contentsbatta/jlab/wp.pdf · 2012. 10. 18. · quarks, the gluon eld. in principle such states...

Contents

1 Preface 2

2 Why Spectroscopy 3

2.1 Historical Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Experiments 10

3.1 Direct channel production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.1.1 Effective Lagrangians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2 Peripheral production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.2.1 Physics at JLab12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2.2 Physics at COMPASS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.3 Annihilation reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.3.1 Physics at VEPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3.2 Physics at BESIII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.3.3 Physics at PANDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4 Theory and Phenomenology 19

4.1 Quark Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.2 Fundamental Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.3 How to do analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5 Tools 23

6 Challenges and future steps 24

Bibliography 24

1

1 Preface

The International Workshop on New Partial Wave Analysis Tools for Next Generation Hadron

Spectroscopy Experiments ATHOS12 took place in Camogli, Italy, from June 20th to June 22nd,

2012. The workshop focused on the development of amplitude analysis tools for meson and baryon

spectroscopy, and complemented other programs in hadron spectroscopy organized in the recent

past, including the INT-JLab Workshop on Hadron Spectroscopy in Seattle in 2009, the Interna-

tional Workshop, on Amplitude Analysis in Hadron Spectroscopy at the ECT*-Trento in 2011, the

School on Amplitude Analysis in Modern Physics in Bad Honnef in 2011 and the Jefferson Lab

Advanced Study Institute Summer School in 2012.

Hadron spectroscopy has been at energy frontier some forty years ago. At that time a profound

understanding of hadron reaction theory has been achieved and sophisticated amplitude analysis

techniques have been proposed. For many years, however, poor data quality and limited com-

putational resource impaired application of high-level amplitude analysis in hadron spectroscopy.

These barriers no longer exist. Several experiments devoted to hadron spectroscopy have been in

operation over the past few years and more are planned for the near future. This new generation

of high statistics and precision experiments demands a level of detailed partial wave decomposition

and amplitude analysis never achieved before. After almost half a century since the birth of the

quark model there is finally an opportunity to reveal the complete hadron spectrum.

The aim of this document is to define the goals for the field of hadron spectroscopy for the next

decade. We discuss the theoretical tools and experimental analyses that need to be carried out in

order to achieve these goals and propose a framework for how to organize future activities.

2

2 Why Spectroscopy

As a consequence of strong interactions, as described by the Quantum Chromodynamics (QCD)

the bulk of hadron mass originates from interactions between quarks and gluons. These interactions

result in forces which are of the order of a ton and are exchanged between constituents over distances

smaller then 10−15m. One the most challenging problems in physics is to understand such systems,

where relativistic quantum mechanic couples with strong interactions. Hadron spectroscopy is

therefore not only a laboratory for studying implications of QCD but it could also serve as a

template for strong interaction models describing the universe beyond the Standard Model.

2.1 Historical Perspective

The bubble chamber experiments carried in the middle of the past century lead to discovery

of plethora of hadrons. Three flavors of quarks were introduced as the fundamental constituents

of hadrons to describe the systematic patterns observed in hadron masses and decay properties.

Observation of hard scattering in deep inelastic scattering (DIS) of electrons on protons confirmed

existence of isolated point-like scattering centers a.k.a quarks. Despite there being no evidence in

nature for isolated quarks their existence inside hadrons is by now well established. Furthermore,

deviations from the ideal hard scattering model, which are manifested in scaling violations in DIS

yielded support to the SU(3) color gauge theory as the fundamental theory of strong interactions

–QCD.

There is by now ample experimental evidence that QCD is the underlying theory of strong

interactions and that quarks and the gauge bosons, gluons are the fundamental constituents of

hadrons. As predicted, by QCD interactions between energetic patrons ı.e. quarks and gluons

becomes asymptotically free. In this domain systematic calculations in QCD are possible and

are based on perturbation theory. Inside hadrons, however, the average energies and momenta of

partons are below the scale at which perturbation theory can be justified and hadron properties

are determined by interactions that are genuinely non-perturbative in nature. In this context it is

for example still a big mystery why the naive quark model gives such a good description of hadron

properties. With various many-body techniques it has been possible to provide some credence to

3

CHAPTER 2. WHY SPECTROSCOPY 4

quark model nevertheless solid understanding of the physics behind it is still lacking. It is therefore

necessary to distinguish the fundamental quarks of QCD and the constituent quarks of the quark

model. In terms of the latter baryons are considered to be three-quark bound states and mesons

are a constituent quark-antiquark pairs.

2.2 Future directions

A new frontier in hadron physics opened with advances in lattice gauge theory simulations.

These are still somewhat limited when applied to hadron spectroscopy, as numerical algorithms for

including open decay channels are not yet fully implemented. Nevertheless, even the current lattice

spectrum compares well with the observed one. Interestingly lattice simulations predict a number

of extra states that are not yet well established experimentally. These include hybrid baryons and

mesons, e.g. states that have significant overlap with operators that contain, besides the valence

quarks, the gluon field. In principle such states could exist in nature and there is no evidence that

these states are lattice artifacts. On the contrary there are numerous studies in phenomenological

models that produce such states.

Perhaps the biggest change in our understanding of the hadron spectrum has been the complete

lattice QCD calculations of the meson and baryon spectrum. The light-quark meson spectrum

has been presented in several publications, which can be most easily summarized by Figure 2.1 [?,

?]. These calculations not only present the masses of the normal light quark mesons, for both

the isovector and isoscalar states, but they also predict the nonet mixing angles. In the cases

where experimental results are available, these results are in remarkable agreement. While these

calculations were carried out using a pion mass of 396MeV/c2, in comparison to experiment, all the

predicted masses are about 15% too high, thus allowing one to scale predictions to the physical mass.

The entire meson spectrum is certainly a tour-de-force by itself, but the calculations also predict

the spectrum of exotic quantum-number states as well. By itself, the spectrum is quite different

from that predicted by the flux-tube model. In particular, the lightest nonet is the JPC = 1−+,

with an excited state seen about 300MeV above it. Roughly degenerate in mass to the second


0.5

1.0

1.5

2.0

2.5

exotics

isoscalar

isovector

YM glueball

negative parity positive parity

Figure 2.1: The light-quark meson spectrum as predicted by lattice QCD[?, ?].

1−+ nonet is a 0+− and a pair of 2+− nonets. The same mechanism that allowed the calculation

to assign explicit JPC quantum numbers to the particular states also allowed the calculation to

measure the amount of gluon field in each of the states. For the exotic quantum-number states,

the gluonic content is large, while for what would be considered the normal qq states, it is small.

There are however three nonet that are roughly degenerate with the lightest 1−+ state. These have

the quantum numbers 1−−, 0−+ and 2−+, allowing us to form the lightest supermultiplet of hybrid

mesons as

JPC = 1−−, (0, 1, 2)−+ .

A similar calculation for the cc system has also been performed [?], where the same conclusions can

be drawn, (see Fig, 2.2). At first glance, this reminds us of the bag-model prediction, but it turns

out that models where the constituent glue can be treated as JPgCgg = 1+− allow us to describe

not only the lowest supermultiplet, but also the higher-mass states. In the latter case, they consist

of the glue coupled to a P -wave meson. The reason why the JPgg = 1+ is energetically favored

over the JPgg = 1− configuration has its rooting in the structure of the QCD non-abelian Coulomb


potential. It is also explains the unusual parity ordering in the spectrum of glue-lumps. These are

hypothetical states of the gluon field bound to a point-like color source, which can be realized, for

example in lattice simulations.

Not only has the spectrum of qq states been calculated, but also the light-quark baryon spec-

trum [?, ?] which has also been extended to include the Ξ states [?] as well as hybrid baryons [?].

While none of the hybrid baryons have exotic quantum numbers, it is interesting to note that the

same conclusions about both the JPC of the constituent glue as well as the mass spitting from the

lightest qqq states to the hybrid states agrees with that in the meson spectrum.

On the experimental front, the state of the field of hybrid hadron spectroscopy is reasonably well

described in recent reviews. On the topic of glueballs [?], lattice QCD [?, ?] predicts a spectrum

of states, with the lightest one having 0++ quantum numbers. Above this, one expects a 2++ and

a 0−+ state. Unfortunately, all of these have normal quantum numbers, just like the ordinary qq

mesons, so in all likelihood, they will be mixed with the isoscalar members of nearby qq nonets of

the same quantum numbers. Unfortunately, there has been little progress since the last review, with

the situation being that the 0++ glueball is mixed with the P -wave scalar mesons. This manifests

itself as the three isoscalar states: f0(1370), f0(1500) and f0(1710). We are starting to see some

results from BES-III that may help with this situation, but they are still very preliminary

For the exotic quantum-number mesons [?], while the situation with the lattice has advanced

significantly over the last two years, experimentally, the situation remains similar to where it was

two years ago. There is evidence for three JPC = 1−+ isovector states, the π1(1400), the π1(1600)

and the π1(2015). The lightest has only been observed decaying to πη, and is too light to be

considered a hybrid meson. There are a number of studies that suggest this is a non-resonant effect,

possibly related to cusp effects due to two-meson thresholds. The π1(1600) has been reported in

a number of final states: ρπ, η′π, b1π and f1π. However, the original very strong signal reported

in 3π has been questioned by alternative analyses. While the COMPASS experiment appears to

see a strong signal in their 3π data off lead, for similar data on hydrogen, the interpretation is still

somewhat open [?]. However, for the η′π decay mode, COMAPSS has shown a clear signal for their

proton data [?]. Finally, CLEO-c has looked at the decay of χ1 states to γη′π and observe a strong


1 arXiv:1204.5425 243, Mπ ≈ 400 MeV

c.f. light mesons [PR D84, 074023 (2011)] and baryons [arXiv:1201.2349]

in L=0, with gluonic 1+-

in L=1, with gluonic 1+-

Charmonium Spectrum Figure 2.2: Charmonuim spectrum from the

lattice. The highlighted levels correspond to

states with significant overlap onto gluonic

operators. They seem to be forming two mul-

tiplets which can be interpreted in a model

which introduces constituent gluons coupled

to the charm-anticharm quark pair in the

color octet state.

signal in the exotic 1−+ wave that is consistent with the π1(1600) [?]. We also note, as reported

here, that the new CLAS analysis on photo production sees no signal for the π1(1600) decaying to

3π in photo production. We note that their analysis applies cuts that limit the production to π

exchange, so studies with both Pomeron and ρ exchange will need to wait for the higher energies

available with GlueX.

While we see suggestions for two isovector 1−+ states that are consistent with the lattice QCD

prediction, what are still missing are the isoscalar partners to these: η1 and η′1, as well as members

of the other exotic quantum number nonets. For the 2+−, these would be the b2, h2 and h′2, while

for the 0+− nonet, this would be the b0, h0 and h′0. Identification of some reasonable subset of these

states is needed to experimentally confirm what we now expect from lattice QCD.

While lattice calculations of the spectrum of excitations from first principles have developed

rapidly in recent years, there is still a lot of work to be done to understand these states in more

detail and realism. As described above most calculations are done at unphysically heavy light

quark masses and this must be rectified. A more substantial issue is how to deal with resonances

and scattering channels in lattice calculations. This is made difficult by the use of the Euclidean

space-time metric in lattice calculations to enable importance sampling Monte Carlo investigation,

which obscures scattering data. Luscher’s method provides a framework for understanding elastic

scattering, but solid foundations for a study of inelastic scattering are missing. It remains to be

seen how these spectra are related to the properties of the scattering amplitudes. In the elastic


approximations the Luscher algorithm for computing the later can be used and Fig. 2.3 shows the

comparison between lattice and experimental phase shifts for isospin-2 ππ S-wave amplitude.

ππ I=2 phase shi+

0

arXiv:1203.6041 Mπ ≈ 400 MeV

Figure 2.3: I = 2 S-wave ππ phase shift

2.3 Goals

Hadron spectroscopy aims at identification of hadron resonances and determination of their

properties. In the naive quark model all hadrons are bound states of constituent quarks. In reality,

these become resonances, which decay strongly to ground state hadrons, i.e. QCD states that are

stable under strong decays – pions, kaons, etas and nucleons. As resonance mass increases multi-

particle channels open up, resonances become broad and overlapping and their identification more

difficult. The goal is therefore to pin down the spectrum in the so called resonance region which

typically corresponds to excitation energies no grater then 2 GeV.

Resonances are properties of partial wave scattering amplitude in the unphysical domain of

kinematical variables, energy and/or angular momenta. Thus identification of resonances requires

amplitude analysis. The fundamentals of amplitude construction follow from the S-matrix theory.

Depending on the kinematical coverage of an experiment different aspects of the S-matrix theory

become relevant. For example, low-energy scattering is dominated by a few elastic partial waves,


which may be constrained by unitarity, while resonance production with high-energy beams may

require knowledge of singularities in the complex angular momentum plane Reggeons.

In general amplitude analysis can be considered as a three-step process. In step-one, theoretical

amplitudes are proposed and constrained by fitting the experimental data. In step-two, these

amplitudes are tested against various constraints that are used to minimize unresolved ambiguities

in amplitude determination. Finally in step-three the amplitudes are extrapolated (analytically

continued) to the unphysical kinematical region of energy and angular momentum to determine

properties of resonances.

It is likely that the lattice will continue to provide a very valuable guide to experimental searches

in the next generation of experiments. Coupling of emerging lattice results with the analysis

technique described above will extend the role of lattice QCD spectroscopy calculations beyond

just to motivate an experiment but to make contact between amplitudes measured experimentally

and QCD. The lattice can measure amplitudes for processes such as radiative transitions, and one

fruitful avenue for starting the process is in photo-production experiments. This is certainly an

active field of research in lattice groups interested in next-generation hadron spectroscopy.

3 Experiments

There are number of hadron programs in operations now and several are expecting for the near

future. The JLab12 upgrade with two new detectors GlueX and CLAS12 foresees a dedicated

program of spectroscopy with the aim of finding sub GeV hybrids. We can expect in the future

further results from e+e− machines SuperB, LhCb, SuperBelle, BES. We have the renascence of

antiproton facility with FAIR at Darmstadt where the antiproton storage ring has been designed

primarily for hadron spectroscopy

The specifications for the next generation experiment in hadron spectroscopy are: hermetic

detectors for both charged and neutral particles, with excellent resolution and particle identification

capability; beam energy high enough to have a sufficient phase space for the production; high

statistics are needed together with sensitivity to production cross sections at the sub-nanobarn

level; network work for the development of common analysis tools.

The type of reactions used of investigations of hadron spectrum can be broadly classified as:

direct production quasi-elastic or diffractive production and annihilation reactions

3.1 Direct channel production

Low energy, elastic or quasi-elastic meson nucleon scattering are key to baryon spectroscopy.

The Particle Data Group (PDG) reports on the status of hadron spectroscopy. It consists of a

comprehensive summary of all results from past and present experiments. Most of our knowledge

on N∗ and ∆ resonances stems from elastic and inelastic πN scattering experiments from more than

30 years ago. Phase shift analysis in the elastic region is a well-defined procedure that yields the

scattering amplitude from the experimental data with only a few discrete alternative solutions. As

the elastic pion nucleon scattering is still the best way for precise partial wave analyses. Availability

of secondary hadron beams, e.g. at JPark or EIC would be required to further improve the data

set. Fortunately in the last 20 years the electron accelerators e.g. at JLab, ELSA, MAMI, have

considerably improved and new detectors and targets have been designed and went in operation.

We are now in a situation, where the photo- and electro-production of pseudoscalar mesons carry

the highest potential to investigate the baryonic spectrum. In addition to the resonance positions

10

CHAPTER 3. EXPERIMENTS 11

and strong residues, which describe couplings to decay channels, the electromagnetic couplings and

transition form factors are being investigated. The data taken at JLab, in particular with the HD-

ICE target, will provide information on the γ-neutron couplings of excited states. As data stems

from the neutron bound in the deuteron, one has to undertake extra effort to unfold the desired

multipoles from deuteron effects, such as Fermi motion, double scattering, and other nuclear effects.

For today, the experimental information on the reactions on the proton is substantially larger then

that on the neutron (15% of the full γ → πN database) especially for polarized experiments (17%

of the neutron database). Only with good data on both proton and neutron targets, one can hope

to disentangle the isoscalar and isovector EM couplings of the various N∗ and ∆∗ resonances, as

well as the isospin properties of the non-resonant background amplitudes. The SAID group at GW

has made much progress in this direction.

The cleanest possibility for this investigation is photo-production of single pseudoscalar mesons

as π, η, K and η′ off the nucleon. In addition ππ photo-production is an important channel that

couples strongly to many baryon resonances. Single pseudoscalar meson photo-production is de-

scribed by a set of only 4 transition amplitudes (invariant, spin, transversity or helicity amplitudes).

Near threshold low energy theorems are very helpful for charged pion production and up to about

500 MeV photon energy, the Watson theorem due to two-body unitarity gives a very important

constraint. Strictly this is violated already at the ππ threshold but it can be extended well above

until the region of the Roper, the second nucleon resonance.

There exist a well established analysis procedure that allows to analyze partial wave amplitudes

directly from the data . It is a truncated partial wave analysis, where t-channel and u-channel

exchanges with poles close to the physical region can give rise to higher partial waves, and may

be treated in terms of Reggeon amplitudes. For photon laboratory energies up to about 1 GeV

typically only a few e.g. S,P,D and F waves (`max = 3) need to be included. For lower energies, e.g.

up to 500 MeV already S and P waves can be sufficient, which was successfully applied in the 80s

by a Kharkov/Lebedev group. With modern accelerators and detectors a much higher statistics

can be reached, so that also in this region a truncation with `max = 2 should be aimed.

This procedure has been used in the past successfully in fits to πN , KN and data. The


powerful technique of finite energy sum rules provides further constraints been the background,

Reggeon exchange and low-spin resonance amplitudes.

3.1.1 Effective Lagrangians

While these well established techniques still await implementation in the analysis of modern data

sets, there have been significant activity in ”interpretation” of the data in terms of various models

of meson-nucleon effective interactions.

The analysis technique discussed above follows the three-step approach outlined in Sec. 2.3. In

recent years a different approach has been pursued. In particular there have been various attempts

to construct reaction amplitudes from an underlying dynamical models. Some models are motivated

by the phenomenological, meson-exchange model of nuclear forces, while other introduce quark de-

grees of freedom thorough a set of ”bare” hadrons together with residual interactions to account for

meson-nucleon channels. These so-called dynamical coupled channel models have been developed,

e.g., at the Excited Baryon Analysis Center (EBAC) and in the Julich/Athens/GWU collaboration.

Yet another class of models aims at restoring unitarity through explicit introduction of coupled-

channels using the pole-dominated K-matrix paramterization of the partial waves. The objective

of these approaches is to: develop a dynamical reaction model to analyze meson production reac-

tions, extract masses (pole position) and coupling constants (residue of amplitude) of the nucleon

resonances, and to provide interpretation resonance parameters. The Julich and the EBAC groups

performed a combined analysis of γN , πN → πN, ηN,Kλ,KΣ reactions. It is an ongoing and un-

settled challenge to connect theory predictions from quark models, Dyson-Schwinger approaches,

or lattice QCD, to the results obtained in the intense experimental programs. These models try to

make a direct connection to these while sidestepping the rigor of S-matrix theory. In the search

for excited baryons, considerable progress has been made in the analysis of the corresponding data.

Still, no consensus has been reached yet on the resonance content

It is clear that with such effective models there is large correlation between the number of

extracted resonance poles and the input parameters. It is a reflection of the CDD ambiguities,


Figure 3.1: Baryon spectrum: messes (left) and widths (right) from the EBAC model

which can only be removed when constraints from crossed channels and analyticity in complex

angular momenta are implemented. An effort should be made to test the various amplitudes

produces in these approaches against such constraints.

3.2 Peripheral production

At small scattering angle, when the center of mass energy of colliding hadrons is significantly

above the resonance region, the reaction amplitude factorizes into a product of beam and target

fragmentation sub-processes mediated by the Pomeron/Reggeon exchange. With a meson or the

photon as a beam and nucleon as a target beam fragments provide the laboratory to study meson

resonances while the target fragments carry information about baryon resonances. Beam fragmen-

tation has been the primary source of information about meson-meson phase shifts and two- and

three-body resonance decays. Description of the vertex representing beam-Reggeon scattering to a

few meson fragments follows the same general principles of the S-matrix program. Regge theory

describes interactions between hadrons at large values of relative energy and angular momenta. It

enables to describe the bulk of the production strength outside of the resonance region. The later

is parameterized in terms of a few partial waves at low masses and spins. Simultaneously removing


Figure 3.2: Baryon spectrum from the Particle Data Group with certain new states from ... analyses

these contributions from Reggeon exchange amplitudes avoids double counting. Parameters of the

low-spin partial waves are fitted to the data and self-consistency between the low- (resonance) and

high-energy (Regge) regions is checked/enforced through constrains which result from analyticity

of the full amplitude, e.g. finite energy sum rules. Thus, for example high-energy pion fragmen-

tation into ρπ is dominated by Pomeron exchange which describes high-energy πN diffraction.

The component of the π-Pmeron→ ρπ vertex at large ρπ invariant mass, ( sρπ > (2 GeV)2 ) is

described by (Reggezed) pion-exchange while the resonance ρπ region is expected to be dominated

by IG = 1− resonances of the a and π mesons. Before the recent generation of experiments, such as

E852 at BNL or COMPASS at CERN there was a huge ambiguity with the a1 resonance. Its pro-


duction in πN → 3πN diffraction could not have been unanimously established do to similarities

of shape of the resonance production amplitude with that of the pion diffraction background. The

double-Regge pion diffraction conventionally parameterized in terms of the Deck-Stodolsky model,

was found significant and when extrapolated to low sρπ would account for a significant part of the

JPCIG = 1++1−, a1 wave. This is shown in Fig. 3.3 and should be contrasted with the a1 resonance

signal observed in the COMPASS experiment.

Figure 3.3: The JPC = 1++ wave. Left : CIPS 40 GeV data compared with two models of the

Deck amplitude,. Right: COMPASS 190 GeV data. compared with the Deck amplitude.

3.2.1 Physics at JLab12

The search for mesons with exotic quantum numbers is the primary aim of the GlueX experiment at

a future 12 GeV upgrade of Jefferson Laboratory, a $300M project with the first physics results in

2014. The GlueX experiment will map out the meson spectrum with unprecedented statistics using

photo-production, which is a complementary reaction mechanism to other, studied so far (which

include hadro-production with pion, kaon, or proton beams, or heavy meson decays). With 9 GeV

photons the mass range extends up to 2.5 ? 3 GeV and will cover the region where the light exotic

multiplet is expected. A complementary meson spectroscopy program will be carried at the Hall-B

with the new CLAS12 detector. The technique, electro-production at very low Q2 (0.01 - 0.1 GeV2)


provides a high photon flux and a high degree of linear polarization and represents a competitive

and complementary way to study the meson spectrum and production mechanisms with respect

to real photo-production experiments. After a calibration period, the detector will begin to record

data in 2015. Both GlueX and CLAS12 physics programs will start in conjunction with the analysis

of the golden channels ?, ?’ and 3 for the detection of hybrid mesons. A detailed theoretical study

on these channels is then required in the near future for the success of these experiments.

3.2.2 Physics at COMPASS

COMPASS is a high-energy physics experiment at the Super Proton Synchrotron at CERN in

Geneva. One of the purposes of this experiment is the study of hadron spectroscopy with high

intensity hadron beams. COMPASS aims, with his high statistical accuracy, to gain more insight

into the new states which cannot be explained within the constituent quark model and which

were interpreted as glueballs or hybrid states. This goal could not be reach without a fruitful

collaboration with theorists. Data with pion and proton beams on proton target have already

been collected in 2008, 2009 and 2012. COMPASS has already recorded events of various final

states in 2008-2009 (110M events for 3π 150k events for KKππ , 110k events for η′π , 35k events

for ηπ , etc.). This collaboration involves 250 physicists in 21 European institutions. Thanks to

their accuracy COMPASS will improve our knowledge on meson spectroscopy and will set up on

the existence or the absence of exotic hadrons. Its goals could be only achieved by mean of an

active collaboration with theorists, i.e. by matching their data with theoretical predictions. This

collaboration should be set up in the near future to be optimal.

3.3 Annihilation reactions

Annihilation of e+e− and pp have been a relatively recent addition to the host of reactions

in hadron spectroscopy. The early experiments in the SLAC-LBL e+e− storage ring (SPEAR)

produced many of the first measurements in the charmonium spectrum. They were followed by


CLEO, BES, Babar with Belle, BESIII and VEPP still in operation. Charmonium decay data sets

have been supplemented by the bottomoum decay data and open flavor D and B meson decays.

Proton-antiproton annihilation was studied at the Low Energy Antiproton Ring (LEAR) at CERN

and new experiments at center of mass energy above charm threshold are plans for the FAIR tacitly.

Decays of heavy flavors are not only a source of light hadrons but are a primary source of

information on the weak sector. During the B-factory age, the program to extract weak interaction

parameters (as the CKM matrix elements) or to study New Physics effects went through the

analysis of decays with final states with at least three particles. Final state interactions can share

light at any new physics at distance scales much shorter then those of strong interactions. Light

hadron final state interactions bring in phases, which interfere with the weak phases and have to

be included in amplitude analysis. For example D0 → Ksππ amplitude depends on the week CKM

phase γ which can only be extracted if the strong Kπ and ππ phases are known.

It should be noted that in principle the same amplitude analysis tools applied to beam or

target fragmentation can be used in the analysis of annihilation channels. Thus a comprehensive

amplitude analysis efforts will serve all experiments.

3.3.1 Physics at VEPP

Since 2010 experiments are in progress at the upgraded VEPP-2000 e+e− collider operated in the

center-of-mass (c.m.) energy range from threshold of hadron production up to 2 GeV with two

detectors, CMD-3 and SND. The peak instantaneous luminosity is currently 2 × 1031 cm−2 s−1

and should reach ∼ 1032 cm−2 s−1 after the new injection complex is commissioned in 2013. The

goal of the CMD-3 and SND experiments is to study spectroscopy of the light vector mesons

(ρ, ω and φ and their excitations) and measure cross sections of various exclusive channels of e+e−

annihilation with high accuracy. Such measurements should help in clarification of the muon g− 2

puzzle and provide detailed studies of the dynamics of the mult-ihadron final states. The expected

data samples should be sufficiently large for disentangling various intermediate mechanisms, as was

already shown in the first high-statistics studies of the four-pion final state in e+e− annihilation


at CMD-2 [?, ?] and τ decays at CLEO [?]. The a1π dominance with admixtures of the ρf0 for

the 2π+2π− and the ωπ0 for the π+π−2π0 final state discovered by CMD-2 was later confirmed by

BaBar [?, ?] in a broader energy range, where the ρf2(1270) as well as some other mechanisms

were observed. A crucial issue for successful partial wave analysis is to use full information about

events rather than separate invariant mass distributions only. With the integrated luminosity of

2-3 fb−1 planned to collect in the c.m. energy range from 1 to 2 GeV one expects data samples of

105 and larger for the dominant final states with three to six pions.

The VEPP-4M e+e− collider covers a c.m. energy range from 2 GeV to 11 GeV. It is currently

operated in the charmonium family range with the KEDR detector. Successful application of two

methods of the high-precision determination of the absolute beam energy, resonant depolarization

and Compton backscattering, resulted in various experiments with record accuracy. Among them

are measurements of the J/ψ and ψ(2S) masses [?], of the total and leptonic width of the J/ψ [?],

ψ(2S) [?], ψ(3770) [?], the D0 and D± masses [?], the τ lepton mass [?] as well as a search for

narrow resonances from 1.85 GeV to J/ψ [?]. Also planned is a new measurement of R up to

8 GeV.

3.3.2 Physics at BESIII

With 1 billion J/ψ and 0.4 billion ψ(2S) expected by the end of 2012 the precision spectroscopy

amplitude analysis can be performed.

3.3.3 Physics at PANDA

PANDA is one of the major projects at the FAIR-Facility in Darmstadt. FAIR is an extension of

the existing Heavy Ion Research Lab (GSI) and is expected to start its operation in 2014. PANDA

studies interactions between antiprotons and fixed target protons and nuclei in the momentum

range of 1.5-15 GeV/c using the high-energy storage ring HESR. The PANDA collaboration with

more than 450 scientists from 17 European countries intends to do basic research on various topics

around the weak and strong forces, exotic states of matter and the structure of hadrons.

4 Theory and Phenomenology

4.1 Quark Model

The quark model not only provided the first classification of the hadron spectrum but it also

shed light on the observed systematics in hadronic reactions. Practical failure of the hadronic

bootstrap and existence of rising Regge trajectories indicate that short-range aka quark exchange

forces are responsible for generation of resonances in the direct channel. Hadron exchange forces

may lead to residual threshold effects but generally are not strong enough to produce bound states.

Quark exchange diagrams therefore explain duality between exchange and direct channel reactions,

aka correlation between exchange degeneracies of selected Regge trajectories and absence of flavor

exotic resonances.

4.2 Fundamental Theory

From Geoffrey: Reaction amplitudes should follow the S-matrix theory. The theory aims at

construction of amplitudes based in principles of analyticity, using as dynamical input unitarity

and crossing symmetry. Singularities are determined by bound states, resonances and thresholds

and Regge theory provides constraints between direct channel and crossed-channel dynamics. The

S-matrix theory is correct but incomplete e.g. it does not specify the number Regge poles, not it

leads to a close set of equations for the amplitudes. Reggeons and particles are not Born terms that

otherwise could, together with unitarity drive the amplitude. They represent the full amplitude in

appropriate kinematical regions and adding effects such as final state interactions on top of Regge

poles can be misleading.

Such S-matrix constraints are the only ”first principle” tools for constructing the amplitudes

and knowing when and how to use them in the prerequisite in amplitude analysis. For example in

the case of peripherally produced particles the basic amplitude is Beam + Reggeon→ Final State

as illustrated in Fig. 4.1, 4.2. The separation between Reggeon and resonance contribution is based

on the range of sub-channel energies and angular momenta. The connection between the two is

provided by duality: exchange Reggeons are dual to Reggeons in the direct-channel and the diffrac-

19

CHAPTER 4. THEORY AND PHENOMENOLOGY 20

tive/Pomeron component is dual to direct-channel backgrounds possibly related to production of

glueballs. A rigorous connection can be formulated on the basis of dispersion relations and represent

in terms of finite energy sum rules.

Reggion- beam closely related to particle-beam (analyticity understood)

target

“slow”

2

rapidity gap

beam

“fast”

3

As12

s23

te3exchange particle

(Reggion)

1

Figure 4.1: Factorization in peripheral production. Upper vertex represents beam fragmentation

and is described by beam + Reggeon scattering.

4.3 How to do analysis

• (Regge - low partial waves) + low partial waves (discuss progress in ππ scattering with chiral

p.t constraints on Roy equations, Pelaez contribution)

• FESR


2

rapidity gap

beam

“fast”

3

As12

s23

te3exchange particle

(Reggion)

1

rapidity gap

rapidity gap

low energy PW/resonances

rapidity gap

=

+Figure 4.2: Specific, non-overlapping contri-

butions to the Beam + Reggeon→ 3 particles

amplitude.


• Words on final state interactions in low partial waves (Schneider contribution)

• Deck and multiple-regge exchanges

• Lovelace-Veneziano (interesting to apply in annihilation)

• Special topics: conspiracy, EXD, daughters, cuts, ...

• Tests: ππ, ππN production.

5 Tools

There are no longer experimental or technological barriers to incorporating theoretical innova-

tions into experimental analyses. Several software packages exist that can perform fits to exper-

imental data using arbitrarily complicated amplitudes (see, for example, the AmpTools package1

developed at Indiana University). These amplitudes can be written either directly by theorists or

by experimentalists in collaboration with theorists. This is an important milestone – there are no

longer experimental or technological excuses for oversimplified analyses.

Tools for Collaborative Code Development

• Common code repository (can link to already existing sourceforge repositories:

– Collect amplitude code, Collect tools: data-readers, minimizers, integrators, plotters,

parallelization libraries ....

– Exchange ideas (code snippets),

– Ecosystem of coexisting, independent codes

– Authorship issues t.b.d.

Amplitude Database

• Start to collect database to consolidate data from present and future experiments

• Guidelines for meanigful amplitude parameterization formats

• Solve authorship issues

• Implement quality assurance

1http://sourceforge.net/projects/amptools

23

6 Challenges and future steps

There needs to be a close collaboration between experimentalists, theorist, phenomenologist and

computer scientists. There are no essential obstacles blocking a theorist’s access to data analysis. If

a theorist is interested in describing a particular physics channel, and if an experiment has relevant

data, the theorist should approach that experimental group and offer to collaborate. Experimental

groups should in turn seek out theorists willing to write amplitudes to describe experimental data.

However, policies need to be put in place to facilitate such interactions.

We propose to establish a set of communication tools to help shorten the feedback-loop between

theorists and experimentalists across different groups and collaborations.

• A web-portal where physicists interested in amplitude analysis can register to and find col-

laborators

• A quarterly(monthly?) newsletter on developments in the filed.

• Wiki (or similar): Multipurpose knowledge database on amplitude analysis: guide to the (old)

literature, references with annotations, mini-reviews, check-lists, ”Lessons learned”, quality

standards.

• VAMP Sessions : Virtual Amplitude-analysis Methods Panel: biweekly amplitude-analysis

seminar via video-conference

24

Bibliography

25

contentsbatta/jlab/wp.pdf · 2012. 10. 18. · quarks, the gluon eld. in principle such states...

Documents