View
8
Download
0
Category
Preview:
Citation preview
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
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
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) statesCharmonium-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-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)
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 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)
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 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
Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 9 / 29
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 = + +
± / ±
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: 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
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: 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
Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 11 / 29
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
Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 12 / 29
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
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
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) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 13 / 29
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!
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
−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
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
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
Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 15 / 29
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)
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-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
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 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
Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 19 / 29
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
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[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
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 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
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
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) 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
(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)
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. - 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
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 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
Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 26 / 29
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
Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 27 / 29
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
Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 28 / 29
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
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 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
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+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.
Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 32 / 29
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++
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 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)
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 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
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-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)
Daniel Mohler (HIM) Heavy hadron interactions from Lattice QCD Wien, Sep 14th, 2017 37 / 29
Recommended