Impact of squark generation mixing on the search for squarks decaying into fermions at LHC
A. Bartl, H. Eberl, B. Herrmann, K. Hidaka, W. Majerotto, W. Porod
aa r X i v : . [ h e p - ph ] A p r DESY 10-059
Impact of squark generation mixing on the searchfor squarks decaying into fermions at LHC
A. Bartl , H. Eberl , B. Herrmann , , K. Hidaka , W. Majerotto and W. Porod , Fakult¨at f¨ur Physik, Universit¨at Wien, A-1090 Vienna, Austria Institut f¨ur Hochenergiephysik der ¨Osterreichischen Akademie der Wissenschaften,A-1050 Vienna, Austria Deutsches Elektronen-Synchrotron (DESY), Theory Group, D-22603 Hamburg,Germany Institut f¨ur Theoretische Physik und Astrophysik, Universit¨at W¨urzburg, D-97074W¨urzburg, Germany Department of Physics, Tokyo Gakugei University, Koganei, Tokyo 184-8501, Japan AHEP Group, Instituto de Fisica Corpuscular - C.S.I.C., Universidad de Val`encia,E-46071 Val`encia, Spain
Abstract
We study the effect of squark generation mixing on squark production and decaysat LHC in the Minimal Supersymmetric Standard Model (MSSM). We show thatthe effect can be very large despite the very strong constraints on quark-flavourviolation (QFV) from experimental data on B mesons. We find that the twolightest up-type squarks ˜ u , can have large branching ratios for the decays into c ˜ χ and t ˜ χ at the same time due to squark generation mixing, leading to QFVsignals ’ pp → c ¯ t ( t ¯ c ) + missing- E T + X ’ with a significant rate. The observationof this remarkable signature would provide a powerful test of supersymmetricQFV at LHC. This could have a significant impact on the search for squarksand the determination of the underlying MSSM parameters. Introduction
The exploration of the TeV scale has begun with the start up of the LHC run. Gluinosand squarks, the supersymmetric partners of gluons and quarks, will be produced copi-ously for masses up to O (1 T eV ) if supersymmetry (SUSY) is realized in nature. Afterthe discovery of SUSY, the determination of SUSY parameters will be one of the mainexperimental programs. The determination of the soft-SUSY-breaking parameters willbe particularly important to pin down the SUSY-breaking mechanism. As the soft-SUSY-breaking terms are the source of flavour violation beyond the Standard Model(SM), the measurement of flavour violating observables is directly linked to the crucialquestion about the SUSY-breaking mechanism. It is usually assumed that productionand decays of gluinos and squarks are quark-flavour conserving (QFC). However, ad-ditional flavour structures (i.e. squark generation mixings) would imply that squarksare not quark-flavour eigenstates, which could result in sizable quark-flavour violation(QFV) effects significantly larger than those due to the Cabibbo-Kobayashi-Maskawa(CKM) mixing.Additional flavour structures will of course give contributions to flavour-changing neu-tral current (FCNC) processes. Up to now all measurements of such processes areconsistent with the SM predictions, which in turn requires that the flavour structureof new physics at the TeV scale is highly constrained. In particular, this flavour struc-ture could be closely related to the flavour structure of the SM Yukawa couplings.The most extreme case is minimal flavour violation (MFV) [1, 2, 3] which assumesthat the Yukawa coupling matrices of the SM are the only source of flavour viola-tion even in interactions involving new particles. Supersymmetric models of this kindare gauge-mediated SUSY-breaking or minimal supergravity (mSUGRA) models withuniversal boundary conditions [4]. However, while the flavour constraints suggest thatthe dominant flavour structure of new physics should be MFV, there is certainly roomfor sub-dominant contributions that are not MFV. The discovery of such non-MFV(NMFV) physics will be of utmost interest. There are also known examples of flavourmodels which do have large flavour violating entries in the squark sector getting con-sistency with the flavour observables in a different way. An example is a model with anextended R-symmetry [5] where the left-right squark mixing terms are absent and thegauginos are Dirac particles. Another possibility would be hybrid gauge and gravitymediation of supersymmetry breaking [6] where one gets sizable NMFV contributions2i.e. sizable squark generation mixing terms) as discussed in [7].The effect of QFV in the squark sector on reactions with external particles being SMparticles [8, 9] (or SUSY Higgs bosons [10]) has been studied in several publications.In this case the effect of QFV in the squark sector is induced only by SUSY particle(sparticle) loops.However, in reactions with external SUSY particles, the QFV effect can already oc-cur at tree-level and hence can be rather large. The QFV decay ˜ t → c ˜ χ [11] andQFV gluino decays [12] were studied in the scenario of MFV, where the only sourceof QFV is the mixing due to the CKM matrix. The QFV decay ˜ t → c ˜ χ is actuallythe standard search mode at the Tevatron for light top-squarks if their decays intobottom-quark plus chargino and top-quark plus neutralino are kinematically forbid-den. Squark pair production and their decays at LHC have been analyzed in scenariosof NMFV, where the effect of the squark generation mixing is also included [13, 14].QFV gluino decays [15] and QFV squark decays [16] have been studied in the MinimalSupersymmetric Standard Model (MSSM) with squark generation mixing in its mostgeneral form.In the present paper, we study the effect of QFV due to the mixing of charm-squarks and top-squarks both on production and subsequent decays of squarks in thegeneral MSSM with R parity conservation. In principle also the mixing between rightup-squark and left top-squark is hardly constrained as pointed out in [17]. Here forsimplicity we do not take into account such a mixing as we are mainly interestedin demonstrating the main QFV effects and signals. Note that in case one cannotdistinguish between the quarks of the first two generations, the corresponding QFVsignals will involve jets whose original quark is not identified, and hence the effects ofthe two mixings (i.e. the 1st and 3rd generation mixing and the 2nd and 3rd generationmixing) cannot be distinguished.We show that the QFV squark decay branching ratios B(˜ u i → c ˜ χ ) and B(˜ u i → t ˜ χ ) ( i = 1 ,
2) can be very large (up to ∼ u , are thetwo lightest up-type squarks and ˜ χ is the lightest neutralino. This leads to QFVsignal events ’ pp → c ¯ t (¯ ct ) + E misT + X ’ and ’ pp → t t (¯ t ¯ t ) + E misT + X ’ at LHC,which we also study in the present article, where E misT is the missing transverse energy.3 Squark mixing with flavour violation
The most general up-type squark mass matrix including left-right mixing as well asquark-flavour mixing in the super-CKM basis of ˜ u γ = (˜ u L , ˜ c L , ˜ t L , ˜ u R , ˜ c R , ˜ t R ), γ =1 , . . . ,
6, is [18] M u = M uLL ( M uRL ) † M uRL M uRR , (1)where the three 3 × M uLL ) αβ = M Q u αβ + (cid:20) ( 12 −
23 sin θ W ) cos 2 β m Z + m u α (cid:21) δ αβ , (2)( M uRR ) αβ = M Uαβ + (cid:20)
23 sin θ W cos 2 β m Z + m u α (cid:21) δ αβ , (3)( M uRL ) αβ = ( v / √ T Uβα − m u α µ ∗ cot β δ αβ . (4)The indices α, β = 1 , , u, c, t , respectively. M Q u and M U are the hermitian soft-SUSY-breaking mass matrices for the left and right up-typesquarks, respectively. Note that in the super-CKM basis one has M Q u = K · M Q · K † due to the SU(2) symmetry, where M Q is the hermitian soft-SUSY-breaking massmatrix for the left down-type squarks and K is the CKM matrix. Note also that M Q u ≃ M Q as K ≃ T U is the soft-SUSY-breaking trilinear coupling matrix of theup-type squarks: L int = − ( T Uαβ ˜ u † Rβ ˜ u Lα H + h.c. ) + · · · . µ is the higgsino mass param-eter. v , are the vacuum expectation values of the Higgs fields with v , / √ ≡ h H , i ,and tan β ≡ v /v . m u α ( u α = u, c, t ) are the quark masses.The physical mass eigenstates ˜ u i , i = 1 , . . . ,
6, are given by ˜ u i = R ˜ uiα ˜ u α . The mix-ing matrix R ˜ u and the mass eigenvalues are obtained by a unitary transformation R ˜ u M u R ˜ u † = diag( m ˜ u , . . . , m ˜ u ), where m ˜ u i < m ˜ u j for i < j .Having in mind that M Q u ≃ M Q , we define the QFV parameters δ uLLαβ , δ uRRαβ and δ uRLαβ ( α = β ) as follows [19]: δ uLLαβ ≡ M Qαβ / q M Qαα M Qββ , (5)4 uRRαβ ≡ M Uαβ / q M Uαα M Uββ , (6) δ uRLαβ ≡ ( v / √ T Uβα / q M Uαα M Qββ . (7)The relevant QFV parameters in this study are δ uLL , δ uRR , δ uRL and δ uRL which arethe ˜ c L − ˜ t L , ˜ c R − ˜ t R , ˜ c R − ˜ t L and ˜ c L − ˜ t R mixing parameters, respectively. The down-type squark mass matrix can be parameterized analogously to the up-type squark massmatrix [18].The properties of the charginos ˜ χ ± i ( i = 1 , m ˜ χ ± < m ˜ χ ± ) and neutralinos ˜ χ k ( k = 1 , ..., m ˜ χ < ... < m ˜ χ ) are determined by the parameters M , M , µ and tan β ,where M and M are the SU(2) and U(1) gaugino mass parameters, respectively. In our analysis, we impose the following conditions on the MSSM parameter space inorder to respect experimental and theoretical constraints:(i) Constraints from the B-physics experiments relevant mainly for the mixing be-tween the second and third generations of squarks: B ( b → s γ ) = (3 . ± ((0 . × . + (0 . × . ) / ) × − = (3 . ± . × − (95% CL), where we have combined the experimental error of0 . × . × − (95% CL) [20] quadratically with the theoretical uncertainty of0 . × . × − (95% CL) [21], 0 . × − < B ( b → s l + l − ) < . × − with l = e or µ (95% CL) [22], B ( B s → µ + µ − ) < . × − (95% CL) [20], | R SUSYBτν − . | < .
76 (95% CL) with R SUSYBτν ≡ B SUSY ( B − u → τ − ¯ ν τ ) /B SM ( B − u → τ − ¯ ν τ ) ≃ (1 − ( m B + tan βm H + ) ) [23]. Moreover we impose the following condition on the SUSYprediction: | ∆ M SUSYB s − . | < ((0 . × . + 3 . ) / ps − = 3 . ps − (95%CL), where we have combined the experimental error of 0 . × . ps − (95%CL) [24] quadratically with the theoretical uncertainty of 3 . ps − (95% CL) [25].(ii) The experimental limit on SUSY contributions to the electroweak ρ parameter[26]: ∆ ρ ( SU SY ) < . m ˜ χ ± >
103 GeV, m ˜ χ > m ˜ u , ˜ d >
100 GeV, m ˜ u , ˜ d > m ˜ χ , m A >
93 GeV, m h >
110 GeV, where A is the CP-odd Higgs boson and h is the lighter CP-even Higgs boson.(iv) The Tevatron limits on the gluino and squark masses [28].(v) The vacuum stability conditions for the trilinear coupling matrix [29]: | T Uαα | < Y Uα ( M Q u αα + M Uαα + m ) , (8) | T Dαα | < Y Dα ( M Qαα + M Dαα + m ) , (9) | T Uαβ | < Y Uγ ( M Q u αα + M Uββ + m ) , (10) | T Dαβ | < Y Dγ ( M Qαα + M Dββ + m ) , (11)with ( α = β ; γ = Max( α, β ); α, β = 1 , ,
3) and m = ( m H ± + m Z sin θ W ) sin β − m Z , m = ( m H ± + m Z sin θ W ) cos β − m Z . The Yukawa couplings of the up-type and down-type quarks are Y Uα = √ m u α /v = g √ m uα m W sin β ( u α = u, c, t )and Y Dα = √ m d α /v = g √ m dα m W cos β ( d α = d, s, b ), with m u α and m d α being therunning quark masses at the weak scale and g the SU(2) gauge coupling. Allsoft-SUSY-breaking parameters are assumed to be given at the weak scale. AsSM parameters we take m W = 80 . m Z = 91 . m t = 174 . m t .We calculate the observables in (i)-(iv) by using the public code SPheno v3.0 [30]. Con-dition (i) except for B ( B − u → τ − ¯ ν τ ) strongly constrains the 2nd and 3rd generationsquark mixing parameters M Q , M U , M D , T U , T D and T D . The constraintsfrom B ( b → sγ ) and ∆ M B s are especially important [16]. B ( b → sγ ) is sensitive to M Q , T U , T D and ∆ M B s is sensitive to M Q · M U , M Q · M D .6 Qαβ β = 1 β = 2 β = 3 α = 1 (920) α = 2 (224) α = 3 (840) M M M µ tan β m A
139 264 800 1000 10 800 M Dαβ β = 1 β = 2 β = 3 α = 1 (830) α = 2 α = 3 M Uαβ β = 1 β = 2 β = 3 α = 1 (820) α = 2 (373) α = 3 (580) Table 1: The basic MSSM parameters in our reference scenario with QFV. All of T Uαβ and T Dαβ are set to zero. All mass parameters are given in GeV.
We study the effect of the mixing between the 2nd and 3rd generation of squarks ontheir decays. The branching ratios of the squark decays˜ u , → c ˜ χ and ˜ u , → t ˜ χ (12)are calculated by taking into account the following two–body decays:˜ u i → u k ˜ g, u k ˜ χ n , d k ˜ χ + m , ˜ u j Z , ˜ d j W + , ˜ u j h , (13)where u k = ( u, c, t ) and d k = ( d, s, b ). The decays into the heavier Higgs bosons arekinematically forbidden in our scenarios studied below. The formulae for the widthsof the two–body decays in (13) can be found in [13], except for the squark decays intothe Higgs boson, for which we take the formulae of [31, 32].We take tan β, m A , M , M , M , µ, M Qαβ , M Uαβ , M Dαβ , T
Uαβ and T Dαβ as the basicMSSM parameters at the weak scale and assume them to be real. Here M is the SU(3)gaugino mass parameter. The QFV parameters are the squark generation mixing terms M Qαβ , M Uαβ , M Dαβ , T Uαβ and T Dαβ with α = β . We study a specific scenario whichis chosen so that QFV signals at LHC may be maximized and hence can serve as abenchmark scenario for further experimental investigations. As such a scenario, we7 u ˜ u ˜ u ˜ u ˜ u ˜ u
472 708 819 837 897 918 ˜ d ˜ d ˜ d ˜ d ˜ d ˜ d
800 820 830 835 897 922˜ g ˜ χ ˜ χ ˜ χ ˜ χ ˜ χ ± ˜ χ ±
800 138 261 1003 1007 261 1007 h H A H ±
122 800 800 804Table 2: Sparticles, Higgs bosons and corresponding masses (in GeV) in the scenarioof Table 1. H is the heavier CP-even Higgs boson. | R ˜ uiα | ˜ u L ˜ c L ˜ t L ˜ u R ˜ c R ˜ t R ˜ u u u u u u R ˜ uiα for the scenario of Table 1.take the scenario specified by Table 1, which was studied for QFV gluino decays in [15].Here we take M = (5 /
3) tan θ W M , assuming gaugino mass unification including thegluino mass parameter M . In this scenario one has δ uLL = 0 . δ uRR = 0 . δ uRL = δ uRL = 0 for the QFV parameters. This scenario satisfies the conditions (i)-(v).For the observables in (i) and (ii) we obtain B ( b → sγ ) = 3 . × − , B ( b → sl + l − ) =1 . × − , B ( B s → µ + µ − ) = 4 . × − , B ( B − u → τ − ¯ ν τ ) = 7 . × − , ∆ M B s =17 . ps − and ∆ ρ ( SU SY ) = 1 . × − . The resulting tree-level masses of squarks,neutralinos and charginos are given in Table 2 and the up-type squark compositionsin the flavour eigenstates in Table 3.For the most important decay branching ratios of the two lightest up-type squarkswe get B (˜ u → c ˜ χ ) = 0 . , B (˜ u → t ˜ χ ) = 0 . , B (˜ u → c ˜ χ ) = 0 . , B (˜ u → t ˜ χ ) = 0 .
40. Note that the branching ratios of the decays of a squark into quarks of dif-ferent generations are very large simultaneously, which could lead to large QFV effects.In our scenario this is a consequence of the facts that both squarks ˜ u , are mainly8trong mixtures of ˜ c R and ˜ t R due to the large ˜ c R − ˜ t R mixing term M U (= (373 GeV) )(see Table 3) and that ˜ χ is mainly the U (1) gaugino. This also suppresses the cou-plings of ˜ u , to ˜ χ and ˜ χ +1 which are mainly SU (2) gauginos. Note that ˜ χ , and ˜ χ ± are very heavy in this scenario.The main decay branching ratios of the other up-type squarks are as follows: B (˜ u → u ˜ χ ) = 0 . , B (˜ u → c ˜ χ ) = 0 . , B (˜ u → t ˜ χ ) = 0 . , B (˜ u → s ˜ χ +1 ) = 0 . , B (˜ u → b ˜ χ +1 ) = 0 . , B (˜ u → c ˜ χ ) = 0 . , B (˜ u → t ˜ χ ) = 0 . , B (˜ u → s ˜ χ +1 ) = 0 . , B (˜ u → b ˜ χ +1 ) = 0 . , B (˜ u → c ˜ g ) = 0 . , B (˜ u → u ˜ χ ) = 0 . , B (˜ u → d ˜ χ +1 ) = 0 .
47, and B (˜ u → u ˜ g ) = 0 . B (˜ u i → c ˜ χ ) and B (˜ u i → t ˜ χ )(i=1,2) can be very large simultaneously in a sizable QFV parameter region satisfyingall of the conditions (i)-(v), which can lead to large rates for QFV signal events atLHC as we will see in the next section.Fig.1 shows the contours of B (˜ u → c ˜ χ ) and B (˜ u → t ˜ χ ) in the (∆ M U , M U )plane with ∆ M U ≡ M U − M U . The range of M U shown corresponds to the range | δ uRR | < .
45 for ∆ M U = 0. In the region shown all of the low energy constraints arefulfilled. We see that there are sizable regions where both decay modes are importantat the same time. The observed behaviour can be easily understood in the limitwhere the ˜ t L - ˜ t R mixing is neglected since in this limit only the mixing between ˜ c R and ˜ t R is relevant for ˜ u , and the corresponding effective mixing angle is given bytan(2 θ eff ˜ c R ˜ t R ) ≡ M U / (∆ M U − m t ). Note that for ∆ M U − m t > M U − m t < u ∼ ˜ t R (+ ˜ c R ) [˜ u ∼ ˜ c R (+ ˜ t R )]. We also find that the behaviour of B (˜ u → c ˜ χ )and B (˜ u → t ˜ χ ) is similar to that of B (˜ u → t ˜ χ ) and B (˜ u → c ˜ χ ), respectively,which is a consequence of the fact that mainly the mixing between ˜ c R and ˜ t R isimportant for the ˜ u , system.Fig.2 presents contours of B (˜ u → c ˜ χ ) and B (˜ u → t ˜ χ ) in the δ uLL − δ uRR planewhere all of the conditions (i)-(v) are satisfied except the b → sγ constraint which weshow by plotting the corresponding B ( b → sγ ) contours. All basic parameters otherthan M Q and M U are fixed as in the scenario of Table 1. For B (˜ u → c ˜ χ ) and B (˜ u → t ˜ χ ) we have obtained similar contours to Fig.2.(b) and Fig.2.(a), respectively,but they are almost flat. From Fig.2 we find that the possibility of the large QFV9 -100-50050100150 M ( G e V ) ∆ M (GeV ) U U X (a) -100-50050100150 M ( G e V ) ∆ M (GeV ) U U X (b) Figure 1: Contours of the QFV decay branching ratios (a) B (˜ u → c ˜ χ ) and (b) B (˜ u → t ˜ χ ) in the (∆ M U , M U ) plane where all of the conditions (i)-(v) are satisfied.effect cannot be excluded by the b → sγ constraint even if the experimental error of B ( b → sγ ) becomes very small. We see also that B (˜ u → c ˜ χ ) and B (˜ u → t ˜ χ ) aresensitive [rather insensitive] to δ uRR [ δ uLL ]. For large values of δ uRR we see that thereis a mild dependence on δ uLL . This is due the fact that for large δ uRR the mass squareddifference between ˜ u (the heavier of the RR sector, i.e. the ˜ c R -˜ t R sector) and ˜ u (thelighter of the LL sector, i.e. the ˜ c L -˜ t L sector) becomes small and of the same size asthe ˜ t L -˜ t R mixing term (= − m t µ cot β (see Eq.(4))) enhancing the mixing between theRR and LL sectors. For small values of δ uRR the RR sector decouples effectively fromthe LL sector and hence the ˜ u decay branching ratios are almost independent of δ uLL .In Fig.3 we show the δ uRL dependences of the ˜ u , decay branching ratios, where allbasic parameters other than T U are fixed as in the scenario of Table 1. The observeddependences are a consequence of the enhanced ˜ t L component in ˜ u , ( ∼ ˜ c R + ˜ t R ) forincreased | δ uRL | . The enhanced ˜ t L content implies an enhancement of the b ˜ χ +1 ( ≃ ˜ W + )mode. The enhancement of B (˜ u → ˜ u h ) for increased | δ uRL | is partly also causedby the enhanced ˜ t L component and, more importantly, by the increased coupling of˜ u ˜ u h which contains a term proportional to T U . Note that in such scenarios squarkdecays could be additional sources of the Higgs boson. The asymmetry with respect to δ uRL = 0 follows from the ˜ t L - ˜ t R mixing term (= − m t µ cot β = 0 (see Eq.(4))) whichalready induces some ˜ t L component in ˜ u , (see Table 3). As for the δ uRL dependence10 δ u RR δ uLL X(a) . . . . . . δ u RR δ uLL X(b) . . . . . . Figure 2: Contours of (a) B (˜ u → c ˜ χ ) and (b) B (˜ u → t ˜ χ ) (solid lines) in the δ uLL − δ uRR plane where all of the conditions (i)-(v) except the b → sγ constraint are satisfied.Contours of 10 × B ( b → sγ ) (dashed lines) are also shown. The condition (i) requires2 . < × B ( b → s γ ) < . B ( u X ) -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 δ uRL ~ x ~ ~ ~ ~ ~ ~ + (a) u c χ u t χ u b χ B ( u X ) -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 δ uRL ~ x ~ ~~ ~ ~ ~ + ~ ~ (b) u c χ u t χ u b χ u u h Figure 3: δ uRL dependences of the (a) ˜ u and (b) ˜ u decay branching ratios. Theshown range of δ uRL is the whole range allowed by the conditions (i) to (v) given inthe text; note that the range | δ uRL | > ∼ . u , decay branching ratios, we have obtained results similar to those for the δ uRL dependence in Fig.3. We now study effects of the squark generation mixing on QFV signals at LHC. Thelarge B (˜ u i → c ˜ χ ) and B (˜ u i → t ˜ χ ) ( i = 1 ,
2) may result in a sizable rate for thefollowing QFV signals: p p → ˜ u , ¯˜ u , X → c ¯ t ˜ χ ˜ χ X, t ¯ c ˜ χ ˜ χ X, (14)where X contains only beam-jets and the ˜ χ ’s give rise to missing transverse energy E misT . The corresponding cross sections are given by σ ijct ≡ σ ( pp → ˜ u i ¯˜ u j X → c ¯ t ( t ¯ c ) ˜ χ ˜ χ X ) ≡ σ ( pp → ˜ u i ¯˜ u j X → c ¯ t ˜ χ ˜ χ X ) + σ ( pp → ˜ u i ¯˜ u j X → t ¯ c ˜ χ ˜ χ X )= σ ( pp → ˜ u i ¯˜ u j X )[ B (˜ u i → c ˜ χ ) · B (¯˜ u j → ¯ t ˜ χ ) + B (˜ u i → t ˜ χ ) · B (¯˜ u j → ¯ c ˜ χ )] . (15)We calculate the relevant squark-squark and squark-antisquark pair production crosssections at leading order using the WHIZARD/O’MEGA packages [33, 34] where wehave implemented the model described in Section 2 with squark generation mixingin its most general form. We use the CTEQ6L global parton density fit [35] for theparton distribution functions and take Q = m ˜ u i + m ˜ u j for the factorization scale, where˜ u i and ˜ u j are the squark pair produced. The QCD coupling α s ( Q ) is also evaluated(at the two-loop level) at this scale Q. We have cross-checked our implementation ofQFV by comparing with the results obtained using the public packages FeynArts [36]and FormCalc [37].Defining QFC production cross sections as σ ijq ¯ q ≡ σ ( pp → ˜ u i ¯˜ u j X → q ¯ q ˜ χ ˜ χ X )= σ ( pp → ˜ u i ¯˜ u j X ) · B (˜ u i → q ˜ χ ) · B (¯˜ u j → ¯ q ˜ χ ) ( q = c, t ) , (16)we obtain the following cross sections at the center-of-mass energy E cm =14 TeV [7TeV] in the scenario of Table 1: σ ct = 172.8 [11.8] fb, σ ct = 11.5 [0.41] fb, σ c ¯ c = 131.4129.0] fb, σ c ¯ c = 6.3 [0.23] fb, σ t ¯ t = 56.8 [3.89] fb, σ t ¯ t = 5.2 [0.19] fb. The expectednumber of the c ¯ t / t ¯ c production events of Eq. (14) is L · P i,j =1 , σ ijct ≃ L = 100 f b − [1 f b − ] at LHC with E cm =14 TeV[7 TeV].The main contribution to σ ( pp → ˜ u i ¯˜ u i X ) ( i = 1 ,
2) comes from the subprocess gg → ˜ u i ¯˜ u i . The gluon-˜ u i -˜ u j coupling vanishes for i = j due to the color SU(3) symmetry.Therefore, σ ( pp → ˜ u i ¯˜ u j X ) and hence σ ijct , σ ijc ¯ c and σ ijt ¯ t are very small for i = j , e.g.O(0.01) fb [O(10 − ) fb] for ( i, j ) = (1 ,
2) at E cm =14 TeV [7 TeV]. We have foundthat the production cross sections of the quark pair ( c ¯ t , t ¯ c , c ¯ c , t ¯ t ) plus two ˜ χ ’s and n ν ’s ( n = 0 , , , . . . ) via production of the heavier up-type squarks ˜ u i ( i ≥
3) are verysmall in this scenario.In Fig.4 we show the δ uRR dependences of the QFV production cross sections σ iict ( i = 1 ,
2) at E cm = 7 and 14 TeV, where all basic parameters other than M U arefixed as in the scenario of Table 1. The QFV cross sections at 14 TeV are about anorder of magnitude larger than those at 7 TeV. We see that the QFV cross sectionsquickly increase with increase of the QFV parameter | δ uRR | around δ uRR = 0 andthat they can be quite sizable in a wide allowed range of δ uRR . The mass of ˜ u (˜ u )decreases (increases) with increase of | δ uRR | . This leads to the increase of σ ct and thedecrease of σ ct with increase of | δ uRR | . σ ct vanishes for | δ uRR | > ∼ .
76, where the decay˜ u → t ˜ χ is kinematically forbidden. We have ˜ u = ˜ u R for | δ uRR | > ∼ .
9, which explainsthe enhancement of σ ( pp → ˜ u ¯˜ u X ) and the vanishing of σ ct for | δ uRR | > ∼ .
9. Notethat in case ˜ u = ˜ u R , the subprocess u ¯ u → ˜ u (= ˜ u R )¯˜ u (= ¯˜ u R ) via t-channel gluinoexchange also can contribute to σ ( pp → ˜ u ¯˜ u X ).We have also studied the δ uRL dependence of the QFV production cross sections σ iict ( i = 1 ,
2) at E cm = 7 TeV and 14 TeV, where all basic parameters other than T U are fixed as in the scenario of Table 1. We find that the QFV cross sections arerather insensitive to the QFV parameter δ uRL and that they can be large in a wideallowed range | δ uRL | < ∼ . σ ct ∼
170 [10] fb, σ ct ∼
10 [0.4] fb at E cm =14 TeV [7TeV]. The masses of ˜ u , decrease (and hence the cross sections σ ii ( i = 1 ,
2) increase)and the branching ratios B (˜ u , → c/t ˜ χ ) tend to decrease with increase of | δ uRL | .This implies that the QFV cross sections are rather insensitive to δ uRL . As for the δ uRL dependence of σ iict ( i = 1 ,
2) we have obtained similar results to those for the δ uRL dependence. 13 σ ( pp X ) ( f b ) -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 δ uRR x(a) ct ct ct σ (7TeV) σ (14TeV) σ (14TeV) σ (7TeV) σ (7TeV) σ (7TeV) 0.11101001000 σ ( pp X ) ( f b ) -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 δ uRR ctct ct x(b) σ (14TeV) σ (7TeV) σ (7TeV) σ (14TeV) σ (7TeV) σ (7TeV) Figure 4: δ uRR dependences of (a) σ ≡ σ ( pp → ˜ u ¯˜ u X ), σ ct and (b) σ ≡ σ ( pp → ˜ u ¯˜ u X ), σ ct at E cm = 7 and 14 TeV. The point ”x” of δ uRR = 0 . δ uRR is the whole range allowed bythe conditions (i) to (v) given in the text; note that the range | δ uRR | > ∼ . m ˜ u > m ˜ χ in (iii).The large ˜ c R - ˜ t R mixing could also give rise to the following QFV production crosssections: σ ijtt ≡ σ ( pp → ˜ u i ˜ u j X → t t ˜ χ ˜ χ X )= σ ( pp → ˜ u i ˜ u j X ) · B (˜ u i → t ˜ χ ) · B (˜ u j → t ˜ χ ) ( i, j = 1 , , (17)where X contains only beam-jets. Here the ˜ u i ˜ u j pair (with ˜ u i,j ∼ ˜ c R +˜ t R in the scenariounder consideration) is produced mainly via a t-channel gluino exchange subprocess c c → ˜ u i ˜ u j with c being the charm-quark in the beam proton. Note that the signalevent ”top-quark + top-quark + E misT + beam-jets” can practically not be producedin the MSSM with QFC (nor in the SM). It turns out however that in the scenario ofTable 1 the corresponding cross section σ tt ≡ σ tt + σ tt is at most O(0.1) fb at E cm =14TeV and hence that it might be relevant for a very high luminosity [38]. Thereforethis QFV process will not be discussed further.In addition, we study QFV in production and decays of squarks at LHC for aQFV scenario based on the mSUGRA scenario SPS1a’ [39] which has served as inputfor several experimental studies. The high energy inputs at the GUT scale M GUT =2 . × GeV in the scenario SPS1a’ are taken as m =70 GeV, m / =250 GeV, A = −
300 GeV and µ > β ( m Z )=10. Here m , m / and A are the common scalar mass, gaugino mass and trilinear coupling at the GUT scale,14 Qαβ β = 1 β = 2 β = 3 α = 1 (526) α = 2 α = 3 M M M µ tan β m A
103 193 572 398 10 373 T U T U T U T D T D T D -0.007 -2.68 -488 -0.19 -3.26 -128 M Dαβ β = 1 β = 2 β = 3 α = 1 (505) α = 2 α = 3 M Uαβ β = 1 β = 2 β = 3 α = 1 (508) α = 2 (280) α = 3 (387) Table 4: The MSSM parameters at the scale Q=1 TeV in the QFV scenario based onthe SPS1a’ scenario. T Uαβ and T Dαβ are set to zero for α = β . All mass parametersare given in GeV. Note that M U =0 in the original SPS1a’ scenario.respectively. We use SPheno v3.0 [30] to obtain the resulting MSSM parameters at thescale Q=1 TeV according to the SPA convention [39]. At this scale, we add the QFVparameters (i.e. the squark generation mixing parameters) and vary them aroundzero (i.e. around the MFV scenario). An example set of the MSSM parameters thusobtained is given in Table 4 and the resulting mass spectrum and the up-type squarkcompositions in the flavour eigenstates in Tables 5 and 6, respectively. In this scenarioone has δ uLL = 0, δ uRR = 0 . δ uRL = δ uRL = 0 for the QFV parameters at thescale Q=1 TeV. Note that the resulting squark and gluino masses are smaller thanthose in the scenario of Table 1. We have checked that all of the constraints in Section3 are fulfilled in this scenario. For the important squark decay branching ratios weobtain B (˜ u → c ˜ χ ) = 0 . , B (˜ u → t ˜ χ ) = 0 . , B (˜ u → c ˜ χ ) = 0 . , B (˜ u → t ˜ χ ) = 0 . u (˜ u ) is dominated by astrong mixture of the flavour eigenstates ˜ t R , ˜ t L and ˜ c R (˜ t L and ˜ c R ) and ˜ χ is nearlythe U(1) gaugino ˜ B which couples to the right up-type squarks sizably. This explainsthe sizable branching ratios of B (˜ u → c ˜ χ ), B (˜ u → t ˜ χ ) and B (˜ u → c ˜ χ ) and thevery small B (˜ u → t ˜ χ ). In this scenario we obtain the following cross sections at thecenter-of-mass energy E cm =14 TeV [7 TeV]: σ ct = 119.7 [11.8] fb, σ ct = 0.197 [0.01] fb.Note that the QFV decay branching ratios B (˜ u , → c/t ˜ χ ) are significantly smallerthan those in the scenario of Table 1, but that the QFV production cross section σ ct is nevertheless large due to the lighter squarks in this scenario based on SPS1a’.15 u ˜ u ˜ u ˜ u ˜ u ˜ u
332 541 548 565 565 612 ˜ d ˜ d ˜ d ˜ d ˜ d ˜ d
506 547 547 547 571 571˜ g ˜ χ ˜ χ ˜ χ ˜ χ ˜ χ ± ˜ χ ±
608 98 184 402 415 184 417 h H A H ±
112 426 426 434Table 5: Sparticles, Higgs bosons and corresponding physical masses (in GeV) in thescenario of Table 4. | R ˜ uiα | ˜ u L ˜ c L ˜ t L ˜ u R ˜ c R ˜ t R ˜ u u u u u u R ˜ uiα , at the scale Q=1 TeV for the scenario ofTable 4.In Fig.5 we show the δ uRR dependence of the QFV production cross section σ ct at E cm = 7 TeV and 14 TeV, where all basic parameters other than M U ( Q = 1 T eV ) arefixed as in the scenario of Table 4. σ ct is very small due to the very small B (˜ u → t ˜ χ ).We see that the QFV cross section increases with increase of the QFV parameter | δ uRR | and that it can be quite sizable in a wide allowed range of δ uRR . The mass of ˜ u decreases and B (˜ u → c ˜ χ ) · B (˜ u → t ˜ χ ) increases with increase of | δ uRR | . This leadsto the increase of σ ct with increase of | δ uRR | . σ ct vanishes for | δ uRR | > ∼ .
62, where thedecay ˜ u → t ˜ χ is kinematically forbidden.Finally, we briefly discuss the detectability of the QFV production process pp → ˜ u i ¯˜ u i X → c ¯ t ( t ¯ c ) ˜ χ ˜ χ X ( i = 1 ,
2) at LHC. The signature is ’(anti)top-quark + charm-jet+ E misT + X ’, where X contains beam-jets only. Therefore, identifying the top-quarksin the final states is mandatory. This should be possible by using the hadronic decays ofthe top-quark. Charm-tagging would also be very useful. There is another QFV signal16 RR23 δ -0.6 -0.4 -0.2 0 0.2 0.4 0.6 ( pp - > X ) ( f b ) σ -2 -1
10 110
10 (14 TeV) σ (7 TeV) σ (14 TeV) ct11 σ (7 TeV) ct11 σ (7 TeV) ct11 σ x Figure 5: δ uRR dependences of σ ≡ σ ( pp → ˜ u ¯˜ u X ) and σ ct at E cm = 7 TeV and 14TeV. The point ”x” of δ uRR = 0 . δ uRR is allowed by the conditions (i) to (v) given in the text.process leading to the same final states, i.e. gluino production and its QFV decay [15] pp → ˜ g ˜ χ X → c ¯ t ( t ¯ c ) ˜ χ ˜ χ X . This cross section is, however, about a factor of 20-30smaller than that of the QFV process via squark pair production in the scenariosstudied here. This suppression is mainly due to the electroweak interactions involved.The QFV production process pp → c ¯ t ( t ¯ c ) X via SUSY-QCD one-loop diagrams [40] alsoyields the signature ’(anti)top-quark + charm-jet + X’. The size of the cross sectionof this process is of the same order as that of our QFV process Eq.(14). However, themissing- E T would be much smaller than that in our signal process Eq. (14).If charm-tagging is not possible, one should search for the process pp → ˜ u i ¯˜ u i X → q ¯ t ( t ¯ q ) ˜ χ ˜ χ X ( q = t, b ), i.e. for the signature ’(anti)top-quark + jet + E misT + X ’.Main backgrounds are single top-quark productions in the SM. The most importantone is due to tW production where the W-boson decays into a tau-lepton which thendecays hadronically: pp → tW X → tτ νX → t τ -jet ν ¯ νX . The cross section for thetW production σ ( pp → tW − X ) + σ ( pp → ¯ tW + X ) is about 66 pb for E cm =14 TeV[41]. It turns out that the W-boson is mainly produced in the central region (seee.g. [42]). To reduce this background one can use the fact that a charm-quark jet hasusually a much higher particle-multiplicity than the τ -jet. By requiring that at leastfour hadrons are contained in the jet, this background cross section can be reduced to17bout 12 fb for E cm = 14 TeV without significant loss of our QFV signal events. Onecan expect that it is much smaller than 12 fb for E cm = 7 TeV. In the case that oneconsiders only hadronic decays of the top-quark, one can require in addition that theinvariant mass of each jet is larger than the tau-lepton mass, which should reduce thisbackground further again without significant loss of our signal events.The second important background is single top-quark production due to t-channelW-boson exchange in the SM. Relevant for us is the reaction pp → t (¯ t ) q (¯ q ) Z X → t (¯ t ) q (¯ q ) ν ¯ νX , where the main contribution is due to W-boson exchange in the t-channel(quite similar to pp → t q X , for which a thorough treatment is given in [17]). Usingthe WHIZARD/O’MEGA package [33, 34] we have calculated the corresponding crosssections and obtained at E cm = 14 TeV [7 TeV]: σ ( pp → tqZ X → tqν ¯ νX ) = 97.4 [17.5] fb, σ ( pp → t ¯ qZ X → t ¯ qν ¯ νX ) = 15.9 [1.89] fb, σ ( pp → ¯ tqZ X → ¯ tqν ¯ νX ) = 46.0 [7.1] fb, σ ( pp → ¯ t ¯ qZ X → ¯ t ¯ qν ¯ νX ) = 13.2 [1.6] fb,where the cross sections summed over q = u, d, c, s are shown. Comparing these toFigs. 4 and 5 we see that for | δ uRR | > ∼ .
45 our signal cross section is larger than thesum of these background cross sections. For | δ uRR | < ∼ .
45 a suitable E misT cut willreduce this background relatively to our signal because the E misT due to ν ¯ ν from the Z decay will on the average be smaller than that due to the two neutralinos.The cross section of single top-quark production via s-channel W-boson exchange ismuch smaller than that of our QFV process. We obtain for E cm = 14 TeV [7 TeV]: σ ( pp → ” W + ” Z X → t ¯ bν ¯ νX ) = 1.42 [0.45] fb, σ ( pp → ” W − ” Z X → ¯ tbν ¯ νX ) = 0.73 [0.18] fb.There could be another background from the QFC top-quark pair production processes(a) pp → ˜ u i ¯˜ u i X → t ¯ t ˜ χ ˜ χ X and (b) pp → t ¯ tZ X → t ¯ tν ¯ νX , where one of the W-bosons from the top-quarks decays leptonically with the charged lepton being missed.However, the probability of such W-boson decay would be very small. Moreover, thesetop-quark pair production cross sections are not so large compared to our QFV crosssections. For the process (a), for example, we see that σ iit ¯ t < σ iict ( i = 1 ,
2) in thescenario studied as shown just after Eq. (16). For (b) we obtain at E cm = 14 TeV [7TeV]: σ ( pp → t ¯ tZ X → t ¯ tν ¯ νX ) = 97.6 [13.8] fb.Of course, a detailed Monte Carlo study including detector effects is required fora proper assessment of the detectability of the proposed QFV signal. However, this18s beyond the scope of this paper and will be presented in a forthcoming publication[43]. To conclude, we have studied the effects of squark mixing of the second and thirdgeneration, especially ˜ c L/R - ˜ t L/R mixing, on squark production and decays at LHC inthe MSSM. We have shown that the effect can be very large in a significant region ofthe QFV parameters despite the very strong constraints on QFV from experimentaldata on B mesons. The QFV squark decay branching ratios B(˜ u i → c ˜ χ ) and B(˜ u i → t ˜ χ ) ( i = 1 ,
2) can be very large (up to ∼ pp → c ¯ t ( t ¯ c ) + E misT + beam-jets’ with a significant rate atLHC. The observation of these remarkable signatures would provide a powerful testof supersymmetric QFV at LHC. Therefore, in the squark search one should take intoaccount the possibility of significant contributions from QFV squark decays. Moreover,one should also include the QFV squark parameters (i.e. the squark generation mixingparameters) in the determination of the basic SUSY parameters at LHC. Acknowledgments
This work is supported by the ”Fonds zur F¨orderung der wissenschaftlichen Forschung(FWF)” of Austria, project No. P18959-N16. The authors acknowledge supportfrom EU under the MRTN-CT-2006-035505 network program. B. H. and W. P. aresupported by the DFG, project No. PO 1337/1-1. The work of B. H. is supported inpart by the Landes-Exzellenzinitiative Hamburg. W. P. is supported by the Alexandervon Humboldt Foundation and the Spanish grant FPA2008-00319/FPA.
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