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Solving the B K Puzzle Cheng-Wei Chiang National Central University & Academia Sinica 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. Third International Conference on Flavor Physics October 3- 8, 2005

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)2 Outline The problem Large color-suppressed amplitude solution Large electroweak penguin solution --- FCNC Z 0 boson The K and K * modes Summary and outlook

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

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)4 Two ratios of the BR’s of K modes (charged and neutral): To the leading order, R c and R n should be the same in the SM; corrections should be ~ O([(C 0 + P 0 EW ) / P 0 ] 2 ) ~ O( 2 ). K Puzzle – Phase I 2.4 1.9 1.5 2.4 1.9 1.5

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)5 Now the bigger puzzle is in two CPA’s of the K modes: In the SM, T 0 and C 0 have the same weak phase ( ) and a small relative strong phase A CP (K + ) and A CP (K ± 0 ) are expected to at least have the same sign. K Puzzle – Phase II 3.6 ! establishing direct CPV in B system at 5.7 level

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)6 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 P EW 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] Possible Explanations

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

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)8 charmless V P modes, 。 。 ; charmless P P modes, 。 。 ; both consistent with constraints from other observables. Global Fits to VP and PP Modes VP PP [CWC, Gronau, Luo, Rosner, and Suprun, PRD 69, 034001 (2004); PRD 70, 034020 (2004)]

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)9 charmless V P modes, 。 ; charmless P P modes, ~ 。 ; both still consistent with constraints from other observables. Updated Global Fits PPVP

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)10 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 ). Large C ( T+C ) exp(i ) ( T+C ) exp(-i ) T exp(i ) P Br ¼ Br

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)11 [Li, Mishima and Sanda, hep-ph/0508041] [Li, Mishima and Sanda, hep-ph/0508041] | C | or | C 0 | is enhanced by a factor of 2 to 3 after including the vertex corrections at NLO. Strong phase changes a lot. NLO Vertex Correction

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)12 PQCD Predictions

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)13 Large Electroweak Penguin Amplitude

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)14 [see also Valencia’s talk] [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 0 neutral-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)] Z 0 Boson

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)15 After flavor mixing, one obtains FCNC Z 0 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-Z 0 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. Z 0 -Induced FCNC

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)16 The effective Hamiltonian of the anti-b → anti-s q anti-q transitions mediated by the Z ' is Even though the operator is suppressed by the heavy Z 0 mass, they can compete with SM loop processes because of their tree-level nature. Low-Energy Effective Hamiltonian s s Z 0Z 0 Z 0Z 0 [Barger, CWC, Langacker and Lee, PLB 580, 186 (2004); 598, 218 (2004)]

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)17 To study the K puzzle Buras et al introduce the ratio [Buras et al, PRL 92, 101804 (2004] [Buras et al, PRL 92, 101804 (2004)] One should note that although c 7,8 play a less important role compared to c 9,10 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. 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 K S will be greater than S K S or even close to unity if one wants to explain the K anomaly. Some Notations

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)18 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. Solutions

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)19 Use the following variables to parameterize our model: We obtain the solutions It is possible to find solutions (except for (A L )) that account for both the K and S K S data because the contributions from the O 7,8 (from RH couplings at the Z 0 -q-qbar vertices) and O 9,10 operators interfered differently in these two sets of decay modes. Fitting S K S Too

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)20 K * and K Decays

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)21 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: K * and K Modes [CWC, hep-ph/0502183]

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)22 With r 1 ≡ |T 0 P / P 0 P | and r 2 ≡ |T 0 V / P 0 V |, we have: With particular choices of r 1 and r 2, one may constrain the weak phase without knowing the relative strong phase. Another Method for Constraining

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)23 Hopefully, higher statistics in data can improve the bounds. (BR’s are measured at (5~10)% for K and (10~20)% for K * and K. ) Result r 1 = 0.37: ≥ 76 or 22

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)24 Instead of treating r 1 and r 2 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 ( , r 1, P, and V ) 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) = 69 。, r 1 = 0.19, P = 170 。, and V = 128 。. (The above results are obtained by cheating because of the assumption |P 0 P | = |P 0 V | (The above results are obtained by cheating because of the assumption |P 0 P | = |P 0 V |.) Combining the K *+ – and – K + Modes

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

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)26 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( + K 0 ) = (8.8 ± 4.1) £ 10 -6, consistent with the current upper bounds. In particular, BR( + K 0 ) thus obtained and the measured BR(K * 0 + ) are about the same, which is an indication of the equality |P ' P | = |P ' V |. Sum Rules

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C.W. ChiangSolving the B to K pi Puzzle (10/6/2005)27 1.5 discrepancy between R c and R n ; 3.6 discrepancy between the CPA’s of K + and K + 0. Nonuniversal Z’FCNC and provide new CP-violating sources for low-energy physics. Nonuniversal Z’ can induce FCNC and provide new CP-violating sources for low-energy physics. BR’s and CPA’s of K and K S modes can be explained in this model. R c and R n 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 0 P | = |P 0 V | for the + K 0 mode, the current data show an approximate agreement between R c and R n. 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 R c -R n relations and the |P’ P |-|P’ V | equality. Summary and Outlook - I

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

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