Solving the B K Puzzle

Solving the B K PuzzleSolving the B K Puzzle

Cheng-Wei ChiangCheng-Wei ChiangNational Central University & Academia SinicaNational Central University & Academia Sinica

Cheng-Wei ChiangCheng-Wei ChiangNational Central University & Academia SinicaNational Central University & Academia Sinica

Based upon following works:Based upon following works:PRD PRD 6969, 034001 (2004) [hep-ph/0307395];, 034001 (2004) [hep-ph/0307395];PLB PLB 580, 580, 186186 (2004) [hep-ph/0310073];(2004) [hep-ph/0310073];PRD PRD 7070, 034020 (2004) [hep-ph/0404073];, 034020 (2004) [hep-ph/0404073];PLB PLB 598598, 218 (2004) [hep-ph/0406126];, 218 (2004) [hep-ph/0406126];hep-ph/0502183.hep-ph/0502183.

Third International Conference on Flavor PhysicsOctober 3- 8, 2005

C.W. Chiang Solving the B to K pi Puzzle (10/6/2005) 2

OutlineOutline

The problemThe problem

Large color-suppressed amplitude solutionLarge color-suppressed amplitude solution

Large electroweak penguin solution --- FCNC Large electroweak penguin solution --- FCNC ZZ 00 boson boson

The The K K and and KK** modes modes

Summary and outlookSummary and outlook


The amplitudes of the four The amplitudes of the four K K modes can be decomposed according to modes can be decomposed according to the flavor flow topology as follows (ignoring smaller amplitudes):the flavor flow topology as follows (ignoring smaller amplitudes):

Flavor Amplitudes of K Modes

Flavor Amplitudes of K Modes


Two ratios of the BR’s of Two ratios of the BR’s of K K modes (charged and neutral): modes (charged and neutral):

To the leading order, To the leading order, RRcc and and RRnn should be the same in the SM; should be the same in the SM;

corrections should be ~ corrections should be ~ OO([(([(CC 00 + + PP 00EWEW) / ) / P P 00] ] 22) ~ ) ~ OO((22).).

K Puzzle – Phase IK Puzzle – Phase I

2.42.41.91.9 1.5 1.5


Now the bigger puzzle is in two CPA’s of the Now the bigger puzzle is in two CPA’s of the K K modes: modes:

In the SM, In the SM, TT 00 and and CC 00 have the same weak phase ( have the same weak phase () and a small ) and a small relative strong phase relative strong phase AACPCP((K K ++) and ) and AACPCP((K K ±±00) are expected to at least have the same ) are expected to at least have the same

sign.sign.

K Puzzle – Phase IIK Puzzle – Phase II

3.63.6 ! !

establishing direct CPV in establishing direct CPV in BB system at 5.7 system at 5.7 level level


For puzzle phase-I only: underestimate of For puzzle phase-I only: underestimate of 00 detection efficiency, thus detection efficiency, thus overestimating the BR’s of those corresponding modes.overestimating the BR’s of those corresponding modes.

[Gronau and Rosner, PLB [Gronau and Rosner, PLB 572572, 43 , 43 (2003)](2003)]

New mechanism in SM: large color-suppressed amplitude New mechanism in SM: large color-suppressed amplitude CC from NLO from NLO vertex corrections.vertex corrections.

[Charng & Li, PRD [Charng & Li, PRD 7171, 014036 (2005); He & McKellar, hep-ph/0410098], 014036 (2005); He & McKellar, hep-ph/0410098]

Beyond SM: large electroweak penguin amplitude Beyond SM: large electroweak penguin amplitude PPEWEW from new from new

physics.physics.[Yoshikawa, JKPS [Yoshikawa, JKPS 4545, S479 (2004);, S479 (2004);Buras et al, PRL Buras et al, PRL 9292, 101804 (2004); NPB , 101804 (2004); NPB 697697, 133 (2004);, 133 (2004);Baek, Hamel, London, Datta and Suprun, PRD Baek, Hamel, London, Datta and Suprun, PRD 7171, 057502 (2005);, 057502 (2005);Hou, Nagashima and Soddu, hep-ph/0503072]Hou, Nagashima and Soddu, hep-ph/0503072]

[see also talks by Baek, Kim, Nagashima, Oh, Yoshikawa and Yu][see also talks by Baek, Kim, Nagashima, Oh, Yoshikawa and Yu]

Possible ExplanationsPossible Explanations


Large Color-Suppressed Large Color-Suppressed AmplitudeAmplitude


charmless charmless V PV P modes, modes, 。。。。 ; charmless ; charmless P PP P modes, modes, 。。。。 ; both consistent with constraints from other ; both consistent with constraints from other observables.observables.

Global Fits to VP and PP Modes

Global Fits to VP and PP Modes

VP PP

[CWC, Gronau, Luo, Rosner, and Suprun, PRD [CWC, Gronau, Luo, Rosner, and Suprun, PRD 6969, 034001 (2004); PRD , 034001 (2004); PRD 7070, 034020 (2004)], 034020 (2004)]


charmless charmless V PV P modes, modes, 。。 ; charmless ; charmless P PP P modes, modes, ~~ 。。 ; ; both still consistent with constraints from other observables.both still consistent with constraints from other observables.

Updated Global FitsUpdated Global Fits

PPVP


The ratio of | The ratio of | C / TC / T | in | in 22 fits to available data in the fits to available data in the and and K K modes ranges from 0.5 to >1.modes ranges from 0.5 to >1.

In a fit to all the available PP data, the ratio is 0.89 (old) In a fit to all the available PP data, the ratio is 0.89 (old) 0.77 (new). 0.77 (new).

They are larger than the naïve expectation (~ 0.25 – 0.3) in SM.They are larger than the naïve expectation (~ 0.25 – 0.3) in SM.

There is a large relative strong phase: arg[There is a large relative strong phase: arg[C / TC / T ] ~ 90 ] ~ 90 。。 ..

Mainly driven by the mysteriously large BR(Mainly driven by the mysteriously large BR(0000).).

Large CLarge C

(T+C) exp(i)

(T+C) exp(-i)

T exp(i)

P

Br ¼ Br


[Li, Mishima and Sanda, hep-ph/0508041][Li, Mishima and Sanda, hep-ph/0508041]

| C || C | or | or | CC 00 | is enhanced by a factor | is enhanced by a factor of 2 to 3 after including the vertex of 2 to 3 after including the vertex corrections at NLO.corrections at NLO.

Strong phase changes a lot.Strong phase changes a lot.

NLO Vertex CorrectionNLO Vertex Correction


PQCD PredictionsPQCD Predictions


Large Electroweak Penguin Large Electroweak Penguin AmplitudeAmplitude


[see also Valencia’s [see also Valencia’s talk]talk]

In most extensions beyond the SM, there are In most extensions beyond the SM, there are always extra heavy neutral always extra heavy neutral Z Z 00 gauge bosons. gauge bosons.

Properties of the new gauge boson, such as Properties of the new gauge boson, such as the mass and couplings, are model dependent.the mass and couplings, are model dependent.

In the gauge eigenbasis, the general In the gauge eigenbasis, the general Z Z 00 neutral-current Lagrangian is given byneutral-current Lagrangian is given by

In string models, it is possible to have family-In string models, it is possible to have family-nonuniversal nonuniversal Z Z 00 couplings to fermion fields couplings to fermion fields due to different constructions for the three due to different constructions for the three families.families.

[Chaudhuri et al, NPB 456, 89 (1995)][Chaudhuri et al, NPB 456, 89 (1995)]

Z0 BosonZ0 Boson


After flavor mixing, one obtains FCNC After flavor mixing, one obtains FCNC ZZ 00 interactions (non-diagonal) interactions (non-diagonal)

in the fermion mass eigenstates, which may lead to new CP-violating in the fermion mass eigenstates, which may lead to new CP-violating effects:effects:

This may induce flavor-violating This may induce flavor-violating ZZ couplings if there is couplings if there is ZZ--ZZ 00 mixing. mixing.

In view of the fact that the In view of the fact that the K K data can be explained with a new EW data can be explained with a new EW penguin amplitude, we assume that the penguin amplitude, we assume that the Z Z 00 mainly contributes to these mainly contributes to these operators and obtainoperators and obtain

This is possible through an This is possible through an OO(10(10-3-3) mixing angle between ) mixing angle between ZZ and and Z Z 00..

Here we only include the LH coupling for the Here we only include the LH coupling for the Z Z 00--bb--ss coupling. RH coupling. RH coupling can be included as well, at the price of more free parameters.coupling can be included as well, at the price of more free parameters.

Z0-Induced FCNCZ0-Induced FCNC


The effective Hamiltonian of the anti-The effective Hamiltonian of the anti-bb → anti- → anti-ss qq anti- anti-qq transitions transitions mediated by the mediated by the Z Z ' is' is

Even though the operator is suppressed by the heavy Even though the operator is suppressed by the heavy ZZ 00 mass, they can mass, they can

compete with SM loop processes because of their tree-level nature.compete with SM loop processes because of their tree-level nature.

Low-Energy Effective Hamiltonian

Low-Energy Effective Hamiltonian

s sZ

0

Z 0

[Barger, CWC, Langacker and Lee, PLB [Barger, CWC, Langacker and Lee, PLB 580, 580, 186186 (2004);(2004); 598598, 218 (2004)], 218 (2004)]


To study the To study the K K puzzle Buras et al introduce the ratio puzzle Buras et al introduce the ratio[Buras et al, PRL [Buras et al, PRL 92, 92, 101804 101804

(2004(2004)]]

One should note that although One should note that although cc7,87,8 play a less important role compared play a less important role compared

to to cc9,109,10 within the SM, they can receive contributions from the within the SM, they can receive contributions from the Z Z ' such ' such

that we that we cannotcannot neglect them. neglect them.

In the analysis of Buras et al, it was implicitly assumed that new physics In the analysis of Buras et al, it was implicitly assumed that new physics contributes dominantly to the (V – A) contributes dominantly to the (V – A) (V (V –– A) EW penguins.A) EW penguins.

As one of their conclusions under this assumption, As one of their conclusions under this assumption, SS K KSS will be will be greater greater

thanthan SS K KSS or even close to unity if one wants to explain the or even close to unity if one wants to explain the K K

anomaly.anomaly.

Some NotationsSome Notations


Using the same hadronic inputs from Using the same hadronic inputs from modes as given by Buras et al, modes as given by Buras et al, we get two sets of solutions:we get two sets of solutions:

((qq,,) = (1.61, –84) = (1.61, –84 。。 ) and (3.04, 83) and (3.04, 83 。。 ) ) (0.94, –85 (0.94, –85 。。 ) and (2.37, ) and (2.37, 8585 。。 ),),

whereas they only take the small whereas they only take the small qq solution. solution.

SolutionsSolutions


Use the following variables to parameterize our model:Use the following variables to parameterize our model:

We obtain the solutionsWe obtain the solutions

It is possible to find solutions (except for (AIt is possible to find solutions (except for (ALL)) that account for both the )) that account for both the

K K and and SS K KSS data because the contributions from the data because the contributions from the OO7,87,8 (from RH (from RH

couplings at the couplings at the ZZ 00--qq--qqbar vertices) and bar vertices) and OO9,109,10 operators operators interfered interfered

differentlydifferently in these two sets of decay modes. in these two sets of decay modes.

Fitting S KS TooFitting S KS Too


KK** and and K K Decays Decays


A distinction between the A distinction between the V PV P system and the system and the P PP P system is that there system is that there are are two types of amplitudes for each topologytwo types of amplitudes for each topology in the former case, in the former case, depending upon whether the spectator quark in depending upon whether the spectator quark in BB ends up in the ends up in the PP or or VV meson in the final state.meson in the final state.

If new physics appears in the If new physics appears in the P PP P system, it is likely to show up in the system, it is likely to show up in the V V PP system too. system too.

The flavor amplitude decompositions and data are given below:The flavor amplitude decompositions and data are given below:

K* and K ModesK* and K Modes[CWC, hep-ph/0502183][CWC, hep-ph/0502183]


With With rr11 ≡ | ≡ |T T 00PP / / P P 00PP| and | and rr22 ≡ | ≡ |T T 00VV / / P P 00VV|, we have:|, we have:

With particular choices of With particular choices of rr11 and and rr22, one may constrain the weak phase , one may constrain the weak phase

without knowing the relative strong phase. without knowing the relative strong phase.

Another Method for Constraining

Another Method for Constraining


Hopefully, higher statistics in data can improve the bounds. (BR’s are Hopefully, higher statistics in data can improve the bounds. (BR’s are measured at (5~10)% for measured at (5~10)% for K K and (10~20)% for and (10~20)% for KK** and and KK. ). )

ResultResult

rr11 = 0.37: = 0.37: ≥ 76 ≥ 76 or or 22 22


Instead of treating Instead of treating rr11 and and rr22 independently, one may employ the independently, one may employ the

factorization assumption and getfactorization assumption and get

This number can be compared with the result of 0.7 This number can be compared with the result of 0.7 ±± 0.1 obtained 0.1 obtained from a global fit. from a global fit. [CWC, Gronau, Luo, Rosner and Suprun, PRD [CWC, Gronau, Luo, Rosner and Suprun, PRD 6969, 034001 (2004)], 034001 (2004)]

There are four parameters (There are four parameters (, , rr11, , PP, and , and VV) for the four observables in ) for the four observables in

the above-mentioned equations. Solving them exactly is possible and the above-mentioned equations. Solving them exactly is possible and gives (up to discrete ambiguities of the phases and central values only)gives (up to discrete ambiguities of the phases and central values only)

= 69= 69 。。 , , rr11 = 0.19, = 0.19, PP = 170 = 170 。。 , and , and VV = 128 = 128 。。 ..

(The above results are obtained by cheating because of the assumption(The above results are obtained by cheating because of the assumption||P P 00PP| = || = |P P 00VV|| .)

Combining the K*+ – and –K+ Modes

Combining the K*+ – and –K+ Modes


One can further consider the following observables:One can further consider the following observables:

As in the case of the As in the case of the K K system, each pair of system, each pair of RRcc and and RRnn should be equal should be equal

as long as the color-suppressed and electroweak penguin amplitudes are as long as the color-suppressed and electroweak penguin amplitudes are negligible, as expected in the SM.negligible, as expected in the SM.

Rc and Rn AgainRc and Rn Again


Note that we have the following two approximate sum rules:Note that we have the following two approximate sum rules:

which are held only when the terms |which are held only when the terms |C C ''V(P)V(P) + + P P ''EW,V(P)EW,V(P)||22 + 2 Re[ + 2 Re[T T 00 * *P(V)P(V) ( (C C

''V(P)V(P) + + P P ''EW,V(P)EW,V(P))] are negligible in comparison with the dominant penguin )] are negligible in comparison with the dominant penguin

contributions.contributions.

The first sum rule is satisfied by current data.The first sum rule is satisfied by current data.

Using the second sum rule, one can deduce from current data that Using the second sum rule, one can deduce from current data that BR(BR(++K K 00) = (8.8 ) = (8.8 ±± 4.1) 4.1) ££ 10 10-6-6,,consistent with the current upper bounds.consistent with the current upper bounds.

In particular, BR(In particular, BR(++K K 00) thus obtained and the measured BR() thus obtained and the measured BR(KK* 0* 0++) ) are about the same, which is an indication of the equality |are about the same, which is an indication of the equality |P P ''PP| = || = |P P ''VV|.|.

Sum RulesSum Rules


1.51.5 discrepancy between discrepancy between RRcc and and RRnn; ; 3.63.6 discrepancy between the discrepancy between the

CPA’s of CPA’s of KK++ and and KK++00..

Nonuniversal Z’Nonuniversal Z’ can induce FCNC and provide new CP-violating FCNC and provide new CP-violating sources for low-energy physics.sources for low-energy physics.

BR’s and CPA’s of BR’s and CPA’s of K K and and K KSS modes can be explained in this model. modes can be explained in this model.

RRcc and and RRnn for for KK** agreeagree, but with a , but with a large uncertaintylarge uncertainty. For the . For the K K

mode, a direct experimental comparison is mode, a direct experimental comparison is not yet availablenot yet available because because there is no data for BR(there is no data for BR(++K K 00). Employing the relation |). Employing the relation |P P 00PP| = || = |P P 00VV| |

for the for the ++K K 00 mode, the current data show an approximate agreement mode, the current data show an approximate agreement between between RRcc and and RRnn..

If the puzzles in the If the puzzles in the K K system is due to new (short-distance) physics, system is due to new (short-distance) physics, we also expect deviations in the we also expect deviations in the KK** and and K K systems. This does systems. This does notnot seem to be the case according to the current data.seem to be the case according to the current data.

A precise determination of the rates of the A precise determination of the rates of the ++K K 00 decay will be very decay will be very helpful in checking the helpful in checking the RRcc--RRnn relations and the | relations and the |P’P’PP|-||-|P’P’VV| equality.| equality.

Summary and Outlook - ISummary and Outlook - I


A true solution to the puzzle is still in the hand of A true solution to the puzzle is still in the hand of experimentalistsexperimentalists..

Summary and Outlook - IISummary and Outlook - II

Documents

Solving the B K Puzzle