Изучение процессов двойного рождения
чармониев на B-фабриках и волновые функции
чармониев В.В. Брагута
Институт Физики Высоких Энергий
Content:Content:
Introduction Charmonia Distribution Amplitudes Properties of Charmonia Distribution
Amplitudes Double Charmonium Production at B-
factories Conclusion
Introduction
FactorizationFactorization
effects) bative(nonpertur 0|| :oncontributi distance Large 2.
QCD) ive(perturbat C :oncontributi distanceShort 1.
n
:onsContributiDifferent
nOM
0|)0(| C T
:formulaion Factorizat
n arg
.
n
Dist.eL
n
DistShort
OM
Nonperturbative effectsNonperturbative effects
q...DD q q,D q q, q
...; qDDD q q,DD q q,D q q, q
...; qDDD q q,DD q q,D q q, q
0
211
321211
321211
555
5555
production tocontribute that Operators
GGG
On
... :section cross The 22
110 nnn sss
At given order approximation in 1/s expansion some operators can be omitted
The leading twist distribution The leading twist distribution amplitudeamplitude
Distribution amplitudes Resume infinite series of operators Resume leading logarithmic radiative corrections
1
1 n
1n 1 n 2
5 1 2
1
Operators that contribute at the leading order approximation:
M(p)|q D ...D q|0 z z ...z ~ (pz) ( ), z 0,
Distribution amplitude ( ) can be c
n d x x
onsidered as a meson wave function.
hard
1
1
E~ ), ,( ),H(
dT
Distribution Amplitudes are the key ingredient
of Light Cone Formalism
Charmonia Distribution Amplitudes
The models of leading twist The models of leading twist DAsDAs
4.0~1
~v velocity sticcharacteri
,5.2 ,03.0
-1-Exp )( )1(~)~,(
2
2.30.8-
32.003.0
222
cm
1S states 2S states
25.0~1
~v velocity sticcharacteri
,7.08.3
-1-Exp )1(~)~,(
2
22
cm
V. Braguta, et.al., Phys.Lett.B646:80-90,2007
V. Braguta, Phys.Rev.D75:094016,2007
V. Braguta, arXiv:0709.3885 [hep-ph]
The twist-3 distribution amplitudesIf one ignores the contribution of the higher Fockstates, EOM unambiguously fix twist-3 distributionamplitudes
P.Ball, et.al., Nucl.Phys. B529
P. Ball, JHEP 9901:010
Properties of distribution amplitudes
Relativistic tailRelativistic tail
75.0||
n
2/32 )( )(a )1(~ ),( nn G
cm~
cm
At DA is suppressed in the region
Fine tuning is broken at due to evolution
This suppression can be achieved if there is fine tuning of an
Improvement of the model for Improvement of the model for DADA The evolution of the second moment
3512 )(a
51
22
The accuracy of the model for DA becomes better at larger scales
increases as decreases in error The
increases as decreases )(a tscoefficien The
2
2
19.0 18.0
state 2
005.0123.0 007.0070.0
state 1
3.04.0GeV 10
25.07.0~
2
GeV 102
~2
c
c
m
m
S
S
Pion distribution amplitudePion distribution amplitude
Distinction from pion distribution amplitude
Much better knowledge of DAs (even for higher twist and excited states) Improvement of the accuracy of models
Rather accurate predictions for exclusive charmonia production
Double charmonium production at B-factories
The processes:
'' ,' ,' / , / cccc JJee
e+e- V(3S1) P(1S0)
This formula was first derived in Bondar, Chernyak, Phys. Lett. B612, 215 (2005)
The results of the calculationThe results of the calculation
Why LO NRQCD predictions are much smaller than the experimental results?
[1] E. Braaten, J. Lee[2] K.Y. Liu, Z.G. He, K.T. Chao[21] D. Ebert, R.N.Faustov, V.O.Galkin, A.P. Martynenko[26] Z.G. He, Y.Fan, K.T. Chao[27] G.T. Bodwin, J. Lee, C.Yu [ ] A.E. Bondar, V.L. Chernyak
1. Relativistic corrections K~3-142. Leading logarithmic radiative corrections K~1.3-2.3
NRQCD resultsNRQCD results
D75 Rev. Phys. al.,et He 20 )/(
D77 Rev. Phys. al.,et Bodwin 6.17)/( 7.103.8
fbJee
fbJee
c
c
NRQCD results are overestimated
ConclusionConclusion Light cone formalism is natural approach to
hard exclusive processes Within the accuracy of the calculation one can
reach the agreement between the experimental results and light cone predictions for the double charmonium production
In hard exclusive processes (e+e- annihilation, bottomonium decays) relativistic and leading logarithmic radiative corrections are very important
Спасибо Спасибо
за вниманиеза внимание