A Possibility of Search for New Physics at LHCb

0.25 MB·English

by  Xiang Liu

A Possibility of Search for New Physics at LHCb
Xiang Liu1, Hong-Wei Ke2, Qing-Peng Qiao2, Zheng-Tao Wei2, and Xue-Qian Li2
1 Department of Physics, Peking University, 100871, Bejing, China,
2 Department of Physics, Nankai University, 300071, Tianjin, China
It is interesting tosearch for new physicsbeyondthestandard model at LHCb. Wesuggest that
weakdecaysofdoublycharmedbaryonsuchasΞcc(3520)+, Ξ+cc+ tocharmlessfinalstateswouldbe
a possible signal for new physics. In this work, we consider two models, i.e. the unparticle and Z′
as examples tostudy such possibilities. Wealso discuss the cases for Ξ0bb, Ξ−bb which havenot been
observed yet, but one can expect to find them when LHCb begins running. Our numerical results
showthatthesetwomodelscannotresultinsufficientlylarge decaywidths,thereforeifsuchmodes
are observed at LHCb, theremust be a new physicsother than theunparticle or Z′ models.
8
PACSnumbers: 14.80.-j,13.30.Eg
0
0
2
I. INTRODUCTION shown in Fig. 1 (c). The mechanism includes two pen-

n guin loops or a crossed box-diagram is very suppressed,
a
sothatcannotresultinanyobservableeffectsandwecan
J LHC will begin its first run pretty soon, and besides
5 searching for the long-expected Higgs boson, its main ignorethemcompletely. If anon-zerorateis observedat
LHCb, it should be a signal of new physics. Definitely
2 goal is to explore new physics beyond the SM. Many
the diagram of Fig. 1 (c) may cause a non-zero contri-
schemes have been proposed to reach the goal. Indeed,
] theLHCbdetector,eventhoughisnotresponsibleforthe bution and contaminate our situation for exploring new
h physics. If we consider the charmless decays of Ξ++ or
p Higgshunting,willprovideanidealplacetostudyheavy bottomless decays of Ξ−, that diagram(Fig. 1 (c))ccdoes
- flavor physics and search for evidence of new physics. bb
p not exist at all. Then, the first question is that can we
One can make careful measurements on rare decays of
e distinguish such direct decays of Ξ into charmless final
B-mesons, b-baryons, B-mixing and CP violation with a cc
h states (or Ξ into bottomless final states) from the sec-
[ huge database available at LHCb, moreover, we are in- bb
ondary decays which result in charmless (or bottomless)
spired by the possibilities of discovering new physics. It
4 products and are the regular modes in the framework of
wouldbebeneficialtoconjecturemorepossibleprocesses
v the SM. The answer is that the direct transitions are fa-
which would signal existence of new physics.
0 vorablytwo-bodydecays,namelyinthefinalstatesthere
0 In 2002, the first event for doubly charmed baryon, are only two non-charmed hadrons by whose momenta
6 Ξ+(3520),was observedby the SELEXCollaborationin
2 thcec channel of Ξ+ Λ+K−π+ [1, 2, 3]. Ξ+ has the one can re-construct the invariant mass spectra of Ξcc
. cc → c cc (or Ξbb), whereas, in the regularmodes with sequent de-
0 mass m = 3519 1 MeV and width Γ < 5 MeV. By cays, there are at least three hadrons in the final states.
1 studying an alter±native channel of pD+K− conducted
7 later, the mass of the baryon-resonance was confirmed
0 as m = 3518 3 MeV [4], which is consistent with that The second question is that is there any mechanism
: ± beyond the standard model available which can result
v given in Ref. [1]. In the present theory, there definitely
in such direct decays? Below, we use two models to
i is no reason to exclude existence of Ξ++ which contains
X ccu valence quarks and as well Ξ0 (bcbcu) and Ξ− (bbd), demonstrate how such direct decay modes are induced
r bb bb and estimate the widths accordingly. One of them is
by the flavor-SU(3) symmetry.
a
the unparticle scenario and another one is the SU(3)
Inthiswork,weproposethatdirectdecaysofΞ with ×
cc SU(2) SU(2) U(1) model where a new gauge
L R B−L
charmless final states or Ξbb with bottomless final states boson Z×′ exists and×mediates an interaction to turn the
wouldbesignalsfornewphysics. Bythequark-diagrams,
charmquarkintoau-quark. Thusbyexchangeofanun-
one can easily notice that the main decay modes of Ξ
cc particle or Z′ between the two charm quarks in Ξ+(++)
wouldbe D+Λ(Σ0), Λ K0, D+PK− and Λ K−π+. The cc
c c (orbetweenthetwobottomquarksinΞ−(0)),thesedirect
later two modes are just the channels where the SELEX bb
transitions occur.
collaboration observed the baryon Ξ . While the di-
cc
rect decays of Ξ (or Ξ ) into charmless (bottomless) Inthis work,forsimplicity,weonlyconsiderthe inclu-
cc bb
finalstatesaresuppressedinthestandardmodel,sothat sivedecaysofΞ++ (Ξ−)intocharmless(bottomless)final
cc bb
would be sensitive to new physics beyond the SM. states. The advantage of only considering the inclusive
SinceinΞ therearetwoidenticalcharmquarkswhich processes is obvious that we do not need to worry about
cc
canneitherannihilate,norexchangeW-bosontoconvert the hadronization of quarks into final states because
intootherquarks. IntheSM,directtransitionofΞ into suchprocessesarefullygovernedbythenon-perturbative
cc
charmlessfinalstatesmayrealizeviathedouble-penguin QCD effects and brings up much uncertainty.
mechanism which is shown in Fig. 1 (a), the crossed Below, we will investigate the processes caused by ex-
box-diagram(Fig. 1(b))andapossibletwo-stepprocess changing unparticles and Z′ separately and then make a
2
For a scalar unparticle field, the propagator with mo-
mentum p and scale dimension d is [6]
U
d4xdip·x 0TO (x)O (0)0
U U
h | | i
Z
A 1
=i dU (2)
2sin(dUπ)( p2 iǫ)2−dU
− −
with
(a)
16π5/2 Γ(d +1/2)
U
A = , (3)
dU (2π)2dU Γ(dU 1)Γ(2dU)
−
with d the scale dimension.
U
For the vector unparticle, the propagator reads
(b) d4xeip·x 0TOµOν(0)0
c s Z h | U U | i
d W u =i AdU −gµν +pµpν/p2, (4)
u 2sin(dUπ) (−p2−iǫ)2−dU
d¯
W where the transverse condition ∂ Oµ =0 is required.
µ U
c s
Intheunparticlephysics,theinclusivedecayofdoubly
(c) charmed baryons into light quarks ccq uuq occurs at
→
the tree level, and the transition is depicted in Fig. 2.
Heretheexchangedagentbetweenthetwocharmquarks
FIG.1: (a)Thedouble-penguindiagramwhichcaninducethe
can be either scalar or vector unparticle.
decay of Ξcc(Ξbb) into non-charm (non-bottom) final states.
(b)Thecrossedboxdiagram. (c)Anemissionwheretheeffec-
tive interaction would be non-local and for charmless decays FIG.2: Theinclusivetransitionofdoublycharmedbaryonin
of Ξ+cc+, it does not exist. unparticle physics, where the double-dashed line denotes the
scalar or vector unparticle in the unparticle model or Z′ in
theleft-right model.
brief discussion on the possibility that new physics may
result in observable phenomena at LHCb.
II. THE INCLUSIVE DECAY OF DOUBLY
CHARMED BARYON
A. The unparticle scenario
(a)
c u
Before entering the concrete calculation, we briefly re-
view the concerned knowledge on the unparticle physics c u
[5],which is neededin laterderivation. The effective La-
q
grangiandescribingtheinteractionoftheunparticlewith q¯
g
the SM quarks is
d d
cqq′
= S q¯γ (1 γ )q′∂µO (b)
L ΛdU µ − 5 U
U
cqq′
+ V q¯γ (1 γ )q′Oµ +h.c., (1) Even though we only consider the inclusive processes
ΛdU−1 µ − 5 U wherethequarksinthefinalstatesaretreatedason-shell
U
free particles and the wavefunctions of the light hadrons
where O and Oµ are the scalar and vector unparticle inthefinalstatesarenotneeded,thebindingeffectofthe
U U
fields respectively. q and q′ denote the SM quark fields. initialbaryons(Ξ++ orΞ−)whicharecomposedofthree
Generally,thedimensionlesscoefficientscqq′ isrelatedto valence quarks mcucst bebbtaken into account. Namely,
S,V
the flavor of the quark field. This interaction induces a whenwecalculatethehadronicmatrixelements,weneed
FCNC and contributes to the processes of concern. toinvokeconcretephenomenologicalmodelstocarryout
3
the computations where the wave function of the initial and the parameters α and α reflect the non-
ρ λ
baryon is needed. In this work, we adopt a simple non- perturbativeeffects andwillbe giveninlatersubsection.
relativistic model, i.e. the harmonic oscillator model [7]. InthecenterofmassframeofΞ (3520)+,thehadronic
cc
Thismodelhasbeenwidelyandsuccessfullyemployedin matrix elements S is written as
fi
similar researches[8, 9, 10, 11, 12, 13, 14]. Thus one can
trustthatforheavyhadrons,suchsimplenon-relativistic S = (2π)4δ4(p +p +p M)T
fi 1 2 3
−
model can work well and the results are relatively reli-
able, even though certain errorsare not avoidable. Thus with T =(TS +TV).
in this work the matrix elements of the effective opera- Forexchangingscalarunparticle,T matrixelementis
S
tors evaluated in terms of the harmonic oscillator wave written as
function is believed to be a good approximation. Ac-
E
cording to the references listed above, the errors in the T = d3p d3p (2π)3 p3
S ρ λ
m
estimate, especially as we only need the wavefunction of spinZ p3
X
the the initial hadron, are expected to be less than 10%. [u¯ (p ,s )γ (1 γ )u (p′,s′)
Bychangingtheinputparametersandthemodelparam- × u 1 1 µ − 5 c 1 1
u¯ (p ,s )γ (1 γ )u (p′,s′)]
eterswhichareobtainedbyfittingotherexperiments,we × u 2 2 ν − 5 c 2 2
scan the region of changes of the numerical results and ( ccSu )2 AdU iqµqν
find that the error range is indeed consistent with our × ΛdUU 2sin(dUπ)(−p2−iǫ)2−dU
expectation.
ψ (p ,p ). (5)
In the harmonicoscillatormodel, the wavefunction of ×N Ξ+cc ρ λ
the doubly charmed baryon Ξ (3520)+ is expressed as
cc For the vector unparticle exchange, T is
V
|ΨΞ+cc(P,s)i T = d3p d3p (2π)3Ep3
V ρ λ
m
= N χSFϕC d3pρd3pλ sXpinZ p3
coloXr,spin Z ×[u¯u(p1,s1)γµ(1−γ5)uc(p′1,s′1)
×ψΞ+cc(pρ,pλ)b†c(p′1,s′1)b†c(p′2,s′2)b†u(p′3,s′3)|0i, ×u¯u(p2,s2)γν(1−γ5)uc(p′2,s′2)]
ccu A i( gµν +qµqν/q2)
which satisfies the normalization condition ( V )2 dU −
× ΛdUU−1 2sin(dUπ) (−p2−iǫ)2−dU
hΨΞ+cc(P,s)|ΨΞ+cc(P′,s′)i ×NψΞ+cc(pρ,pλ). (6)
M
= (2π)3 Ξ+ccδ3(P P′)δ(s s′), Here u and u¯ (q =c,u) denote the Dirac spinors
E − − q q
P
where is the normalization constant. χ and ϕ de- E +m 1
nofotdeouthbNelyscphinar-flmaevdorbaarnydoncoΞlor(3p5a2r0ts)+ofretshpeSeFcwtaivveelfyunwCchtoiosne uq = s q2mq q (cid:18) Eqσ+·pmq (cid:19)χ, (7)
cc
explicit expressions are E +m σ p
u¯ = q qχ† 1, · , (8)
q
s 2mq (cid:18) −Eq+mq(cid:19)
E m′m′m′ 1
= 1 2 3, ϕ = ǫ ,
N sM E1′E2′E3′ C √6 ijk and we can use the expression [15]
1
χSF = √6 2|c↑c↑d↓i−|c↑c↓d↑i−|c↓c↑d↑i . |ccsu|2 = 6m∆m|sindUπ|, (9)
h i ΛU2dU 5f2BˆAdUm2dU
In the harmonic oscillator model, the spatial wavefunc- ccu 2 2m∆m sind π
tion ψΞ+cc(pρ,pλ) reads as Λ|U2dsU|−1 = f2BˆAdU|m2dUU−2|, (10)
ψ (p ,p )
Ξ+cc ρ λ tosimplifyTV andTS. Oneneedstosumoverallpossible
1 3/4 1 3/4 p2 p2 spin assignments for the Dirac spinors.
= 33/4 exp ρ λ
πα2 πα2 − 2α − 2α
ρ λ ρ λ
(cid:16) (cid:17) (cid:16) (cid:17) h i
with the definitions B. The Z′ scenario
p = p′1−p′2, p = p′1+p′2− 2mmdcp′3, The Left-Right models [16] is also a natural extension
ρ √2 λ 22mc+md of the electroweak model. It has been widely applied to
md the analysis on high energy processes. For example, re-
P = p′ +p′ +p′, q cently He and Valencia [17] employed this model with
1 2 3
4
certainmodifications toexplainthe anomalyinAb ob- Then we have the final expression as
FB
served at LEP [18]. Barger et al. studied Z′ mediated
flavor changing neutral currents in B-meson decays [19], E
Bs−B¯s mixing [20] and B →Kπ puzzle [21]. T = spinZ d3pρd3pλ(2π)3mpp33
X
Thegaugegroupofthemodel[17]isSU(3) SU(2)
SU(2)R × U(1)B−L where the four gauge×couplinLg×s ×u[¯u¯u((pp1,,ss1))γγµ((11−γγ5))uuc((pp′′1,,ss′′1))]
g3, gL, gR and g correspond to the four sub-groups re- × u 2 2 ν − 5 c 2 2
spectively. The vacuum expectation values of the three ( igµν)G √2(Vu∗Vu )2
× − F Rti Rtj
Higgsbosonsbreakthesymmetry. Thesymmetrybreak-
ψ (p ,p ). (13)
ing patterns are depicted in literature. The introduction ×N Ξ+cc ρ λ
of a scalar field φ causes Z in the standard model to
0
mix with a new gauge boson Z , then Z, Z′ are the
R
mass eigen-states. C. The expression of the decay width
For the neutral sector the Larangianis
The inclusive decay rate would be obtained by inte-
grating over the phase space which involves three free
g
L = −2cosLθ q¯γµ(gV −gAγ5)q(cosξZZµ−sinξZZ′µ) quarks and the procedure is standard [24],
W
g 1 4 2
+ Y tanθ ( q¯ γµq + u¯ γµu d¯ γµd ) Γ(Ξ (3520)+ u u d)
R L L Ri Ri Ri Ri cc
2 3 3 − 3 →
+(signYξZ(tZaµn−θ c+osξcZoZtθ′µ))(sinξ Z cosξ Z′ ) =Za1a2dp01Zb1b2dp02Z02πdηZ−11d(cosθ)16M|ΞT+cc|2(2π)4,
2 R R Z µ− Z µ (14)
(Vd∗Vd d¯ γµd Vu∗Vu u¯ γµu ). (11)
Rbi Rbj Ri Rj − Rti Rtj Ri Rj
where a , a , b and b are defined as respectively
1 2 1 2
Here θ is the electroweak mixing angle (tanθ =
hggYLan),deθdRWipnateraramcetitoenri(zteasntθhRe=relgagRti)v,eξsZtriesntghtehZof−thZe′rWimghixt-- a1 = 0, a2 = M2Ξ+cc − (m2+2mM3Ξ)+c2c−m21,
ing angle and VRui,jd are two unitary matrices that rotate b1 = 21τ[σ(τ +m+m−)− p012(τ −m2+)(τ −m2−)],
the right-handed up-(down)-type quarks from the weak
q
1
eigen-states to the mass eigen-states. Note that we use b = [σ(τ +m m )+ p02(τ m2)(τ m2)],
current notation for Pati-Salam model, and only third 2 2τ + − 1 − + − −
q
family couples to SU(2)R in this model. σ = M p0, τ =σ2 (p0)2, m =m m .
In the Z′ model, inclusive decay of doubly charmed Ξ+cc − 1 −q 1 ± 2± 3
baryons into light quarks ccq uuq occurs at tree level. Here M , m , m and m denote the masses of the
The Feynman diagram (Fig. →2) is the same as that for doubly Ξch+cca+rmed1 ba2ryon, up3and down quarks respec-
the unparticle scenario, but only the exchanged agent is tively. In the following, for obtaining numerical results,
replaced by Z′. we use the Monte Carlo method to carry out this inte-
In the center of mass frame of Ξ+cc, we can obtain gral. ForbaryonΞ−bb,theexpressionisthesamebutonly
the mass of charm quark is replaced by that of bottom
quark.
E
T = d3p d3p (2π)3 p3
ρ λ
m
spinZ p3
X
[u¯ (p ,s )γ (1 γ )u (p′,s′) III. NUMERICAL RESULTS
× u 1 1 µ − 5 c 1 1
u¯ (p ,s )γ (1 γ )u (p′,s′)]
× u 2 2 ν − 5 c 2 2
igµν g tanθ (tanθ +cotθ )cosξ Now we present our numerical results.
L W R R Z
×(p2−+MZ′2)[ 2 Since only Ξ+cc+ has been measured, in the later cal-
culation, we use its measured mass as input, and for
×VRut∗iVRutj]2NψΞ+cc(pρ,pλ). (12) Ξ−bb we will only illustrate the dependence of its de-
cay rate on the parameters. The input parameters in-
clude: G = 1.166 10−5 GeV−2, m = 1.60 GeV,
F c
TheauthorsofRef. [17,22,23]suggestedthatcotθ is ×
R m = m = 0.3 GeV, m = 0.45 GeV, m = 4.87 GeV.
u d s b
large, so that tanθ can be ignored. They took approx-
R M = 3.519 GeV. α = 0.33 GeV2,α = 0.25 GeV2
imations tanθWcotθRMMW′Z ∼ 1 and cosξZ ∼ 1. Because [1,Ξ2+cc5, 26, 27]. Here, tρhe light quark maλss refers to the
MZ′ is larger than 500 GeV [17], one has p2+1MZ′2 ∼ M1Z′2. constitute mass.
5
TABLEI:ThedecaywidthsofΞcc(3520)+ →uudorΞ+cc+ → FIG. 3: (a) and (b) respectively show the dependences of
uuuandΞ−bb →ddd(ssd)correspondingtodU =3/2(inunits the decay widths of Ξcc(3520)+ → uud and Ξ−bb → ddd re-
of GeV). In the table, the second, third and fourth columns spectivelycomingfromthecontributionsofscalarunparticle,
respectivelycorrespondtothecontributionsfromexchanging vectorunparticle and both on dU.
scalar unparticle, vector unparticle and both.

8
scalar vector scalar+vector
-15
Γ[Ξcc(3520)+ →uud] 4.57×10−18 1.11×10−15 1.24×10−15 7 ASlcl a(l1a0r (1G0e-1V8G)eV)
Γ[Ξ−bb →ddd] 5.85×10−20 1.65×10−17 1.83×10−17 h 6 Vector (10-15GeV)
Γ[Ξ− →ssd] 5.21×10−20 1.23×10−17 1.44×10−17 dt5
bb wi
y 4
a
c
e3
D
2
A. The results in the Unparticle scenario
1
Forthe unknownparametersΛ inthe unparticle sce- 0
U
nario, according to the general discussion, the energy 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
scale may be at order of TeV, thus one can fix Λ = 1
U du
TeV. We choose d =3/2 in our calculation. .
U
In this work, we also calculate the inclusive decay (a)
width of doubly bottomed baryon Ξ−. The mass of Ξ−
bb bb
issetas10.09GeVaccordingtotheestimateofRef. [27],

although there are no data available yet.
2.0
The numerical results are provided in Table I. Fig. 1.8 All (10-16GeV)
-18
3 illustrates the dependence of the decay widths of 1.6 Scalar (10 GeV)
Ξcc(3520)+ →uud and Ξ−bb →ddd on dU, the three lines dth 1.4 Vector (10-16GeV)
(solid, dashed and dotted) correspond to the contribu- wi1.2
tions of scalar unparticle, vector unparticle and both on y 1.0
dU. It is noted here ”both” means that at present we ca0.8
e
cannot determine whether the unparticle is a scalar or D0.6
vector and it is also possible that both scalar and vec-
0.4
tor exist simultaneously. Thus we assume both of scalar
0.2
and vector contribute and they interfere constructively.
0.0
Definitely, it is worth of further investigation.
-0.2
1.4 1.6 1.8 2.0
d u
(b)
B. The results for Z′ exchange
The earlier studies indicate that the mass of MZ′
should be larger than 500 GeV [17] and Vu∗Vu∗ is
Rtc Rtu
bound no more than 2.0 10−4 [22], in our calculation, C. Estimate the contribution from Standard Model
×
we take their extreme values as MZ′ = 500 GeV and
Vu∗Vu∗ = 2.0 10−4, thus we would obtain the upper
Rtc Rtu × As indicated above, in the framework of the SM, Ξ+
limit of the decay width. It is estimated with all the cc
can decay into two-body final states via Fig. 1 (c). It
input parameters as
would be interesting to compare the SM contribution
with that from the two models. Thus, we would roughly
Γ[Ξcc(3520)+ uud]=7.66 10−21 GeV. (15) estimate the ratio of the contribution of Fig. 1 (c) to
→ ×
that of Fig. 2 (b) for the Z′ model. It is easier to com-
pare them because the structures of two diagrams and
This is atoo smallnumericalvalue comparedwiththe
the relevant effective vertices are similar.
width of Ξ+, therefore, it is hopeless to observe a non-
cc
zero branching ratio of Ξ+ into charmless final states if By the order of magnitude estimation and with the
cc
only Z′ is applied. SU(3) symmetry,the ratio ofthe amplitude of Fig. 1 (c)
6
(TSM) to Fig. 2 (b) (Tun or TZ′) is yet,andtheystillneedfurthertheoreticalinvestigations,
but their framework is clear, so that we may use them
T 8G
SM F , (16) as examples to demonstrate how new physics may cause
TZ′ ≈ 4πqα2s√2(VRut∗iVRutj)2 such decay modes and indicate that a sizable observa-
tional rate is a clear signature for new physics beyond
where q is the momentum of unparticle or Z′ (in the the SM. Moreover, the double charmed baryon has only
case of the SM, q2 M2 ) and can be neglected in the been observed by the SELEX collaboration, but not at
≪ W
propagator. Because the contribution from smaller q2 B-factories. It seems peculiar at first glimpse, but care-
is dominant, in the estimation, we set q2 = 0.5GeV2. ful studies indicate that it is quite reasonable due to the
Since the whole case under consideration, may fall in fragmentation process of heavy quarks. The authors of
the non-perturbative QCD region, as a rough estimate, Ref.[28] indicate that the meson B cannot be seen at
c
we take αs = 1, VRut∗iVRutj = 2 × 10−4 and GF = any e+e− colliders because its production rate at such
1.166 10−5GeV−2, we can get TSM 66 (i.e.ΓSM machines is too small, but by contraries, its production
× TZ′ ≈ ΓZ′ ≈ rate is greatly enhanced at hadron colliders. It was first
4300 ). Then we can obtain the ratio of decay widths
ΓUnparticle 40. This ratio indicates that for Ξ+ the observedatTEVATRONanditsproductionrateatLHC
ΓSM ≈ cc would be much larger by several orders [28]. In analog,
contributionoftheSMissmallerthanthatoftheunpar-
onecanexpectthatsuchdouble-charmedbaryonsΞ or
ticle scenario, but larger than that from the Z′ model. cc
double-bottomed Ξ can only be produced at LHC, but
However, for Ξ++, Fig.1(c) does not contribute at all, bb
cc not at B-factories.
so that the decay of Ξ++ into charmless final states (or
cc
Ξ− into bottomless final states) is more appropriate for The inclusive decays of doubly charmed baryons
exbpbloring new physics than Ξ+. Ξcc(3520)+, Ξ+cc+ and Ξ0bb, Ξ−bb are explored in unpar-
cc ticle and Z′ scenarios. Our result indicates that the up-
It is worth noticing that the estimate of the contribu-
per limit of the inclusive decay width of Ξ++ uuu
tionoftheSMtothedecayrateisveryrough,thuswhat is about 10−15 GeV with d = 3/2. For inclcucsive→decay
we can assure to ourselves is its order of magnitude. In- U
Ξ− ddd(ssd),theupperlimitisatorderof10−17GeV.
deed the magnitude contributedby the SM is very small bb →
It is learnt that in the unparticle scenario, the contribu-
and cannot produce sizable observational effects at all,
tion from exchanging a vector unparticle is much larger
even though it has a comparable order with that from
the two sample models, the unparticle and Z′. In the than that from exchanging a scalar unparticle, as shown
in Table I.
future,ifsuchmode wereobservedatLHCb,wecandef-
initelyconcludethatitisnotcausedbytheSM,butnew The parameters which we employ in the numerical
physics. computations are obtained by fitting other experimen-
tal measurements, for example if the recently observed
D0 D¯0 can be interpreted by the unparticle model, an
−
IV. DISCUSSION AND CONCLUSION upper bound on the parameters in the model would be
constrained. Indeed, all the present experimental data
canonly provideupper bounds onthe modelparameters
In this work, we propose to explore for new physics
no matter what new physics model under consideration
beyond the SM at LHCb by measuring direct decays of
Ξ+ Ξ++, (Ξ−, Ξ0 ) into charmless (bottomless) final is.
cc cc bb bb
states. Such decays can occur via the diagrams shown So far it is hard to make an accurate estimate on the
in Fig. 1 in the framework of the SM, but is much sup- productionratesoftheheavybaryonswhichcontaintwo
pressed to be experimentally observed,therefore if a siz- heavy quarks at LHC yet, but one has reason to believe
able rate is measured, it would be a clear signal for new that the production rate would be roughly of the same
physics beyond the SM. We use two models as exam- orderoftheproductionrateofBcwhichwasevaluatedby
ples, namely the unparticle and Z′ models to calculate someauthors[28],orevensmallerbyafactoroflessthan
the decay rates, because both of them allow a transition 10. The production rates indeed will be theoretically
of cc (bb) qq where q may be light quarks to occur evaluated before or even after LHC begins running.
→
at tree level. Thus one expects that these new models In Ref. [29], the authors estimate the number of Ξ
cc
might result in non-zero observation. produced at LHCb as about 109. Since the available en-
Indeed, our work is motivated by three factors, first ergy is much higher than the masses of Ξ and Ξ , one
cc bb
the greatmachineLHC willrunnextyearandaremark- has strong reason to believe that their production rates
able amount of data will be available, then secondly, the are comparable. Unfortunately our numerical results in-
double-charmed baryon Ξ which was observed by the dicate thatthe unparticle andZ′ scenarioscannotresult
cc
SELEX collaboration provides us a possibility to probe in sizable rates for Ξ++ uuu two hadrons and
newphysics,andthelastreasonisthatsomemodelshave Ξ− ddd(ssd) twcocha→drons w→hich can be measured
bb → →
been proposed and they may induce a flavor-changing atLHCbandneitherthe SM.Eventhoughthe twosam-
neutral current, concretely the unparticle and Z′ mod- ple models and SM cannot cause sufficiently large rates,
els are employed in this work. Definitely none of the thechannelsstillmaystandforapossibleplacetosearch
twomodelsareconfirmedbyeithertheoryorexperiment for new physics. If a sizable rate is observedatLHCb, it
7
would be a signal of new physics and the new physics is the National Natural Science Foundation of China un-
also not the unparticle and/or Z′, but something else. der Grants 10475042, 10721063, 10625521, 10705001,
10745002 and 10705015, Key Grant Project of Chi-
nese Ministry of Education (No. 305001), Ph.D. Pro-
Acknowledgments gram Foundation of Ministry of Education of China
and the China Postdoctoral Science foundation (No.
We greatly benefit from constructive discussions with 20060400376).
Prof. Xiao-Gang He. This project was supported by
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