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Solving the B  K  Puzzle

Third International Conference on Flavor Physics October 3- 8, 2005. Solving the B  K  Puzzle. Cheng-Wei Chiang National Central University & Academia Sinica. Based upon following works: PRD 69 , 034001 (2004) [hep-ph/0307395]; PLB 580, 186 (2004) [hep-ph/0310073];

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Solving the B  K  Puzzle

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  1. Third International Conference on Flavor Physics October 3- 8, 2005 Solving the B K  Puzzle Cheng-Wei Chiang National Central University & Academia Sinica Based upon following works: PRD 69, 034001 (2004) [hep-ph/0307395]; PLB 580, 186(2004) [hep-ph/0310073]; PRD 70, 034020 (2004) [hep-ph/0404073]; PLB 598, 218 (2004) [hep-ph/0406126]; hep-ph/0502183.

  2. Outline - • The problem • Large color-suppressed amplitude solution • Large electroweak penguin solution --- FCNC Z0 boson • The  K and K* modes • Summary and outlook Solving the B to K pi Puzzle (10/6/2005)

  3. Flavor Amplitudes of Kp Modes - • The amplitudes of the four K  modes can be decomposed according to the flavor flow topology as follows (ignoring smaller amplitudes): Solving the B to K pi Puzzle (10/6/2005)

  4. Kp Puzzle – Phase I - • Two ratios of the BR’s of K  modes (charged and neutral): • To the leading order, Rc and Rn should be the same in the SM; corrections should be ~ O([(C0 + P0EW) / P 0] 2) ~ O( 2). 2.4s  1.9s 1.5 Solving the B to K pi Puzzle (10/6/2005)

  5. Kp Puzzle – Phase II - • Now the bigger puzzle is in two CPA’s of the K  modes: • In the SM, T0 and C0 have the same weak phase () and a small relative strong phase ACP(K + -) and ACP(K ± 0) are expected to at least have the same sign. establishing direct CPV in B system at 5.7 level 3.6 ! Solving the B to K pi Puzzle (10/6/2005)

  6. Possible Explanations - • For puzzle phase-I only: underestimate of  0 detection efficiency, thus overestimating the BR’s of those corresponding modes. • [Gronau and Rosner, PLB 572, 43 (2003)] • New mechanism in SM: large color-suppressed amplitude C from NLO vertex corrections. [Charng & Li, PRD 71, 014036 (2005); He & McKellar, hep-ph/0410098] • Beyond SM: large electroweak penguin amplitude PEW from new physics. [Yoshikawa, JKPS 45, S479 (2004); Buras et al, PRL 92, 101804 (2004); NPB 697, 133 (2004); Baek, Hamel, London, Datta and Suprun, PRD 71, 057502 (2005); Hou, Nagashima and Soddu, hep-ph/0503072] [see also talks by Baek, Kim, Nagashima, Oh, Yoshikawa and Yu] Solving the B to K pi Puzzle (10/6/2005)

  7. - Large Color-Suppressed Amplitude Solving the B to K pi Puzzle (10/6/2005)

  8. Global Fits to VP and PP Modes - [CWC, Gronau, Luo, Rosner, and Suprun, PRD 69, 034001 (2004); PRD 70, 034020 (2004)] • charmless V P modes, g = 57。~ 69。; charmless P P modes, g = 54。~ 66。; both consistent with constraints from other observables. VP PP Solving the B to K pi Puzzle (10/6/2005)

  9. Updated Global Fits - • charmless V P modes, g ~ 68。; charmless P P modes, g~51。; both still consistent with constraints from other observables. VP PP Solving the B to K pi Puzzle (10/6/2005)

  10. Large C - • The ratio of | C / T | in  2 fits to available data in the  and K  modes ranges from 0.5 to >1. • In a fit to all the available PP data, the ratio is 0.89 (old)  0.77 (new). • They are larger than the naïve expectation (~ 0.25 – 0.3) in SM. • There is a large relative strong phase: arg[C / T ] ~ 90。. • Mainly driven by the mysteriously large BR(00). T exp(i) (T+C) exp(i) P (T+C) exp(-i) Br ¼Br Solving the B to K pi Puzzle (10/6/2005)

  11. NLO Vertex Correction - [Li, Mishima and Sanda, hep-ph/0508041] • | C | or | C0 | is enhanced by a factor of 2 to 3 after including the vertex corrections at NLO. • Strong phase changes a lot. Solving the B to K pi Puzzle (10/6/2005)

  12. PQCD Predictions - Solving the B to K pi Puzzle (10/6/2005)

  13. - Large Electroweak Penguin Amplitude Solving the B to K pi Puzzle (10/6/2005)

  14. Z0 Boson - [see also Valencia’s talk] • In most extensions beyond the SM, there are always extra heavy neutral Z 0 gauge bosons. • Properties of the new gauge boson, such as the mass and couplings, are model dependent. • In the gauge eigenbasis, the general Z 0neutral-current Lagrangian is given by • In string models, it is possible to have family-nonuniversal Z 0 couplings to fermion fields due to different constructions for the three families. [Chaudhuri et al, NPB 456, 89 (1995)] Solving the B to K pi Puzzle (10/6/2005)

  15. Z0-Induced FCNC - • After flavor mixing, one obtains FCNC Z0 interactions (non-diagonal) in the fermion mass eigenstates, which may lead to new CP-violating effects: • This may induce flavor-violating Z couplings if there is Z-Z0 mixing. • In view of the fact that the  K data can be explained with a new EW penguin amplitude, we assume that the Z 0 mainly contributes to these operators and obtain • This is possible through an O(10-3) mixing angle between Z and Z 0. • Here we only include the LH coupling for the Z 0-b-s coupling. RH coupling can be included as well, at the price of more free parameters. Solving the B to K pi Puzzle (10/6/2005)

  16. Low-Energy Effective Hamiltonian Z0 s s Z0 - [Barger, CWC, Langacker and Lee, PLB 580, 186(2004);598, 218 (2004)] • The effective Hamiltonian of the anti-b→ anti-sq anti-q transitions mediated by the Z ' is • Even though the operator is suppressed by the heavy Z0 mass, they can compete with SM loop processes because of their tree-level nature. Solving the B to K pi Puzzle (10/6/2005)

  17. Some Notations - • To study the K  puzzle Buras et al introduce the ratio [Buras et al, PRL 92, 101804 (2004)] • One should note that although c7,8 play a less important role compared to c9,10 within the SM, they can receive contributions from the Z ' such that we cannot neglect them. • In the analysis of Buras et al, it was implicitly assumed that new physics contributes dominantly to the (V – A) ­ (V–A) EW penguins. • As one of their conclusions under this assumption, S KS will be greater thanS KS or even close to unity if one wants to explain the K  anomaly. Solving the B to K pi Puzzle (10/6/2005)

  18. Solutions - • Using the same hadronic inputs from  modes as given by Buras et al, we get two sets of solutions: (q,) = (1.61, –84。) and (3.04, 83。)  (0.94, –85。) and (2.37, 85。), whereas they only take the small q solution. Solving the B to K pi Puzzle (10/6/2005)

  19. Fitting S KS Too - • Use the following variables to parameterize our model: • We obtain the solutions • It is possible to find solutions (except for (AL)) that account for both the K  and S KS data because the contributions from the O7,8 (from RH couplings at the Z0-q-qbar vertices) and O9,10 operators interfered differently in these two sets of decay modes. Solving the B to K pi Puzzle (10/6/2005)

  20. - K* and  K Decays Solving the B to K pi Puzzle (10/6/2005)

  21. K*p and r K Modes - [CWC, hep-ph/0502183] • A distinction between the V P system and the P P system is that there are two types of amplitudes for each topology in the former case, depending upon whether the spectator quark in B ends up in the P or V meson in the final state. • If new physics appears in the P P system, it is likely to show up in the V P system too. • The flavor amplitude decompositions and data are given below: Solving the B to K pi Puzzle (10/6/2005)

  22. Another Method for Constraining  - • With r1≡ |T 0P / P 0P| and r2 ≡ |T 0V / P 0V|, we have: • With particular choices of r1 and r2, one may constrain the weak phase  without knowing the relative strong phase. Solving the B to K pi Puzzle (10/6/2005)

  23. Result - • Hopefully, higher statistics in data can improve the bounds. (BR’s are measured at (5~10)% for K p and (10~20)% for K*p and rK. ) r1 = 0.37:g≥ 76or   22 Solving the B to K pi Puzzle (10/6/2005)

  24. Combining the K*+p– and r–K+ Modes - • Instead of treating r1 and r2 independently, one may employ the factorization assumption and get • This number can be compared with the result of 0.7 ± 0.1 obtained from a global fit. [CWC, Gronau, Luo, Rosner and Suprun, PRD 69, 034001 (2004)] • There are four parameters (g, r1, dP, and dV) for the four observables in the above-mentioned equations. Solving them exactly is possible and gives (up to discrete ambiguities of the phases and central values only) g = 69。, r1 = 0.19, dP = 170。, and dV = 128。. • (The above results are obtained by cheating because of the assumption|P 0P| = |P 0V| .) Solving the B to K pi Puzzle (10/6/2005)

  25. Rc and Rn Again - • One can further consider the following observables: • As in the case of the K  system, each pair of Rc and Rn should be equal as long as the color-suppressed and electroweak penguin amplitudes are negligible, as expected in the SM. Solving the B to K pi Puzzle (10/6/2005)

  26. Sum Rules - • Note that we have the following two approximate sum rules: which are held only when the terms |C 'V(P) + P 'EW,V(P)|2 + 2 Re[T 0 *P(V) (C 'V(P) + P 'EW,V(P))] are negligible in comparison with the dominant penguin contributions. • The first sum rule is satisfied by current data. • Using the second sum rule, one can deduce from current data that BR(r +K 0) = (8.8 ± 4.1) £ 10-6,consistent with the current upper bounds. • In particular, BR(r +K 0) thus obtained and the measured BR(K* 0p +) are about the same, which is an indication of the equality |P 'P| = |P 'V|. Solving the B to K pi Puzzle (10/6/2005)

  27. Summary and Outlook - I - • 1.5 discrepancy between Rc and Rn; 3.6 discrepancy between the CPA’s of K+  and K+0. • Nonuniversal Z’ can induce FCNC and provide new CP-violating sources for low-energy physics. • BR’s and CPA’s of K  and  KS modes can be explained in this model. • Rc and Rn for K*agree, but with a large uncertainty. For the  K mode, a direct experimental comparison is not yet available because there is no data for BR( +K 0). Employing the relation |P 0P| = |P 0V| for the  +K 0 mode, the current data show an approximate agreement between Rc and Rn. • If the puzzles in the K  system is due to new (short-distance) physics, we also expect deviations in the K* and  K systems. This does not seem to be the case according to the current data. • A precise determination of the rates of the  +K 0 decay will be very helpful in checking the Rc-Rn relations and the |P’P|-|P’V| equality. Solving the B to K pi Puzzle (10/6/2005)

  28. Summary and Outlook - II - • A true solution to the puzzle is still in the hand of experimentalists. Solving the B to K pi Puzzle (10/6/2005)

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