Bound states and resonances from sca/ering on the la4ce

Transcription

1 near threshold Bound states and resonances from sca/ering on the la4ce Sasa Prelovsek University of Ljubljana & Jozef Stefan InsBtute, Ljubljana, Slovenia seminar at CP 3 Origins, Odense, Denmark 31 th March 2014 in collaborabon with D. Mohler, C.B. Lang, L. Leskovec, R. Woloshyn FERMILAB Graz Ljubljana Vancouver Sasa Prelovsek, CP3 Origins,

2 Disclaimer I will talk about hadrons which are currently interesbng from experimental point of view in usual QCD (Nc=3, Nf=2+1). KEEP in MIND: The same methods can be employed in your favorite QCD-like BS model scenario: for example for σèππ, ρèππ which may be of interest to you Sasa Prelovsek, CP3 Origins,

3 Motivation need for rigorous treatment of states near or above threshold charmonium (like) Example: charm sector (experimental status) D-mesons Sasa Prelovsek, CP3 Origins,

4 Almost all hadrons are hadronic resonances (decay strongly) c c u u s u c u uud q stable on strong decay: ab-initio OK q others decay strongly; hadronic resonances only resonance simulated properly by several collab. (first simulation: CP-PACS 2007) SP and coll. (Lang, Mohler, Leskovec, Woloshyn) ( ) Sasa Prelovsek, CP3 Origins, 2014 Verduci, Lang (2012) 4

5 Lattice status general overview States well below strong decay threshold: proper treatment & precision calculations already available for some time States near threshold and resonances above threshold: simulations until ~2011: single-meson approx: - effect of th. not taken into account - strong decays of states ignored exception in meson sector: rho channel 2012, 2013,...: first exploratory simulations with rigorous treatment Sasa Prelovsek, CP3 Origins,

6 Most of interesting states appaer near threshold: charged charmonium [BESIII, 2013, arxiv: ] Z c+ (3900) g J/Ψ π + cc du particle decay year coll Z + (4430) ψ(2s) π Belle, BABAR Z + (4050), Z + (4250) χ c1 π Belle, unconfirmed Z c+ (3900) J/ψ π BESIII, Belle, CLEOc Z c+ (4020) h c (1P) π BESIII preliminary Z c+ (4025) ( D* D*) BES III preliminary Sasa Prelovsek, CP3 Origins,

7 Outline hadrons in QCD, focus on mesons near-threshold states and resonances single-meson approximation rigorous treatment: (1) states near threshold D s0* (2317), X(3872), Z c+ (3900) (2) resonances ρ, K*, D 0 *, D 1 some remaining challenges conclusions Sasa Prelovsek, CP3 Origins,

8 Non-perturbaBve method: QCD on la4ce L QCD = 1 4 G a µν G µν a + q iγ µ ( µ + ig s G µ a T a )q m q q q q =u,d,s,c,b,t input : g s, m q a 2 ensembles: (1) Nf=2, m π =266 MeV (2) Nf=2+1, m π =156 MeV (PACS-CS) Evaluation of Feynman path integrals in discretized space-time quantum m. Dx e i S /! DG Dq Dq e i S QCD /! S = dt L[x(t)] quantum field theory S QCD = d 4 x L QCD [G(x), q(x), q (x)] Sasa Prelovsek, CP3 Origins,

9 Discrete energy spectrum from correlators C DG DqDq C(q,q,G) e i S QCD /!, S QCD = d 4 x L QCD Example: meson channel with given J PC O = q Γq, q Γ 'q, (q Γ 1 q)(q Γ 2 q),... C ij (t) = 0 O i (t) O j + (0) 0 = 0O i n n e E n t no + j 0 = A n ij e E n t All physical states appear as energy levels E n in principle : single parbcle, two-parbcle,... examples : J PC =1, I =1: ρ, ρ(1450), ππ J PC =1 ++, c c : χ c1, X(3872), DD* J PC =1 +, c cd u : Z + c (3900), J /ψ π +, DD* J PC = 0 ++, I = 0 : σ, ππ n Sasa Prelovsek, CP3 Origins,

10 Examples of results within single-meson approximabon only interpolabng fields O q q assumpbons: all energy levels correspond to "one-parbcle" states none of the levels corresponds to mulb-parbcle state m=e (for P=0) these are strong assumpbons... Sasa Prelovsek, CP3 Origins,

11 Example: cc spectrum: single meson approx. m-m ref compared between lat and exp in order to cancel leading am c discrebzabon effects D. Mohler, S.P., R. Woloshyn: , PRD: m π 266 MeV, L 2 fm, Nf=2 crosses: naive lat, diamonds: rigorous lat, lines & boxes: exp Sasa Prelovsek, CP3 Origins,

12 cc spectrum: single meson approx. HSC, L. Liu et al: , JHEP: m π 400 MeV, L 2.9 fm, Nf=2+1 reliable J PC determinabon idenbficabon with n 2S+1 L J mulbplets using <O n> green: lat, black: exp Sasa Prelovsek, CP3 Origins, 2014 Hybrids: some of them have exobc J PC large overlap with O= q F ij q 12

13 all spectra you have seen for excited hadrons near and above threshold were almost certainly done with single-hadron approximabon Sasa Prelovsek, CP3 Origins,

14 Single meson approximabon: one of the problems s c c u,d s c Example: D s0 (2317) channel sc with J P =0 + s DK Is the level D s0 (2317) or perhaps D(0)K(0)? md + mk Sasa Prelovsek, CP3 Origins,

15 Rigorous treatment of near threshold states note: most of interesbng states are found near threshold: D s0* (2317), X(3872), Z c+ (3900), Z b + Sasa Prelovsek, CP3 Origins,

16 D s0* (2317) with J P =0 + O = s c O = DK [d γ 5 c] [s γ 5 d] C ij (t) = 0O i (t)o j + (0) 0 D(! p )! p = n! 2π L K( p! ) Extract E n from C ij (t): variabonal method C ij (t) = n A n ij e E nt due to strong int. We use dis+lla+on method [Peardon et al. 2009] to calculate C ij! p =! n 2π L E(L) = m D 2 +! p 2 + m K 2 + (! p ) 2 + ΔE Energy levels that appear in addibon to these discrete two-parbcle states correspond to bound states or resonances 16

17 D s0* (2317) and DK sca/ering (J P =0 + ) qq O 1 4 = s M c Candidate for D s0* (2317) is found in addibon to the DK states for the first Bme. D. Mohler, C. Lang, L. Leskovec, S.P., R. Woloshyn: , PRL : m π 156 MeV, L 2.9 fm, Nf=2+1 Sasa Prelovsek, CP3 Origins,

18 Sasa Prelovsek, CP3 Origins,

19 Extracting δ(p) from E n δ(p)= phase shift for elastic scattering in infinite volume (1) resonances (2) bound state : cot δ(p BS )=i Sasa Prelovsek, CP3 Origins,

20 Meson-meson scattering: extracting δ(p) from E n at P=p 1 +p 2 =0 [M. Luscher,1991 ] extract E n (L) E n renders p in the region "outside-interaction" p E = s = m p 2 + m p 2 p contains info on δ(p) for periodic BC det[δ ll' δ mm' tanδ l (p) M ll',mm' (q 2 )] = 0 tanδ( p) = π 3/2 q Z 00 (1;q 2 ) Z 00 (1;q 2 )! n N 3 1! n 2 q 2 q L 2π p - p Sasa Prelovsek, CP3 Origins,

21 Sasa Prelovsek, CP3 Origins,

22 D s0* (2317) and DK sca/ering O : s c, DK [d γ 5 c] [s γ 5 d] M. Luscher, 80': E g δ(e) phase shi for DK sca/ering in s-wave δ for DK sca/ering in s-wave extracted using Luscher's relabon pcotδ(p) = 1 a r 0 p2 a 0 = 1.33 ± 0.20 fm r 0 = 0.27 ± 0.17 fm a 0 <0 indicates a state below th. relabon above gives pole posibon and the mass of D s0* (2317) S [cotδ i] 1 =, cotδ( p BS ) = i lat, L m Ds 0 = E D ( p BS ) + E K (p BS ) D. Mohler, C. Lang, L. Leskovec, S.P., R. Woloshyn: , PRL : m π 156 MeV, L 2.9 fm, Nf=2+1 Sasa Prelovsek, CP3 Origins, 2014 D s0* (2317) m - ¼ (m Ds +3m ) Ds* lat 266 ± 16±4 MeV exp ± 0.6 MeV 22

23 X(3872): experimental facts first observed in 2003 [Belle PRL 2003] charmonium-like state J PC =1 ++ [LHCb, 2013] sits within 1 MeV of D 0 D 0* threshold selected decays X(3872) g J/Ψ ω ( I=0 ) X(3872) g J/Ψ ρ ( I=1 ) Sasa Prelovsek, CP3 Origins,

24 X(3872): interpolators J PC =1 ++ (T 1 ++ ), P=0, I=0,1 O : c c, DD *, J /ψω S. P. and L. Leskovec : , PRL Sasa Prelovsek, CP3 Origins,

25 X(3872) : J PC =1 ++ [LHCb 2013], I=0: Wick contracbons O : c c, DD *, J /ψω C ij (t) = 0O i (t)o j + (0) 0 we calculate all Wick contracbons Sasa Prelovsek, CP3 Origins,

26 X(3872) : J PC =1 ++ [LHCb 2013], I=0: Wick contracbons O : c c, DD *, J /ψω we calculate all Wick contracbons results are based only on 13 Wick contracbons in Fig. a (where c propagates from source to sink) the effect of remaining ones suppressed by OZI rule [see also Levkova, DeTar 2011] their effect will be addressed on follow-up analysis Sasa Prelovsek, CP3 Origins,

27 X(3872) : J PC =1 ++ [LHCb 2013], I=0 O : c c, DD *, J /ψω δ for DD* sca/ering in s-wave extracted using Luscher's relabon pcotδ(p) = a 0 2 r 0 p2 a 0 = 1.7 ± 0.4 fm r 0 = 0.5 ± 0.1fm large and a 0 <0 indicates a state slightly below DD* threshold: X(3872) pole posibon gives mass of X(3872) S [cotδ i] 1 =, cotδ( p BS ) = i lat, L m X = E D ( p BS ) + E D* (p BS ) X(3872) m - (m D0 +m D0* ) Candidate for X(3872) is found in addibon to the expected two-parbcle states for the first Bme. S. P. and L. Leskovec : , PRL m π 266 MeV, L 2 fm, Nf=2 Sasa Prelovsek, CP3 Origins, 2014 lat - 11 ± 7 MeV exp ± 0.22 MeV lat: simulabons on larger L required exp: Tomaradze et al.,

28 ComposiBon of established X(3872) with I=0 write two interp. it has sizable coupling with cc as well as DD* interpolabng fields overlaps of X with interpolators X(3872) O i S. P. and L. Leskovec : , PRL m π 266 MeV, L 2 fm, Nf=2 Sasa Prelovsek, CP3 Origins,

29 Search for Z c+ (3900) in J PC =1 +-, I=1 channel O : DD *, J /ψ π Z c + (3900) J /ψ π + [BesIII, Belle, CleoC, 2013] J PC =1 + c c d u if Z c (3900)=Z c (3885) [BesIII, arxiv: ] S. P. and L. Leskovec : , PLB m π 266 MeV, L 2 fm, Nf=2 Only expected two-parbcle states observed. No candidate for Z c+ (3900) with J PC =1 +- is found. Possible reasons: ² perhaps J PC 1 +- if Z c (3900) Z c (3885) ² perhaps our interpolators (all of scat. type) are not diverse enough : calls for further simulabons ²?? Sasa Prelovsek, CP3 Origins,

30 Rigorous treatment of resonances Sasa Prelovsek, CP3 Origins,

31 Almost all hadrons are hadronic resonances (decay strongly) c c u u s u c u uud q stable on strong decay: ab-inibo OK q others decay strongly; hadronic resonances only resonance simulated properly by several collab. (first simulabon: CP-PACS 2007) Sasa Prelovsek, CP3 Origins, 2014 SP and coll. (Lang, Mohler, Leskovec, Woloshyn) ( ) Verduci, Lang (2012) 31

32 ρ resonance P 0: s=e 2 -P 2, Luscher-type relabon: s g δ(s) m 1 =m 2 [Rummukainen, Gotlieb 1995] BW fit of phase shi : general conclusion mass and width reasonably agree with experimental value for rho SimulaBon also by CP-PACS, PACS-CS, QCDSF, ETMC [HSC, PRD 2013] [Lang, Mohler, S.P.,Vidmar, PRD 2011] m π 266 m π 400 MeV MeV Sasa Prelovsek, CP3 Origins,

33 σ resonance in s-wave of ππ sca/ering with I=0 phase shi s in this channel have NOT yet been extracted in QCD unfortunately the only exisbng publicabons by: Ziwen Fu (BUT: these results were obtained in rooted staggered QCD and excited states may be other taste combinabons of ππ while they are interpreted as σ) Sasa Prelovsek, CP3 Origins,

34 K*(892) resonance: first lat deterimation of width P 0: s=e 2 -P 2, Luscher-type relation: s g δ(s) m 1 m 2 [Leskovec & S. P., PRD85 (2012) ] K(p) K s u π(-p) (I,I 3 )=(1/2,1/2) π Bound states and resonances, S. Prelovsek 34

35 K*(892) resonance: first lat deterimabon of width Kπ, I=1/2: p-wave phase shift fit with two elasbc Breit-Wigner resonances [S.P.,Lang, Leskovec, Mohler, , PRD 2013] m π 266 MeV Sasa Prelovsek, CP3 Origins,

36 D 0* (2400) resonance in Dπ sca/ering: J P =0 +, I=1/2 "rigorous" treatment illustrated on this example p = n 2π L All states with J P =0 + appear in lat. spectrum: D o* (2400) D(p) π(-p) with p=n 2π/L : "two-parbcle" states horizontal lines indicate their energies in absence of interacbon Rigorous relabon [M. Luscher, 1991]: E g δ(e) phase shi for Dπ sca/ering in s-wave D(p) π(-p) O : u c D(! p )π(-! p ) [d γ 5 c] [u γ 5 d] BW : δ = acot m 2 2 R E cms m R Γ m and Γ for D 0* (2400) D. Mohler, S.P., R. Woloshyn: , PRD Sasa Prelovsek, CP3 Origins,

37 D-meson resonance masses and widths Γ(E) g 2 p E 2 g is compared to exp instead of Γ (Γ depends on phase sp. and m π ) J P =0 + : D π D * 0 (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 J P =1 + : D* π (analysis of spectrum in this case is based on an assumpbon given in paper below) D 1 (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 first la4ce result for strong decay width of a hadron containing charm quark [D. Mohler, S.P., R. Woloshyn: , PRD] m π 266 MeV, L 2 fm, Nf=2 Sasa Prelovsek, CP3 Origins,

38 Experiment: Experimental puzzle: comparison of scalar charmed mesons D 0 * (2400) : M 2318 MeV Γ 267 MeV c u or c us s? D s0 (2317) : M 2318 MeV Γ 0 MeV c s or c s[u u + d d]? D 0 *(2400): our mass is in favorable agreement with exp without valence ss pair. D s0 *(2317): our mass also in favorable agreement with exp a er taking effect of DK threshold into account which pushes mass down Sasa Prelovsek, CP3 Origins,

39 Other channels light axial resonances a 1 (1260) in ρ π sca/ering b 1 (1235) in ω π sca/ering [Lang, Leskovec, Mohler, S.P., ] scalar cc resonances χ c0 in DD sca/ering [S.P., Leskovec, Mohler, PoS LATTICE 2013, arxiv] scalar κ resonance in Kπ sca/ering; width was not (yet) extracted [Lang, Leskovec, Mohler, S. P., arxiv: , PRD] we studied also repulsive channels Sasa Prelovsek, CP3 Origins,

40 Some remaining challenges elastic scattering = only one channel each energy level E gives one equation for one unknown: f( δ(e), E)=0 non-elastic scattering = more than one channel for example f0(980) : π π and KK each E gives one equation for several unknowns: f( δ ππ (E), δ KK (E), ε(e), E)=0 analytic proposals and relations exist no attempt in QCD simulations yet Sasa Prelovsek, CP3 Origins,

41 Conclusions states well below strong decay threshold determined reliably and with good precision excited states: single-meson approximabon excited states: rigorous treatment ρ, first simulabon PACS-CS 2007, this is sbll the only resonance studied by several collaborabons I presented the first simulabons aimed at rigorous treatment of (2013) K*, a1, b1 D 0* (2400), D 1 (2430), D s0* (2317) X(3872) idenbfied Z c+ (3900) The la4ce search for charmonium-like is not over and keeps the excitement Similar methods can be employed in QCD-like theories BS model Sasa Prelovsek, CP3 Origins,

42 Backup slides Sasa Prelovsek, CP3 Origins,

43 La4ce simulabon Two ensembles: A. Hasenfratz PACS-CS On both ensembles: dynamical u, d, (s), valence u,d,s : Improved Wilson Clover valence c: Fermilab method [El-Khadra et al. 1997] dispersion relation for mesons containing charm m s set using ϕ m c set using distillation method: 1 4 [M 2 (η c ) + 3M 2 (J /ψ)] lat = 1 4 [M(η c ) + 3M(J /ψ)] exp (1) conventional distillation method [Peardon et al. (2009)] (2) stochastic version of distillation method [Morningstar et al. (2012)] Sasa Prelovsek, CP3 Origins,

44 IdenBficaBon of shallow bound state and Levinson's theorem applicabon to la4ce[sasaki, Yamazaki, 2006] example: non-rel. QM sca/ering with square-well (3D) potenbal radius R ; V 0 is such that it contains N=1 bound state Levinson's theorem: delta(0)=n π N=number of bound states applicabons to case of DK sca/ering: one DK bound st D s0 (2317) è delta(0)=π and falls at small p è negabve a 0 on la4ce: negabve a 0 è posibve E shi up-shi ed sca/ering state was observed also in the deuterium channel (pn) [NPLQCD: , PACS-CS PRD84 (2011) ] Sasa Prelovsek, CP3 Origins,

45 Search for Y(4140) in J/Ψ Φ sca/ering Experiment: Y(4140) found in J/Ψ Φ, Γ 11 MeV [CDF 2009] not seen in D s D s not seen by Belle, LHCb J/Ψ Φ sca/ering phase shi [radians] La4ce: method to get δ at more E: twisted BC for valence q. q(x + L) = e iθ q(x) instead of periodic BC (convenbonal) q(x + L) = q(x) conclusion: no resonant structure found at energies reported by CDF S. Ozaki and S. Sasaki, , PRD m π 156 MeV, L 2.9 fm, Nf=2+1 Caveats: s-quark annihilabon ignored twisbng is parbal: only on valence quarks Sasa Prelovsek, CP3 Origins,