Kitahara, Teppei

Nierste, Ulrich

Tremper, Paul

KITopen

PoS(ICHEP2016)564Direct CP violation in K → pipi decays andsupersymmetryTeppei KitaharaInstitute for Theoretical Particle Physics (TTP)and Institute for Nuclear Physics (IKP)Karlsruhe Institute of Technology (KIT)76131 Karlsruhe, GermanyE-mail: teppei.kitahara@kit.eduUlrich Nierste∗Institute for Theoretical Particle Physics (TTP)Karlsruhe Institute of Technology (KIT)76131 Karlsruhe, GermanyE-mail: ulrich.nierste@kit.eduPaul TremperInstitute for Theoretical Particle Physics (TTP)Karlsruhe Institute of Technology (KIT)76131 Karlsruhe, GermanyE-mail: paul.tremper@kit.eduThe quantities ε ′K and εK measure the amount of direct and indirect CP violation in K → pipidecays, respectively. Using the recent lattice results from the RBC and UKQCD Collaborationsand a new compact implementation of the ∆S = 1 renormalization group evolution we predictReε ′KεK= (1.06±5.07)×10−4in the Standard Model. This value is 2.8σ below the experimental value ofReε ′KεK= (16.6±2.3)×10−4.In generic models of new physics the well-understood εK precludes large contributions to ε′K , ifthe new contributions enter at loop level. However, one can resolve the tension in ε ′K/εK withinthe Minimal Supersymmetric Standard Model. To this end two features of supersymmetry arecrucial: First, one can have large isospin-breaking contributions (involving the strong insteadof the weak interaction) which enhance ε ′K . Second the Majorana nature of gluinos permits asuppression of the MSSM contribution to εK , because two box diagrams interfere destructively.38th International Conference on High Energy Physics3-10 August 2016Chicago, USA∗Speaker.c© Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/PoS(ICHEP2016)564Direct CP violation in K → pipi Ulrich Nierste1. Formalism and Standard-Model predictionFlavour-changing neutral current (FCNC) transitions of Kaons are extremely sensitive to newphysics and probe mass scales far above the reach of current high-pT experiments. K → pipi de-cays give access to two CP-violating quantities, which are related to FCNC amplitudes changingstrangeness S by one or two units, respectively. To define these quantities ε ′K and εK one first com-bines the decay amplitudes A(K0 → pi+pi−) and A(K0 → pi0pi0) into A0 ≡ A(K0 → (pipi)I=0) andA2 ≡ A(K0 → (pipi)I=2) where I denotes the strong isospin. Indirect CP violation (stemming fromthe ∆S = 2 box diagrams) is quantified byεK ≡ A(KL → (pipi)I=0)A(KS → (pipi)I=0) = (2.228±0.011) ·10−3 · ei(0.97±0.02)pi/4 (1.1)and was discovered in 1964 [1]. The measure of direct CP violation, which originates from the∆S = 1 Kaon decay amplitude, is1ε ′K ≃εK√2[A(KL → (pipi)I=2)A(KL → (pipi)I=0) −A(KS → (pipi)I=2)A(KS → (pipi)I=0)]= (16.6±2.3) ·10−4 · εK . (1.2)This experimental result was established in 1999 and constituted the first measurement of direct CPviolation in any decay [2]. Adopting the standard phase convention for the elements of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, the real parts of the isospin amplitudes are experimentallydetermined asReA0 = (3.3201±0.0018)×10−7 GeV, ReA2 = (1.4787±0.0031)×10−8 GeV. (1.3)The master equation for ε ′K/εK (see e.g. Ref. [3]) reads:ε ′KεK=ω+√2|εexpK |ReAexp0{ImA2ω+− (1− Ωˆeff) ImA0}. (1.4)Here ω+ ≃ ReA2ReA0 = (4.53±0.02) ·10−2 is determined from the charged counterparts of ReA0,2 andΩˆeff = (14.8±8.0) ·10−2 quantifies isospin breaking. The quantities |εexpK | and ReAexp0 are alsotaken from experiment, as indicated.The important theoretical ingredients encoding potential new-physics effects are ImA0 andImA2, which are calculated from the effective hamiltonian H|∆S|=1 describing s → dqq decays.This hamiltonian is known for a while at the level of next-to-leading-order (NLO) in QCD [4]and a precise prediction of ε ′K/εK is challenged by the difficulty to calculate the hadronic matrixelements of the operators in H |∆S|=1. Within the Standard Model (SM) ImA0 is dominated by gluonpenguins, with roughly 2/3 stemming from the matrix element 〈(pipi)I=0|Q6|K0〉 with the operatorQ6 = sjLγµdkL ∑qqkRγµqjR. (1.5)About 3/4 of the contribution to ImA2 stems from 〈(pipi)I=2|Q8|K0〉 withQ8 =32sjLγµdkL ∑qeqqkRγµqjR. (1.6)1PoS(ICHEP2016)564Direct CP violation in K → pipi Ulrich Nierstes dtWγddsdu,c,tu,c,tFigure 1: Sample diagrams of electroweak penguins and boxes, which contribute to the Wilson coefficientof Q8.The Wilson coefficient of Q8 stems from electroweak penguins and box diagrams (Fig. 1). Lattice-gauge theory has 〈(pipi)I=2|Q8|K0〉 (and thereby ImA2) under good control for some time [5], whilelattice calculations of 〈(pipi)I=0|Q6|K0〉 and the other matrix elements entering ImA0 are new [6].The results are consistent with earlier analytic calculations in the large-Nc “dual QCD” approach[7]. Using these matrix elements from lattice QCD we find [8]ε ′KεK= (1.06±4.66Lattice±1.91NNLO±0.59IV±0.23mt )×10−4. (1.7)The various sources of errors are indicated in the subscripts, with “NNLO” referring to unknownhigher-orders of the perturbative expansion and “IV” meaning isospin violation. Adding the errorsin quadrature gives the result in the abstract. We use the methodology of [9], which exploitsthe CP-conserving data of Eq. (1.3) to constrain the matrix elements. To arrive at Eq. (1.7) wehave implemented a novel compact solution of the renormalization group equations; the resultis in full agreement with the calculation in Ref. [3]. Eq. (1.7) disagrees with the experimentalnumber in Eq. (1.2) by 2.8 standard deviations. The original lattice paper, Ref. [6], quotes a smallerdiscrepancy. The discussion at this conference has indicated that the combination of Eq. (1.3) withFierz identities between different matrix elements has lead to the sharper prediction in Refs. [3, 8].2. A supersymmetric solutionThe large factor 1/ω+ multiplying ImA2 in Eq. (1.4) renders ε′K/εK especially sensitive to newphysics in the ∆I = 3/2 decay K → (pipi)I=2. This feature makes ε ′K/εK special among all FCNCprocesses. However, it is difficult to place a large effect into ε ′K without overshooting εK : The SMcontributions to both quantities are governed by the CKM combinationτ =−VtdV∗tsVudV∗us∼ (1.5− i0.6) ·10−3. (2.1)Our quantities scale asε ′SMK ∝ ImτM2Wand εSMK ∝ Imτ2M2W. (2.2)1Accidentally, ε ′K/εK is essentially real.2PoS(ICHEP2016)564Direct CP violation in K → pipi Ulrich NiersteFigure 2: “Trojan penguin” diagrams [12]. The difference of the two boxes contributes to the ∆I = 3/2 am-plitude and increases with the mass difference among right-handed up-type (U˜) and down-type (D˜) squark.Q˜ denotes a left-handed squark, which is a strange-down mixture.In new-physics scenarios τ is replaced by some new ∆S = 1 parameter δ and MW is replaced bysome particle mass M ≫MW . The new-physics contributions scale asε ′NPK ∝ ImδM2, and εNPK ∝ Imδ 2M2. (2.3)If new-physics enters through a loop, the only chance to have a detectable effect in ε ′K is a scenariowith |δ | ≫ |τ |. Using Eqs. (2.2) and (2.3) the experimental constraint |εNPK | ≤ |εSMK | entails∣∣∣∣ ε′NPKε ′SMK∣∣∣∣≤∣∣ε ′NPK /ε ′SMK ∣∣∣∣εNPK /εSMK ∣∣ = O(ReτReδ). (2.4)Thus large effects in ε ′K from loop-induced new physics are seemingly forbidden. Many studiesof ε ′K indeed involve new-physics scenarios with tree-level contributions to ε′K [10], in which therequirement |δ | ≫ |τ | can be relaxed.Here we present an explanation of the measurement in Eq. (1.2) by a supersymmetric loopeffect [11]. We circumvent the argument in Eq. (2.4) by exploiting two special features of theMinimal Supersymmetric Standard Model (MSSM): Firstly, the MSSM permits large ∆I = 3/2transitions mediated by the strong interaction (“Trojan penguins”) [12]. These enhanced ampli-tudes occur if the mass splitting between the right-handed up and down squarks is sizable (seeFig. 2). Secondly, the Majorana nature of the gluino permits the suppression of εK , which receivescontributions from two squark-gluino box diagrams (“regular” and “crossed”). These diagramscancel each other efficiently, once the gluino mass mg˜ and the squark mass mQ˜ in the loop satisfymg˜ ≥ 1.5mQ˜ [13]. In our scenario, the mass scale MS of the supersymmetric particles is large, oforder 3–7TeV. Squark flavour mixing appears only among the left-handed doublets. We choosethe CP-violating phase of the (2,1) element ∆LLsd of the left-handed squark mass matrix equal toarg(∆LLsd ) = pi/4. The results are shown in Fig. 33. SummaryNovel lattice results reveal a tension between the measured value of ε ′K in Eq. (1.2) and theSM prediction in Eq. (1.7). Within the MSSM one can simultaneously enhance ε ′K and suppressunwanted effects in εK . Our MSSM scenario works with large superpartner masses in the 3–7 TeVrange and thereby comply with bounds from collider searches. Crucial elements are mg˜ ≥ 1.5MQ˜,a sizable mass splitting between right-handed up and down squarks, and flavour mixing amongleft-handed squarks.3PoS(ICHEP2016)564Direct CP violation in K → pipi Ulrich NiersteFigure 3: Left: εSUSYK /εSMK as a function of mg˜/MS for a common mass MS = 10TeV of all superpartnersexcept the gluino. Right: Parameter region explaining ε ′K/εK while complying with the measured εK for thepoint mg˜ = 1.5MS and MS = mQ˜ = mD˜. The lines labeled with negative values of the MSSM contributionε ′SUSYK /εK correspond to correct (positive) solutions if the CP phase is appropriately adjusted. The SM pre-diction for εK strongly depends on |Vcb|. The blue (red) lines in both plots delimit the region which complieswith εK if |Vcb| is determined from exclusive (inclusive) b → cℓν decays. If the exclusive determination iscorrect, some new physics in εK is welcome. In the inclusive case the forbidden region is marked with thered shading. For more details see Ref. [11], from which the plots are taken.AcknowledgementsI thank the organizers for quickly letting me give this talk in a vacant slot of the timetable.The presented work has profited from discussions with Andrzej Buras, Chris Sachrajda, ChristophBobeth, Martin Gorbahn, and Sebastian Jäger. The work of UN is supported by BMBF under grantno. 05H15VKKB1.References[1] J. H. Christenson, J. W. Cronin, V. L. Fitch and R. Turlay, Phys. Rev. Lett. 13 (1964) 138.[2] L. K. Gibbons et al., Phys. Rev. Lett. 70, 1203 (1993); G. D. Barr et al. [NA31 Collaboration], Phys.Lett. B 317, 233 (1993); A. Alavi-Harati et al. [KTeV Collaboration], Phys. Rev. Lett. 83, 22 (1999)[hep-ex/9905060]; V. Fanti et al. [NA48 Collaboration], Phys. Lett. B 465, 335 (1999)[hep-ex/9909022]; J. R. Batley et al. [NA48 Collaboration], Phys. Lett. B 544, 97 (2002)[hep-ex/0208009]; E. Abouzaid et al. [KTeV Collaboration], Phys. Rev. D 83, 092001 (2011)[arXiv:1011.0127 [hep-ex]].[3] A. J. Buras, M. Gorbahn, S. Jäger and M. Jamin, JHEP 1511, 202 (2015) [arXiv:1507.06345[hep-ph]].[4] F. J. Gilman and M. B. Wise, Phys. Lett. B 83, 83 (1979). J. M. Flynn and L. Randall, Phys. Lett. B224, 221 (1989); Erratum: [Phys. Lett. B 235, 412 (1990)]. A. J. Buras, M. Jamin,M. E. Lautenbacher and P. H. Weisz, Nucl. Phys. B 370, 69 (1992); Addendum: [Nucl. Phys. B 375,501 (1992)]. A. J. Buras, M. Jamin, M. E. Lautenbacher and P. H. Weisz, Nucl. Phys. B 400, 374PoS(ICHEP2016)564Direct CP violation in K → pipi Ulrich Nierste(1993) [hep-ph/9211304]. M. Ciuchini, E. Franco, G. Martinelli and L. Reina, Nucl. Phys. B 415, 403(1994) [hep-ph/9304257]. A. J. Buras, M. Jamin and M. E. Lautenbacher, Nucl. Phys. B 400, 75(1993) [hep-ph/9211321].[5] T. Blum et al., Phys. Rev. Lett. 108, 141601 (2012) [arXiv:1111.1699 [hep-lat]]; Phys. Rev. D 86,074513 (2012) [arXiv:1206.5142 [hep-lat]]; Phys. Rev. D 91, no. 7, 074502 (2015)[arXiv:1502.00263 [hep-lat]].[6] Z. Bai et al. [RBC and UKQCD Collaborations], Phys. Rev. Lett. 115, no. 21, 212001 (2015)[arXiv:1505.07863 [hep-lat]].[7] A. J. Buras and J. M. Gérard, Nucl. Phys. B 264, 371 (1986); A. J. Buras and J. M. Gérard, Phys. Lett.B 192, 156 (1987); W. A. Bardeen, A. J. Buras and J. M. Gérard, Nucl. Phys. B 293, 787 (1987);W. A. Bardeen, A. J. Buras and J. M. Gérard, Phys. Lett. B 192, 138 (1987); J. M. Gérard, Acta Phys.Polon. B 21, 257 (1990); A. J. Buras, J. M. Gérard and W. A. Bardeen, Eur. Phys. J. C 74, 2871(2014) [arXiv:1401.1385 [hep-ph]]. A. J. Buras and J. M. Gérard, JHEP 1512, 008 (2015)[arXiv:1507.06326 [hep-ph]];[8] T. Kitahara, U. Nierste and P. Tremper, JHEP 1612 (2016) 78 [arXiv:1607.06727 [hep-ph]].[9] A. J. Buras, M. Jamin and M. E. Lautenbacher, Nucl. Phys. B 408, 209 (1993) [hep-ph/9303284].[10] A. J. Buras, F. De Fazio and J. Girrbach, Eur. Phys. J. C 74, no. 7, 2950 (2014) [arXiv:1404.3824[hep-ph]]. A. J. Buras, D. Buttazzo and R. Knegjens, JHEP 1511, 166 (2015) [arXiv:1507.08672[hep-ph]]. A. J. Buras, JHEP 1604, 071 (2016) [arXiv:1601.00005 [hep-ph]]. A. J. Buras, F. De Fazioand J. Girrbach-Noe, JHEP 1408, 039 (2014) [arXiv:1405.3850 [hep-ph]]. A. J. Buras and F. DeFazio, JHEP 1603, 010 (2016) [arXiv:1512.02869 [hep-ph]]. A. J. Buras and F. De Fazio, JHEP 1608(2016) 115 [arXiv:1604.02344 [hep-ph]]. M. Blanke, A. J. Buras and S. Recksiegel, Eur. Phys. J. C76, no. 4, 182 (2016) [arXiv:1507.06316 [hep-ph]].[11] T. Kitahara, U. Nierste and P. Tremper, Phys. Rev. Lett. 117 (2016) no.9, 091802 [arXiv:1604.07400[hep-ph]].[12] A. L. Kagan and M. Neubert, Phys. Rev. Lett. 83, 4929 (1999) [hep-ph/9908404].[13] A. Crivellin and M. Davidkov, Phys. Rev. D 81, 095004 (2010) [arXiv:1002.2653 [hep-ph]].5

Direct CP violation in $K$$→$$ππ$ decays and supersymmetry

https://publikationen.bibliothek.kit.edu/1000073001/4308974

Direct CP violation in $K$ $→$ $ππ$ decays and supersymmetry

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Direct CP violation in KKK→→→ππππππ decays and supersymmetry

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Direct CP violation in $K$ $→$ $ππ$ decays and supersymmetry