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) p+p- -> 4p from 1 to 2 GeV; also hybrids
Glueballs
• 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 data on J/y -> gpp, gKK (and gKKpp); to identify
the gg component requires data on ghh (and ghh’ 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/y data
alone, so these need to be taken from the extensive Crystal
Barrel data. For 0-+, 4p data on rr, ss, a2p and a1p are needed.
It is already known that there is a strong, broad 0-+ signal; data
on KKpp would also be very valuable.
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.
ds/dW = Tr(A*A) = |T|2 + |S|2 and measures Re(interferences);
PNds/dW = Tr(A*sNA) -> Im (interferences), notably Im(T*S);
Phase Sensitive - hence reduces errors of M and G.
PSds/dW = Tr(A*sSA) -> 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 h and w from backgrounds
data at 1800 MeV/c
h->3p in hp
h’ in h’p
w->pg in wp
h in ggp
Experiment for VEPP 2000 (and 4000) in Novosibirsk.
CMS has already excellent data on e+ e- -> 6p.
It would be very valuable to measure transverse polarisation in
e+ e- -> pp and 4p to separate 3S1 and 3D1 components of r
states (preferably up to 2400 MeV) and likewise for w states
in 3p and 5p. 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 f
and cos 2f, where f 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 pp -> KK
and 4p (where data on all charge combinations including 4p0
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 h2(1870) and p2(1880); 1-- hybrids
are also predicted.
The p(1800) 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 effects
The f2(1565) is an example. At the ww threshold, there is a sharp
rise in the Im A(s) of g2wwr(s); analyticity demands a
corresponding change in Re (A) = (1/p)P ds’Im(s’)/(s’ – s).
The result is a sharp cusp in Re A at the ww 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.
My opinion is that h(1475) is a similar P-wave cusp at the KK*
threshold; h(1405) is due to Kk rescattering to hpp. The old
h(1440) can easily fit both.
.
p
k
p
K
a0(980)
h
Likewise p1(1405) is probably due to weak cusps at b1(1235)
and f1(1285) thresholds, because Dudek cannot
accommodate a hybrid at this mass.
General advice on Partial Wave Analysis
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’.
(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. pp, hh, 4p,
KK, KKpp . . . 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!