Experiments on Light Mesons (and nucleons)

David Bugg, Queen Mary, London

1) Glueballs 2) pp -> resonance -> mesons with a polarised target 3) e+e- with transversely polarised electrons 4) from 1 to 2 GeV; also hybrids

• There has been very little progress for 15 years. Why?

• The predicted low-lying glueballs with JPC = 0++, 2++, 0-+ and 2-+ mix with qq. The qq are made of nn and ss; those can be separated with dataon J/> KK (and to identify the gg component requires data on (and ’ as a check if possible). BES 2 did not attempt to study the last two, but I hope BES 3 will give it a high priority.

• For 2++, there are far too many qq states to derive from J/data alone, so these need to be taken from the extensive Crystal Barrel data. For 0-+, 4data on a2and a1are needed. It is already known that there is a strong, broad 0-+ signal; data on would also be very valuable.

Glueballs

pp

Observed states for I=0, C=+1

F states are 50-80 MeV above P states; D states lie midway

•

Quarks and nucleons have spin 1/2, so qq and pp have total spin s=0 or 1 (singlet S or triplet T); polarisation data are needed to separate singlet and triplet.

Triplet states can have L=J or J+1; Polarisation separates 3P2 and 3F2 because Clebsch-Gordan coefficients are orthogonal and very different; for C=-1 states, P separates 3S1 and 3D1; and 3D3 from 3G3. This is vital information.

d/d = Tr(A*A) = |T|2 + |S|2 and measures Re(interferences); PNd/d = Tr(A*NA) -> Im (interferences), notably Im(T*S); Phase Sensitive - hence reduces errors of M and .

PSd/d = Tr(A*SA) -> Re (same interferences) in 3-body final states.

What is needed is an extracted p beam (like LEAR) of ~5 x 104 p/s at FAIR. Is that too much to ask?

hardest case

Separation of and from backgrounds

in

’ in ’

in

in

data at 1800 MeV/c

Experiment for VEPP 2000 (and 4000) in Novosibirsk. CMS has already excellent data on e+ e- ->

It would be very valuable to measure transverse polarisation in e+

e- -> and 4to separate 3S1 and 3D1 components of states (preferably up to 2400 MeV) and likewise for states in 3and 5This requires a Siberian snake, but the technology exists in Novosibirsk. A linearly polarised photon is a superposition of initial states |1,1> and |1,-1>; interferences with S-waves generate distinctive terms cos and cos 2where is the azimuthal angle from the plane of polarisation.The measurement would identify cleanly the 1– states, which are presently poorly identified because of lack of phase information.

• Data needed from CompassAn obstacle to a clear analysis of the mass range 1 to 2 GeV is

the lack of data with good absolute normalisation on KK and 4(where data on all charge combinations including 4 are desirable).

Compass have produced good evidence confirming the existence of the 1-+ hybrid with I=1 at 1650 MeV.

Joe Dudek and collaborators have made an impressive calculation of both hybrids and mesons in the mass range 1500-2500 MeV, 1106.5515. Their masses all come out ~200-300 MeV higher than existing hybrid candidates and regular mesons from Crystal Barrel – probably because calculations were done with a rather high mass for the pion. There are 2-+ candidates 2(1870) and 2(1880); 1-- hybrids are also predicted.

The is a 0-+ candidate, but could be the missing qq second radial excitation (the missing 0-+

problem). Its I=0 companion and the I=0 1-+ hybrid are missing. BES 3 could be a good place to look for strange hybrids.

Comment on dispersive effectsThe f2(1565) is an example. At the threshold, there is

a sharp rise in the Im A(s) of g2(s); analyticity

demands a corresponding change in Re (A) = (1/)P ds’Im(s’)/(s’ – s).

The result is a sharp cusp in Re A at the threshold. The isospin partner a2(1660-1732) would have the same mass as f2(1565) in the absence of the cusp. This demonstrates dramatically that dispersive effects can shift a resonance by at least 100 MeV. WATCH OUT for such effects, even for slowly opening thresholds.

K

a0(980)

My opinion is that is a similar P-wave cusp at the KK*

threshold; is due to K rescattering to The old

can easily fit both.

.

Likewise (1405) is probably due to weak cusps at b1(1235) and f1(1285) thresholds, because Dudek cannot accommodate a hybrid at this mass.

There is an excellent review by Svarc: 1020.3045, `Reviving old, almost lost knowledge on T and K matrix poles and a link to the contemporary QCD spectrum’.

General advice on Partial Wave Analysis

(i) Keep programs as simple as possible: ~1000 trial fits are often needed for a solution. Start with the minimum number of parameters and add others 1 by 1. If in doubt, leave them out.

(ii) Preferably fit with the T-matrix, since it determines the poles which are needed. Be careful with the K-matrix if used: it requires good data on ALL channels: adding up to 1. (iii) Make sure an expert works with students, since

they invariably leave before the data are published!

iv) Many groups fit data from individual channels, e.g. separately. Much better to fit them together, since interferences may cause confusion in one channel but not in others. My experience is that the quality of the fit goes roughly as 2N, where N = number of channels; if you fit them one by one, you finish with a quality factor <N, and the difference can be enormous if N is large. Convergence is actually quicker fitting all channels together.

v) ADVERT: the hypothesis of Extended Unitarity requires the phase of two resonances with the same quantum numbers to be the same in all reactions; but experiment disagrees, see 0801.1908. Better to use the Isobar Model.

vi) GENERAL comment: it would help greatly if experimental groups would cooperate with phenomenologists who have ideas how to fit their data – subject to agreement on results!