeV

) Nucleon FF’s from experiment /Pobylitsa, Strikman,MVP , PRL `01/

/Nambu, Shrauner PR `62/

… ? … very interesting domain Transition from one type of SPTh to another one

0.12

0.10

0.08

0.06

0.04

0.02

5 10 15 20 25 30

E136 point

Ν S

Q2~Λ3/mπ

Q2

Opportunities for PANDA

Direct mesurement of 5+ quark component of nucleon WF

Measuring different mesons we probe different components of nucleon WF

If here is a pion, eta (gluon rich) chiral dynamics and anomaly for 5 quark cluster

Possibility to figure out how the chiral symmetry is restored

Frankfurt, Strikman, MVP `98

Lansberg, Pire, Szymanowski `07

Soft relative to the proton