25
03-Jul-08 1
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.
