Probing new physics using b v 1 v 2
This presentation is the property of its rightful owner.
Sponsored Links
1 / 20

Probing New Physics using B ! V 1 V 2 PowerPoint PPT Presentation


  • 36 Views
  • Uploaded on
  • Presentation posted in: General

Probing New Physics using B ! V 1 V 2. Rahul Sinha The Institute of Mathematical Sciences Work done in collaboration with David London & Nita Sinha. b. c. c. s. d. tree >> penguin. B !  K S. c. B !  K S :. . c. . s. u,c,t. . b. s. B 0. b. s. u,c,t. s. B 0. K S.

Download Presentation

Probing New Physics using B ! V 1 V 2

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Probing new physics using b v 1 v 2

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


Motivation signals of new physics

b

c

c

s

d

tree>>penguin

B! KS

c

B! KS:

c

s

u,c,t

b

s

B0

b

s

u,c,t

s

B0

KS

B0

KS

d

d

penguin

tree

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


Probing new physics using b v 1 v 2

  • 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


Probing new physics using b v 1 v 2

NP

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


B v 1 v 2 and angular analysis

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! V1V2 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

Super B Factory Workshop, Hawaii


Probing new physics using b v 1 v 2

Angular Analysis

CLEO

CDF

Belle

BaBar

Super B Factory Workshop, Hawaii


Observables in b v 1 v 2

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 V2

Super B Factory Workshop, Hawaii


Probing new physics using b v 1 v 2

Total 18 observables

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


Observables in terms of parameters

Vanishing signals of NP

Observables in terms of parameters

b´f1

Super B Factory Workshop, Hawaii


Probing new physics using b v 1 v 2

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


Probing new physics using b v 1 v 2

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

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 b2

Super B Factory Workshop, Hawaii


Bounds

  • 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 b2

Super B Factory Workshop, Hawaii


Probing new physics using b v 1 v 2

Helicity interference observables, only bound combinations

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

(b2§ b2).

(b2§ b2)

  • 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


Probing new physics using b v 1 v 2

0.8

12

10

180

180

0.7

8

0.6

6

135

135

0.5

4

0.4

2

90

90

0

0.3

0.06

0.1

0.2

-2

45

45

0.3

0.2

0.38

-4

0.1

-6

0.41

0

0

0.4

0.3

0

-8

0.2

0.1

0.2

0.3

0.4

0.5

0

0

0.1

0.2

0.3

0.4

0.5

0.1

0.06

45

45

90

90

135

135

180

180

0

0

Super B Factory Workshop, Hawaii


Probing new physics using b v 1 v 2

1

180

180

180

135

135

135

0.8

90

90

90

0.6

45

45

45

0

0

0

0.4

-45

-45

-45

-90

-90

-90

0.2

-135

-135

-135

-180

-180

-180

0

-180

-180

-180

-135

-135

-135

-90

-90

-90

-45

-45

-45

0

0

0

45

45

45

90

90

135

135

180

180

0

45

90

-90

-45

135

180

-180

-135

Super B Factory Workshop, Hawaii


Probing new physics using b v 1 v 2

0.5

12

4

0.4

0.05

10

2

0.1

0.3

8

0.2

0

0.2

6

-2

0.1

4

-4

0

2

-6

0.1

0.2

0.05

-0.1

0

-0.4

-0.2

0

0.2

0.4

-8

-0.4

-0.2

0

0.2

0.4

-0.4

-0.2

0

0.2

0.4

0.7

0.05

0.2

0.1

0.05

0.6

0.1

0.2

0.5

0.4

0.3

0.05

0.1

0.2

0.2

0.1

0.2

0.05

0.1

0

-0.4

-0.2

0

0.2

0.4

0.2

0.1

0.05

0.05

0.1

0.2

Super B Factory Workshop, Hawaii


Probing new physics using b v 1 v 2

  • 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


Conclusions

  • 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

Super B Factory Workshop, Hawaii


B rightarrow v 1 v 2

B\rightarrow V_1 V_2

Super B Factory Workshop, Hawaii


  • Login