ags lekcii newtheor.jinr.ru/~diastp/winter14/talks/shevchenko_l1.pdf · 2 - - ( ): : • . ., 39...
TRANSCRIPT
-
. .
( , )
-
2
- - ( ):
:
• . ., 39 (1960) 1459,
• . ., . . - , .1 (1963) 69,
•E.O. Alt, P. Grassberger, and W. Sandhas, Nucl. Phys. B2 (1967) 167.
:
•W. Sandhas, The three-body problem,
Acta Physica Austriaca, Suppl. IX (1972) 57.
• ., ., ,
., , 1979
• . . ,
., , 1986.
-
3
:
1. vs
2.
3.
4.
-
4
1
2
1
2
3
1
2
3
1
2
3
2- 3-
-
5
Vp
H +=µ2
2
21
21
mm
mm
+=µ
( ),
, , 1, 2,3
j k i j k
i i
j k i j k
m m m m mM
m m m m m
i j k i j
µ+
= =+ + +
≠ ≠ =
321
22
22VVV
M
qpH
i
i
i
i ++++=µ
iiii qpqp���� =,
3 :
2- 3-
:
:
:
:
-
6
1
2
1
2
3
1
2
3
1
2
3
2- 3-
-
7
:
VHHp
H +== 02
0 , 2µ
:
p�
- inn
nninii
q
EH�
ιι
ι
ψφφφ
==– :
n
n
ι
ι
φψ
- 3-
- 2-
3- :)2(
2
2
ni
i
ini E
M
qE +=
2- 3-
iii
i
iii VHHV
M
qpH +=++= ,
22
22
ιµ
-
8
VHHVM
qpH
i
i
i
i +==+= 0022
0 ),0( 22µ
( i = 0):
ii qp��=0φ -3-
3- :i
i
i
i p
M
qE
µ22
22
0 +=
VHHp
H +== 02
0 , 2µ
:
p�
-
2- 3-
-
9
)()(
'
)()(
' +−
±±
=
Ω=
ppS
pp
pp
��
��
��
)(±Ω -
( )
( )
,
i n i i n
jm in jm inS
ψ φ
ψ ψ
(±) ±
− (+)
= Ω
=
)(±Ωi -
2- 3-
-
10
0≥E 0
-
11
:
( )
2- 3-
0
0
( )
0lim
iH tt iH t
a a adt e e eε
εψ φ ε φ−(+) +
→−∞
= Ω = ∫
( )
0lim ( )p i G E i pε
ε ε+→
= +� �
- ( ) H
:1
0 0( ) ( )G z z H−= −
1 1
0 0( ) ( ) G z G z H H V− −− = − = ⇒
1( ) ( )G z z H −= −
-
12
0 0
0 0
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
G z G z G z V G z
G z G z G z V G z
= += +
- .
-
:
( ) ( )
0 ( ) p p G E i V pε+ += + +� � �
:
0 ( ) n n nG E Vψ ψ=
2- 3-
-
13
:
( )
2- 3-
0
0
( )
0lim
iH tt iH t
a a adt e e eε
εψ φ ε φ−(+) +
→−∞
= Ω = ∫
( )
0lim ( )p i G E i pε
ε ε+→
= +� �
- ( ) H
:1
0 0( ) ( )G z z H−= −
1 1
0 0( ) ( ) G z G z H H V− −− = − = ⇒
1( ) ( )G z z H −= −
- H
:
1( ) ( )i i
G z z H −= −
1 1( ) ( ) iiG z G z V− −− = ⇒
1( ) ( )G z z H −= −
in0
)( )( lim φεεψε
iEGi inin += →+
-
14
0 0
0 0
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
G z G z G z V G z
G z G z G z V G z
= += +
- .
-
:
( ) ( )
0 ( ) p p G E i V pε+ += + +� � �
:
0 ( ) n n nG E Vψ ψ=
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
ii i
ii i
G z G z G z V G z
G z G z G z V G z
= +
= +
( ) ( )( ) iin in i in inin i
iG E i V
E i H
εψ φ ε ψε
+ += + ++ −
( ) ( ) ( ) iin in i in inG E i Vψ φ ε ψ+ +⇒ = + +
( ) ( )( ) ijm jm i in jmjm i
iG E i V
E i H
εψ φ ε ψε
+ += + ++ −
inφ
, jmφjm inE E=
( ) ( ) ( ) ijm i in jmG E i Vψ ε ψ+ +⇒ = +
2- 3-
-
15
-
:
( ) ( )
0 ( ) p p G E i V pε+ += + +� � �
:
0 ( ) n n nG E Vψ ψ=
( )
( ) ( ) ( ) iin in i in inG E i Vψ φ ε ψ+ +⇒ = + +
( ) ( ) ( ) ijm i in jmG E i Vψ ε ψ+ +⇒ = +
( i)
( j)
–
!
( )
2- 3-
-
16
3-
• ⇒
• ,
,
⇒
•
-
17
S- :
( )2 2 2
'
'' 2 '
2 2 2p p
p p pS p p i p T i pδ π δ ε
µ µ µ
= − − − +
� �
� � � �
0 0 0( ) ( ) ( ) ( ) ( )G z G z G z T z G z= +
:
( )
2-
3-T
-
18
0 0( ) ( ) ( ) ( ) G z G z G z V G z= + ⇒
0 0 0( ) ( ) ( ) ( ) ( )G z G z G z T z G z= +
2- 3-
0( ) ( ) ( )T z V V G z T z= +
- -
-
19
S- :
( )2 2 2
'
'' 2 '
2 2 2p p
p p pS p p i p T i pδ π δ ε
µ µ µ
= − − − +
� �
� � � �
0 0 0( ) ( ) ( ) ( ) ( )G z G z G z T z G z= +
( ) ( )( ) ( )
, ', '
-2 ' '
jm in j i ij mn j i
jm in j jm ji in in i
S q q q q
i E E q U E i q
δ δ δ
π δ ψ ε ψ
= − −
− +
� � � �
� �
:
( )
2-
3-T
( ) ( ) ( ) ( ) ( )ji i j ji iG z G z G z U z G zδ= +
- ,
T-( )jiU z⇒
-
20
0 0( ) ( ) ( ) ( ) G z G z G z V G z= + ⇒
0 0 0( ) ( ) ( ) ( ) ( )G z G z G z T z G z= + ( ) ( ) ( ) ( ) ( )ji i j ji iG z G z G z U z G zδ= +
( ) ( ) ( ) ( ) jj jG z G z G z V G z= + ⇒
2- 3-
0( ) ( ) ( )T z V V G z T z= +
- -
( ) 10 01ji ji k kik j
U G T G Uδ −≠
= − +∑
- - -
( )
1
0 0 0i k ki
k
U G T G U−= +∑( 0, 0)i j≠ =
-
21
0( ) ( ) ( )T z V V G z T z= +
-
( ', ; ) ' ( )T p p z p T z p=� � � �
,
24 2
2 2
(2 ) ( ', ; ) ,
' 2
dT p p E i
d
p p E
σ π µ ε
µ
= +Ω
= =
� �
( ) 10 01ji ji k kik j
U G T G Uδ −≠
= − +∑
0( ) ( ) ( ),k k k kT z V V G z T z= +
- -
Tk - , 3-
:
( )2
(2)
' , ' ( ) ,
' '2
k k k k k
kk k k k k
k
q p T z q p
qq q p T z p
Mδ
=
− −
� � � �
� � � �
(2)
kT - 2-
2- 3-
Tk
-
22
( )
T-
V λ χ χ=
( ) 11 0 ( ) ,
( ) ( )
T z
z G z
χ τ χ
τ λ χ χ−−
=
= −
' ( ') ( ) p V p p pλ χ χ ∗= ⇒� � � �
21
2
( ') ( ) ' ( )
| ( '') |''
'' / 2
p pp T z p
pdp
z p
χ χχλ
µ
∗
−=
−−∫
� �
� �
�
�
: 0= ( )BN G Eψ χ
-
23
( ) ( )'j ji i j j ji i iU E i q U E i qφ ε φ ψ ε ψ+ = + =� �
( ) ( )i jk j ki+ → +
:
( )0 0' ( ) ( )j j ji i iq G z U E i G z qχ ε χ= +� �
.
( )0 0( ) ( ) ( )ji j ji iX z G z U E i G zχ ε χ= +
( ) 0( ) 1 ( ) ,ji ji j iZ z G zδ χ χ= −
-
24
23
1
( ) ( ) ( ) ( )2
kji ji jk k ki
k k
qX z Z z Z z z X z
Mτ
=
= + −
∑
. ( ) ( ) :i jk j ki+ → +2
2
( ', ; ) (2 ) ' ( ) ,
( ', ; ) ' ( ', ; )
j i i j j ji i
j i j
j i
j
f q q z M M q X z q
d q q z qf q q z
d q
π
σ
= −
=Ω
� � � �
� � �
� �
�
T- :
( )2
' , ' ( ) , ' ( ' ) ' ( )2
kk k k k k k k k k k k k
k
qq p T z q p q q p p z p p
Mδ χ τ χ ∗
= − −
� � � � � � � � � �
-
25
22
3211 12 2 21 13 3 31
2 3
22
3121 21 21 1 11 23 3 31
1 3
2
131 31 31 1 11
1
( ) ( ) ( ) ( ) ( )2 2
( ) ( ) ( ) ( ) ( ) ( )2 2
( ) ( ) ( ) 2
qqX z Z z z X z Z z z X z
M M
qqX z Z z Z z z X z Z z z X z
M M
qX z Z z Z z z X
M
τ τ
τ τ
τ
= − + −
= + − + −
= + −
2
232 2 21
2
( ) ( ) ( )2
qz Z z z X z
Mτ
+ −
1+(23) :
⇒
-
26
2
21 11 1 2 1 12 2 2 2 21 1
2
2
33 1 13 3 3 3 31 1
3
2 21 1 2 2
''' ( ) '' ' ( ) '' '' ( )
2
'' + '' ' ( ) '' '' ( )
2
' ( ) '
qq X z q dq q Z z q z q X z q
M
qdq q Z z q z q X z q
M
q X z q q Z
τ
τ
= − +
−
=
∫
∫
� � � � � � �
� � � � �
� � �
1 1
2
11 2 21 1 1 1 11 1
1
2
33 2 23 3 3 3 31 1
3
( )
'' + '' ' ( ) '' '' ( )
2
'' + '' ' ( ) '' '' ( )
2
z q
qdq q Z z q z q X z q
M
qdq q Z z q z q X z q
M
τ
τ
+
− +
−
∫
∫
�
� � � � �
� � � � �
�
3 31 1 3 31 1
2
11 3 31 1 1 1 11 1
1
2
22 3 32 2 2
2
' ( ) ' ( )
'' + '' ' ( ) '' '' ( )
2
'' + '' ' ( ) ''
2
q X z q q Z z q
qdq q Z z q z q X z q
M
qdq q Z z q z
M
τ
τ
= +
− +
−
∫
� � �
� � � � �
� � �
2 21 1 '' ( )q X z q
∫� �
-
27
:
- T- ,
-
- ( )
-
(3- 3-
; - )
- ( )
–
,
0' ( ) '' ' ( ) ''j ji i j j i iq Z z q q G z qχ χ=� � � �
-
28
T- :
, .
( )2
' , ' ( ) , ' ( ' ) ' ( )2
kk k k k k k k k k k k k
k
qq p T z q p q q p p z p p
Mδ χ τ χ ∗
= − −
� � � � � � � � � �
2(2)
2
kB
k
qz E
M− =
.
: .
2(2) (2)
, 2
kB k B
k
qz E E
M= + ≥ ⇒
(2) Bz E< ⇒
2- T-
-
29
3- 3- -
Z
( )2 2
( ' , '' ; ) ( ' , '' ; ) cos ,' ''
' '' ( ' , '' ; )
' '' 2 2
kji j i ji j i
j i
jk iji j i
j jk iki
mZ q q z y q q z i
q q
qm qy q q z z
q q
ε θ
µ µ
+ −
= − −
� �
∼
0' ( ) '' ' ( ) ''j ji i j j i iq Z z q q G z qχ χ=� � � �
1
,
1
(cos ) (cos )1( ' , '' ; )
2 ( ' , '' ; ) cos
LL ji j j
ji j i
P dZ q q z
y q q z i
θ θε θ−
=+ −∫
∼
:
1−
-
30
''iq
' jq
, ( ' , '' ; )L ji j jZ q q z⇒
1 ( ' , '' ; ) 1ji j iy q q z− < <
( ' , '' ; ) 1ji j iy q q z = ±
( )1 1
1 1
(cos ) (cos )1( ' , '' ; ) cos (cos ) (cos )
2 ( ' , '' ; ) cos
Lji j i L
ji j i
P dP i y q q z P d
y q q z i
θ θ π δ θ θ θε θ− −
= − −
+ − ∫ ∫
-
31
:
3- T-
3- T- +
(2)
,B kz E<
(2)
, 0B kE z< <
0z >
-
32
:
- T- ,
- T- ,
- ,
-
- ( )
- 3- …
⇒
-
33
:
-
3- 4- (3H, 3 He, 4He)
-
-
( – )
-
(π, η d, 3H, 3He)
- -
ΣΝ−πNNK
-
34
- –
?
?
K-pp –
: K-pp ,
(G- , ,
...): EB ~ (- 9) - (- 58) , Γ ~ 34 - 100
:
(FINUDA: EB = -115 , Γ = 67 ; DISTO: EB = -103 , Γ = 118 , OBELIX);
(HADES, LEPS, J-PARK)
3- ΣΝ−πNNK
-
35
– -
:
• , -
( , ):
,
• “ ”
( “ - ”,
):
3- :
1.
2.
NK
-
36
(1405)
PDG: 1406.5 25.0 MeV, 0
:
0 0
E i I
I I KN
π
π
Λ
• Σ Λ= − =
= Σ = :
(1405) - Λ
KN
:
- ,
- , , c n
K p K p K p MB
R Rγ
− − −
•→ →
1 s• 1 1
1 1 283 36 6 eV, 541 89 2
s s
SIDD SIDD
s sE∆ = − ± ± Γ = ± ± 2 eV− − −• → →
-
37
1- 2- Λ(1405) “” , :
Σ−πNK
:
1. :
2. :
- 1 K p (KEK
,
s
K p K p K p MB− − −
•• → →
- 0 p n NKK Km , m , m , m m , m
Λ−Σ− ππNK
( )
−−= , Σ
cn
cnc
RR
RRRR
11 , πγ • =
J. Révai, N.V.S., Phys. Rev. C 79 (2009) 035202,
N.V.S., Phys.Rev. C85 (2012) 034001; Nucl. Phys. A890-891 (2012) 50 (new fits)
-
38
sc VVV +=:
- :
Σ− πNKpK
−
1or 0 ;or ; , ==, = IKggV IIIIs πβαλβαβααβ
,1 2 2
,1 2 2
1- (1405):
1 ( ) ( ) ( )
( ) ( )
2- (1405):
1 ( ) (
( ) ( )
I pole
I pole
g k K KNk
g k K KNk
α αα α
α αα α
α π πβ
αβ
Ι
Ι
• Λ
= = Σ+
• Λ
= =+
2
,2 2 2 2 2 2
)
( )1 ( ) ( ).
( ) ( ) [ ( ) ( ) ]I pole
sg k
k k
αα α
α α α αβ α π π
β βΙ
Ι Ι
= + = Σ+ +
-
39
- -
3
2)2(
2 βα
β
π= ),'k( g
E
M
ff
)s(C)k(g
E
M)s;'k,k(V
��I�� � ����I�� � ��� �I ����
“ - ” ,
( Λ(1405) )
)2( βαβ MMsC)s(C WT
�� −−−=
Λ−Σ− ππNK
απ β IK ff , :
22
2
)()(
)()( αα
ααα
ββ
Ι
Ι
+=
kkg I
-
40
-
41
( )
-
42
1s K-p
-
43
Σ−Σ ππ
( )
-
(2- )
1414 – i 58 MeV 1417 – i 33 MeV
1386 – i 104 MeV 1406 – i 89 MeV
Λ−Σ− ππNKΣ−πNK
-
44
NN (pp)
P. Doleschall, private communication, 2009
∑
∑
=
=
=
→=
2
1,
2
1
ji
jijipp
i
iiipp
ggT
ggV
τ
λ
( )
( ) ( )
2
22
1
3 21 2
1 22 22 2
1 11 2
A: ( ) , 1, 2
B: ( ) , ( )
AA imi
Am
im
B BB Bm m
B Bm m
m m
g k ik
g k g kk k
γβ
γ γβ β
=
= =
= =+
= =+ +
∑
∑ ∑
fm 880.2)( fm, 558.16)(
fm 845.2)( fm, 553.16)(
==
==
pprppa
pprppa
B
eff
B
A
eff
A
:
Argonne V18 NN
( !),
-
45
( ) N NΣ −Λ
( )22
T ( , '; )
V ( , ') ( ) ( ')
1 ( )
N
I
N N N N
I I I I
N
IN
I
k k z
k k g k g k
g kk
λ
β
Σ
Σ Σ Σ Σ
Σ
Σ
=
=+
I=3/2
,
I=1/2
1. ,
2. ,
NN Λ−ΣNΣ
I=3/2
J. Révai, N.V.S., 2009
-
46
-
47
11 2 0 21 3 0 31
1
21 0 1 0 11 3 0 31
1
31 0 1 0 11 2 0 21
:
ij
U T G U T G U
U G T G U T G U
U G T G U T G U
U
−
−
= +
= + +
= + +
(12)3(23)1 :
(31)2(23)1 :
(23)1(23)1 :
31
21
11
+→++→++→+
U
U
U
1 2 3 1 2 3 1 2 3
1405
. ( ):
: , ,
KN
K N N N N
ππ α
α α π α π
Σ Λ( )⇒ Σ
=1 = 2 : Σ = 3: Σ
NNNK Σ−π
-
48
1 2 2 3 3
1 1 2 2 3 3 3
1 2 2 3
- , :
0 0 0 0
0 0 , 0 0 , 0
0 0 0 0 0
, - - ;
2-
i
NN KK K KK K
N N K
N K N
NN N N
KN
T T
T T T T T
T T T T T T T
T T T T
T T T T
T
αβ
π π
π π ππ
π ππ π
π
Σ
Σ
Σ
−
= = =
: : , :
: , :
KK K
K
T KN KN T KN
T KN T
π π
π ππ
ππ π π
Σ → Σ →→ Σ Σ → Σ
0 0 , ijG G Uαβ α αβ
αβδ=
, -
, -
i j
α β
( )( ) ( ) 3,2,1, , 1 1 03
1,
1
0 =−+−= ∑=
−jiUGTGU kj
k
kikijij
γβγ
γ
αγααβ
αβ δδδ
-
49
:
0, 0, 1/ 2
- ,
: 10
KNN N
S L I
π− Σ= = =
( ) ( ) ( ) ( ) ( ) ( ) ( )' ;', ' ',:
,
)2(
,,
)2(
,,,,, kgzkgzkkTkgkgkkV IiIiIiIiIiIiIiIi
��������βαβααββααβαβ τλ =⇒=
( ) ααααβαβαααβ δjijijjiiji IjIiijIIijIjIIijIiIIij
gGgZUGgU ,0,,,,0,, 1 , −≡Ψ≡
( ) ( )
( ) ( )∑ ∑ ∫3
1=
∞
−+
+=
γ
γβα
αγα
ααβ
αβ
µτ
δ
, 0
' ')3('' '
,
2' ')3(
,
)3(' '
,
)3('
,
)3('
,
;, 2
;,
;, ;,
:
k I
kjkIIjk
k
kIkkiIIik
jiIIijjiIIij
k
jkkki
jiji
pdzppXp
zzppZ
zppZzppX
�����
����
-
50
K_pp -
B (MeV) Γ (MeV)
Dote,Hyodo,Weise (PRC79,014003,2009) 17 – 23 40 – 70
Barnea,Gal,Liverts (PLB712,132,2012) 15.7 41.2
NVS,Gal,Mares,Revai (PRC76,044004,2007) 55.1 100.2
Ikeda,Kamano,Sato (Prog.Theor.Phys124,533,2010) :
E-indep 44 – 58 34 – 40
E-dep 9 – 16 34 – 46
67 – 89 244 – 320
(Revai, NVS):
. 1- 53.3 64.8
. 2- 47.4 49.8
- 32.2 48.6
NK
NKNK