QCD to XYZFrom quarks and gluons to exotic hadrons
Daniel Mohler
Graz,April 27, 2016
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 1 / 35
Quantum Chromodynamics (QCD) and hadrons
QCD: Theory that describes the strong interaction between quarks and gluonswithin the Standard Model of Particle Physics
Asymptotic Freedom: Theory perturbative athigh energies/short distances→ Perturbative calculations for high-energyphysics
Confinement: Color-charged particles do not exist individually but onlyconfined into composite objects called hadrons.Textbook classification: Quark-antiquark mesons and three-quark baryons
→
c©Arpad Horvath
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 2 / 35
Exotic mesons in the heavy-quark spectrum
Surprise results from the Belle and BaBar experiments(built to investigate the difference between matter and antimatter):
X(3872):PRL 91 262001 (2003)
D∗s0(2317):PRL 90 242001 (2003)
Y(4260):PRL 95 142001 (2005)
)2) (GeV/cψJ/-π+πm(
3.8 4 4.2 4.4 4.6 4.8 5
2E
ven
ts /
20
MeV
/c
0
10
20
30
40
)2) (GeV/cψJ/-π+πm(
3.8 4 4.2 4.4 4.6 4.8 5
2E
ven
ts /
20
MeV
/c
0
10
20
30
40
)2) (GeV/cψJ/-π+πm(
3.8 4 4.2 4.4 4.6 4.8 5
2E
ven
ts /
20
MeV
/c
0
10
20
30
40
)2) (GeV/cψJ/-π+πm(
3.8 4 4.2 4.4 4.6 4.8 5
2E
ven
ts /
20
MeV
/c
0
10
20
30
40
3.6 3.8 4 4.2 4.4 4.6 4.8 51
10
210
310
410
Highest-cited Belle paperThird-most cited BaBarpaper
Fourth-most cited BaBarpaper
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 3 / 35
10 years later: Many more surprises
Y(4140): CDF, CMS
m [GeV]∆1.1 1.2 1.3 1.4 1.5
) / 2
0 M
eV+
N(B
0
50
100
150
200
250
300-1 = 7 TeV, L=5.2 fbsCMS,
Data
Three-body PS (global fit)
)+, Kφ,ψEvent-mixing (J/ )+ Kφ,ψEvent-mixing (J/
Global fit
1D fit
uncertainty bandσ1±
Zc(3900)±: BESIII,Belle, data from Cleo
)2) (GeV/cψJ/±π(maxM3.7 3.8 3.9 4.0
2E
ve
nts
/ 0
.01
Ge
V/c
0
20
40
60
80
100
)2) (GeV/cψJ/±π(maxM3.7 3.8 3.9 4.0
2E
ve
nts
/ 0
.01
Ge
V/c
0
20
40
60
80
100
)2) (GeV/cψJ/±π(maxM3.7 3.8 3.9 4.0
2E
ve
nts
/ 0
.01
Ge
V/c
0
20
40
60
80
100Data
Total fit
Background fit
PHSP MC
Sideband
Z(4430)±: Belle, LHCb
]2 [GeV2 −π'ψm16 18 20 22
)2C
andi
date
s / (
0.2
GeV
0
500
1000LHCb
Zb(10610)+,Zb(10650)+:Belle
-2000
0
2000
4000
6000
8000
10000
12000
10.4 10.5 10.6 10.7
Mmiss(π), GeV/c2
Events
/ 1
0 M
eV
/c2
(a)
Zc(4020)±: BESIII
)2(GeV/cch±π
M3.7 3.8 3.9 4.0 4.1 4.2
)2
Even
ts/
( 0.0
05G
eV
/c
0
20
40
60
80
100
120
Pc(4450),Pc(4380):LHCb
[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)
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 4 / 35
Exotic hadron spectroscopy: experiment↔ theory
Vigorous and varied experiment program(current and planned)Heavy mesons: LHCb, BESIII, PANDA, BelleII, . . .Light mesons: GlueX, MesonEx, COMPASS, . . .Baryons: CLAS12, ELSA, E45@JPARC, MAMI . . .
Should be accompanied by an equally vigorous theory effort
Current theory understanding of states with exotic properties relies onmodels rather than first-principle calculations.Molecules, Tetraquarks, Hybrid mesons, etc.
Many models – and none match all observations
The research I pursue will aid the understanding of exotic heavy mesonsdirectly from QCD
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 5 / 35
Exotic hadron spectroscopy: experiment↔ theory
Vigorous and varied experiment program(current and planned)Heavy mesons: LHCb, BESIII, PANDA, BelleII, . . .Light mesons: GlueX, MesonEx, COMPASS, . . .Baryons: CLAS12, ELSA, E45@JPARC, MAMI . . .
Should be accompanied by an equally vigorous theory effort
Current theory understanding of states with exotic properties relies onmodels rather than first-principle calculations.Molecules, Tetraquarks, Hybrid mesons, etc.
Many models – and none match all observations
The research I pursue will aid the understanding of exotic heavy mesonsdirectly from QCD
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 5 / 35
Exotic hadron spectroscopy: experiment↔ theory
Vigorous and varied experiment program(current and planned)Heavy mesons: LHCb, BESIII, PANDA, BelleII, . . .Light mesons: GlueX, MesonEx, COMPASS, . . .Baryons: CLAS12, ELSA, E45@JPARC, MAMI . . .
Should be accompanied by an equally vigorous theory effort
Current theory understanding of states with exotic properties relies onmodels rather than first-principle calculations.Molecules, Tetraquarks, Hybrid mesons, etc.
Many models – and none match all observations
The research I pursue will aid the understanding of exotic heavy mesonsdirectly from QCD
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 5 / 35
Outline
1 Introduction and MotivationHadrons - the bound states of quarks and gluonsQuantum Chromodynamics (QCD) and the Lattice
2 Modern lattice hadron spectroscopySpectroscopy and properties of bound statesWhat about resonances/ threshold states?The simplest resonance: The ρ mesonΨ(3770) - a heavier brother of the ρ
3 Towards exotic hadronsD∗s0(2317) and Ds1(2460) and their b-quark cousinsχ′c0 and X/Y(3915)
4 Summary and future research directions
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 6 / 35
Lattice Quantum Chromodynamics: What do we calculate?
Regularization of QCD by a 4-d Euclidean space-timelattice. (Kenneth Wilson 1974)Provides a calculational method for QCD
Euclidean correlator of two Hilbert-space operators O1 and O2.⟨O2(t)O1(0)
⟩=∑
n
e−t∆En〈0|O2|n〉〈n|O1|0〉
=1Z
∫D[ψ, ψ,U]e−SE O2[ψ, ψ,U]O1[ψ, ψ,U]
Last line is a path integral over the Euclidean action SE,QCD[ψ, ψ,U];(a sum over quantum fluctuations)
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 7 / 35
Lattice QCD: What do we calculate?
Fermion integral can be done explicitly
Rest can be evaluated with Monte Carlo simulations using methods wellestablished in statistical physics
ψquarks:
gluons: Uµ
}
a
Λ
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 8 / 35
Why Lattice Quantum Chromodynamics?
Understand the theory of the strong interaction at low energiesConfinement and hadron propertiesChiral Symmetry breaking
(QCD dynamics responsible for > 98% of the nucleon mass)Lattice QCD as a tool to understand strong-interaction contributions
precision flavor physicsmuon physics (g− 2, . . . )neutrino physicsdark matter searchesHiggs boson decays (precision quark masses)
QCD for hadronic (and nuclear) physicsUnderstand hadronic degrees of freedom (and how they arise)Understand connection to nuclei and their properties
Lattice QCD is a non-perturbative, systematically improvable method leadingto quantifiable uncertainties
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 9 / 35
Stable hadron states: A lattice success story
Light mesons and baryons
Example from BMWDürr et al. Science 322 (2008)
Heavy mesons
0
2
4
6
8
10
12
MES
ON
MA
SS (G
eV/c
2 )
c J/
’c
’
hc c0c1c2
b
’b
’’’
b0b1(1P)b2b0b1(2P)b2
(1D)hb(1P)
hb(2P)
Bc
Bc’
BsBB*
sB*
B*c
B*’c B*
c0
DsD
K
exptfix params
postdcnspredcns
Example from HPQCDDowdall et al. PRD 86 094510 (2012)
Hadrons stable under QCD: full control of systematic uncertaintiesRoutinely done for a wide variety of observables(for example for flavor physics)Goal: Extend this success to hadron resonancesDaniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 10 / 35
Two kinds of progress...
Precision results:
1.14 1.18 1.22 1.26
=+
+=
+=
QCDSF/UKQCD 07 ETM 09 ETM 10D (stat. err. only) BGR 11 ALPHA 13
our estimate for =
MILC 04 NPLQCD 06 HPQCD/UKQCD 07 RBC/UKQCD 08 PACS-CS 08, 08A Aubin 08 MILC 09 MILC 09A JLQCD/TWQCD 09A (stat. err. only) BMW 10 PACS-CS 09 RBC/UKQCD 10A JLQCD/TWQCD 10 MILC 10 Laiho 11 RBC/UKQCD 12
our estimate for = +
ETM 10E (stat. err. only) MILC 11 (stat. err. only) MILC 13A HPQCD 13A ETM 13F
our estimate for = + +
/
Example: FLAG reviewSee http://itpwiki.unibe.ch/flag/
Exploratory studies:
-500
-300
-100
600 800 1000 1200 1400 1600
Example: πK-ηK-scatteringDudek et al. PRL 113 182001 (2014)
I will report on exploratory calculations with regard to heavy mesonresonances and bound states
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 11 / 35
Observables: Examples for correlation functions
Need: Interpolating field operator that creates states with correct quantumnumbers.
Example I: Pseudoscalar Mesons with IJPC = 10−+
O(1)π = uγ5d
O(2)π = u
←→D γiγtγ5d
Can obtain mass from 2-point correlator with Oπ and Oπ
Example II: Nucleon
ON = εabc Γ1 ua(uT
b Γ2 dc − dTb Γ2 uc
)In practice: Many (slightly different) constructions possible!
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 12 / 35
(My) Method of choice: The variational method
Matrix of correlators projected to fixed momentum (will assume 0)
C(t)ij =∑
n
e−tEn 〈0|Oi|n〉⟨
n|O†j |0⟩
Solve the generalized eigenvalue problem:
C(t)~ψ(k) = λ(k)(t)C(t0)~ψ(k)
λ(k)(t) ∝ e−tEk(1 +O
(e−t∆Ek
))At large time separation: only a single state in each eigenvalue.Eigenvectors can serve as a fingerprint.Michael Nucl. Phys. B259, 58 (1985)
Lüscher and Wolff Nucl. Phys. B339, 222 (1990)
Blossier et al. JHEP 04, 094 (2009)
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 13 / 35
Technicalities: The “Distillation” method
Peardon et al. PRD 80, 054506 (2009)Morningstar et al. PRD 83, 114505 (2011)
Idea: Construct separable quark smearing operator using low modes ofthe 3D lattice LaplacianSpectral decomposition for an N × N matrix:
f (A) =
N∑k=1
f (λ(k)) v(k)v(k)†.
With f (∇2) = Θ(σ2s +∇2) (Laplacian-Heaviside (LapH) smearing):
qs ≡N∑
k=1
Θ(σ2s + λ(k))v(k)v(k)† q =
Nv∑k=1
v(k)v(k)† q .
Advantages: momentum projection at source; large interpolator freedom,small storageDisadvantages: expensive; unfavorable volume scalingStochastic approach (mostly) eliminates bad volume scalingDaniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 14 / 35
Using single hadron interpolators, what do we see?
In practical calculations qq and qqq interpolators couple very weakly tomulti-hadron states
McNeile & Michael, Phys. Lett. B 556, 177 (2003); Engel, DM et al. PRD 82, 034505(2010);
Bulava et al. PRD 82, 014507(2010); Dudek et al. PRD 82, 034508(2010);
This is not unlike observations in string breaking studiesPennanen & Michael hep-lat/0001015;Bernard et al. PRD 64 074509 2001;
This necessitates the inclusion of hadron-hadron interpolators
We know: Energy levels 6= resonance massesNaïve expectation: Correct up to O(ΓR(mπ))
Was good enough for heavy pion masses where one would deal withbound states or very narrow resonances.
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 15 / 35
An example: Different rho momentum frames
0.4
0.6
0.8
1E
n a
1 2 3 4 5 6 7 8
1
0.4
0.6
0.8
1
En a
1 2 3 4 5 6 7 8interpolator set
0.4
0.6
0.8
1
En a
interpolator set:
qq ππ
1: O1,2,3,4,5
, O6
2: O1,2,3,4
, O6
3: O1,2,3
, O6
4: O2,3,4,5
, O6
5: O1 , O
6
6: O1,2,3,4,5
7: O1,2,3,4
8: O1,2,3
P=(1,1,0)
P=(0,0,1)
P=(0,0,0)
with ππ without ππ
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 16 / 35
Scattering in finite volume: The Lüscher method
M. Lüscher Commun. Math. Phys. 105 (1986) 153;Nucl. Phys. B 354 (1991) 531; Nucl. Phys. B 364 (1991) 237.
E = E(p1) + E(p2) E = E(p1) + E(p2) + ∆E
En(L)(2)−−→ δl
(3)−−→ mR; ΓR or coupling g
(1) Extract energy levels En(L) in a finite box(2) Lüscher formula→ phase shift of the continuum scattering amplitude(3) Extract resonance parameters (similar to experiment)
2-hadron scattering and transitions well understood;progress for 3 (or more) hadrons but difficult
See LATTICE plenaries by Raúl A. Briceño arXiv:1411.6944and Max Hansen arXiv:1511.04737
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 17 / 35
A look at the Particle Data Group booklet
I will discuss the following examples:
Light hadrons Heavy-light hadrons
+ b-quark analogues
Charmonium
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 18 / 35
Studies within our collaboration (look at the past)
ππ scattering and ρ meson widthLang, DM, Prelovsek, Vidmar, PRD 84 054503 (2011)
Kπ scatteringLang, Leskovec, DM, Prelovsek, PRD 86 054508 (2012)Prelovsek, Lang, Leskovec, DM, PRD 88 054508 (2013)
πρ and πω scattering and the a1, b1 resonancesLang, Leskovec, DM, Prelovsek, JHEP 1404 162 (2014)
D mesons including Dπ and D?π with relativistic charm quarksDM, Prelovsek, Woloshyn, PRD 87 034501 (2013)
D∗s0(2317) and Ds1(2460) with qq and D(∗)KDM, Lang, Leskovec, Prelovsek, Woloshyn, PRL 111 222001 (2013)
PRD 90 034510 (2014)
Predicting Bs states with JP = 0+, 1+
Lang, Prelovsek, DM, Woloshyn, Phys. Lett.B750 17-21 (2015)
Heavy meson scattering and charmoniumPrelovsek & Leskovec PRL 111 192001 (2013)
Prelovsek & Leskovec, Phys.Lett. B727 172 (2013)Prelovsek, Lang, Leskovec, DM, PRD 91 014504 (2015)Lang, Leskovec, DM, Prelovsek, JHEP 1509 089 (2015)
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 19 / 35
Technicalities: Lattices used
ID N3L × NT Nf a[fm] L[fm] #configs mπ[MeV] mK[MeV]
(1) 163 × 32 2 0.1239(13) 1.98 280/279 266(3)(3) 552(2)(6)(2) 323 × 64 2+1 0.0907(13) 2.90 196 156(7)(2) 504(1)(7)
Ensemble (1) has 2 flavors of nHYP-smeared quarksGauge ensemble from Hasenfratz et al. PRD 78 054511 (2008)
Hasenfratz et al. PRD 78 014515 (2008)
Ensemble (2) has 2+1 flavors of Wilson-Clover quarks
PACS-CS, Aoki et al. PRD 79 034503 (2009)
On the small volume we use distillationOn the larger volume we use stochastic distillation
Peardon et al. PRD 80, 054506 (2009);
Morningstar et al. PRD 83, 114505 (2011)
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 20 / 35
The ρ resonance - a benchmark calculation
From Lang, DM, Prelovsek, Vidmar, PRD 84 054503 (2011); erratum ibid;
0.1 0.15 0.2 0.25 0.3 0.35 0.4s
0
50
100
150
δ1
gρππ
= 5.61(12); mρ = 0.4846(37)
lattice data
We extract gρππ rather than Γ
Γ(s) =p?3
sg2ρππ
6πResults for mπ = 266(3)(3)MeV
gρππ = 5.61(12) mρ = 772(6)(8) MeV
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 21 / 35
The ρ resonance - comparing results for the coupling
g(phys)ρππ ≈ 5.97 mρ = 775.11(34) MeV
0 100 200 300 400 500M
π/MeV
4
4.5
5
5.5
6
6.5
7
7.5g
ρπ
πPACS-CS (2011)
Lang et al. (2011)
ETMC (2011)
physical value
Caution: To date no simulation with full control of systematics
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 22 / 35
The ρ resonance - comparing results for the coupling
g(phys)ρππ ≈ 5.97 mρ = 775.11(34) MeV
0 100 200 300 400 500M
π/MeV
4
4.5
5
5.5
6
6.5
7
7.5g
ρπ
πPACS-CS (2011)
Lang et al. (2011)
ETMC (2011)
GWU (2012)
HSC (2012)
GWU (2015)
HSC (2015)
Bulava et al. (2015)
Bali et al. (2015)
physical value
Caution: To date no simulation with full control of systematics
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 22 / 35
ρ resonance: Another look at an incomplete basis
Wilson et al. PRD 92 094502 (2015)
0
30
60
90
120
150
180
0.08 0.10 0.12 0.14 0.16
At first sight spectrum seems well determinedEnergy levels cluster close to resonance energy
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 23 / 35
Ψ(3770) resonanceLang, Leskovec, DM, Prelovsek, JHEP 1509 089 (2015)
fit (i) fit (ii)
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
E [
GeV
]
fit (i) fit (ii)
D(0)D_
(0)
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
mD
++mD
-
2mD
0
mπ = 266 MeV mπ=156 MeV exp.
J/ψ
ψ(2S)
ψ(3770)
Mass [MeV] gΨ(3770)DDEnsemble(1) 3784(7)(8) 13.2 (1.2)Ensemble(2) 3786(56)(10) 24(19)Experiment 3773.15(33) 18.7(1.4)
First resonance determination of a charmonium stateProof of principle - many improvements possibleDaniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 24 / 35
Exotic Ds (charm-strange) and Bs (bottom-strange)candidates
Established s and p-wave states:
Ds (JP = 0−) and D∗s (1−)D∗s0(2317) (0+), Ds1(2460) (1+),Ds1(2536) (1+), D∗s2(2573) (2+)
Bs (JP = 0−) and B∗s (1−)
Bs1(5830) (1+), B∗s2(5840) (2+)
Peculiarity: Mcs ≈ Mcd → exotic structure? (tetraquark, molecule)
Traditional lattice studies (using single hadron operators) tend get toolarge or badly determined masses
Observed Bs p-wave states from two body decays into K−B+
(CDF/D0 and LHCb)
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 25 / 35
Exotic Ds (charm-strange) and Bs (bottom-strange)candidates
Established s and p-wave states:
Ds (JP = 0−) and D∗s (1−)D∗s0(2317) (0+), Ds1(2460) (1+),Ds1(2536) (1+), D∗s2(2573) (2+)
Bs (JP = 0−) and B∗s (1−)
Bs1(5830) (1+), B∗s2(5840) (2+)
Peculiarity: Mcs ≈ Mcd → exotic structure? (tetraquark, molecule)
Traditional lattice studies (using single hadron operators) tend get toolarge or badly determined masses
Observed Bs p-wave states from two body decays into K−B+
(CDF/D0 and LHCb)
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 25 / 35
Exotic Ds (charm-strange) and Bs (bottom-strange)candidates
Established s and p-wave states:
Ds (JP = 0−) and D∗s (1−)D∗s0(2317) (0+), Ds1(2460) (1+),Ds1(2536) (1+), D∗s2(2573) (2+)
Bs (JP = 0−) and B∗s (1−)
Bs1(5830) (1+), B∗s2(5840) (2+)
Peculiarity: Mcs ≈ Mcd → exotic structure? (tetraquark, molecule)
Traditional lattice studies (using single hadron operators) tend get toolarge or badly determined masses
Observed Bs p-wave states from two body decays into K−B+
(CDF/D0 and LHCb)
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 25 / 35
Discretization effects for charm and beauty
10−2
10−1
from
1/2
mB
HQET for heavy-light
relative error
10−2
10−1
from
1/4
mE2
0.01 0.1a (fm)
10−3
10−2
10−1
from
1/8
m43
10−2
10−1
from
1/2
mB
NRQCD for quarkonia
relative error
10−2
10−1
from
1/4
mE2
0.01 0.1a (fm)
10−3
10−2
10−1
from
1/8
m43
10−2
10−1
from
w4/6
HQET for heavy-light
relative error
10−2
10−1
from
wB
i/4
0.01 0.1a (fm)
10−3
10−2
10−1
from
(w
4 +
w4′ )/
4
10−2
10−1
from
w4/6
NRQCD for quarkonia
relative error
10−2
10−1
from
wB
i/4
0.01 0.1a (fm)
10−3
10−2
10−1
from
(w
4 +
w4′ )/
4
From Oktay, Kronfeld, PRD 78 014504 (2008)
We still expect sizable discretization effects for bottomonium andcharm-light statesSome discretization effects remain sizable for at < as ≈ 0.1fmModified dispersion relation makes moving frames not straight-forwardDaniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 26 / 35
Testing our tuning: charm and beauty
Ensemble (1) Ensemble (2) ExperimentmJ/Ψ − mηc 107.9(0.3)(1.1) 107.1(0.2)(1.5) 113.2(0.7)mD∗
s− mDs 120.4(0.6)(1.3) 142.1(0.7)(2.0) 143.8(0.4)
mD∗ − mD 129.4(1.8)(1.4) 148.4(5.2)(2.1) 140.66(10)2mD − mcc 890.9(3.3)(9.3) 882.0(6.5)(12.6) 882.4(0.3)2MDs
− mcc 1065.5(1.4)(11.2) 1060.7(1.1)(15.2) 1084.8(0.6)mDs − mD 96.6(0.9)(1.0) 94.0(4.6)(1.3) 98.87(29)mB∗ − mB - 46.8(7.0)(0.7) 45.78(35)
mBs∗ − mBs - 47.1(1.5)(0.7) 48.7+2.3−2.1
mBs − mB - 81.5(4.1)(1.2) 87.35(23)mY − mηb - 44.2(0.3)(0.6) 62.3(3.2)2mB − mbb - 1190(11)(17) 1182.7(1.0)2mBs
− mbb - 1353(2)(19) 1361.7(3.4)2mBc − mηb − mηc - 169.4(0.4)(2.4) 167.3(4.9)
Errors statistical and scale setting only
Bottom quark slightly too light
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 27 / 35
D∗s0(2317): D-meson – Kaon s-wave scatteringM. Lüscher Commun. Math. Phys. 105 (1986) 153;
Nucl. Phys. B 354 (1991) 531; Nucl. Phys. B 364 (1991) 237.
p cot δ(p) =2√πL
Z00(1; q2)
≈ 1a0
+12
r0p2
Mohler et al. PRL 111 222001 (2013)Lang, DM et al. PRD 90 034510 (2014)
Results for ensembles (1) and (2)
-0.1 0 0.1 0.2 0.3 0.4 0.5
p2 [GeV
2]
-1
-0.8
-0.6
-0.4
-0.2
0
p c
ot
δ [
GeV
]
1 2
a0 = −0.756± 0.025fm (1)
r0 = −0.056± 0.031fm
a0 = −1.33± 0.20fm (2)
r0 = 0.27± 0.17fm
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 28 / 35
D∗s0(2317): D-meson – Kaon s-wave scatteringM. Lüscher Commun. Math. Phys. 105 (1986) 153;
Nucl. Phys. B 354 (1991) 531; Nucl. Phys. B 364 (1991) 237.
p cot δ(p) =2√πL
Z00(1; q2)
≈ 1a0
+12
r0p2
Mohler et al. PRL 111 222001 (2013)Lang, DM et al. PRD 90 034510 (2014)
Results for ensembles (1) and (2)
-0.1 0 0.1 0.2 0.3 0.4 0.5
p2 [GeV
2]
-1
-0.8
-0.6
-0.4
-0.2
0
p c
ot
δ [
GeV
]
1 2
a0 = −0.756± 0.025fm (1)
r0 = −0.056± 0.031fm
a0 = −1.33± 0.20fm (2)
r0 = 0.27± 0.17fm
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 28 / 35
B∗s0 and Bs1: Results
B∗s0
aBK0 = −0.85(10) fm
rBK0 = 0.03(15) fm
MB∗s0
= 5.711(13) GeV
Bs1aB∗K
0 = −0.97(16) fm
rB∗K0 = 0.28(15) fm
MBs1 = 5.750(17) GeV
Energy from the difference to the B(∗)K threshold
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 29 / 35
Spectrum resultsMohler et al. PRL 111 222001 (2013)Lang, DM et al. PRD 90 034510 (2014)
Lang, Mohler, Prelovsek, Woloshyn PLB 750 17 (2015)
-200
-100
0
100
200
300
400
500
600
m -
(m
Ds+
3m
Ds*
)/4 [M
eV]
Ensemble (1)
-200
-100
0
100
200
300
400
500
600
PDGLat: energy level
Lat: bound state from phase shift
Ensemble (2)
Ds D
s D
s0 D
s1 D
s1 D
s2
JP : 0
- 1
- 0
+ 1
+ 1
+ 2
+
Ds D
s D
s0 D
s1 D
s1 D
s2
0- 1
- 0
+ 1
+ 1
+ 2
+
* * * * * *
Discretization uncertaintiessizeable for charm
Many improvements possible forthe Ds states
Full uncertainty estimate only formagenta Bs states
Prediction of exotic states fromLattice QCD!
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 30 / 35
Spectrum resultsMohler et al. PRL 111 222001 (2013)Lang, DM et al. PRD 90 034510 (2014)
Lang, Mohler, Prelovsek, Woloshyn PLB 750 17 (2015)
-200
-100
0
100
200
300
400
500
600
m -
(m
Ds+
3m
Ds*
)/4 [M
eV]
Ensemble (1)
-200
-100
0
100
200
300
400
500
600
PDGLat: energy level
Lat: bound state from phase shift
Ensemble (2)
Ds D
s D
s0 D
s1 D
s1 D
s2
JP : 0
- 1
- 0
+ 1
+ 1
+ 2
+
Ds D
s D
s0 D
s1 D
s1 D
s2
0- 1
- 0
+ 1
+ 1
+ 2
+
* * * * * *
Discretization uncertaintiessizeable for charm
Many improvements possible forthe Ds states
5.3
5.4
5.5
5.6
5.7
5.8
5.9
m [
GeV
]
PDGLat: energy level
Lat: bound state from phase shift
Ensemble (2) mπ = 156 MeV
B*K
B K
Bs B
s
* B
s0
* B
s1 B
s1’ B
s2
JP: 0
- 1
- 0
+ 1
+ 1
+ 2
+
Full uncertainty estimate only formagenta Bs states
Prediction of exotic states fromLattice QCD!
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 30 / 35
Comparing to models
0+ 1+
Covariant (U)ChPT 5726(28) 5778(26)NLO UHMChPT 5696(20)(30) 5742(20)(30)LO UChPT 5725(39) 5778(7)LO χ-SU(3) 5643 5690Bardeen, Eichten, Hill 5718(35) 5765(35)rel. quark model 5804 5842rel. quark model 5833 5865rel. quark model 5830 5858HPQCD 2010 5752(16)(5)(25) 5806(15)(5)(25)this work 5713(11)(19) 5750(17)(19)
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 31 / 35
χ′c0 and X/Y(3915)
PDG interprets X(3915) as a regular charmonium (χ′c0)
Some of the reasons to doubt this assignment:
Guo, Meissner Phys. Rev. D86, 091501 (2012)
Olsen, arXiv 1410.6534
No evidence for fall-apart mode X(3915)→ DDSpin splitting mχc2(2P) − mχc0(2P) too smallLarge OZI suppressed X(3915)→ ωJ/ψWidth should be significantly larger than Γχc2(2P)
Zhou et al. (PRL 115 2, 022001 (2015)) argue that what is dubbedX(3915) is the spin 2 state already known and suggests that a broaderstate is hiding in the experiment data.
Investigate DD scattering in S-wave on the lattice!
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 32 / 35
χ′c0 and X/Y(3915)
PDG interprets X(3915) as a regular charmonium (χ′c0)
Some of the reasons to doubt this assignment:
Guo, Meissner Phys. Rev. D86, 091501 (2012)
Olsen, arXiv 1410.6534
No evidence for fall-apart mode X(3915)→ DDSpin splitting mχc2(2P) − mχc0(2P) too smallLarge OZI suppressed X(3915)→ ωJ/ψWidth should be significantly larger than Γχc2(2P)
Zhou et al. (PRL 115 2, 022001 (2015)) argue that what is dubbedX(3915) is the spin 2 state already known and suggests that a broaderstate is hiding in the experiment data.
Investigate DD scattering in S-wave on the lattice!
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 32 / 35
χ′c0: Exploratory lattice calculation
Lang, Leskovec, DM, Prelovsek, JHEP 1509 089 (2015)
-0.6 -0.4 -0.2 0.0 0.2 0.4
p2[GeV
2]
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
p co
tδ/√
s
(a)
-0.6 -0.4 -0.2 0.0 0.2 0.4
p2[GeV
2]
(b)
-0.6 -0.4 -0.2 0.0 0.2 0.4
p2[GeV
2]
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
p co
tδ/√
s
(c)
Assumes only DD is relevant
Lattice data suggests a fairly narrow resonance with3.9GeV < M < 4.0GeV and Γ < 100MeV
Future experiment and lattice QCD results needed to clarify the situation
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 33 / 35
Emerging understanding from QCD
ηc Ψ h
cχ
c0χ
c1χ
c2η
c2 Ψ2
Ψ3
hc3
χc3
-100
0
100
200
300
400
500
600
700
800
900
1000
1100
m-m_ c_ c [
MeV
]
Ds
Ds*D
s0* D
s1D
s1D
s2*
-200-1000100200300400500600
m -
m_ Ds [
MeV
]
D D* D0*D
1D
1D2*D
2
0
200
400
600
800
m-m_
D [
MeV
]
lat: naive levelres. / bound state
Comprehensive studies where feasiblespectrum around lowest few thresholdsradiative transitions
Extend exploratory results to higher masses and search for manifestlyexotic statesDaniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 34 / 35
. . .
Thank you!
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 35 / 35
. . .
Backup Slides
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 36 / 35
First examples of emerging understanding from QCD
-200
-100
0
100
200
300
400
500
600
m -
(m
Ds+
3mD
s*)/
4 [
MeV
]
Ensemble (1) mπ = 266 MeV
-200
-100
0
100
200
300
400
500
600
PDGLat: energy levelLat: bound state from phase shift
Ensemble (2) mπ = 156 MeV
Ds D
s D
s0 D
s1 D
s1 D
s2
JP : 0
- 1
- 0
+ 1
+ 1
+ 2
+
Ds D
s D
s0 D
s1 D
s1 D
s2
0- 1
- 0
+ 1
+ 1
+ 2
+
* * * * * *
Mohler et al. PRL 111 222001
5.3
5.4
5.5
5.6
5.7
5.8
5.9
m [
GeV
]
PDGLat: energy levelLat: bound state from phase shift
Ensemble (2) mπ = 156 MeV
B*K
B K
Bs B
s
* B
s0
* B
s1 B
s1’ B
s2
JP: 0
- 1
- 0
+ 1
+ 1
+ 2
+
Lang, DM et al. PLB 750 17
lattice (mπ~266 MeV)
400
500
600
700
800
900
1000
1100
m -
1/4
(m
η c+3
mJ/
ψ)
[M
eV]
Exp
D(0)D*(0)
J/ψ(0)ω(0)
D(1)D*(-1)
χc1
(1P)
X(3872)
χc1
(1P)
X(3872)
O: cc O: cc DD* J/ψ ω
poleL→∞
Prelovsek, Leskovec, PRL 111
192001 (2013)
400
600
800
1000
1200
1400
E -
E(1
S) M
eV
D(0)D*(0)
D(-1)D*(1)
cc (I=0) cc + DD* (I=0) DD* (I=0)
Lee, DM et al. arXiv:1411.1389
Examples of bound states with a large four-quark component
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 37 / 35
Testing our tuning: charm and light
Ensemble (1) Ensemble (2) Experimentmπ 266(3)(3) 156(7)(2) 139.5702(4)mK 552(1)(6) 504(1)(7) 493.677(16)mφ 1015.8(1.8)(10.7) 1018.4(2.8)(14.6) 1019.455(20)mηs 732.3(0.9)(7.7) 692.9(0.5)(9.9) 688.5(2.2)*
mJ/Ψ − mηc 107.9(0.3)(1.1) 107.1(0.2)(1.5) 113.2(0.7)mD∗
s− mDs 120.4(0.6)(1.3) 142.1(0.7)(2.0) 143.8(0.4)
mD∗ − mD 129.4(1.8)(1.4) 148.4(5.2)(2.1) 140.66(10)2mD − mcc 890.9(3.3)(9.3) 882.0(6.5)(12.6) 882.4(0.3)2MDs
− mcc 1065.5(1.4)(11.2) 1060.7(1.1)(15.2) 1084.8(0.6)mDs − mD 96.6(0.9)(1.0) 94.0(4.6)(1.3) 98.87(29)
A single ensemble: Discrepancies due to discretization and unphysicallight-quark masses expected
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 38 / 35
D∗s0(2317) including D meson - Kaon
DM, Lang, Leskovec, Prelovsek, Woloshyn, PRL 111 222001 (2013)
0
100
200
300
400
500
600
700
800
900
M -
M1S
[M
eV]
Ensemble (1)
0
100
200
300
400
500
600
700
800
900Ensemble (2)
qq qq qq + DKqq + DK
Much better quality of the ground state plateau with combined basisD∗s0(2317) as a QCD bound stateSuggests that including multi-hadron levels is vitalDaniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 39 / 35
Previous lattice results
NRQCD b quarks and staggered light quarksStates predicted slightly below the B(∗)K thresholds:
MB∗s0
= 5752(16)(5)(25) MBs1 = 5806(15)(5)(25)
Gregory et al. PRD 83 014506 (2011)
Static-light mesons with the transition amplitude method
McNeile, Michael, Thompson, PRD 70 054501 (2004)
Static-light mesons plus interpolation between static light states andexperiment Ds states
Green et al. PRD 69 094505 (2004)
Static-light states on quenched and 2 flavor lattices
Burch et al. PRD 79 014504 (2009)
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 40 / 35
Possible interpretations
(1) A sub-threshold state stable under the strong interactionWe call this “bound state scenario”This is irrespective of the nature of the stateOne expects a negative scattering length in this case
See Sasaki and Yamazaki, PRD 74 114507 (2006) for details.(2) A resonance in a channel with attractive interaction
The lowest state corresponds to the scattering level shifted belowthreshold in finite volumeThe additional level would indicate a QCD resonanceOne expects a positive scattering length in this case
This is the situation for the D∗0(2400)
DM, Prelovsek, Woloshyn, PRD 87 034501 (2013).
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 41 / 35
B∗so and Bs1: Systematic uncertainties
source of uncertainty expected size [MeV]heavy-quark discretization 12
finite volume effects 8unphysical Kaon, isospin & EM 11
b-quark tuning 3dispersion relation 2
spin-average (experiment) 2scale uncertainty 1
3 pt vs. 2 pt linear fit 2total 19
discretiation effects from HQET power counting also considering massmismatches
Oktay, Kronfeld Phys.Rev. D78 014504 (2008)
Finite volume from difference between the energy level and the pole
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 42 / 35
Search for Z+c with IGJPC = 1+1+−
Lattice
D(2) D*(-2)D*(1) D*(-1)J/ψ(2) π(−2)ψ3 πD(1) D*(-1)ψ
1Dπ
D* D*η
c(1)ρ(−1)
ψ2S
πD D*j/ψ(1) π(-1)η
c ρ
J/ψ π
Exp.
3.2
3.4
3.6
3.8
4
4.2
4.4
4.6
E[G
eV]
Prelovsek, Lang, Leskovec, DM, Phys.Rev. D91 014504 (2015)
Simple level counting approach
We find 13 two meson states as expected
We find no extra energy level that could point to a Zc candidate
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 43 / 35
Exotic meson physics for PANDA, BelleII, BESIII, LHCb
Simulate a large basis of quark-antiquark (regular and hybrid), meson-mesonand tetraquark operators with a variety of quantum numbers
Study the spectrum and extract bound states and resonances
Study quark mass dependence to confirm/falsify model expectations
Study operator overlaps to learn about structure
Study (radiative) transition amplitudes to learn about structure
Promising examples (similar for heavy-light states):X(3872)
Establish relation between the observed candidate and the X(3872)Study charm-quark variation and compare to models/ EFTStudy radiative transitions of the candidate state
χ′c0/X(3915)
Study DD∗ and J/ψω scattering and establish resonances < 4GeV
Charged charmonium-like Zc states
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 44 / 35
Modern methods
Use Lüscher’s method to access scattering phase shifts/ inelasticities→ bound state and resonance polesState of the art propagator calculations: distillation method
Handles all smeared timeslice-to-timeslice correlatorsAllows for storing the quark propagatorsHighly flexible for large synergy between different projectsProvides flexibility to optionally address light quark exotics, high spinstates and baryons
Improved heavy quark action (either Fermilab approach or highlyimproved actions)→ small and well understood discretization effects
Methods are mostly established but the combination of methods is unique.
A next generation resonance project will profit from lattice gauge fieldsmade available by various lattice collaborations (MILC, CLS, . . . )
Daniel Mohler (HIM) From quarks and gluons to exotic hadrons Graz, April 27, 2016 45 / 35