Measuring Weak Phases using B ! VV

1. Measuring Weak Phases using B! VV Rahul Sinha The Institute of Mathematical Sciences Thursday 12th May 205 2:00 pm Beauty is eternity gazing at itself in a mirror. Kahlil Gibran (1883-1931) Lebanese poet, novelist. The Prophet (1923). Talk at:

2. e- ne DS=1 W- p0 (0.135) sin qc=0.22 K- (0.494) d u u s u u u u e- This is easy to understand if we assumed weak transitions take place in the same generation, but that weak eigenstates are not the same as the mass eigenstaes. The interaction for 3 generations can then be described as Lint=UVDW+, where V is a unitary matrix: ne DS=0 W- p0 (0.135) e+ p- (0.140) ne W+ m+ (0.105) nm The CKM matrix CP violation arises in SM, due to the complex phase in the Cabbibbo-Kobayashi-Maskawa (KM)- relates the weak eigenstates to their mass eigenstates:

3. e-i3 (r,h) 2 e-i1 1 3 (0,0) (1,0) Wolfenstein Unitary Triangle V is a Unitary matrix Þ 6 Orthonormality relations. One such relation is »1 »1 » real Non vanishing value of ) CPV

4. f Final statefinto which both and can decay, two interfering amplitudes. • 1, 2, 3 independent of the parameterization. Physical quantities that can be measured. • Non zero 1, 2, 3 indicate CPV • Sides can indirectly measure the angles BUT involves large hadronic uncertainties • CP violating asymmetries can directly measurethese angles cleanly. A Clean method for-weak phases, based on the fact that neutral B mesons can mix (induced by the box diagrams) Time dependence of Decay Rate where,

5. Determination of 1 • In B!KS , the decay amplitude dominated by only one tree amplitude with a real CKM element • Asymmetry completely free of hadronic uncertainties. • Determination of 2 • Final state  + -. At the tree level, the amplitude involves a • b! u quark transition, • However, there isPenguin Pollution. What one measures through a time dependent asymmetry here is not 22 but some effective POLLUTED angle 22eff. • Problem resolved through Isospin Analysis. • Determination of 3 Most of the talk today

6. How does one measure 3()? • Need to determineall CP violating phases without hadronic uncertainties.3(), phase of the Vub element of the CKM matrix is themost difficult to measure. • Initially proposed to use Bs(t) ! KS(similar to Bd(t) ! KS used to 1). Presence ofpenguin amplitudes completely spoil the measurement of 3(). • Great deal of work has since been done developing new methods to cleanly obtain the CP angles from a wide variety of final states. • K modes: Interference of b! u tree and b! s penguin. Use SU(3). • Avoid penguin pollution, look at modes that involve only tree amplitudes: • DK Methods- interference of b! c and b! u trees, clean. • Time dependent asymmetries in D modes. • Extend techniques to VV with several advantages. Need to study decays to non-CP eigenstates.

7. b! u b! c • K modes Tree is Cabibbo suppressed, Penguin contributions, including Electroweak Penguins cannot be neglected. • Size of tree and penguin unknownhencehadronic uncertainties • Methods using these modes therefore • Resulted in bounds on 3() • Determine 3, using SU(3), neglect of certain contributions • Can only give good first estimates. • DK modes Need to look for decay modes with two weak amplitude contributions:

8. s K+ u b c B+ u B+ u s K+ u D0 D0 D0 B+ c b b u c s K+ u Gronau London Wyler Method b! c b! u Expt. rates do not show enough color suppression Interference is achieved by considering B+decaying toCP eigenstates of D.Net amplitude hastwo contributions with distinct weak phases. If each amplitude separately measured 3 determined. Need measurement of • Experimentally not feasible. Measurement of B+! D0 K+hard • Semileptonic decay cannot be used, due to background from • B+ decay B+! K+[D0! l+l X] vs B+! l+l X • The CP asymmetry is smallreducing sensitivity.

9. Consider decay of to doubly Cabibbo suppressed non-CP eigenstates Atwood Dunietz Soni Method and D0 to the CP conjugate Cabibbo allowed mode. • Leads to similar size of the interfering amplitudes of the B+ decay. Larger asymmetries with such states. • Use knowledge of relevant Cabibbo allowed and suppressed D branching ratios • Enough information even to solve for 3 as well asthe difficult to measure BR(B+! D0 K+). • Only drawback : Accuracy in measurement of 3, directly proportional to accuracy of the input doubly Cabibbo-suppressed rate. We do not discuss Dalitz plot technique or methods that use higher resonances of D. Giri, Grossman, Soffer & Zupan; Nita Sinha

10. Consider a final state f into which both and decay e.g.f= D- + Only one amplitude contributes to each d + A2 u bc b c B0 D d d  For f=D-+ mode(JPC=0-+) D+ A3 bu c g b¿ a B0 b u d hard to measure  d d • Time dependent asymmetries in D modes Dunietz • CPV can occur through interference of Direct Decay and mixing. » a a=0 and b=-3 By measuring the time dependent decay rates, » b determine the weak phase (21+3)

11. Consider Consider decaying into decaying into with with meson further decaying to a final state f that is common both decaying to a final state f that is common both doubly Cabibbo suppressed doubly Cabibbo suppressed f f Cabibbo allowed Cabibbo allowed 3using B§! D* V§ mode Sinha and Sinha, Phys. Rev. Lett. 80, 3706 (1998) The partial decay rate for B! D* K*! (D) () can be written as

12. Amp( B+,B-! f (or its CP conjugate) contributions from 5 Observables ! 23 Parameters ! 14 a, b,a,b,3,, R May not be distinguishable, Still enough observables, Can determine 3. R ¿ 1, a¿ b, help reduce ambiguities Usual Signatures: Additional Signatures:

13. Signals of CP Violation can be obtained by adding Interference terms-essential: If only • Signals of CP Violation not diluted by sine of strong phases. measured It is just like doing additional modes. The azimuthal angle , plays a crucial role. CP Violating Asymmetries It is easy to see that ?0 can be isolated using the asymmetry where as, ?kcan be isolated using the asymmetry It is only in the helicity frame that a sin component is a signal of CP violation. Transversity basis helps when dealing with CP violation.

14. Consider a final state f into which both and decay e.g.f= D- + Only one amplitude contributes to each 21+3 using B0(t)!D*+- In the decay of B !V1 V2 if V1! P1 P10and V2! P2 P20the decay amplitude may be expressed as Using CPT invariance, the total decay amplitudes can be written as g are the coefficients of the helicity amplitudes that depend purely on angles describing the kinematics.

15. Time dependent decay rate Time dependent decay of the neutral B meson to a final state f For VV mode a more complicated form Interference of helicities Total 18 observables in one decay mode

16. Consider a final state f into which both and decay e.g.f´ D*-+ only one amplitude contributes to each • extract a2, ignore b2 if gives 18 more observables. • = {0,k,?}, a,b are weak phases, • are strong phases. a=0b=-3 For the conjugate process one has similarly Cleanly extract weak phases. How??

17. r2r1 Adapted from a figure in talk of Abi Soffer • where and Solve • Use the coefficients of the sin( m t) term • CP phase =-2M + b-a ) • Terms involving interference of different helicity, Multiple helicities more powerful than had been realized. Due to interference between different helicities, enough observables, without even measuring the tiny b2 amplitudes.

18.  and  measured quantities • Put all the information above together, extract weak phase  a2 determined from  and  ai a?sini obtained from ? i and ? i 2 equations involve only 2 unknown quantities tanand aia?cosi, can easily be solved up to a sign ambiguity in each of these quantities. tan2 or, equivalently, sin2 can be obtained from angular analysis

19. The matrix element of the decay where Angular asymmetries in B!K-+l -l + Kruger, Sehgal, Sinha and Sinha, Phys. Rev. D61, 114028 (2000) [Erratum-ibid. D63, 019901 (2001)] Short distance Hamiltonian for b! f l+l- , where f=s,d may be written as

20. D. Melikhov, N. Nikitin, and S. Simula, Eventually,

21. More than 6 observables because of L,R components-like measuring the helicity of fermions in final state. Chiang and Wolfenstein, Phys. Rev. D61, 074031 (2000) The decay rate for the conjugate process can be obtained by the substitution

22. Note that the asymmetries involving 3,4,7 involving the differences and can be obtained from a measurement of the difference of decay rates for process and conjugate process. On the other hand, the asymmetries 5,6,8,9 require only a measurement of the sum of the decay rates for process and conjugate process. In principle, these can be determined even for an untagged equal mixture of

23. Vector –Vector modesprovide clean techniques for measuring weak phases. • Direct CP asymmetry measurements in Can cleanly determine 3. • Time Dependent asymmetryin Can be used to extract (21+3). Conclusions • The hunt for NP demands that we continue to look for more clean methods, to extract the CP violating angles, 1, 2 and 3 or combinations of them. • Comparisons of results using various techniques having almost zero theory error and free from discrete ambiguities can signal new physics.

24. A Thought The cascade of experimental data coming and expected on B-meson (and D-meson) decays is significantly widening our capacity to strongly constrain the parameter space, hence becoming apowerful tool to discriminate and even exclude models of new physics. Look forward to Super Belle, Super BaBar and LHC-b. How does one measure 1 to better than a percent? Hopefully we have convincing signal of New Physics by then.