On the importance of Kpi scattering for Phenomenology

Transcription

1 On the importance of Kpi scattering for Phenomenology Indiana University/Jefferson Lab. Physics with Neutral Kaon Beam at JLab Workshop Thomas Jefferson National Accelerator Facility Newport News, VA, February 2, 2016

2 Outline 1. Introduction and Motivation 2. Test of ChPT 3. Hadron spectroscopy 4. Test of the SM and new physics 5. Conclusion and outlook

3 1. Introduction and Motivation

4 1.1 Why Kπ scattering is important? Hadron spectroscopy: determine resonances and their nature P-wave: K*(892), K*(1410), K*(1680), S-wave: κ(~800), Exotics, ππ and Kπ building blocks for hadronic physics: - Test of Chiral Dynamics - Extraction of fundamental parameters of the Standard Model - Look for physics beyond the Standard Model: High precision at low energy as a key to new physics? Very important when Final State Interactions at play! 4

5 1.2 Ex: Kπ scattering: P-wave π I=1/2 P-wave scattering phase K*π threshold Boito, Escribano & Jamin 10 Tau data τ Kπν τ threshold parameters See also lattice QCD Dudek et al. Wilson et al. 14 5

6 2. Using Kπ scattering to test ChPT

7 Kπ scattering: P-wave Kπ I=1/2 P-wave scattering phase K*π threshold Boito, Escribano & Jamin 10 ChPT Tau data τ Kπν τ threshold parameters 7

8 2.1 Chiral Symmetry Limit L QCD with mk 0 0 L QCD q L/ R 1 ( 2 1 γ 5 )q = 1 4 G µν G µν + q L iγ µ D µ q L + q R iγ µ D µ q R, q u = d s Symmetry: G SU(3) SU(3) SU(3) L R V Chiral Perturbation Theory: dynamics of the Goldstone bosons (kaons, pions, eta) Goldstone bosons interact weakly at low energy and m u, m d m s < Λ QCD Expansion organized in external momenta and quark masses Weinberg s power counting rule L eff = L d, L d = O ( p d ), p { q, m } q d 2 p << Λ = 4 π ~ 1 GeV H F π 8

9 2.2 Chiral expansion L ChPT = + L 4 + L The structure of the lagrangian is fixed by chiral symmetry but not the coupling constants à LECs appearing at each order The method has been rigorously established and can be formulated as a set of calculational rules: LO : L 2 LO : O p 2 ( ) NLO : O ( p 4 ) NNLO : O ( p 6 ) tree level diagrams with NLO: tree level diagrams with 1-loop diagrams with L 2 L 4 L 2 L6 NNLO: tree level diagrams with L 6 = 2-loop diagrams with 1-loop diagrams with one vertex from L 2 : F 0, B 0 L 4 = L 2 L 4 10 L i O i 4, i=1 90 i C i O 6 i=1 Renormalizable and unitary order by order in the expansion 9

10 2.3 ChPT in the meson sector: precision calculations Today s standard in the meson sector: 2-loop calculations Main obstacle to reaching high precision: determination of the LECs: O(p 6 ) LECs proliferation makes the program to pin down/ estimate all of them prohibitive In a specific process, only a limited number of LECs appear The LECs calculable if QCD solvable, instead Determined from experimental measurement Estimated with models: Resonances, large N C Computed on the lattice 10

11 2.4 Test of SU(3) ChPT Interesting framework to test ChPT is offered by the kaons: K l3, K l4, K 3π, etc A very interesting quantity is the scattering length: first term in the expansion: For ππ: SU(2) ChPT very successful! 11

12 ππ scattering lengths H. Leutwyler 12

13 2.4 Test of SU(3) ChPT Interesting framework to test ChPT is offered by the kaons: K l3, K l4, K 3π, etc A very interesting quantity is the scattering length: first term in the expansion: For ππ: SU(2) ChPT very successful! What about SU(3) ChPT? In principle slower convergence if convergence at all! 13

14 Kπ scattering lengths: S-wave m π a 3/ CA S-wave scattering lengths ChPT O(p 4 ) Roy-Steiner Results so far / m π a 1/2 a 0 0 Buettiker, Descotes-Genon, Moussallam one loop two loops? Janowski 14 Weinberg 1966 tree level prediction for a 0 - one loop prediction for a 0 - two loop estimate for a 0 - Buettiker et al Zhou & Zheng 2006 NPLQCD 2006, Fit A NPLQCD 2006, Fit B NPLQCD 2006, Fit C NPLQCD 2006, Fit D NPLQCD 2006 for a 0 - Fu 2011 for a /2 a 0 14

15 Roy-Steiner equations for Kπ Unitarity effects can be calculated exactly using dispersive methods Unitarity, analyticity and crossing symmetry Roy-Steiner equations Input: Data on Kπ Kπ and π π KK for E 1 GeV two subtraction constants, e.g. and Output: the full Kπ scattering amplitude below 1 GeV In poor agreement with the experimental data Numerical solutions of the Roy-(Steiner) equations: π π: Pennington-Protopopescu, Basdevant-Froggatt-Petersen (70s) Bern group: Ananthanarayan et al. 00, Caprini et al. 11 Orsay group: Descotes-Genon, Fuchs, Girlanda and Stern 01 Madrid-Cracow group: Garcia-Martin,et al. 11 K π: Buettiker, Descotes-Genon, Moussallam 04 K N: Ruiz de Elvira et al a 0 0 a 2 0

16 Kπ scattering lengths: P-wave Kπ I=1/2 P-wave scattering phase K*π threshold Boito, Escribano & Jamin 10 ChPT Tau data τ Kπν τ threshold parameters 16

17 Kπ scattering lengths: P-wave Boito, Escribano & Jamin 10 Our Tau results data ChPT O(p 4 )[?] RChPT O(p 4 ) [?] ChPT O(p 6 )[?] Roy-Steiner [?] m 3 a 1/ (5) (3) 0.18(3) (1) m 5 b 1/ (11) 9) (2) m 7 c 1/ (4) (11) Recent analysis combining K l3, tau and D data : ± Bernard, Kaiser, and Meissner, NP B357 (1991). Bernard, Bernard, Kaiser, Kaiser, and Meissner 91 Meissner, NP B364 (1991). Bijnens, Bernard, Dhonte, Kaiser, and Meissner 91 Talavera, JHEP 0405 (2004). Buettiker, Bijnens, Descotes-Genon, Dhonte, Talavera 04 and Moussallam, EPJC 33 (2004). Buettiker, Descotes-Genon, Moussallam 04 Bernard 14 Poor agreement need more data 17

18 3. Hadron spectroscopy

19 3.1 Determining of pole and width Once one gets Kpi scattering amplitude analytical continuation into the complex plane Poles on the second sheet correspond to zeros on the first sheet! Plot from M. Pennington E resonance pole Dispersive analytic continuation 19

20 Kπ scattering lengths: P-wave Kπ I=1/2 P-wave scattering phase K*π threshold Boito, Escribano & Jamin 10 Tau data τ Kπν τ threshold parameters 20

21 3.2 K*(892) mass and width K (892) MASS CHARGED ONLY, HADROPRODUCED VALUE (MeV) EVTS DOCUMENT ID TECN CHG COMMENT ±0.26 OUR AVERAGE ± BAUBILLIER 84B HBC 8.25 K p K 0 π p 888 ±3 NAPIER 84 SPEC π p 2K 0 S X 891 ±1 NAPIER 84 SPEC 200 π p 2K 0 S X ± BARTH 83 HBC + 70 K + p K 0 π + X 891 ± TOAFF 81 HBC 6.5 K p K 0 π p ±1.6 AJINENKO 80 HBC + 32 K + p K 0 π + X ± AGUILAR B HBC ± 0.76 pp K K 0 S π± ± BALAND 78 HBC ± 12 pp (K π) ± X ± COOPER 78 HBC ± 0.76 pp (K π) ± X ± PALER 75 HBC 14.3 K p (K π) X ± AGUILAR B HBC 3.9,4.6 K p (K π) p 891 ± CRENNELL 69D DBC 3.9 K N K 0 π X 890 ± BARLOW 67 HBC ± 1.2 pp (K 0 π) ± K 889 ± BARLOW 67 HBC ± 1.2 pp (K 0 π) ± K π 891 ± DEBAERE 67B HBC K + p K 0 π + p ± WOJCICKI 64 HBC 1.7 K p K 0 π p Wedonotusethefollowing data for averages, fits, limits, etc ±1.1 27k 4 ABELE 99D CBAR ± 0.0 pp K + K π ±0.2 ±0.5 80±0.8k 5 BIRD 89 LASS 11 K p K 0 π p ± ,3 CLELAND 82 SPEC + 30 K + p K 0 π + p S ± ,3 CLELAND 82 SPEC + 50 K + p K 0 S π + p 893 ± ,3 CLELAND 82 SPEC 50 K + p K 0 S π p ± DELFOSSE 81 SPEC + 50 K ± p K ± π 0 p ± DELFOSSE 81 SPEC 50 K ± p K ± π 0 p ± CLARK 73 HBC 3.13 K p K 0 π p ± ,3 CLARK 73 HBC 3.3 K p K 0 π p ± SCHWEING...68 HBC 5.5 K p K 0 π p CHARGED ONLY, PRODUCED IN τ LEPTON DECAYS VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT ±0.20± k 6 EPIFANOV 07 BELL τ K 0 π ν S τ Wedonotusethefollowing data for averages, fits, limits, etc ±0.5 7 BOITO 10 RVUE τ K 0 S π ν τ ±0.9 8,9 BOITO 09 RVUE τ K 0 S π ν τ ±0.2 8,10 JAMIN 08 RVUE τ K 0 S π ν τ ± BONVICINI 02 CLEO τ K π 0 ντ 895 ±2 12 BARATE 99R ALEP τ K π 0 ντ NEUTRAL ONLY PDG 15 VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT ±0.19 OUR AVERAGE Error includes scale factor of 1.4. See the ideogram below ±0.2 ± k 13 DEL-AMO-SA...11I BABR D + K π + e + νe ±0.2 ± k 14 BONVICINI 08A CLEO D + K π + π ± k 15 LINK 05I FOCS D + K π + µ + νµ 896 ±2 BARBERIS 98E OMEG 450 pp p f p s K K ±0.5 ±0.2 ASTON 88 LASS 11 K p K π + n 1 21

22 3.2 K*(892) mass and width K (892) MASS CHARGED ONLY, HADROPRODUCED VALUE (MeV) EVTS DOCUMENT ID TECN CHG COMMENT ±0.26 OUR AVERAGE ± BAUBILLIER 84B HBC 8.25 K p K 0 π p 888 ±3 NAPIER 84 SPEC π p 2K 0 S X 891 ±1 NAPIER 84 SPEC 200 π p 2K 0 S X ± BARTH 83 HBC + 70 K + p K 0 π + X 891 ± TOAFF 81 HBC 6.5 K p K 0 π p ±1.6 AJINENKO 80 HBC + 32 K + p K 0 π + X ± AGUILAR B HBC ± 0.76 pp K K 0 S π± ± BALAND 78 HBC ± 12 pp (K π) ± X ± COOPER 78 HBC ± 0.76 pp (K π) ± X ± PALER 75 HBC 14.3 K p (K π) X ± AGUILAR B HBC 3.9,4.6 K p (K π) p 891 ± CRENNELL 69D DBC 3.9 K N K 0 π X 890 ± BARLOW 67 HBC ± 1.2 pp (K 0 π) ± K 889 ± BARLOW 67 HBC ± 1.2 pp (K 0 π) ± K π 891 ± DEBAERE 67B HBC K + p K 0 π + p ± WOJCICKI 64 HBC 1.7 K p K 0 π p Wedonotusethefollowing data for averages, fits, limits, etc ±1.1 27k 4 ABELE 99D CBAR ± 0.0 pp K + K π ±0.2 ±0.5 80±0.8k 5 BIRD 89 LASS 11 K p K 0 π p ± ,3 CLELAND 82 SPEC + 30 K + p K 0 π + p S ± ,3 CLELAND 82 SPEC + 50 K + p K 0 S π + p 893 ± ,3 CLELAND 82 SPEC 50 K + p K 0 S π p ± DELFOSSE 81 SPEC + 50 K ± p K ± π 0 p ± DELFOSSE 81 SPEC 50 K ± p K ± π 0 p ± CLARK 73 HBC 3.13 K p K 0 π p ± ,3 CLARK 73 HBC 3.3 K p K 0 π p ± SCHWEING...68 HBC 5.5 K p K 0 π p CHARGED ONLY, PRODUCED IN τ LEPTON DECAYS VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT ±0.20± k 6 EPIFANOV 07 BELL τ K 0 π ν S τ Wedonotusethefollowing data for averages, fits, limits, etc ±0.5 7 BOITO 10 RVUE τ K 0 S π ν τ ±0.9 8,9 BOITO 09 RVUE τ K 0 S π ν τ ±0.2 8,10 JAMIN 08 RVUE τ K 0 S π ν τ ± BONVICINI 02 CLEO τ K π 0 ντ 895 ±2 12 BARATE 99R ALEP τ K π 0 ντ NEUTRAL ONLY PDG 15 VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT ±0.19 OUR AVERAGE Error includes scale factor of 1.4. See the ideogram below ±0.2 ± k 13 DEL-AMO-SA...11I BABR D + K π + e + νe ±0.2 ± k 14 BONVICINI 08A CLEO D + K π + π ± k 15 LINK 05I FOCS D + K π + µ + νµ 896 ±2 BARBERIS 98E OMEG 450 pp p f p s K K ±0.5 ±0.2 ASTON 88 LASS 11 K p K π + n 1 22

23 3.2 K*(892) mass and width PDG e.g. K p K0 Mass of K* (892) [MeV] p K D Kπeν e Hadronic Tau lepton D decays 23

24 3.2 K*(892) mass and width PDG Decay width of K* (892) [MeV] e.g. K p K0 p K D Kπeν e Hadronic Tau lepton D decays 24

25 we summarise the results of a few other determinations of the K0 (800) meters in the recent literature. These are derived from input experimental ttering, 3.3 exceptkappa(800) for the result of Aitala et al. [7] which is basedond Kππ one from Bugg [10] who uses the same data combined with BESS II data (890)Kπ. Our results are compatible with those of [15, 16] who have The results coming from Roy-Steiner and data at higher energy not in dispersive methods. The mass which we find is lighter than in previous agreement with low energy experimental data need improvement! A similar effect was observed in ref. [11] in the caseoftheσ and it was Problem: no other precise data re complete treatment of the left-hand cuts in Roy-type representations. Descotes-Genon, Moussallam 06 M κ (MeV) Γ κ (MeV) This work 658 ± ± 24 Zhou, Zheng [16] 694 ± ± 89 Jamin et al. [18] Aitala et al. [7] 721 ± 19 ± ± 43 ± 87 Pelaez [19] 750 ± ± 22 Bugg [9] ± 120 Ablikim et al. [20] 841 ± ± Ishida et al. [14] mass and width of the K0 Existence would (800) from our work and some suggest 0.4 other recent. Refs. [7, 20, 14] quote Breit-Wigner parameters from which we have κ not a glueball 0.2 corresponding pole positions. ary and outlook S-matrix Re[ s ] S-wave Im[ s ]

26 3.3 Kappa(800) Inputs for S wave in Roy-Steiner analysis from LASS Buettiker, Descotes-Genon, Moussallam 04 S-wave Φ E (GeV) 26

27 3.3 Kappa(800) The results coming from Roy-Steiner and data at higher energy not in agreement with low energy experimental data need improvement! δ I 0 [degrees] I=1/2 I=3/2 Estabrooks Estabrooks S-wave Buettiker, Descotes-Genon, Moussallam E (GeV) 27

28 4. Test sof the SM and new physics

29 Kπ scattering lengths: P-wave Kπ I=1/2 P-wave scattering phase K*π threshold Boito, Escribano & Jamin 10 Tau data τ Kπν τ threshold parameters 29

30 4.1 Determination of fundamental parameters: V us Master formula for K πlν l : Γ Gm C 192π ( K l F K 2 K l [ ]) ( 0) 3 K S EW V K π Kl K us f I π πν γ = + K ( 1+ δem + δsu(2 ) ) 2 30

31 4.1 Determination of fundamental parameters: V us Master formula for K πlν l : Γ Gm C 192π ( K l F K 2 K l [ ]) ( 0) 3 K S EW V K π Kl K us f I π πν γ = + K ( 1+ δem + δsu(2 ) ) 2 ΔKπ ΔKπ π( pπ ) sγ µ u K(p K) = ( pk + pπ) ( pk pπ) f ( t) ( pk pπ) f0( t) µ µ + + µ t t vector scalar 31

32 Dispersive representation for the form factors Omnès representation: f +,0 s ( s) exp π Bernard, Oertel, E.P., Stern 06, 09 ds' φ ( s') s' s' s iε +,0 = s th ϕ +,0 (s): phase of the form factor s< s : φ ( s) = δ ( s) in +,0 Kπ ( ) 2 sth mk + m π s s : ( s) in φ +,0 φ ( s) φ ( s) π π +,0 +,0as Kπ scattering phase = = ± ( f,0() s 1/ s + ) [Brodsky&Lepage] Subtract dispersion relation to weaken the high energy contribution of the phase. Improve the convergence but sum rules to be satisfied. 32

33 Global fit to V us & V ud V us 1σ contours! FlaviaNet KaonWG 10 Updated by Moulson@CKM2014 fit" fit with unitarity" V us " V ud = (21)! V us = (7)! χ 2 /ndf = 1.16/1 (28.1%)" Δ CKM = (5)! 1.0σ! V ud unitarity" V ud 33

34 4.2 FSI in the quest for New Physics Ex: CP violating asymmetries: B K* ll Matthias et al 12 Camalich&Jaeger 11 Doering, Meissner, Wang 13 etc XP 2 \ 0.0 XP 5 \ q 2 HGeV 2 L q 2 HGeV 2 L LHCb at EPS13 : 2.9 discrepancy in P 2, 4.0 in P 0 5! [blue: SM unbinned, purple: SM binned, crosses: LHCb] 34

35 4.2 FSI in the quest for New Physics Ex: CP violation in D à Kππ Ex: Dalitz plot 35

36 4.2 FSI in the quest for New Physics Ex: CP violation in D à Kππ Niecknig & Kubis 15 Full set of equations S 2 ππ (u) = Ω2 0 (u) { P 1 ππ (u) = Ω1 1 (u) { S 1/2 πk S 3/2 πk P 1/2 πk D 1/2 πk (s) = Ω1/2(s) 0 (s) = Ω3/2(s) 0 (s) = Ω1/2(s) 1 (s) = Ω1/2(s) 2 u 2 4M 2 π Ŝ 2 ππ (u ) u 2 (u u) dµ2 0 c 0 + c 1 u + u 2 4M 2 π } ˆP 1 ππ (u ) u 2 (u u) dµ1 1 c 2 + c 3 s + c 4 s 2 + c 5 s 3 + s 4 s2 c 6 + s (M K +Mπ ) 2 (M K +Mπ ) 2 (M K +Mπ ) 2 } (M K +Mπ ) 2 Ŝ 3/2 πk (s ) s 2 (s s) dµ3/2 0 ˆP 1/2 πk (s ) s (s s) dµ1/2 1 ˆD 1/2 πk (s ) (s s) dµ1/2 2 Ŝ 1/2 πk (s ) s 4 (s s) dµ1/2 0 36

37 4.2 FSI in the quest for New Physics Ex: CP violation in D à Kππ Niecknig & Kubis 15 Dalitz plot slices t [GeV 2 ] CLEO s [GeV 2 ] 200 full fit: χ 2 /ndof bin number 37

38 4.2 FSI in the quest for New Physics Ex: CP violation in D à Kππ fit fractions Niecknig & Kubis 15 slices Full fit S 2 ππ (8 ± 3)% S 1/2 πk (72 ± 12)% P 1/2 πk (10 ± 2)% S 3/2 πk (16 ± 3)% D 1/2 πk (0.15 ± 0.1)% Σ (106 ± 20)% full fit: χ 2 /ndof bin number fit fractions: hierachy of partial-wave amplitudes compare to previous analyses 38

39 5. Conclusion and Outlook

40 Conclusion and Outlook Determining Kπ scattering reliably very important: Low energy: test of Chiral Dynamics Intermediate energy: Determination of Resonance parameters Very important to help taking into account final state interactions and hunting for new physics CP violation in heavy meson decays Hadronic data on which most of the analyses rely not in good agreement with more recent data coming mainly from tau decays worth remeasuring it. Possibility at Jlab with KL? Major advantage: pure I=1/2 measurement 40

41 6. Back-up

42 2.5 Determination of some low energy constants πk Roy-Steiner πk sum-rules Kl 4, O(p 4 ) Kl 4, O(p 6 ) 10 3 L ± ± ± ± L ± ± ± ± L ± ± ± ± L ± ± ± 0.9 Significant violation of OZI rule in the scalar sector Large values for the condensates! 42

43 3.2 Kappa(800) Inputs for S wave in Roy-Steiner analysis from LASS Buettiker, Descotes-Genon, Moussallam 04 S-wave Φ E (GeV) 43

44 3.2 Kappa(800) The results coming from Roy-Steiner and data at higher energy not in agreement with low energy experimental data need improvement! δ I 0 [degrees] I=1/2 I=3/2 Estabrooks Estabrooks S-wave Buettiker, Descotes-Genon, Moussallam E (GeV) 44

45 P wave Inputs: Buettiker, Descotes-Genon, Moussallam P-wave Φ E (GeV) 45

46 P wave I=1/2 Estabrooks Aston P-wave Buettiker, Descotes-Genon, Moussallam 04 δ 1/2 1 [degrees] E (GeV) 46

47 P wave 0.2 Buettiker, Descotes-Genon, Moussallam 04 P-wave δ 3/2 1 [degrees] Estabrooks E (GeV) 47