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Bc J / (Bs , Bs ) + n Decays
A. Berezhnoy, A. Likhoded, A. Luchinsky

27.09.2011

A. Berezhnoy, A. Likho ded, A. Luchinsky
Bc J / (Bs , Bs ) + n Decays


Aims of research

To estimate the branching ratios for the decays Bc J / (Bs , Bs ) + n To develop the package for simulation these decays within standard LHCb software GAUSS

A. Berezhnoy, A. Likho ded, A. Luchinsky
Bc J / (Bs , Bs ) + n Decays


Fast facts about Bc -mesons
Heavy quarkonium with open flavour
+ ¯ Bc = (b c ) - Bc = (b c ) ¯

mB

CDF = 6.2756 ± 0.0029(stat.) ± 0.0025(sys.) GeV c D0

Independent check of models describing charmonia and bottomonia The ground state can decay only through weak interaction Mass, lifetime and branching fractions of Bc J / , J / , J / + 3 (LHCb) decays are known experimentally about 109 of Bc is expected at LHC

mBc = 6.3000 ± 0.0014(stat.) ± 0.0005(sys.) GeV mBc
theor

= 6.25 ± 0.03 GeV

+0.038 CDF = 0.448-0.036 (stat.) ± 0.032(sys.) ps B c

Bc = 0.475-0.049 (stat.) ± 0.018(sys.) ps Bc
theor

D0

+0.053

= 0.48 ± 0.05 ps.

A. Berezhnoy, A. Likho ded, A. Luchinsky
Bc J / (Bs , Bs ) + n Decays


Factorization approach
GF Vcb J / µ a1 (µR )Hµ , W 2 ¸ Hµ = J / c µ (1 - 5 ) b Bc = Vµ - Aµ ¯ "" ¸ c µ b Bc = i µ p q FV q 2 , Vµ = J / ¯ M[Bc J / + n ] = " "" " "" " " "" A 2 A 2 A 2 pBc F- q pBc F+ q +qµ = µ F0 q +pµ where pBc and pJ / are the momenta of Bc - and J / -mesons; q = pBc - pJ / is the momentum of virtual W -boson; p = pBc + pJ / ;
J / is the polarization vector of J / meson; µ A A A and FV (q 2 ), F0 (q 2 ), F+ (q 2 ), F- (q 2 ) and FV (q 2 ) are form-factors of Bc J / + W decays.

R

¸ Aµ = J / c µ 5 b Bc = ¯

b

c

Bc c

J /

Figure: Diagram for Bc J / + n decay.

A. Berezhnoy, A. Likho ded, A. Luchinsky
Bc J / (Bs , Bs ) + n Decays


Factorization approach
n o 2 2 4 Fi (q ) = Fi (0) exp -c1 q - c2 q d (Bc J / R) = =
22 1 GF Vcb 2 µ W W a1 H H µ d (Bc J / n ) 2M 2

Spectral functions T

determined from theoretical and experimental analysis of some other pro cesses, for example n decay or electron-positron annihilation e + e - n . Bc J / + n Fi (0) c1 c2 5.9 0.049 0.0015 -0.074 0.049 0.0015 0.11 0.049 0.0015
Bc Bs + n Fi (0) c1 8.1 0.30 0.15 0.30 1.08 0.30

"" q 2 are universal and can be

d (Q p1 . . . pn ) = = (2 )
44

" X "Y Q- pi

d 3 pi 2Ei (2 )3

A0 A+ V

` ´ d Bc J / W J / n = = dq 2 2 ` ` ´ ´ d Bc J / W d W n 1 2 = " Z ` ´ W W d W n µ =
2

A0 A+ V

c2 0.069 0.069 0.069 c2 0.069

f+

Bc Bs + n fi (0) c1 1.3 0.30

qµ q - q gµ

"

T

"" "" 2 2 q + qµ q L q

Table: Form-factor parameterization.

conservation and partial axial current conservation. A. Berezhnoy, A. Likho ded, A. Luchinsky
Bc J / (Bs , Bs ) + n Decays

For n 2 R is negligible due to the vector current L


W n transition model
W n transition is described by contribution of virtual mesons [J. H. Kuhn and A. Santamaria, Z. Phys. C 48, 445 (1990)].
2 2 µ = F (q )(k1 - k2 )µ 3 µ = -i

22 3 f

¯ 2 Fa (q ) B (s1 )V1µ + B (s2 )V2µ q (k1,2 - k3 ) q2

V1,2µ = k1,2µ - k3µ - qµ

In EvtGen package this transition model is realized in TAUHADNU model of EvtGen. The decays Bc Bs + n is considered by analogy with Bc J / + n . The case of Bc Bs + n is more simple:
B ¯ Hµs = Bs |c (1 - 5 ) b | Bc

= f+ (q )pµ + f- (q )qµ .

2

2

A. Berezhnoy, A. Likho ded, A. Luchinsky
Bc J / (Bs , Bs ) + n Decays


Branching fractions
R/A 2 3 4 J / 0.17 0.48 0.48 0.77 0.4 Bs 18 7.6 6.1 0.096 6.4 â 10-3
Bs 7 21 13 0.23 0.015

Table: Br(Bc AR) [A. Likhoded and A. Luchinsky, Phys. Rev. D 81 (2010) 014015, Phys. Rev. D 82, 014012 (2010),A.V. Berezhnoy, A. K. Likhoded and A. V. Luchinsky, arXiv:1104.0808]
For Bc decay into Bs or Bs is it important to take into account the -meson width:

= 150 MeV M
A. Berezhnoy, A. Likho ded, A. Luchinsky
Bc J / (Bs , Bs ) + n Decays

B

c

-M

B

s

= 860 MeV


EvtGen and GAUSS

An EvtGen realization of this model is developed and implemented into the GAUSS package of LHCb collaboration (BC NPI-model). Bc V (P ) + n -decays for 1 n 3 are described Form-factor parameters can be changed
Special models for J / , Bs and Bs final states are supplied

A. Berezhnoy, A. Likho ded, A. Luchinsky
Bc J / (Bs , Bs ) + n Decays


BC NPI

Figure: The program structure.
A. Berezhnoy, A. Likho ded, A. Luchinsky
Bc J / (Bs , Bs ) + n Decays


Distributions from BC NPI
Br , q
2

10

2

Ge V

2

1.2

1 d Br , dq 2 GeV
0.005

2

1.0
0.004

0.8
0.003

0.6
0.002

0.4

0.2
2 2

0.001

q , Ge V 0.5 1.0 1.5

1

2

3

4

q 2 , GeV

2

The distribution over the squared 2 invariant mass q 2 = m in Bc J / + 2 decay generated within BC NPI-mo del (histogram) in comparison with the predictions of Likho ded, Luchinsky and Berezhnoy.

Figure:

The distribution over the 2 invariant mass q 2 = m in Bc decay generated within BC NPI-mo de in comparison with the predictions of Luchinsky and Berezhnoy.

Figure:

squared J / + 3 l (histogram) Likho ded,

A. Berezhnoy, A. Likho ded, A. Luchinsky
Bc J / (Bs , Bs ) + n Decays


Results

The branching ratios for the decays Bc J / (Bs , Bs ) + n have been estimated

The width of intermediate mesons must be taken into account The package for simulation these decays within standard LHCb software GAUSS has been developed The experimental LHCb data on Bc J / + 3 decay can be described satisfactorily within the model

A. Berezhnoy, A. Likho ded, A. Luchinsky
Bc J / (Bs , Bs ) + n Decays