1 trend in charm spectroscopy a recap of particles an intro d sj spectroscopy x,y,z states charmed...
TRANSCRIPT
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Trend in Charm Spectroscopy
• A Recap of particles
• An Intro
• DsJ Spectroscopy
• X,Y,Z states
• Charmed baryons
• Measurement of Spins
• D0-D0 Mixing
• Summary and Conclusion
byUsha Mallik (The University of Iowa)
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3 generations of quarks, & leptons
e+ e- hadronse+ e- μ+ μ-R
=
Quarks, leptons spin 1/2
These quarks immediately ‘Dress-up’ as Hadrons by strong interactions (QCD)
e+e- qq , l+l-
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Continuum and Resonance Production
R
cc
Hidden charm
bb
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What happens at BABAR
b
b
b
q
q
b
(4S)
B
B
(10580) MeV
e- beam energy 9.1 GeV, e+ beam energy 3 GeV, E(cm) = 10.58 GeV
e+e- 4S) BB , also cc, ss, uu, dd
e+e- bb) 1.05 nb
(cc) 1.30 nb
(uds) 2.09 nb
time
(5279MeV)
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b
b
(1S) (9460) MeV
q
q
q
q
X
X
time
Since (1S) is below B meson pair production threshold,
the original b quarks can not be present in the final state:
causing the decay rate slower, ie, the lifetime of (1S) longer,
and the resonance narrow.
OZI Suppression in Decays
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The “Periodic Table” of Hadrons
Originally in the 1960’s with only u, d, s quarks:
meson qq {q u, d, s ; q u, d, s }
JP = 0- , Pseudoscalar nonet with '
JP = 1- , Vector nonet
J = ½ + ½ = 0
J = ½ + ½ = 1
Gell-Mann’s Eight-fold Way :
3 3 = 1 8
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JP = 0- , Pseudoscalar nonet and c
JP = 1- , Vector nonet and J/
With u, d, s, c quarks, the picture gets richer
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The BABAR Detector at PEP-II and the Dataset
BBSee )4(Ecm = 10.58 GeVAnd Much More
Peak luminosity > 1.2 x 1034 cm-2 s-1; Delivered luminosity > 425 fb-1
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Charm-strange mesons (cs) : Ds, DsJ
With 400 fb-1 data, over 1 billion charmed hadrons produced
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Expected spectroscopy
3P0
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DSJ(2317)+ and DSJ(2460)+ observed in
States prior to 2003
But for 2573: 2+ not established
DSJ(2317)+ = 2319.6 ± 0.2 ± 1.4 MeV/c2
DSJ(2460)+ = 2460.2 ± 0.2 ± 0.8 MeV/c2
Also observed in B-decays
Ground State DS(1969)+: JP=0-, c and s spins opposite, in S-wave
Observed States
Spin-Parity Established
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(2006)
x 103 x 103 x 103
1
(fits better with a Gaussian, rather than BW)
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Yield =182 30 Mass ( MeV/c2): 2715 +11
-14
Width (MeV/c2): 11520+36-32
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Preliminary (New)
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A Very Rich Spectroscopy in cs is emerging
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NEXT:
The New Charmonia ! The Alphabet Soup !
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The Charmonium(-like) States
Below DD threshold states well understood. The X,Y,Z states are all above the threshold
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Confirmed by BABAR, CDF, D0
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Properties of X(3872)
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Preliminary (New)
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While searching for BABAR finds new state Y(4260)
Not seen in DD
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The Status of Charmed Baryons
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Baryons
baryon qqq, anti-baryon qqq
(uud)(udd)
(uds)(dds)
(uus)
(uss)(dss)
J = ½ + ½ + ½ = ½
Baryon Octet
(uuu)
J = ½ + ½ + ½ = 3/2
(ddd)
(sss)
Baryon Decuplet
333 = 188’10
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Baryons with 4 flavors (u,d,s,c)
3/2+1/2+
1/2-u,d,s, decuplet
u,d,s, octet
Ground states
Ground state
= 4 20’20’20
Anti-symmetric
*
5 ground states with JP = 3/2 observed: only c* was missing
All 9 ground states with JP = ½ observed
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The singly charmed u,d,c sub-multiplets from the 20’ 9 members; JP = 1/2
(2698)
(2285)
(2472)(2466)
(2574)(2579)
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About charmed baryons
c+ -+ + c
0 - +0K-
-+0 -+-+ -K-++
c0 -
p-
-K+
-+0
Anti-symm under the interchange of the two light quarks (u,d,s)
symm. under the interchange of the two light quarks (u,d,s)
Example Decays:
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Charm Baryon production
Charm baryon or anti charm baryon + X
b c, and c s are weak decays, ~10-13 s lifetime
Charm baryon lifetimes are small, even though weak decays
e+e- BB
e+e- cc
Weak Decays of -, - and 0 take ~ 1,000 times longer
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Observation of Λc(2880)+ and Λc(2940)+ decaying to D0p
New Decay mode: Λc(2880)+ D0p First observation of charm baryon charm meson
Nsig=2280310
Λc(2940)Λc(2880)
Wrong sign D0P
D0 mass sidebands
Λc(2765)Λc(2880)
Λc(2940)
Belle confirms in c (c)
BaBar PRL 98:012001(2007)
M(ΛC + -) GeV/c25410 1.8
0.4-1.02937.9 1007060-40-210 )2940(c
4.00.70.3-5.5 0.4
0.3-0.22881.2 4050880 )2880(c
5.95.217.5 1.01.32939.8 3102280 )2940(c
1.11.55.8 0.50l.2881.9 190 2800 )2880(c
[MeV] ]2M[MeV/c Yield sonanceRe
D0p invariant mass GeV/c2
Belle Hep-ex/0608043
Excellent agreement in mass and width
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cx(3077)+
cx(2970)+
New charm strange baryons BaBar confirms these states
Belle, PRL97:162001(2006) BaBar hep-ex/0607042
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c0 Production and Decay
PDG values
c0 Decay
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From B decays
Continnum production
Off-peak data: Below B-pair thres-hold, no peak
c0 Production in B decays
p* distribution, momentum in the e+e- rest frame
hep-ex/0703030, submitted to PRL
-410 Few )0( XcBB
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Discovery of the C*
Combined
BaBar PRL 231 fb-1
97:232001(2006)
)2GeV/c(pdgMMM 0c
0c
*c
Data from all four c0
decay modes are combined and fit yields: 105 21 6 5.2 signal significance
m ( mc* - mc0)= (70.8 1.0 1.1) MeV/c2
Theory range: m = 50 – 94 MeV/c2
= 1.01 0.23 0.11
For XP > 0.5, most/all the c0 may results from
c* production, but uncertainty is large.
No signal found in the c0 mass
Sidebands (hatched area)
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Also observed the charged partner c’+
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Study of b → ccs decay
Inconsistency in the MC and data p* distribution: MC only has b → cud
Search B decays into charm-baryon-anti-charm-baryon pair
B → cc and B → c c K
BABAR, PRL. 95 142003, 2005
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B decays to cc and c cK
E = energy difference between reconstructed B and Ecm
mES : beam momentum substituted reconstructed B mass: e+e- BB
An example
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B decays to cc
PRD 74 (2006) 111105
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B decays to c cK PRL 97 (2006) 202003
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Spin Measurements
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- inherits the spin projections of the c0
Examine implications of - spin hypotheses for angular distribution of from - decay
Initial helicity, λi = λ ()= ± 1/2 Final state helicity, λf = λ () - λ(pseudoscalar) = ± 1/2
Decay amplitude for Ω- → Λ K-: ffifiADA JJ
)0,,(*
λ() = ± 1/2
λ(K) = 0
λ(K) = 0J = 1/2m = + 1/2m = - 1/2
) = + 1/2() = - 1/2
density matrix element for - spin projection i
= density matrix element for charm baryon parent
Transition matrix element does not depend on i
[Wigner-Eckart theorem]
quantization axis
K-
-K+
(+) c0 = 0
c
- = 0
since, no orbital angular momentum projection w.r.t. quantization axis in Ξc0 decay
diagonal density matrix element for - spin projection i = () is i
Total Intensity:
2*
,
2
,
)0,,(2
1
2
1ffi
fi
fii
fi
ADAI Ji
J
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)cos5cos21(
)cos31(
1
42
2
I
I
I
Spin measurement of - from c0 → - K+, -
→ K- decays
→ Fit Prob = 10 -17
→ Fit Prob = 0.64
→ Fit Prob = 10 -7
Background-SubtractedEfficiency-Corrected
J = 1/2
J = 5/2
J = 3/2
Data
~ 116 fb-1
J ≥ 7/2 also excluded: angular distribution increases more steeply near cos ~ ±1 and has (2 J -2) turning points.8
Similar conclusion from c
0 → -+, - → K- decays
Conclusion:J(-) = 3/2 [assumingJ(c
0) = 1/2]
PRL 97 (2006) 112001
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D0 – D0 Mixing
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Example: Mixing
One of the main HEP discoveries in 2006: Bs Oscillations
x=24.8y~0.1?Bs
0 oscillate very rapidly
Rate first measured in 2006 by CDF and D0
Toy MC
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Time-Evolution of D0 → K+ π−
D0 can reach the K+ - final state in two ways:1) Doubly-Cabibbo-Suppressed decay2) Mixing to D0bar, followed by Cabibbo-Favoured decay... and interference between them.
Q: How can we distinguish these?A: By the time evolution.
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Best fit
No mixing
1σ
2σ
3σ
4σ
5σ
Contours include statistical & systematic errors
Fit is inconsistentwith no-mixing at 3.9
Fit Results
RD: (3.03±0.16±0.10)x10-
3 x’2: (-0.22±0.30±0.21)x10-3
y’: (9.7±4.4±3.1)x10-3x'2, y' correlation: -0.94
WS decay time, signal region
data - no mix PDFmix - no mix PDF
Fit to signal & sideband regionsPlot above shows just signal region:
1.843<m<1.883 GeV/c2
0.1445<m< 0.1465 GeV/c2
Evidence for D0-D0 mixing!
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49Ratio of WS/RS events clearly increase with time. Mixing signal!
Inconsistentwith no-mixinghypothesis2=24
Consistent withprediction fromfull likelihood fit2=1.5(stat. only)
Many validation tests done
Most powerful is performing a time-independent fit of the Wrong-Sign and Right-Sign yields in slices of proper lifetime:
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50
Summary
• A new landscape in many areas including spectroscopy has opened up with high luminosity and precision– New DsJ Spectroscopy
– X, Y, Z States– Charmed Baryon Spectroscopy– Spin Measurements (necessary to identify levels, complex
analysis for multi-body states: c (1530), c (1690), in Charmed Baryon decays )
– D0-D0 Mixing Observed
Expecting ~three/four times more data than shown in analyses
A race to find Beyond Standard Model Physics
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51
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52
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53
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54
Legendre Polynomial Moments in Spin Determination
s)polynomial Legendre normalized( ,cos coscos and
0 odd is if and ,12 where
ij
1
1
max
dPP
PlJl
ji
l
For - spin J, the previous angular distributions can be written
N
jjlll PPNdP
d
dN
1
1
1coscoscos
cos that So
)( where,coscos
max
0
l
lll PPN
d
dN
Each assumption for J defines lmax
if J is correct calculable is and
, if ,0 max
l
l
P
llP
NP
PN
j l
jl 1
max
max)(cos
that So
max
max)(cos
l
jlj
P
Pw
i.e. projects the complete signal by giving each event weight:
9
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55
c0 →
[loose cuts]
Illustration of the Use of Legendre Polynomial Moments in Spin Determination
(will prove
useful later)
efficiency-corrected * √10 P2 (cos) weighted
wj = √10 P2(cos)from c
0 signal region
▬ efficiency-corrected *, mass-sideband-subtracted unweighted m( K-) distribution in data
- →signal
For example, for c0 → - K+ and J()=3/2:
20
202
)(cos10
1)(cos
2
1cos31
4cos
PP
PPNN
d
dN
lmaxlmax = 2, < P > =1/√10
efficiency-corrected * (7/ √2) P4 (cos) weighted
wj = (7/ √2) P4(cos) [for J=5/2, lmax=4, < Pl > = √2/7 ]
from c0 signal region
max
- →signal
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56
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57
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58
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59
Observation of b ccs cw- (W- cs)
W- W-
Charm baryon pair production in B Decays
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60
List of Decay Modes (pair production)
2*4/ BES psm 2/* sEE B
2*4/ BES psm
2/* sEE B
Reconstruct the B meson
Use energy momentum conservation between e+e- cm and BB in cm
(also : )
Look for signal events in the mes, 2D distribution
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61
Fit to SignalAnalysis ongoing
B- cc K-
p
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62
Study of c0 (css)
Production Process and Ratio of Branching Fractions of C0
(css)
cc or B C0 + X C
0 - +
- + - +
-K- + +Preliminary results shown at 2005 summer conferencesImproved analysis using likelihood selection in progress
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63
Inclusive c0 Studies
Branching Fractions and Production Mechanism from p* Spectrum
Decay Modes of C0 Studied -+, -+- +, and -K- + +
C0-+
P* > 2.8 GeV/c
225 fb -1
Results:
BABAR
SLAC-PUB-11323, hep-ex/0507011
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64
Helicity Formalism, Spin Determination
Suited to two-body (successive) decays
Can be extended to intermediate resonances
(ie, quasi-twobody decays using Dalitz plots)
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65
quantization axis
Charm baryon rest-frame Hyperon rest-frame
HyperonPseudoscalar
Hyperon daughter
Pseudoscalar
J(Ξc0) = 1/2 in Ξc
0 rest-frame m = ± 1/2 along z (quantization) axis
no angular momentum projection w.r.t. quantization axis Ω- helicity, λi = ± 1/2 final state helicity λf = λf (Λ0) - λf (pseudoscalar) = ± 1/2
Decay amplitude for Ω- → Λ0 K- :
Total Intensity:
ffifiADA JJ
)0,,(*
c0 → K+ - → 0 K-
J = 1/2m = + 1/2m = - 1/2
λi = + 1/2λi = - 1/2
λf = ± 1/2λK = 0
λK = 0
2*
,
2
,
)0,,(2
1
2
1ffi
fi
fi
fi
ADAI Ji
Ji
density matrix element for - spin projection i = density matrix element for charm baryon parent
Does not depend on i
[Wigner-Eckart theorem]
c0 -K+
K-
Helicity angle of Angle made by p() in rest frame with p(-) in c
0
rest frame
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66 )cos5cos21(
)cos31(
1
42
2
I
I
I
Spin measurement of -
→ Fit Prob = 10 -17
→ Fit Prob = 0.64
→ Fit Prob = 10 -7
Background-SubtractedEfficiency-Corrected
J = 1/2
J = 5/2
J = 3/2
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5cos9coscos314
1 I
cos314
1 I
22
2
Spin measurement of - from c0 → - K+, -
→ K- decays
Angular Distribution Parametrizations for JΩ=3/2 hypothesis
No Asymmetry
Asymmetry
Negligible Decay Asymmetry Parameter
Fit for→ = 0.04 ± 0.06
= 0.04 ± 0.06
Background-SubtractedEfficiency-Corrected
9
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68
Spin measurement of c0 from c
0 → - +, - → 0 K- decaysFit parametrization α(1 + 3 cos2θ) for JΩ = 3/2 hypothesis
→ Fit Prob = 0.69; J(-) = 3/2, consistent with
results from c0 → - +
Background-subtractedEfficiency-corrected
Conclusion: J(-) = 3/2 [Assuming J(c0) , J(c
0) <5/2]
PRL version ready for review comm
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Extending the Spin Formalism to 3-body Decays
The (1530)0 Spin from c+ → (- +) K+
also mass, width info. amplitude analysis (in progress)
The (1690)0 Spin from c+ → (0KS
0) K+
also mass, width info. amplitude analysis (to be done) (-p+)/(K0) Branching Ratio Limit
(to be done)
“…nothing of significance on resonances has been added since our 1988 edition.” [PDG(2004), p 967]
12
Study of and
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70
Reconstructed c+
→ - + K+, - → 0 - Events
Data~230 fb-1
m(- +) ↔ c+ mass-signal region
m(- +) ↔ c+ mass-sideband region
. .
m(- +) ↔ (c+) mass-sideband-subtracted
Uncorrected
x
c+
-
0
-
p
-
K+
+
PID Information →Proton →Kaon →+, -
3-σ mass cut on intermediate states
intermd. states mass-constrained [, -]
L > +1.5 mm [sign outgoing].
r > +1.5 mm [sign outgoing].
dE/dx & Cherenkov info (DIRC)
(c+)Mass-sideband-
subtractedUncorrected
c+
→ - + K+
PDG mass
0 → - +
13
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71
Resonant Structures in c+
→ - + K+, - → 0 -
Events Only obvious structure:
(1530) → - +
c+ signal region
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72
Spin measurement of 0(1530) from c+
→ 0(1530) K+, 0(1530) → + decays
α(1 + 3 cos2θ) for J=3/2 hypothesisUncorrected cosθ Spectrum
0(1530) Signal Region
[Not mass-sideband-subtrated]
0(1530) Mass-Sideband Regions
Skewed distribution due to:• Efficiency loss at small angles Not big effect • system decay asymmetry S-P wave interference (next slides)
Clear 1+3cos2θ structure
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73
For pure spin 3/2: dN/dcos = α(1 + 3 cos2)
c+ → + K+ Signal Region
Uncorrected
Legendre polynomials orthogonality condition
Weight = N x P2(cos)
Using the angular structure of (1530)0 → + candidates to project
away background events
Use of angular structure to project away the bkgr.
100
100
c+ Signal Region
c+ Low Mass-Sideband Region
c+ High Mass-Sideband Region
Projects mass distributionhaving cos2 component
No cos2 component in sideband distributions
sidebands
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74
Evidence of S-P wave interference in the (- p+) system produced in the
decay c+ → - p+ K+
m( +) distribution weighted by P1(cos):
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75
K +
Amplitudes describing the (- +) system:
quantization axis
c+ (- +) rest-frame
- - …….
+ ………….
l
S-P wave description of the (-+) system produced in the decay c
+ → + K+
1)1( 2/32/1 ,1
1)1( 2/12/1 ,1
1)1( 2/1 ,0
1
1
1
l
P
l
P
lS
ljlP
ljlP
jlS
f
f
f
)0,,()0,,()0,,(
2/1,2/1
2*2/3
*2/1
*2/1
f
i
ffiffiffiPDPDSDi
)( system ofhelicity where,
theof populationspin thedescribing elementsmatrix density 1/2)(i
c
c
-f
ii
i
Total Intensity ~
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76
.2
1cos3RecosRe2
cosRe24
cos31 I
)()()()()()(2
1
)()()()()()(2
1
)()()()()()(
)()()()()()(
where)0,,()0,,()0,,( I
2*2/12/1
*2/12/12/12/1
*2/12/1
22
2/1
2
2/1
2
2/12/12/1
2
2/12/3
2/1 2/12/12/1
2/1 2/12/12/1
2/1 2/1
2
2/12/3
2/1 2/12/12/1
2/1 2/12/12/1
2/1 2/12/1
2
2/12/3
2/1 2/12/12/1
2/1 2/12/12/1
2/1 2/1
2
2/12/3
2/1 2/12/12/1
2/1 2/12/12/1
2/1 2/12/1
2
2/12/3
2/1 2/12/12/1
2/1 2/12/12/1
2/1 2/1
2
2/12/3
2/1 2/12/12/1
2/1 2/12/12/1
2/1 2/12/1
2
2/12/3
2/1 2/12/12/1
2/1 2/12/12/1
2/1 2/1
2
2/12/3
2/1 2/12/12/1
2/1 2/12/12/1
2/1 2/12/1
2/1,2/1
2*2/3
*2/1
*2/1
PSPS
PSPPS
PdPdSdPdPdSd
PdPdSdPdPdSd
PdPdSdPdPdSd
PdPdSdPdPdSd
PDPDSD fi
f
i
ffiffiffi
Helicity Formalism (3)
)2/3( 1 );2/1( 1
0) ,2/1 1/2, ;1 ,1( 1
:onconservatiParity
j PP)(Pj -PP)(P
SSjSS)(S
ff
πΞ
fff
πΞ
f
ff
πΞ
f
λSSj
PλSSj
P
SSjS
0(Assume 1/2= -1/2)
Assume ~0 to extract cos
S-P interference
S-1/2 = S1/2
P--1/2 = -P-
-1/2
P+-1/2 = P+
1/2
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77
c+
J=1/2
0(1530)J=3/2
p
qK+ (1530)
-
L = 2, 1
l = 1 [(+) parity]
…towards a measurement of the mass & width of 0(1530)
Fit Params:
M: 1531.6 ± 0.1 (stat.)
: 11.9 ± 0.2 MeV
Fit with relativistic Breit-Wigner Function with L=2 & l =1[incorporating a Blatt-Weisskopf barrier factor (R~ 5 (GeV)-1) and resolution “smearing”]
l
tot
L qmmmm
pm
q
m
pm
dm
dN
c
2
220
2220
2
)(
1.
pp
P2(cos) weighted
Uncorrected
PDG:
M: 1531.80 ± 0.32
: 9.1 ± 0.5 MeV(Very preliminary)
In progress
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78
Uncorrected
Reconstructed c+ → 0 KS
0 K+ Events
(c+)Mass-sideband-
subtracted0 → 0 KS
0
Data~200 fb-1 Uncorrected
m(0 KS0) ↔ c
+ mass-signal region
m(0 KS0) ↔ c
+ mass-sideband region . .
m(0 KS0) ↔ (c
+) mass-sideband-subtracted
c+
→ 0 KS0 K+
c+
→ 0KS0K+
Low-mass sideband limit
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79
S-Wave Breit-Wigner Function (& Linear bkgr.)with resolution “smearing”
…towards a measurement of the mass & width of (1690) → 0 KS0
Background-subtractedUncorrected
Fit Params:
M: 1684.7 +- 0.9 (stat.)
: 12.0 +- 0.2 MeV
Only “obvious” structure: (1690) → 0 KS
0
c+
Uncorrected
Stop fit at 1.76
(Very preliminary)
23
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80
[Uncorrected] Background-Subtracted cosθ Spectrum~Flat consistent with J=1/2 hypothesis
Spin measurement of (1690)0 from c+ → (1690)0 K+, 0(1690) → 0KS
0 decays
Spin hypothesis:Weight signal events
by P2(cos)
c+ signal region
Uncorrected
α(1 + 3 cos2θ) for J=3/2 hypothesis [prob = 0.2]
α(1) for J=1/2 hypothesis [prob = 0.9]
m(KS) distribution weighted by P2(cos)
c+ signal events
Uncorrected
No cos2 component anywhere Spin 1/2
Spin 1/2 favored
Direct Method:
- Extract signal cos distribution - Requires large sideband subtraction
Inconclusive
Indirect Method:
24
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81
Uncorrected (- +) invariant mass[ c
+ → - + K+ ]
No signal for (1690)0 → - +
Uncorrected (0 KS0) invariant mass
c+
→ 0 KS0 K+ ]
Clear signal for (1690)0 → 0 KS0
…towards an U.L. on BR( (1690)0 → - + )/BR (1690)0 → 0 KS0 )
Background-subtracted
Background-subtracted
c+
→ 0 KS0 K+
c+
→ - + K+
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82
*0 Production in c+ & c
Decays
cancel
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83
Investigation of c+,0 Decays
to 3-body Final States
c+ → - + +
c+ → 0 KS
0 + c
0 → 0 K- +
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… Reconstructing c+ → 0 KS
0 + Events
Data
~200 fb-1
S = 0 S = -1
Cabbibo-suppressed c+ → 0 K0 +
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“Obvious” resonant structures
(1385)+
Large K*(892) contrib.
c+ → 0 K0 + Dalitz Plot Analysis
Uncorrected
Uncorrected
● Previously observed C.S. mode: c+ → + K*(892)0
K*(
892)
Yie
ld/ 1
0 M
eV/c
2
Evidence for the decay c+ → 0 K*(892)+
K(892)+→ KS0+
→ 0 +
Mass-sideband-subtracted
Mass-sideband-subtracted
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Excited Charm Baryons
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Excited
c States
L=0 straightforward
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X(3872): BELLE Finds Data Disfavors 0++ and 2++, Leaving 1++
cc ? 1++ is c1’
X(3872) is too light
M[Ge
DDThreshold
3872
Solid lines: ExperimentLeft: NR model, Barnes, Godfrey, SwansonRight: “Relativized” model, Godfrey, Isgur(Spin) Singlets: dotted, Triplets: dashed
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90Detector Tomography with pKS0 vertices
230 fb -1BABAR
e- e+
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%d0%92%d1%96%d0%b4%d0%bf%d0%be%d0%b2%d1%96%d0%b4%d1%8c %d0%9e%d0%b1%d1%83%d1%85%d1%96%d0%b2 %d0%bf%d
%d0%a4%d0%93%d0%9e%d0%a1%203 %20%d0%9b%d0%b5%d1%87%d0%b5%d0%b1%d0%bd%d0%be%d0%b5%20%d0%b4%d0%b5%d0%b
1060204 %d0%bb%d0%b8%d1%81%d1%82%d0%be%d0%b2%d0%ba%d0%b0 %d0%bf%d0%be %d1%82%d0%b5%d0%bf%d0%bb%d0%be
%d0%9f%d0%be%d0%bb%d0%be%d0%b6%d0%b5%d0%bd%d0%b8%d0%b5 %d0%9f%d0%be%d1%81%d0%bb%d1%8b%20%d0%9f%d0%be