Study some decays for p-326 setup. INR and IHEP collaboration. V.N. Bolotov (INR of RAS)

V. Bolotov (INR of RAS)CERN p Introduction. ISTRA setup. 1. Semilepton radiative decays. 2. Search of tensor interaction. 3. Search of supersymmetric particles. 0. Introduction. ISTRA setup. Some of the decays described later were studied on ISTRA setup(Fig.0) placed on the secondary beam of accelerator of Institute for High Energy Physic (IHEP) in Protvino by INR and IHEP Collaboration.

V. Bolotov (INR of RAS)CERN p-3263 Fig.0. The setup “ISTRA”: S1  S5 – scintillation counters; C1  C4 – Cherenkov gas counters; M1, M2 – beam and spectrometer magnets; PC1  PC6 – proportional chambers; DV – vacuum decay volume; GS – lead glass guard system;DC-1- 16– drift chambers; EC1 and EC2 – lead glass Cherenkov calorimeters; DT1  DT8 – drift tubes; MH – matrix hodoscope; HC – hadron calorimeter; MD – muon detector.

V. Bolotov (INR of RAS)CERN p Semilepton radiative decays K − → π 0 e − ν γ and K − → π 0 μ − ν γ. The decay K − → π 0 e−ν γ is good testing ground for the Chiral Pertubation Theory (ChPT) [1, 2]. This decay amplitudes are calculated at order ChPT O (p4 ) in [1], and branching ratios are evaluated in [3]. Recently next-to- leading O (p6 ) corrections were calculated for the corresponding neutral kaon decay [4]. The K − → π 0 e − ν e γ decay is one of kaon decays where new physics beyond the Standard Model can be probed. This decay is especially interesting as it is sensitive to T-odd contributions. According to CPT-theorem observation of T violation is equivalent to observation of CP violating effects. CP violation is a subject of continuing interest in K and B meson decays. In the standard model the source of CP violation is given by the phase in the CKM matrix[5, 6, 7]. However it has been argued that this source is not enough to explain the observed baryon asymmetry of the universe and new sources of CP violation have to be introduced[8].

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V. Bolotov (INR of RAS)CERN p-3266 T-odd correlation vanishes at tree level of SM[10], but the SUSY theory gives rise to CP- odd (T-odd) observables already at tree level[11, 12, 13]. T-odd asymmetry value for SU (2)L ×SU (2) R ×U (1) model and scalar models was estimated in Ref[14]. In the ISTRA+ report [15] it present the recent results of the analysis of the K − → π 0 e − νγ data 3852 events of this decay have been observed. The ratio Br(K − → π 0 e − νγ)/Bг(K − → π 0 e − ν ) = (0.63 ± 0.02(stat) ± 0.03(syst)) 10 −2 for E* γ > 30 MeV, Ө* eγ > 200. Br(K − → π 0 e − νγ) is found to be (3.05 ± 0.02)10 −4 (assuming PDG value for K e3 branching ratio). Theoretical predictions give Br = −4 (tree level) and Br = −4 (O(p4) level). The obtained value for the asymmetry A(ε) (with the same cuts for E* γ and Ө* eγ ) is A(ε)= −0.015 ± At present it is the best estimate of this asymmetry. First observation of the radiative kaon K − → π 0 μ − νγ decay[16]:. Br(K¯→μ¯ν π 0 γ) = (4.48 ± 0.68(stat) ±0.99(syst)) x 10 −4 for region 30 < E* γ < 60 MeV.Theoretical prediction is 4.67x10 −4. Asymmetry in the T-odd variable ξ for the region 5 < E* γ < 30 MeV A(ξ) = −0.03 ± 0.13.

V. Bolotov (INR of RAS)CERN p-3267 Fig.1a. The contributions to the radiative decays  (K)  е(μ)  in the framework quark model: a) and b) contain IB; c) and d)  SD. (K) (s) (μ)(μ)(μ)(μ)(μ)(μ)(μ)(μ) 2. Search of tensor interaction.

V. Bolotov (INR of RAS)CERN p-3268 The amplitude of the radiative  (K)  е(μ)  (1) decays is traditionally described in two terms corresponding to the inner bremsstrahlung (IB) and structure-dependent (SD) radiation. The IB contribution is closely connected with the  е decay and calculated by using the standard QED methods. The SD term is parameterized by two form factors (F V, F A ) that describe the vector (F V ) and the axial-vector (F A ) weak currents. The matrix element terms of pion decay (1) are given by: M IB =-i(eG F V ud /  2)f  m e   ē[(k/kq–p/pq)  +   q / 2kq](1+  5 ) e (2) M SD =(eG F V ud /  2m  )   [F V e  p  q  +iF A (pqg  -p  q )]e  (1+  5 ) e, (3) where V ud -CKM matrix element, f  = 131 MeV-const. pion decay,   -photon polarization vector, p,k,q - 4-momenta of pion, electron and photon; F V and F A are vector and axial-vector form factors: F V,A (t)= F V,A (0)[1+  V,A t/m  2 ]. po Accordingly to CVC,F V is defined by  0 life time:  F V  =1/  [  2/  m  0 T  0 ]=  The value F A depends on the model and ranges in a wide region from -3F V to 1.4F V. Usually ratio  = F A /F V is considered. The following kinematical variables are used: x = 2E  /m  and y = 2E e /m . It is also convenient to use variable =(x+y-1)/x = y sin 2 (  e  /2). The differential probability  е  decay is given by dW  е  /dxdy =(  W  е /2  ){IB(x,y)+(F V m  2 /2f  m e ) 2 [(1+  ) 2 SD  (x,y)+ +(1-  ) 2 SD  (x,y)]}, (4) where IB and SD  are known functions: IB(x,y)=(1–y)[(1–x) 2 +1]/x 2 (x+y–1);SD  (x,y)=(1–x) 2 (x+y-1); SD  (x,y)=(1–x) 2 (1–y). (5)

V. Bolotov (INR of RAS)CERN p-3269 There are some points of deviation beyond Standard Model [17], [18]. These deviation can connected with possible destructive interference between electromagnetic term and tensor interaction. In range of simple quark model (Fig.1) matrix element with tensor interaction could be written: M  е  = M IB + M SD + M T ; (6) The tensor interaction may be simulated by adding tensor radiation term to the structure dependent amplitude: M T = i(eG F V ud /  2)   q F T u(p e )   (1  5 ) (p ) (7) The decay rate densities for the SD  radiation and the interference term between the inner bremsstrahlung and the tensor radiation are similar, so destructive interference may reproduce the results of fit, giving F T =  (5.6  1.7)  10  3. This value does not contradict the listed constraints on a tensor coupling from nuclear beta decay as well as from muon decay (if universality is supposed). This result does not contradict the previous experiments carried out with stopped pions either [13]. Several works [14] were devoted to the study of possible deviation from SM in radiative pion decay. In one of them the involving of antisymmetric tensor fields into the standard electroweak theory allows to explain results of this work. It is evident that additional experimental and theoretical investigation of th problem should be carried out.

V. Bolotov (INR of RAS)CERN p In work [15] the authors show that there is region of phase space at large photon energies where the main physical background from muon decay is absent and that is optimal for searching a tensor interaction. In the analysis, it is convenient to describe the differential branching ratio as a function of the photon energy x = 2E  /m  and the variable =(x+y-1)/x = y sin2(  e  /2). To formula (4) is added tensor interferentional terms: dW  е  /dxdy =(  W  е /2  ){IB(x,y)+(F V m  2 /2f  m e ) 2 [(1+  ) 2 SD  (x,y)+ +1-  ) 2 SD  (x,y)]}+(F T 2/f  m e )T 1 (x, )+(F T 2 f  m e ) 2 T 2 (x, ) (8) Here all terms are independently on x and : IB(x,y) =[(1 – )/ ][(1 – x) 2 + 1]/x; SD  (x, )= 2 x 3 (1–x) ; (9) SD  (x, )=(1– ) 2 x 3 (1–x) ; T 1 (x, )= (1– )x ; T 2 = (1– )x 3.

V. Bolotov (INR of RAS)CERN p In work [19] it was assumed a tensoral coupling in the ∆S = 1 sector of effective weak Hamiltonian analogous to the one introduced for explaining a recent experiment on the decay  е  and suggest to test it in decays K  е  and K  μ . It was studied two hypotheses for this tensoral coupling. One is to impose universality for the coupling in the ∆S = 0 and ∆S = 1 sector, including the Cabibbo angle mixing as in standard V-A theory. The other is to impose the universality, but without the Cabbibo mixing. On fig.2-7 different calculated results for these approches are shown.

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V. Bolotov (INR of RAS)CERN p Search of supersymmetric particles. In models with spontaneous supersymmetry breaking the sauperpartners of a Goldstone fermion, pseudoscalar P and scalar S, goldstinos, should exist. In some versions of gravity-mediated and gauge-mediated theories [20] one or both of the weakly interacting bosons(sgoldstinos) are light enough to be observed in kaon decays. Moreover, if sgoldstino interactions with quarks conserve parity, as in left-right extensionsof MSSM, and P is lighter than S, so that mS > (mK - mπ ) and mP < (mK - 2mπ ), sgoldstinos can be observed in the decay K →ππP (Fig.8) rather than in the much better constrained K →πS. The phenomenology of light sgoldstinos in this scenario in detail in [21]. Fig.8. Kaon decay into sgoldstino and 2 pions.

V. Bolotov (INR of RAS)CERN p Under the assumption that sgoldstino interactions with quarks and gluons violate quark flavor and conserve parity, low energy interactions of pseudoscalar sgoldstino P with quarks are described by the Lagrangian:

V. Bolotov (INR of RAS)CERN p The 90% confidence level (CL) constrains on the flavor violating coupling of sgoldstinos to quarks evaluated using the K 0 L − K 0 S mass difference and CP violating parameter ε in the neutral kaon system are: | h D 12 |≤7 ∙ ; |Re( h D 12 )Im( h D 12 )| < 1.5 ∙ It has been shown [21] that, depending on the phase of goldstino-quark coupling, these constrains result in the following 90% CL upper limits on the branching ratio: Br(K − → π − π 0 P) ≤ 1.5 ∙ −4 ∙10 – 4, where the less strong limit corresponds to the case of pure real or pure imaginary h D 12.At present time there are two experiment reaults shown on fig.9 [22],[23]. Fig.9. The 90% CL upper limit for the Br(K− → π−π0 P) versus sgoldstino mass compared with the E787 upper limit(left), ythe 90% CL upper limit for the | hD12| compared with the theoretical limit from K0L− K0S mass difference (right).

V. Bolotov (INR of RAS)CERN p References. [1] J. Bijnens, G. Echer and J. Gasser, Nucl.Phys. B396 (1993) 81; [2] A. Pitch, Rep. Prog. Phys. 58 (1995) 563; [3] L.Maiani, G.Pancheri and N.Paver, The Second DAFNE Physics Handbook, (INFN-LNFDivisione Ricerca, SIS-Ufficio Pubblicazioni, Frascati (Roma) Italy, ISBN ). [4] J. Gasser et.al., arXiv:hep-ph/ [5] Cabibo N. Phys.Rev.Lett 10(1963)531 [6] Kobayashi M., Maskawa T. Progr.Theor. Phys. 49 (1973) 652. [7] C. Jarlskog Z.Phys. C29(1985)491. [8] G.F.Farrar and M.E.Shaposhnikov, Phys.Rev.Lett 70(1993)2833 [Erratum ibid 71(1993)210][arXiv:hep-ph/ ]; P.Het and Sather, Phys.Rev D51(1995)379[arXiv:hep-ph/ ]; M.Carena, M.Quiros and C.E.Wagner, Phys.Lett. B380(1996) 81 [arXiv:hep-ph/ ]. [9] J.Gevas, J.Iliopolus, J.Kaplan Phys. Lett. 20(1966)432. [10] V.V.Braguta, A.A.Likhoded, A.E.Chalov, Phys. Rev. D 65(2002) ; arXiv:hepph/ [11] Y.Kuzuruki Phys. Lett., B193 (1987) 339. [12] A. Bartl, T.Kernreiter and W. Porod Phys Lett., B538 (2002) 59. [13] N. Oshimo Mod. Phys. Lett. A4 (1989) 145.

V. Bolotov (INR of RAS)CERN p [14] V.V.Braguta, A.A.Likhoded, A.E.Chalov Phys.Atom.Nucl.67: ,2004,Yad.Fiz.67: ,2004. arXiv:hep-ph/ [15] V.N. Bolotov etal. Preprint INR-1150/2005, JULY Sent in Yad. Phys. [16] O.Tchikilev et al. Phys. Lett. 3602(2004) [17] V.N/ Bolotov et al. Phys.Lett. B243(1990)308. [18] E. Frlez for the PIBETA Collab., 4th Intern.Workshop on CHIRAL DYNAMIC 2003,Bonn,2003; The PIBETA Experiment:Annual Progress Report, November, [19] E. Gabrielli. Preprint CERN-TH.6700/92, October [20] G.Giudice and R. Rattazzi, Phys.Rev.322 (1999) 419; S. Dubrovsky, D.Gorbunov and S. Troitsky, Usp.Fiz,Nauk 169(1999) 705, English translation in Phys. Usp. 42(1999) 623 (hep-ph/ ). [21] D.S. Gorbunov and V.A. Rubakov. Phys.Rev. D64 (2001) [22]S.Adler et al. E787 Collaboration, Phys.Rev.D63 (2001) [23] O.G. Tchikilev et al. arXiv:hep-ex/ v2 11 Oct