Analysis of Zb decays as heavy meson molecules

Analysis of Zb decays
as heavy meson molecules
( S. O, S. Yasui and A. Hosaka, arXiv:1310.3029 )
S. OhkodaA
S. YasuiB and A. HosakaA
Research Center for Nuclear Physics (RCNP)
B
KEK theory center
A
ヘビークォークハドロンと原子核のスペクトルと構造 at KEK, 2/28/2013
エキゾチックチャンネル
QQ
QQqq
π
QQ(Q=c,b)で作れない量子数をもつ : JPC= 0+ ‒ ,1‒ + , 2+ ‒
荷電状態のQQ ライクな粒子
QQでは説明できない崩壊特性
X(3872), Y(4260), Zc (3900), Zb (10610), Zb (10650),
2
Outline
Introduction
Zb(10610) and Zb(10650)
Spin selection rules for Zb
Decays of Zb➜Υ(nS)π as hadronic
molecules
Summary
b)
Zb共鳴
jBW1 ðs; M1 ; "1 Þ þ aei# BW1 ðs; M2 ; "2 Þ þ
60
40
Υ(5S) ➜[Υ(2S) π ]π
0
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
20
0
0.2
Υ(5S) ➜[hb(1P)π ]π
0.4
0.6
80
100
80
60
60
40
40
20
20
0
10.4 10.45 10.5 10.55 10.6 10.65 10.7 10.75
0
0.2
π
! 120
12000
120
(c)
1.0
1.2
1.4
1.6
π π
π
100
0.8
(a)
17500
10000
(d)
(b)
15000
Events / 10 MeV/c2
20
Events / 10 MeV/c2
and
ecant
to
ion
SÞ!
ere
with
nethe
40
8000
6000
4000
2000
0
-2000
0.3 10.4
0.4
π π
12500
10000
7500
5000
2500
0
0.5 10.5
0.6
0.710.60.8
Mmiss(π), GeV/c
2
0.910.7
10.4
50
10
M
FIG.
The (a) PC
hb ð1PÞ
and (b) hb ð2PÞ yields
(e)
(f) 3. ✴
‒
‒
Υ : J =1
40
+

ð"Þ
(points
with error bars) and results
M
Υ(5S) ➜ Zb π ➜ Υ(nS)π π miss
80
hb : JPC=1+ ‒
✴
gram).
Υ(5S) ➜ Zb π ➜ hb(mP)π30+π
100
60
40
20
20
✴n=1,2,3 m=1,2
10
4
Belle group, PRL108, 112001 (2012).
Zbの質量と崩壊幅
Zb(10610) : Zb
M = 10607.4 2.0
Γ = 18.3 2.4 MeV
MeV
BB*
Zb(10650) : Zb
M = 10652.2 1.5
Γ = 11.5 2.2 MeV
MeV
B*B*
Belle group, PRL108, 112001 (2012).
Zbの特徴
エキゾチック量子数
IG(JP)=1+(1+)
A. Bondar, et al, !
PRD84 054010 (2011)
S. Ohkoda, Y. Yamaguchi, S. Yasui, !
K. Sudoh, and A. Hosaka, !
Phys. Rev. D86, 014004 (2012)
Zbは真性なエキゾチック粒子
エキゾチックな質量
Zbは非常に質量差の小さいツイン共鳴
(BB*とB*B*閾値のわずか上にある)
エキゾチックな崩壊
Υ(5S)➜Zbπ➜hb(mP)ππがボトムクォークのス
ピン反転が必要にも関わらず、抑制されていない
ZbはB*B(*)分子状態 !
6
Spin selection rules
for Zb
S. Ohkoda, Y. Yamaguchi, S. Yasui and A. Hosaka, !
Phys.Rev. D86, 117502 (2012).
7
( )の分岐比
Z
b
Branching fractions (B) of Zb (10610) and Zb (10650) assuming that the observed so far
Belle Collaboration,
arXiv:1206.6450
heir decays.
dence for
Channel
ϒ(1S)π +
ϒ(2S)π +
ϒ(3S)π +
hb (1P)π +
hb (2P)π +
B+ B∗0 + B0 B∗+
B∗+ B∗0
B of Zb (10610), %
0.32 ± 0.09
4.38 ± 1.21
2.15 ± 0.56
2.81 ± 1.10
2.15 ± 0.56
86.0 ± 3.6
–
B of Zb (10650), %
0.24 ± 0.07
2.40 ± 0.63
1.64 ± 0.40
7.43 ± 2.70
14.8 ± 6.22
–
73.4 ± 7.0
オープンフレーバーチャンネルへの崩壊が占有的
neutral
isotriplet member
Zb (10610)0
hbπ抑制されていない
➜ Zbのスピン構造と関係している
h Zb (10610) and Zb (10650) are isotriplets with only charged components observ
8
0 0
ヘビークォークスピン対称性
decay properties
of themLagragian
in Section with
4.5. the velocity-dependent fields Qv (x),
is useful the
to formulate
the eﬀective
quark symmetry
Using
Qv (x), we in
canQCD
decompose the original heavy quark field into the positive energy
sider that the heavy quark mass mQ is much larger than a typical
the negative
energy
heavy
quark
fields
Qvtheory
(x) as with
v (x)
eQof
lowand
energy
QCD.
In
this
case,
an
eﬀective
field
4.2 Heavy quark spin symmetry
expansion isヘビークォーク極限ではスピン-スピン相互作用が抑制さ
useful to study the hadrons containing a single heavy
Q v·x
= e−imfirst
[Q
+ Qheavy
(2.4)
this end, let us start ourQ(x)
discussion
with
v (x)the
v (x)], quark
れる ̶̶ Heavy quark spin symmetry
n;
4.2.1 Heavy quark spin symmetry
where
¯ / − mQ )Q,
LHQ = Q(iD
(1)
In the heavy eﬀective theory, the eﬀective Lagrangian for heavy quark field Qv is given
the heavy quark field, the
by1D−µ v/=
1 + v/ derivative is defined
imcovariant
imQ v·x
Q v·x
as
Q
(x)
=
e
Q(x),
Q(x)
=
e
(2.5)
a
a Q(x).
ta with the gluonv field Aaµ , the gauge
coupling
g
,
and
t
=
λ
/2
s
2
2
a
ell-Mann matrices λ (a = 1, · · · , 8). The
term
from light quark
µν
2
σ
G
(iD
)
µν
⊥
2
¯ v v current
¯m
¯ v fourLHQET
=
·subtracts
iDQv +discussion.
Q
QDenoting
c(µ)g
Q
Q
v Q v µ from
v −the
sthe
v + O(1/mQ ),
The exponential
prefactor
heavy
quark
momentum.
At the(4.1)
sectors
is not relevant
in Q
the
2m
4m
Q
Q
2
the
heavyorder,
quarkThe
as v Q
(vv field
= 1),only
we decompose
quark
field
leading
appears inthe
theheavy
eﬀective
Lagrangian,
whereas the Qv
µ
µQ
µ v ·and
µν negative
µ D ν ]/ig
sitive energy
component
the
energy
component
where
D
−vv(x)
and
σ µν substituting
= i[γ µ , γ ν ]/2.Eq
Here,
covariant
s,Q
ヘビークォーク極限では新たな保存量が定義できる
⊥ =
field is suppressed
byDpowers
ofD,G
1/mQ=. [D
Neglecting
and
.2.4the
into
the
v
derivative is defined as Dµ = ∂µ + igs Aaµ tq with the gluon
field Aaµ , the gauge coupling
¯
part of QCD
Lagrangian
involving
the heavy of
quarkfreedom
field, Q(iD/ − mQ )Q, we obtain the
̶̶
light
spin
degree
−imQ v·x
+Q
v (x)
v (x)] ,
gsQ(x)
, and =tae= λa /2 [Q
with
the
Gell-Mann
matrices λa (a =(2)
1, · · · , 8). c(µ) is the Wilson
eﬀective Lagrangian at lowest order as
Sl : Light spin
jections
S
J
S
l=
H
Jv (iv
: Total
momentum
¯im
1
+
v
/
− v/ vangular
L=Q
,
im v·x
v·x ·1D)Q
Qv (x) = e
Q(x), Qv (x) = e
Q(x).
(3)
S : Heavy
quark spin
2
2
sq + L
Q
Q
(2.6)
H
5
9
スピン選択則
ヘビーハドロンの波動関数はスピンの自由度を用いて
SH
Sl として記述できる
bb(2S+1LJ)
JPC
SH
Sl
ηb :
0-+
:
1S
➜
0H
0l Υ
:
1- -
:
3S
1
➜
1H
0l hb
:
1+-
:
1P
1
➜
0H
1l χbJ :
1++
:
3P
➜
(1H
0
J
1l)J スピン選択則
✗ hbππ
Υ➜
✗ ηbγ
Υ➜
10
Zbのスピン構造
Zbの崩壊特性を調べる
Zbをメソン分子状態と仮定する
Component
Zb
:
Zb
:
1
¯
(B B
2
¯ 3 S1 )
B B)(
¯ ( S1 )
B B
3
Zbのスピン構造?
11
SH
➜
➜
Sl
❓
ˆ Sˆ
jˆ1 jˆ2 L
[[l1 , s1 ] 1 , [l2 , s2 ] 2 ] =
l2 s2 j2 [[l1 , l2 ] , [s1 , s2 ] ] ,
⎪
⎪
⎪
⎩L S J ⎪
⎭
ヘビーメソンペアのスピン構造
L,S
(5.34)
Chapter 5. Spin selection rules for decays and productions of Zb resonances and other
¯ molecules
where [j1 , j2 ]J means that the angular momenta j1 and j2 are coupled to the total angular
BB
69
√
ヘビーメソンペアのスピン構造はスピン組み替え公式を用
ˆ
¯ ∗ (3 S )
momentum J, and J = 2J + 1. By using this, the heavy and light spins of B B
1
∗ ¯¯3 S
¯bq]0 ]1
いて求められる
and
B
are re-coupled
1 )1 )⟩
|B ∗B(
B(3 S
= [[b¯
q ]1 , [as
1 −
1 −
1 −
−
−
−
√
=
−
(0
⊗
1
)
+
(1
⊗
0
)
+
(1
⊗
1
(5.36)
∗
3
0
1
1
H
H
H
l
l
l ),
¯bq] ] 2
¯ ( S1 )⟩ = 2 [[b¯
|B
B
q
]
,
[
Chapter 5. Spin selection rules for decays⎧and productions
⎫ of Z2b resonances and other
¯ molecules
⎪
1/2 1/2 0⎪
BB
69
⎪
⎪
⎨
⎬
)
*
1
∗
∗
3
∗
∗
3
!
1
¯
¯
¯
which give the spin structure of √2 (B
ˆˆBˆ ˆ− B B)( S1 ). For ¯BH B ( l S1 ), we have
=
01H l
[bb] , [¯
q q]
1/2 1/2 1
⎪
⎪
⎪
H,l
⎩
⎭
∗¯ 3
1 ¯ 0 1⎪
H
l
1
|B B(
S
)⟩
=
[[b¯
q
]
,
[
bq]
]
!
"
1
1 ¯ 1 1
¯ ∗ (3 S1 )⟩ = [b¯
|B ∗ B
q
]
1 1 +− ,0[bq]
,
− ⎧1 ,11 1
− + ¯ 1−⎫ 0 ,11
−1 + −
1,
1 1 (5.36)
¯
√
= =
− (0H[b¯b]
⊗ 1, [¯
)
+
(1
⊗
0
)
+
(1
⊗
1
)
− H [bb] l , [¯
q q]
+√
[blb] , [¯
q q]
H
lq q]
⎪
⎪
22
2
2
2
2
1/2
1/2
1
⎪
⎪
⎨
⎬+
,1
#
1 −ˆˆ ˆ ˆ−
1 −
1
H
l
¯b](1,−[¯
−
−
=
H
ll ) −
[b
q
q]
1/2
1/2
1
√
= 1 (0H11⊗
1
(1
⊗
0
)
+
⊗
1
,
(5.35)
∗
∗
3
∗
∗
3
H
H
l For
l )we
¯ −⎪
¯
¯
⎪
which give the spin structure of √2H,l
(B
B
B
B)(
S
).
B
B
(
S
),
have
2
2
1
1
⎪
⎪
⎩
⎭
2
1
! 1 !1 0 1 "1 1 "1
"
1 ! ¯1
∗ ¯∗ 3
0 1
¯bq], [¯
|B B ( S1 )⟩ = √
[b¯
q ] [b
, [¯b]
√
q q]
+
[bb] , [¯
q q]
⎧
⎫
2
2
⎪
1/2
1/2
1⎪
⎪
⎪
1
1
⎨
⎬
−
−
−
+0− ) .
,1
#
√
= √ (0
⊗
1
)
+
(1
⊗
(5.37)
H
l
H
H
l
l
ˆ
¯
ˆ
ˆ
ˆ
=
1
1
H
l
[b
b]
,
[¯
q
q]
1/2 1/2
2
2 1
⎪
⎪
⎪
⎪
H,l
⎩H
⎭
l
1
3 S ), their spin configurations are given
¯ ∗ (12
f the structure of Zb ’s is dominated by B (∗) B
!
" 1
!
"
H
l
Zbのスピン構造
A. Bondar, et al, !
PRD84 054010 (2011)
Zbスピン構造は次のように与えられる
Component
Zb
:
Zb
:
1
¯
(B B
2
¯ S1 )
B B)(
3
¯ (3 S1 )
B B
Zbは0Hと1Hの混合状態!
(0H
(1H
➜
1
(0H
2
➜
1
(0H
2
1l) の崩壊先はhbπ, ηbγ , ...
0l) の崩壊先はΥπ, χbJγ , ...
13
SH
Sl
1l ) +
1
(1H
2
0l )
1l )
1
(1H
2
0l )
Zb ➜ χbJ γ
S. Ohkoda, Y. Yamaguchi, S. Yasui and A. Hosaka, !
Phys.Rev. D86, 117502 (2012).
χb0 + γ(P-wave)
|
b0
(M 1) > |J=1 = (1H
1l )|J=0
(0+
H
1+
l )
1
1
5
(1H 0l )
(1H 1l )|J=1 +
(1H 2l )|J=1
3
3
3
χb1 + γ(P-wave)
1
1
15
| b1 (M 1) > |J=1 =
(1H 0l ) + (1H 1l )|J=1 + (1H 2l )|J=1
2
6
3
=
χb2 + γ(P-wave)
|
b2
(M 1) > |J=1 =
(Zb0
1
5
(1H
3
b0
)
:
:
0l ) +
(Zb0
3
14
15
(1H
6
b1
)
1
1l )|J=1 + (1H
6
:
:
(Zb0
5
b2
)
2l )|J=1
Decays of Zb ➜ Υ(nS)π via triangle diagrams
in heavy meson molecules
S. Ohkoda, S. Yasui and A. Hosaka, !
arXiv: 1310.3029 (2013)
15
( )の分岐比
Z
b
Branching fractions (B) of Zb (10610) and Zb (10650) assuming that the observed so far
Belle Collaboration,
arXiv:1206.6450
heir decays.
Channel
ϒ(1S)π +
ϒ(2S)π +
ϒ(3S)π +
hb (1P)π +
hb (2P)π +
B+ B∗0 + B0 B∗+
B∗+ B∗0
B of Zb (10610), %
0.32 ± 0.09
4.38 ± 1.21
2.15 ± 0.56
2.81 ± 1.10
2.15 ± 0.56
86.0 ± 3.6
–
B of Zb (10650), %
0.24 ± 0.07
2.40 ± 0.63
1.64 ± 0.40
7.43 ± 2.70
14.8 ± 6.22
–
73.4 ± 7.0
オープンフレーバーチャンネルへの崩壊が占有的
dence for neutral
isotriplet member Zb (10610)0
hbπ抑制されていない
h Zb (10610) and Zb (10650) are isotriplets with only charged components observ
16
0 0
( )の分岐比
Z
b
Branching fractions (B) of Zb (10610) and Zb (10650) assuming that the observed so far
Belle Collaboration,
arXiv:1206.6450
heir decays.
dence for
Channel
ϒ(1S)π +
ϒ(2S)π +
ϒ(3S)π +
hb (1P)π +
hb (2P)π +
B+ B∗0 + B0 B∗+
B∗+ B∗0
B of Zb (10610), %
0.32 ± 0.09
4.38 ± 1.21
2.15 ± 0.56
2.81 ± 1.10
2.15 ± 0.56
86.0 ± 3.6
–
B of Zb (10650), %
0.24 ± 0.07
10
2.40 ± 0.63
0.5
1.64 ± 0.40
7.43 ± 2.70
14.8 ± 6.22
–
73.4 ± 7.0
分岐比に位相空間の違いが反映されていない?
neutral isotriplet member Zb (10610)0
h Zb (10610) and Zb (10650) are isotriplets with only charged components observ
17
0 0
ダイアグラム : Zb( )+ ➜ Υ(nS)π+
′ b( )をメソン分子状態であると仮定する
Z
¯
¯ ∗ molecule, we define the wavefunction of them as
and B B, Zb is B ∗ B
∗
1
¯ ∗ − B ∗ B⟩
¯ ,
|Zb ⟩ = √ |B B
2
¯ ∗⟩ .
|Zb′ ⟩ = |B ∗ B
(1
(2
(′)+
dronic molecular picture, the diagrams contributing to the decay Zb
→ Υ(nS)π +
e discribed with the intermediate BB ∗ meson loops at lowest order. To calculat
メソンループを介したZb崩壊のダイアグラム
mplitude, we need to set the eﬀective Lagrangians for the couplings. We set th
B
Υ
menological Lagrangians at vertices of
Zb
B(*)
(′)
Zb
and B
Zb
(∗)
B*
Υ
mesons, which is
µ
¯µ∗ + Bµ∗ B)
¯ *,
∗ = gZBB ∗ Z (B B
LZBB
*
π
B
B
¯β∗ ,
LZ ′ B ∗ B ∗ = gZ ′ B ∗ B ∗ ϵµναβ ∂µ Zν′ Bα∗ B
B(*)
π
(3
(4
∗ B ∗ are determined from the experimenta
the coupling constants gZBB ∗ and gZ ′ B18
"
bed with
the intermediate
BBof open
meson
loops
at lowest
order.represente
To calc
charmonium
states to pairs
charm
mesons.
Here we
consider strong interactions
of mesons H Q containing a
有効ラグランジアン
e, we
need
to setquark
thethe
eﬀective
Lagrangians
for
thef framecouplings.
We Lse$
heavy
Q
which
be described
in the
with
cansingle
be related
to
singlecan
quantity
Fˆ since
!
f
Da
D*
a
(′) theory(∗)
ZBB*とZB*B*のラグランジアン
work
of
the
heavy
quark
effective
#HQET$
%23&,
exstates c
gical
Lagrangians
at
vertices
of
Z
and
B
mesons,
which
is
ˆ
b
!Fploiting
/ m D athe
. heavy
quark spin
flavor symmetries holding
結合定数はZ
B*B*の崩壊幅から決定する
b ➜ BB*とZ
b'➜and
limit. T
It
alsoforpossible
down
expression
forve-the M#
this limit
the an
heavy
quark
four
in is
QCD
m Q →'. toIn write
µ
∗
∗
¯µ + Bµ B)
¯ ,
∗ = gZBB ∗ Mz Z (B B
L
ZBB
coincides
with
that
of
the
hadron
and
it
is conserved
locity
v
strong couplings
involving heavy mesons and the
kaon. The
) strong
interactionsin%24&.
Because
of ′the
µναβ
∗ invariance
∗ can be under
!
¯
D s( *by
D (*)K
couplings,
the
soft
p
→0
limit,
related
′ B ∗ B ∗ = gZ ′ B ∗ B ∗ ϵ
L
K∂µ Zν Bα Bβ ,
Z
P
rotations of the heavy quark spin s Q , states differing only for
to a single low energy parameter g, as it turns out considerthe orientation of s Q are degenerate in mass and form a douing
the
effective
QCD
Lagrangian
describing
the
strong
inblet.
When
the
orbital
angular
momentum
of
the
light
deoupling constants gZBB ∗ and gZ ′ B( ∗ B) ∗ (are
) determined from the experim
パイオンとB(B*)メソンのラグランジアン
teractions
between
the
heavy
D ais* !#0,
D b* mesons
and the
octet
grees
of
freedom
relative
to
Q
the
two
states
in
the
+
′
∗ ¯∗
+
P
"
"
uesof
forthe
Z
→
B
B
.
The
experimental
results
indicate
that
Γ(Z
→
B
lighthave
pseudoscalar
結合定数gはD*➜Dπ崩壊から決定する(HQS)
b
,1 ) and correspond to
doublet
spin-paritymesons
J #(0!26":
and
f$f/
* ′+ (s) ,BB∗+
* ).
¯ ∗0This
(D (s)
, DΓ(Z
can be
represented
5.82 MeV
and
) = doublet
8.44 MeV.
Then
we set the rent,
gBB ∗writt
(s) ), b (B→
(s)B
Zb =
$
g = 0.59 %2.7& tives, read
by a 4$4 matrix:
Ha"
LI !ig Tr! H b # $ # 5 A ba
!
!
= 1.30 to reproduce the decay widths of the open flavor channels. where,
1% v”by (
with
the
operator
A
given
corresp
the eﬀective Lagrangians
reflected
on
heavy
quark
and
)
"M
)
,
#2.1$
H a # for the
% Mcouplings
&
a 5
a (
2
!28". A
6]. Their forms are as follows:
1 †
with m
†
(
with M corresponding
A $ ba ! to
( $vector
' "19'(state
%2.8& In this
% 'the
$ ' &and
ba M to the pseu-
" #
..
˜ 1 •1 1 . T
two heavy quarks Q 1 Q 2 heavy quark flavor symmetry does
where g 1 !g
not hold any longer, but degeneracy is expected under rotathe two heavy-light m
PHYSICAL
REVIEW
D
69,
054023
"2004#
tions of the two heavy quark spins. This allows us to build up
state in S wave, and
P. Colangelo, et al,
heavy meson multiplets for each value of the relative angular
depend
on their relat
PRD64 054023 (2004)
↔
momentum !. For
one has a doublet
comprehensive of
sion is invariant unde
g 2 !!0 (Q
Q
)
1 2 state,
L2 ! 2andTra, Rvector
H 2a -”,H
↔Q 2the
# heavy quarks, rep
. $H.c.$
" Q 1 of
and
J/ / in case
a pseudoscalar
c 1a
charmonium. The corresponding 4$4 matrix reads as !27"
the
infinite heavy qua
"3.11#
considering that unde
1# v”
1" v”
tions
S 1 "SU(2) Q 1 a
which is(Qalso
invariant
under
independent
heavy quark
spin
Q
)
$
1
2
!
,
%3.1&
R
! L # $ "L # 5 "
2
2 produces a factor
formation
rotations. The action
of the derivative
of properties
ΥとB(B*)メソンのラグランジアン
" #
"3.6#
s the
intertates,
hat
" #
the residual momentum k, i.e. the quantity for which the
054023-4
hadron
and
the
heavy
quark
four
momentum
differ:
M Hv !
Vector meson dominance(VMD)によって結合定数を決める
!m Q v ! $k ! , k being finite in the heavy quark limit. The
Bcouplings of heavy-light Bcharmed mesons to J/ / follow
from Eq. "3.11#:
Υ
% D "*s #" p 1 , & 1 # DB"*s #" p 2 , & 2 # ! J/ / " p, & # '
B
< 0|b
µ¯
b|
*1 •q(nS)
!g D * D * / ," & • & *
#" &m
#
2
µ (s) g(s)
BB (nS) =
>= f ⇥
f
gBB
(1S)
= 13.2
gBB
(2S)
= 20.1
(nS) δM of gZbBB
= 24.1of the decay
TABLE I: Coupling constants gn and the mass-shifts
. Mth (3S)
is the thresholds
nd the mass-shifts δM of Zb . Mth is the thresholds of the decay
20
channel. Unit of the values1
is MeV
2
1
2
# " & •q #" & * • & * # $ " & • & * #" & * •q # ]
∗
∗
(2π)
×
×
=
×
×
=
×
×
➜ Υ(nS)π の遷移振幅
Z
"
gB ∗ B ∗ Υ(nS) {(ϵΥ · ϵ+
) (ϵ · (2q − p)) + (ϵΥ · ϵ1+
) (ϵ2 · (2q − p)) − (ϵ1 · ϵ3 = 2) (ϵΥ · (2q − p
b 2 1
1
1
1
2 ⃗2
F(⃗
q
,k )
(q)2 − m2B ∗ (P − q)2 − m2B (q − p)2 − m2B ∗
遷移振幅は次のように計算する
!
d4 q
β
3
µ ν α
′ ϵµναβ P ϵ ϵ ∗+ ϵ ¯ ∗0 ]
(i)
[ig
z
q z B B p=P-k
(2π)4
[igB ∗ B ∗ Υ(nS) ϵδτ θφ v δ ϵτυ ϵαB ∗+ (2q − P + k)φ ][gBB ∗ π (ϵB¯ ∗0 · k)]
q-P+k
P
1
1
1
2 ⃗2
F(⃗
q
,k )
2
2
2
2
2
2
(q) − mB ∗ (P − q) −P-q
mB ∗ (q − p) k
− mB
!
4
d
q
3
µ ν α β
τ θ
′
∗ B ∗ π ϵ0τ θφ MB ∗ ϵ k ϵ2 ]
(i)
[ig
ϵ
P
ϵ
ϵ
ϵ
][ig
!
z
µναβ
B
2
z
1
3
4
4
dq
(2π)
(B)
β
3
µ ν α
iMB∗ B∗ =
(i)
[igz′ ϵµναβ P ϵz ϵB ∗+ ϵB¯ ∗0 ]
"
#
4
(2π)
gB ∗ B ∗ Υ(nS) {(ϵΥ · ϵ1 ) (ϵ3 · (2q − p)) + (ϵΥ · ϵ3 ) (ϵ1 · (2q − p)) − (ϵ1 · ϵ3 ) (ϵΥ · (2q − p))}
× [igB ∗ B ∗ Υ(nS) ϵδτ θφ v δ ϵτυ ϵαB ∗+ (2q − P + k)φ ][gBB ∗ π (ϵB¯ ∗0 · k)]
1
1
1
2 ⃗2
1
1
F(⃗
q
,k )1
2
2
2
2
2
2
2
2
×
F(q
,
k
)
(11)
(q) − mB ∗ (P − q) −(q)
m2B−∗ m
(q2 −
p)
−
m
∗
2
2
2 B
2
∗ (P − q) − m ∗ (q − P + k) − m
B
B
B
Λ2Z finite
Λ2 interaction
Λ2
oduce the form factor F(⃗q 2 , ⃗k 2F(q
) to2 , reflect
the
range, which is given
2
k )=
(12)
形状因子を導入する
2
q 2 + Λ2Z k 2 + Λ2 k 2 + Λ2
2
TABLE I:
partial
ΛThe
Λ2 decay widths
Λ2 of Zb (10610)+ .
⃗2
F(⃗q , k ) =
Z
,
2
2
⃗k 2 + Λ
No2Z Cutoﬀ
ΛZ2 ⃗
=
1100
,
Λ
⃗q 2 + Λ
k + Λ = 600
Υ(1S)π +
95.5
21
0.081
exp
0.059
(17)
結果
+ for various cutoﬀ parameters
S. O, S.Λ
A. Hosaka
TABLE V:
V: The
The partial
partial decay
decay widths
widths of
of Z
Zbb(10610)
(10610)+
units
of
Z
TABLE
for various cutoﬀ parameters
ΛYasui
inand
units
of
Z in
部分崩壊幅 : Zb(10610)
arXiv:1310.3029
MeV. Λ
Λ=
= 600
600 MeV
MeV is
is fixed.
fixed. The
The left
left column
column shows
shows the
the results
MeV.
results without
without the
the form
form factors.
factors.
ΛZZ
1000
Exp.
Λ
-- 1000
Exp. [MeV]
+ 96.3 0.074 0.059 ± 0.017
Υ(1S)π+
Υ(1S)π
96.3 0.074 0.059 ± 0.017
+ 20.0 0.47
Υ(2S)π+
Υ(2S)π
20.0 0.47
+ 0.498 0.14
Υ(3S)π+
Υ(3S)π
0.498 0.14
0.81
0.81 ±
± 0.22
0.22
0.40
0.40 ±
± 0.10
0.10
部分崩壊幅
Zb (10650)
+ . Λ = 600 MeV is fixed. The unit is MeV.
TABLE VI:
VI: The
The
partial decay
decay: widths
widths
of Z
Zbb (10650)
(10650)+
TABLE
partial
of
. Λ = 600 MeV is fixed. The unit is MeV.
ΛZZ
Λ
--
1000
1000
Exp.
Exp. [MeV]
+ 71.3 0.044 0.028 ± 0.008
Υ(1S)π+
Υ(1S)π
71.3 0.044 0.028 ± 0.008
+ 17.6 0.31
Υ(2S)π+
Υ(2S)π
17.6 0.31
+ 0.858 0.18
Υ(3S)π+
Υ(3S)π
0.858 0.18
0.28
0.28 ±
± 0.07
0.07
0.19
0.19 ±
± 0.05
0.05
終状態の運動量が結果を大きく左右する
(2011), arXiv:1105.4473.
arXiv:1105.4473.
(2011),
形状因子が重要
[4] J.-R.
J.-R. Zhang,
Zhang, M.
M.
Zhong, and
and M.-Q.
M.-Q. Huang,
Huang, Phys.Lett.
Phys.Lett. B704,
[4]
Zhong,
B704, 312
312 (2011),
(2011), arXiv:1105.5472.
arXiv:1105.5472.
[5] S. Ohkoda, Y. Yamaguchi, S. Yasui, K. Sudoh,22
and A. Hosaka, Phys.Rev. D86, 014004 (2012),
カットオフ依存性 : Zb(10650)
Zb + ➜ Υ(nS) π+
Zb + ➜ Υ(nS) π+
Λ=600 MeV
ΛZ = 1000 MeV
23
tion, Z. Liu et al., Phys.Rev.Lett. 110, 252002 (2013), arXiv:1304.0121.
+ ➜ ψ(nS)π+
Z
c
., Phys.Rev. D87, 074006 (2013), arXiv:1301.6461.
o, C.-W. Zhao, and Q. Zhao, Phys.Rev. D87, 034020 (2013), arXiv:1212.3
Zc(3900) : M = 3899.0MeV, Γ=46MeV (BESIII)
F. De Fazio, and T. Pham,
Phys.Rev.
D69,
M = 3894.5
MeV, Γ=63
MeV054023
(Belle) (2004), arXiv:
Zc(3900)はDD*分子状態でZbのフレーバーパートナー？
部分崩壊幅
he partial decay
widths: Zofc(3900)
Zc+ . Λ = 600 MeV is fixed. The unit is MeV.
ΛZ
-
1000 Exp.
39.0 0.66
-
ψ(2S)π + 0.305 0.18
-
J/ψπ +
f(Zc+➜J/ψπ+)=1.2-1.3％, f(Zc+➜ψ(2S)π+)=0.31- 0.33％
10
24
まとめ
Zbの崩壊特性をメソン分子状態の観点から調べた
スピン構造はエキゾチック粒子の生成と崩壊の性質を
調査するのに有効
Zb ➜ Υπ崩壊幅は、メソンループと形状因子によって
説明できる
f(Zc+➜J/ψπ+)=1.2-1.3％,
f(Zc+➜ψ(2S)π+)=0.31-0.33％
25

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