gunnarbali withmaurizioalberti,saracollins ... - ias.tum.de fileoutline motivation hadroquarkonium...

Hadroquarkonium from Lattice QCD

Gunnar Bali

with Maurizio Alberti, Sara Collins, Francesco Knechtli, Graham Moir,Wolfgang Söldner

Wuppertal – Regensburg – Cambridge

Symposium on EFTs and LGT TUM IAS, May 21, 2016

Outline

MotivationHadroquarkoniumLattice simulationSummary

Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 2 / 21

Recent charmonium spectrum resultsHPQCD [arXiv:1411.1318] ETMC [arXiv:1510.07862]

0−+ 1−− 1+− 0++ 1++

JPC

3.0

3.2

3.4

3.6

3.8

Mas

s/

GeV χc0

χc1

ηc

η′c

hc

J/Ψ

Ψ′

expt (PDG)

m`/ms = 1/5

m`/ms = 1/10

m`/ms = phys

1

2.8

3

3.2

3.4

3.6

3.8

4

4.2

4.4

0−+

0++

1−−

1++

1+−

2++

2−+

2−−

3−−

ηc χc0 J/Ψ χc1 hc χc2 ηc2 Ψ2

meson m

ass in G

eV

A1T1

ET2

exp.

χQCD [arXiv:1410.3343]

0.6

0.8

1

1.2

1.4

1.6

r0(fm) mc ms MJ/ψ-Mηc

Mχc0

Mχc1

MhcfDs

Ratio

1.09(3)0.095(5)

0.1132(7)3.41475(31)

3.51066(7)3.52541(16)

0.2575(46)

0.465(10)1.118(25)

0.101(7)0.119(7)

3.439(44)3.524(66)

3.518(71)0.2536(43)

Exp (PDG)this work (MDs

, MDs* and MJ/ψ as Input)


However ∃ many states near thresholds

1974 – 1977: 10 cc̄ resonances, 1978 – 2001: 0 cc̄’s2002 – 13: ≤ 12 new cc̄’s found by BaBar, Belle, CLEO-c, CDF, D0

4.6

4.4

4.2

4.0

3.8

3.6

3.4

3.2

3.0

L = 2L = 1L = 0

m/G

eV

ηc

J/ψ

ψ(2S)

ψ(4040)

ψ(4415)

χc

ψ(3770)

ψ(4160)

ηc(2S)

hc

Y(4260)

X(3871/3875)X(3943)

Y(3940)Z(3934)

Y(4660)

Y(4350)

X(4160)

DD

DD*

D*D

*

DD**

DsDs

DsDs* Ds

*Ds

*

---

-

-- -

Z+(4430)

standard?????

new detectorshigher luminositynew channels:

B decaysγγ

ψψ-productiongg in pp collisions.Will there be pp̄?Discoveries at LHC!cq̄qc̄ ?cgc̄ hybrids ?


Near threshold states and resonancesMultihadron channels need to be included!Recent studies, open charm:

D∗s0(2317) [DK ] JP = 0+, Ds1(2460) [D∗K ] JP = 1+ Lang et al.

[1403.8103]D∗

0 (2400) [D̄π] JP = 0+, D1(2430) [D̄∗π] JP = 1+, Mohler et al.[1208.4059]

Hidden charm:ψ(3770) JPC = 1−−, χc0(2P) JPC = 0++ [D̄D] Lang et al. [1503.05363].X (3872) I = 0 [DD̄∗, J/ψω] JPC = 1++, Prelovsek et al. [1307.5172],DeTar et al. [1411.1389], update in [1508.07322].X (3872) I = 1 [DD̄∗, J/ψρ, (c̄ d̄)(cu)] JPC = 1++ Padmanath et al.[1503.03257], no candidate found.Y (4140) [J/ψφ, DsD̄∗

s , (c̄ s̄)(cs)] JPC = 1++ channel Padmanath et al.[1503.03257], s- and p-wave scattering Ozaki et al. [1211.5512], nocandidate found.Zc(3900)+ [J/ψπ, DD̄∗, ηcρ, . . . ] IG (JP) = 1+(1+), Prelovsek et al.[1405.7623], Lee et al. [1411.1389], no candidate found.


Zc(3900)+, IG(JP) = 1+(1+)

Prelovsek et al. [1405.7623]

Lattice

D(2) D*(-2)

D*(1) D*(-1)

J/ψ(2) π(−2)ψ

3 π

D(1) D*(-1)ψ

1Dπ

D* D*η

c(1)ρ(−1)

ψ2S

π

D 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]

Even in this “simple” casewhere the minimal configu-ration consists of four quarksand mixing with standardcharmonia can be excluded,a huge number of channelsneeds to be considered!

Basis of 22 operators: no candidate for a Z+c found below 4.2 GeV.


LHCb: pentaquarks are back

[GeV]pψ/Jm4 4.2 4.4 4.6 4.8 5

Eve

nts/

(15

MeV

)

0

100

200

300

400

500

600

700

800

LHCb(b)

Re A

-0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.1

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

LHCb

(4450)cP

(a)

15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

(4380)cP

(b)

Pc Re APc

Im A

P c

P+c (4380) (JP = 3

2−) and P+

c (4450) (JP = 52+) from Λb → J/ψpK

[LHCb: R. Aaij et al, 1507.03414].

Conjecture of attractive forces between charmonium and pp systems:[S. Brodsky, I. Schmidt, G. de Teramond, PRL64 (90) 1011].

Many interpretations, pre- and post-dictions (190 citations).


5 quark (4 q, 1 q̄) systems are very difficult to study directly on thelattice, in particular if many decay channels are possible.

What about testing a particular model instead?Hadroquarkonia: [S. Dubynskiy, M. Voloshin 0803.2224]: Quarkoniabound within ordinary hadrons.

Many combinations of baryon plus charmonium are close-by. Examples:

JP = 32

−: m(∆) + m(J/ψ) ≈ 4329MeV vs. 4380MeV (width 200MeV).

JP = 52+: m(N) + m(χc2) ≈ 4496MeV vs. 4450MeV (width 40MeV).


Quarkonia and potentialsmQ,mQv � ΛQCD, v � 1 −→ Non-relativistic approach (pNRQCD):

Hψnlm = Enlψnlm , H = 2(mQ − δmQ) +p2

mQ+ V0(r) + · · ·

-1.5

-1

-0.5

0

0.5

1

1.5

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

V(r

)/G

eV

r/fm

Σu-

Πu

Σg+

V0(r) can be computed on thelattice.(also 1/mQ and 1/m2

Q correc-tions)

Does this apply to charmonia?Is v . 0.5� 1?Is mcv ≈ 600MeV� ΛQCD?

Nevertheless, we can say some-thing about bottomonia andprovide guidance for charmonia.


Hadroquarkonia in the static limitThis particular picture can be tested in the static limit.Does the static potential V0(r) become more or less attractive in thebackground of a light hadron?

��

��

��

��

��

ttδ tδ

r

Create a zero-momentum projected hadronic state |H〉 at the time 0.Let it propagate to δt, create a quark-antiquark “string”.Destroy this at t + δt and the light hadron at t + 2δt.In the limit t →∞ compute

∆VH(r , δt) = VH(r , δt)− V0(r)

and extrapolate δt →∞.Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 10 / 21

CLS Ensembles

Nf = 2 + 1 CLS ensembles with 2m` + ms = const.(∃ additional sets with m̃s = const and m` = ms)

150

200

250

300

350

400

450

0 0.002 0.004 0.006 0.008 0.01

physical

U103H101

U102H102

U101H105N101

S100C101D101

D150

H402H400B450

S400

N401

H200N202

N203

S201N200

D200

N300N301

N302

J303

J500

J501

mπ[M

eV]

a2[fm2]

U: 128× 243

B: 64× 323

H: 96× 323

S: 128× 323

C: 96× 483

N: 128× 483

D: 128× 643

J: 192× 643

CLS: HU Berlin, TC Dublin, UA Madrid, Mainz, Milano Bicocca,Regensburg, Roma I, Roma II, Wuppertal, DESY Zeuthen


Lattice details

We want a large volume that comfortably accommodates the hadron.

We wish to go to realistically light quark masses but not too light sincethen correlation functions can become noisy and statistically lessmeaningful.

Nf = 2 + 1 CLS ensemble C101 (96× 483 sites):

Mπ = 220MeV, MK = 470MeV, LMπ ≈ 4.6, L ≈ 4.1 fm, a ≈ 0.086 fm.

High statistics: 1552 configs, separated by 4 MDUs, times 12 hadronsources (1 forward, 1 backward, 10 forward and backward propagating ⇒22 2-point functions). Wilson loops at all positions and in all directions.

Wilson loops are optimized using four smearing levels and ground stateoverlap of the hadronic two-point function is optimized too.


QQ binding energy shift “within” a pion

[M. Alberti et al, PRELIMINARY]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8−6

−5

−4

−3

−2

−1

0

r [fm]

∆VΠ(r

)[M

eV]

Π

Preliminary

δ t = 0

δ t = 3

δ t = 6


Within a kaon

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8−7

−6

−5

−4

−3

−2

−1

0

r [fm]

∆V

K(r

)[M

eV]

K

Preliminary

δ t = 0

δ t = 3

δ t = 6


Within a φ

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9−9

−8

−7

−6

−5

−4

−3

−2

−1

0

r [fm]

∆V

φ(r

)[M

eV]

φ

Preliminary

δ t = 0

δ t = 3

δ t = 6

Here we have to be careful with polarizations!


QQ binding energy shift “within” a nucleon

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8−7

−6

−5

−4

−3

−2

−1

0

r [fm]

∆V

N+(r

)[M

eV]

N+

Preliminary

δ t = 0

δ t = 3

δ t = 6


Within a cascade

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8−7

−6

−5

−4

−3

−2

−1

0

r [fm]

∆VΞ

+(r

)[M

eV]

Ξ+

Preliminary

δ t = 0

δ t = 3

δ t = 6


... and negative parity

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7−8

−7

−6

−5

−4

−3

−2

−1

0

r [fm]

∆VΞ

−(r

)[M

eV]

Ξ−

Preliminary

δ t = 0

δ t = 3


Within a decuplet cascade

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9−12

−10

−8

−6

−4

−2

0

r [fm]

∆VΞ

∗+(r

)[M

eV]

Ξ*+

Preliminary

δ t = 0

δ t = 3

δ t = 6

Again we have to be careful with the helicity!Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 19 / 21

What does this mean?In the absence of a light hadron the slope of V0 is ≈ 1GeV/ fm.Within VH this is reduced by ≈ 3MeV/(0.5 fm) ≈ 6%�.The heavy quarks are a bit weaker bound but is there any energy gain?

Virial theorem for a purely linear potential V (r) = σr :

2〈T 〉 =

⟨r dV

dr

⟩= σ〈r〉 = 2E − 2〈V 〉 = 2E − 2σ〈r〉

This means 〈r〉 = 2E/(3σ). Feynman-Hellmann:

∂E∂σ

=

⟨∂H∂σ

⟩= 〈r〉 =

2E3σ

=⇒ E (σH) = E (σ0) + (σH − σ)∂E∂σ

∣∣∣∣σ=σ0

=

(1 + 2σH

σ0

) E (σ0)

3A 6%� smaller σ gives a 4%� smaller energy (adding to 2mQ). The realworld effect is smaller as the potential also contains a Coulomb term.So this amounts to |∆E | = 1–2MeV.


Summary and Outlook

Heavy quark states are narrower and cleaner than many light quarkresonances. Theoretically, the heavy quark limit provides guidance.This is a prime arena for addressing “exotic” spectroscopy.Threshold states with hidden charm or bottom are a huge challenge,however, some aspects can be addressed within approximationsand/or model assumptions.Pentaquarks are back! For how long?Modifications of the static potential in the presence of light hadronsappear tiny (similarly small as in the deuteron). Is this the end ofhadro-quarkonia?Interestingly, there appears to be similar attraction in all of thechannels investigated so far.


gunnarbali withmaurizioalberti,saracollins ... - ias.tum.de fileoutline motivation hadroquarkonium...

Documents