CP asymmetries in charged Higgs boson decays in MSSM

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by  Elena Ginina

CP asymmetries in charged Higgs boson decays in MSSM
E. Ginina
Contribution to the 4th workshop ”Gravity, Astrophysics, and Strings at the Black Sea”,
Primorsko, June 10-16, 2007
Abstract
8
0 In the Standard Model with Minimal Supersymmetry, the Lagrangian contains
0
complex parameters which lead to additional CP violation. We study CP violating
2
asymmetries in the decays of the MSSM charged Higgs boson H±, induced by loop
n
correctionswithintermediateSUSYparticles, andperformanalyticalandnumerical
a
J analysis. The decay rate asymmetry can go up to 25% and the forward-backward

5 asymmetry can reach up to 10%.
1

] The CP–symmetry is broken in nature and this feature makes it an important tool
h
for testing fundamental theories. An understanding of its non–conservation in particle
p
- physics mayprovideessential informationaboutthemechanism, causing thedominance of
p
e the matter over antimatter in the observable universe. Generally, effects of CP–violation
h originate in non vanishing complex phases in the Lagrangian of the theory. In particular,
[
in the Minimal Supersymmetric Standard Model (MSSM), the Higgs mixing parameter µ

1
in the superpotential, the U(1) and SU(2) gaugino mass parameters M and M , and the
v 1 2
4 trilinear couplings A (corresponding to a fermion f) can have physical phases which can-
f
4
not be rotated away without introducing phases in other couplings [1]. The experimental
3
2 upper bounds on the electron and neutron electric dipole moments (EDMs) constrain the
1. phase of µ, φµ < O(10−2) [2] for a typical SUSY mass scale of the order of a few hundred
0 GeV, however the phases of the other parameters mentioned above are practically uncon-
8
strained. The CP-violating effects that might arise from the trilinear couplings of the first
0
: generation A are relatively small, as they are proportional to m . However, the trilin-
v u,d u,d
i ear couplings of the third generation A can lead to significant effects of CP-violation,
X t,b,τ
especially in top quark physics [3].
r
a In the following, we study CP violation in the decays of the charged Higgs bosons H±
within the MSSM. At tree level, there are three possible decay modes of H+ into ordinary
particles: H+ → t¯b, H+ → ντ+ and H+ → W+h0, where h0 is the lightest neutral Higgs
boson. Loop corrections due to a Lagrangian with complex parameters lead to non zero
decay rate asymmetry between the partial decay widths of H+ and H−,
Γ(H+ → ...)−Γ(H− → ...)
δCP = , (1)
Γ(H+ → ...)+Γ(H− → ...)
andthatwouldbeaclear signalofCPviolation. Weconsider suchdecay rateasymmetries
in MSSM with complex parameters for the quark decay mode H+ → t¯b – the asymmetry
δCP [4], and for the bosonic decay mode H+ → W+h0 [5] – the asymmetry δCP . For
tb Wh0
the quark decay mode H+ → t¯b we go a step further by including the decay products of
the top quark. This allows to examine CP-violating asymmetries due to the polarization
of the top quark [6]. The top-quark decays before forming a bound state due to its large
mass, so that the polarization can be measured by the angular distributions of its decay
products. Moreover, the polarization is very sensitive to CP violation. The considered
CP violating forward-backward (FB) and energy asymmetries are constructed by using
angular or energy distributions of the decay particles, following the formalism of [7]. This
talk is entirely based on the results of [5] and [6].
±
We study the following processes, related to the quark decay mode of H [6] (See
Fig. 1)
H+ →¯bt →¯bb′W+,
H− → bt¯→ b¯b′W−, (2)
and
H+ →¯bt →¯bb′W+ →¯bb′l+ν ,
l
H− → bt¯→ b¯b′W− → b¯b′l−ν¯ . (3)
l
±
The CP–violation is induced by SUSY loop corrections in the H tb–vertices, whose
0 0
b b
(cid:0)
l
t t W+
CP CP
+ +
H + H
W
b b (cid:23)l
Figure 1: The Feynman graphs of the processes we study.
effective amplitudes are given by
M = iu¯(p )[Y+P +Y+P ]u(−p ) (4)
H+ t b R t L ¯b
− −
MH− = iu¯(pb)[Yt PR +Yb PL]u(−pt¯), (5)
±
The one loop diagrams that contribute are shown on Fig. 2. The Yukawa couplings Y
i
(i = t,b) are a sum of the tree-level couplings y and y , and the contributions from the
t b
±
loops – δY (i = t,b):
i
± ±
Y = y +δY i = t,b. (6)
i i i
±
The loop contributions δY have, in general, both CP-invariant and CP-violating parts:
i
δY± = δYinv ± 1 δYCP . (7)
i i 2 i
In addition, both CP-invariant and CP-violating parts have real and imaginary (absorp-
tive) parts. OnlytherealpartsReδYCP enter theCP-violating asymmetries. Weexamine
t,b
the following CP-violating asymmetries related to the processes (2) and (3):
a) t b) t
χ˜0 (χ˜+) t˜
k j i
H+ t˜ (˜b ) H+ χ˜0, g˜
i i k
χ˜− (χ˜0) ˜b
j k j
b b
c) d)
χ˜0 t t˜ (τ˜) t
k i i
W+ W+
H+ H+
χ˜−j b ˜bj (ν˜) b
Figure 2: Sources for CP violation in H+ → t¯b decays at 1-loop level in the MSSM with
complex couplings (i,j = 1,2; k = 1,...,4).
• CP-violating decay rate asymmetry δCP, defined as
N −N
δCP = f f¯, f = b′,l± (8)
f N +N
f f¯
¯
where N is the total number of particles f(f) in (2) or (3) respectively.
f,f¯
• CP-violating forward-backward (FB) asymmetry ∆ACP,whichweconstruct
b(l)
from the FB asymmetries AFB of the processes (2) and (3) using the angular dis-
f,±
′ ±
tributions of the fermions f = b,l from the top quark decay in (2) and (3) . This
asymmetry is defind as
∆ACP = AFB −AFB, (9)
f f+ f−
where AFB are the ordinary FB asymmetries of the processes
±
ΓF −ΓB
AFB = f,± f,± , (10)
f,± ΓF +ΓB
f,± f,±
and we have
π2 dΓ± π dΓ±
ΓF = dcosθ, ΓB = dcosθ, (11)
± ±
Z dcosθ Zπ dcosθ
0
2
i.e. ΓF arethenumberofparticlesf(f¯)measuredintheforwarddirectionofthedecaying
f,±
t(t¯) quarks and ΓB are the number of f(f¯) measured in the backward direction of the
f,±
decaying t(t¯) quarks.
• CP-violating energy asymmetry ∆RCP can be defined analogously, using the
b
energy distributions of the processes (2) and (3), namely
∆RbCP = Rb+ −Rb−, (12)
where R± are given by
Γ±(x > x0)−Γ±(x < x0)
Rb,± = , (13)
Γ±(x > x0)+Γ±(x < x0)
x is a dimensionless variable proportional to the energy, x = Eb′/mH+ and x0 is any fixed
value in the energy interval.
The analythical results for the asymmetries are rather simple:
ΓCP
δCP = δCP = , (14)
b l Γinv
m2 −m2
∆ACP = 2α m2m2 H t PCP , (15)
b(l) b(l) t H(m2 +m2)2
H t
1
∆RCP = α (m2 −m2)PCP , (16)
b 2 b H t
where ΓCP and PCP are two linear combinations of the two formfactors:
ΓCP = y Re(δYCP)+(y Re(δYCP) (p p )−m m y Re(δYCP)+y Re(δYCP) ,
t t b b t ¯b t b t b b t
(cid:2) (cid:3) (cid:2) (cid:3)
(17)
y Re(δYCP)−y Re(δYCP)
PCP = t t b b . (18)
(y2 +y2)(p p )−2m m y y
t b t ¯b t b t b
Here ΓCP is the CP-violating part of the relevant H± partial decay rate and PCP is the
CP–violating part of the polarization of the top-quark. The coefficient α determines
b(l)
the sensitivity of the b-quark (lepton) to the polarization of the top quark:
m2 −2m2
α = t W, α = 1. (19)
b m2 +2m2 l
t W
Further analysis on the results shows that one does not need to explore numerically all
of these asymmetries, as some of them are connected. In this context we reduce the
numerical analysis on the following argumentation:
• All of the discussed asymmetries are linear combinations of the CP-violating form
factors Re(δYCP) and Re(δYCP), through a dependance on PCP (18) or ΓCP (17).
t b
In order to measure these formfactors, one needs to measure: 1) the decay rate
asymmetries δCP which are proportional to ΓCP and 2) the angular and / or energy
b,l
asymmetries which are proportional to PCP for a given process.
± ± ′
• As there is no CP violation in t → bW, the decay rate asymmetries in H → W bb
± ′ ± ±
and H → bbl ν are equal to the decay rate asymmetry in H → tb. We denote
it, following [4], by δCP:
ΓCP Γ+ −Γ−
δCP = δCP = δCP = . δCP = , (20)
b l Γinv Γ+ +Γ−
± ±
where Γ is the partial decay rate of the process H → tb
• The angular and energy asymmetries – ∆ACP and ∆RCP, are not independent
b,l b
either. The angular asymmetries for the b-quarks and the leptons are related by
α
∆ACP = l ∆ACP ≈ 2.6∆ACP . (21)
l α b b
b
Furthermore, there is a simple relation between the b-quark energy and angular
asymmetries:
(m2 +m2)2
∆RCP = H+ t ∆ACP , (22)
b 4m2 m2 b
H+ t
which implies that for m > m , ∆RCP is bigger than ∆ACP. Thus, in general,
H+ t b b
∆RCP is the biggest asymmetry of those defined through the polarization of the top
b
quark for m > 490 GeV.
H+
In the following, we present numerical results only on the decay rate asymmetry δCP and
on the energy asymmetry ∆RCP.
b
In order not to vary too many parameters we fix a part of the parameter space by the
choice:
M = 300 GeV, M = 745 GeV, M = M = M = M = M = 350 GeV,
2 3 U˜ Q˜ D˜ E L
µ = −700 GeV, |A | = |A | = |A | = 700 GeV. (23)
t b τ
According to the experimental limits on the electric and neutron EDM’s, we take φ = 0
µ
or φ = π/10. The remaining CP-violating phases we vary, are the phases of A , A and
µ t b
A . In the numerical code we use running top and bottom Yukawa couplings, calculated
τ
at the scale Q = m . Fig. 3a and Fig. 3b show the asymmetries δCP and ∆RCP as
H+ b
functions of m for φ = π/2, φ = 0 and φ = 0. (Our studies have shown that
H+ At Ab µ
the most important CP-violating phase is φ . There is only a very weak dependence on
At
φ and φ and therefore we take them zero.) For tanβ = 5 the decay rate asymmetry
Ab Aτ
δCP goes up to 20%, while ∆RCP reaches 8% for the same values of the parameters. The
b
asymmetries strongly depend on tanβ and they quickly decrease as tanβ increases. For
m < m +m , the asymmetries are very small. The main contributions to both δCP
H+ t˜1 ˜b1
and ∆RCP come from the self-energy graph with stop-sbottom. The vertex graph with
b
stop-sbottom-gluino also gives a relatively large contribution. The contributions of these
two graphs in δCP and ∆RCP are shown in Fig. 4a and Fig. 4b. The contribution of the
b
rest of the graphs is negligible.
Further, we take avery small phase, φ = π/10, inorder to fit with the experimental data.
µ
As can be seen in Fig. 5a and Fig. 5b, the asymmetries can increase up to 25% for δCP
and 10% for ∆RCP, respectively. The discussed asymmetries δCP and ∆RCP shows a very
b b
strong dependence on the sign of µ. As noted above, our analysis is done for µ = −700
(see (23)), however if µ changes sign, µ = 700, all asymmetries become extremely small.
We now turn to the bosonic decay mode of the charged Higgs boson H+ → W+h0. We
are interested again in the CP violation caused by SUSY loop corrections in the H±Wh0–
vertexandstudythedecayrateasymmetrybetween thechargeconjugateprocesses H+ →
x
0.2 x
CP 0.08
(cid:14) CP
(cid:1)Rb
0.16
tan(cid:12) =5 0.06 tan(cid:12) =5
0.12
0.04
0.08
10 0.02
10
0.04
0.
30 30
0. -0.02
400 600 800 1000 1200 1400 400 600 800 1000 1200 1400
x
mH+ [GeV] x mH+ [GeV]
Figure 3: The asymmetries δCP and ∆RCP as functions of m for φ = π/2, φ =
b H+ At Ab
φ = 0. The red, blue, and green lines are for tanβ = 5,10, and 30.
µ
0.16 x x
0.06
CP
(cid:14) 0.12 t~~b (cid:1)RbCP t~~b
0.04
0.08
0.04 t~~bg~ 0.02 t~~bg~
0. the rest 0. the rest
400 600 800 1000 1200 1400 400 600 800 1000 1200 1400
x mH+ [GeV] x mH+ [GeV]
Figure 4: The contribution of the t˜˜b self-energy (red line), t˜˜bg˜ vertex contribution (blue
line) and the sum of the other (green line) diagrams to δCP and ∆RCP as functions of
b
m for tanβ = 5 and φ = π/2, φ = φ = 0.
H+ At Ab µ
W+h0 and H− → W−h0:
Γ(H+ → W+h0)−Γ(H− → W−h0)
δCP = . (24)
Wh0 Γ(H+ → W+h0)+Γ(H− → W−h0)
The matrix elements of H+ → W+h0 and H− → W−h0 are given by
MH± = igελα(pW)pαhY±, (25)
where ελ(p ) is the polarization vector of W±, Y± are the loop corrected couplings. The
α W
CP-violating asymmetry δCP is determined by the real parts Re(δYCP):
Wh k
2 Re(δYCP)
k
δYCP = Re(δYCP)+iIm(δYCP), δCP ≃ Pk , (26)
k k k Wh0 y
x
x
(cid:14)CP0.24 (cid:1)RbCP0.1
0.08
0.18 tan(cid:12) =5 tan(cid:12) =5
0.06
0.12 0.04
10 0.02 10
0.06
0.
30 30
0. -0.02
400 600 800 1000 1200 1400
400 600 800 1000 1200 1400
x mH+ [GeV] x mH+ [GeV]
Figure 5: The asymmetries δCP and ∆RCP as functions of m for φ = π/2, φ = 0
b H+ At Ab
and a non zero phase of µ, φ = π/10. The red, blue and green lines are for tanβ = 5,10,
µ
and 30.
where the sum is over the loops with CP-violation shown on Fig. 6. We assume that the
squarks are heavy and that the decay H+ → t˜˜b is not allowed kinematically. Thus, we
are left with the loop corrections with sleptons, charginos and neutralinos. In the com-
monly discussed models of SUSY breaking, the squarks are much heavier than sleptons,
charginos and neutralinos. According to the numerical exploration of the H± → W±h0
decay we have the following reasoning.
First,increasingm ,themassm issaturated,approachingitsmaximumvalue,mmax ≃
H+ h0 h0
130 GeV. There is an experimental lower bound for m , m ≥ 96 GeV [8]. Thus, re-
h0 h0
specting both the experimental and theoretical bounds, we consider m in the range 96
h0
≤ m ≤ 130 GeV. Our analysis shows a very weak dependence on m and the results
h0 h0
here are presented for m = 125 GeV.
h0
The second consequence concerns the H±Wh0 coupling which determines the BR (H+ →
W+h0). It falls down quickly when increasing m and, depending on tanβ, we can enter
H+
the so called decoupling limit, cos2(β − α) → 0, where the BR (H+ → W+h0) almost
vanishes. In order to keep the value of BR (H+ → W+h0) at the level of a few percents,
we keep m and tanβ relatively small: 200 ≤ m ≤ 600 GeV and 3 ≤ tanβ ≤ 9.
H+ H+
Inorder not to varytoo many parameters, we againfix part of the SUSYparameter space:
M = 250GeV, M = M −5GeV,M = 120GeV,|A | = 500GeV, |µ| = 150GeV.
2 E L L τ
(27)
In order δCP to be nonzero, we need both new decay channels opened and CP-violating
Wh0
phases present. In accordance with this we have three cases: 1) When only the decay
channels H+ → ν˜τ˜+ are open (Fig. 6a). Then the phase φ is responsible for CP viola-
n τ
tion. 2) When the decay channels H+ → χ˜+χ˜0 are open only (Fig. 6b). In this case CP
i k
violation is due to the phase φ , and 3) When both H+ → ν˜τ˜+ and H+ → χ˜+χ˜0 decay
1 n i k
channels are kinematically allowed ( all diagrams of Fig. 6). In this case the two phases
φ and φ contribute.
τ 1
Examples of the asymmetry as function of m+ for cases 1) and 2) are shown on Fig. 7a
H
Figure 6: The 1-loop diagrams in MSSM with complex parameters that contribute to
δCP
Wh0
δWh0 tanHβL=9 δWh0 ML=140
00..000046 ML=16M0L=180
0.02 tanHβL=6 0.002 250300350400mH+ φµ=πê2φµ=πê4φµ=00.0δ1Wh0 φµ=00.0δ1Wh0
0.01 ttaannHHββLL==69 tanHβL=3 HbL 0.005 −π φµ=πê−4(cid:3)π2(cid:3)(cid:3)(cid:3) (cid:3)π2(cid:3)φ(cid:3)(cid:3)µ=0 π CPphases
tanHβL=3300 400 500 600mH+ −π φµ−=0(cid:3)π(cid:3)(cid:3)(cid:3) (cid:3)π(cid:3)(cid:3)(cid:3) π CPphases -0.01
φµ=πê4 2-0.005 2 -0.02 φµ=πê4 φµ=πê2
-0.01
-0.01 φµ=πê2 -0.03 φµ=πê2
-0.02 HaL
HaL HbL
Figure7: Left:δ asa functionof m a) for different valuesof tanβ, M = 120GeV;
Wh0 H+ L
solid lines are for φ = −π/2, φ = 0; dashed lines are for φ = 0, φ = −π/2. b) for
τ 1 τ 1
different values of M , at tanβ = 9, φ = −π/2, φ = 0. Right: δ at tanβ = 9
L τ 1 Wh0
versus the CP violating phases φ and φ for different values of φ [ φ = 0,π/4,π/2].
τ 1 µ µ
The solid lines are for φ = [−π,π] while φ = 0; the dashed lines are for φ = [−π,π]
τ 1 1
while φ = 0, a) for m = 237 GeV (= m + m ) and b) for m = 387 GeV
τ H+ ν˜ τ˜+ H+
2
(= m +m ).
χ˜+2 χ˜01
for different values of tanβ. It is clearly seen that in both cases the asymmetry strongly
increases with tanβ. In both cases, 1) and 2), the asymmetry reaches up to 10−2. The
dependence on M for case 1) is seen on Fig. 7b. Case 3), when all relevant SUSY par-
L
ticles can be light, is described by the algebraic sum of the two graphs at a given tanβ
and we don’t present it separately. In all these cases the asymmetry does not exceed a
few percents.
The effect of a non-zero phase φ is seen on Fig. 7. In all cases a CP violating phase
µ
of µ does not change the form of the curves but rather shifts the positions of the maxima
and, in general, increases the absolute value of the asymmetry.
Let us summarize. We have calculated different asymmetries concerning the quark
±
and boson decay mode of the charged Higgs boson H , caused by CP-violating phases in
the MSSM Lagrangian. The quark decay mode is dominant for large m and the most
H+
important phase is the phase of A . In this case the decay rate asymmetry can reach up
t
to 25%, and the forward-backward asymmetry can go up to 10%. These asymmetries are
rather large and in principle measureable at LHC, but because of the large background of
the process, require higher luminosity (e.g. SLHC). The boson decay mode is important
for small m andtanβ and sensitive to the phases of M and the phase of A . The decay
H+ 1 τ
rate asymmetry is, typically, of the order of 10−2 ÷ 10−3. Concerning its measurability
more promising are the next generation linear e+e− colliders.
Acknowledgements
This work would not be possible without the valuable contribution of my coauthors Prof.
Ekaterina Christova, Prof. Walter Majerotto, Dr. Helmut Eberl and Dr. Mihail Stoilov.
I am gratefull to all of them.
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