k - + s -wave system from d + meson decays to k - p + p + in e791

Moriond, LaThuile, Mar 14, 2005 Brian Meadows, U. Cincinnati.

K-+ s-wave System from D+ Meson Decays to K-++ in E791

Brian MeadowsUniversity of Cincinnati

Moriond, LaThuile, Mar 14 2005 Brian Meadows, U. Cincinnati

Outline

What is known about s-wave K-+ scattering

Results from D+ ! K-++ Decays

Model Independent Partial Wave Analysis

Comparison with the Watson theorem

Summary and Discussion


K Scattering in Heavy Quark Decays

Understanding the structure of the s-wave K system is important to many analyses, and of vital interest to an understanding of the spectroscopy of scalar mesons.

It may be possible to learn more from the large amounts of data on D and B decays now available.

The applicability of the Watson theorem can be tested.

E791 is the first to try this by making a Model Independent Partial Wave Analysis of the s-wave in the decay

D+ ! K-++ (and cc).


K Scattering

Most information on K-+ scattering comes from the LASS experiment (SLAC, E135)

Data from:

K-p! K-+n

and

K-p! K0-pNPB 296, 493 (1988)

No data below 825 MeV/c2


“Traditional” Dalitz Plot Analyses The “isobar model” has been widely used, with Breit-Wigner resonant

terms, over the past 15 years.

Amplitude for channel {ij}:

Each resonance “R” (mass MR, width R) assumed to have form

2

NRConstant

D formfactor

R formfactor

spinfactor

1 1

12

2

3 3 3

{12} {13} {23}1

2

3

NR


E791 D+ ! K-++

~138 %

2/d.o.f. = 2.7


E791 D+ ! K-++

2/d.o.f. = 0.73(95 %)

~89 %

M = 797 § 19 § 42 MeV/c2

§§eVc

Probability


E791 D+ ! K-++ Dalitz Plot Most interesting feature:

K*(892) bands dominate Asymmetry in K*(892) bands

! Interference with large s–wave component

Also: Structure at » 1430 MeV/c2 mostly

K0*(1430)

Some K2*(1420)? or K1

*(1410)?? Perhaps some K1

*(1680)?

SoAt least the K*(892) can act as

interferometer for s–wavePerhaps other resonances can fill in

some gaps too.


Asymmetry in K*(892)

Helicity angle in K-+ system

Asymmetry:

tan-1m00/(m02-sK)

pq

cos = p¢ q

K-

+

+

! P - s is -750 relative toelastic scattering


s–wave from D+ ! K-++ Dalitz Plot?

Divide m2(K-+) into slices

Find s–wave amplitude in each slice (two parameters) Use remainder of Dalitz plot as an interferometer

For s-wave:

Interpolate between (ck, k) points:

Model P and D S (“partial wave”)


Reference Waves For p- and d-waves:

Use “traditional” Breit-Wigner isobar model:

Unbinned maximum likelihood fit: Use 40 (ck, k) points for S Float (d1680, 1680) and (d1430, 1430)

! 40 x 2 + 4 = 84 free parameters.

P (“partial wave”)

D (“partial wave”)

K892 defines reference phase


Float P and D parameters and find S:

General appearance similar to isobar model fit: Magnitudes at low mass differ Phases above K0

*(1430)

Tests with many MC samples of this size (15K events), produced to simulate the isobar model, produce similar differences in ~15% of the cases

• Major source of systematic uncertainty:

• Contribution of reference waves in region between K*(892) and K*(1680).

Fit E791 Data for s-wave

S

P

D

Phase Magnitude


Comparison with Data

S

2/NDF = 272/277 (48%)


Comparison with Elastic Scattering (LASS)

S is related to elastic scattering amplitude T obtained from LASS by

In elastic scattering K-+ ! K-+ the amplitude is unitary

In D+ decays, the K can come from many sources so we expect the magnitude to differ from sin (sK).

If applicable to these decays, the Watson theorem requires phases (sK) for each wave to be the same, up to the elastic limit (1454 MeV/c2). K.M. Watson, Phys. Rev. 88, 1163 (1952)


Watson Theorem - a direct test

Phases for S, P and D waves are compared with those from LASS. s-wave phase s for E791 is

shifted by –750 wrt LASS.

s energy dependence differs below 1100 MeV/c2.

p does not match well between K*(892) and K*(1680) resonances

d match is excellent up to elastic limit.

S

P

D

Elastic limit

K’ threshold

(1454 MeV/c2)


Summary

A new technique is used to fit the amplitude describing a Dalitz plot distribution

It can provide model independent measurements of the complex amplitude of the K-+ s-wave system, provided a good model for the p- and d-waves is used.

Such measurements are possible at masses below the limit of existing ones.

The Watson theorem does not apply to D+! K-++ decays. This technique will play a role in analyses of the large

samples of heavy meson decays becoming available from B factories, CLEO-c and the TeVatron collider.


Back up Slides


A Different Approach

Instead of expanding the Dalitz plot amplitude in BW’s (or pole terms in a K matrix) for each resonance, expand in partial waves.

For a D decay, barrier factors preclude all but s-, p- and d- waves.

Treat the s-wave, at least, as having completely unknown dependence on invariant mass.

p- and d-waves can be expanded as resonances of appropriate spin


Simulate 150K MC events with isobar model parameters

Find S for them:

Does this Work?

S

S P

D

Phase Magnitude


Milestones in Dalitz Plot Analyses1993-7:

E691/687 find large non-resonant (NR) fraction in Decays

D+ ! -++ and D+ ! K-++

2001:

E791 find that broad, low mass scalar isobars can soak up most of the NR contribution

! NR is not constant

2004:

Focus collaboration use data from K-matrix fit to large number of hadron interactions involving +- production in analysis of

D+ ! -++.

! No new broad scalars required?


Milestones in Dalitz Plot Analyses

2005:

Lots more data is on the way

Clearly, we may be able to learn which scalar resonances really exist

Other information is required from the data

We need new, less model-dependent ways to analyze it.! One possibility is Energy Independent Partial Wave Analysis

(EIPWA).

E791 is the first to try.


E791 D+ ! -++

No “(500)”


E791 D+ ! -++


K Scattering

Most information on K-+ scattering comes from the LASS experiment (SLAC, E135)

a – scattering lengthb – effective rangep – momentum in CM

Data from:

K-p! K-+nand

K-p! K0-pNPB 296, 493 (1988)

Parametrize s-wave (I=1/2)by


E791 D+ ! K-++


Fit the E791 data:

1. Fix P and D parameters at model Find S:

2. Fix S and D parameters at model Find P:

3. Fix S and P parameters at model Find D:

The method works.

Does this Work?

S

SP

D

Phase Magnitude


Comparison with Data

S

MomentsMasses

2/NDF = 272/277 (48%)


Qualitative agreement with data

BUT does not give acceptable 2.

This solution violates the Wigner causality condition.

Other Solution

S

SP

D

Phase Magnitude

E. P. Wigner, Phys. Rev. 98, 145 (1955)

k - + s -wave system from d + meson decays to k - p + p + in e791

Documents

p p c2d

model p

p scattering

p systemasymmetry

p nand

swavefloat p

d parameters

swave system