Flavor violating ๐โฒ in ๐๐(10) SUSY GUT ๆๆพ ็ฅ๏ผๅๅคๅฑๅคงๅญฆ๏ผ @Flavor Physics Workshop 2014 ๅ ฑๅ็ ็ฉถ่ ๏ผๅคงๆ ้ๅธ๏ผๅๅคๅฑๅคงๅญฆ๏ผ ไน ้ ็ดๆฒป๏ผๅๅคๅฑๅคงๅญฆใKavli IPMU๏ผ ๅฑฑไธญ ็ไบบ๏ผๅๅคๅฑๅคงๅญฆ๏ผ ใฏใใใซ๏ผGUTใฃใฆ็ด ๆดใใใ ๆจๆบๆจกๅ gauge theory 3ใคใฎๅ๏ผ3ใคใฎgauge group ็ฒๅญ๏ผgauge groupใฎ่กจ็พ ๅคง็ตฑไธ็่ซ๏ผGUT๏ผ 1ใคใฎgauge groupใงๅ๏ผ็ธไบไฝ็จ๏ผใ่จ่ฟฐ ๏ผๅใฎ็ตฑไธใๅๆใซ็ฒๅญใฎ็ตฑไธ ๆฌๅฝใซ็ตฑไธใงใใใฎ๏ผ 01/19 ๅ ใใฆ๏ผSUSYใ็ด ๆดใใใ boson fermion ็ฉ่ณช squark, slepton quark, lepton gauge gluon, W, B gauge boson gluino, wino, bino gaugino Higgs Higgs ่ฆใคใใฃใฆใใชใใปใปใป โข SUSY flavorใฎๆช่ฆณๆธฌ โข ้ใHiggs Higgsino gauginoใใ่ณช้TeVใชใ motivationใใ squark, sleptonใฏ ้ใ๏ผ 02/19 gauge coupling unification ๐ฒ๐บ๐ผ๐บ๐ ๐ฎ๐ผ๐ป ๐๐๐๐๐ = 1 TeV 03/19 concept of this model ไธ่ฌใซ๐โฒ gauge boson from โข ๐(1)โฒ by hand tree level flavor violation โข ๐(1)โฒ included in GUT group no flavor violation ไปๅ GUTใฎๅ้ก่งฃๆฑบmechanism โflavor violating ๐โฒ gauge boson ๐๐(10) GUT + high scale, split SUSY flavor physicsใ modelใฎprobe 04/19 โฒ ๐ gauge boson (๐ผ ๐ โฒ )ใจใฏ GUT group, large extra dimensionใชใฉใใๅบใ ๆงใ ใชmotivation โข ๐ term problemใฎ่งฃ โข DM candidate (singlet extension) โข electroweak baryogenesis (singlet extension) ใชใฉ 05/19 tree level flavor violation through ๐โฒ exchange โข ๆใงๅ ฅใใ๐(1)โฒ gauge symmetry anomaly cancelใฎใใไธไปฃใใจใซ็ฐใชใcharge โข GUT gauge symmetry groupใซๅซใพใใ๐(1)โฒ anomalyๅ้กใใชใใใไธไปฃuniversal charge 06/19 ๐บ๐ถ(๐๐) GUT modelใฎๅ้ก็น โข quark, (lepton)-mixing โข ่ฑๅฏใชflavorใใจใฎ้ๅฑคๆง้ ใๅบใชใ ่งฃๆฑบmechanism โข matter sectorๆกๅผต โข Higgs sectorๆกๅผต ไปๅใฏใใกใ ใชใฉ 07/19 ๐บ๐ถ(๐๐) GUT model + ๐๐ matter ไพใใฐ tree level FVใ็ใใ ๆณจ ๆญฃ็ขบใซใฏ FVใซ็นๅพดใใใ 08/19 ๐บ๐ถ(๐๐) SUSY GUT model ๐๐(10) symmetryไธญใฎไธ้จใฎsymmetryใไฟใค high scale (split) SUSY ๐(100) TeV SUSY breaking โข ๐(100) TeV ๐๐โฒ โข SUSYใใใฎFV contributionใชใ โข gaugino mass โผ ๐(1) TeVใชใgauge coupling unification โข tan ๐ฝใๅฐใใ 09/19 Giudice, Strumia (2012) 10/19 concept of this model ๏ผ็นฐใ่ฟใ๏ผ ไธ่ฌใซ๐โฒ gauge boson from โข ๐(1)โฒ by hand tree level flavor violation โข ๐(1)โฒ included in GUT group no flavor violation ไปๅ GUTใฎๅ้ก่งฃๆฑบmechanism โflavor violating ๐โฒ gauge boson ๐๐(10) GUT + high scale, split SUSY flavor physicsใ modelใฎprobe 11/19 FV่จ็ฎใฎใใใฎparameter โข ๐่กจ็พๆททๅ่กๅ๏ผ๐ โข flavor mixing matrix๏ผV โข ๐(1)โฒ gauge coupling๏ผ๐๐โฒ โข ๐(1)โฒ gauge boson mass๏ผ๐๐โฒ ใจใใใใไปๅใฏ๐๐โฒ = 100 TeV 12/19 parameterใฎๆฑบๅฎ ไปๅใฏ ใจใใ charged lepton sectorใฏ๐๐(5) limitใง 13/19 FV coupling ๐ A๐๐ ใฎๅฎ็พฉ 1 2 โ1 = โ โ 3 3 14/19 ๐ ๐๐ ๐ด11 ๐ ๐ ๐๐ ๐ด22 ๐ด11๐ฟ ๐ ๐ด23๐ฟ ๐ ๐๐ ๐ด33 ๐ ๐๐ ๐ด๐๐ ๐ ๐ด๐๐๐ฟ ๐ ๐๐ ๐ด13 ๐๐ฟ ๐ด13 ๐ ๐ด12๐ฟ ๐ ๐ด33๐ฟ ๐ ๐ด22๐ฟ ๐ ๐๐ ๐ด12 ๐ ๐๐ ๐ด23 ๐ ๐ 15/19 ๐๐โฒ = 100 TeV 16/19 ๐๐โฒ = 100 TeV 17/19 case 1 case 2 18/19 ใพใจใ โข flavor physicsใprobeใจใใSUSY GUT model โข GUT modelใฎๆใคๅ้ก่งฃๆฑบใflavor violationใๅผ ใ่ตทใใ โข ็ใใflavor violationใซ็นๅพดใใ to do โข ็พ่ฑกใฎ่งฃๆใ้ฒใใ โข SUSY sectorใฎๆจกๅใฎ่ฉณ็ดฐ 19/19 ใ้่ดใใใใจใใใใใพใใ Back up neutrino mass โ inverse seesaw seesaw mechanism in GUT model ๆๅใฏGUT scaleใ1016 GeVใจใใฆใใใใจใใ ไปๅใฏ GUT symmetryใฎไธใคใ็ ดใใscale ใใใใtype-โ seesawใฏๅใใชใ inverse seesaw Mohapatra (1986) ๅ ใ ใใ ใใใๆกๅผตใใ ii. Realistic quark and lepton masses and mixings ๐๐ถ๐พ๐ 0.97 0.23 0.0035 = 0.23 0.97 0.041 , 0.0086 0.040 1.0 0.83 0.54 0.15 U๐๐๐ = โ0.48 0.53 0.70 0.30 โ0.65 0.70 CKM matrix and MNS matrix PDG (2012) complex phase of MNS matrix is 0. Quark and charged lepton mass @ ๐๐ Antusch, Maurer (2013) Neutrino mass PDG (2012) Neutrino mass is upper bound of neutrino mass Riemer-Sorensen et al. (2012) mass ๐๐ข ๐๐ , ๐๐ ๐๐ strong middle hierarchy weak mixing ๐๐ถ๐พ๐ small mixing ๐๐๐๐ large mixing Realistic quark and lepton masses and mixings in ๐บ๐ผ ๐ GUT model โ ๐๐ข ๐๐ , ๐๐ seesaw mechanism ๐๐ The ๐๐ quark and lepton induces stronger hierarchies for Yukawa coupling than the ๐ quark and lepton. ๐๐๐ ๐๐๐ ๐๐๐ ๐3 ๐2 1 ๐๐ ๐๐ ๐๐ ๐3 ๐2.5 ๐2 Quark and lepton masses and mixings can be realized if ๐ = 0.22. โ ๐๐ข ๐๐ , ๐๐ ๐๐ strong hierarchy ๐ฟ๐ข โผ ๐ ๐ข โผ ๐๐ถ๐พ๐โ๐ก๐ฆ๐๐ middle hierarchy ๐ฟ๐ โผ ๐ ๐ โผ ๐๐ถ๐พ๐โ๐ก๐ฆ๐๐ , ๐ ๐ โผ ๐ฟ๐ โผ ๐๐๐๐โ๐ก๐ฆ๐๐ weak hierarchy ๐ฟ๐ โผ ๐๐๐๐โ๐ก๐ฆ๐๐ ๐๐ถ๐พ๐โ๐ก๐ฆ๐๐ 1 โผ ๐ ๐3 ๐ 1 ๐2 ๐3 ๐2 1 ๐๐๐๐โ๐ก๐ฆ๐๐ 1 โผ ๐0.5 ๐ ๐0.5 1 ๐0.5 ๐ ๐0.5 1 ๐๐ถ๐พ๐โ๐ก๐ฆ๐๐ 1 โผ ๐ ๐3 ๐ 1 ๐2 ๐3 ๐2 1 small mixing ๐๐๐๐โ๐ก๐ฆ๐๐ 1 โผ ๐0.5 ๐ as a result of above assumption, ๐0.5 1 ๐0.5 ๐ ๐0.5 1 large mixing diagonalizing matrix for ๐๐ of ๐๐(5) diagonalizing matrix for ๐ of ๐๐(5) Quark and lepton masses and mixings can be realized if ๐ = 0.22. Realistic quark and lepton masses and mixings in ๐บ๐ถ ๐๐ GUT model In ๐๐(10) GUT model, ๐๐ and ๐ quark and lepton induce similar hierarchy because of unification into ๐๐ rep. It is hard to realize realistic quark and lepton masses and mixings. ๐๐ข = ๐๐ = ๐๐ add ๐๐ rep. as SM quarks and leptons ๐๐๐๐ ๐๐๐๐ ๐๐๐๐ ๐3 ๐2 1 hierarchy of ๐๐ ๐๐ rep. hierarchy of ๐๐ of ๐๐ 5 ๐๐๐๐ ๐๐๐๐ ๐๐๐๐ realistic hierarchy of ๐ of ๐๐ 5 ๐ rep. ๐๐ ๐ ๐๐ ๐ ๐๐ ๐ ๐โฒ๐ป ๐3 ๐2 1 ๐2.5 add 5โฒ from ๐๐ of ๐๐(10) massless ๐ of ๐๐(5) (SM quarks and leptons) unrealistic ๐3 ๐2 1 ๐๐1 ๐โ ๐ ๐๐2 ๐3 ๐2.5 ๐2 1 ๐๐3 large Yukawa = superheavy ๐๐1 ๐โ ๐ ๐๐2 ๐๐3 โผ ๐3 ๐2.5 ๐2 1 ๐1 ๐2 ๐3 ๐๐ realistic
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