on!the!lace ! sasaprelovsek!lace!setup! sasaprelovsek,!jlab!2015! 7 • wilon+clover!quarks! •...
TRANSCRIPT
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
Sasa Prelovsek, JLab 2015 3
[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)
Sasa Prelovsek, JLab 2015 4
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
Sasa Prelovsek, JLab 2015 5
[review: Brambilla et al., 1404.3723]
Challenges for the theory community: quarkonium-‐like states at threshold
Sasa Prelovsek, JLab 2015 6
[review: Brambilla et al., 1404.3723]
More challenges: quarkonium-‐like states above threshold
All these believed NOT to be QQ !
La2ce setup
Sasa Prelovsek, JLab 2015 7
• 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
Sasa Prelovsek, JLab 2015
Elas@c sca_ering of two mesons
En=EM1(p)+EM2(-‐p)
Sasa Prelovsek, JLab 2015 9
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
Sasa Prelovsek, JLab 2015 10
Mass predic@on for missing Bs0 below BK thresold
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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
Sasa Prelovsek, JLab 2015 12
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
Sasa Prelovsek, JLab 2015 13
[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
Sasa Prelovsek, JLab 2015 14
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
Sasa Prelovsek, JLab 2015 15
• 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
Sasa Prelovsek, JLab 2015 16
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
Sasa Prelovsek, JLab 2015 17
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 ]
Sasa Prelovsek, JLab 2015
Search for hadrons with manifestly exoPc flavor:
ccud (I=1)
Sasa Prelovsek, JLab 2015 19
Zc+ channel : IG=1+, JPC=1+-‐
Sasa Prelovsek, JLab 2015 20
[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
Sasa Prelovsek, JLab 2015 21
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
Zc+ channel : IG=1+, JPC=1+-‐
Sasa Prelovsek, JLab 2015 22
Zc+ channel : IG=1+, JPC=1+-‐
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
Sasa Prelovsek, JLab 2015 24
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?
Sasa Prelovsek, JLab 2015 26
• 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
Sasa Prelovsek, JLab 2015 28
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
Sasa Prelovsek, JLab 2015 31
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)
Sasa Prelovsek, JLab 2015 33
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)”
Sasa Prelovsek, JLab 2015
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, ... )
Sasa Prelovsek, JLab 2015 35
Backup slides
Sasa Prelovsek, JLab 2015 36
[BESIII, 2013, 1303.5949, PRL]
Zc+(3900) g J/Ψ π+
cc du
Sasa Prelovsek, JLab 2015
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+
Sasa Prelovsek, JLab 2015 38
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+
Sasa Prelovsek, JLab 2015 39
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+
Sasa Prelovsek, JLab 2015 40
€
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
Sasa Prelovsek, JLab 2015 41
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)
Sasa Prelovsek, JLab 2015 43
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
Sasa Prelovsek, JLab 2015
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 ]
46