Exploratory calculations of meson resonances and bound ... · Daniel Mohler (Fermilab) Mesons from...

Exploratory calculations of meson resonances andbound states from lattice QCD

Daniel Mohler

Ashburn, VA,April 14, 2015

Collaborators: C. B. Lang, L. Leskovec, S. Prelovsek, R. M. Woloshyn

Daniel Mohler (Fermilab) Mesons from lattice QCD Ashburn, VA, April 14, 2015 1 / 38

Outline

1 Introduction & Methods

2 The a1(1260) and b1(1230) in πρ and πω scattering

3 P-wave Ds and Bs hadronsD∗s0(2317) and Ds1(2460) as QCD bound statesPositive parity Bs states

4 Conclusions and Outlook


Outline






Recent progress in lattice QCD

Dynamical simulations with 2+1(+1) quark flavors

Simulations at physical pion masses

Isospin splitting and QCD+QED simulations

Improved heavy quark actions for charm

0

2

4

6

8

10

ΔM

[MeV

]

ΔN

ΔΣ

ΔΞ

ΔD

ΔCG

ΔΞcc

experimentQCD+QEDprediction

BMW 2014 HCH

BMW Collaboration, Borsanyi et al. arXiv:1406.4088


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-scatteringSee talk by David Wilson

I will report on exploratory calculations regarding meson resonances andbound states


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)


Euclidean correlators and interpolating fields

On the lattice: Euclidean space correlation functions⟨O2(t)O1(0)

⟩T ∝ ∑

ne−tEn < 0|O2|n >< n|O1|0 >

Use: 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

Example II: Nucleon

ON = εabc Γ1 ua(uT

b Γ2 dc−dTb Γ2 uc

)In practice: Many (slightly different) constructions possible!In a QFT they should all be OK; Overlap?


Using single hadron interpolators, what does one see?

In practical calculations qq and qqq interpolators couple very weakly tomulti-hadron states

McNeile & Michael, Phys. Lett. B 556, 177 (2003); Engel 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 QCD 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

Lang, DM, Prelovsek, Vidmar, PRD 84 054503 (2011) & erratum ibid

0.4

0.6

0.8

1

En 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


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 LATTICE2014 plenary by Raúl A. Briceño, arXiv:1411.6944Daniel Mohler (Fermilab) Mesons from lattice QCD Ashburn, VA, April 14, 2015 10 / 38

Studies within our collaboration (past end present)

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, arXiv:1501.01646

Meson scattering and charmoniumPrelovsek & Leskovec PRL 111 192001 (2013)

Prelovsek & Leskovec, Phys.Lett. B727 172 (2013)Prelovsek, Leskovec, DM, arXiv:1310.8127

Prelovsek, Lang, Leskovec, DM, PRD 91 014504 (2015)Lang, Leskovec, DM, Prelovsek arXiv:1503.05363


Outline






a1(1260) and b1(1230) as resonances in πρ and πω

scattering

Well established resonances a1(1260) and b1(1230)New a1 resonance: a1(1420)

COMPASS Collaboration, Adolph et al. arXiv:1501.05732

See talks by Paul, Krinner

M = 1414+15−13MeV Γ = 153+8

−23MeVAlternative interpretation: Only one a1 resonance (with mass larger thanthe PDG)

Basdevant, Berger arXiv:1501.04643

See talk by Berger

Our simulation was aimed at qualitative results for the a1(1260)Vast (and maybe unrealistic) simplification: Consider only ρπ and ωπ

elastic scatteringWe do a 2-flavor simulation so no KK∗ for the a1

The ρ is assumed to be stable here


Effective energies

4 6 8 10t

0.4

0.6

0.8

1

1.2

1.4

1.6E

eff (t

) a

a1: O

qq, O

ρπ

6 8 10t

a1: O

qq

4 6 8 10t

b1: O

qq,O

ωπ

4 6 8 10t

b1: O

qq

V(0)π(0)

V(1)π(-1)

Combined basis neededClear attractive interaction in the ρπ channelInteraction in the ωπ scattering compatible with no shift→ more statistics needed


Resulting phase shift data for the a1

0.3 0.4 0.5 0.6 0.7 0.8

s a2

0

0.2

0.4

0.6

0.8

(p/√

s) c

ot

δ

ρπ threshold

For the a1 the assumption of a stable ρ is a strong assumption, althoughthe effect at our parameters is probably small

Roca, Oset, PRD 85 054507 (2012)

We assume a simple Breit-Wigner shape and neglect channels other thanπρ


Resulting resonance masses

resonance a1(1260) b1(1235)quantity mres

a1ga1ρπ aρπ

l=0 mresb1

gb1ωπ

[GeV] [GeV] [fm] [GeV] [GeV]lat 1.435(53)(+0

−109) 1.71(39) 0.62(28) 1.414(36)(+0−83) input

exp 1.230(40) 1.35(30) - 1.2295(32) 0.787(25)

Uncertainties statistical and fit choices only

Higher than physical resonance masses but with large systematics

A rigorous future treatment for the a1 will have to includea1↔ ρπ ↔ 3π and further channelsThe rigorous formalism for that is currently being developed

Hansen, Sharpe, PRD 90 116003 (2014);Polejaeva, Rusetsky, EPJ A48 67 (2012);Briceno, Davoudi, PRD 87 094507 (2013)

No indication for a second low-lying a1 resonance, but might missimportant interpolators


Outline






Heavy quarks using the Fermilab method

El-Khadra et al., PRD 55,3933

We tune κ for the spin averaged kinetic mass (Mηc +3MJ/Ψ)/4 toassume its physical valueGeneral form for the dispersion relation

Bernard et al. PRD83:034503,2011

E(p) = M1 +p2

2M2− a3W4

6 ∑i

p4i −

(p2)2

8M34+ . . .

We compare results from three different fit strategiesEnergy splittings are expected to be close to physicalFor MeV values of masses

M = ∆M+Msa,phys


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


Low-lying charmonium spectrum

ηc Ψ h

cχ

c0χ

c1χ

c2η

c2 Ψ2

Ψ3

hc3

χc3

-1000

100200300400500600700800900

10001100

Ene

rgy

diff

eren

ce [

MeV

]

JPC

: 0- +

1- -

1+ -

0+ +

1+ +

2+ +

2- +

2 - -

3- -

3+ -

3++

DM, S. Prelovsek, R. M. Woloshyn, PRD 87 034501 (2013);

Serves as further confirmation of our heavy-quark approachData from 1 ensemble; Errors statistical + scale setting


Experimental Ds spectrum

Established states:Ds (JP = 0−) and D∗s (1−)D∗s0(2317) (0+), Ds1(2460) (1+), Ds1(2536) (1+), D∗s2(2573) (2+)

More recent discoveries:D∗s1(2700) seen by BaBar, Belle, LHCb (1−)D∗sJ(2860) seen by BaBarLHCb overlapping 1− and 3− statesD∗sJ(3040) seen by BaBar (1+?,2−?)

j = 12 doublet almost mass-degenerate with non-strange states

Some models suggest a tetraquark/molecular interpretations forcontroversial states

(Most) lattice studies using single hadron (cs) operators get too large orbadly determined masses

Large mπ : D∗s0(2317) below DK threshold;Small mπ : D∗s0(2317) ≈ DK threshold


D∗s0(2317) including D meson - Kaon

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

0

100

200

300

400

500

600

700

800

900

M -

M1S

[M

eV]

Ensemble (1)

0

100

200

300

400

500

600

700

800

900Ensemble (2)

qq qq qq + DKqq + DK

Much better quality of the ground state plateau with combined basisD∗s0(2317) as a QCD bound stateSuggests that including multi-hadron levels is vital


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).


Using Lüscher’s formula

We can test the plausibility of these scenarios using Lüscher’s formulaand an effective range approximation

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

K−1 = pcotδ (p) =2√πL

Z00(1;q2) ,

≈ 1a0

+12

r0p2 ,

Results for ensembles (1) and (2)

a0 =−0.756±0.025fm r0 = 0.056±0.031fm (1)

a0 =−1.33±0.20fm r0 = 0.27±0.17fm (2)


Results for the scattering length a0

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

0 100 200 300 400Mπ[MeV]

-2

-1.5

-1

-0.5

0

Scat

teri

ng le

ngth

[fm

]

Ensemble (1)Ensemble (2)

We compare to the predictions from an indirect calculationLiu et al. PRD 87 014508 (2013).

Our determination robustly leads to negative values.


Resulting Ds P-wave spectrum

-200

-100

0

100

200

300

400

500

600

m -

(m

Ds+

3mD

s*)/

4 [

MeV

]

Ensemble (1) mπ = 266 MeV

-200

-100

0

100

200

300

400

500

600

PDGLat: energy levelLat: bound state from phase shift


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

+

* * * * * *

Remaining differences of the size of discretization uncertainties

Many improvements possible for the Ds states


Bs states from experiment

Two p-wave states known from experiment:Bs1(5830) with M = 5828.7(4) MeVB∗s2(5840) with M = 5839.96(20) MeV and Γ = 1.6(5) MeV

Discovered in two body decays into K−B+ at CDF/D0 and also seen byLHCb

Remaining B∗s0 and Bs1 states not measuredLHCb is working on this

Could be seen in electromagnetic transitions, transitions with a single π0

or transitions through a virtual σ with σ → 2π .

Bardeen, Eichten, Hill, PRD 68 054024 (2003)

What can we say?Disclaimer: Will not consider B(∗)

s η , isospin breaking and or s-wave –d-wave mixing


Mesons with beauty and the Fermilab method: Expectations

For the Bs meson, noise is expected to fall exponentially with(Mηb +Mηs)/2 < MBs → Results noisier than for Ds

Lepage; also Gregory et al. PRD 83 014506 (2011)

0 3 6 9 12 15 18 21 24 27 30t

1

1.2

1.4

1.6

1.8

2

2.2

2.4

Eff

ecti

ve

mas

ses

- am

Bs ground state

Fitted effective mass (signal)

B noiseFitted effective mass (noise)

Effective masses

m=000

χ2/d.o.f.=18.65/21

χ2/d.o.f.= 5.37/7

Expected heavy-light discretization effects smaller than for charm(unlike onium)Closer to heavy-quark limit: Less mixing for 1+ states


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 to light


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)


B∗so and Bs1: Results

C. B. Lang, DM, S. Prelovsek, R. M. Woloshyn arXiv:1501.01646

aBK0 =−0.85(10) fm

rBK0 = 0.03(15) fm

MBs0 = 5.711(13)GeV

aB∗K0 =−0.97(16) fm

rB∗K0 = 0.28(15) fm

MBs0 = 5.750(17)GeV

Energy from the difference to the B(∗)K threshold


A further sanity check

Discretization errors expected to be smaller than for Ds

5.3

5.4

5.5

5.6

5.7

5.8

5.9

m [

GeV

]

PDGLat: energy level

B*K

B K

Bs B

s

* B

s0

* B

s1 B

s1’ B

s2

JP: 0

- 1

- 0

+ 1

+ 1

+ 2

+

MB′s1= 5.831(9)(6)GeV

MBs2 = 5.853(11)(6)GeV

Uncertainties just statistics and scale setting


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


Resulting Bs P-wave spectrum

C. B. Lang, DM, S. Prelovsek, R. M. Woloshyn arXiv:1501.01646

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

+

Predicted two Bs states with full uncertainty estimateExpecting results from LHCb


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)


Outline






Conclusions & Outlook

Studies of QCD resonances and (close-to-threshold) bound states are ofan exploratory nature

This is in contrast to low lying states (full error budgets)Simulations of the a1(1260) and b1(1230)

Simple simulations a1↔ ρπ and b1↔ ωπ possibleMore statistics and partial wave mixing needed for the b1Conceptional progress needed for a1 (three pions rather than ρπ)

Simulations of p-wave heavy-light states are now possibleDs(2317) and Ds(2460) as QCD bound statesD meson states as resonancesPredictions for two Bs states

Further resonancesResults for the ρ resonanceImpressive data for Kπ – Kη coupled channels→ David WilsonCharmonium resonances close to DD, DD∗ and D∗D∗ can be investigated


. . .

Thank you!


Backup slides

. . .


(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)


Dπ and D?π scattering

DM, Prelovsek, Woloshyn, PRD 87 034501 (2013)

In the JP = 0+ D?0 channel we extract three levels

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6s

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

(p*/

s1/2 )

cot δ

For the JP = 1+ channel there are two resonances D1(2420) andD1(2430)

0 3 6 9 12 15 18 21t

0.8

1

1.2

1.4

1.6

1.8

2

aE

D*(0)π(0)

D*(-1)π(1)

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6s

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

(p*/

s1/2 )

cot δ


Resonances in Dπ and D?π scattering

DM, Prelovsek, Woloshyn, PRD 87 034501 (2013)

For resonances determine coupling g rather than Γ = g2 p∗s (for s-wave)

Data at mπ = 266MeV on a single volume / lattice spacing

D D* D0* D

1D

1 D2* D

2

-100

0

100

200

300

400

500

600

700

800

900

1000m

- 1

/4 (

mD

+3m

D*)

[M

eV]

lat: naive levellat: resonance

PDG values

J P

: 0 -

1 -

0+

1 +

1 +

2 +

2 -

LHCb 2013BaBar 2010

D∗0(2400) D1(2430)glat [GeV] 2.55±0.21 2.01±0.15gexp [GeV] 1.92±0.14 2.50±0.40


Ψ(3770) resonance from Lattice QCDLang, Leskovec, DM, Prelovsek, arXiv:1503.05363

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 possible


χ ′c0 and X/Y(3915)

PDG is identifying the X(3915) with the χ ′c0

Based on BaBar determination of its quantum numbersSome 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) to smallLarge OZI suppressed X(3915)→ ωJ/ψ

Width should be significantly larger than Γχc2(2P)

Investigate DD scattering in S-wave on the lattice!Candidates:

m = 3837.6±11.5 MeV, Γ = 221±19 MeV Guo&Meissner

m = 3878±48 MeV, Γ = 347+316−143

MeV Olsen


χ ′c0: Exploratory lattice calculation

Lang, Leskovec, DM, Prelovsek, arXiv:1503.05363

-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


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


Snapshot of spectrum calculations at mπ = 266MeV

ηc Ψ h

cχ

c0χ

c1χ

c2η

c2 Ψ2

Ψ3

hc3

χc3

-100

0

100

200

300

400

500

600

700

800

900

1000

1100m

-m_ c_ c [M

eV]

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

First principles determination of resonances and bound states just startingProgram will have to be done with a number of lattice spacings/volumes


Heavy-light discretization effects in the Fermilab method

0 0.05 0.1

a [fm]

0

10

20

30

40

∆M

[M

eV

]

Mb

ME

M4

w4

discretiation effects from HQET power counting also considering massmismatches

Oktay, Kronfeld Phys.Rev. D78 014504 (2008)


Contractions

t f tiqqqq cs A1

t f ti

D

K

qqc

sC1

t f ti

D

qq

K

c

sB1

t f ti

DD

KK

c

s

D1

t f ti

DD

KK

c

s

D2

Handled efficiently within the distillation method

Peardon et al. PRD 80, 054506 (2009)Morningstar et al. PRD 83, 114505 (2011)


Exploratory calculations of meson resonances and bound ... · Daniel Mohler (Fermilab) Mesons from...

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