Probing New Physics using B ! V 1 V 2

January 19-22, 2004

Super B Factory Workshop Hawaii

Probing New Physics using Probing New Physics using BB!! V V11 V V22

Probing New Physics using Probing New Physics using BB!! V V11 V V22

Rahul SinhaRahul SinhaThe Institute of Mathematical Sciences

Work done in collaboration with David London & Nita SinhaDavid London & Nita Sinha

January 20, 2004 Super B Factory Workshop, Hawaii

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Motivation: Signals of New Motivation: Signals of New PhysicsPhysics

•B system: a unique testing ground for the SM CP Violation.•Measurement of the angle /1, 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

B! KS:tree >> penguin

tree penguin

c

cb

d

s

u,c,t

c

b s

d

c

B0

B0

KS

B! KS

u,c,t

b s

d

ssB0

KS

CKM elements real, effectively only a single weak amplitudeACP ) the mixing phase, without hadronic uncertainties


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How does New Physics affect the above analysis?If NP affects mixing only: Analysis remains unchanged, measured value of 1 not the true SM value, but shifted by a new-physics phase.If the NP affects the decay amplitude: extraction of 1 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.

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


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

SM NP

No. of parameters: 5 (a, b, ´ (b-a), ,1of observables: 3 ) Cannot solve for the parameters.Signal of NP is direct CP asymmetry:

If strong phase vanishes, NP signal! 0.


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BB!! V V11VV22 and Angular Analysis and Angular Analysis

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

While number of parameters still exceeds number of observables,Additional signals of NP.Additional signals of NP. Possible to bound the size of NP.Possible to bound the size of NP.Constrain its effect on measurement of the mixing phase.Constrain its effect on measurement of the mixing phase.


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0.52§0.07§0.04

0.59§0.06§0.02

0.06§0.03§0.02

0.62§0.02§0.03

0.885§0.016§0.012

0.61§0.14§0.04

0.43§0.09§0.04

0.506§0.139§0.036

Dominant

Dominant

0.16§0.08§0.04

0.13§0.11§0.06

0.16§0.03§0.01

0.19§0.02§0.03

0.23§0.19§0.04

0.07§0.06§0.03

0.41§0.10§0.04

-0.11§0.46§0.03

-0.6§0.5§0.1

-0.17§0.16§0.07

-0.09§0.13§0.06

…

0.48§0.32§0.06

3.00§0.37§0.04

2.2§0.5§0.1

2.50§0.20§0.08

2.83§0.19§0.08

1.1§1.3§0.2

-2.57§0.39§0.09

CLEO

CDF

Belle

BaBar

Angular Analysis


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Observables in BObservables in B!! V V11 V V22

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,


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No. of theoretical parameters: 13

933 623 313

Total 18 observables

No. of independent observables: 11, 6 magnitudes and relative phases

Interference of helicities

Cannot obtain parameters purely in terms of observables, impossible to extract 1


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Vanishing signals of NP

Observables in terms of parameters

´1


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In the In the absence of NPabsence of NP, b, b = 0, = 0, =0.=0. No. of parameters: reduced, 13! 6 3 a's, 2 strong i, and 1.No. of independent observables: 6, .All parameters can be determined cleanly in terms of observables.18 observables- 6 vanish & 6 independent) 6 additional relations

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

•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.


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Is it possible that all NP signals vanish, even if NP is present? Yes! If the singular situation:

1. All the strong phase differences ’s vanish,2. ratio r ´ b/a is same for all helicities,

Then all 12 relations are satisfied.Then all 12 relations are satisfied.

NotationsNotations


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ConstraintsConstraints

11 measurements, 13 parameters, equations highly nonlinear, Constraints possible—Procedure:STEP I: Express a, b , in terms of observables , and variables and

STEP II:Remaining 9 observables: in terms of first 9 and variables i,1, Task not easy, achieved only by introducing new observables. STEP III:To get the actual bounds, on size of NP, extremize b

2


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BoundsBounds

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

If defining, , we get

No bound possible on

No upper bound on b2


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) For non-zero ? i cannot have i = ? =0, but do not bound /1 If , minimization using MINUIT Observation of ?i and ? i with finite ii,??, -- MINUIT used. Note that given 2 measurements, ? i, ? i, Both cos() and sin(i) determined ) known upto ambiguities.

If analytical bounds possible

Can also bound,

Helicity interference observables, only bound combinations Introduced in by relating 2 to the observables like ? i.

(b2§ b

2).(b

2§ b2)


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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.1 0.2 0.3 0.4 0.5

0 45 90 135 180

135

180

0

45

90

0

45

90

135

180

0 45 90 135 180

0.3

0.41 0.4

0.2

0.1 0.06

0.1 0.06

0.2

0.3

0.38

-8-6-4

-2

0 2

4

6 8

10 12

0 0.1 0.2 0.3 0.4 0.5


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-180

-135

-90

-45

0

45

90

135

180

-180-135 -90 -45 0 45 90 135 180-180

-135

-90

-45

0

45

90

135

180

-180-135 -90 -45 0 45-180

-135

-90

-45

0

45

90

135

180

-180-135 -90 -45 0 45 90 135 180 0

0.2

0.4

0.6

0.8

1

-180

-135 -9

0

-45 0 45

90

135

180


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0.2 0.1 0.05

0.2 0.1 0.05

-0.1

0

0.1

0.2

0.3

0.4

0.5

-0.4 -0.2 0 0.2 0.4

0.2 0.1 0.05

0.2 0.1

0.05

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-0.4 -0.2 0 0.2 0.4

0.1 0.2 0.05

0.05 0.1 0.2

-8

-6

-4

-2

0

2

4

-0.4 -0.2 0 0.2 0.4

0.05

0.1

0.2

0.05 0.1 0.2

0

2

4

6

8

10

12

-0.4 -0.2 0 0.2 0.4


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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.

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.


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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 .

CONCLUSIONS


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B\rightarrow V_1 V_2B\rightarrow V_1 V_2

Documents

Probing New Physics using B ! V 1 V 2