Charmonium Aps: 1) GSI cross secs, & 2) nuclear forces Ted Barnes Physics Div. ORNL and Dept. of Physics, U.Tenn. (and p.t. DOE ONP) INT Nov 2009 1. For.

Charmonium Aps:1) GSI cross secs, & 2) nuclear

forces

Ted Barnes Physics Div. ORNL andDept. of Physics, U.Tenn. (and p.t. DOE ONP) INT Nov 2009

1. For PANDA: Associated charmonium production cross sections at low to moderate energies

s ( pp -> (cc) + m )

(Will show all recent theoretical calculations of these cross sections,Together with all the data in the world.)

2. Related process cc -> ppm => Nuclear (NN) Force Models

T.Barnes (ORNL/UT)C.Downum (Oxford/ORNL)J.Stone (Oxford/ORNL) E.S.Swanson (Pittsburgh)

INT seminar11/12/2009

Meson-nucleon Couplings and

NN Scattering Models

1. The problem: What in QCD causes NN (read hadron-hadron) interactions?

2. What does meson exchange predict for the NN {dJLS

} ?

3. How does the theory (2) compare with the data? NN D-waves as an ideal theorists’ laboratory.

4. Can we distinguish between w exchange and q-g forces?

5. Y -> ppm as a possible way to determine NNm couplings?

6. (JLAB too; gp -> wp.)

But first… my philosophy in doing physics:

1. The Way that can be followed is not The Perfect Way. - Lao Tzu

2. It neva’ hurts ta’ work out da’ simple cases furst. - R. P. Feynman

3. Damn the torpedoes… - “

1. We also want to include s and c hadrons – little data.We hope to develop a model of NN forces that can be extrapolated to excited and s,c,b flavor baryons…

and to other hadrons! (“molecules”!)

2. The NN interaction is fundamental to most (all?) of nuclear physics.It would be nice to understand it.

Why not just parameterize NN scattering experiments?

n.b. There are two traditional approaches to studying the NN force:

A. Try to identify the physics (the scattering mechanism(s))B. Try to go through every point. [see slide title]

“We” will follow “A”. (My collaborators CD and JS are also pursuing “B”.)

A quick look at the data (S-, P- and D-wave phase shifts)

n.b. NN = identical fermions, so the overall state must be

Antisymmetric in Space Ä Spin Ä Isospin

I=1 NN (e.g. pp) has

[S=0, even-L] or [S=1, odd-L] :

1S0 , 3P

0,1,2 ,

1D2 ,

...

I=0 NN (pn-np) has

[S=0, odd-L] or [S=1, even-L] :

3S1 , 1P

1 ,

3D1,2,3

...

2S+1LJ

Partial waves:

The totally elastic regime is Tlab

= 0

to ~ 300 MeV.

+mp

1.878 GeV

I = 0

I = 1

A bad place for theorists to start.

“s exchange” ? p exchangeq-g forces ? (1gE)

IRA 1pE

core

rNN

(fm)

VNN

(r)(MeV)

VNN

(

r)s

p p

p pp

p p

p p

A schematic picture of NN forces

historicallyconsidered

w exchange

pp ??

Purgatory for theorists

A nice place for theorists

Needs more experimentalists?

How hadrons interact (1 popular mechanism)

Meson exchange. (traditional nuclear: larger r)

(In terms of hadron d.o.f.s)

Easy to calculate (Feynman diagrams) but the vertices (form factors)are obscure. MANY free params, usually fitted to data.

Not the right physics at small r.

A C

DB

e.g. for NN scat:, , , p r w “s”, …

Form factors andg

NNm coupling consts, normally

treated as free params.We will actually calculate these.

(A selection of) Nucleon-meson coupling constants found in the NN meson-exchange-model literature.

The main ingredients are the p, s , and w. Note especially the NNs coupling and k

w.

from C.Downum, T.Barnes, J.R.Stone and E.S. Swanson “DBSS”nucl-th/0603020, PLB638, 455 (2006).

Meson exchange calculations:

Detailed comparison of Tfi with experiment:

Calculate phase shifts from the one meson exchange T-matrix.

MAPLE algebra program (actually about 6 nested MAPLE programs).

T-matrix -> project onto |NN(JLS)> states -> express as phase shifts.

A difficult task (esp. spin-triplet channels).

These MAPLE programs also generate Fortran code for the phase shifts directly.

p

p p

p p

g g5

g g5

e.g.:

(an e.g.)

Done before?

and x = 1 + M_N^2/2p^2 is a frequently recurring “energy” variable).

A.F. Grashin, JETP36, 1717 (1959):All NN 1pEx phase shifts in closed form!

These phase shifts agree with our 1pEx results in all channels.

Meson exchange calculations:

Now compare to data…

Start with D-wave phase shifts, which were strongly spin-dependent but only moderate in scale. Use a typical g

NNp = 13.5, and

calculate numerical phase shifts. (Will also show typical s and w results.)

The results:

p

p p

p p

gp g

5

gp g

5

s

p p

p p

i gs

i gs

w

p p

p p

i gw G

m

i gw G

m

+

+

G m=

g

m+ (i k

w / 2 ) M s

mnq

n

Dominantly T

(another MAPLE e.g., 0+ exchange)

n.b. small negative L*S

Progress!

All Born-order elastic phase shifts and inelasticities in all J,L,S channels due to 0 - , 0 + and 1- (e.g. ,p s and w) exchange…

(Mainly C.Downum. I checked JLS special cases.)

Summary, D-wave NN phase shifts:

p exchange, gnnp

= 13.5 describes the NN D-waves fairly well for Tlab

< 200 MeV.

It looks real! Some “softening of 3D2 above 200 MeV.

s exchange, gnns

= 5, is much weaker, and nearly spin-independent.

Not testable in D-waves.

w exchange, gnnw

= 12 (a typical value in models) gives moderate phase shifts

which are spin-dependent and repulsive. Not dominant near threshold. May help the 3D

2.

For all terms combined and fitted to data see C.Downum et al., in prep., and

“Low Energy Nucleon-Nucleon Interactions from the Quark Model with Applications”,D. Phil., Oxford University (2009).

Does well for S- and P- as well as D-, but has to be iterated in S- and P- of course.

Issues there are “s” = pp? (future), and “w” versus quark core (q-g) forces.

Nathan Isgur at JLAB, 1999, suggests quark interchange meson-meson scattering diagrams.

Another scattering mechanism:

NN cores from quarks?

Isgur’s confusion theorem…

qc, I=1

Does the quark core ps resemble w exchange? (Isgur’s confusion theorem.)Yes, but … a much smaller NNw coupling (g

NNw = 6 shown) is

required.

Summary, S-wave NN phase shifts:

p exchange, gnnp

= 13.5 is strongly repulsive for Tlab

< 200 MeV.

“s” exchange, gnns

= 5, provides strong attraction and is the binding force.

w exchange, for gnnw

= 6, is repulsive and is indeed similar to the quark core result.

Confusion of the two effects is possible. g

nnw = 12, as is assumed in meson exchange models,

is repulsive and very large.

Naïve iteration of this interaction may be double counting if s exchange is actually pp exchange.

Important future calculation: pp exchange loop diagrams. Is this consistent with the phenomenological “s exchange” ??? (Machleidt)

Meanwhile, what is the REAL NNw coupling? (QM estimates? Extraction from cc -> ppw data?)

Calculating NNm coupling constants and form factors in the quark model.

p

p p

p p

Direct calculation (not fitting) of meson-baryon coupling constants and form factors in the quark model.

No need to guess (or fit) the vertex gBB’m

(Q2) for an effective Lagrangian,

it can be calculated as a decay amplitude, given B, B’, m quark wavefunctions.

(The Orsay group did this in the 1970s for NNp. A lost art.)

p p

p0

DBSS, PLB638, 455 (2006).

g

We reproduced the published Orsay gNNp

(Q2), and can calculate the NNm coupling

constants and form factors for any other exchanged meson (3P0 model).

The calculated quark model gNNp

(Q2) vertex / form factor:

(TB,CD,ESS, 3 indep calcs,confirm ORSAY.)

How does this compare numerically with the experimental coupling

constant, gNNp

@ 13 ?

Quark model calculation of the NNp coupling constant.

a = baryon wfn length scaleb = meson …

Quark model calculation of the NNs coupling constant.

new result

Quark model calculation of the NNw (F1 g

m) coupling constant.

new result:

kw (= F

2 /F

1 )

= -3/2

much larger than is used inmeson exchange models!

Summary of our quark model results for NNm couplings versus the NN meson-exchange-model literature.

The main ingredients are the p, s , and w. Note especially the NNs coupling and k

w.

DBSS, PLB638, 455 (2006).

Finally…

ExtractingNNm coupling constants from charmonium

decays?cc -> p p m

p

we know / want … we want / know …

J/y

p0

p

p

A

p

A

J/y

p0

Now on to CLEO quondam BES futurusque … Recall this crossing relation?

We can also predict the Dalitz plot distributions in (cc) -> ppm decays with this model this will let us extract ppm meson-baryon couplings “directly”.

Y

p

p

The idea:

1) This measured partial width gives g_Ypp

p0

2) This measured partial width gives |g_ppp0 x g_Ypp |2, if this decay model is close to reality. (TBD from the expt DP in all cases.) The ratio G_ppp0 / G_pp then tells us the “ppm” coupling (here g_ppp0 ). Does this work?

g_Ypp

g_ppp0

It works! Can we extract other ppm strong couplings from cc -> ppm in this way?

So what do the Dalitz plot distributions actually look like?

Notes and numerical Dalitz plots (DPs) c/o Xiaoguang Li (U.Tenn. PhD thesis, in prep.)

Predicted way cool h

c -> pp p0

Dalitz plot.

The t=u node in pp -> h

cp0 maps

into a diagonal DP node in h

c -> pp p0.

Mpp

2

[GeV2 ]

Mpp

2 [GeV2 ]

Predicted J/y -> pp p0 Dalitz plot.

Note the local diagonal minimum in the DP(at t = u in pp -> J/yp0 ).

Mpp

2

[GeV2 ]

Mpp

2 [GeV2 ]

J/y -> pp w Dalitz plot density, with wPauli terms (note the kw dependence):

(Reqd. 1024 traces, each having ca. 200 terms. Finished Thurs last week.)

Final example,

J/y -> pp : w

Predicted J/y -> pp wDalitz plot.

(With no w Pauli terms.)

Predicted J/y -> pp wDalitz plot.

With w Pauli terms,

kw = -3/2

(QM prediction).

How well does this comparewith the recent BES data? What does a fit give for g_NNw and k_NNw?

To be determined.

Summary:

1. Re PANDA@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. Meson-baryon couplings:

These are important in NN force models and are difficult to access experimentally. They can be estimated directly from charmonium strong decays of the type Y -> ppm. We have shown that this works well in extracting gNNp from J/ -> y ppp0 . Other cases to be tested.

The End…

or is it only the beginning?