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Interactions of - mesons with heavy quarks Avakyan E. Z. , Avakyan S. L. GSTU, Gomel ,

Interactions of - mesons with heavy quarks

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Interactions of - mesons with heavy quarks. Avakyan E. Z. , Avakyan S. L. GSTU, Gomel. MIXING SCHEMES (only u,d,s -quarks). 1. Mixing: Where The flavor structure of and :. MIXING SCHEMES only u,d,s -quarks. - PowerPoint PPT Presentation

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Page 1: Interactions of           -  mesons with heavy quarks

Interactions of - mesons with heavy quarks

Avakyan E. Z., Avakyan S. L.

GSTU, Gomel

Avakyan E. Z., Avakyan S. L.

GSTU, Gomel

,

Page 2: Interactions of           -  mesons with heavy quarks

MIXING SCHEMES (only u,d,s-quarks)

1. Mixing:

WhereThe flavor structure of and :

ssqq

s

qU

)(

cossin

sincos)(U

q s

ss

dduu

s

q

)(

2

1

Page 3: Interactions of           -  mesons with heavy quarks

MIXING SCHEMES only u,d,s-quarks

2. MIXING IN THE OCTET – SINGLET BASISThe pseudoscalar nonet can be displayed as:

So

36

2362

362

080

0080

080

KK

K

K

P

cossin

sincos

08

08

Page 4: Interactions of           -  mesons with heavy quarks

HEAVY QUARK ADMIXTURES TO LIGHT PSEUDOSCALAR MESONS

Problem: ClEO mesuarment of branching fraction unexpetedly large. [CLEO coll ab. B.H.Behrens et.al. Phis.Rev.Lett.80,3710(1998)]

Mixing :

KB

ccssqq

01)cos()sin(

coscossin

sinsincos

c

s

q

ycyc

yc

yc

c

Page 5: Interactions of           -  mesons with heavy quarks

WAYS TO DEFINE MIXING PARAMETERS

• The radiative decays of η – mesons[T.Feldman, P.Kroll and B. Stech, Phys.Rew. D58,114006 (1998)

• Radiative Ј/Ψ – decays• [K.Chao, Nucl.Phys B317,597(1989)

• Rations of weak decays constants

Page 6: Interactions of           -  mesons with heavy quarks

QUARK MODEL

• The hadronic interactions will be described in the Relativistic Constituent Quark Model (RCQM).

[M.A.Ivanov,M.P.Locher and V.E.Lyubovitskij, Few-Body Syst. 21,131(1996),

M.A.Ivanov, V.E.Lyubovitskij, Phys.Lett., B408,435(1997)]

The coupling of the meson M into its constituents and is given by Lagrangian

where are Dirac and Gell-Mann matrices.

1q 2q

)()(),,()( 212121int xqxqxxxdxdxxMgL MMMM

MM ,

Page 7: Interactions of           -  mesons with heavy quarks

The function characterizes the finite size of meson and is given by:

The coupling constant is determined by compositeness condition:

where - the derivative of the mass function of meson.

QUARK MODEL

M

))(()(),,( 221

21

221121 xxf

mm

xmxmxxxxM

Mg

0)(~

4

31

2

2

MMM

M mg

Z

)(~ 2pM

Page 8: Interactions of           -  mesons with heavy quarks

QUARK MODEL

MM k )( 2 MM k )( 2

pkm ˆˆ,2

km ˆ,1

Page 9: Interactions of           -  mesons with heavy quarks

Example of evaluation of one – loop diagram:

After calculating Tr and performing α-parameterization one finds:

where Next we use Cauchy integral representation for

QUARK MODEL

)( 22 kp

1

0))()((

)(2

22

2

4

2221

)(

)(

2)(~

pkD

pkkmmp

ki

d

i

kddp

)1()1()( 222

21 pmmD

Page 10: Interactions of           -  mesons with heavy quarks

We use α-parameterization once more and find

The contour integral can be done again by Cauchy’s theorem.On substitution of and shift , after rotation ,one receives:

QUARK MODEL

t

t

1

pt

tkt

K

11

1

ukkikk E 2240 ,

)

11

1())((

1)(

~ 221

0 0

22

1

0

2

t

tpu

tmmzuduu

t

dtdp Pp

t

tptDz

1)(

22

Page 11: Interactions of           -  mesons with heavy quarks

MESON-QUARK INTERACTION CONSTANTS

Pseudoscalar meson constant

THE MIXING:

)(~

1

4

32

2

MM

MM

m

gh

ccssqq

),(sinsin),(cos),(

2)(

22222

cPPycsppnpp cmFmFmF

h

),(cossin),(sin),(

2)(

222222

cPPycsppnpp cmFmFmF

h

),()(cos),()(sin),(

2)(

222222

cppycsppycnpp c

c mFmFmFh

Page 12: Interactions of           -  mesons with heavy quarks

DECAY

Decay amplitude:

Decay width:

Experimental values (PDG)

P

2121

2 )()()( qqqqgePA P

223

4)( PP gmPW

keVW

keVW

)19.027.4()(

,)04.046.0()(

exp

exp

Page 13: Interactions of           -  mesons with heavy quarks

2q̂

1q̂

)( 25 kP

DECAYP

Page 14: Interactions of           -  mesons with heavy quarks

THE MIXING:

DECAYP

ccssqq

),(sin9

5sin),(

9

1

cos),(9

5

2

1)(3

)(22

2

mcmFmsmF

mumFhg

PycP

P

),(cos9

5cos),(

9

1

sin),(9

5

2

1)(3

)(22

2

mcmFmmF

mmFhg

PycsP

uP

Page 15: Interactions of           -  mesons with heavy quarks

To define the experimental values

were used.

For mixing:For mixing:So we find the quark content of physical mesons

1exp1exp 341.0,259.0

GeVgGeVg

yc cos,

ssqq 3,39ccssqq 012,0cos,1,33 yc

Page 16: Interactions of           -  mesons with heavy quarks

RADIATIVE TRANSITIONS BETWEEN LIGHT PSEUDOSCALAR AND VECTOR MESONS

Decay amplitude:

Decays width:

VVVP pqpqegPVA )()()(

VVPV pqpqegVPA )()()(

223)( PVV gmVPW 223

3

1)( VPP gmPVW

Page 17: Interactions of           -  mesons with heavy quarks

• NUMERICAL RESULTS FOR RADIATIVE DECAYS

RADIATIVE TRANSITIONS BETWEEN LIGHT PSEUDOSCALAR AND VECTOR MESONS

EXPERIMENT[PDG] scheme

1,51

0,51

0,72

V

)GeV(g 1V

g

g

g

28,0

25,047,1

04,053,0

02,069,0

ccssqq

012,0cos,1,33 yc

Page 18: Interactions of           -  mesons with heavy quarks

• NUMERICAL RESULTS FOR RADIATIVE DECAYS

RADIATIVE TRANSITIONS BETWEEN LIGHT PSEUDOSCALAR AND VECTOR MESONS

VEXPERIMENT

[PDG] scheme

1,24

0,37

0,79

)( 1

GeV

g Vccssqq

012,0cos,1,33 yc

g

g

g

06,031,1

03,045,0

21,0

28,000,1