Rip Van Winkle looks at Multiparticle Phase Shift Analysis

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Rip Van Winkle looks at

Multiparticle Phase Shift Analysis

PTLIU Laboratory for Community Grids PTLIU Laboratory for Community Grids

Geoffrey Fox Geoffrey Fox

Computer Science, Informatics, Physics Computer Science, Informatics, Physics Indiana University, Bloomington IN 47404 Indiana University, Bloomington IN 47404

http://grids.ucs.indiana.edu/ptliupages/presentations/pwajune02.ppt http://grids.ucs.indiana.edu/ptliupages/presentations/pwajune02.ppt

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0X0

0X 0X

0X0 -t

200 GeV hp E260

E350

“infinite” Progress in Jets but not so much in understanding low p_T

hadron-hadron collisions

When I left ……..

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Apologies

 For errors and for not giving enough creditFor errors and for not giving enough credit

 I have not studied since area of science for 22 years and I have not studied since area of science for 22 years and even when I worked full time in high energy physics, I even when I worked full time in high energy physics, I

studied production amplitudes and not partial wave studied production amplitudes and not partial wave

analysis analysis

 I read many papers which suggested that open issues of I read many papers which suggested that open issues of past are still open and many of these could impact

past are still open and many of these could impact PWA

PWA

 I haven’t even adjusted to change in names of particles I haven’t even adjusted to change in names of particles …..

…..

 Think of me as a rather inaccurate conscience from the Think of me as a rather inaccurate conscience from the past

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Issues in Partial Wave Analysis

 Goal:Goal: Extract clear evidence for resonances; determine Extract clear evidence for resonances; determine masses, widths and their decay modes; compare with masses, widths and their decay modes; compare with

theoretical models; especially in areas that extend theoretical models; especially in areas that extend understanding of quark model (exotics, glueballs) understanding of quark model (exotics, glueballs)  Approach:Approach:

– e_e++ e_e-- : very clean but limited statistics and sensitivity to _{: very clean but limited statistics and sensitivity to}

structure (not all mesons/baryons of interest can be structure (not all mesons/baryons of interest can be

produced in reactions that can be detected and analysed) produced in reactions that can be detected and analysed) – _{Hadron-hadron}_{Hadron-hadron}_and_and_{photon-hadron}_{photon-hadron}_{(low p}_{(low p}_T_T_):_):

potentially (but not so far in practice) very high potentially (but not so far in practice) very high

statistics but substantial obfuscatory effects that could statistics but substantial obfuscatory effects that could

(in some cases) be impractical to disentangle (final state (in some cases) be impractical to disentangle (final state

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Hadron(Photon)-Hadron Reactions

 2  2: Obviously very clean but limited to a few obvious reactions such as γ N  π N, π N  π N etc.

– Analyses here are with good enough statistics largely

uncontroversial at partial wave analysis level. Interpretation in terms of resonances may be impossible due to small couplings etc.

 2  3 or more: π N  π π N, p p annihilation etc. where full final state partial wave analyzed

– Large increase in degrees of freedom

– Effective ways of dealing with 3 particle states usually require resonance assumptions which have intrinsic uncertainties

– Some effects (like π exchange) not studied in π N  π N

 2 (state to be analyzed) plus one or more other particles – in particular peripheral production of states to be analyzed

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Some Truths I

 Amplitudes exhibit many features for which there is no clear formalism that expresses in an integrated fashion  Analytic Structure as in S matrix with poles and cuts

– Poles correspond to particles and resonances

– Cuts to multiple exchanges (box and more complex diagrams) – Need to look at all channels to get full analytic structure

 Unitarity as a well understood (but difficult in multi-particle case to implement) constraint in every direct sub-channel

– Constraint only strong at low channel energy when one or a few possible intermediate states

s t

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Direct Channel Constraints

 Impose unitarity in s for Impose unitarity in s for 2 particle PWA

2 particle PWA

s

s₁₂₃

1

2

3

s₁₂ s₂₃

s₁₃

 Impose unitarity in Impose unitarity in ss 12

12

s

s₁₃₁₃ s s₂₃₂₃ for 3 particle for 3 particle PWA

PWA

 This is “final state This is “final state interactions”

interactions”  Unitarity in Unitarity in ss

123

123 not a not a

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Some RVW Truths II

 Spin FormalismSpin Formalism well understood both for full, decay, well understood both for full, decay, and

and ReggeRegge exchange amplitudes exchange amplitudes

– _{Extremely complex}_{Extremely complex}

 Analytic structureAnalytic structure of amplitudes well understood for t- of amplitudes well understood for t-channel (Jackson-Gottfried), s-t-channel frame helicity channel (Jackson-Gottfried), s-channel frame helicity

and transversity amplitudes and transversity amplitudes

– _{Transversity amplitudes have nice selection rules and}_{Transversity amplitudes have nice selection rules and} invariance under rotations

invariance under rotations

– _{But poor analyticity structure}_{But poor analyticity structure}

 s-channel frames-channel frame has particularly good analyticity and has particularly good analyticity and well understood “zero” structure at t=0

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Some RVW Truths III

 t(u)-channel exchanges are “classically” the forces that t(u)-channel exchanges are “classically” the forces that create the s-channel particles

create the s-channel particles

 Thus it is not trivially “wrong” that same effect (e.g. Thus it is not trivially “wrong” that same effect (e.g. diffractively produced A

diffractively produced A₁₁) can be “explained from ) can be “explained from direct or cross channel point of view

direct or cross channel point of view

 Veneziano model illustrates this in a fashion that is not Veneziano model illustrates this in a fashion that is not quantitatively useful

quantitatively useful

t

1

2

3

4 u

1

2

4

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Peripheral Production

 Choose cases where peripheral production strong to Choose cases where peripheral production strong to avoid larger backgrounds than necessary (inevitable) avoid larger backgrounds than necessary (inevitable)

Internal Exchanges

1

2

3

s₁₂ s₂₃

s₁₃

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Backgrounds I

 Many Backgrounds such as “false peripheral signal” Many Backgrounds such as “false peripheral signal”

Internal Exchanges

1

2

3

Another

Exchange Of course if original “production

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Multiperipheral Diagrams

 As in Deck modelAs in Deck model

1

2

3

Another Exchange

Production Exchange

π π

π

p p

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Backgrounds II

 Rescattering in lots of channelsRescattering in lots of channels

Internal Exchanges

1

2

3

Production Exchange

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Some RVW Truths IV

 Quark ModelQuark Model and and QCDQCD can give useful predictions as to both can give useful predictions as to both

particle spectra and branching ratios particle spectra and branching ratios

 Selection rules are always good including those reflecting Selection rules are always good including those reflecting

conservation of quark content conservation of quark content

 Regge Regge theory has a few spectacular successes in describing high theory has a few spectacular successes in describing high

energy energy scattering energy energy scattering

– Linear Linear  and and AA₂₂ exchange degenerate trajectories with exchange degenerate trajectories with =0=0 dip for dip for  and spin and spin flip nucleon coupling

flip nucleon coupling

– Pomeron_Pomeron and and  exchange are only phenomenologically understood exchange are only phenomenologically understood

– Details like polarization not understood_{Details like polarization not understood} – Absorption _Absorption(cuts) not convincing(cuts) not convincing

 Difficult to believe results sensitive to uncertainties in these Difficult to believe results sensitive to uncertainties in these

“partial” theories “partial” theories

– Some exchanges are known to be big or small and this is always seen_{Some exchanges are known to be big or small and this is always seen}

– Small high energy amplitude (e.g. backward _{Small high energy amplitude (e.g. backward}  scattering) must translate to scattering) must translate to (amplitude) cancellation at low

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Partial Wave Analysis Formalism

 Can use Density Matrix or Amplitude Can use Density Matrix or Amplitude

– Amplitude enforces rank and positivity conditions on _{Amplitude enforces rank and positivity conditions on} density matrix

density matrix

– Amplitude has in principle at least well defined _{Amplitude has in principle at least well defined} analyticity properties

analyticity properties

 Factorization (Regge exchange) suggests low rank but Factorization (Regge exchange) suggests low rank but we know this fails for

we know this fails for  exchange due to conspirator exchange due to conspirator

1

2

3

Reggeon Exchange

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Amplitudes?

 Can think in terms of Can think in terms of Beam + ReggeonBeam + Reggeon  1 + 2 + 3 amplitudes but this already shows these are not “simple” amplitudes

– Amplitudes depend on t ( mass_{Amplitudes depend on t ( mass}22_{of Reggeon) and helicities of}_{of Reggeon) and helicities of} Beam, 1 2 and 3.

Beam, 1 2 and 3.

– Multiple exchanges and cuts also increase number of amplitudes _{Multiple exchanges and cuts also increase number of amplitudes}

(even though not much quantitative evidence for them)

 Safest to use amplitude model for cases where exchanges are Safest to use amplitude model for cases where exchanges are strong

strong

 _  and exchange degenerate and exchange degenerate AA₂₂ f f₂₂ families are best families are best

– Pomeron_Pomeron probably OK but we don’t understand as well probably OK but we don’t understand as well

  with adjustment for conspirator (different naturality but with adjustment for conspirator (different naturality but structure determined at t=0)

structure determined at t=0)

– _{For example}_{For example}_B_B₁₁_{exchange (}_{exchange (}___{exchange degenerate partner) isn’t}_{exchange degenerate partner) isn’t}

very good

 Will photon beams prove harder as two helicities unless Will photon beams prove harder as two helicities unless excellent polarization data?

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Factorization Useful?

 In days gone by, we got essentially identical dynamics In days gone by, we got essentially identical dynamics from

from π- p



π0 n ; π- p



π0 inclusive ; π- p



π0 plus

any neutral

 So at least in cases where clear Reggeon exchange involved, doesn’t really matter if “target vertex” reaction clean

1

2

3

Production Exchange

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

Conspiracy

 Problems with double spin flip amplitudesProblems with double spin flip amplitudes

 Interesting to compare with Interesting to compare with  production at target production at target vertexas

vertexas  p p _ does not vanish at t=0 does not vanish at t=0



p _n

  OK with helicity 0  but naïve

factorizable  exchange vanishes when  helicity 1 – not seen

experimentally

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Fitting the Data I

 Assume Assume unlimitedunlimited computer time, disk space and computer time, disk space and network bandwidth

network bandwidth

– At least no significant constraints from these issues_{At least no significant constraints from these issues}

 Not clear to me whatNot clear to me what fitting fitting techniques used techniques used

– Typically Physics ahead of Computer Science in area of multi-_{Typically Physics ahead of Computer Science in area of} multi-parameter fitting

parameter fitting

– Maybe “unlimited computer time” and better management of _{Maybe “unlimited computer time” and better management of} results could lead to new approaches such as:

results could lead to new approaches such as:

 ““Ensemble Fitting techniques” (e.g. genetic algorithms) Ensemble Fitting techniques” (e.g. genetic algorithms) which explore parameter space more completely than

which explore parameter space more completely than

traditional (Taylor expansion) least squares methods

traditional (Taylor expansion) least squares methods – Probably not particularly to find “new solutions” but rather to _{Probably not particularly to find “new solutions” but rather to}

better depict error band of a given “solution” better depict error band of a given “solution”

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Fitting the Data II

 Data miningData mining

– Develop a suite of analysis programs that look for and catalog _{Develop a suite of analysis programs that look for and catalog}

anomalies in experiment, theory or discrepancy between them

anomalies in experiment, theory or discrepancy between them – Link to data management system to more systematically _{Link to data management system to more systematically}

categorize different fits

 Multi-dimensional Multi-dimensional Visualization Visualization (human data-mining)(human data-mining)

– We still seem to be using histograms_{We still seem to be using histograms}

– Perhaps we could develop some better “standard” displays _{Perhaps we could develop some better “standard” displays}

supported as a Web Services with portlet interfaces (to betray my

current expertise)

– Printed version of Phys. Rev. Letter still has histogram playing _{Printed version of Phys. Rev. Letter still has histogram playing}

role of “icon”. There is also a URI (Universal Resource

Identifier) which is active in on-line version and gives the “new

nifty display”

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Some lessons I

 All confusing effects existAll confusing effects exist and no fundamental (correct) way to and no fundamental (correct) way to remove. So one should:

remove. So one should:

– Minimize effect of the hard (insoluble) problems such as _{Minimize effect of the hard (insoluble) problems such as}

“particles from wrong vertex”, “unestimatable exchange effects”

sensitive to slope of unclear Regge trajectories, absorption etc.

 Note many of effects (exchanges) are intrinsically MORE Note many of effects (exchanges) are intrinsically MORE important in multiparticle case

important in multiparticle case than in relatively well than in relatively well

studied

studied π N  π N

 Try to Try to estimate impactestimate impact of uncertainties from each effect on of uncertainties from each effect on results

results

– Need systematic very high statistic studies of relatively clean _{Need systematic very high statistic studies of relatively clean}

cases where spectroscopy may be uninteresting but one can

examine uncertainties

– _{Possibilities are}_{Possibilities are}_A_A₁₁_A_A₂₂_A_A₃₃_B_B₁₁_{peripherally produced and even}_{peripherally produced and even}_{π N}

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Some lessons II

 Theory failed to provide convincing parameterizable Theory failed to provide convincing parameterizable amplitudes one could use to fit/explain data

amplitudes one could use to fit/explain data

 Theory provided some quantitative constraints (pi pole, Theory provided some quantitative constraints (pi pole, unitarity, kinematics …), many qualitative truths

unitarity, kinematics …), many qualitative truths

which overlap and whose effect can be estimated with which overlap and whose effect can be estimated with

errors from 10 to 100% errors from 10 to 100%

 20 years ago, Rip van Winkle dozed off as not clear 20 years ago, Rip van Winkle dozed off as not clear how to make progress

how to make progress

 Now we must take a factor of 100 or so more data to Now we must take a factor of 100 or so more data to tackle problem phenomenologically

tackle problem phenomenologically  First step is to clarify techniqueFirst step is to clarify technique

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Effects to Include I

 Spin Formalism:Spin Formalism: Need BOTH Need BOTH

– _{Amplitude Parameterization – is this practical if}_{Amplitude Parameterization – is this practical if} (potential) rank high as with photon beams or non (potential) rank high as with photon beams or non

factorizing exchanges? factorizing exchanges?

– _{Density Matrix Formalism – how does this cope with}_{Density Matrix Formalism – how does this cope with} explicit contributions, analyticity etc.

explicit contributions, analyticity etc.

– _{Transversity versus helicity formalism needs to be}_{Transversity versus helicity formalism needs to be}

investigated – trade-off of analyticity versus selection investigated – trade-off of analyticity versus selection

rules rules

 Unitarity:Unitarity: use current approaches building in two- use current approaches building in two-particle unitarity (final state interactions)

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Effects to Include II

 Exchange Contributions:Exchange Contributions: Identify all allowed (by Identify all allowed (by

normal Regge phenomenology) exchanges and catalog normal Regge phenomenology) exchanges and catalog

where expected to be large due to coupling constants where expected to be large due to coupling constants

and/or values of

and/or values of (t,u)(t,u)

 Use usual duality type arguments to identify related Use usual duality type arguments to identify related ss AB

AB

t u

t u exchanges i.e. where you might expect the direct exchanges i.e. where you might expect the direct and crossed descriptions to be related

and crossed descriptions to be related

 Develop models for exchange contributions using Develop models for exchange contributions using

simple phenomenological Regge theory but have little simple phenomenological Regge theory but have little

hope this is very reliable except for Pomeron,

hope this is very reliable except for Pomeron,  A A₂₂ etc. etc. exchanges and even these won’t be so good as to be

exchanges and even these won’t be so good as to be used at low direct channel energies

used at low direct channel energies

– Identify all _{Identify all} exchange contributions and expect these to be exchange contributions and expect these to be reliable (with “conspirator) near t=0 but unreliable away from

reliable (with “conspirator) near t=0 but unreliable away from

there --

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Effects to Include III

 Cutkosky style Accelerated Convergence is certainly Cutkosky style Accelerated Convergence is certainly sound but possibly easier to explicitly include high sound but possibly easier to explicitly include high

partial waves rather than choose an expansion that partial waves rather than choose an expansion that

maximizes convergence maximizes convergence

– Certainly examine exchanges and ask if partial waves larger than _{Certainly examine exchanges and ask if partial waves larger than}

those includes are important (in amplitude). If so include

those includes are important (in amplitude). If so include – _{Could also choose Cutkosky style expansion functions}_{Could also choose Cutkosky style expansion functions}

 Dispersion Relations and other AnalyticityDispersion Relations and other Analyticity

– In an amplitude model, it is useful to examine “spin dependent” _{In an amplitude model, it is useful to examine “spin dependent”}

kinematic zeroes and the duality style cancellations

– Present data and fits in a way to display effect (e.g. fixed u cross _{Present data and fits in a way to display effect (e.g. fixed u cross}

sections for reactions with no u channel exchanges) – check

qualitatively reasonable

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What else we can do?

 Exploit modern computing technology forExploit modern computing technology for

– _{More reliable optimization methods}_{More reliable optimization methods}

– _{Management of Data before and after analysis}_{Management of Data before and after analysis}

 GriPhyn and PPDG like efforts will address a lot of base GriPhyn and PPDG like efforts will address a lot of base

technology for data handling before analysis

 Management of Analysis – Computation and Data – open Management of Analysis – Computation and Data – open

issue

– _{Powerful multi-dimensional visualization techniques and}_{Powerful multi-dimensional visualization techniques and}

– _{Data mining to discover anomalies in data and/or fits and/or}_{Data mining to discover anomalies in data and/or fits and/or}

discrepancies between fits and data