Transcript Strong Decays and Couplings

Ted Barnes
Physics Div. ORNL and
Dept. of Physics, U.Tenn.
(and DOE NP)
Fermilab
25 Jan 2008
PP and Charmonium
1. What GSI needs to know:
Associated charmonium production cross sections
at low to moderate energies
s ( pp -> cc + m )
(Will show recent theoretical calculations of these cross sections,
Together with all the data in the world.)
2. Why is this intrinsically interesting?
One e.g. NNJ/y or NNJ/y coupling: How does QCD do this?
How do other cc states compare?
1. What GSI (PANDA) is all about:
The search for non-qq mesons.
To most sane theorists this means qq + gluonic excitation,
= “hybrid mesons”.
(Light-q multiquark systems spontaneously dissociate, leaving their advocates
behind.)
PC
Smoking gun: hybrids can have all J , unlike qq.
PC
Just search for a meson with J -exotic quantum numbers;
0
--
;1
-+
,2
+-
,3
-+
,4
+-
, …
Panda logic:
Light meson studies (u,d,s) were already well underway (prev. LEAR, BNL, JLAB),
How about going to heavy quarks? cc-hybrids? Narrower states, cleaner spectrum.
PC
J -Exotic Charmonium hybrids = the ultimate goal of PANDA / GSI.
We already have the LEAR community (ca. 300 people). Let’s use pp.
PANDA at GSI…
(ProtonAntiprotonaNnihilationexperimentatDArmstadt)
pp -> cc + m, cc-H + m
“m” = light meson(s)
Kinematics of pp -> cc + m
½
s
p beam energies…
KEp = 0.8 – 14.5 [GeV]:
Allows access to cc and
cc-H mass range.
Y(4415)
cc-H 4.3 [GeV]
X(3872)
J/Y(3097) hc(2980)
Why associated production? ( pp -> cc + m, (cc)H + m )
Problem:
PC
You can’t make J -exotics in s-channel pp annihilation (as in
E760/835 here at Fermilab), since pp only accesses conventional
PC
meson (qq) quantum numbers. To make J - exotic hybrids you have
to make something else to recoil against (associated production):
something else
0
e.g. typically p
p
p
qq quant. nos. only
p
PC
p
All J quant. nos.,
including cc-hybrids
PC
with exotic J
New Problem:
Let’sJust
lookhow
at allbig
the
are
world’s
thesedata.
cross sections?
0
s ( pp -> p J/y )
E760
All the world’s (published) data on
pp -> cc + meson (exclusive) processes.
our calc.
Evidently ca. 0.1–0.2 [nb] near threshold for J/y . Other states, other energies??? Nada.
pp  J/y +
0
p
from continuum
Expt…
Only 2 E760 points published.
This is E835, c/o D.Bettoni.
Physical cross sec is
ca. 100x this.
M. Andreotti et al., PRD 72, 032001(2005)
What PANDA needs to know:
What are the approximate low-E cross sections for pp -> Y + meson(s) ?
(Y is a generic charmonium or charmonium hybrid state.)
Recoil against meson(s) allows access to JPC-exotic Y.
2. Theoretical estimates of low to moderate energy
associated charmonium cross sections
s ( pp
->
cc + m )
(What you can do in lieu of a direct measurement of these cross sections.
Also includes other possible experiments.)
The actual processes are obscure at the q+g level, so “microscopic” models
will be problematic. We just need simple “semiquantitative” estimates.
A quick run through the literature (just 4 references) …
Approximate low to moderate-E cross sections for pp -> Y + meson(s) = ?
Four theor. references to date:
1. M.K.Gaillard. L.Maiani and R.Petronzio, PLB110, 489 (1982).
PCAC W(q) (pp -> J/y + p 0 )
2. A.Lundborg, T.Barnes and U.Wiedner, PRD73, 096003 (2006).
Crossing estimates for s( pp -> Y m ) from G( Y -> p p m)
(Y = y, y ’ ; m = several)
3. T.Barnes and X.Li, hep-ph/0611340, PRD75, 054018 (2007).
PCAC-like model W(q), s ( pp -> Y + p 0 ), Y = hc, y, c0, c1, y ‘
4. T.Barnes, X.Li and W.Roberts, arXiv:0709.4491v2, PRD to appear soon.
[3] model, e+e- -> J/y -> pp (for BES), pp -> J/y + p 0
W and s. Dirac and Pauli strong ppJ/y FFs. Polarization.
1. M.K.Gaillard. L.Maiani and R.Petronzio, PLB110, 489 (1982).
PCAC-like model W(q) (pp -> J/y + p 0 )
Soft Pion Emission in pp Resonance Formation
Motivated by CERN experimental proposals. Assumes low-E PCAC-like
dynamics with the pp system in a definite J,S,L channel. (Hence not immediately
useful for total cross section estimates for PANDA.)
Quite numerical, gives W(q) at a specific Ep(cm) = 230 MeV as the only example.
Implicit analytic results completed in Ref.2.
2. A.Lundborg, T.Barnes and U.Wiedner,
hep-ph/0507166, PRD73, 096003 (2006).
“summer in Uppsala, c/o U.Wiedner”
Charmonium Production in pp Annihilation:
Estimating cross sections from decay widths.
Crossing estimates:
We have experimental results for several decays of the type Y -> ppm.
These have the same amplitude as the desired s( pp -> Y m ).
Given a sufficiently good understanding of the decay Dalitz plot, we can
usefully extrapolate from the decay to the production cross section.
n.b. Also completes the derivation of some implicit results for cross sections in
the Gaillard et al. PCAC-like paper.
0th-order estimate: assume a constant amplitude, then
s( pp -> Y m ) is simply proportional to G(Y -> ppm ).
Specific example, s( pp -> J/y + p 0 ):
we know …
we want …
p0
J/y
A
A
p
p
p0
p
p
These processes are actually not widely separated kinematically:
J/y
 dt
For a 0th-order (constant A) cross section estimate we can just swap
2-body and 3-body phase space to relate a generic cc
s( pp -> Y p0 )
to
G( Y
->
pp p0 )
Result:
where AD is the area of the decay Dalitz plot:
Next, an example of the numerical cross sections predicted by this simple
estimate, compared to the only (published) data on this type of reaction…
s( pp -> J/y p0 ) from G( J/y -> pp p0 ),
compared to the E760 data points:
const. amp. model
our calc.
all the world’s published data (E760)
Not bad for a first rough “phase space” estimate.
Improved cross section estimates require a model of the reaction dynamics (next).
Other channels may be larger,
however the constant Amp approx
is very suspect. N* resonances?
3. T.Barnes and Xiaoguang Li,
hep-ph/0611340; PRD75, 054018 (2007).
“summer in Darmstadt, c/o K.Peters”
Associated Charmonium Production in
Low Energy pp Annihilation
Calculates the differential and total cross sections for pp -> Y + p 0
using the same PCAC type model assumed earlier by Gaillard et al.,
but for incident pp plane waves, and several choices for Y: hc, y, c0, c1, y ‘.
The a priori unknown Ypp couplings are taken from the (now known)
pp widths.
PCAC model of pp
->
T.Barnes and X.Li,
hep-ph/0611340; PRD75, 054018 (2007).
Y + p0:
Assume simple pointlike hadron vertices;
gpg5 for the NNp vertex, GY = gY (g5,
Y =
-i gm,
-i, -i gm g5) for
(h , J/y and y’, c ,
c
0
c)
1
Use the 2 tree-level Feynman diagrams to evaluate ds/dt and s.
gpg5
+
GY
mp = 0 limit, fairly simple analytic results…
unpolarized differential cross sections:
simplifications
M = mY
ri = mi / m
m = mp
2
2
x = (t - m ) / m
2
y = (u - m ) / m
2
f = -(x+y)
2
2
2
= (s - mp - M ) / m
also, in both d<s>/dt and <s>,
(in the analytic formulas)
mp = 0 limit, fairly simply analytic results…
unpolarized total cross sections:
(analytic formulas)
However we would really prefer to give results for physical
masses and thresholds. So, we have also derived the more
complicated mp .ne. 0 formulas analytically.
e.g. of the pp -> J/y p0 unpolarized total cross section:
This is where it gets
really interesting.
Values of the {appY} coupling constants?
To predict numerical pp -> Y + p0 production cross sections in this model,
we know gppp = 13.5 but not the { gppY }. Fortunately we can get these new
coupling constants from the known
Y -> pp partial widths:
gpg5
Freshly derived formulas for G( Y -> pp ):
GY
Resulting numerical values for the { gppY } coupling constants:
(Uses PDG2004 total widths and pp BFs.)
!!
!
Now we can calculate NUMERICAL total and differential cross sections for
pp -> any of these cc states + p0.
We can also answer the big question,
Are any cc states more produced more easily in pp than J/y?
0
(i.e. with significantly larger cross sections than s ( pp -> p J/y ) )
0
s( pp -> J/y p ), PCAC-like model versus “phase space” model:
G(J/y -> pp)
and gNNp=13.5
Input
“real dynamics”
0
G(J/y -> p pp)
input
“phase space”
And the big question…
Are any other cc states more easily produced than J/y?
ANS: Yes, by 1-2 orders of magnitude!
Final result for cross sections. (All on 1 plot.)
Have also added two E835 points (open) from a PhD thesis.
An interesting observation:
The differential cross sections have nontrivial angular dependence.
e.g. This is the c.m. frame (and mp=0) angular distribution for
pp -> hc p0
at Ecm = 3.5 GeV:
beam axis
Note the (state-dependent) node, at t = u.
Clearly this and the results for other quantum numbers
may have implications for PANDA detector design.
Predicted c.m. frame angular distribution for pp -> hcp0
normalized to the forward intensity, for Ecm = 3.2 to 5.0 GeV by 0.2.
spiderman plot
Predicted
hc -> pp p0
Dalitz plot.
(c/o Xiaoguang Li)
2
Mp p
2
[GeV ]
The t=u node in
pp -> hcp0 maps
into a diagonal
DP node.
2
Mpp [GeV ]
2
Predicted c.m. frame angular distribution for pp -> J/y p0
normalized to the forward intensity, for Ecm = 3.4 to 5.0 GeV.
Predicted
J/y -> pp p0
Dalitz plot.
(c/o Xiaoguang Li)
2
Mp p
2
[GeV ]
No t=u node, just a
local minmum.
2
Mpp [GeV ]
2
Summary:
1. Re GSI:
For studies of JPC-exotics in pp collisions you need to use
associated production.
In the charmonium system even basic benchmark reactions like
pp -> J/y p0
are very poorly constrained experimentally . Measuring this and
related ss for various cc + light meson(s) m would be very useful.
We have predictions.
2. Re direct s-channel: pp -> Y
Measurement of pp couplings of known cc states and new cc-ish
candidates like X(3872) is very important, both to see if they
are evident, fix widths and BFs, and to quantify their pp couplings.
END