qcd to xyz from quarks and gluons to exotic hadronsdk-user/talks/mohler_ss16.pdf · daniel mohler...

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


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


3.8 4 4.2 4.4 4.6 4.8 5

2E

ven

ts /

20

MeV

/c

0

10

20

30

40


3.8 4 4.2 4.4 4.6 4.8 5

2E

ven

ts /

20

MeV

/c

0

10

20

30

40


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


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)


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


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


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)


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


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


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


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!


(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)


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.


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


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


A look at the Particle Data Group booklet

I will discuss the following examples:

Light hadrons Heavy-light hadrons

+ b-quark analogues

Charmonium


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)


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)


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


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


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


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


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)


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


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


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


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!


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



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

]



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!


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)


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!


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


Emerging understanding from QCD

ηc Ψ h

cχ

c0χ

c1χ

c2η

c2 Ψ2

Ψ3

hc3

χc3

-100

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m-m_ c_ c [

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]

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!


. . .

Backup Slides


First examples of emerging understanding from QCD

-200

-100

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m -

(m

Ds+

3mD

s*)/

4 [

MeV

]


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PDGLat: energy levelLat: bound state from phase shift


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


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

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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


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


D∗s0(2317) including D meson - Kaon

DM, Lang, Leskovec, Prelovsek, Woloshyn, PRL 111 222001 (2013)

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M -

M1S

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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)


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).


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


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


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


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, . . . )


qcd to xyz from quarks and gluons to exotic hadronsdk-user/talks/mohler_ss16.pdf · daniel mohler...

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