in the SM and Beyond
Kwei-Chou Yang (楊桂周)
Chung-Yuan Christian University, Taiwan
2011 Cross Strait Meeting on Particle Physics and Cosmology
Refs:
PRD78:074007(2008) with H. Hatanaka
PRD77:094023(2008) with H. Hatanaka
Eur.Phys.J.C67:149(2010) with H. Hatanaka
Phys.Rev.D78:034018,2008
arXiv:1011.4661 with T.M. Aliev, M. Savci
Outline

→
ℓℓ : SM, new physics, data
 the K1A-K1B mixing angle,
 Results from SM and determination of
 Results for new physics
 Conclusion
In SM, flavor-changing neutral current (FCNC) transitions,
→
ℓℓ, are forbidden at the tree level
Electroweak penguin loops
Weak box diagram
sensitive to new physics
3
In SM, the → ℓ ℓ decay amplitude is given by
Dominant contributions are mainly from
 magnetic dipole operator
 vector current operator
 axial-vector current operator
|
| is constrained by
→
data
4
Data: Forward-Backward Asymmetry of
→
∗
ℓ ℓ
/
Dash: (1) sign-flipped
model; or (2) sign flips for
New physics
Dotted dash: flipped sign( ) (excluded)
models
Dot: (1) sign flips for and
; or sign flip for
and
(OK)
alone (excluded)
5
SUSY phenomenology can enter at same order as SM contributions
Large tan
30, … ⟹ sign flip in
6
Decays involving
and/or
From
Br ( B   K1 (1270 ) )  ( 4.3  0.9  0.9 ) 10 5
Br ( B  K (1400 ) )  1.5 10


1
5
Belle
: New window for studying FCNC
7
Axial-vector mesons
3P
1
(1++)
a1
a1
a10 , f 8 , f1
K1A
K1B
K10B
K1A
K10A
K10A
b1
b1
b10 , h8 , h1
K1B
1P
1
(1+-)
K10B
For JP=1+ light axial-vector mesons, two nonets have been observed:
 3P1 nonet (S=1)
I=0: f1(1285), f1(1420), I=1/2: K1A, I=1: a1(1260),
 1P1 nonet (S=0)
I=0: h1(1170), h1(1380), I=1/2: K1B , I=1: b1(1235)
K1A, K1B→ K1(1270), K1(1400)
8
8
Mixing angles
3P
1
a1
++
(1 )
a1
a10 , f 8 , f1
K1A
K1B
K10B
K1A
K10A
K10A
b1
b1
b10 , h8 , h1
K1B
1P
1
(1+-)
K10B
 3P1 states f1(1285) & f1(1420) have mixing [so are 1P1 states h1(1170) & h1(1380) ]
magnitude of 
sign of 
3P1 & 1P1 depend on the K1A-K1B mixing angle
9
9
 In SU(3) limit, K1A & K1B do not get mixed. However, they have admixture
due to strange and light quark mass difference
 PDG ⇒ |K|  45o
 Strong decays K1(1270), K1(1400)→ K,K* and their masses ⇒ K= 33,57
→ K1(1270),K1(1400)⇒ K= ±37, ± 58 HYC,’03)
(Suzuki,’93)
From
Br ( B   K1 (1270 ) )  ( 4.3  0.9  0.9 ) 10 5
Br ( B  K (1400 ) )  1.5 10


1
5
Br (   K1 (1270 ) )  ( 4.7  1.1) 10 5
Belle
ALEPH
⇒ K= -(34± 13), H. Hatanaka & KCY, Phys.Rev.D77:094023,2008
10
10
For axial-vector mesons: Decay constants
3P1( p,  ) | q    5 q' | 0  if 3 P1m3 P1 * ,
1P1( p,  ) | q    5 q' | 0  f1P1 ( * p  * p )
scale dependent
QCDSR by
KCY, ‘07
Form factors for B → A
By light cone sum rules (KCY,PRD78:034018,2008)
11
11
dependence of differential dilepton mass spectrum
→
,
Charmonium
resonances
:
:
:
34∘
45∘
57∘
→ ℓℓ
:
:
12
The effects of charmonium resonances become large
for 5GeV .
In the low s region, s 2GeV , the differential decay
1400 with
57∘ is
rate for → enhanced by about 80% compared with that with
34∘ ,
The rates for → variation of
.
1270
is not so sensitive to
13
can be well determined by the ratio:
57∘ 45∘
34
Insensitive to form factors and resonances
14
15
Solid curve
Dashed curve
,
,
Dot-dashed curve
The ratio is less than 0.15 for
47∘
21∘
16
,
→
ℓℓdecay
ℓ
B
ℓ
→
1270 →
1400 →
∗
→
→
ℓℓ
Forward-Backward Asymmetry
ℓ
B
ℓ
B
∗
Forward-Backward Asymmetry
0
90∘
90∘
180∘
with hard spectator correction
Non-factorizable contribution,
see Beneke, Feldmann & Seidel hep-ph/0106067
18
Forward-Backward Asymmetry (FBA)
Zero of FBA:
Form factor
̂
0
(zero is insensitive to
19
FBA of
→
∗
ℓℓ decay
H. Hatanaka, KCY, Eur.Phys.J.C67:149-162,2010.
20
New Physics
The sign of
can be flipped in susy models with non-minimal
flavor violation via gluino-down-squark loops
In general flavor violating supersymmetric models the sign of
can be flipped
and
is highly insensitive to
the NP effect
and thus is suitable for
determining the value of
,
=1.0 (solid), 1.2 (dotted),
0.8 (dot-dashed) and −1.0 (dashed)
where
≡
,
21
Ratio of differential widths as function of the dimuon invariant mass, s
The blue and red curves correspond
to
34◦ 57∘
=1.0 (solid), 1.2 (dotted),
0.8 (dot-dashed) and −1.0 (dashed)
where
≡ , ,
is insensitive to variation of
The ratio is increased (decreased) by about 100% (40%) at about s = 1.5
◦
◦
corresponding to
when
equals to −1 (sign flip)
22
Forward-Backward Asymmetry of
Dash: flipped sign of
→
Double-dotted dash: sign flips for and
Dash: flipped sign( )
long-short dash: sign flips for and
Dash: flipped sign( )
23
Conclusions
 the K1A-K1B mixing angle,
determined
can be more precisely
 It is accessible for new physics signals
 The mode is accessible in LHCb and future B-factories
謝謝
24
BACK UP
For axial-vecotr mesons: Decay constants
3P1( p,  ) | q    5 q' | 0  if 3 P1m3 P1 * ,
1P1( p,  ) | q    5 q' | 0  f1P1 ( * p  * p )
scale dependent
QCDSR by
KCY, ‘07
Form factors for B → A
By light cone sum rules (KCY,PRD78:034018,2008)
26
Light-cone distribution amplitudes (LCDAs)
chiral-even
chiral-odd
twist-2: ∥,
twist-3: g(v),g(a), h(t), h∥(p) related to twist-2 ones via WandzuraWilczek relations (neglecting 3-parton distributions)
27
1P
1
meson
Due to G-parity, , h∥(t), h∥(p) are symmetric under u→1-u, while ∥,g(v),
g(a) are antisymmetric with the replacement u→1-u in SU(3) limit
Convention:
1.4
1
1.2
0.51
0.8
0.6
0.2
0.4
0.4
∥
0.2
-0.5
0.2
0.4
0.6
0.6
0.8
0.8
1
1
-1
3P
1
meson
Due to G-parity, , h∥(t), h∥(p) are anti-symmetric under u→1-u, while
∥,g(v), g(a) are symmetric with the replacement u→1-u in SU(3) limit
Convention:
28
Gegenbauer moments
KCY, Nucl. Phys. B776, 187 (2007)
29