physics based mc generators for detector optimization integration with the software development...
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Physics based MC generators for detector optimizationIntegration 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)
Partial Wave Analysis
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Identify old (a2) and new (1) states
Resonances appear as a result of amplitude analysis and are identified as poles on the “un-physical sheet”
A Physics Goal
Use data (“physical sheet”) as input to constrain theoretical amplitudes
Data ResonancesAmplitudeanalysis
(… then need the interpretation: composite or fundamental, structure, etc)
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Analyticity:
Methods for constructing amplitudes (amplitude analysis)
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)
Data (in principle) allows to determine full (including “unphysical” parts)Amplitudes. Bad news : need data for many (all) channels
Approximations:
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Example : 00 amplitude
Only f on C is needed !
To check for resonances:look for poles of f(s,t)on “unphysical s-sheet”
-t 4m2 Re s
Im s
s0 ! 1
Data
To remove the s0 ! 1region introduce subtractions(renormalized couplings)• Chiral, U(1)
For Re s > N use • Regge theory(FMSR)
• Unitarity• Crossing symmetry
N
Partial wave projection Roy eq.
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down-flatup-flat
two different amplitude parameterizations which do not build in crossing
in = theoretical phase shifts
=
out = adds constraints from crossing (via Roy. eq)
Lesniak et al.
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Extraction of amplitudes
t
(t)
f a ! M1,M2,(s,pi)Ea
(2mp Ea)(t)
sa
aM1
Mn
p1
Use Regge and low-energy phenomenology via FMSR To determine dependence on channel variables, sij
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(18GeV) p X p - p ’ p
~ 30 000 events
Nevents = N(s, t, M)
p p
-a2
-
t
M
s
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- p ! 0 n
Assume a0 and
a2 resonances
(A.Dzierba et al.) 2003
( i.e. a dynamical assumption)
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E852 data
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- p ! - pCoupled channel, N/D analysis with L< 3 - p ! ’- p
D
S P
D
P
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|P+|2
(P+)-(D+)
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Some comments on the isobar model
isobar
+(1)
-(3)
+(2)
s13>>s23 otherwise channels overlap : need dispersion relations (FMSR)
isobar model violates unitarity
K-matrix “improvements” violate analyticity
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Ambiguities in the 3 system
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- p ! -+- p
BNL (E852) ca 1985
CERN ca. 1970E852 2003Full sample
Software/Hardware from past century is obsolete
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Preliminary results from full E852 sample
a2(1320)2(1670)
Chew’s zero ?
Interference between elementary particle (2) with the unitarity cut
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s+-(1)s+-(2)
0
0
H000(ma2 - < M3 < ma2 + )
Standard MC O(105) bins (huge !) Need Hybrid MC !
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Theoretical work is needed now to develop amplitude parameterizations
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X
(a p ! X n) Im f( a ! a)
Semi inclusive measurement (all s)
Dispersion relations
Re f(M2X)
Exclusive (low s, partial wave expansion)
s = MX2
f(k) / k2L
k = (s,m21,m2
2)