Semileptonic Lambda(b)-->Lambda neutrino antineutrino decay in the Leptophobic Z-prime model

0.12 MB·English

by  Berin Belma Sirvanli

Λ Λ ¯
Semileptonic νν decay in the Leptophobic Z Model
b ′
→
B.B.S¸irvanlı
GaziUniversity,FacultyofArtsandScience,DepartmentofPhysics
06100, Teknikokullar Ankara,Turkey
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0 February 2, 2008
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Abstract

1
2 We study the exclusive flavor changing neutral current process Λ Λνν¯ in the lepto-
b
′ ′ →
phobic Z model, where charged leptons donot couple to theextra Z boson. Thebranching
1
v ratio, as well as, the longitudinal, transversal and normal polarizations are calculated. Ithas
3 been shown that all these physical observables are very sensitive to the existence of new
7
physics beyond the standard model and their experimental measurements can give valuable
1
1 information aboutit.
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PACS number(s):12.60.–i,13.20.–v,13.20.He
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1 Introduction
Flavor-changingneutralcurrent(FCNC)processespresentasstringesttestsoftheStandartModel
(SM)aswellaslookingfornewphysicsbeyondtheSM.InSM,FCNCprocessestakeplaceonly
at the loop level and therefore these decays are suppressed and for this reason experimentally
their measurement is difficult. Recently, B factory experiments such as Belle and BaBar have
measuredFCNCdecaysduetotheb sℓ+ℓ− transitionatinclusiveandexclusivelevel[1,2,3,4].
→
Theoretically, the b sℓℓ transition is described by the effective Hamiltonian and the FCNC’s
→
are represented by QCD penguin and electroweak penguin (EW) operators. The EW operators
appear in the photon and Z mediated diagrams. Although it is experimentally very difficult to
measure, B X νν¯ decay is an extremely good and ”pure” channel to study Z mediated EW
→
penguincontributionwithintheSM and itsbeyond[5,6,7,8,9].
Another exclusivedecay which is described at inclusivelevel by the b sℓ+ℓ− transition is
→
thebaryonicΛ Λℓℓdecay. Unlikethemesonicdecays,thebaryonicdecaycouldmaintainthe
b
→
helicitystructureoftheeffectiveHamiltonianfortheb s transition[10].
In this work, we study the Λ Λνν¯ decay in →the leptophobic Z′ Model, as a possible
b
→ ′
candidate of new physics in the EW penguin sector. The leptophobic Z gauge bosons appear
naturally in Grand Unified Theories and string inspired E models. Here we would like to note
6
that a similar mesonic B K(K∗)νν¯ decay and ∆m mass difference of B meson in the
context of leptophobic Z′→model are studied in [11] anBds[12], respectively. Inssection 2, we
brieflyconsidertheleptophobicmodelbasedonE model. Insection3,wepresenttheanalytical
6
expressionsforthebranchingratioandthelongitudinal,transverseandnormalpolarizationsofΛ
baryon,aswellaspolarizationofΛ . InSection4,wegivenumericalanalysisandourconcluding
b
remarks.
2 Theoretical background on leptophobic Z model
′
In this section we briefly review the leptophobic Z′ model. From GUT or string-inspired point
′
of view, the E model [13] is a very natural extention of the SM. In this model U(1) gauge
6
group remains after the symmetry breaking of the E group. We assume that the E group is
6 6
broken through the following way E SO(10) U(1) SU(5) U(1) U(1)
6 ψ χ ψ
′ ′→ × → × × →
SU(2) U(1) U(1) , where U(1) is a linear combination of two additional U(1) gauge
L
× ′ ×
groupswithQ = Q cosθ Q sinθ,whereθ isthemixingangle. WhenallcouplingsareGUT
ψ χ
normalized,theinteraction,−LagrangianoffermionswithZ′ gaugebosoncan bewrittenas
g 5sin2θ 3
= λ 2 wψ¯γ Q′ + δY ψZ′ , (1)
Lint − cosθws 3 µ s5 SM! µ
whereλ = gQ′ istheratioofgaugecouplingsδ = tanχ/λ[14]. Inthegeneralcasefermion–Z′
gy −
gauge boson couplings contain two arbitrary free parameters tanθ and δ [15]. From Eq.(1), it
followsthattheZ′gaugebosoncanbeleptophobicwhenQ′+ 3δY = 0fortheleptondoublet
5 SM
and ec, simultaneously. In the conventional embedding, theqZ′ boson can be made leptophobic
with δ = 1/3 and tanθ = 3. In the Leptophobic Z′ model, FCNC’s can arise through the
− 5
mixing between SM fermionsqand exotic fermions. In principle, the mixing of the left handed
1
fermions can lead to the large Z-mediated FCNC’s. In order to forbid this large Z-mediated
FCNC’s, we consider the case when mixing take place only between the right-handed fermions.
So, themixingbetween right-handedordinary and exoticfermions can inducetheFCNC’s when
their Z′ charges are different [16]. In the Leptophobic Z′ model, the Lagrangian for b q(q =
→
s,d)transitioncontainingFCNC at treelevelcan bewrittenas
Z′ = g2 UZ′q¯ γµb Z′ . (2)
L −2cosθ qb R R µ
w
UsingupperexperimentalboundsonbranchingratiofortheB Kνν¯[17]andB πνν¯[18]
′ ′ → ′ →
in [11] for model parameters UZ and UZ following bounds are obtained : UZ 0.29 and
′ sb db | s′b | ≤ ′
UZ 0.61. Analysis of ∆m leads to the more stringest bound for the UZ [12]: UZ
| db | ≤ Bs′ sb ′| sb | ≤
0.036 at mZ′ = 700GeV and |UdZb | ≤ 0.051 at mZ′ = 1TeV. These constraints on UqZb we will
useinournumericalcalculations.
Λ Λ ¯
3 Matrix Elements for the νν Decay
b
→
The Λ Λνν¯ decay at quark level is described by b sνν¯ transition. In the SM, effective
b
→ →
Hamiltonianresponsiblefortheb sνν¯transitionisgivenby
→
G α
SM = F V V∗C s¯γ (1 γ )bν¯γ (1 γ )ν , (3)
Heff 2π√2 tb ts 10 µ − 5 µ − 5
where G and α are the Fermi and fine structure constant respectively, V and V are elements
F tb ts
oftheCabibbo-Kobayashi-Maskawa(CKM)matrix,C is theWilsoncoefficient whoseexplicit
10
′
formcanbefoundin[17,18,19]. Aswehavealreadymentioned,intheleptophobicmodel,U(1)
charge is zero for all the ordinary left and right handed lepton fields within the SM. However,
27 representation of E contain new right handed neutrino which is absent in SM and it can
6
give additional contribution to the processes due to the b sνν¯ transition. Then the effective
→
Hamiltoniandescribingb sν ν¯ transitioncan bewrittenas
R R
→
πα ′ ′
new = UZ QZ s¯γ (1+γ )bν¯γ (1+γ )ν , (4)
Heff sin22θ M2 sb νR µ 5 µ 5
w Z′
where QZ′ = 1x 5sin2θw. UZ′ and x are model dependent parameters and we take x = 1
νR 2 3 qb
for simplicity. Haqving effective Hamiltonian for b sνν¯ transition, our next problem is the
→
derivationofthedecayamplitudefortheΛ Λνν¯decay,whichcanbeobtainedbycalculating
b
→
the matrix element of the effective Hamiltonian for b sνν¯ transition between initial Λ and
b
→
final Λ baryon states. It follows that the matrix elements Λ s¯γ (1 γ )b Λ are needed for
µ 5 b
h | ∓ | i
calculating the decay amplitude for the Λ Λνν¯ decay. These matrix elements parametrized
b
→
interms oftheform factors areas follows([20],[21])
¯
Λ s¯γ b Λ = u¯ f γ +if σ qν +f q u , (5)
h | µ | bi Λ" 1 µ 2 µν 3 µ# Λb
2
Λ s¯γ γ b Λ = u¯ g γ γ +ig σ qνγ +g q γ u (6)
h | µ 5 | bi Λ" 1 µ 5 2 µν 5 3 µ 5# Λb
where q = p p is the momentum transfer and f and g (i = 1,2,3) are the form factors.
Λb − Λ i i
Notethat form factors f and g do not givecontributionto the considered decay since neutrinos
3 3
are massless. Using Eqs. (3)-(4)-(6) and (7) for the decay amplitudeof the Λ Λνν¯ decay in
b
→
leptophobicmodel,wehave
αG
= F V V∗Cν ν¯γ (1 γ )ν u¯ A γ (1+γ )+B γ (1 γ )
M 2√2π tb ts 10( µ − 5 × Λ" 1 µ 5 1 µ − 5
+ iσ qνA (1+γ )+B (1 γ )) u
µν 2 5 2 − 5 # Λb
+ C ν¯γ (1+γ )ν u¯ B γ (1+γ )+A γ (1 γ )
RR µ 5 Λ 1 µ 5 1 µ 5
× " −
+ iσ qνB (1+γ )+A (1 γ )) u , (7)
µν 2 5 2 − 5 # Λb)
′
πQUZ m2
whereC = qb Z .
RR αVtbVt∗sC1ν0 m2Z′
It is shown in [21] that when HQET is applied the number of independent form factors are
reduced to two (F and F ), irrelevant of the Dirac structure of the corresponding operators, i.e.,
1 2
Λ(p ) s¯Γb Λ(p ) = u¯ F (q2) + υF (q2) Γu , where Γ is an arbitrary Dirac matrix and
Λ Λ Λ 1 2 Λ
h | | b i " 6 # b
υµ = pµ/m isthefourvelocityofΛ . Usingthisresultweget
Λb b
f = g = F +√rF ,
1 1 1 2
F
2
f = g = , (8)
2 2
m
Λ
b
wherer = m2/m2 .
Λ Λ
b
Our next problem is the calculation of Λ baryon polarizations using the matrix element in
Eq.(7). In the rest frame of Λ, the unit vectors along the longitudinal, normal and transversal
componentsofΛ arechosen as
p~
sµ = (0,~e ) = 0, Λ ,
L L p~Λ !
| |
~
~e ξ
sµ = (0,~e ) = 0, L × Λb ,
T T  ~e ξ~ 
L × Λb
sµ = (0,~e ) =(0,~e(cid:12) ~e ) .(cid:12) (9)
N N (cid:12)(cid:12)L × T (cid:12)(cid:12)
The longitudinal component of the Λ baryon polarization is boosted to the center of mass frame
ofthenuetrino–antineutrinopairbyLorentztransformation,yielding
~p E ~p
(sµ) = | Λ|, Λ Λ , (10)
L CM mΛ mΛ ~pΛ !
| |
3
where E and m are the energy and mass of the Λ baryon in the CM frame of nuetrino–
Λ Λ
antineutrinopair. The remaining two unit vectors sµ and sµ are unchanged under Lorentz trans-
T N
formation.
After integration over neutrino and antineutrino momentum the differential decay rate of the
Λ Λνν¯decay forany spindirectionξ~alongtheΛbaryon can bewrittenas (in therest frame
b
→
ofΛ )
b
1 I
dΓ = dΓ0 1+ 1~e ξ~ 1+P~ ξ~ . (11)
4 " I0 L · Λb#" Λ · Λ#
1 I I I I
P~ = 2 + 3eˆ ξˆ eˆ + 4eˆ + 5eˆ (12)
Λ 1+ II10eˆL ·ξˆΛb" I0 I0 L · Λb! L I0 N I0 T#
3G2α2 V V∗ 2 C 2
dΓ0 = F em| tb ts| | 10| p~ I dE dΩ (13)
32.32.4π7m | Λ| 0 Λ Λ
Λ
b
ThefunctionsI inEq.(13)havefollowingexpressions:
i
32
2 2 2 2 2 2
I = π (q p p +2p qp q)( A + B + C ( B + A ))
0 3 ( Λ · Λb Λ · Λb · | 1| | 1| | RR| | 1| | 1|
2 2 2 2 2 2 2
+ (q p p 4p qp q)q ( A + B + C ( B + A ))
Λ · Λb − Λ · Λb · | 2| | 2| | RR| | 2| | 2|
2 ∗ ∗ 2 ∗ 2 ∗
+ 6m q p q Re[A A ]+Re[B B ]+ C Re[B B ]+ C Re[A A ]
Λ Λb · " 1 2 1 2 | RR| 1 2 | RR| 1 2 #
2 ∗ ∗ 2 ∗ 2 ∗
6m q p q Re[A B ]+Re[A B ]+ C Re[B A ]+ C Re[B A ]
− Λb Λ · " 2 1 1 2 | RR| 2 1 | RR| 1 2 #
2 ∗ 2 ∗ 2 ∗
6m m q Re[A B ]+q Re[A B ]+ C Re[B A ]
− Λb Λ " 1 1 2 2 | RR| 1 1
+ C 2q2Re[B A∗] (14)
RR 2 2
| | #)
32
2 2 2 2 2 2
I = πp ( m )(q 2p q) ( A B )+ C ( B A )
1 3I0 Λ( − Λb − Λ · " | 1| −| 1| | RR| | 1| −| 1| #
2 2 2 2 2 2 2
+ m q (q +4p q) ( A B )+ C ( B A )
Λb Λ · " | 2| −| 2| | RR| | 2| −| 2| #
2 ∗ ∗ 2 ∗ 2 ∗
+ 6m m q Re[A A ] Re[B B ]+ C Re[B B ] C Re[A A ]
Λb Λ " 1 2 − 1 2 | RR| 1 2 −| RR| 1 2 #
2 ∗ ∗ 2 ∗
+ 2q (p p +p q) Re[A B ] Re[A B ] C Re[B A ]
Λb · Λ Λb · " 1 2 − 2 1 −| RR| 2 1
+ C 2Re[B A∗] (15)
RR 1 2
| | #)
4
32
2 2 2 2 2
I = πp m 2m p ( A + B )+(q +p q)( A B )
2 Λ Λ Λ Λ 1 1 Λ 1 1
3I0 b( | | | | b · | | −| |
2 ∗ 2 ∗
+ 2q (3m +p ) Re[A B ]+ C Re[B A ]
Λb Λ " 2 1 | RR| 2 1 #
2 ∗ 2 ∗
2q (3m p ) Re[A B ]+ C Re[B A ]
− Λb − Λ " 1 2 | RR| 1 2 #
2
4 ∗ 2 ∗
p q Re[A B ]+ C Re[B A ]
Λ 2 2 RR 2 2
− mΛ " | | #
2
2 ∗ 2 ∗
+ q (m p +p p +p q) Re[B B ]+ C Re[A A ]
mΛ Λ Λ Λb · Λ Λ · " 1 2 | RR| 1 2 #
2
2 ∗ 2 ∗
+ q (m p p p +p q) Re[A A ]+ C Re[B B ]
mΛ Λ Λ − Λb · Λ Λ · " 1 2 | RR| 1 2 #
2p
Λ 2 ∗ 2 ∗
+ (q 2p p +2p q 2p q) Re[A B ]+ C Re[B A ]
mΛ − Λb · Λ Λ · − Λb · " 1 1 | RR| 1 1 #
2 2 2 2
+ C (2m p q 2p q) E + D
| RR| Λb Λ − − Λb · "| 1| | 1| #
2 2 2 2
q (4m p +q 4p q) A + B
Λ Λ Λ 2 2
− b − b · "| | | | #
q2 C 2(4m p +q2 4p q) D 2 + E 2 (16)
− | RR| Λb Λ − Λb · "| 2| | 2| #)
64π E
Λ 4 ∗ 2 ∗ ∗
I = q p p Re[A B ] C (Re[B A ] Re[B A ])
3 3I0 (mΛ" Λ Λb 2 2 −| RR| 1 1 − 2 2 !
2 ∗ ∗ 2 ∗ ∗
m q p q Re[A A ]+Re[B B ] C (Re[B B ]+Re[A A ])
− Λb Λ · " 1 2 1 2 −| RR| 1 2 1 2 ##
2 ∗ ∗ 2 ∗ ∗
+ m q p q Re[A B ]+Re[A B ]+ C (Re[B A ]+Re[B A ])
Λ Λb · " 2 1 1 2 | RR| 2 1 1 2 #
2 ∗ 2 ∗
+ C p qp qRe[B A ] (q p p 2p qp q)Re[A B ]
| RR| Λb · Λ · 1 1 − Λb · Λ − Λb · Λ · 1 1 #
m
+ Λbp2 m q2 Re[A A∗]+Re[B B∗]+ C 2(Re[B B∗]+Re[A A∗])
mΛ Λ" Λb 1 2 1 2 | RR| 1 2 1 2 !
+ m q2 Re[A B∗]+Re[A B∗]+ C 2(Re[B A∗]+Re[B A∗]) (17)
Λ 2 1 1 2 RR 2 1 1 2
| | !#)
16π
2 2 2 2 2 2 2 2 2
I = m m q ( A + B )+q ( A + B )+ C ( B + A )
4 3I0 (− Λ Λb " | 1| | 1| | 2| | 2| | RR| | 1| | 1|
2 2 2 2 4 ∗ 2 ∗
+ C q ( B + A ) +2q p p Re[A B ]+ C Re[B A ]
| RR| | 2| | 2| # Λ · Λb" 2 2 | RR| 2 2 #
5
2 ∗ ∗ 2 ∗ ∗
2m q p q Re[A A ]+Re[B B ]+ C (Re[B B ]+Re[A A ])
− Λb Λ · " 1 2 1 2 | RR| 1 2 1 2 #
2 ∗ ∗ 2 ∗ ∗
+ 2m q p q Re[A B ]+Re[A B ]+ C (Re[B A ]+Re[B A ])
Λ Λ 2 1 1 2 RR 2 1 1 2
· " | | #
2(q2p p 2p qp q) Re[A B∗]+ C 2Re[B A∗] (18)
− Λ · Λb − Λ · Λb · " 1 1 | RR| 1 1 #)
16πm p
I = Λb Λ 2m q2 Im[A A∗]+Im[B B∗]+ C 2(Im[B B∗]+Im[A A∗])
5 3I0 ( Λb " 1 2 1 2 | RR| 1 2 1 2 #
2 ∗ ∗ 2 ∗ ∗
+ 2m q Im[A B ]+Im[A B ]+ C (Im[B A ]+Im[B A ])
Λ 2 1 1 2 RR 2 1 1 2
" | | #
4 ∗ 2 ∗
2q Im[A B ]+ C Im[B A ]
2 2 RR 2 2
− " | | #
+ 2(2m2 q2 2p p ) Im[A B∗]+ C 2Im[B A∗] (19)
Λb − − Λ · Λb " 1 1 | RR| 1 1 #)
Here thekinematicsand therelationshipsfortheform factors aregivenas follows
2 2 2
q = m +m 2m E
Λb Λ − Λb Λ
p p = m E
Λ Λ Λ Λ
· b b
2
p q = m m E
Λb · Λb − Λb Λ
p q = m E m2 (20)
Λ · Λb Λ − Λ
and
A = (f g ) ,A = (f g ) ,
1 1 1 2 2 2
− −
B = (f +g ) ,B = (f +g ) . (21)
1 1 1 2 2 2
4 Numerical analysis and discussion
In this section, we present our numerical analysis on the branching ratio and P ,P ,P polar-
L N T
izationsofΛbaryon. Thevalueofinputparameters, weusein ourcalculationsare
m = 5.62GeV , m = 1.116GeV ,
Λ Λ
b
∗ −1
f = 0.2GeV , V V = 0.04 , α = 137,
B | tb ts|
Cν = 4.6, G = 1.17 10−5GeV−2, τ = 1.24 10−12s ,
| 10| F × Λb ×
UZ′ 0.29 , UZ′ 0.61. (22)
| sb | ≤ | db| ≤
Wehaveassumedthatalltheneutrinosaremassless. Fromtheexpressionsofbranchingratioand
Λ baryon polarizations it follows that the form factors are the main input parameters. The exact
calculation for the all form factors which appear in Λ Λ transition does not exist at present.
b
→
6
F(0) a b
F F
F 0.462 0.0182 0.000176
1
− −
F 0.077 0.0685 0.00146
2
− −
Table1: Formfactors forΛ Λνν¯ decay inathreeparameters fit.
b
→
For the form factors, we will use results from QCD sum rules method in corporation with heavy
quark effectivetheory[23,24]. Theq2 dependence ofthetwoform factors are givenas follows:
F(0)
F(q2) = . (23)
1+a (q2/m2 )+b (q2/m2 )2
F Λ F Λ
b b
Thevaluesoftheform factors parameters aregivenlistedin Table1 .
Now, let us examine the new effects to the branching ratio of the Λ Λνν¯ decay and po-
b
larizationeffects oftheΛbaryon intheleptophobicZ′ boson. In theLepto→phobicZ′ model,there
are two new parameters, namely, the effective FCNC coupling constant UZ′ and the mass for
the Z′ boson. Although the mass of Z′ boson range is given 365GeV | sMb |Z′ 615GeV in
the D0 experiment, we take MZ′ = 700GeV and |UsZb′| ≤ 0.29 [22], wh≤ich we ≤will use in our
calculations. InFig. 1,wepresentthedependenceofthedifferentialdecay branchingratio(BR),
for Λ Λνν¯ decay, as function of the momentum square,q2. We observe from this figure that
b
→
the differential branching ratio at low q2 region is one order larger compared to that of the SM
prediction. In Fig.2, we showour prediction forthe branching ratio as a function of theeffective
coupling constant U in the Leptophobic Z′ Model. We see from this figure with increasing
sb
| |
U , BR also increases. We see that difference between two models is clear when U 0.4.
sb sb
| | | | ≥
In Fig.3, the dependence of the longitudinal polarization P for Λ Λνν¯ decay is presented.
L b
→
Forcompleteness,inthisfigurewealsopresentthepredictionofSMforP . Fromthisfigurewe
L
see that the magnitude and sign of P are different in these models. Therefore a measurement
L
ofthemagnitudeand signofP can providevaluableinformationaboutthenew physicseffects.
L
With increasing q2 the difference between two models decreases. At least up to q2 = 10GeV2
thereis noticeabledifference between thesemodelsand thiscan serveas agood testfordiscrim-
inationof thesetheories. ThetransversecomponentP oftheΛ polarizationis a T-oddquantity.
T
A nonzero value of P could indicate CP violation. In the SM, there is no CP violating phase in
T
the CKM element of V V∗ and since parametrization of the form factors are real, they can not
tb ts
induce P in the Λ Λνν¯ decay. Therefore if transverse Λ polarization is measured in the
T b
→
experiments to be nonzero, it is an indication of the existence of new CP violating source and
new types of interactions. The parameter UZ′ in leptophobic Z′ model, in principle, can have
sb
imaginarypart and therefore it can induce CP violation. But in theconsidered model,there is no
interference terms between SM and leptophobic Z′ model contributions and terms proportional
to UZ′ involves to the branching ratio and polarization effects in the form UZ′ 2. Therefore it
sb | sb |
cannot induce CP violation. Depicted in Fig.4 is the dependence of the normal polarization P
N
for Λ Λνν¯ decay. The difference between the two models in prediction of P becomes
b N
→
considerable at q2 10GeV2. Therefore analysis of P in this region can be informative for
N
≥
discriminatingthesemodels.
7
When Λ isnotpolarized, summingovertheΛ spininEq.(11), weget
dΓ0
dΓ = 1+α eˆ ξˆ , (24)
2 Λb L · Λb!
where α = I1. So, the polarization of Λ is P α . In Fig.5 we present the dependence
Λb I0 b Λb ≡ Λb
of polarization of Λ baryon α on q2. We see that up to q2 = 13GeV2 the sign of α in
b Λb Λb
leptophobic model is positive and negative in SM. When q2 > 13GeV2 situation becomes vice
versa. For this reason measurement of the sign and magnitude of α at different q2 can provide
Λ
b
us essential information about existence of new physics. For unpolarized Λ ; i.e. ξˆ = 0, we
b Λb
have
P~ = α eˆ , (25)
Λ Λ L
withα = I2 whichleadstotheresultthattheΛpolarizationispurelylongitudinal,i.e. P = α
Λ Λ Λ
I0
and P = P = 0.
N T
In conclusion, we have studied the Semileptonic Λ Λνν¯ decay in the Leptophobic Z′
b
→
Model. Wehaveanalysedthelongitudinal,transverseandnormalpolarizationoftheΛbaryonon
q2 dependence. Thesensitivityofthebranchingratioon UZ′ isinvestigatedandthedependence
| qb |
of the polarization parameter of Λ baryon on q2 is also investigated. We find that all physical
b
observablesarevery sensitiveto theexistenceofnew physicsbeyondSM.
We wouldliketothank T.M.Alievand M.Savcı for usefuldiscussions.
8
12
10
Z’model
SM
)
νν 8
Λ
→
b
Λ
(
2q 6
d
R/
B
d
x
6 4
0
1
2
0
0 5 10 15 20
2
q
Figure1: Thedependenceofthedifferentialdecay branching ratio(BR),forΛ Λνν¯decay,as
b
→
functionofthemomentumtransfer,q2 .
5
4
Z’-model
SM
)
ν 3
ν
Λ
→
b
Λ
2( 2
q
d
R/
B
x
60 1
1
0
-1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Z’
|U |
sb
Figure 2: Integrated branching ratio(BR)as function of the U , effective coupling constant in
sb
theLeptophobicZ′ Model. . | |
9