Heavy Baryons: the Rooftops - uni-frankfurt.dedietrich/SLIDES/Williams.pdfHeavy Baryons: the...

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Heavy Baryons: the Υ Rooftops Richard Williams and Felipe Llanes-Estrada Dept. F´ ısica Te´ orica I, Univ. Complutense de Madrid, 28040 Madrid, Spain STRONG INTERACTIONS BEYOND THE STANDARD MODEL Physikzentrum Bad Honnef, Germany, February 13-15, 2012 1 / 15 Richard Williams, Felipe Llanes-Estrada Heavy Baryons: the Υ Rooftops N

Transcript of Heavy Baryons: the Rooftops - uni-frankfurt.dedietrich/SLIDES/Williams.pdfHeavy Baryons: the...

Page 1: Heavy Baryons: the Rooftops - uni-frankfurt.dedietrich/SLIDES/Williams.pdfHeavy Baryons: the Rooftops Richard Williams and Felipe Llanes-Estrada Dept. F´ısica Te ´orica I, Univ.

Heavy Baryons: the Υ Rooftops

Richard Williams and Felipe Llanes-EstradaDept. Fısica Teorica I, Univ. Complutense de Madrid, 28040 Madrid, Spain

STRONG INTERACTIONS BEYOND THE STANDARD MODELPhysikzentrum Bad Honnef, Germany, February 13-15, 2012

1 / 15Richard Williams, Felipe Llanes-Estrada Heavy Baryons: the Υ Rooftops

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Page 2: Heavy Baryons: the Rooftops - uni-frankfurt.dedietrich/SLIDES/Williams.pdfHeavy Baryons: the Rooftops Richard Williams and Felipe Llanes-Estrada Dept. F´ısica Te ´orica I, Univ.

Introduction

IntroductionBottomoniumCorner of QCD where we understand how the hadronic bound-states are composed of quarks.

9000

9500

10000

10500

11000

E (MeV)

PDG 08

J PC

= 1− −

ϒ(5S)

ϒ(4S)

ϒ(3S)

ϒ(2S)

ϒ(1S)

RPA

ϒ(1S)

ϒ(2S)

ϒ(3S)

ϒ(4S)

ϒ(5S)

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Page 3: Heavy Baryons: the Rooftops - uni-frankfurt.dedietrich/SLIDES/Williams.pdfHeavy Baryons: the Rooftops Richard Williams and Felipe Llanes-Estrada Dept. F´ısica Te ´orica I, Univ.

Introduction

Υ-spectrumPure Exotics

9460

11020

Y spectrum Observation Resonances in BcBc

should be (hidden) exotic.

Direct test of weak vs strongpNRQCD regime (Coulombicinteraction: very weak resonances,bound states)

Roof of future B-factory’s energyshould reach Bc Bc threshold to beexhaustive (B , Bs , Bc ).

Triple CharmLook for Ωccc in e+e− → ΩcccpDDD by recoil method.

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Page 4: Heavy Baryons: the Rooftops - uni-frankfurt.dedietrich/SLIDES/Williams.pdfHeavy Baryons: the Rooftops Richard Williams and Felipe Llanes-Estrada Dept. F´ısica Te ´orica I, Univ.

Introduction

Υ-spectrumPure Exotics

9460

11020

Y spectrum open b−flavor

B B

Bs Bs

Bc Bc

Observation Resonances in BcBc

should be (hidden) exotic.Direct test of weak vs strongpNRQCD regime (Coulombicinteraction: very weak resonances,bound states)

Roof of future B-factory’s energyshould reach Bc Bc threshold to beexhaustive (B , Bs , Bc ).

Triple CharmLook for Ωccc in e+e− → ΩcccpDDD by recoil method.

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Page 5: Heavy Baryons: the Rooftops - uni-frankfurt.dedietrich/SLIDES/Williams.pdfHeavy Baryons: the Rooftops Richard Williams and Felipe Llanes-Estrada Dept. F´ısica Te ´orica I, Univ.

Introduction

Υ-spectrumPure Exotics

9460

11020

Y spectrum open b−flavor

B B

Bs Bs

Bc Bc

Triple charm

Ω Ω

3D N

6 D

Ω

Observation Resonances in BcBc

should be (hidden) exotic.Direct test of weak vs strongpNRQCD regime (Coulombicinteraction: very weak resonances,bound states)

Roof of future B-factory’s energyshould reach Bc Bc threshold to beexhaustive (B , Bs , Bc ).

Triple CharmLook for Ωccc in e+e− → ΩcccpDDD by recoil method.

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Page 6: Heavy Baryons: the Rooftops - uni-frankfurt.dedietrich/SLIDES/Williams.pdfHeavy Baryons: the Rooftops Richard Williams and Felipe Llanes-Estrada Dept. F´ısica Te ´orica I, Univ.

Introduction

Double charmonium/charm productionSince 1987 (WA75 collaboration)

Mrecoil

(J/ψ) (GeV/c2)

N/2

0 M

eV

/c2

0

10

20

30

40

50

2.2 2.6 3 3.4 3.8

J/ψDD

J/ψDD*J/ψD

*D

*

Mrecoil(J/ψD) GeV/c2

N/2

0 M

eV

/c2

0

10

20

30

40

1.6 1.8 2 2.2 2.4

Using recoil method and missing mass.Tagging D-mesons in final state.Lots of experience.

BELLE collaboration hep-ex/0507019

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Page 7: Heavy Baryons: the Rooftops - uni-frankfurt.dedietrich/SLIDES/Williams.pdfHeavy Baryons: the Rooftops Richard Williams and Felipe Llanes-Estrada Dept. F´ısica Te ´orica I, Univ.

Introduction

Triple charm?ThresholdsClosed charm: Triple c not reported (3×MJ/ψ = 9300 MeV )Open charm: Produce ccc + c c c

DDD + DDD → 6× 1867 = 11202

Triply charmed baryon Ωccc + DDD + N

No measurement of triply charmed baryons yet: theory .

Recoil

ccc

e+

e−

D

DD

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Page 8: Heavy Baryons: the Rooftops - uni-frankfurt.dedietrich/SLIDES/Williams.pdfHeavy Baryons: the Rooftops Richard Williams and Felipe Llanes-Estrada Dept. F´ısica Te ´orica I, Univ.

Two-body Problem

Static potential in pNRQCD

Expansion in α, 1/m

V (0) = V(0)LO + V

(0)NLO + V

(0)NNLO . . .

Leading Order (LO)The leading order potential is just the colour Coulomb potential

V(0)LO = −4

3

αs(r−2)

r

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Two-body Problem

Static potential in pNRQCDNLO and NNLO

V(0)NLO = V

(0)LO (a1 + 2γEβ0)

αs

(r−2)

V(0)NNLO = V

(0)LO

(γE (4a1β0+2β1)+

(π2

3+4γ2

E

)β2

0 +a2

)α2s (r−2)

(4π)2

V1/m (convention dependent)

Vm−1 =−α2

s (µ)

mr r2×(

7

9

)− α3

s

3πmr r2

−b2 + log(e2γEµ2r2)

(7β0

6+

68

3

)(A. Vairo 2001; N. Brambilla et al. 2000)

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Three-body Problem

Ωccc : Potential in pNRQCD

∆ or Y-Shaped potential

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Three-body Problem

Ωccc : Potential in pNRQCDLO Potential: ∆-shaped

V(0)LO =

−2αs

3

3∑i=1

1

|ri |(with r1 = r2 − r3, etc)

i.e. sum of two-body Coulomb interactions

NLO Potential: Still ∆-shaped

V(0)LO +V

(0)NLO =

−2

3

∑i

αs(|ri |−2)1

|ri |

[1+

αs(|ri |−2)

4π(2β0γE +a1)

]

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Page 12: Heavy Baryons: the Rooftops - uni-frankfurt.dedietrich/SLIDES/Williams.pdfHeavy Baryons: the Rooftops Richard Williams and Felipe Llanes-Estrada Dept. F´ısica Te ´orica I, Univ.

Three-body Problem

Ωccc : Potential in pNRQCDLO Potential: ∆-shaped

V(0)LO =

−2αs

3

3∑i=1

1

|ri |(with r1 = r2 − r3, etc)

i.e. sum of two-body Coulomb interactions

NLO Potential: Still ∆-shaped

V(0)LO +V

(0)NLO =

−2

3

∑i

αs(|ri |−2)1

|ri |

[1+

αs(|ri |−2)

4π(2β0γE +a1)

]

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Page 13: Heavy Baryons: the Rooftops - uni-frankfurt.dedietrich/SLIDES/Williams.pdfHeavy Baryons: the Rooftops Richard Williams and Felipe Llanes-Estrada Dept. F´ısica Te ´orica I, Univ.

Three-body Problem

Ωccc : Potential in pNRQCDNNLO Potential: ∆-shaped Component

V(0)NNLO−2 =

−2

3

∑i

αs(r−2i )

|ri |αs(r−2

i )2

(4π)2×(

a2 − 36π2 + 3π4 +

(π2

3+ 4γ2

E

)β2

0 + γE (4a1β0 + 2β1)

)

NNLO Potential: Finally a Y -shaped potential

V(0)NNLO−3 = 2 (Vaux(r2, r3) + Vaux(r1,−r3) + Vaux(−r2,−r1))

Vaux(r2, r3) = FT . Vaux(q2,q3) =(−i/2)(4π)3α3

s

8|q2|2|q3|2×[

|q2 + q3||q2||q3|

+q2 · q3 + |q2||q3||q2||q3||q2 + q3|

− 1

|q2|− 1

|q3|

]

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Page 14: Heavy Baryons: the Rooftops - uni-frankfurt.dedietrich/SLIDES/Williams.pdfHeavy Baryons: the Rooftops Richard Williams and Felipe Llanes-Estrada Dept. F´ısica Te ´orica I, Univ.

Three-body Problem

Ωccc : Potential in pNRQCDNNLO Potential: ∆-shaped Component

V(0)NNLO−2 =

−2

3

∑i

αs(r−2i )

|ri |αs(r−2

i )2

(4π)2×(

a2 − 36π2 + 3π4 +

(π2

3+ 4γ2

E

)β2

0 + γE (4a1β0 + 2β1)

)NNLO Potential: Finally a Y -shaped potential

V(0)NNLO−3 = 2 (Vaux(r2, r3) + Vaux(r1,−r3) + Vaux(−r2,−r1))

Vaux(r2, r3) = FT . Vaux(q2,q3) =(−i/2)(4π)3α3

s

8|q2|2|q3|2×[

|q2 + q3||q2||q3|

+q2 · q3 + |q2||q3||q2||q3||q2 + q3|

− 1

|q2|− 1

|q3|

]10 / 15

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Three-body Problem

Variational

Jacobi coordinates

F (kρ, kλ) = ψ

(kραρ

(kλαλ

)

Minimize

〈N|H|N〉(αρ, αλ)

Parameters αρ, αλ

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Three-body Problem

Binding of three-body forceMY - M∆

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0ccc

ccb

bbc

bbb

Including three-body force → increased binding.

Equal flavour objects more tightly bound than mixed flavour

Little quark mass dependence.

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Page 17: Heavy Baryons: the Rooftops - uni-frankfurt.dedietrich/SLIDES/Williams.pdfHeavy Baryons: the Rooftops Richard Williams and Felipe Llanes-Estrada Dept. F´ısica Te ´orica I, Univ.

Three-body Problem

Faddeev equations in QCDCovariant Faddeev equations

Good news for Faddeev Equations (three-body force neglected).

Nucleon studies suggest quark-diquark picture reasonable.

= + +

Also apply to triply heavy quark systems.

H. Sanchis-Alepuz et al, Phys. Rev. D 84 (2011) 096003.H. Sanchis-Alepuz et al, PoS QCD-TNT-II (2011) 041

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Results in Brief

Results for Ωccc

Predicted MassesNNLO pNRQCD

4800(250) MeV

Covariant Faddeev equations4400 MeV (Gluon model MRT)

4900 MeV (Gluon model AFW)

Parameter FittingIn both approaches, observables from meson sector are fit.(see papers for details)

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Summary

Summary and OutlookSummary

pNRQCD static potential at NLO, NNLO. Fit experimentaldata.

Covariant Faddeev equations in RL. Best fit to experiment.

Constrain triply heavy baryon systems.Three-body force is small at NNLO

Good news for Faddeev equation.

Super-B should pay attention to triple charm

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Backup

Error estimate: Variational MethodCompare to (simple) atomic/molecular systems

Para-Helium Ortho-Helium Dihydrogen cation

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Backup

Error estimate: Variational MethodBinding energies

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Para-Helium

Ortho-Helium

H2

+

Calc

Calc

Calc Para-Helium:−79.0 eV (Calc. −59 eV)

Ortho-Helium:−59.2 eV (Calc. −48 eV)

H+2 :−15.4 eV (Calc. −12.5 eV)

Binding energy underestimated by 25%.For 3-body, sign known.

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