excited heavy mesons from lattice qcd › conferences › hadron2015 › talks › ...excited heavy...
TRANSCRIPT
Excited heavy mesons from lattice QCD
Christopher Thomas, University of Cambridge
Hadron 2015, Newport News, VA, 13 – 18 Sept. 2015
Hadron Spectrum Collaboration
1
Outline
• Introduction
• Excited charmonia
• DK scattering
• Outlook
2
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
3
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
4
JPC
c J/ χc0 χc1 χc2 hc
Excited charmonia
Mp 400 MeV [HadSpec, JHEP 07 (2012) 126]
4
Exotics
JPC
c J/ χc0 χc1 χc2 hc
Excited charmonia
Mp 400 MeV [HadSpec, JHEP 07 (2012) 126]
4
S-wave
P-wave
D-wave
F-wave
part of G-wave Exotics
JPC
c J/ χc0 χc1 χc2 hc
L ½
½
J = L S
Excited charmonia
Mp 400 MeV [HadSpec, JHEP 07 (2012) 126]
4
S-wave
P-wave
D-wave
F-wave
part of G-wave Exotics
JPC
c J/ χc0 χc1 χc2 hc
L ½
½
J = L S
Excited charmonia
Mp 400 MeV [HadSpec, JHEP 07 (2012) 126]
5
c J/ χc0 χc1 χc2 hc
JPC
Excited charmonia
Mp 400 MeV [HadSpec, JHEP 07 (2012) 126]
in L=0, with gluonic 1+-, scale 1.2 – 1.3 GeV
5
c J/ χc0 χc1 χc2 hc
JPC
in L=1, with gluonic 1+- Excited charmonia
Mp 400 MeV [HadSpec, JHEP 07 (2012) 126]
in L=0, with gluonic 1+-, scale 1.2 – 1.3 GeV
5
c J/ χc0 χc1 χc2 hc
JPC
in L=1, with gluonic 1+- Excited charmonia
Mp 400 MeV [HadSpec, JHEP 07 (2012) 126]
in L=0, with gluonic 1+-, scale 1.2 – 1.3 GeV
Resonances etc?
Can’t study scattering directly in Euclidean time...
6
Continuous spectrum above threshold
Discrete spectrum
Infinite volume
Finite volume
Two hadrons
L [periodic b.c.s]
Scattering in lattice QCD
Non-interacting:
6
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:
7
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
7
DK (I=0) scattering and charm-strange mesons
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]
8
DK (I=0) spectra
JP = 0+, 4+, ... [ℓ = 0, 4, ...]
P = [0,0,0] A1+
DK
Dsη
L / as
8
DK (I=0) spectra
JP = 0+, 4+, ... [ℓ = 0, 4, ...]
P = [0,0,0] A1+
DK
Dsη
L / as
9
DK (I=0) spectra
JP = 1-, 3-, (4-), ... [ℓ = 1, 3, ...]
P = [0,0,0] T1-
L / as
10
DK (I=0) spectra
|| = 0+, 4, ... [ℓ = 0, 1, 2, 3, 42, ...]
P = [0,0,1] A1
L / as
11
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)
DK (I=0) scattering and charm-strange mesons
12
DK (I=0): S-wave only P = [0,0,0] A1+
L / as
13
P = [0,0,1] A1
L / as
DK (I=0): S and P-waves
14
DK (I=0): S and P-waves
(at k) cot 0
at Ecm
14
DK (I=0): S and P-waves
(at k) cot 0
at Ecm
(at k)3 cot 1
at Ecm
15
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
DK (I=0): S and P-waves
S-wave
15
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
DK (I=0): S and P-waves
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
16
‘ ’ operators
Isospin = 1 Strangeness = -1 Charm = 1 Flavour exotic
17
JP = 0+, 4+, ... [ℓ = 0, 4, ...]
P = [0,0,0] A1+ (I=1) spectra
L / as
18
(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
19
• 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
19
• 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
20