Clean Signals of New Physics in B decays

Transcription

1 KEK Clean Signals of New Physics in B decays Talk at: Rahul Sinha The Institute of Mathematical Sciences KEK Physics Seminar, Tuesday 27 th June :00 pm the effect is telling us that at some tiny level there is a fundamental asymmetry between matter and antimatter,. We know that improvements in detector technology and quality of accelerators will permit even more sensitive experiments in coming decades. We are hopeful, then at some epoch, perhaps distant, this cryptic message from nature will be deciphered Cronin (Nobel lectures 1980)

2 KEK Physics Seminar 2 Spectacular performance at B factories Belle ~1000 fb -1 BaBar Over10 9 B B pairs seen Confirmation of KM theory. Look for deviations not alternatives. Any deviation from KM not breakdown of KM but New Physics. Fortunate, since NP must be small. Large data sets herald start of a new era B physics becomes precision physics.

3 KEK Physics Seminar 3 CKM matrix has hierarchical structure Wolfenstein Parameterization V= V ud V us Vub V cd V cs Vcb V td V ts Vtb = 1 λ2 2 λ4 8 λ Aλ 3 (ρ+iη) λ+a 2 λ 5 ( 1 2 ρ iη) 1 λ2 2 λ4 8 (1+4A2 ) Aλ 2 Aλ 3 (1 ρ i η) Aλ 2 +Aλ 4 ( 1 2 ρ iη) A2 λ 4 +O(λ6 ) How sensitive are we to λ 4 order terms? Don t give up. New Physics (NP) can be at this order or smaller. Fortunately we already see hints of NP, probably at this order. The value of sin2φ 1 measured using various modes differs. Ratios of branching fractions of B Kπ modes inconsistent with SM expectation: Kπ puzzle. An unexpectedly large transverse polarization amplitude in B 0 φ K* has also been observed.

4 KEK Physics Seminar 4 Unfortunately, curse of QCD. Weak decays are masked by nonperturbative QCD effects. Difficult to estimate. These effects do not allow simple signal of NP. One wonders whether these hints are mere hadronic/qcd effects or signals of NP. Dilemma in B-physics B today because convincing arguments lacking. Correct questions: Under what conditions can these discrepancies be regarded as an unambiguous signal of NP? Are there any clean signals of NP, i.e. signals free of QCD/hadronic effects. We examine these questions within a model independent approach.

5 Discrepancy in measured sin2φ 1 Rahul Sinha, Basudha Misra and Wei-Shu Hou, hep-ph/ World Averages q= u,d,s C.L. ~ (2.6 σ) Deviation from SM New Physics???... b s Penguins sin2φ 1 (b c cs)=0.69±0.03 sin2φ 1 (b sq q)=0.50±0.06 Naive average Discussion does not really depend on naïve average Compare withckmfitter valuesin2φ 1 = KEK Physics Seminar 5

6 The most general amplitude for b s transition modes within SM may be written as Unitarity of CKM A b s =A u e iδ u v u +A c e iδ c v c +A t e iδ t v t Amplitudes for quark level contributions v u =Aλ 4 (ρ+iη) γ φ 3 60 o v u +v c +v t =0 KEK Physics Seminar 6 Strong phases v j =V jb V js v c isrealupto O(λ 6 ) v t = Aλ 2 +A( 1 2 ρ iη)λ4 +O(λ 6 ) β s φ 4 =1.045 o o o The same amplitudes may be written as CKM Fitter A b s =(A c e iδ c A t e iδ t )v c +(A u e iδ u A t e iδ t )v u v t = v u v c a = v c â = v c Ac e iδ c A t e iδ t A b s [ =e iθ a +b e iδ e iφ ] 3, b = v u ˆb = v u Au e iδ u A t e iδ t Θ overallstrongphase 0 δ is the strong phase difference between a andb,

7 Or using v u = v t v c A b s =(A c e iδ c A u e iδ u )v c +(A t e iδ t A u e iδ u )v t a = v c â = v c Ac e iδ c A u e iδ u A b s [ =e iθ a +b e iδ e iφ ] 4 Θ 0 b = v t ˆb = v t Au e iδ u A t e iδ t δ is the strong phase difference between a andb Amplitude for decay of Bd 0 f i A i =a i +b i e iδ i e iφ φ can be φ B d 0 f i Ā i =a i +b i e iδ i e iφ 3 or φ Measured 4 Time dependent decay rate value Γ(B 0 (t) f i ) B i (1+C i cos( Mt) S i sin( Mt)) B i = A i 2 + Āi 2 =a 2 2 i+b 2 i+2a i b i cosφcosδ i, C i = A i 2 Āi 2 A i 2 + Āi 2 = 2a ib i sinφsinδ i B i S i = 1 C 2 i sin2φi 1 = 1 Ci 2 KEK Physics Seminar 7 Im(e 2iφ 1 A i Ā i ) A i Ā i polluting phase in SM

8 KEK Physics Seminar 8 Since the measured sin2φ 1 differs between two modes, we must relate this difference with the weak phase φ. sin(2φ i 1) 2φ i 1,π 2φ i 1 2-fold ambiguity 4 fold ambiguity in the difference between the values measured using two different modes. ±(2φ i 1 2φ j 1),±π (2φ i 1+2φ j 1) Worry only about the principal values. Derive a relation or bound between the deviation in the principal values and φ. We can then conclude that sin2φ 1i for the two modes must be such that their principal values obey the relation or bound. Define η i =arga i argāi A iāi= A i Āi e iη i η i =2φ i 1 2φ 1 ω=(2φ i 1 2φ j 1 )=η 1 η 2 Defineω>0 2φ (1) 1 >2φ (2) 1

9 KEK Physics Seminar 9 4 observables B i,c i,s i,φ 4 variables a i,b i,δ i,φ 1 A i =a i +b i e iδ i e iφ Ā i =a i +b i e iδ i e iφ Easy to derive Relation between η i and φ SP=2b i sinφ a 2 i = b 2 i = tanδ i = B i 2sin 2 φ B i 2sin 2 φ A i Āi=2b i sinφ A i e iφ Āie iφ = 2a i sinφ ( ) 1 1 Ci 2cos(η i 2φ) ( 1 ) 1 Ci 2cos(η i) C i sinφ cosφ 1 C 2 i cos(η i φ) SameA i andāi usingdifferent a i,b i,η i,δ i V can lie along bisector of SP Essential to express all quantities in terms of irreducible variables Geometric approach superior over algebraic

10 φ>0,0<δ i < π 2 tanδ c i = C itanφ 1 1 C 2 i Easily generalize toφ<0and/or π 2 <δ i<0 φand η i havesamesignas longas δ i < δ c i KEK Physics Seminar 10

11 QSO& VPO QPO& VSO O O φ>0,0<δ i < π 2 sinζ i = sin(δ i+φ) a i A i sin ζ i a i = sin(δ i φ) Āi KEK Physics Seminar 11 A i sinζ i Āi sin ζ i =2a i sinφcosδ i δ< π sin ζ i < A i <1 ζ i <ζ i 2 sinζ i Āi

12 KEK Physics Seminar 12 Reasonable to assume that A c dominates in b c cs η 1 0 2ω=η 1 η 2 η 2 <0 since 0<η i <2φ Contradiction Only way to resolve the contradiction is to assume that δ i > δ c i We need to determine when δ i > δ c i and when δ i < δ c i before drawing any conclusions. φ=φ 3 φ=φ 4 (x 1,y 1 ),(x 2,y 2 ),l /l can be solved in terms of A u,a c,a i,b i,δ i a 2 i,b 2 i,tanδ i evaluated in terms of η i,φ and observables A t, δ c δ u expressed in terms of A u,a c,η i

13 A u,a c,a t CKM parameterization independent. Set C i =0 consistent with data Finite C i implies large a i,b i and tanδ i larger Aq Normalization: A u =A t =0 A c =1 Clear hierarchy in values of A q which depends only on η i =0, π 6, π 3,π 2,π KEK Physics Seminar 13 A u 2 ( A u 2 ), A t times observed branching ratio If 2ω =5 o in future, 10 times observed branching ratios.

14 Parametrization φ=φ 4 sin2φ 1 (b c cs)=0.69±0.03 sin2φ 1 (b s qq)=0.50±0.06 2ω=(13.63±5.41)o Note that when η i <0 or η i >2φ one must have δ i > δ c i In none of the cases it is possible to have δ i < δ c i for both modes Unless 0<2ω<2φ one cannot have 0<η 2 <η 1 <2φ, hence we do not consider this specific case. The values close to 10 are possible only by lowering 2φ 1 away from 2φ i 1beyond acceptable values, close to2φ i 2 KEK Physics Seminar 14

15 KEK Physics Seminar 15 ˆb = ˆb =ˆb sin2 φ 4 sin 2 = v u 2 φ 3 v t 2 = sin2 β s sin 2 β NP indeed tested To conclude, without making any hadronic model based assumptions we have shown that within the SM, it is impossible to explain the observed discrepancy in B 0 B 0 mixing phase measured using theb c cs andb s qq modes. The only possibility to forgo this conclusion is to accept that the observed branching ratios result from considerable fine tuned cancellations of significantly larger quark level amplitudes. This scenario of ``observed decay rates resulting from fine-tuned cancellations of large quark level amplitudes'' would be very difficult to accommodate, given the successful understanding of B d decay rates.

16 KEK Physics Seminar 16 Can B VV help discover NP? David London, Nita Sinha and Rahul Sinha, hep-ph/ , Euro. Phys. Lett. 67, 579 (2004). David London, Nita Sinha and Rahul Sinha, hep-ph/ , Phys. Rev. D 69, While number of parameters still exceeds number of observables, Additional signals of NP. Possible to bound the size of NP. Constrain its effect on measurement of the mixing phase. In the presence of NP, decay amplitude for each of the helicity states: A λ Amp(B V 1 V 2 ) λ = a λ e iδa λ +bλ e iφ e iδb λ, Ā λ Amp( B V 1 V2 ) λ = a λ e iδa λ +bλ e iφ e iδb λ The time dependent decay of B VV must have a more complicated form and may be written as Γ(B 0 (t) f)=e Γt λ<=σ ( Λ λσ +Σ λσ cos( Mt) ρ λσ sin( Mt) ) f λσ

17 KEK Physics Seminar 17 B VV decays provide large number of observables Total 18 Λ λλ = A λ 2 + Āλ 2 2 Σ λλ = A λ 2 Āλ 2 2 ρ ii =Im( q p A iāi) ρ = Im( q p A Ā ) 3 3 = 9 Λ i = Im(A A i Ā Ā i) Σ i = Im(A A i +Ā Ā i) q ) ρ i =Re( p [A Āi+A iā ] 3 2 = = 3 Λ λσ terms and Σ λσ terms can be obtained without time dependent study. Infact, Λ λσ terms can be obtained without even flavor tagging. We have 13 theoretical parameters A λ,āλ Λ 0 =Re(A A 0+Ā Ā 0) Σ 0 =Re(A A 0 Ā Ā 0) q ) ρ 0 = Im( p [A Ā0+A 0Ā ] 3a λ s+3b λ s+φ 1 +φ+3δ λ s(δ λ δ b λ δ a λ)+2 i s( i δ a δ a i) No. of independent observables: 11, 6 magnitudes and relative phases Cannot obtain parameters purely in terms of observables, impossible to extract φ 1 or φ cleanly.

18 Observables in terms of parameters Λ λλ = a 2 λ+b 2 λ+2a λ b λ cosδ λ cosφ, Σ λλ = 2a λ b λ sinδ λ sinφ, ρ ii = a 2 isin2φ 1 +2a i b i cosδ i sin(2φ 1 +φ)+b 2 isin(2φ 1 +2φ), ρ = a 2 sin2φ 1 2a b cosδ sin(2φ 1 +φ) b 2 sin(2φ 1+2φ), Vanishing signals of NP Λ i = 2[a b i cos( i δ i ) a i b cos( i +δ )] sinφ, Λ 0 = 2 [ a a 0 cos( 0 )+a b 0 cos( 0 δ 0 )cosφ+a 0 b cos( 0 +δ )cosφ +b b 0 cos( 0 +δ δ 0 ) ], Σ i = 2 2[a a i sin i +a b i sin( i δ i )cosφ+a i b sin( i +δ )cosφ +b b i sin( i +δ δ i )], Σ 0 = 2 [ a b 0 sin( 0 δ 0 ) a 0 b sin( 0 +δ ) ] sinφ, ρ i = 2[a i a cos i cos2φ 1 +a b i cos( i δ i )cos(2φ 1 +φ)+a i b cos( i +δ )cos(2φ 1 +φ) +b i b cos( i +δ δ i )cos(2φ 1 +2φ)], ρ 0 = 2 [ a 0 a cos( 0 )sin2φ 1 +a b 0 cos( 0 δ 0 )sin(2φ 1 +φ) +a 0 b cos( 0 +δ )sin(2φ 1 +φ)+b 0 b cos( 0 +δ δ 0 )sin(2φ 1 +2φ) ]. KEK Physics Seminar 18

19 KEK Physics Seminar 19 In the absence of NP,, b λ = 0, φ=0. No. of parameters: reduced, aλ's, 2 strong i, and β. No. of independent observables: 6, (Λ λλs,1ρ λλ,2σ i ) All parameters can be determined cleanly in terms of observables. 18 observables- 6 vanish & 6 independent) 6 additional relations Σ λλ =Σ 0 =Λ i =0 ρ 2 i 4Λ Λ ii Σ 2 i = Λ2 ρ2 Λ 2 ρ ii Λ ii = ρ Λ = ρ 0 Λ 0 Λ 0 = 1 [ Λ 2 λλ ρ 0ρ +Σ 0 Σ (Λ 2 λλ ρ2 λλ ) 2Λ Λ 2 λλ ρ2 λλ any of Violation of these 12 relations, smoking gun signals of New Physics! ]

20 KEK Physics Seminar 20 Observable Λ i deserves special attention. Even if λ 0,Λ i 0 in contrast to direct asymmetry. Λ i does not require flavor tagging, nor time dependence. δ a,b i terms are CP-odd Λ i survives in an untagged sample. Λ i has been measured. Is it possible that all NP signals vanish, even if NP is present? Yes! If the singular situation: 1. All the strong phase differences δ λ s vanish, 2. ratio r λ =b λ /a λ is same for all helicities, Then all 12 relations are satisfied. Forthis veryspecialconditions,angularanalysisof B V 1 V 2 leads to nosignalfor NP evenif present,measured valueof φ 1 =B 0 B 0 mixingphase.

21 KEK Physics Seminar 21 Conclusions The discrepancy in the measured values of sin2φ 1 can be a clean signal of NP. How the signals stay and we discover NP. The Kπ puzzle can be resolved using K*π modes. An anomaly in the size of the observed topological amplitudes (or derived asymmetries) is the only sign of NP. NP if it exists will provide clean signals in B VV modes. There are 12 smoking gun signals which are unlikely to fail us.