the scalar mesons proposal stefan spanier university of tennessee, knoxville

1Stefan Spanier, Scalar Mesons, PDG Meeting 2008

The Scalar MesonsProposal

Stefan SpanierUniversity of Tennessee, Knoxville

PDG Collaboration meeting 10/10/2008CERN, Geneva

Scalar Meson Review: Claude Amsler, Nils Tornqvist, Stefan Spanier

2Stefan Spanier, Scalar Mesons, PDG Meeting 2008

below 2 GeV

• Experimental Challenges:

- Broad states- Strongly overlapping- Close to several thresholds- Extra dynamical features (left-hand cuts, Adler zero)- Featureless angular distributions (like background)- Often covered by tensor or/and vector mesons

Present a long standing puzzle Measurements of phase motions since 1970s

• Quantum number of vacuum – fundamental role in chiral symmetry breaking• Glueball

• Low receiving end of hadronic reactions

mixtures: ann + bss + cqqqq + dglue + _ _ _ _

• Scalar Mesons are special

3Stefan Spanier, Scalar Mesons, PDG Meeting 2008

• Scalar Meson Spectrum

2+

4Stefan Spanier, Scalar Mesons, PDG Meeting 2008

• Model Dependent Analysis

Non-perturbative regime

Static models Dynamics: production decay need both to piece puzzle together

No simple Breit-Wigner fits combined sample analysis coupled channel analysis

• Do not describe with individual resonances but parameterize complete (partial wave) amplitude

I=0 () S-Wave

(600) ?

f0(980)

f0(1370)

f0(1500)

T112

KK thre

shol

d

_

[EP A16, 229 (2003)]

• In optimum case the underlying resonances show up as same poles in the unphysical sheet of the complex energy plane evaluate denominator of complex amplitude for singularities

5Stefan Spanier, Scalar Mesons, PDG Meeting 2008

• Formalism

Try to start from dominance by 2-body interaction

• Watson theorem: same phase motion in T and F in elastic range

• Adler zero: at m 0 for p=0: T = 0 near threshold; also/where for F ?

• K-matrix poles % T-matrix poles in unphysical sheet of complex energy plane

a

b

c

d

ll

R

L

l

Spectator ?

d

R c

2-body scattering production / decay

T = R K F = R P P-vector = Q T Q-vector

e.g.

In very formal way using K-matrix

R = (1-iK)-1

2-body PS

Dynamic amplitude requirements:- Lorentz invariant- 2-body Unitarity- Analytic / Crossing

6Stefan Spanier, Scalar Mesons, PDG Meeting 2008

• I=1/2 Scalar Data from:

K-p K-+n

and

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

No data below 825 MeV/c2

K Scattering LASS

0.7 0.9 1.1 1.3 1.5 MK (GeV)

150

100

50

0

-50

Ph

ase

(deg

rees

)

0.7 0.9 1.1 1.3 1.5MK (GeV)

• Most information on K-+ scattering comes from the

LASS experiment (SLAC, E135)

K’ threshold

• use directly in production if re-scattering is small• require unitarity approach …

LASS parameterization

• Disentangle I=1/2 and I=3/2 with K++ [NPB133, 490 (1978)]

PenningtonChPT compliant

7Stefan Spanier, Scalar Mesons, PDG Meeting 2008

• I=1/2 Scalar

LASS experiment used an effective range expansion toparameterize the low energy behavior: : scattering phase q cot = + a: scattering length b: effective range q: breakup momentumTurn into K-matrix: K-1 = cot

K = + and add a pole term (fits also pp annihilation data)

Both describe scattering on potential V(r) (a,b predicted by ChPT)

Takes left hand cuts implicitly into account

Instead treat with meson exchange in t- () and u-channel (K* ) [JPA:Gen.Phys 4,883 (1971), PRD 67, 034025 (2003)]

only K0*(1430) appears as s-pole

same phase motion, different parameterization / pole pattern

1 b q2

a 2___ ______

a m g0

2 + a b q2 m02 – m2

___________ ___________

8Stefan Spanier, Scalar Mesons, PDG Meeting 2008

• I=1/2 Scalar

D+ (K-+) +

• K system dominated by K*(892)• Observe ~15% forward-backward asymmetry in K rest frame• Hadronic phase of 45o corresponds to I=1/2 K wave measured by LASS required by Watson theorem in semileptonic decay below inelastic threshold

• S-wave is modeled as constant (~7% of K*(892) Breit-Wigner at pole). a phase of 90o would correspond to a kappa resonance, but …

Study semileptonic D decays down to threshold !

FOCUS

Reconstructed events: ~27,000D+

K-

+

csW+

[PLB 621, 72 (2005)][PLB 535, 43 (2002)]

9Stefan Spanier, Scalar Mesons, PDG Meeting 2008

• I=1/2 Scalar E791

K*(892)

K*(1430)

D+ K-++

#15090

• Fit with Breit-Wigner (isobar model):

M = (797 19 42) MeV/c2

eVcD+K-

+

W++

+

+

K-

W+

• Fit with Breit-Wigner + energy- independent fit to K S-wave(P(K*(892), K*(1680)) and D-waves (K*2(1430))act as interferometer)

Model P- and D-wave (Beit-Wigner),

S-wave A = ak eik bin-by-bin (40)

[PRL 89, 121801 (2002)]

[PR D73 (2006) 032004]

Extracted phase motion from both analysesare similar.

10Stefan Spanier, Scalar Mesons, PDG Meeting 2008

• I=1/2 Scalar E791

K’ threshold

-75o

… but differs from LASS elastic scattering

T11 from LASS ( same poles ?)

Constraint: Q smooth functions

Adler zero s0I removed

A(s) eis = F1/2(s) + F3/2(s) , s = mK2

FI(s) = QI(s) eiIT11

I(s)

s – s0I

Q-vector approach with Watson:

[Edera, Pennington: hep-ph/0506117]

|FI |

big !

• Quasi-two body K interaction (isobar model ) broken ?

if not

• Watson theorem does not apply ?

if not• Isospin composition I=1/2 % I=3/2 in D decay same as in K K?

11Stefan Spanier, Scalar Mesons, PDG Meeting 2008

Example: Input for B CP – physics - B0 J/ K* study K mass from 0.8 – 1.5 GeV/c2

- add penguin modes for New Physics Search, e.g. B0 f0 K0

- CP composition of 3-body modes, e.g. B0K0K+K-

- hadronic phase for CP angle in BDK from D-Dalitz plot

• Pole structure of the amplitude in complex energy plane PDG table

• Isospin amplitude for 2-body scattering is as important- Data on phase motion and modulus (or/and elasticity)- Parameterizations (limited number) Compare on level of 2-body scattering (unitarity, analyticity) phase motion and modulus often in close agreement, but underlying parameterization and/or pole structure different Increase confidence with combined data-set coupled channel analyses increase constraints; updates extract iteratively the bare 2-body wave Provide input for analyses that include scalars (likelihood analyses)

• Summary - Role that PDG can play …

• Proposal: Archive (pdglive) scalar amplitude information.