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2015 Mar. 18 Hiroshima Univ. Probing high scale SUSY in low energy FCNC Kei Yamamoto （ Niigata Univ. ⇒ KEK from this April ） Collaborated with Morimitsu Tanimoto (Niigata Univ.) arXiv: 1503.XXXX

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Standard model has been established ? ・ Higgs discovery [PDG 2014] [CMS ]

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SM explains CP violation of K and B mesons successfully We examine the sensitivity of High Scale SUSY in the CP violations of K and B mesons Standard model has been established ? Also, no signals of lepton flavor Flavor side ⇒ see briefly

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CP symmetry : Symmetry between particle and antiparticle Neutral meson mixing CP violation have been observed in K and B mesons decays. These neutral mesons oscillate between particle and antiparticle. Box diagram of CP violation C (charge) transformation P (parity) transformation CP symmetry is violated

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CP violation If CP symmetry is conserved, the decay rate of neutral meson and should be equal. 2 CP violation 2 : mixing : decay f : CP conjugate state CP violation CP asymmetry

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フレーバー固有状態と質量固有状態のずれ フレーバーを変える 1 つの複素位相 CP 対称性を破れを引き起こす Mass eigenstate basis CP violation in SM Deviation between flavor eigenstate and mass eigenstate ⇒ change flavor One complex phase ⇒ induce CP violation CKM matrix (wolfenstein parametrization, λ(Cabbibo angle)~0.2)

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Unitarity ： Im Re K meson system （ d-s system ） 三辺が同オーダーの B 中間子系が最も見やす い（ Im が大きい） CP violation in SM CKM matrix The unitarity triangle B meson system （ d-b system ） Bs meson system （ s-b system ）

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Unitarity ： Im Re K meson system （ d-s system ） 三辺が同オーダーの B 中間子系が最も見やす い（ Im が大きい） CP violation in SM CKM matrix The unitarity triangle B meson system （ d-b system ） Bs meson system （ s-b system ） These angles and lines of UT are determined by various measurements of B and K meson ⇒ Belle, Babar,,

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SM explains CP violation of K and B mesons successfully No significant deviation, but - a number of tensions - future measurements can improve a lot New Physics contributions to loop processes are still possible We examine the sensitivity of High Scale SUSY in the CP violations of K and B mesons Standard model has been established ? Also, no signals of lepton flavor

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Physics beyond SM ・大統一理論 ・暗黒物質の存在 ・宇宙のバリオン数非対称性 ・ニュートリノ質量 ・階層性問題 ・ … Neutrino oscillations Dark matter （ 25% of the Universe ） Dark energy Baryon asymmetry of universe Hierarchy problem We need new physics(NP) beyond SM

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Example of NP : Supersymmetry (SUSY) 2HDM Symmetry between fermion and boson スクォーク グルイーノ Spin 1 / 2 0 Spin 1 1 / レプトン - ino S- Spin 1/2Spin 1 Spin 0 Spin 1/2 Spin 0 Squark Slepton Gluino Bino Wino Higgsino Neutralino Chargino }

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Direct search (e.g. ATLAS, High energy Produce new particle directly with high energy collider High Energy Low Energy How to search NP Indirect search (e.g. LHCb, Low energy Probe the effect NP in low energy physics induced by quantum correction

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Direct search (e.g. ATLAS, High energy Produce new particle directly with high energy collider Indirect search (e.g. LHCb, Low energy Probe the effect NP in low energy physics induced by quantum correction High Energy Low Energy ⇒ Indirect search for NP is important There are no evidence for new physics How to search NP

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・ Lepton universality ・ （ g−2 ） μ ・ EW precision test １： See processes forbidden or suppressed in SM ・ Rare decay 、 CPV ・ μ→ ｅ γ 、 τ→μγ 、 τ→ ｅ γ 、 ・ Electric magnetic moment （ EDM ） d e 、 d N ・ Proton decay 王道 2 ：精密測定による標準模型との差 Flavor physics How to search NP indirectly 2 ： Precise measurement

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・ Lepton universality ・ （ g−2 ） μ ・ EW precision test １： See processes forbidden or suppressed in SM ・ Rare decay 、 CPV ・ μ→ ｅ γ 、 τ→μγ 、 τ→ ｅ γ 、 ・ Electric magnetic moment （ EDM ） d e 、 d N ・ Proton decay Flavor physics How to search NP indirectly 2 ： Precise measurement

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Exp. SM [The CKMfitter,2011] Time dependent CP asymmetry in -1, ] -1, ] Exp. SM [M. Bartsch et al ] Progress of B physics measurements Time dependent CP asymmetry in The LHCb collaboration has reported new data of the CP violation of Bs meson. Bs βsβs SM consistent

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In SM, - loop suppressed - CKM suppressed :BR |V tb * V tq | 2 - helicity suppressed :BR m μ 2 /m Bs 2 ⇒ Rare decay ： BR(Bs→μμ) SM 〜 BR(B→μμ) SM 〜 10 −10 Progress of B physics measurements Rare decay of Bs meson

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Progress of B physics measurements Rare decay of Bs meson [Bobeth et al ] [LHCb+CMS] SM consistent

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Progress of B physics measurements Rare decay of Bs meson [Bobeth et al ] [LHCb+CMS] SM consistent New data of CP violation of Bs are consistent with SM. ⇒ Constrain to NP

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ＮＰへの感度 SM NP loop suppressedCKM suppressed Loop process Sensitivity to NP It has sensitivity to high scale NP

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NP SM NP model depend Sensitivity to NP Neutral meson mixing

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Effective Theory Wilson coefficient b c - d u W b c d - u g Searching for SUSY particle at LHC By integrating out heavy particle which mediate, B transition is described in terms of interaction between light particles. Dim.6 Local operator ex) b → cud -

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49 9 Wilson coefficient b c - d u W b c d - u g Searching for SUSY particle at LHC By integrating out heavy particle which mediate, B transition is described in terms of interaction between light particles. Dim.6 Local operator ex) b → cud - Wilson coefficients have both contributions, SM and New physics. Effective Theory

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i : index of mode Effective Hamiltonian Decay amplitude Ex) Hadronic matrix element Effective Theory

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Flavor physics ⇔ SUSY search by LHC CP asymmetry in B 0 meson Time dependent CP asymmetry Semileptonic CP asymmetry ε K (CPV of K meson) Kaon rare decay Neutron EDM ~ m q, m g = 10 TeV & 50 TeV ~ High scale SUSY K L → π 0 νν K + → π + νν εKεK SUSY search and Flavor physics Our motivation No evidence of SUSY, and SUSY scale may be much higher than 1 TeV Indirect Search for SUSY is needed ⇒ Flavor physics We examine the sensitivity of High Scale SUSY in the CP violations of K and B mesons

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Contents SUSY setup Squark flavor mixing Squark mass spectrum Numerical analysis CP asymmetry in B meson decays chrome EDM of the strange quark ε K and Kaon rare decay ←new

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Contents SUSY setup Squark flavor mixing Squark mass spectrum Numerical analysis CP asymmetry in B meson decays chrome EDM of the strange quark ε K and Kaon rare decay ←new

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： complex ⇒ new CP violating phase 超対称標準模型での CP 対称性の破れ ほぼうまく説明できている ※クォーク質量行列と同時対角化できるとは限らないので非対角成分が残る SM ： The off diagonal elements in the CKM matrix MSSM ： The off diagonal elements in the squark mass matrices The origin of flavor violation ↑ It contains the new CP-violating phase Squark flavor mixing

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Horyuu The soft squark mass matrices contain the CP-violating phases, which contribute to the flavor changing neutral current (FCNC) with the CP violation. SM ： The off diagonal elements in the CKM matrix MSSM ： The off diagonal elements in the squark mass matrices The origin of flavor violation ↑ It contains the new CP-violating phase We work in the basis of mass eigenstate. Mixing matrix The magnitude of mixing parameters s ij ⇨ The magnitude of the SUSY contributions ※ 1st and 2nd family squarks are degenerate: s 12 =0

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SUSY SM Squark flavor mixing Mass difference Quark squark Gluino interaction

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Squark mass spectrum We should consider SUSY particle spectrum, which is consistent with Higgs Discovery. SUSY breaking scale Λ = GeV, GeV SM-SUSY matching scale Q 0 =10, 50 TeV SM scale m H, 126 GeV Running soft masses in SUSY Running Higgs coupling in SM λ, m 2 H 1, H 2 H SM Q0Q0 mHmH Λ Taking universal soft parameters at SUSY breaking scale Λ [M.Tanimoto and KY (2014)]

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H1 H1 bL bL bRbR d L,R, s L,R H2 H2 RGE running 0 =10TeV gluino tR tR

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※ Parameter case1 : 0.5 case2 : λ (Cabibbo angle) [Delgado, Garcia, Quiros, PRD90(2014) ] squark and gaunino mass mixing parameters random tanβ and L-R mixing angle : m 3 = m q m g 〜 m q ~~ ~ 11 5 m q [TeV] tanβ ~ Xt θdθd θuθu ： free parameter For simplicity, [M.Tanimoto and KY (2014)]

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※ Parameter case1 : 0.5 case2 : λ (Cabibbo angle) [Delgado, Garcia, Quiros, PRD90(2014) ] squark and gaunino mass tanβ and L-R mixing angle : m 3 = m q m g 〜 m q ~~ ~ 11 5 m q [TeV] tanβ ~ Xt θdθd θuθu [M.Tanimoto and KY (2014)]

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Parameter

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LR mixing angle θd θu θe 10TeV50TeV Parameter mixing parameters random ： free parameter For simplicity,

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Contents SUSY setup Squark flavor mixing Squark mass spectrum Numerical analysis CP asymmetry in B meson decays chrome EDM of the strange quark ε K and Kaon rare decay

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ΔF=2 process K-K, B-B, Bs-Bs mixing: ― ― ― The gluino-sbottom-quark interaction observed value is very sensitive, so it becomes a severe constraint. + Standard model Time dependent CP asymmetry : SM + SUSY Meson mixing & Time dependent CP asymmetry

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ΔM B /ΔM B SUSY SUSY+SM ΔM Bs /ΔM Bs SUSY SUSY+SM We scan s ij randomly in the region of 0 ～ 0.5 with taking |s ij L |= |s ij R | Sin(2Φ 1 ) SUSY /Sin(2Φ 1 ) SUSY+SM Sin(2Φs) SUSY /Sin(2Φs) SUSY+SM S 13 We scan δ ij randomly in the region of 0 ～ 0.5 S 23 S 13 S 23 φ 1 =β 6% 0.4% 6% 8%

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S 13 S 23 40% ⇒ We scan δ ij randomly in the region of 0 ～ 0.5 εK /εKεK /εK SUSY SUSY+SM sensitiv e SM component Taking account of Gluino squark interaction

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Time dependent CP asymmetry Experimental results [HFAG,2012] Both CP violations come from CP phase in the mixing. SM prediction Time dependent CP asymmetry [S. Khalil,E. Kou(2003), A.L. Kagan(2002), M.Endo,S.Mishima,M.Yamaguchi (2005)] depends on S 23 Difference of sign comes from parity of final state SUSY contribution

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C 8g /C 8g SUSY SM S ηK vs. S ΦK S ΦK /S η’K Q 0 =10 TeV tanβ=10 Our predictions SM insensitive… S % Time dependent CP asymmetry

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Experimental results CP asymmetry in the semileptonic decay in mixing SM + SUSY [LHCb ] Experimental results [A.Lenz and U.Nierste, arXiv: [hep -ph]] [PDG 2012] SM predictions Semi-leptonic CP asymmetry depend on, depend on

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Our predictions SM a sl vs. a sl s d a sl d insensitive… a sl d < 1×10 -3, a sl s < 5 × Semi-leptonic CP asymmetry

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Upper bound S 23 Q 0 =50 TeV tanβ=3 Chromo-EDM of strange quark [K.Fuyuto, J.Hisano and N.Nagata, 2013] sensitiv e |d s C |< 4 × cm

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Q 0 =50 TeV tanβ=3 Chromo-EDM of strange quark vs. ε K

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Q 0 =10TeV ➡ Q 0 Q 0 =50TeV Chromo-EDM of strange quark vs. ε K

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Contents SUSY setup Squark flavor mixing Squark mass spectrum Numerical analysis CP asymmetry in B meson decays chrome EDM of the strange quark ε K and Kaon rare decay

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Clean theoretically : theoretical uncertainty 〜 2 ％ K L → π 0 νν and K + → π + νν Rare decay : BR SM 〜 [Buras et all, 2006] ⇒ Sensitive to New Physics

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CP - CP + K L → π 0 νν K + → π + νν Hadronic matrix element, isospin relation K to pinunu Relation K to pinunu deference K → πνν in SM Direct CPV

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CP - CP + K L → π 0 νν K + → π + νν Hadronic matrix element, isospin relation K to pinunu Relation K to pinunu deference K → πνν in SM Future (20XX) ρ η K L → π 0 νν K + → π + νν Direct CPV

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Clean theoretically : theoretical uncertainty 〜 2 ％ K L → π 0 νν and K + → π + νν Rare decay : BR SM 〜 [Buras et all, 2006] ⇒ Sensitive to New Physics ←KOTO Experiment

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[yamanaka, Flavor in new J-PARC (2015) ]

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SUGRA model with MFV MSSM [T.Goto, Y,Okada and Y.Shimizu(1998)] It is known there are no large enhancement in K → πνν decay in the Minimal flavor violation(MFV) Squark mass < 600 GeV, Gaugino mass < 600 GeV with non-MFV [A.J.Buras,et al Squark mass = 600 GeV, Gluino mass = 1 TeV, δ 13, δ 23 ~ 0.3 It is known there are no large enhancement in K → πνν decay in the Minimal flavor violation(MFV) scheme K → πνν and ε K in MSSM

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exchange In the MSSM exchange SM K → πνν and ε K in MSSM exchange

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Numerical analysis Q 0 =10 TeV K→πνν : Chargino dominant ε K : Gluino dominant

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Numerical analysis Q 0 =10 d =s u d =0, s u d =s u =0.1 with 90%C.L. |ε K | exp constraint 1σ exp. bound Grossman-Nir bound SMSM 〜 8 × SM 〜 3 × SM at most 30% at most 3%

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s d & s u dependense Numerical analysis Q 0 =10 TeV 1σ exp. bound 〜 100 × SM 〜 20 × SM

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@s d =s u d =0, s u d =s u =0.3 Numerical analysis Q 0 =50 TeV 1σ exp. bound Grossman-Nir bound SMSM 〜 2 × SM at most 10% at most 1.5%

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Summary We have studied the contribution of the high-scale SUSY to B and K meson systems We consider the high-scale SUSY at TeV scale in the framework of the mass eigenstate basis of the SUSY particles assuming the non-minimal squark (slepton) flavor mixing We expect the measurement of these processes will be improved by the J-PARC KOTO experiment (and CERN NA62 experiment) in the near future. If large NP contribution to both and come out, it may suggest the contribution of chargino and gluino are comparable. Even if the NP contribution to is small, can be enhanced. As results, CP asymmetry and mass difference of B meson are insensitive to high scale SUSY is most sensitive even if the SUSY scale is higher than 50 TeV Chrome EDM has a sensitivity at SUSY scale 10-50TeV

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Summary Intensity frontier is crucial to probe BSM ! [Iijima, Flavor of new J-PARC (2015) ]

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