New Frontiers in QCD (QCD-2011) Yonsei University, Seoul Korea, October 27 ~ 28, 2011
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Transcript of New Frontiers in QCD (QCD-2011) Yonsei University, Seoul Korea, October 27 ~ 28, 2011
New Frontiers in QCD (QCD-2011)Yonsei University, Seoul Korea, October 27 ~ 28, 2011
Observation of charged bottomonium-like states
-and a few other items-
Stephen Lars OlsenSeoul National University
Constituent Quark Model
2
Λ= (uds))( ud
Mesons are quark-antiquark pairs Baryons are quark-quark-quark thriplets
Fabulously successfulQuarks are probably the most
well known particle physics quantityamong the general public
Are there other color-singlet spectroscopies?
Pentaquark: H-diBaryon
Glueball
Tetraquarkmesons
qq-gluon hybrid mesons
u cuc
c c
u du
sd
Other possible “white” combinations of quarks & gluons:
_
_
__
u d
usds
_
_ u c
uc
__
_
D0
D*0_
S=+1 Baryon tightly bound6-quark state
Color-singlet multi-gluon bound state
tightly bounddiquark-diantiquark
loosely boundmeson-antimeson“molecule”
predictedmeasuredStrategy:
Search for a meson that decays to a final state containing a c and c quark, If it is a standardqq meson, it has to occupy one of the unfilledstates indicated above. If not, it is exotic.
__
unassigned
cc production at B factories
“XYZ” mesons
Zb(10610) 10608 ± 2 15 ± 3 1+ ±hb(1,2P),±Y(1,2,3S) Y5S Zb(10610)±
Zb(10610) 10653 ± 2 14 ± 3 1+ ±hb(1,2P),±Y(1,2,3S) Y5S Zb(10650)±
The X(3872)
????
Study +J/y produced in BK + J/y decays
EB=Ecm/2
Polarized along flightdirection in B rest frame
The X(3872) in BK +J/y discovered by Belle (140/fb)
M(J/y) – M(J/y)
y’+J/yX(3872)+J/y
PRL 91, 262001 (2003)
X(3872)+J/y with all Belle data
B+XK+
B0XK0
3-dimensional fitsM(J/ψπ+π-) MB EB-Ecm/2
diquark-diantiquark?
Predict : DM(Mx(B+)-Mx(B0)) =8±3 MeV
Maiani e al PRD71, 014028 diquark-diantiquark (tetra-quark) model
u cuc
d cdc
Xu= Xd=
X l (B0)
Xh (B±)
cos sin sin cos
XuXd
Expect two neutral states:
Plus charged partners:d c
ucu c
dcX+=
X-=
€
B(B+ →K 0X(3872)+) = 2 × B(B0 →K 0X(3872)0)
B(B0 →K −X(3872)+) = 2 × B(B+ →K +X(3872)0)
Isospin relations:
Two neutral states?B+XK+
B0XK0
€
DM = MX (from B±) −MX (from B0) = −0.69 ± 0.97 ± 0.13MeV
Predict : DM(Mx(B+)-Mx(B0)) =8±3 MeV
Maiani e al PRD71, 014028
charged partners of the X(3872) ? X+(3872)+0J/y : Isospin triplet?
B0X+K-
B+X+K0
Nevts =4.2±7.8
B(B0K-X+)xB(X++0J/y)<3.9 x10-6
No signals B(B+K0X+)xB(X++0J/y)<4.5x10-6
Rule out isospin triplet model
2-dim. Fit
€
B(B+ →K +X(3872)0) × B(X(3872)0 →π +π − J /ψ ) = (8.61± 0.82 ± 0.78) ×10−6
€
B(B0
→K0X(3872)
0)×B(X(3872)
0→π
+π
− J/ψ)= (4.3±1.2±0.4)×10
−6
not 2x larger!!
X(3872)+ J/y Massrecent results
~6000 evts!
MX = 3871.61 ± 0.16 ± 0.19 MeV
MX = 3871.85 ± 0.27 ± 0.19 MeV
MX = 3871.96 ± 0.46 ± 0.10 MeV
CDF Belle
LHCb
X(3872) mass (in +J/y channel only)
MX(3872) –(MD0+MD*0)= -0.12 ± 0.35 MeV_
=3871.79 ± 0.30 MeV
D0D*0 molecule?
an “old” idea
__
D0-D*0 “Binding Energy” smallDm = -0.12 ± 0.35 MeV
…coincidence??
_
De Rujula, Glashow & Georgi (1976)PRL 38, 317 (1976)
DD* _
(DD*)molrJ/y_
+-
predictions:
JPC=1++
Also: L. Okun& M. VoloshinJETP Lett. 23, 333 (1974)
+-system in X(3872)+-J/ycomes from r+-
M(+- )
Belle: hep-ex/0505038
r+- lineshape
X3872
r
+
J/y
CDF: PRL 96 102002
M(+- )
CDF results on JPC
CDF: PRL 98 132002
O++
1- -
2- +2 adj. params1++ no adj. params
1++ fits well with no adjustable parameters
2-+ looks like 1++ for some choice of params, at least with current statistics
All JPC values otherthan 1++ or 2-+areruled out with highconfidence
Angular distributions for BKX(3872)KrJ/y
L: S-Wave D-waveS: 1 1,2
L: P-Wave F-waveS: 1,2 1,2
3872 MeV
775 MeV
3097 MeV
Only 1 amplitude: BLS=B01
1 free parameter:
2 amplitudes: BLS=B11& B12
3 free parameters
€
B11
B12
= δe iφ complex
normalization
Partial Wave basis:
normalization
X(3872)r J/y is right at threshold neglect higher partial waves
JPC of the X(3872)
Include relative phase f
1++ 2-+
JPC of the X(3872)
22 sinsincoscos
)1(
++
ddd
J. Rosner PRD 70, 092023 (2004)
X
y /J
r
K
+
1++ fits data well withno free parameters.
2-+ has a free complexparameter; one value
gives an acceptable fit
+
+
2/dof =0.56/4
2/dof =1.56/4
2/dof =5.24/4
2/dof =4.60/4
1++ cc assignment? c1‘_
huge for Isospin-violating decay c.f.: (y’0J/y)≈0.4 keV
‘•(c1 gy’) ~180 keV (c1 g J/y) ~14 keV
• (c1 gy’)/(c1 g J/y)>>1• expt’l upper limit: <2.1
‘
•+ J/y=(3.4±1.2)gJ/y ~45 keV
•Mass is too low? • 3872 vs 3905 MeV• nr=2 splitting> nr=1
pinnedto:
M c2=3930 MeV
‘
T.Barnes et al PRD 72, 054026
X(3872) g y’ ??Belle 2010:
no signals!!
B(B+K+ X3872)xB(X3872gy’)
B(B+K+ X3872)xB(X3872gJ/y)< 2.1 (90%)
B+
B0B0
B+
y’J/y+y’ l+l-
M(gy’) M(gy’)
2-+ cc assignment? hc2
• huge for Isospin-violating decayc.f.: (y’0J/y)≈0.4 keV
•(hc2 gy’) ~0.4 keV•(hc2 g J/y) ~9 keV
(hc2 gy’)/(hc2 g J/y)<<1
•+ J/y=(3.4±1.2) gJ/y ~30 keV
•Mass is too high?: • 3872 vs 3837 MeV
pinned to:
My”=3770 MeV
Y. Jiaet al arXiv:0107.4541
hc2ghc(1S) & hc modes expected to dominate
•BKhc2 violates factorization• BKhc not seen• BKc2 barely seen
•hc2 DD* expected to be tiny
• Belle & BaBar::(XDD*)/(X+J/y)9.5±3.1
Y. Kalasnikovaet al arXiv:1008.2895
_
_
_
Belle (May 2010): B+ K+ g J/y
Belle: arXiv 1105.0177
Bf(B+K+ c1)=(49±3)x10-5
= 0.022 ± 0.007
factorizationsuppressionpenalty
Bf(B+K+ c2)=(1.11±0.37)x10-5
B(B+K+ c2)B(B+K+ c1)
3.6s
c1gJ/y
calibration reaction
B+K+ c2: 1st evidence
M(gJ/y)M(gJ/y)
Narrow width: <1.2 MeV
at = 0.95MeV90 %
Belle prev: <2.3 MeV<1.2 MeV @ 90% CLinflate by +0.23 MeV
for possible biases
= ~ 0.0 best fit
below experimental resolution
B(B0 →X(K+π–)non_res) x B(X→J/ψπ+π–) = (8.1±2.0 )x10–6 dominant !
B(B0 →XK*0) x B(X→J/ψπ+π–) < 3.4x10–6 @90% CL small !!
+1.1 - 1.4
Mass(Kπ)
K*0→Kπnon-resonant Kπ
sideband bkgd
X(3872)→J/ψπ+π–
5σ
Nsig= 9019 (Nsig=8.2 10.0)
Belle arXiv:0809.1224(2008)
B0→X(3872)K+ (B→X(3872) K*?) 605 /fb
No K*K signal!!
BKX(3872) is very different from other BKCharmonium
KX(3872)
M(K) / GeV
Belle arXiv:0809.0124
Belle arXiv:0809.0124
Ky′ KJ/y Kc1
M(K) M(K) M(K)
BaBar, Phys. Rev. D71(2005)032005
Belle, Phys. Lett.B634(2006)155
all K* comesfrom sideband
K* dominates
B KD0D*0
605 fb-1
Agrees with M from J/y mode
X(3872)D0D*0 is observed
= (9.5±3.1)x Bf(+J/y)
D*0→D0γ
D*0→D0π0
& Belle PRL97, 162002(2006)
See also:BaBarPRD77, 011102(2008)
M = 3872.9 MeV + 0.6− 0.4
+ 0.4− 0.5
(BW) = 3.9 MeV+ 0.2− 1.1
+ 2.8− 1.4
Bf(BK X3872)xBf(X3872D*0D0) = (0.80±0.20± 0.10)x10-4
2-dim. Fits
PRD81, 031103(2010)
_
Molecular Picture
~ 10 fermis!!
E. Braaten, J. Stapleton PRD81, 0140189
If the X couples to D0 D*0 in an S-wave:
X(3872)-J/y relative sizes
drms(J/y) ≈ 0.4 fm
•Overlap of the cc necessary to form the J/y in X +-J/y decays is rare
•How can such a fragile object be produced in H.E. pp collisions? heavy ion collisions??
Volume(J/y)
Volume(X3872) ≈ 10-3
-- arXiv 0906.0882: sCDF(meas)>3.1±0.7nb vs stheory(molecule)<0.11nb
_
_
C. Bignamini et al, PRL 103, 162001:
drms(X3872) ~ 5 fm
drms(208Pb nucleus)≈5.5 fm
++ +
++
+
++
++
++
++
++
++
+
J/y
X(3872)
208Pb
X(3872) as a probe for Heavy Ion physics?
Size is huge (but it is produced in pp collisions)
4 valance quarks unique probe for quark number scaling
_
JPC = 1- - Y(4260) meson
Zb(10610) 10608 ± 2 15 ± 3 1+ ±hb(1,2P),±Y(1,2,3S) Y5S Zb(10610)±
Zb(10610) 10653 ± 2 14 ± 3 1+ ±hb(1,2P),±Y(1,2,3S) Y5S Zb(10650)±
Radiative return
ss cc
bb
Ecm(GeV)
10.58 GeV
gB-factoryenergies
3~5GeV
e+e- gisr Y(4260) at BaBar
233 fb-1
Y(4260)
BaBar PRL95, 142001 (2005)
~50pb
M=4259 ± 8 +2 MeV
= 88 ± 23 +6 MeV -6
-9
fitted values:
+- J/y
Y(4260) confirmed by Belle
M=4247 ± 12 +17 MeV
= 108 ± 19 ±10 MeV -32
C.Z Yuan et al (Belle) PRL 99, 182004
M=4259 ± 8 +2 MeV
= 88 ± 23 +6 MeV -6
-9
BaBar values:
Not seen in e+e- hadrons
(Y4260+ J/y) > 1.0 MeV @ 90% CL
X.H. Mo et al, PL B640, 182 (2006)
BES data
~3nb
speak(Y(4260)+J/y)~50 pb Huge by charmonium
standards
J.Z.Bai et al (BES), PRL 88, 101802 (2006)
s(e+e- hadrons)s(e+e- +-)
4260 No sign of Y(4260)D(*)D(*)
_
€
Bf (ψ (3770) →π +π −J /ψ ) = (0.19 ± 0.03)%
Bf (Y (4260) →π +π −Υ(1S)) >~50pb3nb
=1.6%
Exclusive cross sections contribution to the total cross section
DD DD* D*D* DDπ
DD*π
DsDs +DsDs* +Ds
*Ds*
ΛcΛc
Contributions of D+D*–, D*+D*–, D0D–π+ and D0D*–π+ are scaled following isospin symmetry
peaks in e+e- gISR +- y’ e+e-gISR+-y’
BaBar
Peak is 4324 MeV, distinct from 4260 MeV
M=4324 ± 24 MeV
= 172 ± 33 MeV
M(+-
y’)
4325 MeV +y’ peak also seen
M=4324 ± 24 MeV
= 172 ± 33 MeV
548 fb-1
X.L. Wang et al (Belle)PRL 99, 142002 (2007)
Two peaks!
M=4664 ± 11 ±5 MeV
= 48 ± 15 ±3 MeV
M=4361 ± 9 ±9 MeV
= 74 ± 15 ±10 MeV
BaBar values
(both relatively narrow)(& neither consistent with 4260 MeV)
4260
At least three peaks for only one unassigned 1- - level
33D1
4260MeV4361MeV
4664MeV
If these are mesons, they must be more complex than simply cc_
Zb mesons
Zb(10610) 10608 ± 2 15 ± 3 1+ ±hb(1,2P),±Y(1,2,3S) Y5S Zb(10610)±
Zb(10610) 10653 ± 2 14 ± 3 1+ ±hb(1,2P),±Y(1,2,3S) Y5S Zb(10650)±
XYZ counterparts with b-quarks?
What about here?
W.S. Hou PRD 74, 017504 (2006)
“bottomonium” bb mesons
2MB = 10358.7 MeV
_
(4S) + (1S) ?
Belle: (4S)+-(1S)
2S3S
4S
(4S) (1S) +
477 fb-1
52±
10 e
vts
N(4S) N(+-1S) B(Y4S1S) (Y4S1S) theory
535x106 52±10 9 ± 2 x10-5 1.75 ± 0.35 keV 1.47±0.03 keV
2MB = 10358.7 MeV
(5S) + (1S) ?
Belle: (5S)+(1S)
23.6 fb-1 vs477 fb-1~1/20th the data~1/5ththe cross-section
K.F. Chen et al (Belle) PRL 100, 112001 (2008)
>6 times as many events!
325±20 evts!
“(5S)” is very different from other states Belle PRL100,112001(2008) (MeV)
X10--2
Anomalous production of (nS) +-
Recall Y(4260) with anomalous (J/y +-) Is there a Yb equivalent close to (5S)
€
Bf (Υ(4S) →π +π −Υ(1S)) = (0.008 ± 0.0003)%
Bf (Y (5S) →π +π −Υ(1S)) = (0.53 ± 0.06)%
Belle PRD82,091106R(2010)
Nature of (5S) is puzzling and not yet understood
(5S)hadrons
Comparison of s(e+e-+-) vs s(e+e- hadrons)
(5S)+-
~2s discrepancies in thepeak mass and width
5S:
121.4 fb-1
X=(1S) (2S) (3S)hb(2P)hb(1P)
Look at +- recoil mass in (5S)+-+ X
MM(+-) residuals
MM(+-) spectrum
hb(1,2P)JPC=1+-
1st observations
MM(0)
hb(1,2P)(bb) : S=0 L=1 JPC=1+
DMHF test of hyperfine interaction
_
Expected mass (Mb0 + 3 Mb1 + 5 Mb2) / 9
(3S) → 0 hb(1P)
BaBar
arXiv:1102.4565
3.0s
Previous search
Deviations from CoG of bJ masses
hb(1P) (1.6 ± 1.5) MeV/c2
hb(2P) (0.5 +1.6 ) MeV/c2-1.2
Agrees with expectations
((5S) hb(nP) +- ) is large
Mechanism of (5S) hb(nP) +- decay is exotic
for hb(1P)
for hb(2P)no spin-flip
=
Process with spin-flip of heavy quark is not suppressed
spin-flip
hb(1P)~50,000 evtshb(2P)~85,000 evts
Resonant structure of “(5S)” hb(nP)+-
M(hb(1P)+)
measure (5S)hb yield in bins of MM()
data
MeV/c2M1 =
MeV/c2M2 = MeV2 =
MeV1 =
non-res.~0
PHSP
~BB* threshold_
~B*B* threshold__
data
PHSP
M(hb(2P)+)
MeV/c2
MeV
MeV/c2
MeV
53
Look at “Υ(5S)”Υ(nS) +-
Υ(1S)π+π- Υ(2S)π+π- Υ(3S)π+π-
M2(π+π-) > 0.10 GeV2M2(π+π-) > 0.16 GeV2M2(π+π-) > 0.20 GeV2
9.43 GeV <MM(π+π-) < 9.48 GeV 10.05 GeV <MM(π+π-) < 10.10 GeV 10.33 GeV <MM(π+π-) < 10.38 GeV
Dalitz distributions for events in Y(nS) signal regions.
M2(π+π-)M2(π+π-)M2(π+π-)
To exclude contamination from gamma conversions we require:
Fitting the Dalitz plots
Signal amplitude parameterization:
S(s1,s2) = A(Zb1) + A(Zb2) + A(f0(980)) + A(f2(1275)) + ANR
ANR = C1 + C2∙m2(ππ)
Parameterization of the non-resonant amplitude is discussed in [1] M.B. Voloshin, Prog. Part. Nucl. Phys. 61:455, 2008.
[2] M.B. Voloshin, Phys. Rev. D74:054022, 2006.
A(Zb1) + A(Zb2) + A(f2(1275))A(f0(980))
– Breit-Wigner – Flatte
(5S) Zb, Zb (nS) – no spin orientation changeS-wave
S-wave
Spins of (5S) and (nS) can be ignored
Angular analysis favors JP=1+
Fit results
M(Υ(2S)π)max M(Υ(3S)π)maxM(Υ(1S)π)max
(5S) (1S)+- (5S) (2S)+- (5S) (3S)+-
M=10611±4±3 MeV=22.3±7.7±4.0 MeV
M=10609±2±3 MeV=24.2±3.1±3.0 MeV
M=10608±2±3 MeV=17.6±3.0±3.0 MeV
M=10657±6±3 MeV=16.3±9.8±6.0 MeV
M=10651±2±3 MeV=13.3±3.3±4.0 MeV
M=10652±1±2 MeV=8.4±2.0±2.0 MeV
Zb1
Zb2
Consistent peaks in all three channels
Zbϒ(1S) Zbs must contain a bb quark pair
charge = ± 1 Zbs must contain additional quarks
_
“minimal” quarkconfiguration
d bub _
__
Zb+=
57
Summary of parameter measurements
Zb(10610)M=10607.2±2.0 MeV
=18.4±2.4 MeV
Zb(10650)
M=10652.2±1.5 MeV
=11.5±2.2 MeV
[preliminary]
mB+
mB*
2mB*
B-B* & B*-B* molecules??
B
B*
b
b_
B-B* “molecule”
B*
B*
b
b_
B*-B* “molecule”_ _
_ _
Zb(106010)± Zb(106050)±
MZb(106010) –(MB+MB*) = + 3.6 ± 1.8 MeV MZb(106010) –2MB* = + 3.1 ± 1.8 MeV
Slightly unbound threshold resonances??
M=10608.1±1.7 MeV=15.5±2.4 MeV
M=10653.3±1.5 MeV=14.0±2.8 MeV
PDG: MB + MB* = 10604.5±0.6 MeV MB* + MB* = 10650.2 ± 1.0 MeV
Bellepreliminary
Are similar things happening withthe Y(4260)?
is it decaying to Zc-, +J/y ? ( & +hc ?)
+
I
c-quark counterpart of Zb+
Y(4260)
BaBar data
Belle results on Y(4260)+-J/y
M2(±J/y)
(MD+
MD*
)2
see D.V.Bugg hep-ex/0701002
C.Z.Yuan et al (Belle), PRL99,182004
Inconclusive. Need~ 10x more data,expected in BelleII
SummaryProperties of X(3872) consistent with expectations for DD* S-wave molecule-like state
- JPC=1++ favored (2-+ not ruled out)- Mass = MD0 + MD*0to a part in 104
- No isospin partners are seen- Isospin violating X(3872)rJ/y is a strong decay mode- <1.2 MeV
Y(4260) seen in three experiments- JPC = 1 ++; no unassigned cc state available for it- Very large partial decay width to +-J/y
Anomalously large “ϒ(5S)”+-ϒ(1,2,3S) widths due to “ϒ(5S)”Zb1,2-; Zbϒ(nS)+
Similarly large widths for “ϒ(5S)”+-hb(1,2P) also due to “ϒ(5S)”Zb1,2-; Zbhb+
MZb1-( MB + MB* ) = +3.6 ±1.8 MeV; MZb2- 2MB* = 3.1 ±1.8 MeV more S-wave molecules?
Why such large widths to hidden charm and hidden beauty?
+
+ +
+
_
Large decay widths to hidden quarkonia
Zb(10610) 10608 ± 2 15 ± 3 1+ ±hb(1,2P),±Y(1,2,3S) Y5S Zb(10610)±
Zb(10610) 10653 ± 2 14 ± 3 1+ ±hb(1,2P),±Y(1,2,3S) Y5S Zb(10650)±
Lots of pieces
Y(4360)
Y(46
60)
Y(4260)
Y(40
08)
X(3872)
X(3940
)
Z b(10
610
)
Z(4430) Y(3940)Are
they
all f
rom th
e sam
e puz
zle?
Thank You
감사합니다
Backup Slides
Experiment X mass
CDF 2 3871.61 ± 0.16 ± 0.19 MeV
BaBar (B+) 3871.4 ± 0.6 ± 0.1 MeV
BaBar (B0) 3868.7 ± 1.5 ± 0.4 MeV
D0 3871.8 ± 3.1 ± 3.0 MeV
Belle (This result) 3871.84 ± 0.27 ± 0.19 MeV
World Average 3871.62 ± 0.19 MeV
LHCb (new) 3871.96 ± 0.46 ± 0.10 MeV
World Average again
3871.67 ± 0.17 MeV
M(D0)+M(D*0) PDG2010
3871.79 ± 0.30 MeV
X(3872) mass in +J/y channel only
“Binding Energy” getting smaller:
Old: m = -0.32 ± 0.35 MeVNew: Dm = -0.17 ± 0.36
MeV
Dm(deuteron) = -2.2 MeV
New: Dm = -0.12 ± 0.35 MeV
<MX>prev_WA= 3871.46 ± 0.19 MeV
67
(5S) (nS)+-(nS) +-
(n = 1,2,3)
(1S)
(2S)
(3S)
reflections
Y(nS) +- selections
68
(5S) (1S) (5S) (2S) (5S) (3S)
(3S) (1S) (2S) (1S) Shapes of signals
tail (8%) – ISR of soft gs = 5.7 – 7.5 MeV
CrystalBall function
Calibration channels(5S) (nS)+-
(nS) +-(n = 1,2,3)
Shapes of reflections
69
Residuals(1S)
Example of fit
BG: Chebyshev polynomial: max C.L. of fit
Signal: shape is fixed from +-+- data
“Residuals” – subtract polynomial from data points
KS contribution: subtract bin-by-bin
6th or 7th order
Description of fit to MM(+-)Three fit regions
1 2 3
in region #3 only
70
Fits to MM(+-) spectra in MM() bins
(2S)hb
71
Fitting theDalitz PlotsSignal amplitude parameterization:
S(s1,s2) = A(Zb1) + A(Zb2) + A(f0(980)) + A(f2(1275)) + ANR
ANR = C1 + C2∙m2(ππ)
Parameterization of the non-resonant amplitude is discussed in [1] M.B. Voloshin, Prog. Part. Nucl. Phys. 61:455, 2008.
[2] M.B. Voloshin, Phys. Rev. D74:054022, 2006.
and references therein.
A(Zb) = BW(s1,MZ,ΓZ) + BW(s2,MZ,ΓZ)
Zb amplitudes are parameterized by Breit-Wigner functions and symmetrized with respect to interchange of the two pions π1 and π2:
A(f0(980)) – Flatte function with parameters m=950 MeV, gππ=0.23 and gKK=0.73 determined from the analysis of B→Kππ.
A(f2(1275)) – Breit-Wigner function
72
Dalitz Plot
It will also produce a signal like reflection on the other axis
If there is a signal in the Yπ system
M2( U(2S)+), (GeV2/c4)
M2 ( U
(2S)- ),
(GeV
2 /c4 )
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Results: Y(2S)π+π-
Results: Y(2S)π+π-
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Expectations1+ isotropic1-
2+
2-
neglect Zb recoil motion(<0.02 very good approximation)
(5S) Zb1 [(2S) 2] 1
– beam direction
1, 2 – polar angles of 1st and 2nd pions
p – angle btw planes defined by (1) 1& Z axis, (2) 1& 2 .
many thanks to
A. Milshtein
(BINP)
also formulae for hb are available
Interference terms vanish after integration over other angular variables subtraction of non-resonant contribution is possible.
Consider 1D projections
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Example : (5S) Zb+(10610) - [(3S)+] -
JP=1+ 1- 2+ 2-
Best discrimination: cos2 for 1-; cos for 2+ and 2-
Example : (5S) Zb+(10610) - [hb(1P)+] -
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Summary on angular analyses
All angular distributions are consistent with JP=1+ for Zb(10610) & Zb(10650).
All other JP with J2 are disfavored at typically 3s level.
The probabilities at which different JPhypotheses are disfavored to1+
[preliminary]