measuring weak phases using b ! vv

May 12,2005 1Yonsei Yonsei UniversitUniversit

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Measuring Weak Phases using B! VV

Measuring Weak Phases using B! VV

Rahul Sinha

The Institute of Mathematical SciencesThursday 12th May 205

2:00 pm

Talk at:

Beauty is eternity gazing at itself in a mirror.

Kahlil Gibran (1883-1931) Lebanese poet, novelist. The Prophet

(1923).

May 12, 2005 2Yonsei Yonsei UniversitUniversit

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1 ratese

+

(0.105)

W

e+

e

cc sd

u

d

u

sincos

cc ds

c

s

c

sincos

sin c=0.22

This is easy to understand if we assumed weak transitions take place in the same generation, but that weak eigenstates are not weak eigenstates are not the same as the mass eigenstaesthe same as the mass eigenstaes. The interaction for 3 generations can then be described as LLintint==UUVVDWDW++,, where V is a unitary matrix:

The CKM matrixe

K-

(0.494)

u u

s u

W

S=1e

cratesus 2sin

-

(0.140)

u u

d u

W

S=0

e

e

cratesud 2cos

CP violation arises in SM, due to the complex phase in the Cabbibbo-Kobayashi-Maskawa (KM)- relates the weak eigenstates to their mass eigenstates:

CP violation arises in SM, due to the complex phase in the Cabbibbo-Kobayashi-Maskawa (KM)- relates the weak eigenstates to their mass eigenstates:


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Wolfenstein Unitary TriangleWolfenstein Unitary Triangle

V is a Unitary matrix Orthonormality relations. One such relation is V is a Unitary matrix Orthonormality relations. One such relation is 0*** tbtdcbcdubud VVVVVV

11 11real

real

*

*

cbcd

ub

VV

V *cbcd

td

VV

V2

3 1 e1

e3

tbtstd

cbcscd

ubusud

VVV

VVV

VVV

V

Non vanishing value of ) CPV


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1, 2, 3 independent of the parameterization. Physical quantities that can be measured.

Non zero 23 indicate CPVSides can indirectly measure the angles BUT involves large

hadronic uncertaintiesCP violating asymmetries can directly measure these angles

cleanly.A Clean method for-weak phases, based on the fact that neutral B mesons can mix (induced by the box diagrams)

Final state f into which both and

can decay, two interfering amplitudes.Time dependence of Decay Rate

where,

f


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•In B! KS , the decay amplitude dominated by only one tree amplitude with a real CKM element

Determination of Determination of 11

•Asymmetry completely free of hadronic uncertainties.

Determination of Determination of 22 • Final state +. At the tree level, the amplitude involves ab! u quark transition,

•However, there is Penguin PollutionPenguin Pollution. What one measures through a time dependent asymmetry here is not 22 but some effective POLLUTED angle 22

eff.Problem resolved through Isospin Analysis.Isospin Analysis.

Determination of Determination of 33 Most of the talk today


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How does one measure 3()?How does one measure 3()?

Need to determine all CP violating phases without hadronic without hadronic uncertainties.uncertainties.3(), phase of the Vub element of the CKM matrix is the most difficult to measure.most difficult to measure.Initially proposed to use Bs(t) ! KS (similar to Bd(t) ! KS used to 1). Presence of penguin amplitudes completely spoil the penguin amplitudes completely spoil the

measurement of measurement of 33((). ). 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 pollutionAvoid penguin pollution, look at modes that involve only tree amplitudes:

•DK Methods- interference of b! c and b! u trees, clean.clean.•Time dependent asymmetries in D modes.

Extend techniques to VV with several advantagesseveral advantages.

Need to study decays

to non-CP

eigenstates.


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Tree is Cabibbo suppressed, Penguin contributions, including

Electroweak Penguins cannot be neglected.

KK modes modes

Size of tree and penguin unknown hencehence hadronic 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 modesDK modes

Need to look for decay modes with two weak amplitude contributions:

b! c b! u


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B+

u

u

b c

s

K+

D0

B+

s

D0

u

b c

K+

u

B+

s

D0

c

b u

K+

u

b! c b! u

Interference is achieved by considering B+ decaying to CP eigenstates of D. Net amplitude has two contributions with distinct weak phases. If each amplitude separately measured 3 determined.

Need measurement of•Experimentally not feasible.not feasible. Measurement of B+! D0 K+ hardhard

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 small reducing sensitivity.

Gronau London Wyler Method

Expt. rates do not

show enough color

suppression


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Atwood Dunietz Soni Method

•Leads to similar size of the interfering amplitudes of the B+ decay. Larger asymmetries with such states.

•Enough information even to solve for 3 as well as the difficult to measure BR(B+! D0 K+).

•Use knowledge of relevant Cabibbo allowed and suppressed D branching ratios

•Consider decay of to doubly Cabibbo suppressed non-CP eigenstates

•Only drawback : Accuracy in measurement of 3, directly proportional to accuracy of the input doubly Cabibbo-suppressed rate.

and D0 to the CP conjugate Cabibbo allowed mode.

We do not discuss Dalitz plot technique or methods that use higher resonances of D. Giri, Grossman, Soffer & Zupan; Nita Sinha


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Consider a final state f into which both and decay e.g. f= D+ Only one amplitude contributes to each

Time dependent asymmetries in DTime dependent asymmetries in D modes modes

B0bd

cd

du

D

bc

B0bd d

u

D+

bu

cd

A2

A3

b¿ a

•CPV can occur through interference of Direct Decay and mixing.

For f=D-+ mode (JPC=0-+)

a=0 and b=-3

By measuring the time dependent decay rates,

determine the weak phase (21+3)

hard to measure

Dunietz

» a

» b


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The partial decay rate for B! D* ! (D) () can be written as

3 using B§! D* V§ mode

meson furtherdecaying into withConsider

decaying to a final state f that is common both

f

doubly Cabibbo suppressed

Cabibbo allowed

decaying into withConsider

decaying to a final state f that is common both

f

doubly Cabibbo suppressed

Cabibbo allowed

Sinha and Sinha, Phys. Rev. Lett. 80, 3706 (1998)


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Amp( B+,B-! f (or its CP conjugate) contributions from

Observables ! 23

Parameters ! 14

a, b,a,b,3,, R

May not be distinguishable,Still enough observables,

Can determine 3.R ¿ 1, a¿ bhelp reduce ambiguities

Usual Signatures:

5

Additional Signatures:

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It is just like doing additional modes. The azimuthal angle plays a crucial role. It is easy to see that ?0 can be isolated using the asymmetry

where as, ?k can 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.

Interference terms-essential: If only measured

CP Violating AsymmetriesCP Violating Asymmetries

Signals of CP Violation not diluted by sine of strong phases.

Signals of CP Violation can be obtained by adding


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2+3 using B0(t) ! D*+

In the decay of B ! V1 V2 if V1! P1 P10 and V2! P2 P2

0 the 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.

Consider a final state f into which both and decay e.g. f= D+ Only one amplitude contributes to each


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Time dependent decay of the neutral B meson to a final state f

Time dependent decay rate

For VV mode a more complicated form

933 623 313

Total 18 observables in one decay mode

Interference

of helicities


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Consider a final state f into which both and decay e.g. f´ D*-+ only one amplitude contributes to each

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??

extract a2, ignore b

2


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where and Solve

Use the coefficients of the sin( m t) term

CP phase = 2M + 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.

r2 r 1

Adapted from a figure in talk of Abi Soffer


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a2 determined from and

ai a?sini obtained from ? i and ? i

2 equations involve only 2 unknown quantities tanand aia?cosi, can easily be solved up to a sign ambiguity in each of these quantities.

tan2 or, equivalently, sin2 can be obtained from angular analysis

and measured quantities

Put all the information above together, extract weak phase


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Angular asymmetries in B!K +l l +

The matrix element of the decay where

Short distance Hamiltonian for b! f l+l, where f=s,d

may be written as

Kruger, Sehgal, Sinha and Sinha, Phys. Rev. D61, 114028 (2000) [Erratum-ibid. D63, 019901 (2001)]


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Eventually,

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


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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


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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


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Conclusions

Vector –Vector modes provide clean techniques for measuring measuring

weak phases.weak phases.

Direct CPDirect CP asymmetry measurements in

Can cleanly determine 3.

Time Dependent asymmetryTime Dependent asymmetry in

Can be used to extract (21+3).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.


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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 a powerful powerful tool to discriminate and even exclude models of new physicstool 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 percentbetter than a percent? Hopefully we have convincing signal of New Physics by then.

A Thought

measuring weak phases using b ! vv

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