The Effects of Non Standard Neutrino Interactions (NSIs) in 5 1 K0 π0νν,B+ π+νν,B+ K +νν and 0 L ∗ 2 → → → B X νν n s → u J Shakeel Mahmood(1); Farida Tahir; Azeem Mir 6 Comsats Institute of Information Technology, 1 Department of Physics, Park Road, Chek Shazad,Islamabad ] (1) h shakeel [email protected] p - p e Abstract h WestudytheraredecaysK0 →π0νν,B+ →π+νν,B+ →K∗+ννand [ L B → X νν for the search of NSIs. We want to constraint the NSIs by s 2 usingthesereactions. Weshowthatthereisastrongdependenceofthese v reactionsonnewphysicsfreeparameterǫQL,whereQ=u,c,t. Weinclude ττ 3 second and third generation of quarks in the loop for these decays. We 8 show that the K0 →π0νν is providing very precise bounds as compared 8 L toall othersemileptonic decays,havingneutrinosin theirfinalstate. We 4 further show that the interference between standard model and NSIs is 0 . giving dominant contribution for B+ → π+νν,B+ → K∗+νν and B → 1 X νν. WepointoutthattheconstraintsforǫcL andǫtL aremoreprecise 0 asscompared to ǫuL. The analysis of B+ →ττπ+νν,Bττ+ → K∗+νν and 5 ττ B → X νν, provide us that the u quark induced Br of NSIs are giving 1 s veryverysmallcontribution. Wealsocomparethesedecaystothedecays : v of charm and kaonshaving neutrinos in thefinal state. i Keywords: NSIs;rare decays; B decays. X PACS numbers: 12.60.-i, 13.15.+g, 13.20.-v r a 1 Introduction After the remarkable discovery of Higgs by the ATLAS [1] and CMS [2] col- laboration and confirmation in [3] that it is Standard Model (SM) higgs, one importantquestionarises. Isthereanyroomfornewphysics(NP)beyondSM? No doubt SM predictions have been verifiedexperimentally to the highest level of precision [4][5]. But, along with other limitations, SM lacks any explana- tion for a possible pattern for particle mass, known as mass hierarchy problem. SM can not predict top quark mass without experimental evidence. The ex- periments on B meson [6][7][8] are also giving some cracks in standard model. 1 We are yet unable to explain dark matter and matter anti-matter asymmetry. Gravity is not included in the SM. Theoretically SM is thought to be unsat- isfactory and there can be some new particles as well as new interactions. It has been believed that standard model is a low energy approximation of more generaltheory. So,manytheoreticalextensionsofSMhasbeenpresented. But, so far, the only concrete evidence against it has been provided by the neutrino oscillations [9] [10][11][12][13][14][15]. To explore NP the study of mesonic rare decays involving neutrinos in final state, can be interesting. These decays pro- ceeds through flavor changing neutral currents (FCNC), highly suppressed [16] due to GIM mechanism [17] and occur at loop level [18][19]. The discrepancies betweenexperimentsandtheory(SM)forsuchreactionsprovideusanexcellent windowtowardsNP.Newparticlescanbe addedinthe loopstoimprovetheory orwecanhavenewinteractions. So,FCNCreactionsinvolvingneutrinosinthe final state can be interesting. Theoretically, B+ π+νν and K0 π0νν thought to be more clean than → L → K+ π+νν because it has only top quark contribution and no contribution → from charm sector. Non standard neutrino interactions (NSIs) of K+ π+νν → and D+ D+νν are studied in [20] and [21] respectively and constrained are s → foundforǫuL. The NSIs constraintsforthree generationsofquarksaregivenin ττ [22] As all of these have same loop structure, so, similar thing should happen to B+ π+νν and K0 π0νν. Two more loop level processes useful for the searcho→f new physics aLre→inclusive B X νν and exclusive B+ K∗+νν due s → → to their theoretical cleanliness [23]. In this paper we the scheme of study is as: first of all we give experimental status of B+ π+νν,K0 π0νν,B+ K∗+νν and B X νν then we → L → → → s revise the SM contribution of these reaction. Next, we study these reactions in NSIs with u quark in the loop which is the usual case of NSIs and obtain the constraints ǫuL. Then we modify the operators for c and t quarks. and find ττ out the constraints ǫcLand ǫtL.We compare these constraints among the three ττ ττ generations. We also compare these constraintsto the constraints of same type of reactions from D and K decays. Then discussion and results are provided and conclusion is given at the end. 2 Experimental Status of B+ π+νν Decay → B decays are being studied in the detectors like CLEO, CDF, BaBar, Belle, ALEPH collaborations and LHCb but the decays involving neutrinos in the final state will be tested at super B factories in experimentally clean environ- ment. The detection of B+ π+νν is a hard task and currently we have only → experimental bound for this reaction but this will be in the range of super B factories. The experimental bound is given in the Table 1 along with their SM prediction. Current experimental bounds for this are < 9.8 10−5but our ex- × perience with K+ π+νν guide us that the experimental value should be of the orderof10−7.It→meanswearenotdiscardingthe SMvaluesbutjustsearch- ing for the small room for new physics. Experimental value for K0 π0νν is L → 2 Figure 1: SM b decays to d netrino antinetrino <2.6 10−8[36]. B+ K∗+νν is easy to measure experimentally because we × → havevector particle in the final state, so polarizationdoes matter andits latest bound is <4 10−5. × Inclusive process B X νν are very difficult to observe experimentally be- s → causeweneedtotagalltheparticlesinvolveinX alongwithmissingneutrinos. s The limit available till to date is <64 10−5, given in table 1 with reference. × 2.1 M M/νν Decays in the Standard Model → Here mass of M > mass of M/and both are representing the mesons. The SM calculation can be divided into two categories, short distance and long distance..This can be found from [24] [25] [26] and [27] that the dominant con- tributionfor M M/νν comes fromshortdistance because longdistance con- tribution is 10−3→less than short distance, if the quark level process is b dνν → or s dνν. The quark level process for our decay is b dνν which can be → → represented by the feynman diagrams shown in figure 1. In such reactions we can easily separate hadronic interactions from leptonic interaction. For B decays the dominant contribution comes from the short distance just like K decays and we use perturbation theory due to asymptotic freedom. The effective Hamiltonian for such reactions quark level reaction will be G α HeSfMf = √F22πsinem2θWα,β=Σe,µ,τVt∗bVtdX(xt))×(db)V−A(νανβ)V−A where V A in the subscript represents the vector and axial vector current − 3 respectively. Forsuchreactionscharmquarkcontributioninthe loopis negligi- ble in contrast to K decay due to smallness of off diagonal CKM element and X(x ) is the loopintegraloftop-quarkexchange[19]. For this reactionwe have t two penguin and one box diagram [30] and sum of all give the contribution x x +2 3x 6 X(x )=η t[ t + t− lnx ] t X 8 x 1 (x 1)2 t t t − − Here x = m2t and η = 0.985 is QCD small distance correction. By using t m2w X above Hamiltonian we can obtain Br as 3α2 Br(B+ π+νν) =r em V∗V X(x )2Br(B+ π0l+ν ) → SM iso V 22π2sin4θ | tb td t | −→ l ub W | | r 0.94 is the isospin breaking effect for B. It is discussed for K mesons in iso ≃ [32] which depends on at least three things (1) mass effect (2) a suppression of about 4% in neutral form factor comes from η π mixing and (3) about 2% − suppression due to absence of log leading correction. The reaction B+ K∗+υυ,proceed through quark level process b sνν −→ → and the effective Hamiltonian is same except to replace d with s. Here we do nothaveatreelevelreactionfornormalizationsowehavetouseB+ ρ0l+ν l −→ 3α2 Br(B+ K∗+νν) =r em V∗V X(x )2Br(B+ ρ0l+ν ) → SM iso V 22π2sin4θ | tb ts t | −→ l ub W | | For B X νν again the effective Hamiltonian is same except to replace d s → with s,and we do not have a tree level process like B+ π0l+ν . So we have l −→ to normalize with the process B X νν and due to different phase spaces for c → X and X ,we have to include other factors. The Br will be s c 3α2 V V X(x ) η Br(B X νν) = em ts tb t 2 Br(B X lν ) → s SM 4π2sin4θW| Vcb | f(z)κ(z) −→ c l where f(z)=1 8z+8z3 z4 12z2ln(z) with z = m2c − − − m2b and κ(z)=0.88, η =κ(0)=0.83. Ausefuldiscussioncanaboutthefactorscanbefoundin[27]and[30]. With the latest values of the constants we have the Br Br(B X νν) =3.6 10−5 c SM → × K0 π0νν along with K+ π+νν is thought to be theoretically clean reac- L → → tions for the search of new physics. The effective Hamiltonian for K0 π0νν L → can be written as G α HeSfMf = √F22πsinem2θWα,β=Σe,µ,τVt∗sVtdX(xt))×(ds)V−A(νανβ)V−A 4 Figure 2: NSIs b decays to d neutrino antineutrino and the Br can be extracted by normalizing with tree level reaction, so that all the hadronic uncertainties are absorbed 3α2 τ(K0) Br(K0 π0νν) =R em L V∗V X(x )2Br(K+ π0e+ν ) L → SM iso V 216π2sin4θ τ(K+)| ts td t | −→ e ub W | | Here isospin symmetry is exploited as π0 (ds)V−A K0 = π0 (su)V−A K+ h | | i h | | i and isospin breaking effect is R = 0.94, and other values from [36] are used iso to obtained the Br Br(K0 π0νν) =2.06 10−11 L → SM × 2.2 Model Independent Approach The NSI for the process is shown by the Fig 2 and represented by G α Λ HeNfSfI = √F2(Vt∗bVtq4πsinem2θWǫuαLβlnmw)×(νανβ)V−A(qb)V−A We useV =(4.15 0.49) 10−3andBr(B+ π◦l+ν )=(7.78 0.28) ub l 10−5 to find out Br ± × −→ ± × 5 α2 Λ Br(B+ π+υυ) =r em V∗V ǫuLln 2Br(B+ π0l+ν ) −→ NSI iso Vub 28π2sin4θW| ub ud αβ mw| −→ l | | Although the current experimental results of B decays are narrowing the gape between theory and experiments but when we will get more precise ex- perimental data than we will need more accurate theoretical results. With the assumption that experiments will give us the value of 10−7,we can constraint the NSIs from this reaction. As α and β can be any lepton we take them as τ,because for other leptons we have already more precise constraints [33]. Similarly NSIs Br of B+ K∗+υυ can be found as −→ α2 Λ Br(B+ K∗+υυ) = em V∗V ǫuLln 2Br(B+ ρ0l+ν ) −→ NSI Vub 28π2sin4θW| ub us αβ mw| −→ l | | For B X νν NSIs Br s → α2 V V Λ η Br(B X νν) = em us ubǫuLln 2 Br(B X lν ) → c NSIs 16π2sin4θW| Vcb αβ mw| f(z)κ(z) −→ c l α2 Λ Br(K0 π0υυ) =r em V∗V ǫuLln 2Br(K+ π0e+ν ) L −→ NSI iso Vub 216π2sin4θW| ub ud αβ mw| −→ e | | 2.3 Inteference between Standard Model and NSIs For all above decays the dominant contributionis coming from the interference between the SM and NSIs. The Br of interference are obtained as 2α2 Λ Br(B+ π+υυ) =r em V∗V X(x )V∗V ǫuLln Br(B+ π0l+ν ) −→ Interference iso Vub 28π2sin4θW| tb td t ub ud αβ mw| −→ l | | 2α2 Λ Br(B+ K∗+υυ) =r em V∗V X(x )V∗V ǫuLln Br(B+ ρ0l+ν ) −→ Interference iso Vub 28π2sin4θW| tb ts t ub us αβ mw| −→ l | | α2 Λ η Br(B X νν) = em V V X(x )V V ǫuLln Br(B X lν ) → c Interference 16π2sin4θW Vcb | ts tb t us ub αβ mw|f(z)κ(z) −→ c l | | 2α2 Λ Br(K0 π0υυ) =r em V∗V X(x )V∗V ǫuLln Br(K+ π0e+ν ) L −→ Interference iso Vub 216π2sin4θW| ts td t ub ud αβ mw| −→ e | | The contribution from interference for B decays is is so large as compared to the NSIs that NSIs effects can easily be ignored. So that the bounds on the constraints are obtained from the interference only. But for the K0 the L Br(K0 π0υυ) is 10−3less than the Br(K0 π0υυ) , so L −→ Interference L −→ NSIs the contribution is ignored. The numerical values are given in table 1 and 2. 6 2.3.1 c-quark in the Loop For c-quark we have to modify the operators as and obtain the constraints 2α2 Λ Br(B+ π+υυ) =r em V∗V X(x )V∗V ǫuLln Br(B+ π0l+ν ) −→ Interference iso Vub 28π2sin4θW| tb td t cb cd αβ mw| −→ l | | ǫcL 1.5 ττ ≤ 2α2 Λ Br(B+ K∗+υυ) =r em V∗V X(x )V∗V ǫuLln Br(B+ ρ0l+ν ) −→ Interference iso Vub 28π2sin4θW| tb ts t cb cs αβ mw| −→ l | | ǫcL 1.5 ττ ≤ For B X νν the Br and constraints are s → α2 Λ η Br(B X νν) = em V V X(x )V V ǫuLln Br(B X lν ) → c Interference 16π2sin4θW Vcb | ts tb t cs cb αβ mw|f(z)κ(z) −→ c l | | ǫcL 0.8 ττ ≤ 2α2 Λ Br(K0 π0υυ) =r em V∗V X(x )V∗V ǫcL ln Br(K+ π0e+ν ) L −→ Interference iso Vub 216π2sin4θW| ts td t cb cd αβ mw| −→ e | | 2.3.2 t-quark in the Loop With t-quark we have following operator and constraint 2α2 Λ Br(B+ π+υυ) =r em V∗V X(x )V∗V ǫtL ln Br(B+ π0l+ν ) −→ Interference iso Vub 28π2sin4θW| tb td t tb td αβ mw| −→ l | | ǫtL 1.5 ττ ≤ 2α2 Λ Br(B+ K∗+υυ) =r em V∗V X(x )V∗V ǫtL ln Br(B+ ρ0l+ν ) −→ Interference iso Vub 28π2sin4θW| tb ts t tb ts αβ mw| −→ l | | ǫtL 1.5 ττ ≤ For B X νν the Br and constraints are s → α2 Λ η Br(B X νν) = em V V X(x )V V ǫtL ln Br(B X lν ) → c Interference 16π2sin4θW Vcb | ts tb t ts tb αβ mw|f(z)κ(z) −→ c l | | ǫtL 0.8 ττ ≤ 2α2 Λ Br(K0 π0υυ) =r em V∗V X(x )V∗V ǫuLln Br(K+ π0e+ν ) L −→ Interference iso Vub 216π2sin4θW| ts td t tb td αβ mw| −→ e | | 7 Reaction Theoretical Experimental NSIs with u NSIs with c NSIs with t B+ π+υυ 3 10−8 1 10−7 1 10−7 −→ 1.5 10−7 <9.8 10−5 × × × B(ub)−→X(υdυu)υυ ×[35] [3×6] ǫ˜uτ1τL0−≤81.5 ǫ1cτLτ ≤101−.55 ǫ1tτLτ ≤101−.55 −→ s 3.6 10−5 <64 10−5 × × b−→sυυ × [×37] ǫuττL ≤0.8 ǫcτLτ ≤0.8 ǫtτLτ ≤0.8 B+ K∗+υυ ˜10−8 1.5 10−6 1.5 10−6 −→ 3.56 10−6 <4 10−5 × × ub (us) υυ × × ǫuL 1.5 ǫcL 1.5 ǫtL 1.5 −→ ττ ≤ ττ ≤ ττ ≤ Table 1: Comparison of the contstraints for B decays 3 Discussion and results We study threeprocessesB+ π+υυ,B+ K∗+υυ (exclusive)andB −→ −→ −→ X υυ (inclusive). whicharetheoreticallycleanprocesses. So,theseareidealfor s the search of new physics. Very high Br of B+ π+υυ and B+ K∗+υυ −→ −→ making it very attractive for the experimentalists too. Although, B X υυ s −→ is very difficult to detect but it is much clean as compared to any other rare decay that’s why it is studied for the search of new physics. The results are summarizedintable1andplotsareprovidedinfigures3,4,5,6,7and8tomake the comparison more clear. The constraints on NSIs with the decays of charm and kaon rare decays involving neutrinos in their final states are calculated in [21][22][34], whichgiveverypreciseconstraintsO(10−2)forthe uptype quarks. ForthecharmandkaonstheinterferencebetweenthestandardmodelandNSIs isverysmall,O(10−3)lessthanNSIs. But,forthecaseofB raredecayshaving two neutrinos in their final state the dominant contribution is coming from the interference. One more difference is that for charm and kaons the Br of first andsecondgenerationaregivinghighervalues,but,forBthecontributionfrom secondandthirdgenerationisprovidingleadingcontributionascomparedtothe firstgeneration. Asforasthecomparisonwithinthegenerationisconcernedwe aregetting moreprecise constraintswith secondgenerationof quarks(c quark) for B, D and K rare decays having neutrino in final state. But, the constrains fromB decaysarelesspreciseforu-quarkthanDandKdecays. Itiscontraryto theusualNSIs,inwhichthedominatecontributioncomesfromu-quarkinduced processes. The rare B decays will be in the range of much clean environment of the B factories. That’s why the analysis of such reaction is very important for the new physics. We analysis K0 π0υυ for the study of NSIs with L −→ three generations of quarks which provides even be more precise constraints as comparedtoDandKdecaysofsametype. TheconstraintforK0 π0υυ are O(10−3) for all the generations but the Br for third generationLs−is→very small and can be ignored. This is shown in figures 9,10 and 11. 8 Figure3: uquarkinducedNSIsofB+DecaystoPi+,neutrinoandantineutrino Figure4: cquarkinducedNSIsofB+DecaystoPi+,neutrinoandantineutrino Reaction Theoretical Experimental NSIs with u NSIs with c NSIs with t 1.4 10−11 1.5 10−11 3 10−17 K(uL0b)−−→→(dπu0)υυυυ 2.06×10−11 <2.6[3×6]10−8 ǫuττL×≤O(10−3) ǫcτLτ×≤O(10−3) ǫtτL×τ ≤O(10−3) Table 2: Comparison of the contstraints for KL 9 Figure5: tquarkinducedNSIsofB+DecaystoPi+,neutrinoandantineutrino Figure 6: u quark induced NSIs of B Decays to Xc, neutrino and antineutrino 10