B-factory signals for a warped extra dimension Page: 3 of 5
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butions and M12 M Rs is the SM (box diagram) and RS1
(KK gluon exchange) AF 2 transition amplitudes re-
spectively. We see that the KK gluon contribution to
Bd- B, BO - E mass difference, EK and the CP asym-
metry in B -> vKs is comparable to SM ones.
The SM predictions depend on Vtd which is currently
not severely constrained by tree-level decays and unitar-
ity [14] which are not affected by NP contributions. The
data, therefore, can be fitted even with RS1 contributions
comparable to SM [6].
This, however, leads to a "coincidence problem" : why
is SM fit (usually presented as a plot of the constraints
in the p - plane, see e.g. [14]) so good? At present, this
problem is not so severe since there are 0 (20%) uncer-
tainties in SM predictions for EK and AmhB (due mainly
to hadronic matrix elements) [15] and also the RS1 con-
tributions have 0(1) uncertainties due to fluctuations in
A5D. Consequently, clean measurements of a and -y via
B -> mur, rp, pp, DK are likely to be affected.
The case of B8 - B mixing is slightly different than
Bd - Bd mixing and EK as the SM contribution is known
(up to hadronic matrix elements) since 148 is constrained
by unitarity and tree-level decays [14]. Hence, for a
generic order one complex coefficient (it is complex due
to physical phases in DL [6]), we expect an 0(1) devia-
tion from SM prediction in AmB, (see reference [13] for
a larger effect). Similarly, an 0(1) time-dependent CP
asymmetry in B8 -> J/pp is induced compared with the
SM 0 (A) prediction, where A, ~ 0.22. Also deviations
from SM expectation for -y ought to occur in B8 -> DK.
Next, we consider AF 1 transitions. We start with
the discussion of processes which in the SM are dom-
inated by QCD penguin diagrams such as b -> sss.
There is a contribution from KK gluon exchange as in
the AF 2 case. The coupling of KK gluon to s is sup-
pressed by ~ log (Mpj/TeV) since the strange quark
is localized near Planck brane whereas the KK gluon is
localized near TeV brane (this is the universal part of
coupling of fermions to gauge KK modes). Thus, it is
clear that KK gluon contribution ~ 1/5 SM QCD pen-
guin. In addition, there is dilution of NP effect in QCD
penguin after RG scaling from TeV to mb. So, KK gluon
NP contributions in AF 1 transition cannot compete
with SM QCD penguin ones (see however [13] for a 0(1)
effect with ~ 1 TeV KK masses).
The contribution from exchange of KK mode of Z is
smaller than that from KK gluon. However, as mentioned
above, the KK mode of Z mixes with zero-mode of Z
due to Higgs vev, in turn, generating a flavor-violating
coupling to the physical Z. Thus, we get the following
contributions to coefficients of EW penguin operators,
C7-10 (four quark) and C9V, 10A (leptonic operators):CZ, RS
7-10, 9V, 10A
C 1,SM
07-10, 917, bOA162 KK log (MpI/TeV) 2Z
92 LZ mKKgzKK (3TeV 2
9z mKK ((4)
where superscript Z on C7-10, 9V, 10A denotes Z penguin
part and, as for AF 2 case, the SM contribution is
from top quark loop and mixing angles are of same size
in both contributions. Thus, the two contributions are
comparable. This leads to an 0(1) effect in BR for rare
flavor-changing decays, for example, b -> sl+l- [16][12],
where uncertainty in theory prediction is of 0 (20%) and
current experimental error (from BABAR and BELLE)
is of 0 (30%) [17]. In addition a smoking gun signal is
that significant departure from SM is expected in the
direct CP asymmetry and in the spectrum of leptons in
this decay, as well as in the forward-backward asymmetry
since the new physics effect is only in the Z penguin (with
almost axial couplings of leptons, i.e., in C10A) and not
in the photon penguin (with vector couplings of leptons,
i.e., in C9V).
As mentioned above, the b -> sss transition is dom-
inated by SM QCD penguin. Similar RS1 contribution
from flavor-violating Z vertex is suppressed by at least
2 ~ 20% and therefore subleading [16][12]. Con-
sequently, RS1 can accomodate only mild deviations[6]
(unlike[13], as mentioned above) from the SM in time de-
pendent CP asymmetry in "penguin-doiminated" B de-
cays, such as O(n', 0, L, p )K,.
We next consider radiative decay processes. Since
these require helicity flip, related NP contributions ap-
pear only at the loop level in our framework. The dom-
inant contribution comes from loops of Higgs and KK
fermions since couplings of KK fermions to Higgs are en-
hanced. We show elsewhere [6] that KK gluon contribu-
tion is aligned in flavor space with fermion mass matrix
and hence is not flavor-violating. We find the following
contribution to dipole operator for b -> s transition:ClMS
CSM7AjD m& (DR)23
2 2
92 m~KK Vt8
(D)23 (A5D 3TeV ),
4 mKK(5)
where C7 y and C7 are coefficients of dipole operators
with bR and bL, respectively and (DR)23 -> (DL)23 for
CRS. For b -> d transition, (DL, R)23 > (DL, R)13 and
8-*Vu.
Let us now estimate the right-handed (RH) down
quark mixing appearing in the above RS1 contribution.
Due to anarchic A5D, the ratio of masses are also given
by ratio of wave-functions on TeV brane (just like the
mixing angles) so that:mb (DL)23
(DR)23 T m 1
mb0(1), (6)
where we used the bottom and strange quark masses at
the ~ TeV scale and also (DL)23 ~ Vt. Similarly, we
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Agashe, Kaustubh; Perez, Gilad & Soni, Amarjit. B-factory signals for a warped extra dimension, article, August 24, 2004; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc793293/m1/3/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.