Excited heavy mesons from lattice QCD › conferences › hadron2015 › talks › ...Excited heavy mesons from lattice QCD Christopher Thomas, University of Cambridge Hadron 2015,

Excited heavy mesons from lattice QCD

Christopher Thomas, University of Cambridge

Hadron 2015, Newport News, VA, 13 – 18 Sept. 2015

[email protected]

Hadron Spectrum Collaboration

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Outline

• Introduction

• Excited charmonia

• DK scattering

• Outlook

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X(3872), Y(4260), Z+(4430), Zc+(3900), Zb

+, Ds(2317), ... Exotic 1-+ in charmonium? Gluonic excitations?

Resonances or near threshold

Excited heavy-meson spectroscopy

Exotic JPC (0 - -, 0

+ -, 1 - +, 2

+ -, ...) or flavour quantum numbers – can’t just be a pair

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Excited charmonia from lattice QCD

• Same lattice setup as previous talk

• Variational method with large no. of ‘single-meson’ operators, including ops sensitive to gluonic excitations

• HadSpec, JHEP 07 (2012) 126 [D,Ds mesons in JHEP 05 (2013) 021]

• mp 400 MeV

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JPC

c J/ χc0 χc1 χc2 hc

Excited charmonia

Mp 400 MeV [HadSpec, JHEP 07 (2012) 126]

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Exotics

JPC


Excited charmonia


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S-wave

P-wave

D-wave

F-wave

part of G-wave Exotics

JPC


L ½

½

J = L S

Excited charmonia


4

S-wave

P-wave

D-wave

F-wave

part of G-wave Exotics

JPC


L ½

½

J = L S

Excited charmonia


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JPC

Excited charmonia


in L=0, with gluonic 1+-, scale 1.2 – 1.3 GeV

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JPC

in L=1, with gluonic 1+- Excited charmonia



5


JPC

in L=1, with gluonic 1+- Excited charmonia



Resonances etc?

Can’t study scattering directly in Euclidean time...

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Continuous spectrum above threshold

Discrete spectrum

Infinite volume

Finite volume

Two hadrons

L [periodic b.c.s]

Scattering in lattice QCD

Non-interacting:

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Continuous spectrum above threshold

Discrete spectrum

Infinite volume

Finite volume

Two hadrons

L [periodic b.c.s]

Scattering in lattice QCD

c.f. 1-dim:

scattering phase shift

Non-interacting:

Interacting:

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DK (I=0) scattering and charm-strange mesons

JP = 0+ Ds0*(2317), ...

JP = 1- Ds*, ...

JP = 2+ Ds2*(2573), ...

Isospin = 0 Strangeness = 1 Charm = 1

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JP = 0+ Ds0*(2317), ...

JP = 1- Ds*, ...

JP = 2+ Ds2*(2573), ...

‘single-meson ‘

+ ‘D K ’ operators

Isospin = 0 Strangeness = 1 Charm = 1

mp = 391 MeV, mK = 549 MeV, mD = 1890 MeV; 2 volumes (L ≈ 2 – 3 fm)

CT et al (HadSpec) in preparation (these are preliminary results) [methods in PR D86, 034031; PR D87 034505; PRL 113, 182001; PR D91 054008]

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DK (I=0) spectra

JP = 0+, 4+, ... [ℓ = 0, 4, ...]

P = [0,0,0] A1+

DK

Dsη

L / as

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DK (I=0) spectra

JP = 0+, 4+, ... [ℓ = 0, 4, ...]

P = [0,0,0] A1+

DK

Dsη

L / as

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DK (I=0) spectra

JP = 1-, 3-, (4-), ... [ℓ = 1, 3, ...]

P = [0,0,0] T1-

L / as

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DK (I=0) spectra

|| = 0+, 4, ... [ℓ = 0, 1, 2, 3, 42, ...]

P = [0,0,1] A1

L / as

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Lüscher method scattering phase shifts (elastic DK scattering) Various different:

• parameterizations of the scattering t-matrix (effective range, Breit-Wigner, various K-matrix params.)

• number of energy levels across relevant irreps on two volumes (up to 35 levels)


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DK (I=0): S-wave only P = [0,0,0] A1+

L / as

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P = [0,0,1] A1

L / as

DK (I=0): S and P-waves

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(at k) cot 0

at Ecm

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(at k) cot 0

at Ecm

(at k)3 cot 1

at Ecm

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Pole in t-matrix on real axis (physical sheet): at m ≈ 0.420 m ≈ 2380 MeV Bound state, below DK threshold: at m ≈ 0.010 m ≈ 55 MeV C.f. experimentally for Ds(2317): m ≈ 40-50 MeV


S-wave

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Pole in t-matrix on real axis (physical sheet): at m ≈ 0.420 m ≈ 2380 MeV Bound state, below DK threshold: at m ≈ 0.010 m ≈ 55 MeV C.f. experimentally for Ds(2317): m ≈ 40-50 MeV


Deeply bound state: at m ≈ 0.366 m ≈ 2070 MeV A long way below DK threshold (≈ 2430 MeV) C.f. Ds

*(2112)

S-wave

P-wave

(I=1) scattering

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‘ ’ operators

Isospin = 1 Strangeness = -1 Charm = 1 Flavour exotic

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JP = 0+, 4+, ... [ℓ = 0, 4, ...]

P = [0,0,0] A1+ (I=1) spectra

L / as

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(I=1): S-wave only

/

at Ecm

N.B. just to get rough first idea – ignored higher partial waves and potential coupling to other channels above inelastic thresholds

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• Significant progress in resonances/scattering on the lattice

• Many (multi-hadron) energy levels map out energy dep. of scattering amplitudes in detail

• This talk: some work in charm-strange sector (not as far advanced as our work in light meson sector – talks by David Wilson and Jozef Dudek)

Summary

Summary and outlook

• Many other interesting cases (particularly in charmonium)

• Transitions (talk by Raul Briceño)

• Lighter pion masses etc.

• >2 hadrons is a challenge

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• Significant progress in resonances/scattering on the lattice

• Many (multi-hadron) energy levels map out energy dep. of scattering amplitudes in detail

• This talk: some work in charm-strange sector (not as far advanced as our work in light meson sector – talks by David Wilson and Jozef Dudek)

Summary

Summary and outlook

Outlook

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Excited heavy mesons from lattice QCD › conferences › hadron2015 › talks › ...Excited heavy mesons from lattice QCD Christopher Thomas, University of Cambridge Hadron 2015,

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