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### Probing New Physics using B! V1 V2

Rahul Sinha

The Institute of Mathematical Sciences

Work done in collaboration with David London & Nita Sinha

Super B Factory Workshop

Hawaii

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B! KS

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B! KS:

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Motivation: Signals of New Physics- B system: a unique testing ground for the SM CP Violation.
- Measurement of the angle /f1, using the golden mode J/KS
- in agreement with SM.Yet expect physics beyond SM.
- Hint of NP ACP(B! KS) ACP(B! KS).
- Need to corroborate the result with direct and perhaps cleaner tests.
- Important to study sensitivity of signals at Super B

CKM elements real, effectively only a single weak amplitude

ACP) the mixing phase, without hadronic uncertainties

Super B Factory Workshop, Hawaii

If NP affects mixing only: Analysis remains unchanged, measured value of /f1 not the true SM value, but shifted by a new-physics phase.

- If the NP affects the decay amplitude:extraction of /f1 not clean, contaminated by hadronic uncertainties.
- We consider this scenario.
- NP can affect decay amplitude at loop level (in b! s penguin amplitude) or at tree level.

How does New Physics affect the above analysis?

- Specific models that can give NP contributions:
- Non minimal SUSY
- Z-mediated FCNC
- T2HDM Top quark two Higgs doublet model
- …… …

Super B Factory Workshop, Hawaii

SM

In presence of NP, the decay amplitude may be written as,

No. of parameters: 5(a, b, ´ (b-a), ,/f1)

No.of observables: 3 )Cannot solve for the parameters.

Signal of NP is direct CP asymmetry:

If strong phase vanishes,NP signal! 0.

Super B Factory Workshop, Hawaii

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.

B decays to two vector mesons special due to the presence of 3 helicity amplitudes

B ! V1 V2

Spin 0 ! 1+1) L=0,1,2

Need to perform angular analysis to obtain the helicity amplitudes from expt. data. This has already been done for several B! V1V2 decay modes. Such final states result in large number of observables

Super B Factory Workshop, Hawaii

The decay amplitude for each of the the helicity states:

g: coefficients of the helicity amplitudes, depend only on the angles describing the kinematics. Time-dependent decay rates can be written as,

Observables in B! V1 V2Super B Factory Workshop, Hawaii

Interference

of helicities

No. of theoretical parameters: 13

No. of independent observables: 11, 6magnitudes and

relative phases

Cannot obtain parameters purely in terms of observables,

impossible to extract /f1

Super B Factory Workshop, Hawaii

In the absence of NP, b = 0, =0.

No. of parameters: reduced, 13! 6 3 a\'s, 2 strong i, and /f1.

No. of independent observables: 6, .

All parameters can be determined cleanly in terms of observables.

18 observables- 6 vanish & 6 independent)6 additional relations

- Observable ? i deserves special attention.
- Even if in contrast to direct asymmetry.
- ?i does not require flavour tagging, nor time dependence.
- ? i terms are CP-odd )? i survives in an untagged sample.
- No reason why ? i cannot be measured.

Violation of these 12 relations, smoking gun signals of New Physics!

Super B Factory Workshop, Hawaii

Is it possible that all NP signals vanish, even if NP is present?

Yes! If the singular situation:

- All the strong phase differences ’s vanish,
- ratio r´ b/a is same for all helicities,
- Then all 12 relations are satisfied.

Notations

Super B Factory Workshop, Hawaii

Constraints

11 measurements, 13 parameters, equations highly nonlinear,

Constraintspossible—Procedure:

STEP I: Express a, b , in terms of observables ,,

and variables /f1 and .

STEP II:

Remaining 9 observables: in terms of first 9 and variables i,/f1,

Task not easy, achieved only by introducing new observables.

STEP III:

To get the actual bounds, on size of NP, extremize b2

Super B Factory Workshop, Hawaii

If defining, , we get

Bounds- Trivial Bound: If direct CPV observed in any helicity,
- Minimization w.r.t. /f1, )

- No bound possible on

- No upper bound on b2

Super B Factory Workshop, Hawaii

Helicity interference observables, only bound combinations

Introduced in by relating 2 to the observables like ? i.

(b2§ b2).

(b2§ b2)

- If analytical bounds possible

) For non-zero ? i cannot have i = ? =0, but do not bound /f1

- If , minimization using MINUIT

- Observation of ?i and ? i with finite ii,??, -- MINUIT used.

Note that given 2 measurements,? i, ? i,

Both cos(i) and sin(i) determined ) known upto ambiguities.

Can also bound,

Super B Factory Workshop, Hawaii

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Super B Factory Workshop, Hawaii

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Super B Factory Workshop, Hawaii

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Super B Factory Workshop, Hawaii

If more number of measurements made,

ambiguity in solutions get reduced, ) tighter bounds.

- A-priori, one does not know which of the above constraints is

strongest -depends on the actual values of the observables.

- Quite possible that, if one combines many NP signals,

the combined constraints will be stronger.

- In practice, fit to obtain the best lower bounds on NP parameters.

Applications:

- B0! J/ K* and B0! K*

would allow one to determine if new physics is indeed present.

- Within SM, decays such as B0! D*+ D*- have tree and penguin

contributions ! cannot be extracted cleanly.

If NP=0, one can obtain bounds on P/T and on .

- Modes B! Ds*D*: no direct/indirect CPV possible in SM

Any CPV signal ) NP.

Super B Factory Workshop, Hawaii

To establish NP, search for as many signals as possible.

- Hints, need to be corroborated with direct tests.
- B! VV provide many model independent clean tests of NP.
- Several of these tests, non-vanishing even if strong phase differences

between SM and NP vanish.

- Should a signal be found, can bound the size of NP,

as well as constrain .

CONCLUSIONSSuper B Factory Workshop, Hawaii

B\rightarrow V_1 V_2

Super B Factory Workshop, Hawaii

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