Exotic Baryons at LHCb - CERN Document Server...Sebastian Neubert (Uni Heidelberg) Exotic Baryons at...

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), ..


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



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)


3 fb−1

26007± 166Λb candidates

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.102003



1 fb−1

of Λb → J/ψpK + previous measurements: τ = 1.482± 0.018± 0.012ps

→PRL111(2013)102003


(Run I)


3 fb−1


Λ∗




1 fb−1

of Λb → J/ψpK + previous measurements: τ = 1.482± 0.018± 0.012ps

→PRL111(2013)102003


(Run I)


3 fb−1


Λ∗

???


2-Body Mass Spectra →PRL115(2015)072001



2-Body Mass Spectra →PRL115(2015)072001


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



http://arxiv.org/abs/1604.05708

Isobar-model amplitude analysis


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


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∗)


→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


→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


→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


→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


→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


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


(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


(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


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


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 )


→ arXiv:1604.05708 (subm. to PRL)


Extracted pK moments

Minimal assumption on Λ∗ spectrum Moments extracted from data


Only low-spin states

at low masses

theory predictions

well established states

Λ∗ can’t contribute here



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




Compare to the model dependent analysis

Data Simulation, driven by amplitude model




Interpretations

Inspirations


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


???

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


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?


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?


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


No J/ψK resonances needed, No extra Λ∗ needed

Program to confirm and search for new states

Confirmation from other experiments needed!




Backup


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


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


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.


`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 `


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


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)


MPc

∣∣∣∣∣∣∣∣∣∣∣∣

2


Reminder: 3-body decays and Dalitz-Plots

all particles spin 0:

X → ABC

Γ ∝ |M|2dm2ABdm2

BC


M = constphasespace

plots by Antimo Palano



X → ABC

Γ ∝ |M|2dm2ABdm2

BC


J = 0 resonancein [AB]

J = 0 resonancein [BC]

M = constphasespace




X → ABC

Γ ∝ |M|2dm2ABdm2

BC






”Reflection”peak in [BC]

M = constphasespace




X → ABC

Γ ∝ |M|2dm2ABdm2

BC






”Reflection”peak in [BC]

2 resonanceswith ∆φ = 0

2 resonanceswith ∆φ = π

M = constphasespace


Phasemotion of Breit-Wigner Resonances


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


2 Fit-Models used!

`s couplings

anchor→

Known Λ∗ States


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


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


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


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


→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

−


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

− −


alignment factor

e iλµαµ︸︷︷︸µ alignment

∑λPcp =± 1

2

d1/2

λPcp ,λp(θp)


→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)


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


→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.


Exotic Baryons at LHCb - CERN Document Server...Sebastian Neubert (Uni Heidelberg) Exotic Baryons at...

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