Heavy hadron interactions from Lattice QCD Daniel Mohler Wien, Sep - - PowerPoint PPT Presentation

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

u c d ¯ d u ¯ u s u ¯ d u c c W + Ξ++

cc

π+ Λ+

c

K− π+

]

2

c ) [MeV/

++ cc

Ξ (

cand

m

3500 3600 3700

2

c Candidates per 5 MeV/ 20 40 60 80 100 120 140 160 180 Data Total Signal Background

LHCb 13 TeV

Ξ++

cc

with mass 3621.40 ± 0.72 ± 0.27 ± 0.14 seen in both 13 TeV and 8 TeV data Previous claim of Ξcc by SELEX wit mass ≈3519 MeV not seen by BaBar, Belle, LHCb What 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 uncertainty Empty symbols: Continuum extrapolation missing All simulations neglect isospin splittings Ξ++

cc

– Ξ+

cc

Publications also contain a number of further predictions and successful postdictions History of earlier calculations, most notably

Mathur, 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

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 uncertainty Empty symbols: Continuum extrapolation missing All simulations neglect isospin splittings Ξ++

cc

– Ξ+

cc

Publications also contain a number of further predictions and successful postdictions History of earlier calculations, most notably

Mathur, 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 states

Roel Aaij et al., LHCb collaboration PRL 118 182001 (2017)

) [MeV]

−

K

+ c

Ξ ( m 3000 3100 3200 3300 Candidates / (1 MeV) 100 200 300 400 LHCb 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 resonances JP not identified All states are narrow → can compare to Lattice QCD simulations treating them as stable

Daniel 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)

c K S 'c K S c K D 'c K cΗ 12 32 12 12 12 32 32 32 52 Lattice Expt. 0. 0.1 0.2 0.3 0.4 0.5

E E12 GeV

0.000 0.005 0.010 0.015 0.020

a2

100 200 300 400 500 600

∆EΩ0

c

: ∆E(3

2 + )L1

: ∆E(1

2 − )L1

: ∆E(3

2 − )L1

: ∆E(3

2 + )L2

: ∆E(1

2 − )L2

: ∆E(3

2 − )L2

: Expt

Pattern of lattice states agrees well with experiment second study with smaller basis can not resolve two states with same JP; checks systematics Scattering thresholds somewhat unphysical

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 5 / 29

Outline

1

Motivation – Charmed baryons

2

Recent progress in Lattice QCD

3

D, Ds, and Bs

4

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

5

Exotic doubly-heavy states

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 6 / 29

Lattice Quantum Chromodynamics: What do we calculate?

Regularization of QCD by a 4-d Euclidean space-time

• lattice. (Kenneth Wilson 1974)

Provides a calculational method for QCD Euclidean correlator of two Hilbert-space operators ˆ O1 and ˆ O2.

• ˆ

O2(t)ˆ O1(0)

• =
• n

e−t∆En0|ˆ O2|nn|ˆ O1|0 = 1 Z

• D[ψ, ¯

ψ, U]e−SEO2[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)

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 7 / 29

Recent progress in Lattice QCD

Dynamical simulations with 2+1(+1) flavors of sea quarks Simulations at physical pion (light-quark) masses Isospin splitting and QCD+QED simulations Improved heavy quark actions for charm Efficient methods for all-to-all propagation (disconnected diagrams)

2 4 6 8 10

ΔM [MeV] ΔN ΔΣ ΔΞ ΔD ΔCG ΔΞcc experiment QCD+QED prediction

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

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 8 / 29

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 with regard 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 the rest-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 scattering

2 3 4 5 6 7 8L mΠ 2.0 2.5 3.0 3.5 4.0 EmΠ Reviews by R. A. Briceño arXiv:1411.6944 and M. Hansen arXiv:1511.04737

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 9 / 29

Fully systematic calculation vs. exploratory study

Important lattice systematics from Taking the continuum limit: a(g, m) → 0 Taking the infinite volume limit: L → ∞ Calculation at (or extrapolation to) the physical pion mass I cover many exploratory results Should be compared only qualitatively to experiment Provide an outlook on future Lattice QCD results Example for fully systematic results: Flavor physics results listed in the FLAG review http://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 = + +

±/ ±

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 10 / 29

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: Mc¯

s ≈ Mc¯ d

→ 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

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 11 / 29

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: Mc¯

s ≈ Mc¯ d

→ 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

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 11 / 29

D∗

s0(2317): D-meson – Kaon s-wave scattering

• M. 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 √πLZ00

• 1;

L 2πp 2 ≈ 1 a0 + 1 2r0p2

Mohler et al. PRL 111 222001 (2013) Lang, DM et al. PRD 90 034510 (2014)

Results for ensembles (1) and (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) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 12 / 29

D∗

s0(2317): D-meson – Kaon s-wave scattering

• M. 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 √πLZ00

• 1;

L 2πp 2 ≈ 1 a0 + 1 2r0p2

Mohler et al. PRL 111 222001 (2013) Lang, DM et al. PRD 90 034510 (2014)

Results for ensembles (1) and (2)

• 0.1

0.1 0.2 0.3 0.4 0.5

p

2 [GeV 2]

• 1
• 0.8
• 0.6
• 0.4
• 0.2

p cot 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) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 12 / 29

B∗

s0 and Bs1: Results

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

B∗

s0

aBK = −0.85(10) fm rBK = 0.03(15) fm MB∗

s0 = 5.711(13) GeV

Bs1 aB∗K = −0.97(16) fm rB∗K = 0.28(15) fm MBs1 = 5.750(17) GeV Energy from the difference to the B(∗)K threshold

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 13 / 29

Ds and Bs: Spectrum results

Mohler et al. PRL 111 222001 (2013) Lang, Mohler et al. PRD 90 034510 (2014) Lang, Mohler, Prelovsek, Woloshyn PLB 750 17 (2015)

• 200
• 100

100 200 300 400 500 600

m - (mDs+3mDs*)/4 [MeV]

Ensemble (1)

• 200
• 100

100 200 300 400 500 600

PDG Lat: energy level Lat: bound state from phase shift

Ensemble (2)

Ds Ds Ds0 Ds1 Ds1 Ds2 J

P : 0

• 1

+ 1 + 1 + 2 +

Ds Ds Ds0 Ds1 Ds1 Ds2

• 1

+ 1 + 1 + 2 + * * * * * *

Discretization uncertainties sizeable for charm Many improvements possible for the Ds states

5.3 5.4 5.5 5.6 5.7 5.8 5.9

m [GeV]

PDG Lat: energy level Lat: bound state from phase shift

Ensemble (2) mπ = 156 MeV B

*K

B K

Bs Bs

* Bs0 * Bs1 Bs1’ Bs2

J

P: 0

• 1

+ 1 + 1 + 2 +

Full uncertainty estimate only for magenta Bs states Prediction of exotic states from Lattice QCD!

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

Positive parity Ds: More comprehensive results from RQCD

Bali, Collins, Cox, Schäfer, arXiv:1706.01247

−2 −1 − 1

2

− 1

4

−3002 −2002 −10020 1002 2002 3002 4002

p cot δ [fm−1] p2 [MeV2] 0+ D∗

s(2317) channel mπ = 156 MeV Lang et.al. mπ = 290 MeV mπ = 150 MeV 64 64 40 40 32 32 24 24 64 64 48 48

−2 −1 − 1

2

− 1

4

−3002 −2002 −10020 1002 2002 3002 4002

p cot δ [fm−1] p2 [MeV2] 1+ Ds1(2460) channel

mπ = 156 MeV Lang et.al. mπ = 290 MeV mπ = 150 MeV 64 64 40 40 32 32 24 24 64 64 48 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

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 15 / 29

Positive parity Ds: More comprehensive results from RQCD

Bali, Collins, Cox, Schäfer, arXiv:1706.01247

• 150
• 100
• 50

∞ ∆E

0+ D∗

s(2317)

• 150
• 100
• 50

∞ ∆E

1+ Ds1(2460)

mπ = 290

mπ = 150

mπ = 156

mπ = 290

mπ = 150

mπ = 156

Study with different volumes at pion masses of 150, 290 MeV Remaining discretization effects non-negligible Results confirm basic behavior seen in previous simulation

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 15 / 29

Coupled-channel study of Dπ, Dη, DsK scattering

Moir et al., JHEP 1610 011 (2016)

• ηDπ

ηDη ηDs ¯

K

δDπ δDs ¯

K

δDη atEcm δ/◦ η

• atEcm

δ/◦ η ηDπ ηDη ηDs ¯

K

δDπ δDs ¯

K

δDη atEcm δ/◦ η

Lattice data from multiple volumes at mπ = 391 MeV Shallow bound state seen in coupled channel s-wave Narrow spin-2 D-wave resonance seen as well For older single-channel results see

DM, Prelovsek, Woloshyn PRD 87 034501 (2013)

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 16 / 29

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.

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 17 / 29

A look at the spectrum of scattering states

Expect level close to non-interacting scattering 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) Lattice

3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2

E[GeV]

ψ3 π D(1) D*(-1) ψ(3770) π D* D* ψ(2S) π D D* j/ψ(1) π(-1) ηc ρ J/ψ π

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 18 / 29

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 π D(1) D*(-1) ψ1D π D* D* ηc(1)ρ(−1) ψ2S π D D* j/ψ(1) π(-1) ηc ρ J/ψ π

Exp.

3.2 3.4 3.6 3.8 4 4.2 4.4 4.6

E[GeV]

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) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 19 / 29

Zc(3900) with the HALQCD method I

Ikeda 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) and mπ = 410, 570, 700 HALQCD method Ishii et al.

PLB 712, 437 (2012)

Calculate a potential as a function of distance r Solve Schrödinger equation with given V(r) and determine scattering phase shifts

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 20 / 29

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[f0

πJ/ψ,πJ/ψ] x25

Zc(3900)

Im[z] Re[z]

m ¯

D + mD∗

mρ + mηc mπ + mJ/ψ [bbb] sheet [ttt] sheet [btt] sheet [bbt] sheet quasi-bound pole resonance pole quasi-bound pole bound pole

Zc(3900)

Im[z] Re[z]

m ¯

D + mD∗

mρ + mηc

mπ + 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

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 21 / 29

χ′

c0 and X/Y(3915)

PDG interpreted X(3915) as a regular charmonium (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) → ¯ DD Spin splitting mχc2(2P) − mχc0(2P) too small Large OZI suppressed X(3915) → ωJ/ψ Width should be significantly larger than Γχc2(2P)

Zhou et al. (PRL 115 2, 022001 (2015)) argue that what is dubbed X(3915) is the spin 2 state already known and suggests that a broader state 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

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 22 / 29

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

p

2[GeV 2]

• 0.40
• 0.20

0.00 0.20 0.40 0.60 0.80 1.00

p cotδ/√s (a)

• 0.6
• 0.4
• 0.2

0.0 0.2 0.4

p

2[GeV 2]

(b)

• 0.6
• 0.4
• 0.2

0.0 0.2 0.4

p

2[GeV 2]

• 0.40
• 0.20

0.00 0.20 0.40 0.60 0.80 1.00

p cotδ/√s (c)

Assumes only ¯ DD is relevant Lattice data suggests a fairly narrow resonance with 3.9GeV < M < 4.0GeV and Γ < 100MeV Future experiment and lattice QCD results needed to clarify the situation

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 23 / 29

An X(3872) candidate from Lattice QCD

lattice (mπ~266 MeV) 400 500 600 700 800 900 1000 1100

m - 1/4 (mηc+3 mJ/ψ) [MeV]

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 pole L→∞

Prelovsek, Leskovec, PRL 111 192001 (2013)

400 600 800 1000 1200 1400

E - E(1S) MeV 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 are similar)

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 24 / 29

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. - OMM

17

• Lat. - OMM

17 - 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

10

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

mX(3872)−mD−m-

D*

770 790 810 830 850

mX(3872)−ms.a.

Without ¯ qq interpolators signal vanishes Simulations still unphysical in many ways Discretization and finite volume effects sizable! Makes interpretation as pure molecule or pure tetraquark unlikely

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 25 / 29

Recent simulations of charm or beauty tetraquarks

Searches for charmed tetraquarks

Doubly 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 quarks

Tetraquark bound states in heavy-light heavy-light systems

Brown and Orginos PRD 86 114506 (2012)

Lattice QCD results for a bottom-bottom tetraquark

Bicudo and Wagner PRD 87 114511 (2013)

Search for ud¯ b¯ b ss¯ b¯ b and cc¯ b¯ b tetraquarks

Bicudo et al., PRD 92 014507 (2015)

BB interactions with static bottom quarks

Bicudo, Cichy, Peters, Wagner, PRD 93 034501 (2016); Bicudo, Scheunert, Wagner, PRD 95 034502 (2017)

Deeply bound doubly-heavy tetraquarks with NRQCD b-quarks

Francis,Hudspith,Lewis,Maltman, PRL 118 142001 (2017) Junnarkar, Mathur, Padmanath, presented at Lattice 2017

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 26 / 29

BB interactions with static bottom quarks

Bicudo, 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 quarks Search for bound states (rather than resonances) Lattices with a = 0.079 fm and mπ ≈ 650, 480, 340 Fit function used for the lattice QCD potentials V(r) = −α r exp

• −

r d p + V0

0.1 0.15 0.2 0.25 0.3 0.35 0.4 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 extrapolation vector isotriplet B40 vector isotriplet B85 vector isotriplet B150 rmin=2a scalar isosinglet extrapolation scalar isosinglet B40 scalar isosinglet B85 scalar isosinglet B150

Resulting binding energy: EB = 90+43

−36 MeV

Including heavy ¯ b spins: EB = 59+30

−38 MeV

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 27 / 29

Doubly bottom JP = 1+ tetraquarks with NRQCD b-quarks

Francis, Hudspith, Lewis, Maltman, PRL 118 142001 (2017)

Study at a single lattice spacing and three pion masses 164MeV ≤ Mπ ≤ 415MeV Authors obtain bound 4-quark states for both ud¯ b¯ b and ls¯ b¯ b Potential issues

Binding energies extracted from ratios can be misleading For a bound state, excited state naively expected above threshold Finite volume effects alter the binding energy

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 28 / 29

ud¯ bb JP = 1+ tetraquarks on HISQ lattices

Junnarkar, Padmanath, Mathur, reported at Lattice 2017

Meff

10 20 30 t 0.70 0.75 0.80 0.85 E0 =-83.14 ±11.24 MeV

mπ =684 MeV

10 20 30 t E0 =-101.47 ±15.36 MeV

mπ =645 MeV

10 20 30 t E0 =-102.67 ±17.8 MeV

mπ =577 MeV

10 20 30 t E0 =-103.56 ±19.01 MeV

mπ =550 MeV

a =0.0583 fm

ud¯ b¯ b MB MB ∗

Results from 483 × 144 HISQ ensemble with Mπ,sea ≈ 310 MeV Four valence pion masses in range 550MeV ≤ Mπ ≤ 684MeV Same quantum numbers than Francis et al. (but notable difference in binding energy) Preliminary results confirm existence of a bound state

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

ud¯ bb JP = 1+ tetraquarks on HISQ lattices

Junnarkar, Padmanath, Mathur, reported at Lattice 2017

550 600 650 700

mπ

120 80 40

∆E

ud¯ b¯ b

a =0.0583 fm

Results from 483 × 144 HISQ ensemble with Mπ,sea ≈ 310 MeV Four valence pion masses in range 550MeV ≤ Mπ ≤ 684MeV Same quantum numbers than Francis et al. (but notable difference in binding energy) Preliminary results confirm existence of a bound state

Daniel 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 me unpublished updates

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 30 / 29

The X(5568)

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

The D0 collaboration is reporting evidence 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 ¯ bs¯ du Most model studies accommodating a X(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 5.9 10 20 30 40 50 60 70 80 90 2

N 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

5 10 15

]

2

) [GeV/c

±

π

S

(B m

Residuals (Data-Fit)

)

2

c Candidates / ( 4 MeV/ 50 100 150 200 250

Claimed X(5568) state Combinatorial

LHCb Preliminary ]

2

c ) [MeV/

±

π

s

m(B 5520 5540 5560 5580 5600 5620 5640 5660 5680 5700

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 31 / 29

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+mK mX +/- ΓX/2

Analytic predictions for energies of eigenstates for an elastic resonance in Bsπ (with JP = 0+) as a function of the lattice size L. Orange (blue) dashed lines show the Bsπ (BK) eigenstates when Bs and π (B and K) do not interact Red lines show the expectation for lattice energy levels in elastic Bsπ scattering (decoupled from BK) for a resonance with a mass and width of the X(5568). In the scenario of a deeply bound BK state, the simulation would result in an eigenstate with E ≈ mX up to exponentially small corrections in L.

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 32 / 29

Lattice results and conclusions

Lang, 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+mK mX +/- ΓX/2

(a) (b)

Exploratory calculation with a single ensemble at Mπ = 156 MeV Left pane: eigenenergies of the ¯ bs¯ du system with JP = 0+ Right pane: Analytic prediction based on the X(5568) Results stable under variations of the fit methodology Lattice simulation at close-to-physical quark masses does not yield a second 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 bb¯ b¯ b state

• C. Hughes, C. Davies, E. Eichten, presented at Lattice 2017

A number of recent potential model predictions of a very deeply bound bb¯ b¯ b state Lattice study using NRQCD b quarks, 3 different lattice spacings Upshot: No deeply bound states but deficiencies in models understood

20 40 60 80

t/a

0.50 0.55 0.60 0.65 0.70 0.75 0.80

aEeff

2ηb→2ηb(t) 1 2 3 4 5 6 7 8

t (fm)

a0.09fm Ns32

PRELIMINARY Eeff,t

0++(t) : rx = 0

Eeff

0++(t) : rx = 0

Eeff,t

0++(t) : rx = 1

Eeff

0++(t) : rx = 1

Eeff,t

0++(t) : rx = 2

Eeff

0++(t) : rx = 2

2Mlat

ϒ

2Mlat

ηb

Efit

0++ 20 40 60 80

t/a

0.50 0.55 0.60 0.65 0.70 0.75 0.80

aEeff

D3ׯ 3→3ׯ 3(t) 1 2 3 4 5 6 7 8

t (fm)

a0.0 Ns32

PRELIMINARY Eeff,t

0++(t) : rx = 0

Eeff

0++(t) : rx = 0

Eeff,t

0++(t) : rx = 1

Eeff

0++(t) : rx = 1

Eeff,t

0++(t) : rx = 2

Eeff

0++(t) : rx = 2

2Mlat

ϒ

2Mlat

ηb

Efit

0++

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 34 / 29

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 cc¯ u¯ d and cs¯ u¯ d These contain no quark line diagrams with quark annihilation Uses 2+1 flavor gauge configurations with a = 0.907(13) and mπ = 410, 570, 700 HALQCD method

Ishii et al. PLB 712, 437 (2012)

Calculate a potential as a function of distance r Solve Schrödinger equation with given V(r) and determine scattering phase shifts

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

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 35 / 29

Tetraquarks with the HALQCD method: Results

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

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

5 10 15 20 25 30 35 50 100 150 200 δ[deg] Wc.m. - MD - MD* [MeV] (c) D-D* phase shift Mπ=700MeV Mπ=570MeV Mπ=410MeV 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 a [fm] Mπ

2 [GeV2]

Scattering lengths aD-D* aKbar-D* aKbar-D

No bound states or resonances at simulated mπ Attraction becomes more prominent at light pion masses Authors have some indication that BB∗ with IJP = 01+ is bound

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 36 / 29

Lattice simulation

We use lattices with 2+1 flavors of Wilson-Clover quarks by PACS-CS N3

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)

Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 37 / 29