B -> Xsγconstraints on the top quark anomalous t-> cγ coupling

0.27 MB·English

by  Xing-Bo Yuan

B¯ X γ constraints on the top quark anomalous t cγ coupling
s
→ →
Xingbo Yuan1, Yang Hao1 and Ya-Dong Yang1,2
1Institute of Particle Physics, Huazhong Normal University, Wuhan, Hubei 430079, P. R. China
2KeyLaboratoryofQuark&LeptonPhysics, MinistryofEducation, HuazhongNormalUniversity,
Wuhan, Hubei, 430079, P. R. China
Abstract
Observation of top quark flavor changing neutral process t c + γ at the LHC would be
→
the signal of physics beyond the Standard Model. If anomalous t cγ coupling exists, it will
1
→
1
0 affect the precisely measured (B¯ Xsγ). In this paper, we study the effects of a dimension
B →
2
5 anomalous tcγ operator in B¯ X γ decay to derive constraints on its possible strength. It
n → s
a γ
J is found that, for real anomalous t → cγ coupling κtcR, the constraints correspond to the upper
2
bounds (t c+γ) < 6.54 10 5 (for κγ > 0) and (t c+γ) < 8.52 10 5 (for κγ < 0),
1 B → × − tcR B → × − tcR

] respectively, which are about the same order as the 5σ discovery potential of ATLAS (9.4 10−5)
h ×
p and slightly lower than that of CMS (4.1 10 4) with 10 fb 1 integrated luminosity operating at
− −
- ×
p
e √s = 14 TeV.
h
[

4
v
2
1
9
1
.
0
1
0
1
:
v
i
X
r
a
1
I. INTRODUCTION
In the Standard Model (SM), top quark lifetime is dominated by the t bW+ process,
→
and its flavor changing neutral current (FCNC) processes t qV(q = u,c;V = γ,Z,g)
→
are extremely suppressed by GIM mechanism. It is known that the SM predicts very tiny
top FCNC branching ratio (t qV), less than (10 10) [1], which would be inaccessible
−
B → O
at the CERN Large Hadron Collider(LHC). In the literature [2, 3], however, a number of
interesting questions have been intrigued by the large top quark mass which is close to the
scale of electroweak symmetry breaking. For example, one may raise the question whether
new physics (NP) beyond the SMcould manifest itself innonstandardcouplings of topquark
which would show up as anomalies in the top quark productions and decays.
At present, the direct constraints on (t qV) are still very weak. For its radiative
B →
decay, the available experimental bounds are (t uγ) < 0.75% from ZEUS [4] and
B →
(t qγ) < 3.2% from CDF [5] at 95% C.L., respectively. These constraints will be
B →
improved greatlybythelargetopquarksampletobeavailableattheLHC,whichisexpected
to produce 8 106 top quark pairs and another few million single top quarks per year at
×
low luminosity (10 fb 1/year). Both ATLAS [6] and CMS [7] have got analyses ready for
−
hunting out top quark FCNC processes as powerful probes for NP. With 10 fb 1 data, it is
−
expected that both ATLAS and CMS could observe t qγ decays if their branching ratios
→
are enhanced to (10 4) by anomalous top quark couplings [6, 7]. However, if the top quark
−
O
anomalous couplings present, they will affect some precisely measured qualities with virtual
top quark contribution. Inversely, these qualities can also restrict the possible number of top
quark FCNC decay signals at the LHC. The precisely measured inclusive decay B X γ
s
→
is one of the well known sensitive probes for extensions of the SM, especially the NPs which
alter the strength of FCNCs [8]. Thus, when performing the study of the possible strength
of t cγ decays at the LHC, one should take into account the constraints from B X γ
s
→ →
[9, 10].
In this paper, we will study the contribution of anomalous tγc operators to the B¯ X γ
s
→
branching ratio and derive constraints on its strength. In the next section, after a brief
discussion of a set of model-independent dimension 5 effective operators relevant to t cγ
→
decay, we calculate the effects of operator c¯ σµνt F in B X γ decay, which result in a
L R µν s
→
modification to C . In Sec. III we present our numerical results of the constraints on its
7γ
2
strength and the corresponding upper limits on branching ratio of t cγ decays. Finally,
→
conclusions are made in Sec. IV. Calculation details are presented in Appendix A, and input
parameters are collected in Appendix B.
II. TOP QUARK ANOMALOUS COUPLINGS AND THEIR EFFECTS IN B¯
→
X γ DECAY
s
Without resorting to the detailed flavor structure of a specific NP model, the Lagrangian
describing the top quark anomalous couplings can be written in a model independent way
with dimension 5 operators [11]
κg g κW κγ
= g tqLq¯ σµνTat Ga tqLq¯ σµνt W e tqLq¯ σµνt F
L5 − s Λ R L µν − √2 Λ R L µ−ν − Λ R L µν
q=u,c,t q=d,s,b q=u,c,t
X X X
g κZ
tqLq¯ σµνt Z +(R L)+h.c., (1)
R L µν
− 2cosθ Λ ↔
W
q=u,c,t
X
where κ is the complex coupling of its corresponding operator, θ is the weak angle, and
W
Ta is the Gell-Mann matrix. Λ is the possible new physics scale, which is unknown but may
be much larger than the electroweak scale. There are also Lagrangian describing the top
quark anomalous interactions with dimension 4 and 6 operators, and the dimension 4 and
5 terms can be traced back to dimension 6 operators [12, 13]. In fact top quark anomalous
interactions can be generally described by the gauge-invariant effective Lagrangian with
dimension 6 operators in a form without redundant operators and parameters [10, 14].
A recent full list of dimension 6 operators could be found in Ref. [15]. But for on-shell
gauge bosons, the Lagrangian in Eq. (1) works and is commonly employed in high energy
phenomenology analysis [3, 6, 16].
The operators in Eq. (1) relevant to t qγ decays read
→
κγ κγ
= e tqLq¯ σµνt F e tqRq¯ σµνt F +h.c.. (2)
γ R L µν L R µν
L − Λ − Λ
q=u,c q=u,c
X X
It is understood that the Dirac matrix σ connects left-handed fields to right-handed
µν
fields, the t cγ transition will involve two independent operators m q¯ σµνt F and
q R L µν
→
m q¯ σµνt F , where the mass factors must appear whenever a chirality flip L R or
t L R µν
→
R L occurs. Due to the mass hierarchy m m , the effect of m q¯ σµνt F can be
t c q R L µν
→ ≫
neglected unless κγ is enhanced to be comparable to mtκγ by unknown mechanism.
tqL mc tqR
3
γ γ γ
t q=u,c q=u,c t t t
b s b s b s
(a) (b) (c)
FIG. 1: Feynman diagrams for b sγ. (a) and (b) are the penguin diagrams with the anomalous
→
tqγ couplings. (c) Sample LO penguin diagram in the SM.
The anomalous tγq coupling affects b sγ decays through the two Feynman diagrams
→
depicted in Figs. 1(a) and 1(b). It is interesting to note that the CKM factors in Fig. 1(a)
and Fig. 1(b) are V V and V V , respectively. Since V V V V for q = u,c, the
tb q∗s qb t∗s | tb q∗s| ≫ | qb t∗s|
contribution of Fig. 1(a) would be much stronger than that of Fig. 1(b). Furthermore, given
the strengths of t uγ and t cγ comparable, the contribution of Fig. 1(a) to b sγ is
→ → →
stilldominatedbyt cγ becauseof V V . Hencewewill onlyconsider Fig.1(a)with
cs us
→ | | ≫ | |
anomalous tcγ coupling. From the Feynman diagram of Fig. 1(a), it is easy to observe that
the large CKM factor V V 1 makes b sγ very sensitive to the strength of anomalous
tb cs
≈ →
tcγ coupling.
The calculation of Fig. 1(a) can be carried out straightforwardly. The calculation details
are presented in Appendix A, and the final result reads
i (b sγ) = s¯[eΓν(k)]bǫ (k),
ν
M →
G
eΓν(p,k) = ie F V V [iσνµk (m f (x)L+m f (x)R)]. (3)
4√2π2 c∗s tb µ s L b R
Usually m term can be neglected, and the function f (x) is calculated to be
s R
κγ 1 x2 x2
f (x) = tcR2m c lnx + t lnx ,
R Λ t −(x 1)(x 1) − (x 1)2(x x ) c (x 1)2(x x ) t
(cid:20) c − t − c − c − t t − c − t (cid:21)
(4)
with x = m2/m2 . Now we are ready to incorporate the NP contribution into its SM
q q W
counterpart for B¯ X γ decay.
s
→
¯
In the SM, it is known that B X γ decay is governed by the effective Hamiltonian at
s
→
scale µ = (m ) [17]
b
O
6
4G
F
(b sγ) = V V C (µ)Q (µ)+C (µ)O (µ)+C (µ)O (µ) , (5)
Heff → − √2 t∗s tb" i i 7γ 7γ 8g 8g #
i=1
X
4
where C (µ) are the Wilsion coefficients, O are the effective four quark operators and
i i=1 6
−
e g
O = m (s¯ σµνb )F , O = m (s¯ σµνTab )Ga . (6)
7γ 16π2 b L R µν 8g 16π2 b L R µν
For calculating (B¯ X γ), instead of the original Wision coefficients C , it is convenient
s i
B →
to use the so called “effective coefficients” [18]
8
C(0)eff(m ) = η2136C(0)SM(M )+ 8(η2134 η2136)C(0)SM(M )+C(0)SM(M ) h ηai, (7)
7γ b 7γ W 3 − 8g W 2 W i
i=1
X
where η = α (µ )/α (µ ) and
s W s b
h = 626126 56281 3 1 0.6494 0.0380 0.0185 0.0057 , (8)
i 272277 −51730 −7 − 14 − − − −
a = (cid:0) 14 16 6 12 0.4086 0.4230 0.8994 0.1456 (cid:1). (9)
i 23 23 23 − 23 − −
(cid:0) (cid:1)
To the leading order approximation, the (B¯ X γ) is proportional to C(0)eff(m ) 2 [21].
B → s | 7γ b |
In terms of the operator basis in Eq. (5), the contribution of the anomalous t cγ
→
couplings in Eq. (3) would result in the deviation of
C (M ) C (M ) = C (M )+CNP(M ) (10)
7γ W → 7′γ W 7γ W 7γ W
and CNP(M ) can be read from Eq. (3) as
7γ W
κγ V 1 x2 x2
CNP(M ) = tcR c∗sm + c logx t lnx .
7γ W Λ V t (x 1)(x 1) (x 1)2(x x ) c − (x 1)2(x x ) t
t∗s (cid:20) c − t − c − c − t t − c − t (cid:21)
(11)
From this equation, one can see that the NP contribution is suppressed by a factor of m /Λ
t
but enhanced by V /V .
cs ts
Since NP contribution does not bring about any new operator, the renormalization group
evolutionofCeff fromM tom scaleisjustthesameastheSMoneinEq.(7). Form = 172
7γ W b t
GeV, m = 4.67 GeV, α (M ) = 0.118 and Λ = 1 TeV, we have
b s Z
8
8
C7′eγff(mb) = η2136 C7(0γ)SM(MW)+C7(0γ)NP(MW) + 3(η2134 −η2136)C8(0g)SM(MW)+C2(0)SM(MW) hiηai
h i Xi=1
(0)SM (0)NP (0)SM (0)SM
= 0.665 C (M )+C (M ) +0.093 C (M ) 0.158 C (M )
7γ W 7γ W 8g W − 2 W
= 0.665[h 0.189+κγ ( 1.092)]+0.i093 ( 0.095) 0.158. (12)
− tcR − − −
In principle, C eff(m ) will receive corrections from anomalous t cg couplings in Eq. (1)
7′γ b →
(0)SM
which will cause a deviation to C (M ). However, as shown by Eq. (12), the coefficient
8g W
5
η2136 of C7(0γ)(MW) is about one order larger than 38(η1243 − η1263) of C8(0g)NP(MW). Given the
relativestrengthofC(0)NP(M )toC(0)SM(M )at10%level, C eff(m )willbeshiftedbyonly
8g W 8g W 7′γ b
few percentage. For simplifying the numerical analysis, we would neglect the contribution
of the anomalous t cg couplings. We also find that the operator q¯ σµνt F contributes
R L µν
→
to B¯ X γ only through the term m s¯σ (1 γ )b as shown by Eq. (3) and Eq. (A7).
s s µν 5
→ −
Combined with the previous remarks on this operator, the effects of q¯ σµνt F could be
R L µν
safely neglected.
III. NUMERICAL RESULTS AND DISCUSSIONS
The current average of experimental results of (B¯ X γ) by Heavy Flavor Average
s
B →
Group is [19]
exp(B¯ X γ) = (3.55 0.24 0.09) 10 4. (13)
s −
B → ± ± ×
On the theoretical side, the NLO calculation has been completed [20, 21], and gives
(B¯ X γ) = (3.57 0.30) 10 4. (14)
s −
B → ± ×
Therecent estimationatNNLO[22]gives (B¯ X γ) = (3.15 0.23) 10 4, whichisabout
s −
B → ± ×
1σ lower than the experimental average in Eq. (13). Thus the experimental measurement
of (B¯ X γ) is in good agreement with the SM predictions with roughly 10% errors on
s
B →
each side. The agreement would provide strong constraints on the top quark anomalous
interactions beyond the SM [9, 10].
The decay amplitude of t cγ has been calculated up to NLO [16]. For a consistent
→
treatment of the constraints from t cγ and b sγ decays, we use the NLO formulas
→ →
in Ref. [20] to calculate (B¯ X γ). The experimental inputs and main formulas are
s
B →
collected in Appendix B. For numerical analysis, we will use the notation κγ = κγ eiθtγcR
tcR | tcR|
and set Λ = 1 TeV.
At first, we analyze the dependence of SM+NP(B¯ X γ) on the new physics parameters
s
B →
κγ /Λ and θγ , which is shown in Fig. 2. From the figure, one can find that the contribu-
| tcR | tcR
tion of anomalous t cγ coupling is constructive to the SM one for θγ [ 50 ,50 ], thus
→ tcR ∈ − ◦ ◦
(B¯ X γ) is very sensitive to κγ . However, when θγ [80 ,130 ], the sensitivity
B → s | tcR| | tcR| ∈ ◦ ◦
of (B¯ X γ) to κγ becomes weak. For θγ 180 , the contribution of anomalous
B → s | tcR| | tcR| ∼ ◦
6
FIG. 2: The contour-plot describes the dependence of (B¯ X γ)( 10 4) on κγ /Λ and θγ .
B → s × − | tcR | tcR
The dashed lines correspond to the experimental center value of (B¯ X γ).
s
B →
t cγ coupling is destructive to the SM one and there are two separated possible strengths
→
for κγ /Λ .
| tcR |
2.0
AllowedbyBHB®XsΓLat95%C.L.
1.5
ExcludedbyCDFat95%C.L.
L
1
-
V
e
T
ÈHL 1.0
(cid:144)
R
c
Γt
Κ
È
0.5
0.0
-150 -100 -50 0 50 100 150
ΘΓ @degD
tcR
γ γ
FIG. 3: The 95% C.L. upper bounds on anomalous coupling κ /Λ as a function of θ . The
| tcR | tcR
shadowed region is allowed by exp(B¯ X γ) and the dash-line is the CDF [5] upper limit.
s
B →
The allowed region for the parameters κγ /Λ and θγ under the constraints from
| tcR | tcR
(B¯ X γ) at 95% C.L. is shown in Fig. 3. The corresponding 95% C.L. upper bound on
s
B →
7
γ
FIG. 4: (t cγ) as a function of θ . The shadowed region is allowed by the combined
B → tcR
constraints of (B¯ X γ) and CDF searching at 95% C.L.
s
B →
(t cγ) is shown in Fig. 4.
B →
Now we turn to discuss the our numerical results. From Eq. (12), the explicit relation
between the SM and the t cγ coupling contributions is
→
C eff(m ) = 0.293 0.726 κγ . (15)
7′γ b − − tcR
Obviously, when Re κγ > 0, the interference between them is constructive, and it turns to
tcR
be destructive when θγ > 90 . Thus the features of these constraints shown in Figs. 3 and
tcR ◦
4 for different θγ are
tcR
(i) the bound on κγ /Λ is very strong for θγ [ 50 ,50 ]. For θγ 0 , as shown
| tcR | tcR ∈ − ◦ ◦ tcR ≈ ◦
in Fig. 3, we obtain the most restrictive upper bound κγ /Λ < 4.9 10 5 GeV 1,
| tcR | × − −
which implies (t cγ) < 6.54 10 5;
−
B → ×
(ii) the bound on κγ /Λ is rather weak for θγ around 110 . For such a case, Re κγ ) is
| tcR | tcR ◦ tcR
destructive to the SM contribution as shown by Eq. (15), so, the allowed strength for
the anomalous coupling is much larger than the one for real κγ . When θγ 135
tcR | tcR| ≈ ◦
and κγ 0.571, C eff(m ) is almost imaginary since Re C eff(m ) 0. Then the
| tcR| ≈ 7′γ b 7′γ b ≈
restriction on κγ /Λ is provided by the CDF search for (t cγ) [5];
| tcR | B →
(iii) as shown in Fig. 3, when θγ 180 , there are two solutions for κγ /Λ . The
tcR ∼ ± ◦ | tcR |
larger one κγ /Λ 1.4 10 3 GeV 1(S2 column in Table I) corresponds to the
| tcR | ∼ × − −
8
TABLE I: The 95% C.L. constraints on the anomalous t cγ coupling by (B¯ X γ) and
s
→ B →
γ
(t cγ) for some specific θ values.
B → tcR
γ γ γ γ
θ = 0 θ = 180 S1 θ = 180 S2 θ = 110
tcR ◦ tcR ± ◦ tcR ± ◦ tcR ± ◦
(B¯ X γ) κγ < 0.049 κγ < 0.056 1.35 < κγ < 1.45 κγ < 0.55
B → s | tcR| | tcR| | tcR| | tcR|
γ γ γ γ
(t cγ) CDF bounds[5] κ < 1.09 κ < 1.09 κ < 1.09 κ < 1.09
B → | tcR| | tcR| | tcR| | tcR|
γ γ γ
Combined bounds κ < 0.049 κ < 0.056 κ < 0.55
| tcR| | tcR| − | tcR|
(t cγ) < 6.54 10 5 < 8.52 10 5 < 8.17 10 3
− − −
B → × × − ×
situation that the sign of Ceff is flipped. However, it has been excluded by the CDF
7γ
upper bound of (t cγ) < 0.032 [5]. The another solution (S1 column in Table I)
B →
κγ /Λ < 5.6 10 5 GeV 1 will result in the upper limit (t cγ) < 8.52 10 5.
| tcR | × − − B → × −
Taking θγ = 0 , 180 and 110 as benchmarks, we summarize our numerical con-
tcR ◦ ± ◦ ± ◦
straints on κγ and their corresponding upper limits on (t cγ) in Table I. From the
tcR B →
table, we can find that our indirect bound on real κγ is much stronger than the CDF
tcR
direct bound. The corresponding upper limits on (t cγ) are about the same order as the
B →
ATLAS sensitivity (t cγ) > 9.4 10 5 [6] and CMS sensitivity (t cγ) > 4.1 10 4
− −
B → × B → ×
[7] with an integrated luminosity of 10 fb 1 of the LHC operating at √s = 14 TeV [6].
−
IV. CONCLUSIONS
In this paper, starting with model independent dimension five anomalous tcγ operators,
we have studied their contributions to (B¯ X γ). It is noted that the t cγ transition
s
B → →
will involve two independent operators κγ c¯ σµνt F and κγ c¯ σµνt F . The first oper-
tcR L R µν tcL R L µν
ator will produce a left-handed photon in t cγ decay, while the second one will produce
→
a right-handed photon. It is found that B¯ X γ is sensitive to the first operator, but not
s
→
to the second one.
For real κγ , the constraint on the presence of κγ c¯ σµνt F is very strong, which
tcR tcR L R µν
corresponds to the indirect upper limits (t cγ) < 6.54 10 5 (for positive κγ ) and
B → × − tcR
(t cγ) < 8.52 10 5 (for negative κγ ), respectively. These upper limits for (t cγ)
B → × − tcR B →
are close to the 5σ discovery sensitivities of ATLAS [6] and slightly lower than that of CMS
[7] with 10 fb 1 integrated luminosity operating at √s = 14 TeV. For nearly imaginary κγ ,
− tcR
9
the constraints are rather weak since C in the SM is a real number. If (t cγ) were
7γ
B →
found to be of the order of (10 3) at the LHC in the future, it would imply the weak phase
−
O
of κγ to be around 100 . However, such a coupling might be ruled out by the other
tcR ± ◦
observable in B meson decays [30].
In summary, we have studied the interesting interplay between the precise measurement
of b sγ decay at Bfactoriesand thepossible t cγ decay at the LHC. For real anomalous
→ →
coupling, it is shown that (t cγ) has been restricted to be blow 10 4 at 95% C.L. by
−
B →
B¯ X γ decay, which is already two order lower than the direct upper bound from CDF
s
→
[5]. The result also implies that one may need data sample much larger than 10 fb 1 to hunt
−
out t cγ signals at the LHC.
→
ACKNOWLEDGMENTS
The work is supported by National Natural Science Foundation under contract
Nos.11075059 and 10735080. We thank Xinqiang Li for many helpful discussions and cross-
checking calculations.
10