2-nd vienna central european seminar, nov 25-27, 2005 1 rare meson decays in theories beyond the...

2-nd Vienna Central European Seminar, Nov 25-27, 2005

1

Rare Meson Decays in Theories Beyond the

Standard Model

A. Ali (DESY), A. V. Borisov,

M. V. Sidorova (MSU)


2

MM

2L

SM MM

Beyond the SM: -Massive Majorana neutrinos-R-parity-violating SUSY


3

Feynman diagrams for the rare meson decay mediated by Majorana neutrinos

MMM M

M M

2q

3q1q

4q

W WN 2q

1q 3q

4q

W

W

Ntree

box


4

1. Rare Meson Decays mediated by massive Majorana neutrinos

,

)2(22

||)()2()

2

11(

00093

3332)4(4

kkp

kkddpd

m

AApkkp

M

bt

tA - tree diagram - box diagrambA

,)2(

1)(

)(448

ii

i LHqqddA ;,bti

)(iL )(iH - lepton tensor - hadron tensor

The width of the decay:


5

N

NNNNWiWi

i mUUmp

g

mp

ggL

2222

4

)( 4

,)(2

1

)()()( 5

2222

kmkpmkp

kNiNi

С

LEPTON TENSOR

1Т the relative CP-phases,

,ppt ,ppt ,)(2

1qqpppb .)(

2

1qqpppb

-

ii

iU U - neutrino mixing matrix


6

HADRON TENSOR

2

1)(

2

1)( 5

435

12)( VqTrVqTrH pp

t

.2

1)(

2

1)( 5

425

13)(

VqVqTrH pp

b


7

The Bethe-Salpeter Formalism

Mesons as bound states of a quark and an antiquark:

)()()()(0),( 221121 xepMxqxqTN

ixx p

Xipa

a

C

p

X 21 xxx

3,2,1a 3CN

- the center-of-mass - the relative coordinates

- color index


8

GpMpxiq

p qpxxedq )()1()()( 54

221 /)( MM mmm

Mm

2,1 mm

2)( 21 ppq

pp

21 ppp

- the mass of the meson M

21,qq

- the total 4-momentum of the meson

quark masses-

- the relative 4-momentum

G )()( Cf NSUNSU - -group factor


9

2

2

2

2122

22

1exp)(1

4)( q

m

qpmq

MMMp

- parameter of the model

)(qp - model dependent scalar function

The definition of the decay constant of the meson:

)}0({)()0()0(0 51

52 xTrNipMqqpif pC

aaM

)()2(

44

4

qqd

Nf pMCM


10

)(43124

1tMMt LppVVffA

)(2 4213

ppippgppppVVA MMb

)(4

4

4

4

)()()2()2( bpp Lqqqdqd

MM

Amplitude for tree and box diagrams of the meson decay


11

MN mm Heavy neutrinos

In this case the total decay width is model independent

,||128

212223

74

mKff

mGVMM

MF

N NNNN m

UUm11 - the effective inverse Majorana mass

42134312

1VV

NVVK

CV


12

The branching ratios ,)(

)(

allM

MMB

.21

m

BС

Using bounds on matrix elements from the others processes one can obtain indirect bounds on the branching ratios.

The bound from of nucleus:

Also there are bounds on other mixing parameters:

decay0 Ge76 181 102.1 GeVmee

32 106.6|| N

eNU32 100.6|| N

NU


13

From the heavy neutral Majorana lepton detecting experiments:

Assuming one heavy neutrino scenario:

GeVmN 7.90

141 )105.1( GeVm141 )104.1( GeVme


14

Exp. upper boundson

10104.6 eeK K eK

eeKD KD eKD

c Ind. Boundson

B 2MeV

9100.3 10100.5

10105.8 32109.5 10104.2 24101.1 9100.1

24101.5

4102.1 5103.1 4103.1

9102.2 9100.2 9102.4

31105.1 24109.8 23101.2

Rare decay B

Experimental and indirect bounds on the branching ratios for the rare meson decays mediated by heavy Majorana neutrinos


15

Light neutrinos mmmN ,

tbbt

N

NNNN mUUm

b-amplitude is model dependent

t-amplitude is model independent

- the effective Majorana mass


16

tMM

MFt mVVff

mG 22

431222

3

34

16

bMMM

MMFb m

a

aVV

mmG

2

222

421322

8

434

12

tbMMMMM

MMFtb m

a

aVVVVff

mmG

22

421343126

324

14

t

b

tb

- 1-dimensional integral



The numerical calculations of multidimensional phase integ-rals were carried out using the program VEGAS based on Monte-Carlo mechanism.

2

M

Ma


17

The bound from :decay0 eVmee 51.0

From cosmological data and neutrino oscillation experiments, assuming the existence of 3 light massive neutrino 321 mmm

eVm 23.03 the constraint

Taking into account i

iU 1|| 2 eVmee 23.0

Using the best fit of mixing matrix from neutrino oscillation experiments

71.059.039.0

71.059.039.0

00.055.084.0

bfU

eVme 15.0


18

Rare decay

20103.5

tc bc tbc 2MeV 2MeV 2MeV

eeK K eK

eeKD KD eKD

c Ind. Boundson

B 2MeV

20104.1 22102.1 19101.1

22106.3

22102.7

21108.8 20104.4 33103.2 21101.2 20102.1 34102.6 20108.1 20108.8 33100.2

23101.4 23100.4 23102.8

21106.3 21103.3 21103.7

22105.8 22106.7 21107.1

21105.4 21101.4 21101.9

34104.2 34102.2 34100.2

Contribution of tree, box diagrams, their interference and indirect bounds on the branching ratios for the rare meson decays mediated by light Majorana neutrinos


19

2. Rare Meson Decays in R-parity-violating SUSY Theories

SLBpR 23)1( S, B, L – spin, barion and lepton quantum numbers

The SM fields, including additional Higgs boson fields appearing in the extended gauge models, have Rp=+1 while their superpartners have Rp=-1. This symmetry has been imposed on the minimal supersymmetric SM to ensure B and L number conservation. However, SUSY doesn’t require Rp conservation.

The most general gauge invariant form of the superpotential inminimal SUSY SM is

RPVR WWWp

R-parity is a discrete, multiplicative symmetry defined as


20

kjiijkkjiijkkjiijkRPV DQUDQLLLLW

- generation indices;kji ,, QL, are lepton and quark doublet superfields

are lepton and up, down quark singlet superfields.DUE ,,

All are the coupling constants. MSSM

proton stability

L B

0,0 0

0,0 0

and

RpAn alternative discrete symmetry with the same physical result, for example:

2,12,1 ,,,,,,,,, HELHELDUQDUQ

0


21

LLLL gRPV ~

KLagrangian, that yields contributions to the decay

The lepton number violating part of the Lagrangian has the form:

, LLLRPV

.,.)()()~

(~~

2

1 * chjiL jL

ciL

kR

iL

kR

jL

jL

kR

iLijk

..)()~

(~~)()

~(

~~ ** chudduudddddddL jL

ciL

kR

iL

kR

jL

jL

kR

iL

jL

ciL

kR

iL

kR

jL

jL

kR

iLijk


22

The Lagrangian terms corresponding to gluino and neutralino interactions with fermions and their superpartners are

iiii du ,, iii duq ,

iiii du ~,~

,~~ iii duq~

,~~ ,

.,.)~~~~(2

23

1,,

8

1

)()()(

3~ chqgqqgqgLiba

ibRi

aRi

bLi

aL

abg

..)~)(~)((24

1

3

12 chgL

i

iR

iRR

iL

iLL

Here are 3x3 Gell-Mann matrices.

)(

i - neutralino coupling constants.

,))()((tan)()( 1323 NQTNT WL

,tan)()( 1 NQ WR

Here and are the electric charge and weak isospin of the field .

)(Q )(3 T

,


23

Feynman diagrams for the rare meson decay

in SUSY model K

K

K

s

du

u

~ ~s

ud

u

K

s

u

u

d

~

~

,0

,0

g~,0

cu~

d~

tree

box

3


24

4

12~

2~

**

12112222312

223

)2

11(

)()(2(

2)

2

11(

C

LL

K

KK

Nmmmg

ffM

LL

4

12~

2~

*

1211

22

,,,,2~

2~

**1112

)()()

2

11(

mmm

ud

N

g

Nmmm

UU

LRkLLk

kjik

ud

LR

CNkkji CN

jNiNkk

.))(14 2

2~

2~

12112

23

gudC mmmN

g

LR

),1(4)(4)1(3

221 )(

211

2210

20

z

zzz

zzzzzzzzzzdz

,2

2

0

KM

Mz ,2

2

1

KM

mz ,2

2

2

KM

mz ,)1( 2

03 zz

.)(

2

2

KM

ppz

- the 4-momentum of the initial and final mesonspp ,


25

Using the input parameters for mesons:

Bounds on RPV couplings

and the masses of the various superpartners to be comparable the SUSY mass scale

We found that these R-parity violating contributions could be much larger then those from massive neutrinos.

3''' 10 kjiijk

GeVmSUSY 200

values of neutralino mixing matrix elements (hep-ph/0311123):

MeVf

MeVf

MeVf

D

K

228

,160

,131

.1015.3,1000.9,1043.9,1047.5

,1016.1,1006.6,1002.1,1086.91

422

321

222

12

141

231

121

111

NNNN

NNNN


26

Rare decay10SUSYmB

eeK K eK

eeKD KD eKD

2112111

7 )(1058.0 2

2122117 )(1020.0

2112211212111

7 )(1019.0 2

11212210 )(1026.0

2212222

10 )(1024.0 2

11222221212210 )(1012.0

B

Bounds on the branching ratios for the rare meson decays in SUSY theories with R-parity non-conservation.

221057.0 221020.0 221073.0 191025.0 191024.0 191047.0

2-nd vienna central european seminar, nov 25-27, 2005 1 rare meson decays in theories beyond the...

Documents

meson decay slide

matrix slide

susy slide

hadron tensor slide

effective majorana mass

sidorova msu slide

heavy majorana neutrinos

rare meson decays