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 J PC = 0 ++, 2 ++, 0 -+ and 2 -+ mix with qq. The qq are made of nn and ss; those can be separated with data  on 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 -+, 4  data on  a 2  and a 1  are 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 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); P N d  /d  = Tr(A*  N A) -> Im (interferences), notably Im(T*S); Phase Sensitive - hence reduces errors of M and . P S d  /d  = Tr(A*  S A ) -> Re (same interferences) in 3-body final states. What is needed is an extracted p beam (like LEAR) of ~5 x 10 4 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 4  to separate 3S1 and 3D1 components of  states (preferably up to 2400 MeV) and likewise for  states in 3  and 5  This 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 2  where  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 Compass An 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 MeV, Their masses all come out ~ 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= hybrid are missing. BES 3 could be a good place to look for strange hybrids.

Comment on dispersive effects The f 2 (1565) is an example. At the  threshold, there is a sharp rise in the Im A(s) of g 2   (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 a 2 ( ) would have the same mass as f 2 (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    a 0 (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 b 1 (1235) and f 1 (1285) thresholds, because Dudek cannot accommodate a hybrid at this mass.

There is an excellent review by Svarc: , `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 2 N, 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 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!