Charmonium Production at PANDA

1. Estimates of associated charmonium cross sections at PANDA1. Estimates of associated charmonium cross sections at PANDA

( ( pppp ccc + m + m ) )

2. Comments re vector charmonium strong decays:

and

Ted BarnesPhysics Div. ORNL andDept. of Physics, U.Tenn.Hirschegg 18 Jan. 2007

1. Estimates of associated charmonium cross sections 1. Estimates of associated charmonium cross sections at PANDAat PANDA

( ( pppp ccc + m + m ) )

PANDA at GSI… pp cc + m, cc-H + m (ProtonAntiprotonaNnihilationexperimentatDArmstadt)

p beam energies… KEp = 0.8 – 14.5 [GeV]: “m” = light meson(s); needed

to allow cc-H = JPC exotics

c

Invariant mass formed in pp collision in s-channel.

J/

X(3872)

cc-H 4.3 [GeV]

Production cross sections??

What PANDA needs to know:

What are the approximate low-E cross sections for pp + meson(s) ?

( is a generic charmonium or charmonium hybrid state.) Recoil against meson(s) allows access to JPC-exotic .

The actual processes are obscure at the q+g level, so “microscopic” models will be problematic. We just need simple “semiquantitative” estimates.

Three references to date:

1. M.K.Gaillard. L.Maiani and R.Petronzio, PLB110, 489 (1982). PCAC Wpp J )

2. A.Lundborg, T.Barnes and U.Wiedner, PRD73, 096003 (2006). Crossing estimates for ( pp m) from ( p p m) (’ ; m = several)

3. T.Barnes and X.Li, hep-ph/0611340. PCAC-like model W ( pp ),

c

‘

1. M.K.Gaillard. L.Maiani and R.Petronzio, PLB110, 489 (1982). PCAC Wpp J )

Soft Pion Emission in pp Resonance Formation

Motivated by CERN experimental proposals. Assumes low-E PCAC dynamicswith 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() at a specific E

(cm) = 230 MeV as the only example.

Implicit analytic results completed in Ref.2.

Crossing estimates:

We have experimental results for several decays of the type ppm. These have the same amplitude as the desired ( pp 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 paper.

0th-order estimate: assume a constant amplitude, then ( pp m) is simply proportional to ppm ).

Specific example, pp J ):

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.

These processes are actually not widely separated kinematically:

p

we know … we want …

J/

p

p

A

p

A

J/

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

( pp ) to ( pp

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…

( pp J/ ) from ( J/ pp

compared to the E760 data points:

our calc.

Not bad for a first rough “phase space” estimate. Improved cross section estimates will require a detailed model of the reaction dynamics.…but is that really ALL the data?

const. amp. model

all the world’s published data (E760)

pp pp J/ J/ + + 00 from from continuumcontinuum

M. Andreotti et al., PRD 72, 032001(2005)

Expt…

Only 2 E760 points published.

This is E835(D.Bettoni, yesterday)Physical cross sec is ca. 100x this.

Other channels may be larger,however the constant Amp approxis very suspect. N* resonances?

Calculates the differential and total cross sections for pp

using the same PCAC type model assumed earlier by Gaillard et al.,but for incident pp plane waves, and several choices for

c

‘

The a priori unknown pp couplings are taken from the (now known)pp widths.

3. T.Barnes and Xiaoguang Li, hep-ph/0611340.

“summer in Darmstadt, c/o K.Peters”

Associated Charmonium Production in Low Energy pp Annihilation

Assume simple pointlike hadron vertices;

g

5 for the NN vertex,

= g

(

5, -i

, -i, -i

5) for

cJ/and’

Use the 2 tree-level Feynman diagrams to evaluate d/dt and .

g

5

PCAC model of pp + 0: (T.Barnes and X.Li, hep-ph/0611340)

+

m = 0 limit, fairly simple analytic results…

unpolarized differential cross sections:

(in the analytic formulas)

simplifications

M = m

m = mp

x = (t - m2) / m2

y = (u - m2) / m2

f = -(x+y) = (s - m

2 - M 2) / m2

also, in both d</dt and <,

r i = m

i / m

(analytic formulas)

m = 0 limit, fairly simply analytic results…

unpolarized total cross sections:

However we would really prefer to give results for physicalmasses and thresholds. So, we have also derived the morecomplicated m

.ne. 0 formulas analytically.

e.g. of the pp J/ 0 unpolarized total cross section:

Values of the {} coupling constants?

To predict numerical pp + 0 production cross sections in this model, we know g

pp = 13.5 but not the { g

pp }. Fortunately we can get these new

coupling constants from the known pp partial widths:

Freshly derived formulas for ( pp ):

Resulting numerical values for the { gpp

} coupling constants:

(Uses PDG2004 total widths and pp BFs.)

g

5

!!

!

Now we can calculate NUMERICAL total and differential cross sections for pp any of these cc states + .

We can also answer the big question,

Are any cc states more produced more easily in pp than J/?

(i.e. with significantly larger cross sections)

( pp J/ ), PCAC-like model versus “phase space” model:

And the big question…

Are any other cc states more easily produced than J/? ANS: Yes, by 1-2 orders of magnitude!

Final result for cross sections. (All on 1 plot.)

Have also added two E835 points from a PhD thesis (open pts.).

An interesting observation:

The differential cross sections have nontrivial angular dependence.e.g. This is the c.m. frame (and m

=0) angular distribution for

pp c at E

cm = 3.5 GeV:

Note the (state-dependent) node, at t = u.

Clearly this and the results for other quantum numbers may have implications for PANDA detector design.

beam axis

Predicted c.m. frame angular distribution for pp c

normalized to the forward intensity, for Ecm

= 3.2 to 5.0 GeV by 0.2.

spiderman plot

Predicted c.m. frame angular distribution for pp J normalized to the forward intensity, for E

cm = 3.4 to 5.0 GeV.

Next steps using this model:

1. Publish this paper! (hep-ph/0611340)

2. Polarization predictions are nontrivial.

3. Extend to other baryon resonances, e.g. N*(1535). This is important e.g. for production.

2. Comments re vector charmonium strong decays:

and

Most results shown here are abstracted from T.Barnes, S.Godfrey and E.S.Swanson, PRD72, 054026 (2005).

S*S OGE

Z(3931), X(3943), Y(3943) C = (+)

Fitted and predicted cc spectrumCoulomb (OGE) + linear scalar conft. potential

model black = expt, red = theory.

states fitted

(4260), (4320) JPC = 1- -

What are the total widths of cc states above 3.73 GeV?

(These are dominated by open-flavor decays.)

23.0(2.7) [MeV]

80(10) [MeV]

62(20) [MeV]

103(8) [MeV]

PDG2006 values

X(3872)

Open-charm strong decays: 3P0 decay model (Orsay group, 1970s)qq pair production with vacuum quantum numbers.

LI = g

A standard for light hadron decays. It works for D/S in b1 .

The relation to QCD is obscure.

(Feynman rules from E.S.Ackleh et al., PRD54, 6811 (1996).)

Strong Widths: 3P0 Decay Model

Parameters are = 0.4 (from light meson decays), meson masses and wfns.

X(3872)1D

DD

3D3

0.5 [MeV]

3D2

-

3D1

43 [MeV]

1D2

-

23.0(2.7) [MeV]

E1 Radiative Partial Widths

1D -> 1P

3D3 3P

2 272 [keV]

3D2 3P

2 64 [keV]

3P1

307 [keV]

3D1 3P

2 5 [keV]

3P1

125 [keV]

3P0

403 [keV]

1D2 1P

1 339 [keV]

X(3872)

Strong Widths: 3P0 Decay Model

X(3872)33S

1 74 [MeV]

31S0

80 [MeV]

3S

DDDD*D*D*D

sD

s

80(10) [MeV]

Recall J.Napolitano (CLEO) yesterday:

4040 4160

After restoring this “p3 phase space factor”, the expt BFs were:

D0D0 : D0D*0 : D*0D*0

One success of strong decay models

An historical SLAC puzzle explained:the weakness of DD

e.g. D*D* molecule?

famous nodal suppression of a 33S

1 (4040) cc DD

std. cc and D meson SHO wfn. length scale

partial widths [MeV](3P

0 decay model):

DD = 0.1 DD* = 32.9 D*D* = 33.4 [multiamp. mode]D

sD

s = 7.8

D*D* amplitudes(3P

0 decay model):

1P1 = 0.034

5P1 = 0.151 = 1P

1

5F1

= 0

2D 23D3

148 [MeV]

23D2

92 [MeV]

23D1

74 [MeV]

21D2

111 [MeV]

DDDD*D*D*D

sD

s

DsD

s*

103(8) [MeV]

Strong Widths: 3P0 Decay Model

Recall J.Napolitano (CLEO) yesterday:

4040 4160 4040 4160

std. cc SHO wfn. length scale

partial widths [MeV](3P

0 decay model):

DD = 16.3 DD* = 0.4 D*D* = 35.3 [multiamp. mode]D

sD

s = 8.0

DsD

s* = 14.1

D*D* amplitudes:(3P

0 decay model):

1P1 = 0.049

5P1 = 0.022 1P

1

5F1 = 0.085

Strong Widths: 3P0 Decay Model

4S 43S1

78 [MeV]

41S0

61 [MeV]

DDDD*D*D*DD

0*

DD1

DD1’

DD2*

D*D0*

DsD

s

DsD

s*

Ds*D

s*

DsD

s0*

62(20) [MeV]

X(3872)

DD1 amplitudes:

(3P0 decay model):

3S1 = 0 !!! (HQET)

3D1 = + 0.093

BGS results (3P0 decay model):

partial widths [MeV]

DD = 0.4 DD* = 2.3 D*D* = 15.8 [multiamp.]

DsD

s = 1.3

DsD

s* = 2.6

Ds*D

s* = 0.7 [m]

New S+P mode calculations:

DD1 = 30.6 [m] MAIN MODE!!!

DD1’ = 1.0 [m]

DD2* = 23.1

D*D0* = 0.0

Theor R from the Cornell model.Eichten et al, PRD21, 203 (1980): 4040

DD

DD*

D*D*

4159

4415

An “industrial application” of the (4415).

Sit “slightly upstream”, at ca. 4435 MeV, and you should have a copious source of D*

s0(2317). (Assuming it is largely cs 3P

0.)

END