Meson spectroscopy - glueballs

• Making a glueball• Decay products• Kaon detection• Kinematic fitting• Partial wave analysis• Glueball candidates & spectra• Further Research

1

Meike Door

Making a glueball

J/ψ: meson, mass: 3097 MeV/c2 , lifetime ~10-20s, SpinParity (JP): 1-

Glueball: particle consisting solely of gluons , JP=0+

Short lifetime: decay products are among others K+K- ,K0K0, π+π- , …qq

Quantum Numbers are conserved

2

Measure the decay products of a glueball

• Let‘s focus on K+K-, because this is the favored decay process

(shown by M.S. Chanowitz, „chiral suppression of scalar-Glueball decay“, Physical review letters, 2005)

3

Kaon detection (16.09.09)

4

Charged particles: Use drift chamber & TOF

B-field in the drift chamber →

Kaons follow a curved path → calculate the momentum of the Kaon

Drift chamber xy view

5

Energy deposition dE/dx in the chamber → particle identification

Kaons are well distinguishablefrom other particles

TOF: mass & velocity of particle

Kaon detection (16.09.09)dE

/dx

Intermezzo: Kaons• Spin parity 0-, lifetime ~10-8s

• K+ : K- : K0: :

• due to weak interaction there is a coupling between K0K0 . → the physical Kaon states are a mixure!

→ Discovery of two kinds of neutral Kaons: Kl0 (long-lived, ~10-8s)

and Ks0(short-lived, ~10-10s). Subject of another Semimar!

• But: Kaons are decay products of other reactions, too… how can you prove that a measured Kaon came from a glueball?

usus

6

ds K0 ds_

Conservation of energy & momentum

K

K

PE

K

K

PE

&

Remember last week:

²)²()²( 2121 gKKKK MPPEE Invariant mass of the glueball

7

Requirement for being a glueball !

Glueball decays in e.g. Kaons: energy & momentum has to be conserved!

²²² PEm

Decay into two Kaons:

(in natural units, c=1)

Addtionally, must hold.

Advantage: The mass of a kaon is very well known:mK = 493,677±0,013 MeV

E and are measured with an uncertainty.→ modify E and so that mK is obtained

This is called kinematic fitting!

²²² 111 KKK mPE

P

P

8

Kinematic fitting §3.4

Idea: use known properties of a given process to improve the measurements and resolution.

Mathematical method…

9

Until now we know…

• what are the decay products of a glueball (Kaons favored)

• how Kaons are detected

• under which conditions Kaons are a decay product of glueball

• How to improve measurements & resolution Kinematic fitting

²)²()²( 2121 gKKKK MPPEE

10

Invariant mass spectrum

We had a glueball…What was its mass, witdh, spin, parity?

Apply Partial Wave Analysis (PWA) (widely used in high energy physics).Use the fact that

Cross section is measureable.

How does the amplitude look like? Write it as Legendre Polynomial * weighting factor

11

²),( f Cross section ~ Amplitude²

PWA

12

lmlm AYfml,

),(),( Legendre Polynomial x weighting factor

→Spherical harmonic

→

Partial wave amplitude

Get Alm using the orthogonality relation:

'''' ),(),( mmlllmml YYd *

→

Put in measured amplitude

→ Calculate partial wave amplitude Alm

(This is for spin=0. Spin ≠0 is more complicated)

Glueball spin

Spin 0: no favored direction after decay

→ uniform angular distribution, flat spectrum

Spin ≠ 0 : favored direction after decay

→ no uniform angular distribution, no flat spectrum

Learn about the spin of your glueball

Diagrams: „Physics at BES-III“, Kuang-Ta Chao and Yifang Wang, 2008, §3.5.513

Θ is the decayangle w.r.t. thereconstructedmomentum ofthe glueball

What about parity?• Glueballs can have all

states indicated in the mass spectrum

• Kaons: 0-

• There are JPC states, which supress decay into KK

→ Can you imagine why?

14

Conservation of charge/parity violated

Scalar Glueball candidates

• f0(1370)

• f0(1500)

• f0(1710)

Note:There are also vector- and tensor- glueballs, and pseudoscalar glueballs. Too much for today!

15

Glueball f0(1370)

16

3 particles measured: φ, π+ , π-

f0(980) candidate for multiquark or molecule states(Chapter 11, Physics of soft Pions)

f0(1790) discussed later

f0(980)

f0(1370)f0(1790)

Glueball f0(1370)

17

f0(1370)

Figure: broad enhancement around f0(1370)

BES II: strong f0(1370) signal for J/ψ → π+ π-

No significant f0(1370) signal for J/ψ → K+ K-

Mass M=1350±50MeVWidth Γ = 265±40MeV

f0(980)

f0(1790)

PWA: peak around 1370MeV comes from a dominant f0(1370) term that interferes with an f2(1270) and a smaller f0(1500)

Glueball f0(1500)

18

backgroundf2(1270)

f0(1500) observed in many experiments,Interpreted as non- state

Strong f2(1270) signal

Shoulder at ~1.45 GeV

Enhancement at ~1.7GeV

Peak at ~2.1GeV

Shaded area: background

qq

~1.45GeV~1.7GeV

~2.1GeV

J/ψ→γ π+ π-

Glueball f0(1500)

19

• PWA: background flat, peaks are left over Two 0+ states in the 1.45GeV & 1.75GeV mass regions

In contrast to f2(1270), the f0(1500) is not directly observed in certain production channels of J/ψ hadronic decays (f0(1500) has a larger branching ratio to ππ than KK)

→ but existance of a 0++ scalar at 1.5GeV is suggested for other production channels with a larger branching ratio to KK than to ππ

f0(1500):M = 1466±6±20 MeV

→ future: search for f0(1500) in more decay modes & studying its spin-parity

J/ψ→γ π+ π-

f2(1270),

Glueball f0(1710)

• f0(1710) main competitor of f0(1500) for the lightest 0+ glueball (large production rate, also in J/ψ decay)

• Different experiments before BES gave different masses, widths and spin-parities

• Most experiments give JP= 0+ • BES-II: M=1738±30MeV; Γ=125±20MeV, JP= 0+

20

Glueball f0(1710)

Where does the background come from?

Spectrum: „Physics at BES-III“, Kuang-Ta Chao and Yifang Wang, 2008, §9.3.2 21

f2‘(1525)f0(1710) Pseuodoscalar glueball (not treated

in this lecture)

J/ψ→γKK_

M(K+K-) (GeV/c²)

Glueball f0(1710)

22

PWA fit projection

Peak at 1765±13MeV

This state may be the f0(1710) ,

the f0(1790) or a superposition!

f0(1790) & f0(1710): 1 or 2 states?

23

f0(1790)

left: f0(1790) peak, right: f0(1710) peak. Masses lie close together!

PWA shows that these states are distinct

f0(1710)

J/ψ→γKK_

Current & Further Research

• 1~2GeV: at least 3 scalar mesons (glueball candidates) (f0(1370), f0(1500) & f0(1710)) which are explored

• Behaviour has unexpected features• Questions arise about → structure→ decay mechanism→ glueball (yes or no?)→ If yes: is the glueball pure or mixed?→ nature of the candidates remains a mystery

24

BES-III

• Large data sample & excellent detector performance will increase the sensitivity

• Search for other hadron states is possible with BES-III

• Recently, two additional scalar meson candidates (f0(1790)& f0(1810)) were reported by BES-II → confirmation required by BES-III

25

References

• „Physics at BES-III“, Kuang-Ta Chao and Yifang Wang, 2008

• M.S. Chanowitz, „chiral suppression of scalar-Glueball decay“, Physical review letters, 2005

• BES-III detector properties, G.J. Tambave, lecture 16th sept. 2009

26