QCD sum rules analysis of the $B_{s}\to D_{sJ}(2460)lν$ decay

0.16 MB·English

by  T. M. Aliev

International Conference on Hadron Physics, 30 Aug - 3 Sep 2007, Canakkale, Turkey 1
QCD sum rules analysis of the Bs DsJ(2460)lν decay
→
T. M. Aliev, K. Azizi *, A. Ozpineci
Physics Department, Middle East Technical University, Ankara, Turkey
*: Speaker
Using three point QCD sum rules method, the form factors relevant to the semileptonic B D (2460)ℓν
s sJ
8 →
0 decayarecalculated. Theq2dependenciesoftheseformfactorsareevaluated. Thedependenceoftheasymmetry
0
2 parameterα,characterizingthepolarizationofD meson,onq2 isstudied. Thisstudygivesusefulinformation
sJ

n
about the structure of the D meson. Finally the branching ratio of this decay is also estimated and is shown
a sJ
J
that it can be easily detected at LHC. Note that this talk is based on the original work in [1].
7

]
h I. INTRODUCTION
p
-
p
e Recently, very exciting experimentalresults have been obtained in charmedhadronspectroscopy. The obser-
h
[ vationoftwonarrowresonanceswithcharmandstrangeness,DsJ(2317)intheDsπ0 invariantmassdistribution

1 [2, 3, 4, 5, 6, 7], and D (2460) in the D∗π0 and D γ mass distribution [3, 4, 5, 7, 8, 9], has raised discus-
sJ s s
v
8 sions about the nature of these states and their quark content [10, 11]. Analysis of the D (2317) D∗γ,
5 s0 → s
9 D (2460) D∗γ andD (2460) D (2317)γ indicatesthatthe quarkcontentofthesemesonsareprobably
0 sJ → s SJ → s0
. cs [12]. In [12] it is also shown that finite quark mass effects for the c-quark give non-negligible corrections.
1
0
When LHC begins operation, an abundant number of B mesons will be produced creating a real possibility
8 s
0
for studying the properties of B meson and its various decay channels. One of the possible decay channels of
: s
v
i B meson is its semileptonic B D (2460)lν decay. Analysis of this decay might yield useful information
X s s → sJ
r for understanding the structure of the D (2460) meson.
sJ
a
It is well known that the semileptonic decays of heavy flavored mesons are very promising tools for the
determination of the elements of the CKM matrix, leptonic decay constants as well as the origin of the CP
violation. In semileptonic decays the long distance dynamics are parameterized by transition form factors,
calculation of which is a central problem for these decays.
Obviously,for the calculation of the transitionform factors,nonperturbative approachesare needed. Among
thenonperturbativeapproaches,theQCDsumrulesmethod[13]receivedspecialattention,becausethismethod
is based on the fundamental QCD Lagrangian. This method has been successfully applied to a wide variety of
0
problemsin hadronphysics(fora review see[14]). The semileptonic decay D K lν is studiedusing the QCD
→
sum rules with three point correlation function in [15]. Then, the semileptonic decays D+ K0∗e+ν e [16],
→
International Conference on Hadron Physics, 30 Aug - 3 Sep 2007, Canakkale, Turkey 2
∗
D π lν [17], D ρ lνe [18] and B D(D )lν e [19] are studied in the same framework. In the present
→ → →
work we study the semileptonic decay of B meson to positive parity D (2460) meson,i.e, B D (2460)ℓν,
s sJ s sJ
→
within QCD sum rules method. Note that, in [20], the decay B D (2317)lν has been studied using the
s → s0
QCD sum rules.
The paper is organized as follows: In section II the sum rules for the transition form factors are calculated;
section III is devoted to the numerical analysis, discussion and our conclusions.
II. SUM RULES FOR THE Bs →DsJ(2460)ℓν TRANSITION FORM FACTORS
The B D transition proceeds by the b c transition at the quark level. The matrix element for the
s sJ
→ →
quark level process can be written as:
G
F
M = V ν γ (1 γ )l c γ (1 γ )b (1)
q cb µ 5 µ 5
√2 − −
In order to obtain the matrix elements for B D (2460)ℓν decay, we need to sandwich Eq. (1) between
s sJ
→
initial and final meson states. So, the amplitude of the B D (2460)ℓν decay can be written as:
s sJ
→
G
F
M = V ν γ (1 γ )l <D c γ (1 γ )b B > (2)
cb µ 5 sJ µ 5 s
√2 − | − |
The main problem is the calculation of the matrix element < D cγ (1 γ )b B > appearing in Eq. (2).
sJ µ 5 s
| − |
Both vector and axial vector part of c γ (1 γ )b contribute to the matrix element considered above. From
µ 5
−
Lorentz invariance and parity considerations, this matrix element can be parameterized in terms of the form
factors in the following way:
f (q2)
<D (p′,ε) cγ γ b B (p)>= V ε ε∗νpαp′β (3)
sJ µ 5 s µναβ
| | (m +m )
Bs DsJ
<D (p′,ε) cγ b B (p)> = i f (q2)(m +m )ε∗
sJ | µ | s 0 Bs DsJ µ
f+(q2) ∗ (cid:2) f−(q2) ∗
+ (ε p)P + (ε p)q (4)
µ µ
(m +m ) (m +m )
Bs DsJ Bs DsJ (cid:21)
where fV(q2), f0(q2), f+(q2) and f−(q2) are the transition form factors and Pµ =(p+p′)µ, qµ =(p p′)µ. In
−
all following discussions, for customary, we will use following redefinitions:
f (q2)
f′ (q2) = V , f′(q2)=f (q2)(m +m )
V (m +m ) 0 0 Bs DsJ
Bs DsJ
f+′ (q2) = (m f++(qm2) ) , f−′ (q2)= (m f−+(qm2) ) (5)
Bs DsJ Bs DsJ
For the calculation of these form factors, QCD sum rules method will be employed. We start by considering
the following correlator:
ΠV;A(p2,p′2,q2)=i2 d4xd4ye−ipxeip′y <0 T[J (y)JV;A(0)J (x)] 0> (6)
µν | νDsJ µ Bs |
Z
International Conference on Hadron Physics, 30 Aug - 3 Sep 2007, Canakkale, Turkey 3
where J (y) = sγ γ c, J (x) = bγ s , JV = cγ b and JA = cγ γ b are the interpolating currents of the
νDsJ ν 5 Bs 5 µ µ µ µ 5
D , B , vector and axial vector currents respectively.
sJ s
To calculate the phenomenological part of the correlator given in Eq. (6), two complete sets of intermediate
states with the same quantum number as the currents J and J respectively are inserted. As a result of
DsJ Bs
this procedure we get the following representationof the above-mentioned correlator:
ΠV,A(p2,p′2,q2)=
µν
<0 Jν D (p′)ε ><D (p′)ε JV,A B (p)><B (p) J 0>
| DsJ | sJ sJ | µ | s s | Bs | +
(p′2 m2 )(p2 m2 ) ···
− DsJ − Bs
(7)
where represent contributions coming from higher states and continuum. The matrix elements in Eq. (7)
···
are defined in the standard way as:
f m2
<0 Jν D (p′)>=f m εν , <B (p) J 0>= i Bs Bs (8)
| DsJ | sJ DsJ DsJ s | Bs | − m +m
b s
where f and f are the leptonic decay constants of D and B mesons, respectively. Using Eq. (3), Eq.
DsJ Bs sJ s
(4) and Eq. (8) and performing summation over the polarization of the D meson, Eq. (7) can be written as:
sJ
ΠV (p2,p′2,q2) = fBsm2Bs fDsJmDsJ [f′g +f′ P p
µν −(m +m )(p′2 m2 )(p2 m2 ) × 0 µν + µ ν
b s − DsJ − Bs
′
+ f q p ]+excited states.
− µ ν
ΠA (p2,p′2,q2) = iε p′αpβ fBsm2Bs fDsJmDsJ f′ +
µν − µναβ (m +m )(p′2 m2 )(p2 m2 ) V
b s − DsJ − Bs
excited states. (9)
In accordance with the QCD sum rules philosophy, Π (p2,p′2,q2) can also be calculated from QCD side
µν
with the help of the operator product expansion(OPE) in the deep Euclidean region p2 (m +m )2 and
b c
≪
p′2 (m +m )2. The theoretical part of the correlator is calculated by means of OPE, and up to operators
c s
≪
having dimension d = 6, it is determined by the bare-loop and the power corrections from the operators with
d = 3, < ψψ >, d = 4, m < ψψ >, d = 5, m2 < ψψ > and d = 6, < ψψψ¯ψ >. In calculating the d = 6
s 0
operator, vacuum saturation approximation is used to set < ψψψ¯ψ >=< ψψ >2. In calculating the bare-loop
contribution, we first write the double dispersion representation for the coefficients of corresponding Lorentz
structures appearing in the correlation function as:
Π′per = 1 dsds′ ρi(s,s′,q2) + subtraction terms (10)
i −(2π)2 (s p2)(s′ p′2)
Z − −
The spectraldensities ρ (s,s′,q2) canbe calculatedfromthe usualFeynmanintegralwith the helpofCutkosky
i
rules, i.e. by replacing the quark propagators with Dirac delta functions: 1 2πδ(p2 m2), which
p2−m2 → − −
implies that all quarks are real. After standard calculations for the corresponding spectral densities we obtain:
ρ (s,s′,q2) = N I (s,s′,q2)[m +(m m )B +(m +m )B ],
V c 0 s s b 1 s c 2
−
International Conference on Hadron Physics, 30 Aug - 3 Sep 2007, Canakkale, Turkey 4
ρ (s,s′,q2) = N I (s,s′,q2)[8(m m )A 4m m m
0 c 0 b s 1 b c s
− −
+ 4(m m +m )m2 2(m +m )(∆+m2)
s− b c s− s c s
2(m m )(∆′+m2)+2m u]
− s− b s s
ρ (s,s′,q2) = N I (s,s′,q2)[4(m m )(A +A )+2(m 3m )B
+ c 0 b s 2 3 b s 1
− −
2(m +m )B 2m ],
c s 2 s
− −
ρ−(s,s′,q2) = NcI0(s,s′,q2)[4(mb ms)(A2 A3) 2(mb+ms)B1
− − −
+2(m +m )B +2m ]
c s 2 s
(11)
where
1
I (s,s′,q2) = ,
0 4λ1/2(s,s′,q2)
λ(s,s′,q2) = s2+s′2+q4 2sq2 2s′q2 2ss′,
− − −
∆′ = (s′ m2+m2),
− c s
∆ = (s m2+m2),
− b s
u = s+s′ q2,
−
1
′ ′
B = [2s∆ ∆u],
1 λ(s,s′,q2) −
1
′
B = [2s∆ ∆u],
2 λ(s,s′,q2) −
1
A = [∆′2s+2∆′m2s+m4s+∆2s′+2∆m2s′
1 2λ(s,s′,q2) s s s
+m4s′ 4m2ss′ ∆∆′u ∆m2u ∆′m2u m4u+m2u2],
s − s − − s − s − s s
1
A = [2∆′2ss′+4∆′m2ss′+2m4ss′+6∆2s′2
2 λ2(s,s′,q2) s s
+12∆m2s′2+6m4s′2 8m2ss′2 6∆∆′s′u
s s − s −
6∆m2s′u 6∆′m2s′u 6m4s′u+∆′2u2+2∆′m2u2
− s − s − s s
+m4u2+2m2s′u2],
s s
1
A = [4∆∆′ss′+4∆m2ss′+4∆′m2ss′+4m4ss′
3 λ2(s,s′,q2) s s s
3∆′2su 6∆′m2su 3m4su 3∆2s′u 6∆m2s′u
− − s − s − − s
3m4s′u+4m2ss′u+2∆∆′u2+2∆m2u2+2∆′m2u2
− s s s s
+2m4u2 m2u3]
s − s
(12)
The subscripts V, 0 and correspondto the coefficients ofthe structures proportionalto iε p′αpβ, g and
µναβ µν
±
1(p p p′p ) respectively. In Eq. (11) N =3 is the number of colors.
2 µ ν ± µ ν c
International Conference on Hadron Physics, 30 Aug - 3 Sep 2007, Canakkale, Turkey 5
The integration region for the perturbative contribution in Eq. (10) is determined from the condition
that arguments of the three δ functions must vanish simultaneously. The physical region in s and s’ plane is
described by the following inequalities:
2ss′+(s+s′ q2)(m2 s m2)+(m2 m2)2s
1 − b − − s s− c +1 (13)
− ≤ λ1/2(m2,s,m2)λ1/2(s,s′,q2) ≤
b s
For the contributionof powercorrections,i.e. the contributions of operatorswith dimensions d=3, 4 and 5,
we obtain the following results:
′(3) ′(4) ′(5) 1 ms mc mb
f +f +f = <ss> <ss>[− + ]
V V V rr′ − 2 rr′2 r′r2
m2 2m2 m2+m2 q2 2m2
+ s <ss>[ c + b c − + b]
2 r′3r r′2r2 r′r3
m2 3m2 3m2 2
0 <ss>[ c + b + i
− 6 r′3r r′r3 r′r2
2m2+2m2+m m 2q2
+ b c b c− ]
r′2r2
f′(3)+f′(4)+f′(5) = (mb−mc)2−q2 <ss>
0 0 0 2rr′
m 2m m2+m m2+m3 m q2
+ s <ss>[− b c c b c − c
4 rr′2
m +m 2m m2 m3 m m2+m q2
c b + c b − b − b c b ]
− rr′ r′r2
m2 16m m3+8m2m2+8m4 8m2q2
+ s <ss> − b c c b c − c
16 r′3r
(cid:26)
16m3m +8m4+8m2m2 8m2q2
+− b c b c b − b
r′r3
4m2 8m m +4m2 4q2
+ c − b c b −
r′2r
4m2 8m m +4m2 4q2 8
+ c − b c b −
r′r2 − r′r
1
+ 8m3m 8m m3+8m m q2+4m4
r′2r2 − b c− b c b c b
+ 8m2m(cid:2)2+4m4 8m2q2 8m2q2+4q4
c b c − b − c
m20 <ss>[3m2c(m2c +m2b −2mbmc−q(cid:3)(cid:9)2)
−12 r′3r
m2+m2 2m m q2
+3m2 c b − b c−
b r′r3
3m m (m2+m2 q2)+2(m2+m2 q2)2 2m2m2
+− b c c b − c b − − c b
r′2r2
3m (m m )+2(m2 q2)
+ c c− b b −
rr′2
3m ( 3m +m )+4(m2 q2) 2
+ b − c b c − ]
r2r′ − rr′
f′(3)+f′(4)+f′(5) = 1 <ss>+ms <ss>[−mc + mb ]
+ + + −2rr′ 4 rr′2 r′r2
m2 16m2 16m2 16 8m2 8m2+8q2
+ s <ss>[ c b + + − b − c ]
32 − r′3r − r′r3 r′r2 r2r′2
International Conference on Hadron Physics, 30 Aug - 3 Sep 2007, Canakkale, Turkey 6
m2 3m2 3m2 2
+ 0 <ss>[ c + b
12 r′3r r′r3 − r′r2
2m2+2m2+m m 2q2
+ b c b c− ]
r′2r2
f−′(3)+f−′(4)+f−′(5) = 2r1r′ <ss>−m4s <ss>[−rrm′2c + rm′rb2]
m2 16m2 16m2 16 8m2+8m2 8q2
+ s <ss>[ c + b + + b c − ]
32 r′3r r′r3 r′r2 r2r′2
m2 3m2 3m2 6
0 <ss>[ c + b +
−12 r′3r r′r3 r′r2
2m2+2m2+m m 2q2
+ b c b c− ] (14)
r′2r2
where r = p2 m2,r′ = p′2 m2. We would like to note that the contributions of operators with d = 6 are
− b − c
also calculated. Numerically their contributions to the corresponding sum rules turned out to be very small
and therefore we did not present their explicit expressions. Note also that, in the present work we neglect the
α correctionsto the bare loop. For consistency,we also neglectα correctionsin determination of the leptonic
s s
decay constants f and f .
Bs DsJ
′ ′ ′ ′
The QCD sum rules for the form factors f , f , f and f is obtained by equating the phenomenological
V 0 + −
expressiongiven in Eq. (9) and the OPE expressiongiven by Eqs. (11-14) and applying double Boreltransfor-
mations with respect to the variables p2 and p′2 (p2 M2,p′2 M2) in order to suppress the contributions
→ 1 → 2
of higher states and continuum:
f′(q2)= (mb+ms) 1 em2Bs/M12+m2DsJ/M22
i − f m2 f m
Bs Bs DsJ DsJ
[ 1 s0 ds s′0 ds′ρ (s,s′,q2)e−s/M12−s′/M22
×−(2π)2)Z(mb+ms)2 Z(mc+ms)2 i
+Bˆ(f(3)+f(4)+f(5))]
i i i
(15)
wherei=V,0and ,andBˆ denotesthedoubleBoreltransformationoperator. InEq. (15),inordertosubtract
±
the contributions of the higher states and the continuum, quark-hadron duality assumption is used, i.e. it is
assumed that
ρhigherstates(s,s′)=ρOPE(s,s′)θ(s s )θ(s s′) (16)
− 0 − 0
In calculations the following rule for double Borel transformations is used:
Bˆ 1 1 ( 1)m+n 1 1 em2b/M2em2c/M′2 1 . (17)
rmr′n → − Γ(m)Γ(n) (M2)m−1(M′2)n−1
International Conference on Hadron Physics, 30 Aug - 3 Sep 2007, Canakkale, Turkey 7
III. NUMERICAL ANALYSIS
InthissectionwepresentournumericalanalysisfortheformfactorsfV(q2),f0(q2),f+(q2)andf−(q2). From
sum rule expressionsof these formfactors we see that the condensates, leptonic decay constants of B andD
s sJ
mesons, continuum thresholds s and s′ and Borel parameters M2 and M2 are the main input parameters. In
0 0 1 2
furthernumericalanalysiswechoosethevalueofthecondensatesatafixedrenormalizationscaleofabout1GeV.
Thevaluesofthe condensatesare[21]: <ψψ >= (240 10MeV)3,<ss>=(0.8 0.2)<ψψ >and
µ=1 GeV
| − ± ±
m2 =0.8 GeV2. The quark masses are taken to be m (µ=m )=1.275 0.015 GeV, m (1 GeV) 142 MeV
0 c c ± s ≃
[22]andm =(4.7 0.1)GeV [21]alsothemesonsmassesaretakentobem =2.46GeV andm =5.3GeV.
b ± DsJ Bs
ForthevaluesoftheleptonicdecayconstantsofB andD mesonsweusethe resultsobtainedfromtwo-point
s sJ
′
QCD analysis: f =209 38 MeV [14] and f = 225 25 MeV[12]. The threshold parameters s and s
Bs ± DsJ ± 0 0
are also determined from the two-point QCD sum rules: s = (35 2) GeV2 [13] and s′ = 9 GeV2 [12]. The
0 ± 0
BorelparametersM2 andM2 areauxiliaryquantitiesandthereforetheresultsofphysicalquantitiesshouldnot
1 2
dependonthem. InQCDsumrulemethod,OPEistruncatedatsomefiniteorder,leavingaresidualdependence
on the Borel parameters. For this reason,working regions for the Borelparameters should be chosensuch that
intheseregionsformfactorsarepracticallyindependentofthem. TheworkingregionsfortheBorelparameters
M2 andM2 canbe determined by requiringthat, onthe one side, the continuumcontributionshouldbe small,
1 2
and onthe other side, the contribution ofthe operatorwith the highest dimension shouldbe small. As a result
oftheabove-mentionedrequirements,theworkingregionsaredeterminedtobe 10GeV2 <M2 <20GeV2 and
1
4 GeV2 <M2 <10 GeV2.
2
In order to estimate the width of B D lν it is necessary to know the q2 dependence of the form factors
s sJ
→
fV(q2), f0(q2), f+(q2) and f−(q2) in the whole physical region m2l ≤q2 ≤(mBs −mDsJ)2. The q2 dependence
of the form factors can be calculated from QCD sum rules (for details, see [16, 17]). For extracting the q2
dependenceoftheformfactorsfromQCDsumrulesweshouldconsiderarangeq2 wherethecorrelatorfunction
canreliably be calculated. For this purpose we have to stay approximately1 GeV2 below the perturbative cut,
i.e., up to q2 =8 GeV2. In order to extend our results to the full physical region,we look for parameterization
of the form factors in such a way that in the region 0 q2 8 GeV2, this parameterization coincides with
≤ ≤
the sum rules prediction. The dependence of form factors fV(q2), f0(q2), f+(q2) and f−(q2) on q2 are given in
Figs.1, 2, 3 and 4, respectively. Our numerical calculations shows that the best parameterization of the form
factors with respect to q2 are as follows:
f (0)
f (q2)= i (18)
i 1+α˜qˆ+β˜qˆ2+γ˜qˆ3+λ˜qˆ4
where qˆ=q2/m2 . The values of the parameters f (0),α˜,β˜,γ˜, and λ˜ are given in the Table 1.
Bs i
International Conference on Hadron Physics, 30 Aug - 3 Sep 2007, Canakkale, Turkey 8
f(0) α˜ β˜ γ˜ λ˜
fV 1.18 -1.87 -1.88 -2.41 3.34
f0 0.076 1.85 0.89 19.0 -79.3
f+ 0.13 -7.14 11.6 21.3 -59.8
f− -0.26 -4.11 -3.27 15.2 18.6
TABLE I: Parameters appearing in theform factors of the BS →DsJ(2460)ℓν
decay in a four-parameter fit,for M2 =15 GeV2, M2 =6 GeV2
1 2
For B D (2460)lν decay it is also possible to determine the polarization of the D (2460) meson. For
s sJ sJ
→
this aim we determine the asymmetry parameter α, characterizing the polarization of the D (2460) meson,as
sJ
dΓ /dq2
L
α=2 1 (19)
dΓ /dq2 −
T
where dΓ /dq2 and dΓ /dq2 aredifferential widths of the decayto the states with longitudinalandtransversal
L T
polarized D (2460) meson. After some calculations for differential decay rates dΓ /dq2 and dΓ /dq2 we get
sJ L T
dΓ 1
T = −→p′ G2 V 2 (2A+Bq2)[ f′ 2 (4m2 −→p′ 2)+ f′ 2] (20)
dq2 8π4mBs2 | | F | cb | { | V | Bs | | | 0 | }
dΓ 1
L = −→p′ G2 V 2 (2A+Bq2) f′ 2 (4m2 −→p′ 2
dq2 16π4mBs2| | F| cb| n h| V | Bs | |
−→p′ 2
+m2 | | (m2 m2 q2))+ f′ 2
Bs m Bs − DsJ − | 0 |
DsJ
m2 −→p′ 2 m2 −→p′ 2
−|f+′ |2 BmS2| | (2m2BS +2m2DsJ −q2)−|f−′ |2 BmS2| | q2
DsJ DsJ
2 m2BS |−→p′ |2(Re(f′f′∗+f′f′∗+(m2 m2 )f′ f′∗))
− m2DsJ 0 + 0 − Bs − DsJ + − #
m2 −→p′ 2
2B BS | | f′ 2 +(m2 m2 )2 f′ 2 +q4 f′ 2
− m2 | 0 | Bs − DsJ | + | | − |
DsJ
+2(m2Bs −m2DsJ(cid:2))Re(f0′f+′∗)+2q2f0′f−′∗+2q2(m2Bs −m2DsJ)Re(f+′ f−′∗)
io
(21)
where
λ1/2(m2 ,m2 ,q2)
−→p′ = BS DsJ
| | 2m
BS
1
A = (q2 m2)2I
12q2 − l 0
1
B = (q2 m2)(q2+2m2)I
6q4 − l l 0
π m2
I = (1 l )
0 2 − q2
(22)
International Conference on Hadron Physics, 30 Aug - 3 Sep 2007, Canakkale, Turkey 9
Thedependenceoftheasymmetryparameterαonq2isshowninFig. 5. Fromthisfigureweseethatasymmetry
parameterαvariesbetween-0.3and0.3whenq2liesintheregionm2 q2 6GeV2. Aninterestingobservation
l ≤ ≤
isthataroundq2 =5.2GeV2theasymmetryparameterchangessign. Thereforemeasurementofthepolarization
asymmetry parameter α at fixed values of q2 and determination of its sign can give unambiguous information
about quark structure of D meson.
sJ
At the end of this section we would like to present the value of the branching ratio of this decay. Taking
into account the q2 dependence of the form factors and performing integration over q2 in the limit m2 q2
l ≤ ≤
(m m )2 and using the total life-time τ =1.46 10−12s [27] we get for the branching ratio
Bs − DsJ Bs ×
B(B D (2460)ℓν) 4.9 10−3 (23)
s sJ
→ ≃ ×
which can be easily measurable at LHC.
In conclusion,the semileptonic B D (2460)ℓν decay is investigated in QCD sum rule method. The q2
s sJ
→
dependence of the transition form factors are evaluated. The dependence of the asymmetry parameter α on q2
is investigated and the branching ratio is estimated to be measurably large at LHC.
International Conference on Hadron Physics, 30 Aug - 3 Sep 2007, Canakkale, Turkey 10
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