03-jul-08 1superb.kek.jp/inaug/slide/sinha.pdf · 03-jul-08 5 refer to the work of pundits for more...

03-Jul-08 1

Look for deviations not alternatives.

Any deviation from KM not breakdown of KM but New Physics.

Fortunate, that New Physics is small:

Not just because we get to build the Super B but we know that

CKM is correct.

CKM matrix has hierarchical structure

Wolfenstein Parameterization

How sensitive are we to 4 order terms? Don’t give up. New

Physics (NP) can be at this order or smaller.

V=

0BB@

Vud Vus V ub

Vcd Vcs V cb

Vtd Vts V tb

1CCA =

0BB@

1¡ ¸2

2 ¡¸4

8 ¸ A¸3(½¡ i´)

¡¸+A2¸5(12¡ ½¡ i´) 1¡ ¸2

2¡¸4

8(1 + 4A2) A 2

A¸3(1 ¡ ¹½ ¡ i¹) ¡A¸2+A¸4(12 ¡ ½ ¡ i´) 1¡12A

2¸4

1CCA+O (

6)

03-Jul-08 3

There are good reasons to expect NP exists- I wont elaborate.

Too much has been talked about it and every one here should be

convinced about it.

Standard Model leaves many questions about the flavor sector

unanswered : Origin of generations, masses and mixing,

disappearance of antimatter.

Good reason to expect NP to have connection with flavor issues.

Tantalizing hints of NP already exist in the flavor sector:

Discrepancy in S measurements (S )

Phase of the BS mixing amplitude

CP asymmetries BKπ

Leptonic DS decays

03-Jul-08 4

Last meeting Nakano san already elaborated modes. I cannot do

a better job…

At the SuperB, several modes will be studied to search for NP.

03-Jul-08 5

Refer to the work of Pundits for more details:Browder, Gershon, Pirjol, Soni, Zupan arXiv:0802.3201

Very good summary of clean tests (Null Tests).

In light of all the literature I will look at only two possibilities

and convince you one can indeed have very clean signals model

independent signals of NP

After all with large sample of B mesons is obtained at Super B

one cannot still leave the fate of discovery of NP in the hands of

theorists and their estimates…

Super B will a precision machine. What about theory?

The hurdle between hint and discovery is precision: Both

theoretical and experimental.

Theory is import too…

03-Jul-08 6

03-Jul-08 7

How much can the measured values sin(21eff)

differ from sin(21) ?

How much can sin(21eff) differ between any two

modes.

Is there an evidence of New Physics?

Penguin diagram carries more than one weak phase

and can alter the measured value of sin(21).

Measured value “sin(21eff)” is an effective value that

can differ from sin(21) and vary for each mode.

Why do the various measurements of sin(21) not

agree?

03-Jul-08 8

strong phase difference between a0 and b0Ab!s = ei£

0£a0 + b0 ei±

0eiÁ3

¤overall strong phase

Ab!s = (Acei±c ¡Atei±t)vc+ (Auei±u ¡Atei±t)vu

a0 = jvcj a0 = jvcj¯Acei±c ¡Atei±t

¯

b0 = jvuj b0 = jvuj¯Auei±u ¡Atei±t

¯

Unitarity of CKM )vu =A¸

4(½+ i ) vt =¡A¸2 +A(12 ¡ ½¡ i´)¸4+O( 6)

vu+ vc + vt = 0 vc real to order O(6)

Strong phasesAmplitudes for quark level contributions

Ab!s =Auei±uvu +Acei±cvc+Atei±tvtvj = V

¤jbVjs

In SM most general amplitude for bs transition

03-Jul-08 9

a00 = jvcj a00 = jvcj¯Acei±c ¡Auei±u

¯

b00 = jvtj b00 = jvtj¯Auei±u ¡Atei±t

¯

Ab!s = ei£00£a00 + b00 ei±

00eiÁ4

¤

Ab!s = (Acei±c ¡Auei±u)vc+ (Atei±t ¡Auei±u)vt

strong phase difference between a00 and b00

overall strong phase

Amplitudes for decay of may in general be written as:

can be 3 or 4B0d ! fi Ai = ai + bie

i±ieiÁ

¹B0d ! fi ¹Ai = ai + biei±ie¡iÁ

Si =p1 ¡C2i sin2Ái1 =¡

q1¡C2i

Im(e¡2iÁ1A¤i¹Ai)

jAijj ¹Aij

03-Jul-08 10

‘i’ is mode index

Measured effective value for

mode ‘i’

¡(B0(t)! fi)/ Bi(1+Ci cos(¢Mt)¡Si sin(¢Mt))

Bi =jAi j2 + j ¹Ai j2

2= a2i + b

2i +2 ai bi cos Á cos ±i;

Ci =jAij2 ¡ j ¹Aij2

jAij2 + j ¹Aij2=¡2 ai bi sinÁsin ±i

Bi

ai; bi; ±i ;Á1Bi ;Ci; Si; Á)s ´ Á4 = 1:045o+0:061

o

¡0:057o

´i = argAi ¡ arg ¹Ai ! = (2Ái1 ¡ 2Áj1) = ´1¡´2

03-Jul-08 11

¹Ai = ai + biei±ie¡iÁ

Ai ¡ ¹Ai = 2bi sinÁ

Aie¡iÁ ¡ ¹Aie

iÁ = ¡2aisinÁ

A¤i¹Ai = jAijj ¹Ai je¡i´i ) i =2Á

i1 ¡ 2Á1

! > 0) 2Á(1)

1 > 2Á(2)

1

SP=2bi sinÁ

Ai = ai + biei±ieiÁ

03-Jul-08 12

03-Jul-08 13

O

O

4 QSO&4 VPO 4 QPO &4 VSO

¹³i

³i<jAi jj ¹Ai j

< 1 ) ¹³i < ³i

03-Jul-08 14

03-Jul-08 15

¢=0; ¼6 ;¼3 ;¼2; ¼

•To conclude, without making any hadronic model based

assumptions we have shown that within the SM, it is impossible

to explain a discrepancy of more than a few degrees in the ‘S’

measurement.

03-Jul-08 16

03-Jul-08 17

03-Jul-08 18

The decay amplitude for each of the helicity states:

helicity index takes the values ={0,||,}.

The full decay amplitudes are:

g: coefficients of the helicity amplitudes, depend only

on the angles describing the kinematics.

03-Jul-08 19

Time-dependent decay rates can be written as,

Interference

of helicities

33=932=6 31=3

03-Jul-08 20

03-Jul-08 21

No. of theoretical parameters: 13

No. of independent observables: 11,

magnitudes and relative phases of In the absence of NP, b = 0, f =0.# of parameters reduced, 13! 6 3 a, 2 i, and f1.

No. of independent observables: 6.

All parameters can be determined cleanly in terms of

observables.

03-Jul-08 22

Violation of these 12 relations, smoking gun signals

of New Physics!

03-Jul-08 23

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 b/a is same for all helicities,

Then all 12 relations are satisfied.

For this very special conditions, angular analysis of

B V1 V2 leads to no signal for NP.

Measured value of f1 not the mixing phase.

•Even if .•?i does not require flavor tagging/ time dependence.•?i terms are CP-odd

)?i survives in untagged sample.

03-Jul-08 24

If analytical bounds possible.

Obtain bounds on the b and deviation of the measured

values of f1 from mixing phase.

Many more bounds; detailednumerical study also done.

03-Jul-08 25

One should make sure that discovery of NP is not tied

down to the precision of hadronic estimates given that

we will have such a large sample of B mesons.

It is possible to have clean signals of NP.

All sin21 measurements must agree to within a few

degree for all modes within the SM. Failure of this

precondition would be a clean signal of NP.

Time dependent angular analysis of bs VV modes

can provide unambiguous signals of NP.