Transcript Columbia 2012

Nucleon Transition Formfactors with MAID
from Low to High Q²
Lothar Tiator
Johannes Gutenberg Universität Mainz
CRC 1044
Nucleon Resonance Structure in Exclusive Electroproduction at High Photon Virtualities
EmNN*2012, University of South Carolina, Columbia, SC, 2012
2 very recent review articles on this subject:
Electromagnetic excitation of nucleon resonances
LT, Dieter Drechsel, Sabit Kamalov and Marc Vanderhaeghen
European Journal Special Topics 198, 141-170 (2011)
Electroexcitation of nucleon resonances
Inna Aznauryan and Volker Burkert
Progress in Particle and Nuclear Physics 67, 1-54 (2012)
theoretical poles and experimental bumps
poles in the
complex plane
bumps on the
physical axis
W
N and D resonances with overall 3 and 4 stars
below 2 GeV (new, PDG2012)
<- new in PDG2012
<- upgraded from **
99
7
4
5
1
weak
2
2
weak
very strong
weak
weak
8
strong
3
strong
6
6
no pole
weak
nucleon response
to real and virtual photons
Inclusive Cross Section for Real and Virtual Photo Absorption
Inelastic Electron Scattering in the Resonance Region
in general:
transition form factors can only be obtained by
•
partial wave analysis, e.g. MAID, JLab
separate S11, P11, P33, D13, F15, etc from angular distributions
•
and background / resonance separation
separate bg and res parts in each partial wave
Form Factors in the Electroproduction Process
Form Factors in MAID2007
MAID
s-channel resonance contributions
unitarity is build in through coupling to other open channels:
e.g.
for S11(1535)
background - I
background - II
background - III
background from unitarization (in K-matrix approximation):
(Born + Vec)(1 + i tpN) = Born+Vec + i BV tpN
other background contributions, not included in MAID:
- loop contributions from pion rescattering
- loop contributions from channel coupling with hN, KL, KS, rN, ...
- u-channel resonance contributions
- t-channel Regge contributions (more important for high W than high Q²)
data base for pion electroproduction
(from Mainz, Bonn, Bates and JLab, mostly from CLAS)
definition of the NN* transition form factors
helicity amplitudes:
Sachs form factors:
covariant form factors:
for spin ½ resonances as Roper P11 or S11 we get only 2 ff
helicity amplitudes and form factors
N to Delta (1232) transition form factors
MAID analysis
JLab analysis
one of few cases with disagreement
between Mainz and JLab analysis
MAID
Sato-Lee
N to Delta (1232) transition form factors
MAID analysis
JLab analysis
MAID analysis revisited
for narrow energy range ~ 1232 MeV
one of few cases with disagreement
between Mainz and JLab analysis
MAID
Sato-Lee
perturbative QCD
helicity asymmetry and pQCD limit
P33
(hard) spin-flavor excitation, pQCD may show up at much larger Q²
D13, F15 (soft) orbital excitation in the quark model
D15, P13 behave differently (A3/2 dominates at Q²~ 3 GeV²)
empirical parametrizations
the magnetic ND form factors has a very simple form
Q²max
10 GeV²
for all other resonances we use the general form:
numerical examples for a few resonances:
(complete results are found in our Review EPJ ST 198 (2011) 141)
5 GeV²
5
5
5
5
5
5
?
4
?
4
4
4
empirical parametrizations for large Q²
the Maid parametrization with Gaussian forms for large Q²
is convenient and leads to fewer terms
However, it violates pQCD, which predicts:
A1/2(Q²) ~ 1/Q3
A3/2(Q²) ~ 1/Q5
S1/2(Q²) ~ 1/Q3
new ansatz:
transition FFs for N -> N*(1440) and N -> N*(1535) excitation
from MAID and JLab analysis
transition FFs for N -> N*(1520) and N -> N*(1680) excitation
data :
practically all
underlying cross sections
that went into the fits
are from CLAS
analysis :
MAID
MAID
JLab
new JLab pp
Mokeev et al.
spatial distribution of charge and magnetization
spherical charge densities in a 3-dim sphere:
r
traditional way for nuclei A>>1 with ff in the Breit frame
F(Q2) = GE(Q2), GM(Q2) : Sachs ff
transverse charge densities on a 2-dim disc:
by
bx
more correct way for light systems with ff in the infinite momentum frame
F(Q2) = F1(Q2), F2(Q2) : Dirac/Pauli ff
transverse transition densities
for the Nucleon and N -> Roper excitation
transition form factors on the lattice
N -> Delta
N -> Roper
Huey-Wen Lin et al., 2008
Constantia Alexandrou et al., 2008
N-Roper
quenched with mp=720 MeV
N-Delta
unquenched with mp=360 MeV
F1
GM
F2
pion cloud problem at small Q²
lattice update 2011/12
N -> Delta
Constantia Alexandrou et al., 2011
preliminary result 2012
with large error
N -> Roper
Huey-Wen Lin et al., 2011
Summary
with the unitary isobar model we have analyzed p0 and p+
electroproduction data in the range 0 < Q² < 5 GeV²
(in the D(1232) range up to 8 GeV²)
for most 4* resonances we have obtained
single-Q² amplitudes A1/2, A3/2, S1/2
and Q²-dependent transition form factors
this kind of analysis should also work up to Q² = 10 GeV²
at least for helicity l=1/2 : A1/2(Q²) and S1/2(Q²)
A3/2ND(Q²) is perhaps the only l=3/2 transition form factor
surviving at Q² = 10 GeV²
transition FFs for N -> N*(1675) and N -> N*(1720) excitation