Scrutinizing final-state interactions
in charmed hadronic B decays
Satoshi Mishima (KEK)
Flavor Physics Workshop, Sep. 27, 2021
M. Endo, S. Iguro and S. M., arXiv:2109.10811

Anomaly?
✦ #⚥꟦㶨‫ؙحصٗسعך‬䄶㠨%⚥꟦㶨‫׾‬穄朐䡾‫ח‬ろ‫ך׮׬‬‫ⴓך‬䀄嫰‫ך‬椚锷⦼ָ㹋꿀‫ر‬٦‫׮׶״ة‬㣐ְֹ‫ָהְֲֿה‬㜠デׁ‫׷ְג׸‬<latexit sha1_base64="nEk2juW2shYa8h3dH5oDO7tRKbo=">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</latexit>

103 B(B̄s0 ! Ds+ ⇡ )103 B(B̄ 0 ! D + K )103 B(B̄s0 ! Ds⇤+ ⇡ )103 B(B̄ 0 ! D ⇤+ K )Data
3.00 ± 0.23
0.186 ± 0.020
2.0 ± 0.5
0.212 ± 0.015

SM 2109.10811
4.09 ± 0.21
0.303 ± 0.015
4.46 ± 0.22
0.327 ± 0.016

3.5 σ
4.7 σ
4.5 σ
5.3 σ
u

u
π−

W

b
0

Bs

d
c

K−

W

b
B

0

s
c

(∗)+

Ds

s

Bordone et al., 2007.10338
Cai et al, 2103.04138
Fleischer & Malami, 2109.04950
Endo, Iguro & S.M., 2109.10811

D (∗)+dsd✦ ֿ‫ך‬椚锷⦼‫ג׃חֲ״ךוכ‬鎘皾ׁ‫ַך׋׸‬խ铎䊴‫ך‬鐰⣣‫⥋כ‬걾‫׷ֹד‬‫ַך‬խ罋䣁ׁ‫ְזְג׸‬ꅾ銲‫ז‬㺔♷‫כ‬㶷㖈‫ַךְז׃‬

2 / 15

Calculation of B→MM decays✦ ♧菙涸‫ח‬#̔...⚥꟦㶨‫ך‬䄶㠨䮶䌴‫ך‬鎘皾‫כ‬㔭ꨇ✦ 2$%‫ך‬ꬊ䶏⹛⸬卓‫׾‬ろ‫׋׭‬鎘皾ָ䗳銲✦ -BUUJDF2$%‫ד‬鎘皾‫ל׸ׅ‬鍑寸#̔% GPSNGBDUPST!MPXSFDPJM‫כ‬礵䏝‫ֻ״‬鎘皾‫ָ׷ֹד‬#̔..‫כגְאח‬㔭ꨇ✦ 1/mb㾜Ꟛ‫װ‬GBDUPSJ[BUJPO‫׾‬꽀⢪‫ג׃‬鵚⡂涸‫ח‬鎘皾‫׷ׅ‬✦ ㉏겗‫׷ְג׏זה‬#̔% .䄶㠨‫כד‬GBDUPSJ[BUJPOָ葺ְ礵䏝‫ד‬䧭‫׶‬甧‫הא‬罋ִ‫׷ְג׸׵‬

3 / 15Color-allowed B→D(*) M decays
u

u
K−

W

b
B

s
c

0

mW >> mbb
B

D (∗)+

d

K−
s
c

0

D (∗)+

d
d

d

GF ⇤
p VuD Vcb (C1 Q1 + C2 Q2 ) + h.c.
2
⇥ µ a
⇤⇥
⇤
a
Q1 = c̄ T (15 )b D̄ µ T (1
5 )u
⇥ µ
⇤⇥
⇤
Q2 = c̄ (15 )b D̄ µ (1
5 )u

Le↵ =

(D = d, s)

SM values:
C1 (mb ) ⇠0.3

C2 (mb ) ⇠ 1.0✦ 8‫ان‬ٝ‫ה‬穠さ‫׷ְג׃‬‫ؙؓךא‬٦‫גⰋָؙ‬殯‫׭׋׷ז‬⡚ؒ‫ؘٕط‬٦怴皾㶨‫כ‬չ‫ٔخ‬٦怴皾㶨պ‫ד׫ך‬չ‫ل‬ٝ‫ؘ‬ٝ怴皾㶨պ‫כ‬㺔♷‫ְז׃‬✦ "OOJIJMBUJPOFYDIBOHF‫ךف؎ة‬䮶䌴‫׮‬㺔♷‫ְז׃‬✦ $PMPSBMMPXFEUSFF䄶㠨‫ה‬ㄎ‫׷׸ל‬

B

c

b
0

4 / 15

Factorization✦ VCBST‫כ‬1/mb玎䏝‫ַ׃‬ꨄ‫׆׵ֶג׸‬㹀䚍涸‫כח‬,‫ה‬#%‫ך‬꟦‫ך‬

TPGUHMVPO❛䳔‫ך‬㺔♷‫כ‬㼭ְׁ‫ה‬罋ִ‫׷׸׵‬uK−

Bjorken (89)b✦ 㹋ꥷ4PGU$PMMJOFBS&FDUJWF5IFPSZ 4$&5 ‫׶״ח‬1/mb‫ך‬

B

0

h
G
F
⇤
A(B ! D + K ) = p Vus
Vcb C1 (mb ) hD + K2[c̄+ C2 (mb ) hD + K

GF ⇤0
A(B ! D + K ) = i p Vus
Vcb (m2B2

a1 (D + K ) =

2
X

i=1

Ci (mb )

µ

a

a

T (1

5 )b][s̄ µ T[c̄ µ (15 )b][s̄ µ (1(10du TiI (u)

K (u)

d

0

i(mb )i05 )u] B i(mb )m2D ) a1 (D + K ) fK F0B̄!D (m2K )Z 1

D (∗)+d

MFBEJOHQPXFS‫כד‬TPGUDPMMJOFBSHMVPO❛䳔‫ך‬㺔♷ָ‫ָהְֿז‬Bauer, Pirjol, Stewart, hep-ph/0107002
爙ׁ‫׷ְג׸‬0sc5 )u] Bꫬmb‫؛أך♳׶״‬٦ٕ饔mb‫؛أך♴׶״‬٦ٕ
5 / 15

Inputs
GF ⇤0
A(B ! D + K ) = i p Vus
Vcb (m2B m2D ) a1 (D + K ) fK F0B̄!D (m2K )
2
Z 1
2
X
+
a1 (D K ) =Ci (mb )du TiI (u) K (u)ꫬmb‫؛أך♳׶״‬٦ٕ饔mb‫؛أך♴׶״‬٦ٕ0i=1✦ 䄶㠨㹀侧fK‫כ‬-BUUJDF2$%‫ד‬鎘皾〳腉铎䊴‫כ‬玎䏝✦ ,‫ך‬麊⹛ꆀⴓ䋒ꟼ侧ΦK(u)‫כ‬MJHIUDPOF2$%TVNSVMFT -$43 ‫ד‬鎘皾✦ a1‫ך‬Q2$%‫ך‬//-0‫✮ךד‬鎉⦼‫ך‬铎䊴‫כ‬玎䏝 2&%酡姻‫כ‬刿‫ח‬㼭ְׁ 
a1 (D + K ) = 1.025 + [0.029 + 0.018i]NLO + [0.016 + 0.028i]NNLO+0.023= (1.069+0.009)+(0.0460.012
0.015 )i

Huber et al., 1606.02888
Beneke et al., 2107.03819✦ Vcb F0(mK2)‫ؙحصزفٖىإכ‬䄶㠨‫ך‬㹋꿀⦼ 椚锷 -BUUJDF -$43 ַ‫ⵖ׵‬ꣲ铎䊴‫כ‬侧玎䏝
0hD(p )|c̄µb|B(p)i =

µ

p +p

0µ

m2B

m2D
q2

q

µ

!

m2B
B̄!D
2
F1
(q ) +

m2D
q2

q µ F0B̄!D (q 2 )q=pp0
6 / 15

SM predictions
uncertainties<latexit sha1_base64="nEk2juW2shYa8h3dH5oDO7tRKbo=">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</latexit>

103 B(B̄s0 ! Ds+ ⇡ )103 B(B̄ 0 ! D + K )103 B(B̄s0 ! Ds⇤+ ⇡ )103 B(B̄ 0 ! D ⇤+ K )Data
3.00 ± 0.23
0.186 ± 0.020
2.0 ± 0.5
0.212 ± 0.015

SM 2109.10811
4.09 ± 0.21
0.303 ± 0.015
4.46 ± 0.22
0.327 ± 0.016

3.5 σ
4.7 σ
4.5 σ
5.3 σ

Data

SM

7.7 %
10.8 %
25.0 %
7.1 %

5.1 %
5.0 %
4.9 %
4.9 %

✦ ⚺銲‫ז‬椚锷铎䊴‫כ‬Vcb‫ה‬#̔% GPSNGBDUPST‫ח‬饯㔓✦ 邌‫ٌךגⰋך‬٦‫דس‬椚锷⦼ָ㹋꿀⦼‫׮׶״‬㣐ְֹ✦ 倜暟椚

Bordone et al., 2007.10338; Cai et al, 2103.04138; Iguro & Kitahara, 2008.01086; Bordone et al., 2103.10332;
Fleischer & Malami, 2109.04950✦ 0  ‫ך‬倜暟椚‫כ‬➭‫ٖؿך‬٦‫غ‬٦暟椚ꆀַ‫ך׵‬( Bq , ⌧Bs /⌧Bd , · · · )<latexit sha1_base64="zj0+q6V0EXNt6JswyVQu0eX51HU=">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</latexit>ⵖꣲ‫ה‬濨湼‫ְז׃‬✦ ֿ‫כ׸‬劤䔲‫ח‬倜暟椚‫׾⦪⯐ך‬䯝ִ‫ַך׷ְג‬

7 / 15

新物理以外の可能性✦ 㹋꿀‫ر‬٦‫㉏ךة‬겗#"#"3 #&--&-)$C‫ך‬穠卓‫כ‬DPOTJTUFOU
✦ Vcb#̔% GPSNGBDUPSTcfJODMVTJWFWTFYDMVTJWFVcbQV[[MF✦ 椚锷鎘皾‫ד‬搀鋔‫׷ְג׃‬0 ąNC ‫ך‬TVCMFBEJOHQPXFS酡姻

Bordone et al., 2007.10338
OPDIJSBMMZFOIBODFEDPOUSJCVUJPOBUąNCUXJTUUXPQBSUJDMFMJHIUDPOFEJTUSJCVUJPOBNQMJUVEF -$%" PGMJHIUNFTPO̔0 ēTą. ‫ٍؗכ‬ٝ‫ٕ̔إ‬0 ēTąNC 
IFBWZRVBSL C D ‫ה‬MJHIUNFTPO‫ך‬꟦‫ך‬IBSEDPMMJOFBSHMVPO❛䳔̔UISFFQBSUJDMF-$%"  7" TUSVDUVSF̔UXJTU#%‫ה‬MJHIUNFTPO‫ך‬꟦‫ך‬TPGUHMVPO❛䳔̔-$43‫׷״ח‬FTUJNBUF

ֿ‫כ׵׸‬0  ‫ה‬鋅琎‫ָ׷ְג׸׵׮‬0  ‫ַ׷֮כהֿ׷זה‬✦ ‫׮׉׮׉‬GBDUPSJ[BUJPO‫כ‬1/mb‫ך‬MFBEJOHQPXFS‫ַ׃ד‬爙ׁ‫ְזְג׸‬

♳鎸⟃㢩‫ך‬TVCMFBEJOHQPXFS‫ך‬酡姻ָ⸬ְ‫׷ְג‬〳腉䚍‫כ‬✦ 䧮ղ‫ך‬锷俑‫כד‬穄朐䡾‫ך‬NFTPONFTPOSFTDBUUFSJOH‫ך‬㺔♷‫גְאח‬锃‫׋ץ‬

Endo, Iguro & S.M., 2109.10811

8 / 15

Quasi-elastic rescattering✦ #‫ך‬䄶㠨‫ד‬‫⚥ךא‬꟦㶨ָ⡲‫׸׵‬‫ָ׵׸׉‬SFTDBUUFSJOH‫׷ׅ‬㺔♷‫׾‬罋ִ‫׷‬

D

B

M

= Σ

M1

D

M2

M

B

{M1, M2}✦ 3FTDBUUFSJOH‫כ‬mb‫؛أ‬٦ٕ‫דךז‬6  ‫ٖؿ‬٦‫غ‬٦㼎獥䚍 V E T ‫⟎׾‬㹀亻‫ٓؕأ‬٦⚥꟦㶨‫כגְאח‬6  "،‫ٔوظ‬٦ָ֮‫דך׷‬46  㼎獥䚍✦ ずׄꆀ㶨侧‫א׮׾‬朐䡾꟦‫ד‬SFTDBUUFSJOHָ饯ֿ‫׷‬<latexit sha1_base64="J4tTkyF+hlfRLofCA16BeCY0SSs=">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</latexit>

Sres = e

i 15

15
X

a=1

↵⌦

15; a 15; a + e

i 6

6
X

b=1

↵⌦

6; b 6; b +✦ #̔%1#̔% 1#̔%7‫גְאח׸׊׸׉‬锃‫׷ץ‬

Chua, Hou & Yang, hep-ph/0112148
Chua & Hou, hep-ph/0504084, 0712.1882

X3
X

m,n=3̄,3̄0 c=1

m; c

↵

1/2
Umn

⌦

n; c

9 / 15

B→DP decays
Transitionb ! cūd{S, Iz }{1, 1}{0, 3/2}{0, 1/2}

Mode
B s ! Ds+ ⇡B s ! D0 K 0
B ! D0 ⇡0
B ! D+ ⇡0
B ! D0 ⇡00

B ! D0 ⌘0

B ! D0 ⌘00b ! cūs{ 1, 0}{ 1, 1}{0, 1/2}

B ! Ds+ K
0

B ! D+ K00
B ! D0 K
B ! D0 K
B s ! Ds+ K
B s ! D0 ⌘B s ! D0 ⌘0

B s ! D0 ⇡0
B s ! D+ ⇡AmplitudeTDCP
TD + C P
TD + E
p1 ( CP + E)
2cp (CP + E)
2sp (CP + E)
2

E
TD
CP
TD + C P
TD + Ecs C P + p2 Ecs
CP + p
p1 E
2

E

2

E

Data
30.0 ± 2.3
4.3 ± 0.9
46.8 ± 1.3
25.2 ± 1.3
2.63 ± 0.14
2.36 ± 0.32
1.38 ± 0.16

0.27 ± 0.05

1.86 ± 0.20
0.52 ± 0.07
3.63 ± 0.12
2.27 ± 0.19 †
—

T

π

C

−

d

u

c

D0

E

u

c

Ds+

s

b

b

b

c

D0

B−
u

u

color-allowed tree

d

B

π−

B−
u

0
d
u

u

color-suppressed treesK−exchange✦ T‫כ‬GBDUPSJ[BUJPO‫׶״ח‬鎘皾✦ C‫ה‬E‫כ‬鎘皾‫דךְזֹד‬‫ًٓػ‬٦———‫ة‬٦‫׷ׅה‬ 46  CSFBLJOHFFDUT‫כ‬EFDBZDPOTUBOUT‫װ‬GPSNGBDUPST‫ך‬嫰‫׾‬欽ְ‫ג‬《‫׷׸Ⰵ׶‬椚锷‫ה‬㹋꿀‫כך׷ָٖ֮ؤח‬랕葿‫ך‬䄶㠨麓玎ble 1. List of B ! DP decays with b ! cūd and b ! cūs transitions. The values in thend column✦are the strangeness and the z component of isospin of the final state. The fourth
mn shows the SU (3) decomposition of the decay amplitudes. The experimental data for the CPaged branching ratios (in units of 10 4 ) in the fifth column correspond to the PDG values [36],ch are consistent with the HFLAV ones [48]. † The data for B s ! Ds+ K represents a sum of
averaged branching ratios, B(B s ! Ds+ K ) and B(B s ! Ds K + ).

3FTDBUUFSJOH‫כ‬T‫ה‬C‫׾ֽ׌‬罋ִ‫ְ״ל׸‬<latexit sha1_base64="2wjF8hEDYaTxMRVRgF7zJHg6t8I=">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</latexit>

e.g., B s !

⇢

Ds+ ⇡
D0 K 0! Ds+ ⇡
10 / 15

Tensions in B→DP
<latexit sha1_base64="phDJMQNq3gnZG8Nsge4hsikJS0s=">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</latexit>

Transitionb ! cūd{S, Iz }{1, 1}

b ! cūs{ 1, 0}Mode
B s ! Ds+ ⇡B s ! D0 K 00
B ! D+ K00
B ! D0 K

Amplitude
TD
CP
TD
CP

Data
30.0 ± 2.3
4.3 ± 0.9
1.86 ± 0.20
0.52 ± 0.07

✦ Rescattering ‫ך‬㺔♷‫כ‬ꬊ暟椚涸‫ז‬PWFSBMM⡘湱‫׾‬ꤐֻ‫ה‬‫ًٓػךא‬٦‫ة‬٦δ'‫ד‬邌‫׷ׇ‬<latexit sha1_base64="0adfQ381KmlS2sIpwmunkDmeaJY=">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</latexit>

1/2
1/2
=
S
1
1,0 =

S1,

ei 15
2

1 + ei

0

1

ei

1+e

0

i 0

!

✦ ⡘湱δ'ֶ‫ן״‬醱稆䮶䌴C ‫⟣׾‬䠐‫ًٓػך‬٦‫ة‬٦‫׮ג׃ה‬‫ךא‬䄶㠨‫ך‬㹋꿀⦼‫׾‬ず儗‫ח‬铡僇‫ְזֹדכהֿ׷ׅ‬
㔳⚥‫ך‬瘝넝简‫ך‬侧⦼‫|כ‬C|‫ח‬湱䔲‫ًٓػ׷ׅ‬٦‫ة‬٦‫⦼ך‬δ' ‫ה‬C‫ך‬⡘湱‫׵ַכ‬Ģ‫דת‬㢌⻉ׁ‫׷ְגׇ‬11 / 15

NP in a1(mb)✦ $PMPSBMMPXFEUSFF䮶䌴T‫ךפ‬倜暟椚‫ך‬㺔♷ָ֮‫⟎ה׷‬㹀‫׷ׅ‬̔⤘侧a1(mb)ָ4.‫⦼ך‬a1SM(mb)_ַ‫׷׸׆׵‬

DPMPSTVQQSFTTFEUSFF䮶䌴]$]

✦ 㹋꿀⦼‫ה׷ׅزح؍ؿד‬a1(mb) < a1SM(mb)‫׾‬䖤‫׷‬
4.

DPMPSBMMPXFEUSFF䮶䌴]5]

✦ a1(mb) ‫׾‬刿‫ⵖח‬ꣲ‫ח׭׋׷ׅ‬➭‫ך‬䄶㠨麓玎‫׮‬ろ‫ؚٗג׭‬٦‫׷ׅزح؍ؿٕغ‬

12 / 15

Global fit✦ 46  ‫ٖؿ‬٦‫غ‬٦㼎獥䚍‫⟎׾‬㹀‫ؚٗג׃‬٦‫̔زح؍ؿٕغ‬a1(mb)‫ח‬0  ‫ך‬倜暟椚
Transitionb ! cūd{S, Iz }{1, 1}{0, 3/2}{0, 1/2}

Mode
B s ! Ds+ ⇡B s ! D0 K 0
B ! D0 ⇡0
B ! D+ ⇡0
B ! D0 ⇡00

B ! D0 ⌘0

B ! D0 ⌘00b ! cūs{ 1, 0}{ 1, 1}{0, 1/2}

B ! Ds+ K
0

B ! D+ K00
B ! D0 K
B ! D0 K
B s ! Ds+ K
B s ! D0 ⌘AmplitudeTDCP
TD + C P
TD + E
p1 ( CP + E)
2cp (CP + E)
2sp (CP + E)
2

E

Data
30.0 ± 2.3
4.3 ± 0.9
46.8 ± 1.3
25.2 ± 1.3
2.63 ± 0.14
1.38 ± 0.16

0.27 ± 0.05

1.86 ± 0.20
0.52 ± 0.07
3.63 ± 0.12
2.27 ± 0.19 †—B s ! D0 ⌘0c C P + p2 E——

B s ! D+ ⇡

p1 E
2

E

—

B s ! D0 ⇡0<latexit sha1_base64="TgMTJrw8s8VPSWRPX/JhoUKwu0Y=">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</latexit>

2.36 ± 0.32

TDCP
TD + C P
TD + Ecs C P + p2 EsNPEFT<latexit sha1_base64="TgMTJrw8s8VPSWRPX/JhoUKwu0Y=">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</latexit>ble 1. List of B ! DP decays with b ! cūd and b ! cūs transitions. The values in the)
BMM<latexit sha1_base64="toTCWlLB6uFnsA2eZNlGNdG9lLg=">AAAJUnicdVZbb9s2FFbaXZys29rtcS/CggAdkGWSE8/uw4Y23e1hQLOiaQpERkFJtCyYIgWScmoQ+hF73f7WXvZX9rRDSZRJyxUggTrfx3P7ji5xSXIhg+Dfg3v3P/jwo49Hh0efPPj0s88fPvritWAVT/B1wgjjb2IkMMkpvpa5JPhNyTEqYoJv4tVzjd+sMRc5o6/kpsTzAmU0X+QJkmC6iS7zLIvqtw+Pg7OgOfzhIuwWx153XL19NJpEKUuqAlOZECTEbRiUcq4Ql3lCcH0UVQKXKFmhDN/CkqICi7lq8q39E7Ck/oJxOKn0G6u9Q6FCFEguT+MCyHoljk4igmW0jBFnPM+aBdisKKWAXdofxIGV2BTxns29B3dzJRezucppWUlMkzbDRUV8yXzdNT/NOU4k2cACJTyHIv1kiThKJPTWSR2LNTBr3zHCrixm7+ojN+qrcK50xjqkgyiSxxhaSXF9cuK/oBAYCR+/Q0VJcNM4ucQ+ZwWi4jsBl6aRwvUuEkRw+kNwNpvMFbhDBaMMUnAyq2guBRgj3ahuUFTMSNoQU7yAHBp9IKVsKWNS4VolxWZVq+Bsctqcp0HtUtc5g35vedPJaQjU8WTALCsOFdkew9bnLi+nq571nqiMI5phlxUOWDFnd9QtYbqPl+inyHY2hvN8mBgSEpMNJoTdWez91bY0P+MYuynsiS9WG7fZF+Az/H5P3RStOyrPYs0MdPjmMhmfGx0jQ1PRzrbWXdTrawhbwTtGK6uBO5E7rBXSYJ2sBgPxekQL2dlbwQzSyddhjUwGajXrkEYYg7QqmTiWFn08W5+O1941KhiaZTKsTgDDMHoMnotnJc8TJu1ROR83vR8o9ZJtELnaGfmpHsEnwR5hX+L0xWCmp1O4zKYD8iVksYIdNnf2RLvWgzOe7dB/R2tMU8xt+sVsXxJVDGvHcXimR7F/FiLUdsB0yjSkQ7ku2h0Puw+GhVN3HLbF9xMBBQLNEPqCzfx2FRm8r9BEaAqxHGwr05rqV3MzXhp7prYJmbHb2m3LpeoTs83PVVRsUsRX7UhZyE9qm4lt/1mZPtrWX5Q9rTbyq+qf6GYkKb5LWAEfBKgP3ugqWopVXuqP+AwX9Q7uEi4GhMJmfPseistoorgUyrju/y185dTj4/Ab6DP8aIS7vxXDxesxvOnOwj8ujp/+2P1yjLyvvK+9x17oTb2n3m/elXftJd7K+9P7y/t79M/ov8ODw/st9d5Bt+dLzzkOH/wPlO1Qzw==</latexit>

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B→D*P & B→DV decays✦ #̔% 1‫ה‬#̔%7䄶㠨‫׮גְאח‬ず圫‫ך‬穠卓ָ䖤‫׋׸׵‬

✦ #̔%7‫כגְאח‬46  ‫ֻזכד‬6  㼎獥䚍‫׾‬铬‫׭׋ׅ‬SFTDBUUFSJOH‫ًٓػ‬٦‫ة‬٦꟦‫ח‬ꟼ⤘ָ➰ֻ‫ךא‬㜥さָ罋ִ‫ ׷׸׵‬TPMTPM 

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Summary✦ $PMPSBMMPXFE䄶㠨‫ך‬䄶㠨ⴓ䀄嫰‫ך‬㹋꿀⦼‫ה‬B s ! Ds(⇤)+ ⇡B ! D (⇤)+ K
0

2$%GBDUPSJ[BUJPO‫׷״ח‬椚锷⦼‫ך‬꟦‫ה׷ָٖ֮ؤח‬陽锷‫׷ְג׏זח‬✦ 'BDUPSJ[BUJPO JOMBSHFmbMJNJU ‫כד‬搀鋔‫׷ְג׃‬RVBTJFMBTUJDSFTDBUUFSJOH‫ח‬‫ג׏״‬ֿ‫׾ٖؤך‬铡僇‫׾ֲַוַ׷ֹד‬锃‫׋ץ‬✦ 2VBTJFMBTUJDSFTDBUUFSJOH‫כד‬DPMPSBMMPXFE䄶㠨‫ה‬DPMPSTVQQSFTTFE䄶㠨‫ך‬⚕倯‫׾‬ず儗‫ח‬铡僇‫׾הְֿזֹדָהֿ׷ׅ‬爙‫׋׃‬✦ ‫׃׮‬倜暟椚‫⟎׾‬㹀‫ל׵ז׷ׅ‬⤘侧a1(mb)‫׾‬0  幾‫ׅ׵‬㺔♷ָ䗳銲‫׷֮ד‬✦ 倜暟椚‫ך‬〳腉䚍‫׾‬鷄実‫ה׷ׅ‬ず儗‫ח‬垥彊垷㘗‫ך➭׷ֶֽח‬1/mb酡姻‫װ‬GPSNGBDUPST !MBSHFSFDPJM ‫ךגְאח‬刿‫׷ז‬灇瑔ָꅾ銲‫׷֮ד‬

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