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Exotic Baryons at LHCb
Sebastian Neubert
on behalf of the LHCb collaboration
Heidelberg University
Baryons 2016, May 16 - 20, 2016, Tallahassee
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 1 / 27
The LHCb Experiment [IJMP A30(2015)1530022] Precision Beauty and Charm Physics
LHCb is a single-arm (2 < η < 5) spectrometer at the LHC
CP violation measurements, rare decays,
heavy flavor decays as source for exotic hadrons
Exploits the correlated production of bb pairs in the LHC environment
250mrad
100mrad
0/4π
/2π
/4π3π
0
/4π
/2π
/4π3
π [rad]1
θ
[rad]2
θ
1θ
2θ
b
b
z
LHCb MC
= 8 TeVs
Clean B-hadron samples through excellent vertex resolution: O(15) µm (VELO)
Flavor tagging, final state discrimination needs excellent particle ID (RICH)
Highly efficient trigger: di-muons, displaced vertices (topological B-hadron), ..
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 2 / 27
Run I: 3 fb−1
1011bb pairs
B : Λb : B0s
4 : 2 : 1[PRD85(2012)032008]
The decay Λb → J/ψpK
p p
µ−
µ+
K
p
Λ0b
J/ψ
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 3 / 27
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 4 / 27
Λb → J/ψpK
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 4 / 27
Λb → J/ψpK
A Surprise in Λb Decays
Initial goal: a precise measurement of the Λb lifetime
1 fb−1 of Λb → J/ψpK + previous measurements: τ = 1.482± 0.018± 0.012ps
→PRL111(2013)102003
But looking closer at the J/ψ p K Dalitz-Plot with a dataset of 3 fb−1
(Run I)
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 5 / 27
3 fb−1
26007± 166Λb candidates
A Surprise in Λb Decays
Initial goal: a precise measurement of the Λb lifetime
1 fb−1
of Λb → J/ψpK + previous measurements: τ = 1.482± 0.018± 0.012ps
→PRL111(2013)102003
But looking closer at the J/ψ p K Dalitz-Plot with a dataset of 3 fb−1
(Run I)
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 5 / 27
3 fb−1
26007± 166Λb candidates
Λ∗
A Surprise in Λb Decays
Initial goal: a precise measurement of the Λb lifetime
1 fb−1
of Λb → J/ψpK + previous measurements: τ = 1.482± 0.018± 0.012ps
→PRL111(2013)102003
But looking closer at the J/ψ p K Dalitz-Plot with a dataset of 3 fb−1
(Run I)
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 5 / 27
3 fb−1
26007± 166Λb candidates
Λ∗
???
2-Body Mass Spectra →PRL115(2015)072001
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 6 / 27
2-Body Mass Spectra →PRL115(2015)072001
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 6 / 27
Λ∗(1520)Reflection of
Λ∗ states?
Two Analysis Approaches
1 Isobar-model amplitude analysis →PRL115(2015)072001
Use known Λ∗ spectrum as input
Parameterize the decay matrix element (model dependent)
Search for J/ψ p resonances
Extract their masses/widths and quantum numbers
2 Model independent moments analysis → arXiv:1604.05708 (subm. to PRL)
Minimal assumptions, no modelling of decay amplitude
Hypothesis test:
Can the structures in J/ψ p be explained by reflections of Λ∗ resonances?
Cannot extract properties of potential J/ψ p resonances
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 7 / 27
Two Analysis Approaches
1 Isobar-model amplitude analysis →PRL115(2015)072001
Use known Λ∗ spectrum as input
Parameterize the decay matrix element (model dependent)
Search for J/ψ p resonances
Extract their masses/widths and quantum numbers
2 Model independent moments analysis → arXiv:1604.05708 (subm. to PRL)
Minimal assumptions, no modelling of decay amplitude
Hypothesis test:
Can the structures in J/ψ p be explained by reflections of Λ∗ resonances?
Cannot extract properties of potential J/ψ p resonances
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 7 / 27
Isobar-model amplitude analysis
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 8 / 27
Isobar-model Helicity Amplitudes for Λb → J/ψΛ∗
Matrix ElementMΛ∗parametrized as a function of 5 angles and one mass m2
pK
ΛΛ
μ
μ
μ
μ
ψ
ppKKθ θ φ
θ
*
+
−
+
−K − −
ψ Λ
Λ
b
*ψ *
φ = 0
Λ
Λ
φ μψ*
Λ
b
lab frame
rest frame0
0
rest frame
∗
x
z
b
Λ
rest frame
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 9 / 27
Λb unpolarised
→PRL115(2015)072001
Isobar-model Helicity Amplitudes for Λb → J/ψΛ∗
Angular structures (no free parameters)
Helicity couplings ← complex numbers, floating in fit
Λ∗ resonant amplitudes rel. Breit-Wigner / Flatté parameterizations
MΛ∗ =∑
nRn(mKp) H
Λ∗n→Kpλp
∑λψ
e i λψφµ d 1λψ ,∆λµ(θψ) ×
∑λΛ∗
HΛb→Λ∗nψλΛ∗ , λψ e i λ
Λ∗φK d
12
λΛb , λΛ∗−λψ(θΛb) d
JΛ∗n
λΛ∗ , λp
(θΛ∗)
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 10 / 27
→PRL115(2015)072001
2 Fitters - Cross-check of Background Treatment
Log-likelihood fitters:
sFit : subtract background with the sWeight method
cFit : explicitly model background from sidebands (default)
Misidentified B-meson decays vetoed B →J/ψ K π and B0s →J/ψ K K
Efficiency from MC
]2 [GeV2Kpm
2 3 4 5 6
]2 [
GeV
2p
ψJ/
m
16
18
20
22
24
26
0
0.2
0.4
0.6
0.8
1
1.2
LHCb
(a) efficiency
Background density shape (5.4%)
]2 [GeV2Kpm
2 3 4 5 6
]2 [
GeV
2p
ψJ/
m
16
18
20
22
24
26
0
0.5
1
1.5
2
2.5
LHCb
(b) background
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 11 / 27
→PRL115(2015)072001
Results with only Λ∗ States
cFit with extended Λ∗ model (14 states allowed):
Adding two new Λ∗ states with floating mass/width does not improve fit
Λ∗ reflections don’t explain the structure in mJ/ψp
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 12 / 27
→PRL115(2015)072001
Interference between Λb → J/ψΛ∗ and Λb → PcK
X
A
B
C
= X
A
B
C
+ X
A
B
C
+ · · ·
Coherent sum over amplitudes, incoherent sum over external helicities
|M|2 =∑
λΛb=±12
∑λp=± 1
2
∑∆λµ=±1
∣∣∣∣∣∣∣∣∣∣∣∣MΛ
∗+ e iλµαµ︸ ︷︷ ︸
µ alignment
∑λPcp =± 1
2
d1/2
λPcp ,λp(θp)
︸ ︷︷ ︸proton align.
MPc
∣∣∣∣∣∣∣∣∣∣∣∣
2
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 13 / 27
→PRL115(2015)072001
Results with 2 J/ψ p Resonances
[GeV]pKm1.4 1.6 1.8 2 2.2 2.4 2.6
Eve
nts/
(15
MeV
)
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
LHCb(a)
datatotal fitbackground
(4450)cP(4380)cP(1405)Λ(1520)Λ(1600)Λ(1670)Λ(1690)Λ(1800)Λ(1810)Λ(1820)Λ(1830)Λ(1890)Λ(2100)Λ(2110)Λ(2350)Λ(2385)Λ
[GeV]pψ/Jm4 4.2 4.4 4.6 4.8 5
Eve
nts/
(15
MeV
)
0
100
200
300
400
500
600
700
800
LHCb(b)
Improvement w.r.t to fit without Pc :√∆2L = 18.7σ
Adding further Pc states did not improve the fit significantly
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 14 / 27
→PRL115(2015)072001
Why a second state with opposing parity?
Eve
nts/
(20
MeV
)
0
200
400
(a) (b)
[GeV]pψJ/m4 4.5 5
Eve
nts/
(20
MeV
)
0
200
400 (c)
[GeV]pψJ/m4 4.5 5
(d)
LHCb
The peaking structure in mJ/ψp is
asymmetric as a function of mKp (or cosθPc )
This can be explained by interference of
two states with opposing parity
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 15 / 27
mKp < 1.55GeV 1.55 < mKp < 1.70GeV
1.70 < mKp < 2.00GeV 2.00GeV < mKp
→PRL115(2015)072001
Fit describes data well in all variables
Angular distributions
θcos1− 0.5− 0 0.5 10
500
1000
1500
2000
2500
0bΛθcos
[rad]φ2− 0 2
0
500
1000
1500
2000
2500
Kφ
θcos1− 0.5− 0 0.5 10
500
1000
1500
2000
2500
*Λθcos
[rad]φ2− 0 2
0
500
1000
1500
2000
2500
LHCb
datatotal fitbackground
(4450)cP(4380)cP(1405)Λ(1520)Λ(1600)Λ
(1670)Λ(1690)Λ(1800)Λ(1810)Λ(1820)Λ(1830)Λ(1890)Λ(2100)Λ(2110)Λ
θcos1− 0.5− 0 0.5 10
500
1000
1500
2000
2500
ψJ/θcos
[rad]φ2− 0 2
0
500
1000
1500
2000
2500
µφ
mJ/ψK in bins of mKp
[GeV]KψJ/m4 4.5
Eve
nts/
(15
MeV
)
0
200
(a)
[GeV]KψJ/m4 4.5
Eve
nts/
(15
MeV
)
0
200
(b)
[GeV]KψJ/m4 4.5
Eve
nts/
(15
MeV
)
0
200
(c)
[GeV]KψJ/m4 4.5
Eve
nts/
(15
MeV
)
0
200
LHCb
(d)
[GeV]KψJ/m4 4.5
Eve
nts/
(15
MeV
)0
500(e)
[GeV]KψJ/m4 4.5
Eve
nts/
(15
MeV
)
0
500
datatotal fitbackground
(4450)cP(4380)cP(1405)Λ(1520)Λ(1600)Λ
(1670)Λ(1690)Λ(1800)Λ(1810)Λ(1820)Λ(1830)Λ(1890)Λ(2100)Λ(2110)Λ
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 16 / 27
No J/ψ Kresonances
needed!
→PRL115(2015)072001
Extracted Resonance Parameters [PRL115(2015)072001]
State Mass [MeV] Width [MeV] fav. JPFit fraction Signi.
Pc(4380)+ 4380± 8± 29 205± 18± 86 3/2− (8.4± 0.7± 4.2)% 9σ
Pc(4450)+ 4449.8± 1.7± 2.5 39± 5± 19 5/2+ (4.1± 0.5± 1.1)% 12σ
Significances evaluated on Toy-MC
samples
Λ∗ states fit-fractions:
Λb → Λ(1405)J/ψ (15± 1± 6)%Λb → Λ(1520)J/ψ (19± 1± 4)%
Spin-parity assignment not
conclusive:
Fit ∆(−2 lnL) Pc (Low) Mass Pc (Low) Γ Pc (High) Mass Pc (High) Γ
3/2−, 5/2+ 0 4.3799± 0.0064 0.205± 0.011 4.4498± 0.0017 0.0387± 0.0037
3/2+, 5/2− 0.92 4.3696± 0.0063 0.211± 0.012 4.4504± 0.0017 0.0492± 0.0040
5/2+, 3/2− 2.32 4.3770± 0.0098 0.239± 0.024 4.4486± 0.0018 0.0444± 0.0053
.
.
.Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 17 / 27
→PRL115(2015)072001
Model independent moments analysis
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 18 / 27
Model independent analysis of Λb → J/ψpK
Observation of the Pc(4380) and
Pc(4450) used a model for the
decay matrix element
Λ∗ spectrum biggest uncertainty
In bins of m(pK): decompose
decay-angle distribution into
Legendre-moments
〈P`〉 =Nevents∑
i=0
wiεi
P`(cosθipK)
Helicity angle cosθpK vs. mpK
efficiency corrected (εi ), bkg subtracted (wi )
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 19 / 27
→ arXiv:1604.05708 (subm. to PRL)
Extracted pK moments
Minimal assumption on Λ∗ spectrum Moments extracted from data
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 20 / 27
Only low-spin states
at low masses
theory predictions
well established states
Λ∗ can’t contribute here
→ arXiv:1604.05708 (subm. to PRL)
Model-independent analysis of Λb → J/ψpK
Construct `max-filtered toy MC:
Reflections of p K-system in J/ψ p
p K-reflections cannot explain
the narrow structure in J/ψ p
Testing sensitivity on MC for various models
Hypothesis ”only Λ∗” rejected with > 9σ
Confirms findings of amplitude analysis
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 21 / 27
→ arXiv:1604.05708 (subm. to PRL)
Compare to the model dependent analysis
Data Simulation, driven by amplitude model
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 22 / 27
→ arXiv:1604.05708 (subm. to PRL)
Interpretations
Inspirations
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 23 / 27
What causes these resonant structures in J/ψ p?
Valence quark content: uudccWhat are the relevant degrees of freedom?
Challenges:
Why two states with opposite parity?
Small mass gap ≈ 100MeV
Narrow width of Pc(4450)
Proposed paradigms:
Rescattering effects
Meson-Baryon molecules
Crypto-exotics in chiral-unitary dynamics
Pentaquarks in the Di-Quark model
See talks by Jean-Marc Richard, today and Eulogio Oset, tomorrow
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 24 / 27
???
Deja-vu: Threshold Effects?
Exotic states with hidden charm appear close to 2-body thresholds
[MeV] X(3872)Mass 3871.69± 0.17DD
∗3871.81
Pure molecule disfavoured
by radiative decays
[MeV] Z+(4430)
Mass 4475± 7+15−25
D∗(2007)D
+1 (2420) 4430.16
D∗(2007)D
+2 (2460) 4471.26
S-wave molecules excluded by parity
[MeV] Pc(4380)+ Pc(4450)
+
Mass 4380± 8± 29 4449.8± 1.7± 2.5Σ∗+c D
04382.3± 2.4
χc1(1P)p 4448.93± 0.07Λ+c
∗D
04457.09± 0.35
ΣcD0∗
4459.9± 0.5ΣcD
0π04452.7± 0.5
Studies of further decay modes needed
Are thresholds the unifying pattern across the meson and baryon sectors?
Or are these just coincidences, because the density of thresholds is so high?
Most ambitious theory attempts try to explain exotic states together with
’known’ spectrum
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 25 / 27
Deja-vu: Threshold Effects?
Exotic states with hidden charm appear close to 2-body thresholds
[MeV] X(3872)Mass 3871.69± 0.17DD
∗3871.81
Pure molecule disfavoured
by radiative decays
[MeV] Z+(4430)
Mass 4475± 7+15−25
D∗(2007)D
+1 (2420) 4430.16
D∗(2007)D
+2 (2460) 4471.26
S-wave molecules excluded by parity
[MeV] Pc(4380)+ Pc(4450)
+
Mass 4380± 8± 29 4449.8± 1.7± 2.5Σ∗+c D
04382.3± 2.4
χc1(1P)p 4448.93± 0.07Λ+c
∗D
04457.09± 0.35
ΣcD0∗
4459.9± 0.5ΣcD
0π04452.7± 0.5
Studies of further decay modes needed
Are thresholds the unifying pattern across the meson and baryon sectors?
Or are these just coincidences, because the density of thresholds is so high?
Most ambitious theory attempts try to explain exotic states together with
’known’ spectrum
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 25 / 27
Deja-vu: Threshold Effects?
Exotic states with hidden charm appear close to 2-body thresholds
[MeV] X(3872)Mass 3871.69± 0.17DD
∗3871.81
Pure molecule disfavoured
by radiative decays
[MeV] Z+(4430)
Mass 4475± 7+15−25
D∗(2007)D
+1 (2420) 4430.16
D∗(2007)D
+2 (2460) 4471.26
S-wave molecules excluded by parity
[MeV] Pc(4380)+ Pc(4450)
+
Mass 4380± 8± 29 4449.8± 1.7± 2.5Σ∗+c D
04382.3± 2.4
χc1(1P)p 4448.93± 0.07Λ+c
∗D
04457.09± 0.35
ΣcD0∗
4459.9± 0.5ΣcD
0π04452.7± 0.5
Studies of further decay modes needed
Are thresholds the unifying pattern across the meson and baryon sectors?
Or are these just coincidences, because the density of thresholds is so high?
Most ambitious theory attempts try to explain exotic states together with
’known’ spectrum
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 25 / 27
Pc(4380)&Pc(4450): a New Sector in Baryon Spectroscopy?
What are they?
Observe Pc → J/ψp as subsystems in different final states
Λb →J/ψ p π COMING SOON!
Υ →J/ψ p pΛb →J/ψ p π K0
S
Search for new decay modes of PcΛb →χc1(1P) p KΛb →Λ+
c D0 K
Are there more of their kind?
Explore a possible multiplet of pentaquarks
Λb →J/ψ p π K0S
Λb →J/ψ Λ φTriply charged baryons?
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 26 / 27
Pc(4380)&Pc(4450): a New Sector in Baryon Spectroscopy?
What are they?
Observe Pc → J/ψp as subsystems in different final states
Λb →J/ψ p π COMING SOON!
Υ →J/ψ p pΛb →J/ψ p π K0
S
Search for new decay modes of PcΛb →χc1(1P) p KΛb →Λ+
c D0 K
Are there more of their kind?
Explore a possible multiplet of pentaquarks
Λb →J/ψ p π K0S
Λb →J/ψ Λ φTriply charged baryons?
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 26 / 27
Pc(4380)&Pc(4450): a New Sector in Baryon Spectroscopy?
What are they?
Observe Pc → J/ψp as subsystems in different final states
Λb →J/ψ p π COMING SOON!
Υ →J/ψ p pΛb →J/ψ p π K0
S
Search for new decay modes of PcΛb →χc1(1P) p KΛb →Λ+
c D0 K
Are there more of their kind?
Explore a possible multiplet of pentaquarks
Λb →J/ψ p π K0S
Λb →J/ψ Λ φTriply charged baryons?
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 26 / 27
All
mo
des
un
ob
serv
ed
sofa
r!
Summary: First observation of J/ψ p resonances
Full amplitude analysis of 3 fb−1 Λb → J/ψpK at LHCb
→PRL115(2015)072001
Two states of opposite parity required
Pc(4380)+
: m = (4380± 8± 29)MeV, Γ = (205± 18± 86)MeV, JP = 3/2− or 5/2+
Pc(4450)+
: m = (4449.8± 1.7± 2.5)MeV, Γ = (39± 5± 19)MeV, JP = 5/2+ or 3/2−
Model-independent analysis confirms need for exotic contributions
→ arXiv:1604.05708 (subm. to PRL)
No J/ψK resonances needed, No extra Λ∗ needed
Program to confirm and search for new states
Confirmation from other experiments needed!
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 27 / 27
Backup
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 28 / 27
Systematic Uncertainties
Source M0 (MeV) Γ0 (MeV) Fit fractions (%)
low high low high low high Λ∗(1405) Λ∗(1520)Extended vs. reduced 21 0.2 54 10 3.14 0.32 1.37 0.15Λ∗ masses & widths 7 0.7 20 4 0.58 0.37 2.49 2.45Proton ID 2 0.3 1 2 0.27 0.14 0.20 0.0510 < pp < 100 GeV 0 1.2 1 1 0.09 0.03 0.31 0.01Non-resonant 3 0.3 34 2 2.35 0.13 3.28 0.39Separate sidebands 0 0 5 0 0.24 0.14 0.02 0.03JP
(3/2+, 5/2−) or (5/2+, 3/2−) 10 1.2 34 10 0.76 0.44d = 1.5− 4.5 GeV
−1 9 0.6 19 3 0.29 0.42 0.36 1.91`PcΛb
Λb → P+c (low/high)K− 6 0.7 4 8 0.37 0.16
`PcP+
c (low/high)→ J/ψp 4 0.4 31 7 0.63 0.37`Λ
∗n
ΛbΛb∗ → J/ψΛ∗ 11 0.3 20 2 0.81 0.53 3.34 2.31
Efficiencies 1 0.4 4 0 0.13 0.02 0.26 0.23Change Λ∗(1405) coupling 0 0 0 0 0 0 1.90 0Overall 29 2.5 86 19 4.21 1.05 5.82 3.89sFit/cFit cross check 5 1.0 11 3 0.46 0.01 0.45 0.13
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 29 / 27
Pre Selection
Table: Pre-selection requirements used. The stripping line is
FullDSTDiMuonJpsi2MuMuDetachedLine.
# Selection variables Requirements
1 All tracks χ2/ndof < 42 Muon PID DLL(µ − π) > 03 PT of muon > 550 MeV4 PT of hadron > 250 MeV
5 J/ψ vertex χ2 < 166 J/ψ mass window −48 < m(µ+µ−)−m(J/ψ ) < 43 MeV
7 Hadron χ2IP > 9
8 K− ID DLL(K − π) > 0 and DLL(p − K) < 39 p ID DLL(p − π) > 10 and DLL(p − K) > 3
10 pK− vertex χ2 DOCA χ2 < 16
11 Λb χ2IP < 25
12 Λb vertex χ2/ndof < 1013 Λb flight distance > 1.5 mm14 Λb pointing, cosθp > 0.99915 Trigger HLT1 and HLT2 TOS on J/ψ (see text)16 Clone track rejection on hadron Ghost probability < 0.2
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 30 / 27
BDT Classifier
BDT variables:
minimum DLL(µ − π) of the µ+ and µ−(mmPIDmu);
minimum of the χ2IP of the K− and the p
[log(pmipCHI2)];
Λb (DIRA);
Λb χ2IP log(BCHI2);
Λb FD;
PT of the Λb (BPT);
Λb vertex χ2 (LogBIPCHI2);
PT sum of the K− and p (SumPT).
Trained on signal MC and
sideband data for bkg
Cut optimzed by maximising
S/√
S + B in data, subsequently
tightened to reduce background
across DP
mmPIDmu
2 4 6 8 10 12 14
0.35
5 /
(1/N
) d
N
0
0.05
0.1
0.15
0.2
0.25SignalBackground
U/O
-flo
w (
S,B
): (
0.0,
0.0
)% /
(0.0
, 0.0
)%
Input variable: mmPIDmu
log(pmipCHI2)3 4 5 6 7 8 9 10
0.21
6 /
(1/N
) d
N
0
0.2
0.4
0.6
0.8
1
1.2
1.4
U/O
-flo
w (
S,B
): (
0.0,
0.0
)% /
(0.0
, 0.0
)%
Input variable: log(pmipCHI2)
dira
0.99940.99950.99960.99970.99980.9999 1
1.76
e-05
/
(1/N
) d
N
0
5000
10000
15000
20000
25000
30000
35000
U/O
-flo
w (
S,B
): (
0.1,
3.1
)% /
(0.0
, 0.0
)%
Input variable: dira
log(BCHI2)-3 -2 -1 0 1 2 3 4
0.19
5 /
(1/N
) d
N
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
U/O
-flo
w (
S,B
): (
0.0,
0.0
)% /
(0.0
, 0.0
)%
Input variable: log(BCHI2)
FD [mm]20 40 60 80 100
2.7
mm
/ (1
/N)
dN
0
0.05
0.1
0.15
0.2
0.25
U/O
-flo
w (
S,B
): (
0.0,
0.0
)% /
(0.1
, 0.1
)%
Input variable: FD
BPT [MeV]500010000150002000025000300003500040000
1.09
e+03
MeV
/ (1
/N)
dN
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
-310×
U/O
-flo
w (
S,B
): (
0.0,
0.0
)% /
(0.0
, 0.0
)%
Input variable: BPT
LogBIPCHI2-8 -6 -4 -2 0 2
0.32
1 /
(1/N
) d
N
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
U/O
-flo
w (
S,B
): (
0.0,
0.0
)% /
(0.0
, 0.0
)%
Input variable: LogBIPCHI2
SumPT [MeV]2000 4000 6000 800010000120001400016000
402
MeV
/ (1
/N)
dN
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
-310×
U/O
-flo
w (
S,B
): (
0.0,
0.0
)% /
(0.0
, 0.0
)%
Input variable: SumPT
Figure: Distributions of variables used in
BDTG.
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 31 / 27
`S Couplings
The angular momentum barrier should suppress decays
with high orbital angular momentum.
Express helicity couplings through `S-couplings B`Susing Clebsch-Gordan coefficients
HA→B CλB ,λc =
∑`
∑S
√2`+12JA+1 × B`,S ×
(JB JC SλB −λC λB − λC
)︸ ︷︷ ︸
Spin−Spin coupling
×(` S JA0 λB − λC λB − λC
)︸ ︷︷ ︸
Spin−Orbit coupling
Limit the allowed range of ` in the fit model
Automatically implements parity conservation in strong decays
by choice of `
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 32 / 27
Efficiency corrected Signal PDF
Ω = 6 kinematical variables (mKp + 5 angles)−→ω = fit parameters (couplings, masses, widths)
dPdΩ ≡ Psig(Ω|−→ω ) =
1
CI(−→ω )
∣∣M(Ω|−→ω )∣∣2 Φ(Ω) ε(Ω)
Phase space volume element
efficiency
With the normalisation calculated by MC-integration over accepted MC
events
I(−→ω ) ≡∫Psig(Ω) dΩ ∝
ΣjwMCj∣∣M(Ωj |−→ω )
∣∣2Σjw
MCj
,
weights wCj account for differences inΛb production kinematics and PID
between simulation and data
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 33 / 27
Interference between Λb → J/ψΛ∗ and Λb → PcK
Coherent sum over amplitudes, incoherent sum over external helicities
Set Λb polarisation to 0
|M|2 =∑
λΛb=±12
∑λp=± 1
2
∑∆λµ=±1
∣∣∣∣∣∣∣∣∣∣∣∣MΛ
∗+ e iλµαµ︸ ︷︷ ︸
µ alignment
∑λPcp =± 1
2
d1/2
λPcp ,λp(θp)
︸ ︷︷ ︸proton align.
MPc
∣∣∣∣∣∣∣∣∣∣∣∣
2
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 34 / 27
Reminder: 3-body decays and Dalitz-Plots
all particles spin 0:
X → ABC
Γ ∝ |M|2dm2ABdm2
BC
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 35 / 27
M = constphasespace
plots by Antimo Palano
Reminder: 3-body decays and Dalitz-Plots
all particles spin 0:
X → ABC
Γ ∝ |M|2dm2ABdm2
BC
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 35 / 27
J = 0 resonancein [AB]
J = 0 resonancein [BC]
M = constphasespace
plots by Antimo Palano
Reminder: 3-body decays and Dalitz-Plots
all particles spin 0:
X → ABC
Γ ∝ |M|2dm2ABdm2
BC
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 35 / 27
J = 0 resonancein [AB]
J = 0 resonancein [BC]
J = 1 resonancein [AB]
J = 2 resonancein [AB]
”Reflection”peak in [BC]
M = constphasespace
plots by Antimo Palano
Reminder: 3-body decays and Dalitz-Plots
all particles spin 0:
X → ABC
Γ ∝ |M|2dm2ABdm2
BC
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 35 / 27
J = 0 resonancein [AB]
J = 0 resonancein [BC]
J = 1 resonancein [AB]
J = 2 resonancein [AB]
”Reflection”peak in [BC]
2 resonanceswith ∆φ = 0
2 resonanceswith ∆φ = π
M = constphasespace
plots by Antimo Palano
Phasemotion of Breit-Wigner Resonances
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 36 / 27
Known Λ∗ States
State JpPDG class Mass (MeV) Γ (MeV) # Reduced # Extended
Λ∗(1405) 1/2
−**** 1405.1+1.3
−1.0 50.5± 2.0 3 4
Λ∗(1520) 3/2
−**** 1519.5± 1.0 15.6± 1.0 5 6
Λ∗(1600) 1/2
+*** 1600 150 3 4
Λ∗(1670) 1/2
−**** 1670 35 3 4
Λ∗(1690) 3/2
−**** 1690 60 5 6
Λ∗(1710) 1/2
+* 1713± 13 180± 40 0 0
Λ∗(1800) 1/2
−*** 1800 300 4 4
Λ∗(1810) 1/2
+*** 1810 150 3 4
Λ∗(1820) 5/2
+**** 1820 80 1 6
Λ∗(1830) 5/2
−**** 1830 95 1 6
Λ∗(1890) 3/2
+**** 1890 100 3 6
Λ∗(2000) ? * ≈ 2000 ? 0 0
Λ∗(2020) 7/2
+* ≈ 2020 ? 0 0
Λ∗(2050) 3/2
−* 2056± 22 493± 60 0 0
Λ∗(2100) 7/2
−**** 2100 200 1 6
Λ∗(2110) 5/2
+*** 2110 200 1 6
Λ∗(2325) 3/2
−* ≈ 2325 ? 0 0
Λ∗(2350) 9/2
+*** 2350 150 0 6
Λ∗(2585) ? ** ≈ 2585 200 0 6
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 37 / 27
2 Fit-Models used!
`s couplings
anchor→
Known Λ∗ States
State JpPDG class Mass (MeV) Γ (MeV) # Reduced # Extended
Λ∗(1405) 1/2
−**** 1405.1+1.3
−1.0 50.5± 2.0 3 4
Λ∗(1520) 3/2
−**** 1519.5± 1.0 15.6± 1.0 5 6
Λ∗(1600) 1/2
+*** 1600 150 3 4
Λ∗(1670) 1/2
−**** 1670 35 3 4
Λ∗(1690) 3/2
−**** 1690 60 5 6
Λ∗(1710) 1/2
+* 1713± 13 180± 40 0 0
Λ∗(1800) 1/2
−*** 1800 300 4 4
Λ∗(1810) 1/2
+*** 1810 150 3 4
Λ∗(1820) 5/2
+**** 1820 80 1 6
Λ∗(1830) 5/2
−**** 1830 95 1 6
Λ∗(1890) 3/2
+**** 1890 100 3 6
Λ∗(2000) ? * ≈ 2000 ? 0 0
Λ∗(2020) 7/2
+* ≈ 2020 ? 0 0
Λ∗(2050) 3/2
−* 2056± 22 493± 60 0 0
Λ∗(2100) 7/2
−**** 2100 200 1 6
Λ∗(2110) 5/2
+*** 2110 200 1 6
Λ∗(2325) 3/2
−* ≈ 2325 ? 0 0
Λ∗(2350) 9/2
+*** 2350 150 0 6
Λ∗(2585) ? ** ≈ 2585 200 0 6
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 37 / 27
2 Fit-Models used!
`s couplings
anchor→ 2-body systems
Λ∗ → pK
spin-spin and spin-orbit coupling
J = 1/2⊗ 0⊗ `
P = (+1)× (−1)× (−1)`
` 0 1 2 3
JP 1
2
− 1
2
+
, 32
+ 3
2
−, 52
− 5
2
+
, 72
+
can you guess how this
looks like for J/ψ p?
Known Λ∗ States
State JpPDG class Mass (MeV) Γ (MeV) # Reduced # Extended
Λ∗(1405) 1/2
−**** 1405.1+1.3
−1.0 50.5± 2.0 3 4
Λ∗(1520) 3/2
−**** 1519.5± 1.0 15.6± 1.0 5 6
Λ∗(1600) 1/2
+*** 1600 150 3 4
Λ∗(1670) 1/2
−**** 1670 35 3 4
Λ∗(1690) 3/2
−**** 1690 60 5 6
Λ∗(1710) 1/2
+* 1713± 13 180± 40 0 0
Λ∗(1800) 1/2
−*** 1800 300 4 4
Λ∗(1810) 1/2
+*** 1810 150 3 4
Λ∗(1820) 5/2
+**** 1820 80 1 6
Λ∗(1830) 5/2
−**** 1830 95 1 6
Λ∗(1890) 3/2
+**** 1890 100 3 6
Λ∗(2000) ? * ≈ 2000 ? 0 0
Λ∗(2020) 7/2
+* ≈ 2020 ? 0 0
Λ∗(2050) 3/2
−* 2056± 22 493± 60 0 0
Λ∗(2100) 7/2
−**** 2100 200 1 6
Λ∗(2110) 5/2
+*** 2110 200 1 6
Λ∗(2325) 3/2
−* ≈ 2325 ? 0 0
Λ∗(2350) 9/2
+*** 2350 150 0 6
Λ∗(2585) ? ** ≈ 2585 200 0 6
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 37 / 27
2 Fit-Models used!
`s couplings
anchor→
Two Λ∗ models
Extended: Explore model space
Reduced: only keep non-vanishingcomponents for final result
For the experts: Agreement checkedby moments analysis
Resonance parametrisation
Dynamical Terms Rn(mKp) given by
Relativistiv, single-channel Breit-Wigner amplitudes BW (MKp |MΛ∗n
0 ,ΓΛ∗n
0 )
BW (M|M0,Γ0) =1
M20 −M2 − iM0Γ(M)
,
where
Γ(M) = Γ0
(qq0
)2 `Λ∗+1 M0
M B ′`Λ∗ (q, q0, d)
2 .
Angular-momentum barrier factors B ′`(p, p0, d)
Rn(mKp) = B ′`Λb
(p
MΛb
)`Λb× BW (MKp)× B ′`
Λ∗n
(q
MΛ∗n
)`Λ∗n.
special case Λ(1405) is subthreshold: Flatté (K p and Σ π channels)p(q) are momenta of the daughter particles in the rest-frame of the decaying particle.
p0(q0) calculated on the nominal resonance mass
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 38 / 27
→PRL115(2015)072001
Adding Helicity Amplitudes for Λb → PcK
K
μ
Λ
−
ΛΛψ *
Λ
−
−*
lab
θΛcPPc
ψ ppψ
b
φ −πφ −π
φ −πcP
b rest frameψ rest frame
Pc rest frame
frame
b
θPc
Pc
PcψP
μμ
+μ
μ+
θψ
c
−
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 39 / 27
ConstructMPcλΛb ,λ
Pcp ,∆λPc
µin the
helicity formalism,
analogously toMΛ∗
λΛb ,λp ,∆λµ
→PRL115(2015)072001
An important detail: Aligning reference frames
Helicities of final state particle have to be evaluated in the same reference
system!
Λ
Λ*K
Λ−
*
zz 00p p PΛ c∗
p
rest framePc
ψ pp
b rest frame
ψP rest framec
ψ K
K Kpp
rest framep
θ
− −
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 40 / 27
alignment factor
e iλµαµ︸ ︷︷ ︸µ alignment
∑λPcp =± 1
2
d1/2
λPcp ,λp(θp)
︸ ︷︷ ︸proton align.
→PRL115(2015)072001
Results with One J/ψ p Resonance
Extended Λ∗ model + 1 J/ψ p resonance (floating mass and width, JP = 5/2+)
[GeV]pKm1.4 1.6 1.8 2 2.2 2.4 2.6
Eve
nts/
(15
MeV
)
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
LHCb(a)
datatotal fitbackground
cP(1405)Λ(1520)Λ(1600)Λ(1670)Λ(1690)Λ(1800)Λ(1810)Λ(1820)Λ(1830)Λ(1890)Λ(2100)Λ(2110)Λ(2350)Λ(2385)Λ
[GeV]pψ/Jm4 4.2 4.4 4.6 4.8 5
Eve
nts/
(15
MeV
)
0
100
200
300
400
500
600
700
800
LHCb(b)
Improvement w.r.t to fit without Pc :√∆2L = 14.7σ
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 41 / 27
→PRL115(2015)072001
Heavy Flavour Signatures at LHCb Prompt Charm and Charm from Beauty
Beauty and charm hadron typical decay topologies:
PV
SV
L
IPp p
PVSV
L
IPp p
B± mass ∼ 5.28 GeV,
daughter pT O(1 GeV)
τ ∼ 1.6 ps,
Flight distance ∼ 1 cm
Important signature: Detached muons
from B → J/ψX , J/ψ → µµ
D0mass ∼ 1.86 GeV,
appreciable daughter pT
τ ∼ 0.4 ps,
Flight distance ∼ 4 mm
Also produced as ’secondary’ charm
from B decays.
Sebastian Neubert (Uni Heidelberg) Exotic Baryons at LHCb Baryons 2016 42 / 27