Semileptonic Bs DsJ2460 l

1

• Semileptonic Bs ? DsJ(2460) l?
• decay in
• QCD
• Kazem Azizi
• Middle East Technical University
• (Based on T. M. Aliev, K. Azizi, A. Ozpineci,
  Eur.Phys.J. C51 (2007) 593)

2
Outline

• Bs and DsJ(2460)

• MethodQCD Sum rules

• Importance of the analysis of such type transition

• Sum rules for the Bs ? DsJ(2460)l? transition
  form factors

• Numerical analysis of the form factors

• The Heavy Quark Mass Limit of Form Factors

• Determination of the polarization of the
  DsJ(2460) meson

• Branching Ratio

• Conclusion

3
Bs
?

(Not exactly known yet)
?

DsJ(2460)
4

• MethodQCD Sum rules
• Analysing ? form factors
• Transition form factors ? nonperturbative
  approaches.
• QCD sum rules method ? (fundamental QCD
  Lagrangian)
• Correlation function ? (two languages)
• Three point

5

• Importance of the analysis of such type
  transition
• yields useful information for understanding the
  structure of the
• DsJ(2460) meson.
• The semileptonic decays of heavy flavored mesons
  are very promising tools for the determination of
  the elements of the CKM matrix and leptonic decay
  constants.

6
Sum rules for the Bs ? DsJ(2460)l?
transition form factors

• The Bs ? DsJ transition proceeds by the b ? c
  transition at the quark level.

• The matrix element for the quark level is

7

• sandwich the matrix elements between initial and
  final meson states

• Both vector and axial vector part contribute to
  the matrix element

8

• From Lorentz invariance and parity
  considerations, this matrix element can be

parameterized in terms of the form factors in the
following way
where fV (q2), f0(q2), f(q2) and f-(q2) are the
transition form factors and Pµ (p p')µ, qµ
(p-p')µ.
9

• We start with the following correlator

the interpolating currents of the DsJ , Bs,
vector and axial vector currents respectively.
10

• phenomenological part of the correlator
• Two complete sets of intermediate states with the
  same quantum number as
• the currents JDsJ and JBs respectively are
  inserted.

? contributions coming from higher states
and continuum.
11

• By definitions

fDsJ ? leptonic decay constants of DsJ fBs
? Bs
12

• performing summation over the polarization of the
  DsJ meson

13
Theoritical Part

• The theoretical part of the correlator is
  calculated by means of OPE, and up to operators
  having dimension d 6, it is determined by the
  bare-loop and the power corrections from the
  operators with

Bare loop
d3,4,5 d5
d5
14

• The bare loop diagram is as

15
(No Transcript)
16
(No Transcript)
17
contribution of power corrections (operators with
dimensions d 3, 4 and 5)
18
(No Transcript)
19
(No Transcript)
20
The QCD sum rules for the form factors f'V , f'0,
f' and f'- is obtained by equating the
phenomenological expression and the OPE
expression and applying double Borel
transformations with respect to the variables p2
and p'2
Borel transformations to suppress the
contributions of higher states and continuum
21
to subtract the contributions of the higher
states and the continuum, quark-hadron duality
assumption is used, i.e. It is assumed that
double Borel transformations
22
Numerical analysis
23
(No Transcript)
24
(No Transcript)
25
(No Transcript)
26
(No Transcript)
27
parameterization of the form factors
.
28
The Heavy Quark Mass Limit of Form Factors
mb ? 8 mc ? 8
we see that finite mass corrections are essential
for fV (q2) and f0(q2) .
29
Determination of the polarization of the
DsJ(2460) meson
The asymmetry parameter
30
where
31
The dependence of the asymmetry parameter a on q2

• a varies between -0.3 and 0.3 when q2 lies in the
  region m2l q2 6 GeV 2.
• An interesting observation is that around q2
  5.2 GeV 2 the asymmetry parameter changes sign.
• Therefore measurement of the polarization
  asymmetry parameter a at fixed values of q2 and
  determination of its sign can give unambiguous
  information about quark structure of DsJ meson

32
Branching Ratio
Taking into account the q2 dependence of the form
factors and performing integration over q2 in the
limit m2l q2 (mBs-mDsJ )2 and using
the total life-time tBs 1.4610-12s
33
Conclusion
In conclusion,we investigated the semileptonic
Bs ? DsJ(2460)l? decay in QCD sum rule method
and evaluated The q2 dependence of the transition
form factors .Also we calculated the asymmetry
parameter and branching ratio.
34
Thank You