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