A closer look at the R D and R D* anomalies
Received: October
closer look at the
Debjyoti Bardhan 0 1 2 5 6 7
Pritibhajan Byakti 0 1 2 3 6 7
Diptimoy Ghosh 0 1 2 4 6 7
0 Rehovot 76100 , Israel
1 2A & 2B , Raja S.C. Mullick Road, Jadavpur, Kolkata 700 032 , India
2 1 Homi Bhabha Road , Mumbai 400005 , India
3 Department of Theoretical Physics, Indian Association for the Cultivation of Science
4 Department of Particle Physics and Astrophysics, Weizmann Institute of Science
5 Department of Theoretical Physics, Tata Institute of Fundamental Research
6 Open Access , c The Authors
7 Munich , Germany (2016)
The measurement of RD (RD ), the ratio of the branching fraction of predictions are not correlated. We identify the operators that can explain the experimental measurements of RD and RD individually and also together. Motivated by the recent ment of RD in bins of q2, the square of the invariant mass of the lepton-neutrino system, ArXiv ePrint: 1610.03038
Beyond Standard Model; Heavy Quark Physics
-
(B ! D
) to that of B
! Dl l(B ! D l l), shows 1:9
(3:3 ) deviation
e ective
(NP) signals assuming SU(3)C
SU(2)L
U(1)Y gauge invariance. We rst show that, in
polarisation in B ! D
decay, P (D ) by the Belle
collaboraalong with the information on
helicities in the
Contents
1 Introduction
2 Operator basis
3 Observables
4 B ! D form factors
5 B ! D form factors
6 Expressions for a`D, b`D and c`D for B ! D` `
8 Results
9 Summary 8.1 8.2 8.3
Explaining RD alone
Explaining RD alone
Explaining RD and RD together
A Full expressions for a`D, b`D and c`D
B Full expressions for a`D , b`D and c`D
C Contribution of the Tensor operator OTcbL`
C.1 B ! D
C.2 B ! D
D SU(3)C
SU(2)L
U(1)Y gauge invariance
E RG running of Wilson coe cients
Introduction
B B ! D( )l l
B ! D( )` ` decay processes.
List of Observables
Experimental Results
Measured value
HFAG average 0.397
HFAG average 0.316
Experiment
Our average
HFAG average
HFAG average
0.042 [20, 21]
0.028 [17]
0.015 [18]
0.011 [25]
0.018 [20, 21]
0.030 [26]
0.010 [17]
0.11 %
0.12 %
0.09 %
0.11 %
SM Prediction
0.011 [19]
0.008 [22]
0:003 [23]
0.003 [24]
0:09 %
2:11+00::1120 %
5:04+00::4442%
0:009 [28]
0:013 [27, 29]
0:360+00::000021
Observable
RD
B B ! D
B B ! D
B B ! Dl l
B B ! D l l
section 5 for more details.
or ) and l to denote
only the light leptons, e and .
explanations have been proposed.
helicities for all the
can be explained together.
Very recently, the Belle collaboration reported the
rst measurement of the
-polarisation in the decay B ! D
[27]. While the uncertainty in this measurement is
polarisation in both the B ! D
and B ! D
decays can completely distinguish
of the
lepton (in the
NP Lorentz structures.
we summarise our ndings in section 9.
Operator basis
The e ective Lagrangian for the b ! c `
process at the dimension 6 level is given by,
cb` 0 + Ccb` cb` + Ccb` 0 cb` 0
s
+ Cpcb`Opcb` + Cpcb` 0 cb` 0 + CTcb`OTcb` + CTcb5` OT 5
cb`
Op
C cb` =
responding Wilson coe
cients de ned at the renormalization scale
mb. In the SM,
The other possible tensor structures are related to
cb` and
cb` in the following way,
= [c
= [c
PR b][`
PR b][`
= [c PR b][` ]
= [c PR b][[`
= [c
= [c
= [c
PL b][`
PL b][`
= [c PL b][` ]
= [c PL b][[`
= [c
= [c b][` PL
= [c
= [c
= [c
= [c
5 b][[` PL
cb` +C
cb` +C
] =
] =
] =
The Wilson coe
= [c
= [c
= [c
= [c
5 b][[` PR
= [c b][` PR
cb` +C
cb` +C
+C10
+C10
+ CT 5
WCs in eq. (2.1) satisfy the following relations,
C9cb` =
C9cb` 0 =
CTcb` =
CTcb5` :
only in the appendix (see appendix C).
in appendices A and B.
Observables
be written as
dq2 d(cos )
= N jpD( ) j a`D( )
+ b`D( ) cos + c`D( ) cos2
are given by,
2(ab + bc + ca). The angle
is de ned as the angle
The total branching fraction is given by,
N =
jpD( ) j =
B G2F jVcbj2q2
256 3MB2
(MB2 ; M D2( ) ; q2)
binned RD( ) in the following way,
For the decays with
lepton in the nal state, the polarisation of the
also constitutes
polarisation fraction is de ned in the following way,
D( ) (+) and
leptons respectively.
forward-backward asymmetry, AFDB( ) is de ned as
RD( ) [q2 bin] = B
D( ) [q2 bin]
P (D( )) =
D( ) (+) +
AF B =
R =2 d D( )
R bD( ) (q2)dq2
D( ) is the total decay width of D( ) and the angle
has already been de ned
information on the nature of the short distance physics.
D form factors
hD(pD; MD)jc
5bjB(pB; MB)i = 0
hD(pD; MD)jc
bjB(pB; MB)i =
i(pBpD
hD(pD; MD)jc
5bjB(pB; MB)i = "
pBpD) MB + MD
2FT (q2)
2FT (q2)
MB + MD
r:h:s: = F0(q2)(MB2
M D2):
5 =
hD(pD; MD)jc
5bjB(pB; MB)i =
hD(pD; MD)jc
bjB(pB; MB)i
= "
i(pB pD
2FT (q2)
MB + MD
2FT (q2)
MB + MD
in [19].3 They are given by the following expressions,
= (mb
mc)hD(pD; MD)jcbjB(pB; MB)i
multiplication by q and gives
F+(z) =
F0(z) =
+(z) k=0
0(z) k=0
z(q2) =
p(MB + MD)2
p(MB + MD)2
4MBMD
4MBMD
q2(GeV2)
q2(GeV2)
2(x) = (x
for F0 and F+ correspond to a
1:646 where the
2 is computed using the expression
10% uncertainty
on the central value.
The functions +(z) and 0(z) are given by,
+(z) = 1:1213
0(z) = 0:5299
(1 + z)2(1
z)1=2
[(1 + r (...truncated)