on!the!lace ! sasaprelovsek!lace!setup! sasaprelovsek,!jlab!2015! 7 • wilon+clover!quarks! •...

Charmonium-‐like and other near-‐threshold mesons on the la2ce

University of Ljubljana & Jozef Stefan Ins@tute, Slovenia

February -‐ August 2015 Theory & Computa@onal Physics, JLab (office A206)

1

in collabora@on with: Chris@an B. Lang, Luka Leskovec, Daniel Mohler, Richard Woloshyn

Sasa Prelovsek

Graz Ljubljana FERMILAB TRIUMF

Sasa Prelovsek, JLab 2015

JLab Theory Seminar, 23rd February, 2015

Outline •  Experimental appe@zer for states with heavy quarks: most interes@ng experimental states are located near threshold ! •  I will discuss hadronic states that have to be address by simula@ng the sca_ering of two mesons on the la2ce

•  States slightly below threshold : Bs0 , Bs1 , Ds0 , Ds1 , X(3872)

Flavor according to quark model: s b s c c c “deuterium-‐like” bound states: first la2ce simula@ons of such states in mesonic system

Only few such states in heavy-‐meson spectrum; none (to my knowledge) in light-‐meson spectrum

•  Search for flavor exo@c states: Zc+ , c c d u

•  Resonances above threshold: K*, a1 , b1 , D0*, D1, Ψ(3770)

•  Conclusions

Sasa Prelovsek, JLab 2015 2


[BESIII, 2013, 1303.5949, PRL]

Zc+(3900) g J/Ψ π+

cc du

state confirmed by

BeSII, Belle, Cleo-‐c

Experimental appe@zer

A charged charmonium-‐like state: Zc+(3900)

DD* thr.

Charged bottomonium-like states: Zb+(10610) and Zb

+(10650)


Y(1S) π+

Y(2S) π+

Y(3S) π+

€

Zb+ → Y (1S) π +

Y (2S) π +

Y (3S) π +

hb (1P) π +

hb (2P) π +

average

BB*+ th. B*B*+ th.

•  both: IG(JP)=1+(1+)

•  both: observed only by Belle [1105.4583]

Zb+ è Y(nS) π+

b b d u


[review: Brambilla et al., 1404.3723]

Challenges for the theory community: quarkonium-‐like states at threshold


[review: Brambilla et al., 1404.3723]

More challenges: quarkonium-‐like states above threshold

All these believed NOT to be QQ !

La2ce setup


•  Wilon-‐clover quarks

•  Fermilab method for c and b : [El Khadra, Kronfeld et al, 1997]

Rest hadron energies have sizable discre@za@on errors but these largely cancel in spli2ngs.

Only spli2ngs with respect to a chosen reference mass are compared to experiment.

•  evalua@ng Wick contr.: dis@lla@on (Ensemble 1) [Peardon et. al., HSC, 2009] stochas@c dis@lla@on (Ensemble 2) [Morningstar et al., 2011]

PACS-‐CS

8

O = qΓq, (qΓ1q)(qΓ2q), [qq ][qq]

Cij (t) = 0Oi (t)Oj+(0) 0 =

n∑ Zi

n Z jn* e−En t Zi

n = 0Oi n

Example: meson channel with given JPC

Discrete energy spectrum from correlators

All physical states with given JPC appear as energy levels En in principle : single par@cle, two-‐par@cle,...

channel : "eigenstates" JPC = 0+, sb : Bs0 ,BKJPC =1++, cc : χc1 ,X(3872), DD*,JPC =1+−, ccdu : Zc

+, J /ψ π +,...JPC =1−−, su : K*, KπJPC =1++, ud : a1, ρπ

Two-‐meson states:

•  In experiment: two-‐meson decay products with con@nuous E.

•  On la2ce: discrete E due to finite L and periodic BC: p=n 2π/L

Bound state and narrow resonance:

typically lead to extra energy level (in addi@on to two-‐meson levels)

Energies and overlaps extracted using GEVP


Elas@c sca_ering of two mesons

En=EM1(p)+EM2(-‐p)


at total momentum P=0

En(L) p δ(p) Luscher’s eq.

Sca_ering matrix for par@al wave l:

Bound state: cot[δ(pB)] = i , pB2<0 mB=EM1(pB)+EM2(-‐pB)

Resonance (of Breit-‐Wigner type):

cot �(p) =2Z00(1; (

pL2⇡ )

2)

Lpp⇡

M1(p)

M2(-‐p)

Bound states slightly below threshold


Mass predic@on for missing Bs0 below BK thresold


JP =0+ : O = s̄b, B(0)K(0), B(1)K(�1)

•  Scalar Bs state has not been experimentally found yet. •  It is expected slightly below BK threshold. •  We simulated BK sca_ering on PACS-‐CS Ensemble (2).

“Bs0” “B(0)K(0)” “B(1) K(-‐1)”

p=2π/L

pB = i|pB | cot �(pB) = i

pB cot �(pB) = �|pB |

The sca_ering matrix has a pole at the posi@on of the bound state

(on the first Riemann sheet)

mlatB = EB(pB) + EK(�pB)

|p|

[C. Lang, D. Mohler, S.P. , R. Woloshyn: 1501.0164]

δ interpolated using eff. range approx

p cotδ = 1a0+12r0p

2

Mass predic@on for missing Bs0 and Bs1


Quan@@es shown:

•  Bs1’ and Bs2 agree well with exp •  Bs0 and Bs1 are predic@ons for

yet unobserved states (errors contain sta@s@cal and several sources of systema@cal uncertain@es)

Ensemble (2), mπ=156 MeV

[C. Lang, D. Mohler, S.P. , R. Woloshyn: 1501.0164]

Ds0 and Ds1 below DK and D*K thresholds


[D. Mohler, C. Lang, L. Leskovec, S.P. , R. Woloshyn: 1308.3175, Phys. Rev. Le_ 2013

1403.8103, PRD 2014]

•  Analogy, just b replaced with c •  In this case Ds0 and Ds1 have been observed

experimentally •  Quark models expected them above thresholds

but they were found below them

•  Our post-‐dic@ons agree with measured masses

Ds0 from indirect simula@on (1) Five channels that do not include Wick contrac@ons are simulated (2) Sca_ering lengths for four mπ extracted

(3) simultaneous fit using SU(3) unitarized ChPT is performed and LEC's are determined

(4) using these LEC's indirect predic@ons for Ds0 channel with DK (S=1,I=0):

pole in the first Riemann sheet found


L. Liu, Orginos, Guo, Hanhart, Meissner, 1208.4535, PRD, mπ≈300-‐620 MeV, Nf=2+1

€

a = limp→ 0tanδ(p)

p

€

DK (S = −1, I =1)

€

DK (−1, 0)

€

DK (S = 2, I = 12)

€

Dπ (0, 32)

€

DK (1,1)

Ds0*(2317) m Γ [Ds0*gDs π] indirect lat 2315 +18-‐28 MeV 133±22 keV

exp 2317.8 ±0.6 MeV < 3.8 MeV

€

DK (S =1, I = 0)

points: D. Mohler, S.P. et al 1308.3175, PRL

X(3872) , JPC=1++ , charmonium-‐like


•  First charmonium-‐like state discovered [Belle, PRL, 2003] •  sits within 1 MeV of D0D0* threshold 8 MeV below D+D*-‐ threshold

•  believed to have a large molecular D0D0* Fock component •  Γ < 1.2 MeV •  decays to I=0, 1 equally important X(3872) g J/Ψ ω ( I=0 ) X(3872) g J/Ψ ρ ( I=1 )

[LHCb, PRL 2013]

isospin breaking effects my be important

X(3872), 1++, I=0


O : c c, DD*= (cu)(uc)+ (cd)(dc), J /ψω = (cc)(uu+ dd)

[S.P. and L. Leskovec, Phys.Rev.Le_. 2013 ]

•  all Wick contrac@ons calculated using dis@lla@on method [Peardon et al. 2009] •  charm annihila@on contrac@ons not used in analysis

charm annihila@on

X(3872) below DD* threshold, I=0


O : c c, DD*, J /ψω

[S.P. and L. Leskovec : 1307.5172,

Phys. Rev. Le_. 2013]

Ensemble (1), mπ≈266 MeV, Nf=2

X(3872) m -‐ (mD0+mD0*)

lat -‐ 11 ± 7 MeV

exp -‐ 0.14 ± 0.22 MeV

X(3872) appears only if both cc and DD* interp. used.

Assump@ons/approxima@ons:

•  charm Wick annihila@on omi_ed

•  DD* sca_ering analyzed assuming

J/ψω is decoupled (good evidence for

that from the la2ce data)

•  mu=md

•  δ for DD* sca_ering in s-‐wave extracted using Luscher's rela@on

•  δ interpolated near threshold

•  pole found in the sca_ering matrix

T ∝[cotδ − i]−1 =∞, cotδ(pBS ) = imDs0

lat, L→∞ = ED (pBS )+EK (pBS )

New evidence for X(3872) : JPC=1++, I=0

18

O : c c, DD*

Interpreta@on

D(0)D*(0)

X(3872)

χ c1

X(3872) m -‐ (mD0+mD0*)

lat -‐ 13 ± 6 MeV

exp -‐ 0.14 ± 0.22 MeV

D(1)D*(-‐1) state is not found although O incorporated

HISQ quarks , mu = md = ms/5, 163 x 48, a =0.15 fm [C. DeTar, Song-‐haeng Lee, et al., 1411.1389, Lat14 proceedings ]


Search for hadrons with manifestly exoPc flavor:

ccud (I=1)


Zc+ channel : IG=1+, JPC=1+-‐


[S.P., Lang, Leskovec, Mohler, 1405.7612v2, PRD 2015] Ensemble (2), mπ≈266 MeV, L≈2 fm, Nf=2

La2ce: lines represent energies of 13 two-‐meson states E = E[ M1(p1) ] + E[ M2(p2) ] in non-‐interac@ng case

Extrac@ng 13 two-‐meson states

is a huge challenge!

BESIII

Γ

Interpola@ng fields


O14q ≈ [c Cγ5 d ]3c [c γ iC u]3c

O24q ≈ [c C d ]3c [c γ iγ5C u]3c

and 13 others ..

18 two-‐meson (MM) 4 diquark-‐an@diquark (4Q) and 2 others ..

Aiming at 9 two-‐meson states listed in previous slide

Aiming to find addi@onal state related to exo@c Zc+

Wick contrac@ons

Cij (t) = 0Oi (t)Oj+(0) 0

cud




Conclusion: •  we find 13 two-‐meson states

(black circles) as expected

•  we find no addi@onal state below 4.2 GeV

•  we find no candidate for Zc below 4.2 GeV

[S.P., Lang, Leskovec, Mohler, 1405.7612v2, PRD 2015] Ensemble (1), mπ≈266 MeV, L≈2 fm, Nf=2

23

spectrum from 18 interp.

Zc+ channel spectrum from 22 interp.

Results from the extended basis: based on En and •  lowest 13 states (black): two-‐meson states •  no extra state below 4.2 GeV •  no extra state at 4.16 GeV

(extended basis gives an extra state at 4.4 GeV)

•  a_ribu@ng a state at 4.16 GeV to Zc+ (green) was a premature conclusion

•  we can not exclude that state at 4.16 GeV was a linear combina@on of omi_ed two-‐meson states, induced via O4q

Conclusion: we do not find Zc+ candidate below 4.2 GeV 1405.7623v1 1405.7623v2

Zin = 0Oi n

[S.P., Lang, Leskovec, Mohler] Sasa Prelovsek, JLab 2015

Similar conclusion concerning Zc+ channel


S.-‐H. Lee, C. DeTar, H. Na, La2ce 2014 proc.: 1411.1389

mu=ms/5; Nf=2+1+1; HISQ

Zc channel, I=1, JPC=1+-‐

Only expected two-‐meson states, no candidate for Zc

Puzzle: why there is no addi@onal eigenstate related to Zc+(3900) on the la2ce?

Why does such large basis of crea@on operators not excite observed Zc+ (in addi@on to two-‐meson states) ? ²  Even more interpolators needed ? ²  Is mπ=266 MeV to high?

²  Could the neglect of charm annihila@on contribu@on significantly modify the conclusion?

²  Is something wrong with working assump@on that Zc+

should lead to an addi@onal eigenstate? Note: we have observed addi@onal levels for resonances: : ρ, K*, D0

*, D1, a1, b1 , Ψ(3770) bound states: Ds0

*, Ds1, Bs0*, Bs1, X(3872)

Is Zc is of different origin and does not lead to addi@onal level? ²  Perhaps an addi@onal eigenstate does not have to arise if it is a

coupled channel effect: more analy@cal work is needed 25

JPC=1+-‐

O14q ≈ [c Cγ5 d ]3c [c γ iC u]3c

O24q ≈ [c C d ]3c [c γ iγ5C u]3cSasa Prelovsek, JLab 2015

Is Zc related to coupled-‐channel effect?


•  la2ce, HALQCD method, mπ≈410 MeV, Nf=2+1+1

HALQCD coll, Iketa et al [not available on arXiv yet, slides from Quarkonium 2014]

Is Zc related to coupled-‐channel effect?

27

la2ce (HALQCD method) experiment

HALQCD is inves@ga@ng if extracted sca_ering matrix has a pole. It needs to be inves@gated whether this scenario would lead to an addi@onal energy level or not.

It is not clear yet whether this scenario could be compa@ble with absence of the Zc energy level in our spectrum.

σ ∝ Im[T ]J /ψ π

σ ∝ Im[T ]D D*

mπ≈410 MeV, Nf=2+1+1

Mesons above threshold – resonances


O = qΓq, (qΓ1q) !p1

(qΓ2q) !p2= M1( !p1) M2 ( !p2 )

29

Almost all hadrons are resonances above threshold

well below strong decay th.

€

u u

€

s u

€

c u

€

uud

€

c c

well below open charm decay th.

rigorous treatment a_empted

30

Kπ , I=1/2: p-wave phase shift

[S.P. ,Lang, Leskovec, Mohler, 1307.0736, PRD 2013] mπ≈266 MeV

K*(892) resonance Kπ

irreps where p-‐wave does not mix with s-‐wave, Lusher-‐type rel.: [Lekovec, S.P. PRD 2012]

p3 cot δ / s1/2

•  qq, Kπ, Kη interpolators •  a number of different 0<P≤2 •  for each En: one determinant equa@on for many unknowns •  T-‐matrix parametrized to get around this problem •  the loca@on of poles of T-‐matrix in complex plain is

given below •  K*(892) and κ are below threshold for this mπ

•  K0* , K2* are resonances •  mπ=391 MeV, NL=16, 20, 24 [Dudek, Edwards, Thomas, Wilson, HSC, 1406.4158, PRL; 1411.2004]

Resonances in Kπ, Kη coupled channels


loca@on of poles in T matrix in complex plane

•  Simula@ng sca_ering:

ρ π in 1++ channel to extract a1(1260) ω π in 1+-‐ channel to extract b1(1235)

•  One mo@va@on: COMPASS claim for a1’(1420) from f0(980) π [1312.3678]

Our spectrum supports only one a1 below 1.8 GeV (not two)

•  mπ≈266 MeV, L≈2 fm, Nf=2 , P=0 [Lang, Leskovec, Mohler, S.P. , 1401.2088, JHEP]

PDG exp 1.40(2) [Basdevant, Berger, 1501.04643]

•  ρ and ω assumed to be stable, good approx. for given simula@on parameters : [Roca, Oset, 1201.0438]

•  going beyond that approxima@on will be very challenging

•  3-‐par@cles: [Hansen, Sharpe 1311.4848; Polejaeva, Rusetsky, 1203.1241; Briceno, Davoudi, 1212.3398,.... ]

Lightest axial resonances a1 and b1

32

€

Γ(E) ≡ g2 pE 2

D-‐meson resonances in Dπ and D*π g is compared to exp instead of Γ (Γ depends on phase sp. and mπ)


D0*(2400) m -‐ 1/4(mD+3 mD*) g

lat 351 ± 21 MeV 2.55 ± 0.21 GeV

exp 347 ± 29 MeV 1.92 ± 0.14 GeV

D1(2430) m -‐ 1/4(mD+3 mD*) g

lat 381 ± 20 MeV 2.01 ± 0.15 GeV

exp 456 ± 40 MeV 2.50 ± 0.40 GeV

€

Γ(E) ≡ g2 pE 2

first la2ce result for strong decay width of a hadron containing charm quark [D. Mohler, S.P. , R. Woloshyn: 1208.4059, PRD] •  mπ≈266 MeV, L≈2 fm, Nf=2

JP=0+ : D π JP=1+ : D* π (analysis of spectrum in this case is based on an assump@on given in paper below)

Resonance ψ(3770) in p-‐wave DD sca_ering

34

c̄c, JPC= 1

��: J/ , (2S) below D ¯D threshold

(3770) lowest state above threshold

PRELIMINARY

“Ψ(3770)” “D(1)D(-‐1)” “Ψ(3770)” “D(1)D(-‐1)”


Γexp ~ 27 MeV

�(s) =g2

6⇡

p3

s

Conclusions

Status of meson spectrum from la2ce simula@ons (in brief): q  Evidence found for states with non-‐exoPc flavor: •  states well below th. : charmonium , D, π, K ... and all the others •  resonances via BW : ρ, K*, K0*(1430), K2, D0

*, D1, a1, b1 , Ψ(3770) •  shallow bound states : Ds0, Ds1, Bs0, Bs1 , X(3872) with I=0

All these manifest themselves via an addi@onal energy level (in our experience so far) !

q  No evidence for manifestly exoPc states (yet), at least by searching an addi@onal energy level •  Zc+ = ccud

Theory is facing a serious challenge to establish whether exo@c states arise from QCD or not.

Only a�er this is se_led, theory can claim structure (mesonic molecules, diquark an@diquark, coupled channel effects, ... )


Backup slides


[BESIII, 2013, 1303.5949, PRL]

Zc+(3900) g J/Ψ π+

cc du


Charged charmonium Zc+ : experimental status

parPcle C JP decay year coll

Z+(4430) -‐ 1+ ψ(2S) π+ 2008 Belle, BABAR, LHCb

Zc+(3900) -‐ ? J/ψ π+ 2013 BESIII, Belle, CLEOc

Zc+(3885) -‐ 1+ ( DD*)+ 2013 BESIII

Zc+(4020) -‐ ? hc(1P) π+ 2013 BESIII

Zc+(4025) -‐ ? ( D* D*)+ 2013 BES III

Z+(4200) -‐ 1+ J/ψ π+ 2014 Belle

Z+(4050) + ? χc1 π+ 2008 Belle

Z+(4250) + ? χc1 π+ 2008 Belle

candidates with preferred

IG=1+, JPC=1+-‐ [review: Brambilla et al., 1404.3723]

Γ

37

Challenge : precision simula@on of Zc+


On larger volume: more two par@cle states

Rigorous treatment very challenging: at least 6 two-‐par@cle channels coupled !!

And there are other two-‐par@cle states!

Physical masses used

E(L) = m12 +!p1

2 + m22 +!p2

2 +ΔE

!p1 = 2πL!n1 !p2 = 2π

L!n2

Another challenge: Zb+


On larger volume: more two-‐par@cle states

Rigorous treatment very challenging: at least 6 two-‐par@cle channels coupled !!

And there are other two-‐par@cle states!

Zb+ -‐> YnS π+

b u b d

Belle 2011 Y1S π+

Y2S π+

Y3S π+

Physical masses used

E(L) = m12 +!p1

2 + m22 +!p2

2 +ΔE

!p1 = 2πL!n1 !p2 = 2π

L!n2

•  δ for DK sca_ering in s-‐wave extracted using Luscher's rela@on

•  δ interpolated near threshold •  pole found in the sca_ering matrix

Ds0*(2317) : bound state below DK threshold, JP=0+


€

O : s c, DK ≈ [d γ5c] [s γ5d]

[D. Mohler, C. Lang, L. Leskovec, S.P. , R. Woloshyn: 1308.3175, Phys. Rev. Le_ 2013

1403.8103, PRD 2014]

T ∝[cotδ − i]−1 =∞, cotδ(pBS ) = imDs0

lat, L→∞ = ED (pBS )+EK (pBS )

[1403.8103 PRD 2014]

mD+mK

mD+mK


X(3872) channel: I=1, JPC=1++

S. P. and L. Leskovec : 1307.5172 PRL 2013, mπ≈266 MeV, Nf=2

Only expected two-‐par@cle states observed. No candidate for X(3872) with I=1 found. In agreement with experiment that does not find charged X either. The simula@on is done in the isospin limit mu=md. The absence of I=1 state for mu=md is in agreement with two interpreta@ons: (1)

(2) X(3872) pure I=0 state

isospin breaking decay X(3872) -‐> J/ψ ρ (I=1)

is due to isospin spli2ng D0 D0* , D+D-‐* €

aI =1(mu = md ) = 0aI =1(mu ≠ md ) << aI =0

42 Sasa Prelovsek, JLab 2015

BESIII

²  Zc(3900) was found in J/ψ π inv. mass only in [BESIII, Belle, CLEOc, 2013]

²  Zc(3900) was NOT found in J/ψ π inv. mass in

Belle 2014, 1408.6457 LHCb, 2014, 1404.5673 COMPASS, 2014, 1407.6186

Puzzle from experiment: Zc+(3900) seen only in Y decays

What about other channels in experiment and other experiments?

Checking our implementa@on of Fermilab method: spli2ngs on Ensemble (2)


cc spectrum: single-‐hadron approxima@on

[HSC , L. Liu et al: 1204.5425, JHEP] •  mπ≈400 MeV, L≈2.9 fm, Nf=2+1 •  reliable JPC determina@on •  iden@fica@on with n 2S+1LJ mul@plets using <O|n> •  green: lat, black: exp Sasa Prelovsek, JLab 2015

Hybrids: some of them have exo@c JPC large overlap with O= q Fij q

44

D spectrum: single-‐hadron approxima@on

G. Moir et al, HSC (Hadron Spectrum Coll.): 1301.7670, JHEP: •  mπ≈400 MeV, L≈2.9 fm, Nf=2+1 •  reliable JP determina@on; many excited states

•  iden@fica@on with n 2S+1LJ mul@plets using <O|n> •  green: lat, black: exp

1S-‐2S:

~ 700 MeV


Hybrids:

large overlap with O= q Fij q gluonic tensor Fij=[Di , Dj ]

45

Ds spectrum: single-‐hadron approxima@on

G. Moir et al., HSC : 1301.7670, JHEP: •  mπ≈400 MeV, L≈2.9 fm, Nf=2+1 •  reliable JPC determina@on •  iden@fica@on with n 2S+1LJ mul@plets using <O|n> •  green: lat, black: exp Sasa Prelovsek, JLab 2015

Hybrids: large overlap with O= q Fij q gluonic tensor Fij=[Di , Dj ]

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on!the!lace ! sasaprelovsek!lace!setup! sasaprelovsek,!jlab!2015! 7 • wilon+clover!quarks! •...

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