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

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)

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:

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.

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.

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

(18GeV) p X p - p ’ p

~ 30 000 events

Nevents = N(s, t, M)

p p

-a2

-

t

M

s

- p ! 0 n

Assume a0 and

a2 resonances

(A.Dzierba et al.) 2003

( i.e. a dynamical assumption)

E852 data

- p ! - pCoupled channel, N/D analysis with L< 3 - p ! ’- p

D

S P

D

P

|P+|2

(P+)-(D+)

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

Ambiguities in the 3 system

- p ! -+- p

BNL (E852) ca 1985

CERN ca. 1970E852 2003Full sample

Software/Hardware from past century is obsolete

Preliminary results from full E852 sample

a2(1320)2(1670)

Chew’s zero ?

Interference between elementary particle (2) with the unitarity cut

s+-(1)s+-(2)

0

0

H000(ma2 - < M3 < ma2 + )

Standard MC O(105) bins (huge !) Need Hybrid MC !

Theoretical work is needed now to develop amplitude parameterizations

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)