LHCb results on Tetra- and Penta-Quark candidates Tomasz Skwarnicki - - PowerPoint PPT Presentation

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LHCb results on Tetra- and Penta-Quark candidates Tomasz Skwarnicki - - PowerPoint PPT Presentation

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LHCb results on Tetra- and Penta-Quark candidates Tomasz Skwarnicki Syracuse University Nov 10, 2015 at LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 2 Quark hypothesis SU(3) flavor symmetry Eightfold Way symmetry

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SLIDE 1

LHCb results on Tetra- and Penta-Quark candidates

Tomasz Skwarnicki

Syracuse University Nov 10, 2015 at

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SLIDE 2

Quark hypothesis – SU(3) flavor symmetry

  • Quarks initially treated as mathematical abstractions

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 2

Y=S Ιz

  • 1 0 1

+1

  • 1

Q -electric charge J = 0 Meson octet Isospin Strangeness (Y=S+A) Ιz

  • 1 0 1

+1

  • 1

Q I = ½ I = 0

  • 1

S= u d s Isospin Y=S+1/3 Quark triplet “Eightfold Way” symmetry – Gell-Mann 1961 (also J=1/2 baryon octet and J=3/2 decuplet)

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SLIDE 3

“Exotic” mutiquark states conceived already at the birth of Quark Model

3 LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015

… …

Murray Gell-Mann 1929- US

Nobel Prize 1969

George Zweig 1937- US

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SLIDE 4

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 4

Charmonium – narrow (i.e. long-lived) states

cc

n 2S+1 l J

Hyperfine splitting Fine splitting

J 1974 c 1975 c

1980

c’ hc

2005

2002

Threshold for (cd)(cd) decay i.e. DD

1 2

s s

  • 1

2 1 2

, L S s r s r s s ⋅ ⋅ ⋅ − ⋅

  • rn

L s1 s2

1 2

S=s +s

  • +

J = S L

  • L+1

L+S

P = (-1) C = (-1) L S J L+S − ≤ ≤

  • Quark Model and qq

hypothesis for mesons firmly established!

  • However, near mass

equality of light quarks was coincidental 1974 November revolution: “ionization threshold”

ψ’ 1974

Coulomb potential Linear potential is confining

quarks to stay inside hadrons

750 MeV

Forces between quarks are 10-100 times stronger than between nucleons! large for l=0 states

c c Non-relativistic quantum mechanics!

spin-orbit

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SLIDE 5

SU(3) color symmetry

  • Fundamental parts of SU(3)flavor symmetry

discovered by Gell-Mann & Zweig:

– Quark flavor independence of strong interactions – Rules for making hadrons out of quarks – led to development of exact theory of strong interactions, QCD based on SU(3)color symmetry

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 5

Strength of color interactions raises with separation of color charges → confinement

  • f color charge → hadrons must be color neutral i.e. “white” (qq, qqq, ….)

Breaking of color field flux tube by popping of qq pair:

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SLIDE 6

_

⊗

= ⊕

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 6

Mesons from quarks & antiquarks in QCD

(qq) meson e.g. K+

+ + +

u s _

Color flux tube stretched between quark and antiquark with attractive potential

3 _ 3 1 8

attractive color force repulsive color force

1 3 1 3 1 3 2 6 − 1 6 1 6 1 2 1 2 −

quarks will pull apart in any

  • ctet configuration

gluons happen to belong to the color octet

q q

1 2 1 2 2 i 2 i − 1 2 1 2 2 i 2 i − 1 2 1 2 2 i − 2 i

color singlet color octet color triplet color antitriplet quark antiquark

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SLIDE 7

_

= ⊕

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 7

(Colored) diquarks in QCD

(qq) diquark _

Color flux tube stretched between the quarks and extending to other color partners

attractive color force (half as strong as in the meson) quarks will pull apart in any sextet configuration

q q color antitriplet color triplet color triplet

1 2 1 2 − 1 2 1 2 − 1 2 1 2 −

_ 3

color sextet

1 2 1 2

6

1 2 1 2 1 2 1 2

1 1 1

repulsive color force

(antisymmetric) (symmetric) u s

⊗

3 3

Not a particle, just a building block in QCD

quark quark

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SLIDE 8

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 8

Baryons from quarks and diquarks

u s

Color flux tube stretched between the diquark and the third quark

q color triplet e.g. Λ Λ Λ Λ d color singlet

1 6 1 6 − 1 6 1 6 − 1 6 1 6 −

attractive color force

... ⊕

1

(q(qq)) baryon

3

⊗

=

(qq) diquark

attractive color force

color antitriplet

1 2 1 2 − 1 2 1 2 − 1 2 1 2 −

_ 3

quark

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SLIDE 9

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 9

Baryons directly from 3 quarks

u s

Color flux tube stretched between three quarks

q color triplet d color singlet

1 3 1 3 1 3

attractive color force

... ⊕

1

(qqq) baryon

3

⊗

=

color triplet

3

⊗

color triplet

3

q q in QCD gluons can couple to each other

Different forms of quark configurations in a baryon can

  • coexist. Relative importance of diaquarks can depend
  • n quark flavors.
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SLIDE 10

⊗

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 10

Tetraquarks from diquarks and diantiquarks

(qq) diquark d s _

Color flux tube stretched between the diquark and diantiquark

attractive color force

color antitriplet color triplet color singlet

attractive color force

... ⊕

1

((qq)(qq)) tetraquark

1 2 1 2 − 1 2 1 2 − 1 2 1 2 −

3

attractive color force

(qq) diantiquark u s _ _

=

1 2 1 2 − 1 2 1 2 − 1 2 1 2 −

_ 3

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SLIDE 11

⊗

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 11

Pentaquark directly from two diquarks and antiquark

(qq) diquark

attractive color force

color antitriplet (qq) diquark

attractive color force

color antitriplet

1 2 1 2 − 1 2 1 2 − 1 2 1 2 −

_ 3

=

color singlet

attractive color force

_ 3

color antitriplet

1 2 1 2 − 1 2 1 2 − 1 2 1 2 −

_ 3

⊗

u s u d s _ q

Color flux tube stretched between the diquarks and antiquark

Different forms of quark configurations in a pentaquark can coexist. Modeling of pentaquarks is complicated.

antiquark ((qq)(qq)q) pentaquark

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SLIDE 12

⊗

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 12

Hexaquark directly from three diquarks

(qq) diquark

attractive color force

color antitriplet (qq) diquark

attractive color force

color antitriplet

1 2 1 2 − 1 2 1 2 − 1 2 1 2 −

_ 3

color singlet

attractive color force

1 2 1 2 − 1 2 1 2 1 2 −

_ 3

⊗

(qq) diquark

attractive color force

color antitriplet

1 2 1 2 − 1 2 1 2 1 2 −

_ 3

=

u s u d u d ((qq)(qq)(qq)) hexaquark (dibaryon)

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SLIDE 13

Tightly and loosely bound multiquark states

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 13

u s s d d u

(((sq)(sq))(qq)) hexaquark

d s u

(q(sq)) (q(sq)) ΛΛ molecule

Λ Λ

dihyperon

predicted by Jaffe to be stable

PRL 38,195(1977)

d u s d _ s u _ _

((q(sq))(q(sq))) hexaquark (q(sq)) (q(sq)) ΛΛ molecule

Λ

s u d _ _ _ u s s u _ _ d u

((q(sq))(qq)) pentaquark ((sq)(sq)) tetraquark

_ u d _

π+

(q(sq)) (qq)) Λπ+ molecule

K−

s _ u

K+

_ u s _

Bayronium (sq) (sq) K+K− molecule

u s d _ d s u

Λ

d s u _

Λ

d s u Any of these states would be considered an “exotic” hadron.

π π π π

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SLIDE 14

Tightly versus loosely bound multiquark systems

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 14

(((qq)(qq))(qq)) hexaquark (dibaryon) (q(qq)) (q(qq)) molecule e.g. deuteron

d _ d

π0

Molecular forces can be described as exchange of a pion

n p

The same quark content Quite different spectroscopy

These quarks pop-out of gluon field, later annihilate

u d u d d u d s u d s u

Difficult to get more than

  • ne state (n=1,l=0).

M = M1+M2 – (a few MeV) JP = (J1± J2)P1*P2 Γ ~ max(Γ1,Γ2)

⊗ Such structures may be extremely unstable (wide). No firm input from lattice QCD (yet) which, if any, multiquark structures form well defined bound states.

  • Rich excitation spectrum, in

principle, possible:

– n, l, S – hundreds of MeV in energy between different excitations – high = + values possible

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SLIDE 15

Two waves of past pentaquark claims (with s)

15 e.g. PDG 1976 Last mention of baryonic Z*’s PDG 1992 Last mention of 2nd pentaquark wave: PDG 2006

… …

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015

Found/debunked by looking for “bumps” in mass spectra

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SLIDE 16

16 LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015

CMS LHCb

  • Advantages over e+e-

B-factories (Belle, BaBar):

– ~1000x larger b production rate – produce b- baryons at the same time as B- mesons – long visible lifetime

  • f b-hadrons (no

backgrounds from the other b-hadron)

  • Advantages over

ATLAS, CMS, CDF, D0:

– RICH detectors for π/K/p discrimination (smaller backgrounds) – Small event size allows large trigger bandwidth (up to 5 kHz in Run I); all devoted to flavor physics

p K- µ+ µ−

RICH1 RICH2 VELO

LHCb: first dedicated b,c detector at hadronic collider

VELO

(B) (B)

(π+)

The LHCb detector described in JINST 3 (2008) S08005

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SLIDE 17

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 17

X(3872) – discovered in 2003

ΓX(3872) <1.2 MeV very narrow

J c c’ hc

“ionization threshold”

ψ’

21P1 23P2 23P1 23P0 13P0 13P1 13P2

c

X(3872)

BaBar data preferred JP=2-+ (without ruling out 1++) from the shape of m3π distribution → η(11D2) cc state?

ψ ψ ψ ψ(2S)

Belle

B→ → → →X(3872)K, X(3872) → → → → J/ψρ ψρ ψρ ψρ0

0,

, , , ρ ρ ρ ρ0

0→

→ → → π π π π+

+ + +π

π π π−

− − − ,

, , , J/ψ ψ ψ ψ→ → → →l+

+ + +l− − − −

X(3872)

34±7 events

DD DD*

PRL 91, 262001 (2003)

“ionization threshold” for states which cannot decay to DD: 1++,2-+

DD DD* 11D2

4000

c c _

?

BaBar

PR D82, 011101 (2010)

B→ → → →X(3872)K, X(3872) → → → → J/ψω ψω ψω ψω, , , , ω ω ω ω→ → → →π π π π0

0π

π π π+

+ + +π

π π π−

− − − ,

, , , J/ψ ψ ψ ψ→ → → →l+

+ + +l− − − −

MX(3872) – [MD0+MD*0] = - 0.11±0.19 MeV

2-+ (CL=68%) (isospin violating decays)

Mass indistinguishable from D0D*0 thresholds

1++ 2-+

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SLIDE 18

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 18

Helicity amplitudes for B+→X(3872)K+, X(3872) → J/ψ ρ , J/ψ→µ+µ− , ρ→ π+π−

,

* * 1 * 1 0, , , ,0 , 1,0,1 1,0,1

(0, ,0) ( , ,0) ( , ,0)

X X

X X X J J X

M D A D D

µ ψ ρ ψ µ ρ ρ λ ψ ρ ψ λ

ψρ λ λ λ λ λ ψ ψ λ ρ ρ λ λ

θ φ θ φ θ

→ ∆ − ∆ =− =−

= ∆ ∆

  • ,

,

( , , , , )

X X X ψ ρ ψ ρ

θ θ θ φ φ Ω ≡ ∆ ∆ Helicity couplings: nuisance parameters

, ,

X X

X L J J L S S

J J S S A L J B

ψ ψ ρ

ρ ψ ρ ψ ρ ψ ρ ψ λ λ ρ λ

λ λ λ λ λ λ λ

  • =
  • −

− − −

  • ( 1)

( 1)

X X L L X

J J S J J J S L J S P P P

ψ ρ ψ ρ ψ ρ

− ≤ ≤ + − ≤ ≤ + = − = −

Number of BLS coupling equals number of independent Aλψ,λρ couplings (1-5 depending on JX) – no gain, unless high L values neglected

(P-conservation since strong decay)

5D analysis

,

2 2 1,1

( | , )

X

X X J

J M A M

µ µ λ λ ψ ρ

ψρ λ λ → ∆ ∆ =−

Ω =

Clebsch-Gordan coefficients λ – particle helicity (spin projection onto its momentum)

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SLIDE 19

Determination of JPC for X(3872)

  • It is important to analyze data

in all sensitive dimensions

  • simultaneously. Angular

correlations by far more powerful than 1D projections.

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 19

3 x 1D χ2 analysis

1++ 2−+

2−+: α2−+=B12/(B11+B12) =(0.64,0.27) Belle 711 fb-1 173±16 events

PRD84(2011)052004

1++: no BLS couplings to fit Could not distinguish between 1++ and 2−

− − −+

LHCb 1 fb-1 (2011 data) 313±26 events 313/173 = 1.3 small gain is statistical errors

5D unbinned likelihood ratio analysis

(L=Lmin)

α2-+=(0.671±0.046, 0.280±0.046)

data 8.4σ

Very clear separation between 1++ and 2−

− − −+

The data choose 1++

PRL 110, 222001 (2013)

likelihood ratio

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SLIDE 20

2015 update to X(3872) JPC determination

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 20

CDF 2007 LHCb 2013

LHCb 2015

Many more amplitudes to fit L LHCb 3 fb-1 (2011+2012 data) 1011±38 events PRD92, 011102 (2015)

(all L values allowed)

LHCb

X(3872)

<4% at 95% CL JPC = 1++ at 16σ

likelihood ratio

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SLIDE 21

X(3872) interpretation

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 21

21P1 23P2 23P1 23P0 X(3872) D0D*0

4000

1++

c c _ χc(23P1) “attracted” by D0D*0 threshold? _ c _ u _ u c _

MX(3872) – [MD0+MD*0] = - 0.11±0.19 MeV

D0 D*0 L=0 Meson-meson molecule?

essentially no binding energy?

c u c u _ _ mixture? tightly bound tetraquark “attracted” by DD* threshold ?

[cu]S=1 [cu]S=0 + [cu]S=0 [cu]S=1

e.g. L. Maiani, F. Piccinini, A.D. Polosa, V. Riquer, PRD 89 (2014) 114010

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SLIDE 22

Growing XY zoo

  • Many more neutral states at higher masses of the charmonium system

have been discovered since then, which are candidates for exotic hadrons (none as narrow as X(3872))

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 22

Black: Observed conventional cc states Blue: Predicted conventional cc states Red: Exotic state candidates with cc inside

Esposito et al., Int. J. Mod. Phys. A30 (2014)1530002

  • Many of them await experimental confirmation.
  • Many of them discovered near D(s)

(*)D(s) (*) thresholds.

  • No single model can explain all of them.
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SLIDE 23

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 23

Phys.Rev.Lett. 100, 142001 (2008)

Z(4430)+ discovery and its importance

c c _ c u c d _ _ _ c _ d _ u c _ neutral charged

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SLIDE 24

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 24

Z(4430)- previous measurements

18 30 13 13

M( signifi ) 44 ( ) 33 4 cance 45 MeV .5 2 MeV 6 Z Z σ

+ + − −

= ± Γ = ±

1D M(ψ’π−) mass fit

41 26 4 22 28 22 1 6 35 1

( ) 20 M( ) 448 6.4 (5.6 with sys 5 MeV M V . e ) Z Z σ σ

+ − − − − + + +

Γ = =

4D amplitude fit

B→ψ’π−K

JP=1+ preferred by >3.4σ

non-B bkg

bkg

No Z With Z(4430)- PRL 100, 142001 (2008) PRD 88, 074026 (2013)

(“K* veto region”) (“K* veto region”)

1D4D Belle

M(ψ’π−) GeV

BaBar 2009 Belle 2008

BaBar did not confirm Z(4430)- in B sample comparable to Belle.

Did not numerically contradict the Belle results. PRD 79, 112001 (2009)

Harmonic moments of K*s (2D) reflected to M(ψ’π−)

Ad hoc assumption about the K*→Kπ− background shape.

[ ψ’ ψ(2S) ]

  • Bkg. subtracted efficiency corrected

Almost model independent approach to K*→Kπ− backgrounds.

Belle 2013

Z(4430)-

K*→Kπ− bkg.

(2D amplitude fit in 2009)

Model dependent approach to K*→Kπ− backgrounds. Higher statistical sensitivity.

(subsample with ψ’ →l+l−)

Z- K*

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SLIDE 25

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 25

Z(4430)+ in LHCb

  • B0→ψ’K+π− , ψ’→µ+µ− (3 fb-1)

An order of magnitude larger signal statistics than in Belle or BaBar thanks to hadronic production of b-quarks at LHC. Even smaller non-B background than at the e+e- experiments thanks to excellent performance of the LHCb detector (vertexing, PID)

bkg (4.1±0.1)%

  • vs. bkg in Belle: 7.8%

vs Belle: 2,010±50 BaBar: 2,021±53

LHCb-PAPER-2014-014 PRL 112, 222002 (2014)

25,176±174 signal events

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SLIDE 26

Β0→ ψ’π+K-

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 26

Zc (4430)+ → J/ψπ+ ?

K*(892) J=1 K*2(1430) J=2

Kaon excitations u s _ c u c d Tetraquark _ _ Is it a reflection of interfering K*’s → π+K- ?

Proper amplitude analysis necessary to check

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SLIDE 27

Amplitude Analysis of Β0→ ψ’π+K-, ψ’→µ+µ−

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 27

4D analysis

* * * * * * *

* 1 * ,0 , 1 0,1 , ,

(0, ,0) ( | , ) ( , ,0)

K n n n

B K K K K K n J K K

D R M D M A m

ψ ψ µ ψ µ λ ψ

ψ λ ψ λ λ ψ λ λ π

θ φ θ

∆ =− → ∆

∆ = Γ

* *

,

( , , )

K K ψ ψ

θ θ φ Ω ≡ ∆

* *

2 2 1,1 K

( | ) m ,

n

B K K

M A M

λ ψ µ µ

λ ψ π λ ∆ ∆ =− →

= Ω

  • 1-3 independent complex helicity

couplings per Κn

* resonance

1 mass, 3 angles

* * * * * * * 2 3

0 : (800), (1430), ; 1 : (892), (1410), (1680) 2 : (1430) (3 : (1780)) n K K NR K K K K K

+ − + −

=

' ' 2 1 ' 2 2 2

( , , ) ( , , ) ( | , ) ( ) ( , , ) ( )

B X X B X X

L L L L L B X X X X L X X

p q B p p d B q q d M m q M R m M m B q q d q m M m iM m

+

  • Γ

= Γ = Γ

  • −

− Γ

  • Breit-Wigner

amplitude:

Blatt-Weisskopf functions

# of fit parameters: 32

slide-28
SLIDE 28

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 28

Amplitude fits without Z(4430)-

  • The χ2 p-value < 2x10-6
  • The data cannot be adequately described with the

J 3 K* contributions alone

(“K* veto region”) (“all data”)

slide-29
SLIDE 29

Amplitude Analysis of Β0→ ψ’π+K-, ψ’→µ+µ−

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 29

* 1 * , , , 1,0,1

(0, ,0) ( | ) ( , ,0 , )

Z

Z J Z Z Z Z Z Z

A m M D R D M

µ ψ ψ ψ µ ψ λ ψ

ψπ ψπ ψ λ λ λ λ λ λ ψ

θ φ θ

∆ ∆ =− →

Γ = ∆

  • 1 independent complex helicity

coupling after L=Lmin 1 mass, 3 angles all derivable from the Κ* variables

4D analysis

* *

2 2 1, K 1

( | , ) m , , , ,

n

Z B Z K i Z Z Z K

M M J A M e A M

λ λ µ ψ µ ψ µ µ µ

ψ λ α λ π π λ ψ λ → ∆ ∆ ∆ =− → ∆

Ω = + Γ

  • # of fit parameters: 32 + 4 = 36
slide-30
SLIDE 30

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 30

Amplitude fits with JP=1+ Z(4430)+

  • The χ2 p-value = 12%
  • The data are well described when JP=1+ Z(4430)+ is included in the fit
  • Z(4430)+ significances from ∆(-2lnL) is 18.7σ (13.9σ with systematic

variations)

(log)

c u c d Kaon excitations u s _ Tetraquark

(“all data”)

_ _

∆

slide-31
SLIDE 31

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 31

Amplitude fits with JP=1+ Z(4430)-

1 1 2 3 2 3 4 4

“K* veto region” “below K*(892)” “K*(892) region” “K*2(1430) and above”

K*(892) J=1 K*2(1430) J=2

Z(4430) +

Z(4430) Z(4430) including interferences

slide-32
SLIDE 32

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 32

Z(4430)- parameters: LHCb vs Belle

  • Overall excellent consistency between LHCb and Belle
  • Errors substantially improved

Amplitude fractions [%] (statistical errors only) LHCb Belle LHCb Belle

(with interferences)

I (new large systematic effect included by LHCb)

(not in the default fit K*

3(1780) 0.5 ± 0.2 )

slide-33
SLIDE 33

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 33

Z(4430)+ spin-parity analysis

  • JP=1+ now established beyond

any doubt

26σ

PRD 88, 074026 (2013)

Belle

18σ

using a conservative approach

Rejection level relative to 1+ Disfavored JP LHCb Belle 0- 9.7σ 3.4σ 1- 15.8σ 3.7σ 2+ 16.1σ 5.1σ 2- 14.6σ 4.7σ

Including systematic variations:

threshold cusp

d c _ c u _ c c _ d u _

D1

0,(D2 0*)

D*+

JP=0-,1-,2-,(3-)

ψ’ π+

slide-34
SLIDE 34

Hadronic resonances – Argand diagram

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 34

ext

d d m = d b d F cos( t) t k d d t t x x x

  • −

− −

  • Forced harmonic oscillator:

ext ext e 2 2 2 2 xt

/ m (t) cos( t ) ( )

  • F
  • (2

)

t

x ϕ γ

→∞

→ + − +

2m b γ =

dumping factor: Restoring force Damping force: Driving force ext ex 2 t 2

  • 2

= atan

  • γ

ϕ

  • −
  • driving

frequency phase lag

slide-35
SLIDE 35

Hadronic resonances – Argand diagram

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 35

  • mψπ ~ ωext driving frequency
  • MΖ ~ ω0 resonance frequency
  • ΓΖ = / τΖ ~ γ/2 dumping

factor (mass indeterminacy)

AZ(ψ) ~

  • = AZ(ψ)

Breit-Wigner amplitude

|AZ(ψ)|2 ~

  • ψ = atan

!Γ! !

2 − ψ 2

ext

d d m = d b d F cos( t) t k d d t t x x x

  • −

− −

  • Forced harmonic oscillator:

ext ext e 2 2 2 2 xt

/ m (t) cos( t ) ( )

  • F
  • (2

)

t

x ϕ γ

→∞

→ + − +

0 = k

  • m

resonant frequency:

2m b γ =

dumping factor: Restoring force Damping force: Driving force ext ex 2 t 2

  • 2

= atan

  • γ

ϕ

  • −
  • driving

frequency phase lag

mψπ ~ ωext MΖ ~ ω0

|AZ(ψ)|2 ψ

Phase or magnitude-squared

slide-36
SLIDE 36

Hadronic resonances – Argand diagram

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 36

  • mψπ ~ ωext driving frequency
  • MΖ ~ ω0 resonance frequency
  • ΓΖ = / τΖ ~ γ/2 dumping

factor (mass indeterminacy)

AZ(ψ) ~

  • = AZ(ψ)

Breit-Wigner amplitude

|AZ(ψ)|2 ~

  • ψ = atan

!Γ! !

2 − ψ 2

ψ= ! ψ> ! Re AZ Im AZ

  • ext

d d m = d b d F cos( t) t k d d t t x x x

  • −

− −

  • Forced harmonic oscillator:

ext ext e 2 2 2 2 xt

/ m (t) cos( t ) ( )

  • F
  • (2

)

t

x ϕ γ

→∞

→ + − +

0 = k

  • m

resonant frequency:

2m b γ =

dumping factor: Restoring force Damping force: Driving force ext ex 2 t 2

  • 2

= atan

  • γ

ϕ

  • −
  • driving

frequency phase lag

mψπ ~ ωext MΖ ~ ω0

|AZ(ψ)|2 ψ

|AZ(ψ)|2

ψ

DEMO

Phase or magnitude-squared

slide-37
SLIDE 37

Argand diagram of Z(4430)+

37 LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 4411 4475 4541 4605

  • P. Pakhlov, T. Uglov

PL B748, 183 (2015)

2 2 '

1

Z Z Z

M m i M

ψ π +

− − Γ

Breit-Wigner amplitude

rules out

rescattering model

= 4277 MeV

  • Thanks to the large data statistics LHCb has been able to

extract Argand diagram of Z(4430)+ amplitude from its interference with the K* amplitudes:

4344 4208 4277 4345 4411 4477 4542

slide-38
SLIDE 38

38

17±4 MeV above the DD* threshold

Previously confirmed Zc

+ state: Zc(3900)+

e+e- →Y(4260) → π−(π+J/ψ)

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015

Presented at Modern Exotic Hadrons, Seattle, Nov.3,2015 However, some parameters were fixed in this exercise.

Belle: reached via ISR from 10.6 GeV

m= 3888.7±3.4 MeV Γ Γ Γ Γ= 35±7 MeV

BESIII: PRL 110, 252001 (2013) Belle: PRL 110, 252002 (2013)

slide-39
SLIDE 39

Z(4430)+ and other Zc

+ states

  • The only threshold still at play for Z(4430)+: DD(2600) if D(2600) exists (needs

confirmation!) and if it is 1- states (23S1)

  • Other charged Zc

+,Zb + states are near D(*)D(*), B(*)B(*) thresholds LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 39

1+ ? 0-, 1-,2-,3-

_ c _ d _ u c _

DD(2600) D*D1,D*D2*

Well established (>1 experiment)

c u c d Tetraquark Molecule or threshold cusp Radial excitation

  • f tightly

bound tetraquark Radial excitation

  • f the 3S1

meson inside meson molecule

Zc(3900)+ is 17±4 MeV above the DD* threshold, favors tetraquark picture. However, DD* rescattering above the threshold is also possible.

_ _

1+

slide-40
SLIDE 40

LHCb Λb

0→ J/ψ p K-

40 LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015

  • The decay first observed by LHCb and used to measure

Λb

0 lifetime (LHCb-PAPER-2013-032, PRL 111, 102003)

LHCb-PAPER-2015-029, arXiv:1507.03414, PRL 115, 07201 The background is only 5.4% in the signal region! The sideband distributions are flat → no major reflections from the

  • ther b-hadrons

after the selection 26,007±166 Λb

0 candidates

Run I 3 fb-1

slide-41
SLIDE 41

41 LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015

Λ(1520) and other Λ*’s → p K- Pc

+→ J/ψ p

?

LHCb

  • Unexpected, narrow peak

in mJ/ψ p

Λb

0→ J/ψpK-: unexpected structure in mJ/ψ p

Λ baryon excitations Exotic pentaquark

Λ∗

d s u c u u d c _ a reflection of interfering Λ*’s → p K- ?

Proper amplitude analysis absolutely necessary to check

slide-42
SLIDE 42

Amplitude Analysis of Λb→ J/ψpK-, J/ψ→µ+µ−

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 42

6D analysis

* * * * * * * * * * * *

1 * 2 , 1,0, , 1 , , * , , * 1 , ,

(0, ,0) ( , ,0) ( | , ) ( , ,0)

b p b n p n b n b p n b

n p K J K Kp

M A A D D R M m D

ψ ψ ψ µ µ ψ λ

ψ λ λ λ λ λ ψ ψ λ λ λ λ λ λ λ λ λ

θ φ θ φ θ

Λ Λ Λ Λ Λ Λ Λ

Λ → Λ Λ ∆ Λ Λ → Λ − =− ∆ Λ Λ Λ Λ

= Γ ∆ ∆

* *

, ,

( , , , , )

b b b

ψ ψ

θ θ φ θ φ

Λ Λ Λ Λ Λ

Ω ≡ ∆ ∆

* * * *

K , , , 2 2 1/ 2, 1/ 2 1/ 2, 1/ 2 1,1

( | ) m , ,

b n n p p b p b

pK p

A M A M

µ ψ µ

ψ λ λ λ λ λ λ λ λ λ

Λ Λ Λ

Λ → Λ Λ → Λ =− + =− + ∆ =− ∆

Ω =

  • 4-6 independent complex helicity

couplings per Λn

* resonance

1 mass, 5 angles

slide-43
SLIDE 43

Λ* resonance model

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 43

No high-JP high-mass states limit L All states, all L

?

# of fit parameters: 64 146

All known Λ* states from KN scattering experiments

slide-44
SLIDE 44

Fit with Λ*→pK- contributions only

  • Include all known Λ excitations:
  • mKp looks fine, but not mJ/ψp

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 44

d s u c u u d c _

# of fit parameters: 146

slide-45
SLIDE 45

Amplitude Analysis of Λb→ J/ψpK-, J/ψ→µ+µ−

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 45

6D analysis

*

1 * 2 , 1,0,1 * , , , , 1 * , , ,

( , ,0) ( , ,0) ( | , ) ( , ,0)

n c c b c p P c b c n n b P n P c c c n n p c b c c c c P c n p P c c

P P P K P n J P P p P P p P P P

D D M A A m M R D

ψ ψ ψ ψ µ µ

λ λ λ λ λ ψ λ λ λ λ λ λ λ ψ ψ λ λ λ ψ

φ θ φ θ φ θ

Λ Λ

Λ → ∆ Λ → Λ =− − ∆

∆ Γ ∆ =

* * * *

2 2 1 2 , 1/ 2, 1/ 2 1/ 2, 1/ 2 1,1 1/ 2, , , , , / , 1 K , 2

( | ) m ( ) , , , , , , ,

b n n p p b n n b c c n n n n p c c P P c c c P c P c p p P c p p b p b

pK p P i p K P p P P P

M e M J A A d A A M M

µ µ µ ψ µ ψ µ

λ α λ λ ψ λ λ λ λ λ λ λ ψ λ λ λ λ λ λ λ λ λ

θ

Λ Λ Λ Λ

Λ → Λ Λ → Λ ∆ =− + =− + ∆ =− =− + Λ → ∆ → ∆

Ω Γ + =

  • 3-4 independent complex helicity

couplings per Pc

n resonance

1 mass, 6+2 angles all derivable from the Λ∗ variables

slide-46
SLIDE 46

Fit with Λ*’s and one Pc

+→J/ψp state

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 46

  • Try all JP of Pc

+ up to 7/2±

  • Best fit has JP =5/2±. Still not a good fit

d s u c u u d c _

# of fit parameters: 146 + 10 = 156

slide-47
SLIDE 47

Fit with Λ*’s and two Pc

+→J/ψp states

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 47

  • Obtain good fits even with the reduced Λ* model
  • Best fit has JP=(3/2-, 5/2+), also (3/2+, 5/2-) & (5/2+, 3/2-) are

preferred

Pc(4450)+ Pc(4380)+

State Mass (MeV) Width (MeV) Fit fraction (%) Significance Pc(4380)+ 205±18±86 8.4±0.7±4.2 9σ σ σ σ Pc(4450)+ 4449.8±1.7±2.5 39± 5±19 4.1±0.5±1.1 12σ σ σ σ

d s u c u u d c _

# of fit parameters: 64 + 20 = 84

slide-48
SLIDE 48

Fit with Λ*’s and two Pc

+→J/ψp states

Need for the 2nd broad Pc

+ state

becomes visually apparent in the region where the Λ*→pK- background is the smallest

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 48

Events/(20 MeV) mKp<1.55 GeV Events/(20 MeV) 1.55<mKp <1.70 GeV 1.70<mKp <2.00 GeV 2.00 GeV<mKp

slide-49
SLIDE 49

Data preferrence for opposite parity Pc

+ states

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 49

mKp<1.55 GeV 1.55<mKp <1.70 GeV 1.70<mKp <2.00 GeV 2.00 GeV<mKp Events/(20 MeV) Events/(20 MeV) Positive interference between the Pc states

  • This interference pattern only for states with opposite parity

Negative interference between the Pc states

(display before efficiency) (display after efficiency)

  • +
slide-50
SLIDE 50

Angular distributions

  • Good description of the data in all 6 dimensions!

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 50

LHCb all mKp LHCb mKp>2 GeV

  • +

Λ* interferences

All data Pc enriched region

PRL 115, 07201 (2015)

∆φΛb,Λ∗ ∆φΛb,J/ψ ∆φΛb,J/ψ ∆φΛb,Λ∗

slide-51
SLIDE 51
  • J/ψK- system is

well described by the Λ∗ and P

(+

reflections. )

*

51 LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015

No need for exotic J/ψK- contributions

mKp<1.55 GeV 1.55<mKp <1.70 GeV 1.70<mKp <2.00 GeV 2.00 GeV<mKp All mKp

PRL 115, 07201 (2015)

slide-52
SLIDE 52

Argand diagrams

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 52

Breit- Wigner Breit- Wigner Pc

+ amplitudes for 6 mJ/ψp bins between +Γ & -Γ around the resonance mass

  • Good evidence for the resonant character of Pc(4450)+
  • The errors for Pc(4380)+ are too large to be conclusive

PRL 115, 07201 (2015)

slide-53
SLIDE 53

Baryon-meson molecules?

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015

u c _ c d u c c _ u d u

M.Karliner, J.Rosner [arXiv:1506.06386], R.Chen et al [arXiv:1507.03704 L.Roca,J.Nieves,E.Oset [arXiv:1507.04249].J.He [arXiv:1507.05200], U.Meissner,A.Oller [arXiv:1507.07478],T.J. Burns [arXiv:1509.02460]

I= 1/2 I= 1/2 (Λ,Σ), 3/2 (Σ)

Σc

+D0

1 2

  • Σc

*+D0

3 2

  • Σc

+D*0

Σc

*+D*0

1 2

  • , 3

2

  • 1

2

  • , 3

2

  • , 5

2

  • Pc(4450)+

5 2

∓

3 2

∓

  • r

Pc(4380)+ 3 2

±

5 2

±

  • r

10±3 MeV 2±30 MeV Binding energy for L=0

Λc

+D0

Λc

+D*0

Λc

*+D*0

Λc

*+D0

7±3 MeV 1 2

  • 1

2

  • , 3

2

  • 1

2

  • 1

2

  • , /
  • , 0
  • p χc0

p J/ψ p χc1 p χc2

1 2

  • , 3

2

  • 1

2

  • , 3

2

  • 1±3 MeV
  • 27±30 MeV

45±3 MeV 3 2

  • , 5

2

  • p

χc1 Λc

+,Σc +

D0 Cannot accommodate a

  • ±

state with a plausible S-wave molecule L>0 molecules not likely to be bound Rich spectrum of relatively narrow states expected: all shown + isospin partners + strange partners + b quark + …

slide-54
SLIDE 54

Tightly bound pentaquarks?

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 54

Pc(4380)+ Pc(4450)+ 3 2

±

5 2

±

  • r

3 2

∓

5 2

∓ or

Can accommodate

  • ±

when at least one diquark in S=1 state

u c u d c

Maiani, Polosa,Riquer [arXiv:1507.04980], Anisovich et al [arXiv:1507.07652,1509.04898], Li,He,He [arXiv:1507.08252], Ghosh et al [arXiv:1508.00356]

_ u c u d c _

  • R. Lebed [arXiv:1507.05867]

Such mass difference and the opposite parity can be explained by ∆l=1

l

Rich spectrum of states expected: S=0 (lower J)+ l + n + isospin partners + strange partners + b quark + …

c[cu]S=1 [ud]S=1 (l=0) c[cu]S=1 [ud]S=0 (l=1)

_ _ e.g.

slide-55
SLIDE 55
  • Conventional hadrons produced and then rescatter (rearrange

quarks) to produce a peak in the exotic channel.

  • Peaking structures related to the same mass thresholds, discussed

already for molecules, but can occur above them.

  • Effective JP like for molecules (L=0). Cannot accommodate
  • ±

.

  • Ad hoc parameter values to generate desired structures.
  • Can sometimes arrange for the resonant-like phase running.
  • Given proliferation of thresholds, why aren’t they everywhere?
  • Not clear these models can describe decay angles distributions;

predictions and tests on the data are needed.

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 55

Z.-H.Liu,Q.Wang,Q.Zhao [arXiv:1507.05359],

  • M. Mikhashenko [arXiv:1507.06552],
  • A. Szczepaniak [arXiv:1510.01789]

Rescattering (triangular singularity)

slide-56
SLIDE 56

Outlook to the future

  • At present there are many plausible explanations for the observed Pc

+ states.

  • The main competition is between tightly bound models based on diquark

substructure, loosely bound molecules and rescattering effects.

  • Clarifying JP values and resonant nature of the discovered Pc

+ states with

more statistics will be very important.

  • All models predict many other related states to exist. Different models predict

different mass spectra. We badly need to discover more elements of future periodic table of such states!

  • Interactions forming pentaquark states must also play a role in tetraquark
  • states. It is important to pursue both spectroscopies together!
  • Searches for states with even more quarks e.g. sextquarks (i.e. dibaryons)

interesting.

  • We can do more to test the diquark idea in ordinary baryons! Need

experimentalists to do better on identifying all excited baryons.

  • So far the most compelling tetraquark and pentaquark candidates have been

discovered with hidden charm inside (cc). The other heavy quark systems should also be creating bound structures (bb, bc, ccc, …, cc, bb, …)

  • We are only at the beginning of hopefully very interesting road ahead…

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 56

slide-57
SLIDE 57

Conclusion

  • Two pentaquark candidates decaying to J/ψp observed by LHCb with
  • verwhelming significance in a state of the art amplitude analysis: they will

not go away!

57 LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015

Pentaquark candidates rise from the ashes for the 2nd time.

  • LHC resurrects them: should not be a surprise given baryon cross-

sections. cc pair inside:

  • Given the history of Quark Model should not be a surprise either.
  • The simplicity of lower mass excitations of mesons and baryons, which led

us to the discovery of quarks via qq, qqq structures, also misled us to believe that we had already understood hadronic structures. Much experimental and theoretical work remains to be done to achieve this goal.

Frank Wilczek’s twit on 7/14/15: “Pentaquarks rise from the ashes: a phoenix pair”

Hopefully true July 2015 revolution! u c u d c _

slide-58
SLIDE 58

BACKUP SLIDES

slide-59
SLIDE 59

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 59

Z(4430)+ in LHCb: 2D model independent analysis (a la BaBar) cos(θK*)

  • vs. mK+π−

“Rectangular Dalitz plot”

  • vs. mK+π−

Decompose into Legendre moments Pass only moments with l not more than lmax=Jmax/2

cos(θK*)

  • vs. mK+π−

“K* Jmax filtered” “K* Jmax filtered”

correlated statistical errors In the filtered distribution

spin J

Jmax=2

4D Belle

K*(892) J=1

Dalitz plot

K*2(1430) J=2

Excess of events over the K* Jmax=2 filtered distribution in the Z(4430)- region is apparent ! Dalitz plot

*

1

1 (cos )

data

N U l l K i i i

P P θ ε

=

< >=

Z(4430)- ?

This qualitative analysis was included in the 2014 paper

u s _

slide-60
SLIDE 60

Quantitative results from the model independent approach

LHCb Tetra- and Penta-quarks, T. Skwarnicki SLAC, Nov 2015 60

LHCb-PAPER-2015-038 arXiv:1510.0195 (Oct 7, 2015)

K* Jmax=2 lmax=4 K* Jmax=3 lmax=6 K* Jmax=15 lmax=30

mKπ MeV lmax=2 - 836 3 836-1000 4 1000 -

Test significance of implausible lmax< l <30 cos(θK*) moments using the log-likelihood ratio:

Allows for a tail of K*3(1780) Allows implausible K* contributions Allows for K* states up to K*2(1430)

Statistical simulations of pseudo-experiments generated from the l < lmax hypotheses:

Data Data Data

Explanation of the data with plausible K* contributions is ruled at high significance without assuming anything about K* resonance shapes or their interference patters!

data data data data data