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bJ/J/ decay within light cone formalism
V.V. Braguta
Institute for High Energy Physics Protvino, Russia


Hard exclusive processes
Exclusive processes : 1. Decays : b J / J / ,... 2. Annihilation : e + e - J / J / ,... 3. Different formfactors : F (Q 2 ),...
General property : E h >> QCD , M

h
b

M2 / J Expansion parameter : ~ 2 M an (E h = ) a = + n Eh
n +1

~

1 10

(E h = ) + ... n +1 Eh

Light cone expansion formalism


Factorization
Factorizat ion formula : T=


n

Short Dist .

C

n

в < M | On (0) | 0 >
L arg e Dist.

Different Contributions:
1. Short distance contribution : Cn (perturbative QCD) 2. Large distance contribution : < M | On | 0 > (nonperturbative effects)


The leading twist distribution amplitude
Operators that contribute at the leading order approximation: < M(p)|q 5 D 1 ...D n q|0 > z z ...z
1
n

~ (pz)

n +1

-1



1

d n ( ), z 2 = 0, = x1 - x2

Distribution amplitude ( ) can be considered as a meson wave function.

Resume infinite series of operators Resume leading logarithmic radiative corrections

Distribution amplitudes

T=

-1



1

d H( , ) ( , ),

~E

hard


bJ/J/ decay

The amplitude of the process T= Fe
p1 1 p 2
2

F is the only formfactor of the process

Helicity conservation + angular momentum conservation => J/=0 Helicity flip in gluon-quark-quark vertex leads to the suppression of the amplitude

bJ/J/ is a next-to-next-to-leading twist process


Distribution amplitudes of J/ up to twist-4

There are 10 distribution amplitudes needed in the calculation


The result of the calculation

Fine tuning between parameters at the leading order approximation in NRQCD

Fine tuning is broken due to relativistic and radiative corrections what leads to the dramatic enhancement of the branching ratio


Numerical results

Approximately 100 events of the bJ/J/ decay at LHC per year


Thank you