Isoscalar!! scattering and the σ/f0(500) resonance

Transcription

1 Isoscalar!! scattering and the σ/f(5) resonance Raúl Briceño [ with Jozef Dudek, Robert Edwards & David Wilson] HadSpec Collaboration Lattice 216 Southampton, UK July, 216

2 Motivation scattering/spectroscopy precision tests of SM u d d u d u d d K d b d d ū d d ū f (5)/ f (5)/ d ū n n d d long range nuclear forces d u u d n d d n d d u u Sample of previous lattice efforts: Alford & Jaffe (2) Prelovsek, et al. (21) Fu (213) Wakayama, et al. (215) Howarth & Giedt, (215) Z. Bai et al. (RBC, UKQCD) (215)

3 The experimental situation summary of various experiments

4 The experimental situation f (5)/ E = 449( 22 16) MeV = 55(24) MeV Peláez (215)

5 Finite vs. infinite volume spectrum Im[s] Infinite volume first Riemann sheet bound state Re[s] threshold branch cut - where scattering takes place s=e 2 cm

6 Finite vs. infinite volume spectrum Im[s] Infinite volume second Riemann sheet narrow resonance Re[s] s=e 2 cm broad resonance s R =(E R i 2 R ) 2

7 Finite vs. infinite volume spectrum finite volume finite volume eigenstates only a discrete number of modes can exist in a finite volume no continuum of states: no cuts no sheet structure no resonances no asymptotic states: no scattering

8 Lüscher formalism spectrum satisfy: det[f 1 (E L,L)+M(E L )] = an exact mapping L finite volume spectrum E L = finite volume spectrum L = finite volume F = known function scattering amplitude M = scattering amplitude

9 Lüscher formalism spectrum satisfy: det[f 1 (E L,L)+M(E L )] = Lüscher (1986, 1991) [elastic scalar bosons] Rummukainen & Gottlieb (1995) [moving elastic scalar bosons] Kim, Sachrajda, & Sharpe/Christ, Kim & Yamazaki (25) [QFT derivation] Bernard, Lage, Meissner & Rusetsky (28) [N" systems] RB, Davoudi, Luu & Savage (213) [generic spinning systems] Feng, Li, & Liu (24) [inelastic scalar bosons] Hansen & Sharpe / RB & Davoudi (212) [moving inelastic scalar bosons] RB (214) / RB & Hansen (215) [moving inelastic spinning particles]

10 Extracting the spectrum Two-point correlation functions: C 2pt. ab (t, P) h O b(t, P)O a(, P) i = X n Z b,n Z a,ne E nt Evaluate all Wick contraction - [distillation - Peardon, et al. (Hadron Spectrum, 29)] e.g. [] [11] m = 236 MeV.2 e E t C(t, )

11 Extracting the spectrum Two-point correlation functions: C 2pt. ab (t, P) h O b(t, P)O a(, P) i = X n Z b,n Z a,ne E nt Evaluate all Wick contraction - [distillation - Peardon, et al. (Hadron Spectrum, 29)] e.g. [] [11] m = 236 MeV close up.2 (d) (b) (a) -.2 (c) (c)

12 Extracting the spectrum Two-point correlation functions: C 2pt. ab (t, P) h O b(t, P)O a(, P) i = X n Z b,n Z a,ne E nt Evaluate all Wick contraction - [distillation - Peardon, et al. (Hadron Spectrum, 29)] Use a large basis of operators with the same quantum numbers Diagonalize correlation function variationally PL ~d = ~ 2 = [11] m = 391 MeV e.g. L/a s = 24 atecm.25 thr..2 KK thr. KK.15 all mm KK.1

13 Extracting the spectrum Two-point correlation functions: C 2pt. ab (t, P) h O b(t, P)O a(, P) i = X n Z b,n Z a,ne E nt Evaluate all Wick contraction - [distillation - Peardon, et al. (Hadron Spectrum, 29)] Use a large basis of operators with the same quantum numbers Diagonalize correlation function variationally PL ~d = ~ 2 = [11] correct spectrum m = 391 MeV e.g. L/a s = 24 atecm.25 thr..2 KK thr. KK.15 all mm KK.1

14 Finite volume spectra m " =236 MeV m " =391 MeV

15 Finite volume spectra m " =236 MeV m " =391 MeV Spectrum satisfies:.14 Use a various parametrizations det[f 1.14 (E L,L)+M(E.14 L )] = One channel, ignoring partial wave mixing: cot (E cm ) + cot (P, L) = e.g M 1 = K 1 + I, Im(I) = [unitarity] K = s g2 s + c

16 Scattering amplitude vs m " HadSpec Collaboration

17 Scattering amplitude vs m " 1.5 [scattering lengths] HadSpec Collaboration

18 Scattering amplitude vs m " [bound state] -1 HadSpec Collaboration

19 Scattering amplitude vs m " HadSpec Collaboration

20 Scattering amplitude vs m " [no narrow resonance] HadSpec Collaboration

21 The σ/f (5) vs m " s =(E i 2 ) 2, g 2 = lim s!s (s s) t(s) /MeV -1 Im p s =

22 The σ/f (5) vs m " s =(E i 2 ) 2, g 2 = lim s!s (s s) t(s) /MeV -1 Im p s =

23 The σ/f (5) vs m " s =(E i 2 ) 2, g 2 = lim s!s (s s) t(s) /MeV -1 Im p s =

24 The σ/f (5) vs m " s =(E i 2 ) 2, g 2 = lim s!s (s s) t(s) /MeV -1 Im p s = Re s σ 1/2 (MeV) PDG estimate poles in RPP 21 poles in RPP 1996 Im s σ 1/2 (MeV) -3-4 Historical perspective -5 J. R. Peláez (215) Review of Particle Physics (RPP)

25 The σ/f (5) vs m " s =(E i 2 ) 2, g 2 = lim s!s (s s) t(s) m " ~35 MeV UχPT - Nebreda & Peláez (215)

26 The σ/f (5) vs m " s =(E i 2 ) 2, g 2 = lim s!s (s s) t(s) UχPT - Nebreda & Peláez (215)

27 Outlook!!-KK / f (98) dispersive analysis chiral extrapolation Elastic form factors of composite particles

28 Outlook!!-KK / f (98) dispersive analysis chiral extrapolation Elastic form factors of composite particles

29 Outlook!!-KK / f (98) dispersive analysis chiral extrapolation, more quark masses(?) Elastic form factors of composite particles m = 14 MeV 1/ E /MeV? cm Bolton, RB & Wilson Phys.Lett. B757 (216) 5-56.

30 Outlook!!-KK / f (98) dispersive analysis chiral extrapolation, more quark masses(?) Elastic form factors of composite particles first implementation: "γ*-to-""/"γ*-to-ρ formalism understood: RB, Hansen - Phys.Rev. D94 (216) no.1, 138. RB, Hansen - Phys.Rev. D92 (215) no.7, RB, Hansen, Walker-Loud - Phys.Rev. D91 (215) no.3, Bernard, D. Hoja, U. G. Meissner, and A. Rusetsky (212) RB, Dudek, Edwards, Thomas, Shultz, Wilson - Phys.Rev. D93 (216) RB, Dudek, Edwards, Thomas, Shultz, Wilson - Phys.Rev.Lett. 115 (215) 2421

31 Take-home message Wilson HadSpec Collaboration Dudek Edwards arxiv: [hep-ph]

32 HadSpec talks Resonance in coupled channels- David Wilson, Monday 1:3 Searches for charmed tetraquarks- Gavin Cheung, Monday 13:55 Radiative transitions in charmonium - Cian O'Hara, Monday 17:25 Optimised operators and distillation - Antoni Woss, Tuesday 14:4 a resonance in "η, KK - Jozef Dudek, Tuesday 15:5 Charmed meson spectroscopy - David Tims, Thursday 14:2 D", Dη and D s K scattering - Graham Moir, Thursday 15: DK scattering - Christopher Thomas, Thursday 15:2 Charmed-bottom mesons - Nilmani Mathur, Friday 15:4

33 Scattering amplitude vs m " 18 [Levinson s theorem] HadSpec Collaboration