Flavor Physics in SUSY at large tan(beta)
Flavor Physics in SUSY at large tan β
Paride Paradisi
Departament de F́ısica Teòrica and IFIC, Universitat de València-CSIC, E-46100, Burjassot, Spain.
We discuss the phenomenological impact of a particularly interesting corner of the MSSM: the
large tanβ regime. The capabilities of leptonic and hadronic Flavor Violating processes in shedding
light on physics beyond the Standard Model are reviewed. Moreover, we show that tests of Lepton
Universality in charged current processes can represent an interesting handle to obtain relevant
information on New Physics scenarios.
I. INTRODUCTION
Despite the great phenomenological success of the
Standard Model (SM), it is natural to consider this the-
ory only as the low-energy limit of a more general model.
The direct exploration of New Physics (NP) particles
at the TeV scale will be performed at the upcoming
LHC. A complementary strategy in looking for NP is
provided by high-precision low-energy experiments where
NP could be detected through the virtual effects of NP
particles. In particular, flavor-changing neutral-current
(FCNC) transitions may exhibit a sensitivity reach even
beyond that achievable by the direct searches at the LHC
while representing, at the same time, the best (or even
the only) tool to extract information about the flavor
structures of NP theories.
In view of the above considerations, it is clear that
flavor physics provides necessary and complementary in-
formation to those obtainable by the LHC.
Besides FCNC decays, also the Lepton Flavor Univer-
sality (LFU) tests (Kℓ2 and πℓ2) offer a unique opportu-
nity to probe the SM and thus, to shed light on NP: the
smallness of NP effects is more than compensated by the
excellent experimental resolution and the good theoreti-
cal control.
II. LFV IN SUSY
The discovery of neutrino masses and oscillations has
unambiguously pointed out the existence of the Lepton
Flavor Violation (LFV) thus, we expect this phenomenon
to occur also in the charged-lepton sector.
Within a SM framework with massive neutrinos,
FCNC transitions in the lepton sector like ℓi → ℓjγ are
strongly suppressed by the GIM mechanism at the level
of B(ℓi → ℓjγ) ∼ (mν/mW )
4 ∼ 10−50 well beyond any
realistic experimental resolution [1]. In this sense, the
search for FCNC transitions of charged leptons is one of
the most promising directions where to look for physics
beyond the SM.
Within a SUSY framework, LFV effects originate from
any misalignment between fermion and sfermion mass
eigenstates. In particular, if the light neutrino masses
are obtained via a see-saw mechanism, the radiatively
induced LFV entries in the slepton mass matrix (m2
are given by [2]:
)i6=j ≈ −
ν )i6=j ln
, (1)
where MX denote the scale of SUSY-breaking media-
tion andm0 the universal supersymmetry breaking scalar
mass. Since the see–saw equation 1 allows large (YνY
entries, sizable effects can stem from this running [2].
The determination of (m2
)i6=j would imply a complete
knowledge of the neutrino Yukawa matrix (Yν)ij , which
is not possible even if all the low-energy observables from
the neutrino sector were known. As a result, the predic-
tions of leptonic FCNC effects will remain undetermined
even in the very optimistic situation where all the rele-
vant NP masses were measured at the LHC.
This is in contrast with the quark sector, where similar
RGE contributions are completely determined in terms
of quark masses and CKM-matrix elements.
More stable predictions can be obtained embedding
the SUSY model within a Grand Unified Theory (GUT)
where the see-saw mechanism can naturally arise (such
as SO(10)). In this case the GUT symmetry allows us to
obtain some hints about the unknown neutrino Yukawa
matrix Yν . Moreover, in GUT scenarios there are other
contributions stemming from the quark sector [3]. These
effects are completely independent from the structure of
Yν and can be regarded as new irreducible LFV contribu-
tions within SUSY GUTs. For instance, within SU(5),
as both Q and ec are hosted in the 10 representation, the
CKM matrix mixing the left handed quarks will give rise
to off diagonal entries in the running of the right-handed
slepton soft masses [3].
There exist to different classes of LFV contributions to
rare decays:
i) Gauge-mediated LFV effects through the exchange
of gauginos and sleptons,
ii) Higgs-mediated LFV effects through effective non-
holomorphic Yukawa interactions [4] .
1 The effective light-neutrino mass matrix obtained from a see-
saw mechanism is mν = −YνM̂
ν 〈Hu〉
2, where M̂R is the
3 × 3 right-handed neutrino mass matrix and Yν are the 3 ×
3 Yukawa couplings between left- and right-handed neutrinos
(the potentially large sources of LFV), and 〈Hu〉 is the vacuum
expectation value of the up-type Higgs.
http://arxiv.org/abs/0704.0358v1
The above contributions decouple with the heaviest mass
in the slepton/gaugino loops mSUSY (case i)) or with the
heavy Higgs mass mH (case ii)).
In principle, mH and mSUSY refers to different mass
scales. Higgs mediated effects start being competitive
with the gaugino mediated ones when mSUSY is roughly
one order of magnitude heavier then mH and for tanβ ∼
O(50) [5].
While the appearance of LFV transitions would un-
ambiguously signal the presence of NP, the underlying
theory generating LFV phenomena will remain undeter-
mined, in general.
A powerful tool to disentangle among NP theories is
the study of the correlations of LFV transitions among
same families [5, 6, 7].
Interestingly enough, the predictions for the correla-
tions among LFV processes are very different in the
gauge- and Higgs-mediated cases [5]. In this way, if sev-
eral LFV transitions are observed, their correlated anal-
ysis could shed light on the underlying mechanism of
LFV. In the case of gauge-mediated LFV amplitudes the
ℓi → ℓjℓkℓk decays are dominated by the ℓi → ℓjγ
∗ dipole
transition, which leads to the unambiguous prediction:
B(ℓi → ℓjℓkℓk)
B(ℓi → ℓjγ)
B(µ− e in Ti)
B(µ→eγ)
≃αel . (3)
If some ratios different from the above were discovered,
then this would be clear evidence that some new process
is generating the ℓi → ℓj transition, with Higgs mediation
being a potential candidate 2.
As regards the Higgs mediated case, Br(τ → ljγ) still
gets generally the largest contribution among all the pos-
sible LFV decay modes [5]. The following approximate
relations hold [5]:
Br(τ → ljγ)
Br(τ → ljη)
& 1 ,
Br(τ → ljη)
Br(τ → ljµµ)
3+5δjµ
. (4)
Br(τ → ljee)
Br(τ → ljµµ)
3+5δjµ
. (5)
Br(µ → eγ)
Br(µAl → eAl)
∼ 10 ,
Br(µ → eee)
Br(µ → eγ)
∼ αel . (6)
On the other hand, a correlated study of processes of the
same type but relative to different family transitions, like
2 As recently shown in [7], a powerful tool to disentangle between
Little Higgs models with T parity (LHT) and SUSY theories
is a correlated analysis of LFV processes. In fact, LHT and
SUSY theories predict very different correlations among LFV
transitions [7].
Br(µ → eγ)/Br(τ → µγ) ∼ [(m2
)21/(m
2, provides
important information about the unknown structure of
the LFV source, i.e. (m2
)i6=j .
III. LFU IN SUSY
High precision electroweak tests, such as deviations
from the SM expectations of the LFU breaking, represent
a powerful tool to probe the SM and, hence, to constrain
or obtain indirect hints of new physics beyond it. Kaon
and pion physics are obvious grounds where to perform
such tests, for instance in the π → ℓνℓ and K → ℓνℓ
decays, where l = e or µ. In particular, the ratios
B(P → µν)
B(P → eν)
can be predicted with excellent accuracies in the SM,
both for P = π (0.02% accuracy [8]) and P = K (0.04%
accuracy [8]), allowing for some of the most significant
tests of LFU.
As recently pointed out in Ref. [9], large departures
from the SM expectations can be generated within a
SUSY framework with R-parity only once we assume i)
LFV effects, ii) large tanβ values.
Denoting by ∆r
NP the deviation from µ−e universal-
ity in RK due to NP, i.e.: R
K = (R
K )SM
1 + ∆r
it turns out that [9]:
|∆31R |
2 tan6β. (8)
The deviations from the SM could reach ∼ 1% in the
K case [9] (not far from the present experimental res-
olution [10]) and ∼ few × 10−4 in the R
π case while
maintaining LFV effects in τ decays at the 10−10 level. In
the pion case the effect is quite below the present experi-
mental resolution [11], but could well be within the reach
of the new generation of high-precision πℓ2 experiments
planned at TRIUMPH and at PSI. Larger violations of
LFU are expected in B → ℓν decays, with O(10%) devi-
ations from the SM in R
B and even order-of-magnitude
enhancements in R
B [12].
IV. FLAVOR PHYSICS AT LARGE tanβ AND
DARK MATTER
Within the MSSM, the scenario with large tanβ and
heavy squarks is particularly interesting. On the one
hand, values of tanβ ∼ 30–50 can allow the unification
of top and bottom Yukawa couplings, as predicted in
well-motivated grand-unified models [13]. On the other
hand, a Minimal Flavor Violating (MFV) structure [14]
with heavy (∼ TeV ) soft-breaking terms in the quark
sector and large tanβ ∼ 30 − 50 values leads to in-
teresting phenomenological virtues [12, 15]: the present
(g − 2)µ anomaly and the upper bound on the Higgs
boson mass can be easily accommodated, while satisfy-
ing all the present tight constraints in the electroweak
and flavor sectors. Additional low-energy signatures of
this scenario could possibly show up in the near future
in B(Bu → τν), B(Bs,d → ℓ
+ℓ−) and B(B → Xsγ). In
the following, as discussed in [16], we analyze the above
scenario under the additional assumption that the relic
density of a Bino-like lightest SUSY particle (LSP) ac-
commodates the observed dark matter distribution
0.094 ≤ ΩCDMh
2 ≤ 0.129 at 2σ C.L. . (9)
In the regime with large tanβ and heavy squarks, the
relic-density constraints can be easily satisfied mainly in
the so called A-funnel region [17] where MB̃ ≈ MA/2.
The combined constraints from low-energy observables
and dark matter in the tanβ–MH plane are illustrated
in Figure 1 (left). The light-blue areas are excluded since
the stau turns out to be the LSP, while the yellow band
denotes the allowed region where the stau coannihilation
mechanism is also active. The remaining bands corre-
spond to the following constraints/reference-ranges from
low-energy observables:
• B → Xsγ [1.01 < RBsγ < 1.24]: allowed region
between the two blue lines.
• aµ [2 < 10
−9(aexpµ − a
µ ) < 4 [18]]: allowed region
between the two purple lines.
• B → µ+µ− [Bexp < 8.0×10−8 [19]]: allowed region
below the dark-green line.
• ∆MBs [∆MBs = 17.35 ± 0.25 ps
−1 [20]]: allowed
region below the gray line.
• B → τν [0.8 < RBτν < 0.9]: allowed region be-
tween the two black lines [ red (green) area if all
the other conditions (but for aµ) are satisfied].
From Figure 1 (right), we deduce that there is a quite
strong correlation between ∆aµ and B(Bu → τν) thanks
to the A-funnel region condition MH ≈ 2M1. A SUSY
contribution to aµ of O(10
−9) generally implies a sizable
effect in 0.7 < B(Bu → τν) < 0.9. A more precise de-
termination of B(Bu → τν) is therefore a key element to
test this scenario.
The interplay of B physics observables, dark-matter
constraints, ∆aµ of O(10
−9), and LFV rates is shown
in Figure 2. For a natural choice of |δ12LL| = 10
B(µ → eγ) is in the 10−12 range, i.e. well within the
reach of MEG [21] experiment. On the other hand,
B(τ → µγ) lies within the 10−9 range for a |δ23LL| = 10
that is a natural size expected in many models.
Acknowledgments
I wish to thank the conveners of WG3 for the kind
invitation and G. Isidori, F. Mescia and D. Temes for
collaborations on which this talk is partly based. I also
acknowledge support from the EU contract No. MRTN-
CT-2006-035482, ”FLAVIANET” and from the Spanish
MEC and FEDER FPA2005-01678.
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FIG. 1: Left plot: Combined constraints from low-energy observables and dark matter in the tan β–MH plane setting [µ,Mℓ̃] =
[0.5, 0.4] TeV. The light-blue area is excluded by the dark-matter conditions [16]. Within the red (green) area all the reference
values of the low-energy observables (but for aµ) are satisfied. The yellow band denote the area where the stau coannihilation
mechanism is active (1 < Mτ̃R/MB̃ < 1.1); in this area the A-funnel region (where MH ≈ 2M1) and the stau coannihilation
region overlap. Right plot: ∆aµ = (gµ−g
µ )/2 vs. the slepton mass within the funnel region taking into account the B → Xsγ
constraint and setting RBτν > 0.7 (blue), RBτν > 0.8 (red), RBτν > 0.9 (green) [16]. The supersymmetric parameters have
been varied in the following ranges: 200 GeV ≤ M2 ≤ 1000 GeV, 500 GeV ≤ µ ≤ 1000 GeV, 10 ≤ tan β ≤ 50. In both plots,
we have set AU = −1 TeV, Mq̃ = 1.5 TeV, and imposed the GUT relation M1 ≈ M2/2 ≈ M3/6.
FIG. 2: Isolevel curves for B(µ → eγ) and B(τ → µγ) assuming |δ12LL| = 10
−4 and |δ23LL| = 10
−2 in the tan β–MH plane [16].
The green/red areas correspond to the allowed regions for the low-energy observables illustrated in Figure 1 for [µ,M
[0.5, 0.4] TeV.
