heavy hadron interactions from lattice qcd · daniel mohler (him) heavy hadron interactions from...

Heavy hadron interactions from Lattice QCD

Daniel Mohler

Wien, Sep 14th, 2017

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 1 / 29

Observation of a doubly-charmed Ξ++cc by LHCb

Roel Aaij et al., LHCb collaboration arXiv:1707.01621

ucdduusu

d

uc

c

W+

Ξ++cc π+

Λ+c

K−

π+

1

]2c) [MeV/++ccΞ(candm

3500 3600 3700

2 cC

andi

date

s pe

r 5

MeV

/

0

20

40

60

80

100

120

140

160

180

DataTotalSignalBackground

LHCb 13 TeV

Ξ++cc with mass 3621.40± 0.72± 0.27± 0.14

seen in both 13 TeV and 8 TeV dataPrevious claim of Ξcc by SELEX wit mass ≈3519 MeVnot seen by BaBar, Belle, LHCbWhat about Lattice QCD Predictions?Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 2 / 29

Ξcc – Recent Lattice QCD predictions

3500 3550 3600 3650 3700 3750 3800 3850

Alexandrou et al., PRD90 074501 (2014)

Briceno et al., PRD86 094504 (2012)

Brown et al. 094507 (2014)

Namekawa et al. PRD87, 094512 (2013))

Perez Rubio et al., PRD92 034504 (2015)

Observation claimed by SELEX

Mathur, Padmanath, Mondal (preliminary)

Full symbols: Good control of systematic uncertaintyEmpty symbols: Continuum extrapolation missingAll simulations neglect isospin splittings Ξ++

cc – Ξ+cc

Publications also contain a number of further predictionsand successful postdictionsHistory of earlier calculations, most notablyMathur, Lewis, Woloshyn, PRD 64 094509 (2001);PRD 66 014502

(2002)Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 3 / 29

Observation of 5 narrow Ωc statesRoel Aaij et al., LHCb collaboration PRL 118 182001 (2017)

) [MeV]−

K+cΞ(m

3000 3100 3200 3300

Can

dida

tes

/ (1

MeV

)

0

100

200

300

400LHCb Resonance Mass [MeV] Γ [MeV]

Ωc(3000)0 3000.4± 0.2± 0.1+0.3−0.5 4.5± 0.6± 0.3

Ωc(3050)0 3050.2± 0.1± 0.1+0.3−0.5 0.8± 0.2± 0.1

Ωc(3066)0 3065.6± 0.1± 0.3+0.3−0.5 3.5± 0.4± 0.2

Ωc(3090)0 3090.2± 0.3± 0.5+0.3−0.5 8.7± 1.0± 0.8

Ωc(3119)0 3119.1± 0.3± 0.9+0.3−0.5 1.1± 0.8± 0.4

Observation of 5 new Ωc resonancesJP not identifiedAll states are narrow→ can compare to Lattice QCD simulationstreating them as stableDaniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 4 / 29

What can Lattice QCD say about their spin-parity?

Padmanath, Mathur, PRL 119 042001 (2017)

Xc K HSL

X'c K HSL

Xc K

X D

X'c K

WcΗ

12+

32+

12-

12-

12-

32-

32-

32-

52-

LatticeExpt.

0.

0.1

0.2

0.3

0.4

0.5

E-

E12

+@G

eVD

0.000 0.005 0.010 0.015 0.020

a2

0

100

200

300

400

500

600

∆E

Ω0 c

: ∆E(32

+)L1

: ∆E(12

−)L1

: ∆E(32

−)L1

: ∆E(32

+)L2

: ∆E(12

−)L2

: ∆E(32

−)L2

: Expt

Pattern of lattice states agrees well with experimentsecond study with smaller basis can not resolve two states with same JP;checks systematicsScattering thresholds somewhat unphysical


Outline

1 Motivation – Charmed baryons

2 Recent progress in Lattice QCD

3 D, Ds, and Bs

4 Charmonium(-like) statesCharmonium-like states: Zc

Charmonium-like states: X(3915)Charmonium-like states: X(3872)

5 Exotic doubly-heavy states


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]

Path integral over the Euclidean action SE,QCD[ψ, ψ,U];(a sum over quantum fluctuations)

Can be evaluated with Markov Chain Monte Carlo(using methods well established in statistical physics)


Recent progress in Lattice QCD

Dynamical simulations with 2+1(+1) flavors of sea quarksSimulations at physical pion (light-quark) massesIsospin splitting and QCD+QED simulationsImproved heavy quark actions for charmEfficient methods for all-to-all propagation (disconnected diagrams)

0

2

4

6

8

10

ΔM

[MeV

]

ΔN

ΔΣ

ΔΞ

ΔD

ΔCG

ΔΞcc

experimentQCD+QEDprediction

BMW 2014 HCH

BMW Collaboration, Borsanyi et al. Science 347 1452 (2015)


Progress from an old idea: Lüscher’s finite-volume method

M. Lüscher Commun. Math. Phys. 105 (1986) 153;Nucl. Phys. B 354 (1991) 531; Nucl. Phys. B 364 (1991) 237.

Basic observation: Finite volume, multi-particle energies are shifted withregard to the free energy levels due to the interaction

E = E(p1) + E(p2) + ∆E

Energy shifts encode scattering amplitude(s)

Original method: Elastic scattering in therest-frame in multiple spatial volumes L3

Coupled 2-hadron channels well understood

2↔ 1 and 2↔ 2 transitions well understood(example ππ → πγ∗)

significant progress for 3-particle scattering2 3 4 5 6 7 8

L mΠ2.0

2.5

3.0

3.5

4.0

EmΠ

Reviews by R. A. Briceño arXiv:1411.6944 and M. Hansen arXiv:1511.04737


Fully systematic calculation vs. exploratory study

Important lattice systematics fromTaking the continuum limit: a(g,m)→ 0Taking the infinite volume limit: L→∞Calculation at (or extrapolation to) the physical pion mass

I cover many exploratory resultsShould be compared only qualitatively to experimentProvide an outlook on future Lattice QCD results

Example for fully systematic results:

Flavor physics results listed in theFLAG reviewhttp://flag.unibe.ch/→ See talk by U. Wenger

1.14 1.18 1.22 1.26

=+

+=

+=

QCDSF/UKQCD 07 ETM 09 ETM 10D (stat. err. only) BGR 11 ALPHA 13A ETM 14D (stat. err. only) FLAG average 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 RBC/UKQCD 14B FLAG average for = + ETM 10E (stat. err. only) MILC 11 (stat. err. only) MILC 13A HPQCD 13A ETM 13F FNAL/MILC 14A ETM 14E FLAG average for = + +

± / ±


Exotic Ds and Bs candidates

Established s and p-wave Ds and Bs hadrons:

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+)

Corresponding D∗0(2400) and D1(2430) are broad resonances

Peculiarity: Mcs ≈ Mcd → exotic structure? (tetraquark, molecule)

Bs cousins of the D∗s0(2317) and Ds1(2460) not (yet) seen in experiment

The LHCb experiment at CERN should be able to see these


Exotic Ds and Bs candidates

Established s and p-wave Ds and Bs hadrons:

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+)

Corresponding D∗0(2400) and D1(2430) are broad resonances

Peculiarity: Mcs ≈ Mcd → exotic structure? (tetraquark, molecule)

Bs cousins of the D∗s0(2317) and Ds1(2460) not (yet) seen in experiment

The LHCb experiment at CERN should be able to see these


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.

Charm-light hadrons p cot δ0(p) =2√πL

Z00

(1;

(L

2πp)2)

≈ 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

Lang, Mohler, Prelovsek, Woloshyn PLB 750 17 (2015)

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


Ds and Bs: Spectrum resultsMohler et al. PRL 111 222001 (2013)

Lang, Mohler 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!


Positive parity Ds: More comprehensive results from RQCD

Bali, Collins, Cox, Schäfer, arXiv:1706.01247

−2

−1

−12

−14

0

−3002 −2002 −10020 1002 2002 3002 4002

pcotδ

[fm−1]

p2 [MeV2]

0+ D∗s(2317) channel

mπ = 156 MeV Lang et.al.mπ = 290 MeVmπ = 150 MeV

64 6440 4032 3224 2464 6448 48

−2

−1

−12

−14

0

−3002 −2002 −10020 1002 2002 3002 4002

pcotδ

[fm−1]

p2 [MeV2]

1+ Ds1(2460) channel

mπ = 156 MeV Lang et.al.mπ = 290 MeVmπ = 150 MeV

64 6440 4032 3224 2464 6448 48

Study with different volumes at pion masses of 150, 290 MeV

Remaining discretization effects non-negligible

Results confirm basic behavior seen in previous simulation


Positive parity Ds: More comprehensive results from RQCD

Bali, Collins, Cox, Schäfer, arXiv:1706.01247

-150

-100

-50

0

50

100

150

200

1 2 3 4 5 ∞

∆E

[

M

e

V

L [fm

0+ D∗s(2317) hannel

-150

-100

-50

0

50

100

150

200

1 2 3 4 5 ∞∆E

[

M

e

V

L [fm

1+ Ds1(2460) hannel

mπ = 290 MeV

mπ = 150 MeV

mπ = 156 MeV Lang et.al.

Expt.

mπ = 290 MeV

mπ = 150 MeV

mπ = 156 MeV Lang et.al.

Expt.

Study with different volumes at pion masses of 150, 290 MeV

Remaining discretization effects non-negligible

Results confirm basic behavior seen in previous simulation


Coupled-channel study of Dπ, Dη, DsK scatteringMoir et al., JHEP 1610 011 (2016)

-

-

-

D0

D0

DsK0

D0

DsK0

D0

atEcm

/

-

-

-

atEcm

/

D0

D0

DsK0

D0

DsK0

D0

atEcm

/

Lattice data from multiple volumes at mπ = 391 MeVShallow bound state seen in coupled channel s-waveNarrow spin-2 D-wave resonance seen as wellFor older single-channel results see

DM, Prelovsek, Woloshyn PRD 87 034501 (2013)


Search for a Z+c state from Lattice QCD

Prelovsek, Lang, Leskovec, DM, Phys.Rev. D91 014504 (2015)

Search for a Z+c in the IGJPC = 1+1+− channel

Aim at simulating all meson-meson states below ≈ 4.3GeV

Caveat: Neglects 3-particle states

Include tetraquark interpolators of type 3c × 3c

Count energy levels and identify them according to their overlaps

Hope: See an extra level, as would be expected for a (narrow) resonance

More rigorous approach (a la Lüscher) quite challenging

Coupled channel system with many channels

Small shifts in finite volume and (largish) discretization effects

Thresholds should be close to physical

Suitable ensembles are (probably) not available at the moment.


A look at the spectrum of scattering states

Expect level close to non-interactingscattering states

J/Ψπ

ηcρ

JΨ(1)π(−1)

DD∗

Ψ2Sπ

D∗D∗

Ψ3770π

D(1)D∗(−1)

Ψ3π

JΨ(2)π(−2)

D∗(1)D∗(−1)

D(2)D∗(−2)

Lattice3.3

3.4

3.5

3.6

3.7

3.8

3.9

4

4.1

4.2

E[G

eV]

ψ3 πD(1) D*(-1)ψ(3770) πD* D*ψ(2S) πD D*j/ψ(1) π(-1)η

c ρ

J/ψ π


Search for Z+c with IGJPC = 1+1+−

Prelovsek, Lang, Leskovec, DM,

Phys.Rev. D91 014504 (2015)

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]

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


Zc(3900) with the HALQCD method IIkeda et al. PRL 117 242001 (2016); Ikeda arXiv:1706.07300

Coupled-channel scattering J/Ψπ, ηcρ, DD∗, IG(JPC) = 1+1+−

Uses 2+1 flavor gauge configurations with a = 0.907(13) andmπ = 410, 570, 700HALQCD method Ishii et al. PLB 712, 437 (2012)

Calculate a potential as a function of distance rSolve Schrödinger equation with given V(r) and determine scatteringphase shifts


Zc(3900) with the HALQCD method II

Ikeda et al. PRL 117 242001 (2016);

Ikeda arXiv:1706.07300

0.00

0.02

0.04

0.06

0.08

0.10

3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2

Im[f

(E)]

(fm

)

E (GeV)

(a) case I

Im[fDD

*,DD

*

]

Im[fρηc,ρηc]

Im[fπJ/ψ,πJ/ψ

] x5

Im[f0πJ/ψ,πJ/ψ

] x25

Zc(3900)

Im[z]

Re[z]

mD + mD∗mρ + mηcmπ + mJ/ψ

[bbb] sheet

[ttt] sheet

[btt] sheet

[bbt] sheetquasi-bound pole

resonance pole

quasi-bound pole

bound pole

Zc(3900)

Im[z]

Re[z]

mD + mD∗mρ + mηcmπ + mJ/ψ

[bbb] sheet

[ttt] sheet

[btt] sheet

[bbt] sheet

Pole found far below DD∗ threshold for all quark masses

Authors conclude Zc(3900) not a usual resonance but a threshold cusp

Structure comes from strong πJ/Ψ – DD∗ coupling

Analysis at close-to-physical pion mass planned


χ′c0 and X/Y(3915)

PDG interpreted X(3915) as a regularcharmonium (χ′c0)

Some of the reasons to doubt this assignment:Guo, Meissner Phys. Rev. D86, 091501 (2012)

Olsen, PRD 91 057501 (2015)

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.Observation of an alternatice χc0(2P) by Belle:

Chilikin et al. PRD 95 112003 (2017)

M = 3862+26+40−32−13 Γ = 201+154+88

−067−82


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


An X(3872) candidate from Lattice QCD

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, DeTar, DM, Na,

arXiv:1411.1389

Neglects charm annihilation and J/ψω

Seen only when qq and D∗D are used

The two simulations have vastly different systematics (yet results aresimilar)


An X(3872) candidate from Lattice QCD II

Padmanath, Lang, Prelovsek, PRD 92 034501 (2015)

3.45

3.6

3.75

3.9

4.05

4.2

4.35

4.5

En [

GeV

]

Lat. - OMM17 Lat. - O

MM17 - O

-c c

D(0) -D*(0)

J/Ψ(0) ω(0)

D(1) -D* (-1)

J/Ψ(1) ω(-1)

ηc(1) σ(-1)

-30

-20

-10

0

10

Exp. Lat. Lat.-O4q [31] [32]

mX(3872)−mD−m-D*

770

790

810

830

850mX(3872)−ms.a.

Without qq interpolatorssignal vanishes

Simulations stillunphysical in many ways

Discretization and finitevolume effects sizable!

Makes interpretation aspure molecule or puretetraquark unlikely


Recent simulations of charm or beauty tetraquarks

Searches for charmed tetraquarksDoubly charmed and charmed-strange tetraquarks by HALQCD

Ikeda et al. PLB 729 85-90 (2014)

Search for doubly charmed tetraquarks on CLS lattices (preliminary)Guerrieri et al. arXiv:1411.2247

HHLL systems with bottom quarksTetraquark bound states in heavy-light heavy-light systems

Brown and Orginos PRD 86 114506 (2012)

Lattice QCD results for a bottom-bottom tetraquarkBicudo and Wagner PRD 87 114511 (2013)

Search for udbb ssbb and ccbb tetraquarksBicudo et al., PRD 92 014507 (2015)

BB interactions with static bottom quarksBicudo, Cichy, Peters, Wagner, PRD 93 034501 (2016);

Bicudo, Scheunert, Wagner, PRD 95 034502 (2017)

Deeply bound doubly-heavy tetraquarks with NRQCD b-quarksFrancis,Hudspith,Lewis,Maltman, PRL 118 142001 (2017)

Junnarkar, Mathur, Padmanath, presented at Lattice 2017


BB interactions with static bottom quarksBicudo, Cichy, Peters, Wagner, PRD 93 034501 (2016)

Bicudo, Scheunert, Wagner, PRD 95 034502 (2017)Potentials of two static antiquarks in the presence of two light quarksSearch for bound states (rather than resonances)Lattices with a = 0.079 fm and mπ ≈ 650, 480, 340Fit function used for the lattice QCD potentials

V(r) = −αr

exp(−( r

d

)p)+ V0

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.1 0.2 0.3 0.4 0.5

α

d in fm

qq = (ud-du)/√2 qq= uu, (ud+du)/√2, dd

0 MeV

-20 MeV

-60 MeV

-100 MeV

rmin=3a

vector isotriplet extrapolationvector isotriplet B40vector isotriplet B85

vector isotriplet B150

rmin=2a

scalar isosinglet extrapolationscalar isosinglet B40scalar isosinglet B85

scalar isosinglet B150

Resulting binding energy:

EB = 90+43−36 MeV

Including heavy b spins:

EB = 59+30−38 MeV


Doubly bottom JP = 1+ tetraquarks with NRQCD b-quarksFrancis, Hudspith, Lewis, Maltman, PRL 118 142001 (2017)

Study at a single lattice spacing and three pion masses164MeV ≤ Mπ ≤ 415MeVAuthors obtain bound 4-quark states for both udbb and lsbbPotential issues

Binding energies extracted from ratios can be misleadingFor a bound state, excited state naively expected above thresholdFinite volume effects alter the binding energy


udbb JP = 1+ tetraquarks on HISQ latticesJunnarkar, Padmanath, Mathur, reported at Lattice 2017

Meff

10 20 30t

0.70

0.75

0.80

0.85 E0 =-83.14±11.24 MeV

mπ =684 MeV

10 20 30t

E0 =-101.47±15.36 MeV

mπ =645 MeV

10 20 30t

E0 =-102.67±17.8 MeV

mπ =577 MeV

10 20 30t

E0 =-103.56±19.01 MeV

mπ =550 MeVa=0.0583 fmudbb

MBMB ∗

Results from 483 × 144 HISQ ensemble with Mπ,sea ≈ 310 MeVFour valence pion masses in range 550MeV ≤ Mπ ≤ 684MeVSame quantum numbers than Francis et al.(but notable difference in binding energy)Preliminary results confirm existence of a bound stateDaniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 29 / 29

udbb JP = 1+ tetraquarks on HISQ latticesJunnarkar, Padmanath, Mathur, reported at Lattice 2017

550 600 650 700mπ

120

80

40

0

∆E

udbba=0.0583 fm

Results from 483 × 144 HISQ ensemble with Mπ,sea ≈ 310 MeVFour valence pion masses in range 550MeV ≤ Mπ ≤ 684MeVSame quantum numbers than Francis et al.(but notable difference in binding energy)Preliminary results confirm existence of a bound stateDaniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 29 / 29

. . .

Thank you!

Thanks to Parikshit Junnarkar and Nilmani Mathur for sending meunpublished updates


The X(5568)

Abazov et al. PRL 117, 022003 (2016).

The D0 collaboration is reportingevidence for a peak in the Bsπ

+

invariant mass not far above threshold

D0 attributes this to resonance X(5568)

mX = 5567.8± 2.9+0.9−1.9 MeV

ΓX = 21.9± 6.4+5.0−2.5 MeV

Decay to Bsπ+ implies exotic flavor

structure bsdu

Most model studies accommodating aX(5568) propose JP = 0+

LHCb did not find any peak in the Bsπ+

invariant mass (with increased statistics)

5.5 5.55 5.6 5.65 5.7 5.75 5.8 5.85 5.90

10

20

30

40

50

60

70

80

90

2N

events

/ 8

MeV

/c

1 D0 Run II, 10.4 fb

DATA

Fit with background shape fixed

Background

Signal

a)

5.5 5.55 5.6 5.65 5.7 5.75 5.8 5.85 5.9

10

5

0

5

10

15

]2 ) [GeV/c± π S

0 (Bm

Resid

uals

(D

ata

Fit)

)2 cC

and

idat

es /

( 4

MeV

/0

50

100

150

200

250Claimed X(5568) state

Combinatorial

LHCb Preliminary

]2c) [MeV/±πs0m(B

5520 5540 5560 5580 5600 5620 5640 5660 5680 5700


Expected signatures of the X(5568)

2 2.5 3 3.5 4

L [fm]

5.3

5.4

5.5

5.6

5.7

5.8

5.9

6

E [

GeV

]

Bs(n)π(-n)

B(n)K(-n)

mBs

+mπ

mB+m

K

mX

+/- ΓX

/2

Analytic predictions for energies ofeigenstates for an elastic resonance in Bsπ(with JP = 0+) as a function of the latticesize L.

Orange (blue) dashed lines show the Bsπ (BK) eigenstates when Bs andπ (B and K) do not interact

Red lines show the expectation for lattice energy levels in elastic Bsπscattering (decoupled from BK) for a resonance with a mass and width ofthe X(5568).

In the scenario of a deeply bound BK state, the simulation would resultin an eigenstate with E ≈ mX up to exponentially small corrections in L.


Lattice results and conclusionsLang, DM, Prelovsek, PRD 94 074509 (2016)

5.3

5.4

5.5

5.6

5.7

5.8

5.9

E [

GeV

]

5.3

5.4

5.5

5.6

5.7

5.8

5.9

mBs

+mπ

mB+m

K

mX

+/- ΓX

/2

(a) (b)

Exploratory calculation with a single ensemble at Mπ = 156 MeVLeft pane: eigenenergies of the bsdu system with JP = 0+

Right pane: Analytic prediction based on the X(5568)Results stable under variations of the fit methodologyLattice simulation at close-to-physical quark masses does not yield asecond low-lying energy level (expected for the case of the X(5568))Results do not support the existence of X(5568) with JP = 0+.Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 33 / 29

Search for a deeply bound bbbb stateC. Hughes, C. Davies, E. Eichten, presented at Lattice 2017

A number of recent potential model predictions of a very deeply boundbbbb stateLattice study using NRQCD b quarks, 3 different lattice spacingsUpshot: No deeply bound states but deficiencies in models understood

0 20 40 60 80t/a

0.50

0.55

0.60

0.65

0.70

0.75

0.80

aEef

f2η

b→2 η

b(t)

1 2 3 4 5 6 7 8

t (fm)

a0.09fmNs32

PRELIMINARY

Eeff,t0++(t) : rx = 0

Eeff0++(t) : rx = 0

Eeff,t0++(t) : rx = 1

Eeff0++(t) : rx = 1

Eeff,t0++(t) : rx = 2

Eeff0++(t) : rx = 2

2Mlatϒ

2Mlatηb

Efit0++

0 20 40 60 80t/a

0.50

0.55

0.60

0.65

0.70

0.75

0.80

aEef

fD

3×3→

3×3(

t)

1 2 3 4 5 6 7 8

t (fm)

a0.09fmNs32

PRELIMINARY

Eeff,t0++(t) : rx = 0

Eeff0++(t) : rx = 0

Eeff,t0++(t) : rx = 1

Eeff0++(t) : rx = 1

Eeff,t0++(t) : rx = 2

Eeff0++(t) : rx = 2

2Mlatϒ

2Mlatηb

Efit0++


Search for charmed tetraquarks by HALQCD

Ikeda et al. PLB 729 85-90 (2014)

Search for bound states or resonances in DD, KD, DD∗ and KD∗

interactions with flavor structure ccud and csud

These contain no quark line diagrams with quark annihilation

Uses 2+1 flavor gauge configurations with a = 0.907(13) andmπ = 410, 570, 700

HALQCD method

Ishii et al. PLB 712, 437 (2012)

Calculate a potential as a function of distance rSolve Schrödinger equation with given V(r) and determine scatteringphase shifts

Uses variant of the Fermilab method (relativistic heavy quark action)


Tetraquarks with the HALQCD method: Results

Ikeda et al. PLB 729 85-90 (2014)

Repulsive interaction in all I = 1 channels consideredAttractive interaction in all I = 0 channels considered

0

5

10

15

20

25

30

35

0 50 100 150 200

δ[de

g]

Wc.m. - MD - MD* [MeV]

(c) D-D* phase shift

Mπ=700MeVMπ=570MeVMπ=410MeV

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7a

[fm]

Mπ2 [GeV2]

Scattering lengths

aD-D*aKbar-D*aKbar-D

No bound states or resonances at simulated mπ

Attraction becomes more prominent at light pion massesAuthors have some indication that BB∗ with IJP = 01+ is bound


Lattice simulation

We use lattices with 2+1 flavors of Wilson-Clover quarks by PACS-CSN3

L × NT Nf a[fm] L[fm] #configs mπ[MeV] mK[MeV]323 × 64 2+1 0.0907(13) 2.90 196 156(7)(2) 504(1)(7)

For a description of the heavy-quark methodology see

Lang, DM, Prelovsek, Woloshyn PLB 750 17 (2015)

Interpolator basis

OBs(0)π(0)1,2 =

[bΓ1,2s

](p = 0)

[dΓ1,2u

](p = 0)

OBs(1)π(−1)1,2 =

∑p=±ex,y,z 2π/L

[bΓ1,2s

](p)[dΓ1,2u

](−p)

OB(0)K(0)1,2 =

[bΓ1,2u

](p = 0)

[dΓ1,2s

](p = 0)


heavy hadron interactions from lattice qcd · daniel mohler (him) heavy hadron interactions from...

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