Transcript Partial Wave Analysis Physics based MC generators for detector optimization Integration with the software development (selected final state, with physics backgrounds event generator) Phenomenology/Theory.

Partial Wave Analysis
Physics based MC generators for detector optimization
Integration with the software development
(selected final state, with physics backgrounds event generator)
Phenomenology/Theory of amplitude parameterization
and analysis
(how to reach the physics goals. Framework exists but needs to be updated)
Software tools, integration with with the GRID
(data and MC access, visualization, fitting tools)
A Physics Goal
Identify old (a2) and new (p1) states
Data
Use data (“physical sheet”)
as input to constrain
theoretical amplitudes
Amplitude
analysis
Resonances
Resonances appear as a result
of amplitude analysis and
are identified as poles
on the “un-physical sheet”
(… then need the interpretation: composite or fundamental,
structure, etc)
Methods for constructing amplitudes (amplitude analysis)
Analyticity:
Data (in principle) allows to determine full (including “unphysical” parts)
Amplitudes. Bad news : need data for many (all) channels
Approximations:
Crossing relates “unphysical regions” of a channel with a
physical region of another another
Unitarity relates cuts to physical data
Other symmetries (kinematical, dynamical:chiral, U(1), …) constrain low-energy
parts of amplitudes (partial wave expansion, fix subtraction constant)
Example : p0p0 amplitude
Only f on C is needed !
For Re s > N use
• Regge theory
(FMSR)
To remove the s0 ! 1
region introduce subtractions
(renormalized couplings)
• Chiral, U(1)
To check for resonances:
look for poles of f(s,t)
on “unphysical s-sheet”
Im s
-t
• Unitarity
Data • Crossing
symmetry
4mp2
N
Re s
s0 ! 1
Partial wave projection  Roy eq.
in = theoretical
phase shifts
out = adds constraints
from crossing
(via Roy. eq)
Lesniak et al.
down-flat =
up-flat
two different amplitude
parameterizations which do not build in crossing
Extraction of amplitudes
t
Ea
p1
M1
a
fa a ! M1,M2,L(s,pi)
a
s
Mn
x (2mp Ea)a(t)
a
ba(t)
Use Regge and low-energy phenomenology via FMSR
To determine dependence on channel variables, sij
p- (18GeV) p  X p  h p- p
 h’ p- p
t
p-
h
a2
s
pp
Nevents
p
=
N(s, t, Mhp , W)
~ 30 000 events
Mhp , W
(A.Dzierba et al.) 2003
p- p ! hp0 n
Assume a0 and
a2 resonances
( i.e. a dynamical
assumption)
E852 data
Coupled channel, N/D analysis with L< 3
p- p ! hp- p
p- p ! h’p- p
D
D
P
S
P
f(P+)-f(D+)
|P+|2
Some comments on the isobar model
p+(1)
p-(3)
isobar
p+(2)
s13>>s23 otherwise channels overlap :
need dispersion relations (FMSR)
isobar model violates unitarity
K-matrix “improvements” violate
analyticity
Ambiguities in the 3p system
p- p ! p-p+p- p
CERN ca. 1970
E852 2003
Full sample
BNL (E852) ca 1985
Software/Hardware from
past century is obsolete
Preliminary results from full E852 sample
a2(1320)
p2(1670)
Chew’s zero ?
Interference between
elementary particle (p2)
with the unitarity cut
H000(ma2 - G < M3p < ma2 + G)
Standard MC
O(105) bins (huge !)
Need Hybrid MC !
sp+p-(1)
sp+p-(2)
r0
r0
Theoretical work is needed now to develop amplitude
parameterizations
Semi inclusive measurement (all s)
s(a p ! X n)
s = MX2
Im f(a a ! a a)
Dispersion
relations
X
Re f(M2X)
Exclusive (low s, partial wave expansion)
k = l(s,m21,m22)
f(k) / k2L