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S-Waves & the extraction of b s

S-Waves & the extraction of b s. Sheldon Stone FPCP 2010, Torino, Italy, May 2010. Outline. Mystery of Scalar Mesons Appearances of S-waves D-> K pi  nu Ds-> K+K-pi+ Ds -> K+K-  nu B -> J/psi K* Measuring b s in VV decays J/psi phi phi phi & NP

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S-Waves & the extraction of b s

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  1. S-Waves & the extraction of bs Sheldon Stone FPCP 2010, Torino, Italy, May 2010

  2. Outline • Mystery of Scalar Mesons • Appearances of S-waves • D-> K pi  nu • Ds-> K+K-pi+ • Ds -> K+K-  nu • B -> J/psi K* • Measuring bs in VV decays • J/psi phi • phi phi & NP • Possible effects of S-waves on bs (Franz example) • A new possibility J/psi f0 decays • Predictions of branching ratios from Ds decays • Theoretical predictions (El-Bennich, Colangelo) • Estimation of possible sensitivity • Conclusions (other places S-waves can appear -> K* mu mu) FPCP 2010, Torino, Italy

  3. Mystery of Scalar Mesons • 0+nonet is not well understood • Compare 0- versus 0+ • For 0- nonet, the mass increases by ~400 MeV for each s quark. Why isn’t this true for the 0+ nonet? • Why aren’t the ao & the s degenerate in mass? • Suggestions that the 0+ are 4-quark states FPCP 2010, Torino, Italy

  4. S-waves in DsK+K-p+ decays • Dalitz analyses (also E687) • Fit using a linear S-wave + Breit-Wigner convoluted with Gaussian for the f. Find 6.3% (8.9%) S-wave for 10 MeV (15 MeV) CLEO Bkgrnd subtracted FPCP 2010, Torino, Italy

  5. S-waves via Interference in semileptonic decays • D+K-+m+: Though K is dominantly K*, FOCUS observed an interfering S-wave amplitude with a rate fraction of (2.7±0.4)% for 0.8 < m(K) < 1.0 GeV • DsK+K-e+: S-wave fraction of for 1.01 < m(K+K-) < 1.3 GeV (BaBar) weighted by cosqV FPCP 2010, Torino, Italy

  6. The S-Wave in BJ/ K* • Two Vectors in final states so a transversity analysis is required • BaBar & Belle measure interference between S & P waves in K* decay angle • The fraction of S-wave intensity is (7.31.8)% for 0.8 < m(Kp) <1.0 GeV • BaBar uses this interference to remove ambiguities in the measurement of cos(2b) B MC no interference BaBar FPCP 2010, Torino, Italy

  7. Measuring bs in Bs Decays • Thus far BsJ/ used exclusively • Bs suggested, for null measurement, as decay phase cancels mixing phase • These modes are Vector- Vector final state, so must disentangle CP+ & CP- final states using an angular analysis Vts Vts FPCP 2010, Torino, Italy

  8. Technique • Without S-waves & DG=0 • A0 P=+ longitudinal, A||P=+ trans, AP= - trans • For Bs replace A by -A. • S-Wave term cannot be ignored (Stone & Zhang [arXiv:0812.2832]) • Must add in S-wave amplitude and finite DG. FPCP 2010, Torino, Italy

  9. All terms [Xieet al, arXiv:098.3627] • Time dependence (for ex.) • Can write FPCP 2010, Torino, Italy

  10. Estimate of S-wave Effect • Adding AS can only increase the experimental error. The size of the effect depends on many factors including the magnitude & phase of the S-wave amplitude, bs, values of the strong phases, detector acceptances, biases.. • One simulation for LHCb by Xieet al • Assumes either 5% or 10% S-wave with phases either 0 or 90o. • Simulates many Pseudo experiments • Bias of -10%, error increases by 15%. Can also use to eliminate ds ambiguity Ignore AS Include AS -2bs -2bs FPCP 2010, Torino, Italy

  11. Estimates of J/y f0(980) • Can use S-wave materializing as fo(980) for CP measurements (Stone & Zhang [arXiv:0812.2832]) • The final state J/yfo is a CP+ eigenstate • No angular analysis is necessary! This is just like measuring J/y Ks. The modes J/yh & J/y h can also be used, but they involved g’s in the decay & thus have lower efficiency at hadron colliders • Define: FPCP 2010, Torino, Italy

  12. Estimate Using Hadronic Ds Decays • M(Bs)-M(J/y)=5366- 3097 = 2270 MeV • M(Ds)-M(p) = 1830 MeV, not too different • Use CLEO result for DsK+K-p+ extrapolated to zero f width to extract B(Dsfp+, fK+K-) = (1.6±0.1)% FPCP 2010, Torino, Italy

  13. Estimate from Dsh+h-p+ • CLEO: B(Dsp+p+p-) = (1.11±0.07±0.04)% • Use BaBarDalitz analysis to estimate fraction of fop+[arXiv:0808.0971] • Estimate (27±2)% of final state is in narrow fo peak There is more S-wave under fo peak fo bkgrnd FPCP 2010, Torino, Italy

  14. Estimate from Ds(f/fo) e+n • Compare semileptonic rates near q2=0 to get maximum phase space CLEO [arXiv:907.3201] foe+n fe+n FPCP 2010, Torino, Italy

  15. Semileptonic estimate • At q2=0, where phase space is closest to BsJ/(/fo) • Note that at q2=0 and in the case of Dsfp, the f is forced into a longitudinal polarization state • CDF measures only 53% fL, so these rates may be too large by x2 FPCP 2010, Torino, Italy

  16. Theory Estimates of Rfo/f • Colangelo, De Fazio & Wang [arXiv:1002.2880] • Use Light Cone Sum Rules at leading order in as. • Prediction 1: B(f) measured = (1.3±2.4)x10-3 • B(fo)=(3.1±2.4)x10-4 (0th order), R=24% • B(fo)=(5.3±3.9)x10-4 (leading order), R=41% • Prediction 2: Using ff for f from Ball & Zwicky[arXiv:hep-ph/0412079]RL =0.13±0.06 (0th order), 0.22±0.10 1st order FPCP 2010, Torino, Italy

  17. Check on Prediction • Note that Colangelo et al predict • BR(Ds foe+) = (2.0+0.5−0.4) × 10−3 , • While CLEO measures • BR(Ds  foe+) = (4.0 ± 0.6 ± 0.6) × 10−3, • Which implies that the calculated form-factor is low by a factor of 2, thus compensating for GfL/Gtotal = 0.53 FPCP 2010, Torino, Italy

  18. QCD Factorization • O. Leitneretal [arXiv:1003.5980] • Assume fBs = 260 MeV, ffo = 380 MeV • Predict B(BsJ/ fo) = 1.70 x 10-4. • B(BsJ/ f) = 9.30 x 10-4. • Rfo/f = 0.187. They show small variation with Bsfo form factor; “annihilation” effects important and decrease fo rate. • “S-wave kaons or pions under the f peak in J/yf are very likely to originate from the similar decay J/yfo. Therefore, the extraction of the mixing phase from J/yf may well be biased by this S-wave effect which should be taken into account in experimental analysis” FPCP 2010, Torino, Italy

  19. Summary of R estimates • Measurement will constrain theories FPCP 2010, Torino, Italy

  20. bs Sensitivity Using J/yfo • From Stone & Zhang [arXiv:0909.5442] for LHCb • Assume Rfo/f = 25% • Assume 2 fb-1 at 14 TeV (~4 fb-1 at 7 TeV) • Error in -2bs • J/y f:0.03 rad (not including S-wave) • J/yfo, fop+p-: 0.05 rad • J/yfo+ J/y h′, h′p+p-g:0.044 rad • The fo mode should be useful FPCP 2010, Torino, Italy

  21. BsJ/fo Signal Selection FPCP 2010, Torino, Italy

  22. Conclusions • S-waves are ubiquitous, they appear whenever looked for, & must be taken into account in BsJ/ f measurements of amplitudes, phases, & CP violation • Suggestions: add S-wave amplitudes in the analysis of BK*m+m- & surely in Bs • BsJ/ fo may be a useful mode to add to the statistical precision on the measurement of -2bs, & hopefully will provide useful checks since angular measurements are not necessary FPCP 2010, Torino, Italy

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