Hadron spectroscopy at LHCb
M. Kreps on behalf of the LHCb Collaboration
ICNPF, Kolymbari, Crete, Greece, 2014
Physics Department
www2.warwick.ac.uk
Introduction
arXiv:1403.1254
00
11
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
We think of hadrons as qq or
qqq
But there is nothing preventing
other combinations
Can we find
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
2
molecule
tetraquark
your other favourite choice
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb
Belle
Candidates
Events/0.01 GeV
30
20
10
0
3.8
400
(b)
200
0
4.05
4.3
M(π+ψι) (GeV)
4.55
4.8
200
Seen by Belle, but not
Babar
0
Data consistent
Charged state
-200
3.8
→ Cannot be cc
Latest Belle result uses 4D
analysis
Is it real and if yes, is it resonance?
B → ψ(2S)π K
-,0
-
(d)
0,+
Residuals
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
Flat cosθ K
ψ(2S)π K moments
J/ ψπ-K moments
PRD 79, 112001
PRL 100, 142001
Z(4430)+ history
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
00
11
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
00
11
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
4
4.2
4.4
2
mψ(2S)π- (GeV/c )
4.6
4.8
00
11
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
3
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb
30
Belle
30
Belle
(a)
Events/10 MeV/c2
Events/0.01 GeV
20
20
10
10
PRD 79, 112001
PRL 100, 142001
Z(4430)+ history
0
BABAR (*1.18)
30
(b)
20
0
3.8
4.05
4.3
M(π+ψι) (GeV)
4.55
4.8
10
0
Seen by Belle, but not
Babar
10
Data consistent
0
-10
Charged state
-20
→ Cannot be cc
3.8
Latest Belle result uses 4D
analysis
Is it real and if yes, is it resonance?
Diff./10 MeV/c2
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
00
11
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
11
00
00
11
000
111
00
11
000
111
00
11
000
111
00
11
000
111
000
111
(c)
χ2/NDF = 54.7/58
4
4.2
4.4
4.6
4.8
2
mψ(2S)π- (GeV/c )
00
11
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
3
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb
Data sample
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
Use B 0 → ψ(2S)Kπ decays
Large statistics (> 25k), about 10 times what B-factories had
Very clean signal, background 4 % of events (about 8% at
B-factories)
Perform both model-independent analysis (BABAR) and amplitude
fit (Belle)
400
200
0
4
3
LHCb
fb−1
m2ψ'π- [GeV2]
1800
1600
1400
1200
1000
800
600
102
22
21
20
10
19
18
17
signal
sideband
04 Aug 2014
sideband
range
1
16
LHCb
15
5250
5300
mψ'K+π- [MeV]
0.5
1
1.5
2
2.5
mK2 +π- [GeV2]
PRL 112 (2014) 222002
Candidates / 1 MeV
Only 2 out of 4 dimensions
K ∗ (892)
KJ∗ (1430)
Michal Kreps – Hadron spectroscopy at LHCb
Amplitude analysis
Full 4D amplitude analysis
Rotation between
Amplitude
helicity frames
2
X X X
X
Z
i∆µ α 2
|M | =
Ak,λψ (Ω|m0k , Γ0k ) +
AZ,λZψ (Ω |m0Z , Γ0Z )e
∆λµ λψ
k
λZ
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
ψ
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
5
Mass described by relativistic Breit-Wigner
Angular part using helicity formalism
Imposes model how invariant mass distribution should look like
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb
mψ2 'π- [GeV2]
PRL 112 (2014) 222002
Model independent method
102
22
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
21
20
10
19
18
17
1
16
LHCb
15
0.5
1
1.5
2
2.5
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
04 Aug 2014
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
mK2 +π- [GeV2]
Test whether contributions in Kπ
system can describe data
Do not impose specific model for
resonances
→ Model independent test
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
6
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
Look to cos(θK ) in bins
of Kπ mass
Allows to find out which
spins contribute
X1
Pl (cos θKi )
ǫi
i
Take only moments
corresponding to J ≤ 2
Construct Dalitz plot
and project on ψ(2S)π
axis
Michal Kreps – Hadron spectroscopy at LHCb
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
LHCb
0.03
0.02
0.01
0
3.8
4
4.2
4.4
4.6
4.8
mψ’π− [GeV]
Clearly, pure kaon resonances cannot explain M (ψ(2S)π) spectrum
Understanding details difficult
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
7
0.04
PRL 112 (2014) 222002
Efficiency corrected yield / ( 25 MeV )
Model independent result
Resonances in ψ(2S)π will contribute to Kπ and its moments
Any fit to ψ(2S)π on top of reflections neglects interference
between two axes
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb
Candidates / ( 0.2 GeV2 )
1000
LHCb
500
0
8
16
04 Aug 2014
18
20
22
m2ψ'π− [GeV2]
LHCb
200 1.0 < m2K+π− < 1.8 GeV2
100
0
16
18
20
22
m2ψ'π− [GeV2]
PRL 112 (2014) 222002
Candidates / ( 0.2 GeV2 )
Only K∗ resonances
Michal Kreps – Hadron spectroscopy at LHCb
Candidates / ( 0.2 GeV2 )
1000
LHCb
500
0
16
a
t
Da
8
04 Aug 2014
18
n
a
c
t
o
n
20
d
e
b
c
s
e
e
b
ri
22
m2ψ'π− [GeV2]
LHCb
200 1.0 < m2K+π− < 1.8 GeV2
∗
K
y
b
d
o
y
l
n
100
0
16
18
20
22
m2ψ'π− [GeV2]
PRL 112 (2014) 222002
Candidates / ( 0.2 GeV2 )
Only K∗ resonances
Michal Kreps – Hadron spectroscopy at LHCb
10
LHCb
500
LHCb
-
Z(4430) excluded
*
K (892)
*
K S-wave
18
20
10
*
K 2 (1430)
Z(4430)background
*
K (1680)
*
K (1410)
1
0.5
22
mψ2 ’π− [GeV2]
1
1.5
2
m2K +π−
2.5
[GeV2]
Candidates / 20o
16
600
1000
400
500
200
LHCb
0
-1
9
-
total fit with no Z(4430)
total fit
3
102
0
Candidates / 0.05
Candidates / ( 0.02 GeV2 )
1000
data
PRL 112 (2014) 222002
Candidates / ( 0.2 GeV2 )
Adding Z+
04 Aug 2014
-0.5
LHCb
0
0.5
1
cos θψ’
0
-100
0
100
φ [degrees]
Michal Kreps – Hadron spectroscopy at LHCb
Candidates / ( 0.2 GeV2 )
PRL 112 (2014) 222002
Results
1000
LHCb
500
0
16
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
00
11
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
10
M (Z)
Γ(Z)
fZ
fZI
Significance
04 Aug 2014
18
20
22
mψ2 ’π− [GeV2]
4475 ± 7+15
−25 MeV
172 ± 13+37
−34 MeV
+1.5
%
5.9 ± 0.9−3.3
+2.6
%
16.7 ± 1.6−5.2
> 13.9σ
Data are described well with 1+ Z(4430)+ contribution
(χ2 p-value 12%)
Parameters extracted consistent with Belle
Large interference effects seen
Adding additional K ∗ resonances to model does not alter
conclusion
R
AZ (Ω)dΩ
R
fZ =
A(Ω)dΩ
fZI
=1−
R
A (Ω)dΩ
R noZ
A(Ω)dΩ
Michal Kreps – Hadron spectroscopy at LHCb
Pseudo-experiments / 10.0
PRL 112 (2014) 222002
Z(4430)+ spin
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
11
300
250
200
LHCb
Simulated
experiments
−
J PZ = 0
Data
150
Simulated
experiments
J PZ = 1+
100
50
0
-200
0
200
Hypothesis
0−
1−
2+
2−
Rejection
9.7 σ
15.8 σ
16.1 σ
14.6 σ
400
∆(-2 ln L)
As we use full kinematic information, we have sensitivity to quantum
numbers
Test spins 0,1 and 2 with both parities
Based on likelihood ratio
Quote exclusion based on asymptotic formula (lower bound)
Verified by simulation
All rejections relative to 1+
Z(4430)+ is 1+ state without any doubts
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb
Is Z(4430)+ resonance?
1
m2R − m2 − imR Γ(m, ΓR )
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
00
11
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
12
04 Aug 2014
Data are consistent with BW for
Z(4430)+
But will they follow if BW is not
imposed?
Change BW in Z(4430)+
amplitude to 6 complex numbers
in 6 M (ψ(2S)π) bins
Plot resulting amplitude on
Argand plot
Michal Kreps – Hadron spectroscopy at LHCb
Is Z(4430)+ resonance?
1
m2R − m2 − imR Γ(m, ΓR )
Data are consistent with BW for
Z(4430)+
But will they follow if BW is not
imposed?
Change BW in Z(4430)+
amplitude to 6 complex numbers
in 6 M (ψ(2S)π) bins
Plot resulting amplitude on
Argand plot
⇒ It shows resonance behaviour
without imposing it
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
12
Im AZ
PRL 112 (2014) 222002
−
00
11
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
0.2
LHCb
0
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
-0.2
-0.4
-0.6
-0.6
04 Aug 2014
-0.4
-0.2
0
0.2
Re AZ
−
Michal Kreps – Hadron spectroscopy at LHCb
Candidates / ( 0.2 GeV2 )
PRL 112 (2014) 222002
Second Z+ state
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
13
200 1.0 < m2K+π− < 1.8 GeV2
100
0
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
M (Z0 )
Γ(Z0 )
fZ0
fZI 0
Significance
LHCb
16
18
20
4239 ± 18+45
−10 MeV
220 ± 47+108
−74 MeV
+1.9
%
1.6 ± 0.5−0.4
+1.7
%
2.4 ± 1.1−0.2
6σ
22
m2ψ’π− [GeV2]
Data can be described even better by adding second ψ(2S)π state
On its own, it is significant
Preferred 0− (but 660 ± 150 MeV wide 1+ option cannot be ruled out)
Argand diagram is inconclusive
No evidence in model-independent approach
Will need more data to clarify situation
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb
DsJ spectroscopy
00
11
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
00
11
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
00
11
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
14
Lowest lying Ds and
Ds∗ well established
∗
(2573)
Ds1 (2536), Ds2
reasonably
studied,
“narrow” L = 1 states
!"##$$%!&'(
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
,.++
,-++
,),1
,+++
)*++
)121
)
6#$$!"##$08&9:;<=$
PRD 89 (2014) 074023
/,++
//+* //,/4 //))
/,+. /,).4 /)1+
/,1.
/)3- /)1/
/).*
/++3 /+/.4 /+-.
,.11 ,1,*4 ,1)2
/+).
,1++
,2/,
,*2/
,33*4 ,31,
,-.,3-1
/
/
/
/
/
/
/
0+ 0) 5+ 5) 5, 6 ) 6 , 6 / 7, 7/ 7-
∗
(2317) and Ds1 (2460) interpreted as “wide” L = 1 states,
Ds0
lower than expected
States with unnatural spin parity (J P = 0− , 1+ , 2− , ...) cannot
decay to DK
∗
∗
(2700), DsJ
(2860) and DsJ (3040) seen by Babar and LHCb
Ds1
in inclusive production
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb
0
− +
2500
3 fb−1 LHCb
(a)
2000
Data
Full fit
1500
0
B s signal
Combinatorial bkg.
0
1000
0
B → D Kπ
*0
0
Bs → D K π
500
0
5200
5400
5600
0
0
B → D
(*)0
Λb → D
(*)0
−
ππ
pπ
5800
m(D K π +) [MeV/c2]
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
15
0
− +
arXiv:1407.7574,arXiv:1407.7712
Candidates / (7 MeV/c2)
Bs → D K π decay
0
Decay Bs → D K π allows to study DsJ states in D K −
Clean sample of about 11k signal decay (87% purity)
Dalitz plot analysis allows to access also spin
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb
(Square) !"#$%&'()*#+$,)-./0$1-2/$
Dalitz plot
!"#$
!"#$
!"#$
!"#$
32*$4256#5.#54#$7#$/*)5&82*9$.5/2$:.88#*#5/$1)*)9#/#*&$/")/$9)1$/"#$
Contributions in DK − and K − π +
DJ+ would decay to D0 π + , so would contribute only through
doubly Cabibbo suppressed D0 decay
As most activity in corners and around boundary, transform to
square Dalitz plot
m′ is effectively m(DK) and θ′ is the DK helicity angle
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
16
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb
Dalitz model
17
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb
18
Candidates / (30 MeV/c2)
Candidates / (30 MeV/c2)
arXiv:1407.7574,arXiv:1407.7712
Dalitz plot fit
1800
1000
LHCb
(a)
800
1400
1200
1000
600
400
200
0
04 Aug 2014
LHCb
(c)
1600
1
2
−
m(K π +)
800
600
400
200
0
3
2
[GeV/c ]
3
4
0
−
5
m(D K ) [GeV/c2]
Michal Kreps – Hadron spectroscopy at LHCb
Candidates / (30 MeV/c2)
800
1400
1200
1000
400
200
0
1
2
−
m(K π +)
800
600
400
200
0
3
3
4
2
400
300
200
100
−
0
5
m(D K ) [GeV/c2]
[GeV/c ]
LHCb
(a)
500
04 Aug 2014
LHCb
(c)
1600
600
0
0.5
18
LHCb
(a)
Candidates / (9 MeV/c2)
Candidates / (30 MeV/c2)
1800
1000
Candidates / (13 MeV/c2)
arXiv:1407.7574,arXiv:1407.7712
Dalitz plot fit
400
LHCb
(b)
350
300
250
200
150
100
50
1
0
1.5
−
m(K π +)
2
[GeV/c ]
2.4
2.6
2.8
0
−
3
3.2
2
m(D K ) [GeV/c ]
Michal Kreps – Hadron spectroscopy at LHCb
Candidates / (30 MeV/c2)
1800
1000
LHCb
(a)
800
1400
1200
1000
600
400
200
1
2
θ'
0
LHCb
(c)
1600
−
m(K π +)
800
600
400
200
0
3
3
0.9
3
0.8
2
5
1
0.6
0
0.5
0.4
-1
0.3
04 Aug 2014
−
LHCb
1
0.2
-2
0.1
-3
0
0
m(D K ) [GeV/c2]
[GeV/c ]
0.7
18
4
2
Pull
Candidates / (30 MeV/c2)
arXiv:1407.7574,arXiv:1407.7712
Dalitz plot fit
0
0.2
0.4
0.6
0.8
1
m'
Michal Kreps – Hadron spectroscopy at LHCb
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
19
LHCb
(a)
500
400
300
160
LHCb
(b)
140
120
100
80
60
200
40
100
0
0.5
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
Candidates / 0.04
Candidates / (13 MeV/c2)
arXiv:1407.7574,arXiv:1407.7712
Helicity angle projections
20
1
1.5
−
m(K π +)
2
0
-1
-0.5
0
[GeV/c ]
0.5
cos
1
−
θ (K π+)
Angular distribution depends on spin of the resonance
Spin 1: cos2 θ
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
19
LHCb
(a)
500
400
300
70
LHCb
(d)
60
50
40
30
200
20
100
0
0.5
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
Candidates / 0.04
Candidates / (13 MeV/c2)
arXiv:1407.7574,arXiv:1407.7712
Helicity angle projections
10
1
1.5
−
m(K π +)
2
0
-1
-0.5
0
[GeV/c ]
0.5
cos
1
−
θ (K π+)
Angular distribution depends on spin of the resonance
Spin 1: cos2 θ
Spin 0: Flat
Spin 2: ( 32 cos2 θ − 21 )2
Spin 3: (− 32 cos θ + 25 cos3 θ)2
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb
400
LHCb
(b)
350
300
250
200
400
350
250
200
150
100
100
50
50
2.4
2.6
2.8
0
−
3
3.2
LHCb
300
150
0
0
-1
-0.5
0
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
0.5
−
1
cos θ (D K )
0
m(D K ) [GeV/c2]
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
19
Candidates / 0.04
arXiv:1407.7574,arXiv:1407.7712
Candidates / (9 MeV/c2)
Helicity angle projections
Angular distribution depends on spin of the resonance
Spin 1: cos2 θ
Spin 0: Flat
Spin 2: ( 32 cos2 θ − 21 )2
Spin 3: (− 32 cos θ + 25 cos3 θ)2
Spin of Ds2 (2573) determined as 2 for the first time
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb
20
Candidates / 0.04
Candidates / (9 MeV/c2)
arXiv:1407.7574,arXiv:1407.7712
2860 MeV region
400
LHCb
(b)
350
300
250
200
150
50
χ2 = 47.3, 214.0, 150.0
Nbins = 50
LHCb
40
30
20
100
10
50
0
2.4
2.6
Spin
1+3
0
0+1
0+2
0+3
1
1+2
2
2
2+3
3
04 Aug 2014
2.8
0
−
3
3.2
0
-1
m(D K ) [GeV/c2]
√
hypothesis ∆NLL
2∆NLL
0
—
141.0
16.8
113.2
15.0
155.1
17.6
105.1
14.5
156.8
17.7
138.6
16.6
287.9
24.0
365.5
27.0
131.2
16.2
136.5
16.5
-0.5
0
0.5
−
1
cos θ (D K )
0
Masses and widths
2862
2446*
2870
2415*
2866
2851
3243*
2569*
2878
2860
57
250
61
188
92
99
81
17
12
57
2855
2569*
2860
96
17
52
3134*
174
2860
56
Michal Kreps – Hadron spectroscopy at LHCb
Results
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
∗
(2573)
Best measurement of mass and width of Ds2
Uncertainties are statistical, systematic and Dalitz model
∗
(2573)− ) = 2568.39 ± 0.29 ± 0.19 ± 0.18 MeV/c2
m(Ds2
∗
(2573)− ) = 16.9 ± 0.5 ± 0.4 ± 0.4 MeV/c2
Γ(Ds2
00
11
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
00
11
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
00
11
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
00
11
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
21
Some tension with world average
∗
(2573)
Confirm spin 2 for Ds2
With high significance, peak at m(DK) ≈ 2860 MeV is due to two
resonance with spins 1 and 3
∗
(2860)− ) = 2859 ± 12 ± 6 ± 23 MeV/c2
m(Ds1
∗
(2860)− ) = 159 ± 23 ± 27 ± 72 MeV/c2
Γ(Ds1
∗
(2860)− ) = 2860.5 ± 2.6 ± 2.5 ± 6.0 MeV/c2
m(Ds3
∗
(2860)− ) = 53 ± 7 ± 4 ± 6 MeV/c2
Γ(Ds3
Measured also branching fractions of Bs to several intermediate state,
see backup or arXiv:1407.7574,arXiv:1407.7712
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb
Ξ0b Mass
Candidates / (5 MeV/c2)
PRL 113 (2014) 032001
LHCb
400
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
Full fit
Ξ0b→ Ξ+cπΞ0b→ Ξ+cρ-
3 fb−1
Ξ0b→ Ξ+cK
-
Comb
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
200
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
5600
5700
5800
5900
6000
M(Ξ+cπ-) [MeV/c2]
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
Candidates / (1 MeV/c2)
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
LHCb
Full fit
Ξ0b→
Ξ+cπ-
Combinatorial
200
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
100
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
0
22
2440
2460
04 Aug 2014
2480
-
2500
M(pK π+) [MeV/c2]
Mass of the Ξ0b difficult to measure as high
branching fraction decays are difficult to
reconstruct
At LHCb, data sample allows to exploit
more suppressed decays
−
+
π
with
Ξ
Here, we use Ξ0b → Ξ+
c →
c
pK − π +
Have about 3800 signal decays
Mass measured
M (Ξ0b ) = 5791.80±0.39±0.17±0.26 MeV
In the process we exploit also large sample
of Ξc baryons to measure
M (Ξ+
c ) = 2467.97±0.14±0.10±0.14 MeV
The most precise measurements
Uncertainties: statistical, systematic, Λb/c mass
Michal Kreps – Hadron spectroscopy at LHCb
Conclusions
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
23
Z(4430)+ from Belle confirmed and J P = 1+ without any doubts
From Argand plot, resonance character of Z(4430)+ is demonstrated
Charge and quantum numbers rule out conventional explanations
∗
(2573)
Confirm spin of Ds2
Demonstrated that peak around 2860 MeV is due to two states
∗
∗
(2860)
(2860) and Ds3
Ds1
∗
∗
∗
(2860)
(2860) and Ds3
(2573), Ds1
Measured mass and width of Ds2
Amplitude analyses of exclusive B decays good systems for study of
charm spectroscopy
At LHCb, we are effectively only at the beginning of the program
Much more is possible and much more will come
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb
Backup
24
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb
LHCb detector
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
00
11
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
00
11
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
25
04 Aug 2014
Good mass resolution
Good time resolution
High trigger rate on c
and b
Uniform running
conditions
Michal Kreps – Hadron spectroscopy at LHCb
LHCb detector
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
00
11
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
00
11
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
25
04 Aug 2014
Good mass resolution
Good time resolution
High trigger rate on c
and b
Uniform running
conditions
Michal Kreps – Hadron spectroscopy at LHCb
Candidates / ( 0.2 GeV2 )
Candidates / ( 0.2 GeV2 )
Dalitz plot slices
data
total fit
80
LHCb
m2K+π− < 0.7 GeV
-
Z(4430) excluded
*
K (892)
2
*
K S-wave
Z(4430)
60
background
*
K (1410)
*
K (1680)
*
K 2(1430)
40
LHCb
200 1.0 < m2K+π− < 1.8 GeV2
100
20
16
18
20
22
[GeV2]
mψ2 'π−
0
m2ψ'π- [GeV2]
0
10
22
16
18
20
2
22
mψ2 'π− [GeV2]
21
20
10
19
PRL 112 (2014) 222002
18
17
1
16
LHCb
Candidates / ( 0.2 GeV2 )
0.5
LHCb
400
0.7 <
m2K+π−
< 1.0 GeV
2
200
1
1.5
2
2.5
mK2 +π- [GeV2]
Candidates / ( 0.2 GeV2 )
15
200
LHCb
mK2 +π−
> 1.8 GeV2
150
100
50
0
26
16
04 Aug 2014
18
20
22
mψ2 'π− [GeV2]
0
16
18
20
22
mψ2 'π− [GeV2]
Michal Kreps – Hadron spectroscopy at LHCb
Amplitude analysis
2
X
X X X
Z
i∆
α
2
µ A
(Ω|m
,
Γ
)
+
A
Z (Ω |m0Z , Γ0Z )e
|M | =
k,λ
0k
0k
Z,λ
ψ
ψ
∆λµ λψ
k
λZ
ψ
Ak,λψ (Ω|mR , ΓR ) =
FBLB
pB
mB
Blatt-Weisskopf form factor
LB
R(m|mR , ΓR )FRLR
pR
mR
LR
Z(Ω)
Angular distribution (Helicity)
Orbital momentum part
1
R(m|mR , ΓR ) = 2
mR − m2 − imR Γ(m, ΓR )
2LR +1
mR 2
pR
FR
Γ(m, ΓR ) =ΓR
pR0
m
27
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb
Excitement?
Z(4430) is the first confirmed unambiguous four-quark candidate
28
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
300
Events/0.010 GeV
PRL 91, 262001
X(3872) enigma
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
200
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
100
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
Discovered in 2003 by Belle
Huge number of results available
Quantum numbers J P C = 1++
Nature of X(3872) still unclear
Today radiative decays
0
0.40
0.80
+ -+-
1.20
+-
X(3872) yield / unit volume
PRL 98, 132002
CDF Run II Preliminary
500
|cos(θJ/ ψ)| < 0.6
-1
L ≈ 780pb
|cos(θJ/ ψ)| > 0.6
400 |cos(θπ π)| < 0.5 |cos(θπ π)| > 0.5 |cos(θπ π)| < 0.5 |cos(θπ π)| > 0.5
acc. corrected
prediction for
300
0++
p
1-s
1++
p
2-+
p
200
100
0
0
PRL 110, 222001
7
10
LHCb
106
Simulated JPC=1++
Simulated JPC=2-+
5
10
104
t data
3
10
102
0.63 1.15 π/2
0 0.63 1.15 π/2
0 0.63 1.15 π/2
0 0.63 1.15 π/2
||∆ Φ - π| - π/2|
29
X(3872)
data points
Number of experiments / bin
M(π π l l ) - M(l l ) (GeV)
04 Aug 2014
-200
-100
0
100
200
t = -2 ln[ L(2-+)/ L(1++) ]
Michal Kreps – Hadron spectroscopy at LHCb
500
0
5
5.1
5.2
5.3
5.4
5.5
M (J/ψγK + )[GeV/c2 ]
40
30
20
10
0
5.1
5.2
5.3
5.4
5.5
M (ψ(2S)γK + )[GeV/c2 ]
04 Aug 2014
Candidates/(10 MeV/c2 )
1000
Candidates/(10 MeV/c2 )
Candidates/(15 MeV/c2 )
30
1500
400
591 ± 48
300
200
100
3.7
3.8
3.9
4
4.1
arXiv:1404.0275
Candidates/(10 MeV/c2 )
X(3872) → ψγ
M (J/ψγ)[GeV/c2 ]
40
30
20
36.4 ± 9.0
4.4σ
10
0
3.8
3.9
4
M (ψ(2S)γ)[GeV/c2 ]
Michal Kreps – Hadron spectroscopy at LHCb
X(3872) → ψ(2S)γ
00
11
111
000
00
11
000
111
00
11
000
111
00
11
000
111
000
111
We measure
B(X(3872) → ψ(2S)γ)
R=
= 2.46 ± 0.64 ± 0.29
B(X(3872) → J/ψ γ)
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
Compare to theory for different interpretations
00
11
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
31
04 Aug 2014
40
arXiv:1404.0275
Candidates/(10 MeV/c2 )
00
11
00
11
000
111
00
11
111
000
00
11
000
111
00
11
000
111
000
111
Clear inconsistency with pure molecule
Pure cc or mixture of molecule with cc possible
30
20
10
0
3.8
3.9
4
M (ψ(2S)γ)[GeV/c2 ]
Michal Kreps – Hadron spectroscopy at LHCb
0
− +
0.003
0.0025
0.002
0.0015
0.001
0.0005
0.4
0.6
1
0
0.003
0.0025
0.002
0.0015
0.001
0.0005
0.2
0.4
0.6
0.8
m'
Combinatorial
100
80
60
40
20
0.2
0.4
0.6
0.8
04 Aug 2014
B 0 → D (∗) ππ
1
0
LHCb Simulation (b)
1600
1400
1200
1000
800
600
400
200
0.2
0.4
0.6
0.8
1
m'
0
θ'
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
Entries
LHCb (a)
θ'
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0
1
m'
Λb → D (∗) pπ
m'
32
0.8
0.004
0.0035
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
LHCb Simulation (c)
12000
10000
Entries
0.2
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
LHCb Simulation (b)
Efficiency
0.004
0.0035
θ'
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
TIS
LHCb Simulation (a)
Efficiency
θ'
TOS
Entries
θ'
arXiv:1407.7574,arXiv:1407.7712
Bs → D K π efficiency, bg
8000
6000
4000
2000
0.2
0.4
0.6
0.8
1
0
m'
Michal Kreps – Hadron spectroscopy at LHCb
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
Entries
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
Verify the significance of having two states around 2.86 GeV by
simulations
Generate samples with only single resonance
Compare likelihood ratios on data to distribution from generated
experiments
In data we have 2∆NLL of 313.6 and 273
Entries
111
000
000
111
000
111
000
111
000
111
000
111
000
111
000
111
000
111
LHCb
(a)
102
LHCb
(b)
102
∗ (2860)
Ds1
10
10
1
1
10-1
33
∗ (2860)
Ds3
0
04 Aug 2014
20
40
60
2∆ NLL
10-1
0
20
40
arXiv:1407.7574,arXiv:1407.7712
DsJ spin
60
2∆ NLL
Michal Kreps – Hadron spectroscopy at LHCb
0
− +
Bs → D K π BFs
Resonance R
Product branching fraction
(10−5 )
∗
K (892)0
28.6 ± 0.6 ± 0.7 ± 0.9 ± 4.2
∗
K (1410)0
1.7 ± 0.5 ± 0.2 ± 1.4 ± 0.2
LASS nonresonant 13.7 ± 2.5 ± 1.5 ± 4.1 ± 2.0
∗
K 0 (1430)0
20.0 ± 1.6 ± 0.7 ± 3.3 ± 2.9
LASS total
21.4 ± 1.4 ± 1.0 ± 4.7 ± 3.1
∗
K 2 (1430)0
3.7 ± 0.6 ± 0.4 ± 1.1 ± 0.5
∗
K (1680)0
< 2.0 (2.4)
∗
K 0 (1950)0
< 3.7 (4.1)
∗
K 3 (1780)0
< 0.33 (0.38)
∗
K 4 (2045)0
< 0.21 (0.24)
∗
(2573)−
25.7 ± 0.7 ± 0.8 ± 1.1 ± 3.8
Ds2
∗
(2700)−
1.6 ± 0.4 ± 0.4 ± 0.5 ± 0.2
Ds1
∗
(2860)−
5.0 ± 1.2 ± 0.7 ± 3.3 ± 0.7
Ds1
∗
(2860)−
2.2 ± 0.1 ± 0.3 ± 0.4 ± 0.3
Ds3
Branching fraction
(10−4 )
4.29 ± 0.09 ± 0.11 ± 0.14 ± 0.63
3.86 ± 1.14 ± 0.45 ± 3.18 ± 0.89
2.06 ± 0.38 ± 0.23 ± 0.62 ± 0.30
3.00 ± 0.24 ± 0.11 ± 0.50 ± 0.44
3.21 ± 0.21 ± 0.15 ± 0.71 ± 0.47
1.11 ± 0.18 ± 0.12 ± 0.33 ± 0.15
< 0.78 (0.93)
< 1.1 (1.2)
< 0.26 (0.30)
< 0.31 (0.36)
arXiv:1407.7574,arXiv:1407.7712
34
04 Aug 2014
Michal Kreps – Hadron spectroscopy at LHCb