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I. Doršner, Leptoquark Mass Limit in SU(5)

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Balkan Workshop BW2013 …

Balkan Workshop BW2013
Beyond the Standard Models
25 – 29 April, 2013, Vrnjačka Banja, Serbia


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  • 1. LEPTOQUARK MASS LIMIT IN SU(5)*Ilja DoršnerUniversity of Sarajevo, Bosnia and HerzegovinaBALKAN WORKSHOP 2013 — BW2013Vrnjačka Banja, SerbiaApril 28, 2013I. Doršner, Phys. Rev. D 86:055009, 2012, 1206.5998;I. Doršner, S. Fajfer and N. Košnik, Phys. Rev. D 86:015013, 2012, 1204.0674.*
  • 2. • MINIMAL UNIFICATION OF MATTERTHE GEORGI-GLASHOW SU(5) SCENARIO• d = 6 PROTON DECAY OPERATORSSCALAR CONTRIBUTIONS• MINIMAL VIABLE SU(5) UNIFICATION• p-DECAY PREDICTIONSSCALAR CONTRIBUTIONSOUTLINE
  • 3. THE STANDARD MODEL COMPRISES 15 FERMIONS.THE GEORGI-GLASHOW SU(5) MODEL**See talk by Borut Bajc.
  • 4. SU(5) SCENARIO**H. Georgi and S.L. Glashow (1974).LEPTONSQUARKSFIFTEEN FERMIONS OF THE STANDARD MODEL:
  • 5. *H. Georgi and S.L. Glashow (1974).LEPTONSQUARKSSU(5) SCENARIO*FIFTEEN FERMIONS OF THE STANDARD MODEL:
  • 6. *H. Georgi and S.L. Glashow (1974).LEPTONSQUARKSFIFTEEN FERMIONS OF THE STANDARD MODEL:SU(5) SCENARIO*
  • 7. FERMION MASSES(SCALAR REPRESENTATIONS IN THE MINIMAL SU(5))&UTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11
  • 8. NOTATION(VACUUM EXPECTATION VALUE)MD = Y1v⇤4512Y3v⇤5ME = 3Y T1 v⇤4512Y T3 v⇤5(Y1)ij10i5j45⇤(Y3)ij10i5j5⇤h45151 i = h45252 i = h45353 i = v45/p2E†RDLMdiagD MdiagE ETL D⇤R = 4Y1v45h55i = v5/p2|v5|2/2 + 12|v45|2= v2t ¯t(g 2)µ45 2 126&
  • 9. *H. Georgi and S.L. Glashow (1974).WHAT GOES WRONG WITH SU(5)?*
  • 10. FERMION MASSES*v = 246 GeVY 10ij 10i10j45Y 5ij10i5j45⇤Y 10ij 10i10j5Y 5ij10i5j5⇤MD = Y 5v⇤45⇤MD =12Y 5v⇤5ME = 3Y 5 Tv⇤451 5 T ⇤1|v5|2/2 + 12|v45|2= v2v = 246 GeVY 10ij 10i10j45Y 5ij10i5j45⇤Y 10ij 10i10j5Y 5ij10i5j5⇤MD = Y 5v⇤45⇤MD =12Y 5v⇤5Y 10ij 10i10j45Y 5ij10i5j45⇤Y 10ij 10i10j5Y 5ij10i5j5⇤MD = Y 5v⇤45⇤MD =12Y 5v⇤5ME = 3Y 5 Tv⇤45ME =12Y 5 Tv⇤5p 5 5 TY 5ij10i5j45⇤Y 10ij 10i10j5Y 5ij10i5j5⇤MD = Y 5v⇤45⇤MD =12Y 5v⇤5ME = 3Y 5 Tv⇤45ME =12Y 5 Tv⇤5MU = 2p2(Y 5Y 5 T)v45p 10 10 T45ME =12Y 5 Tv⇤5MU = 2p2(Y 5Y 5 T)v45MU =p2(Y 10+ Y 10 T)v510 ⇥ 10 = 5 45 : MU10 ⇥ 5 = 5 45 : ME, MD10+1⇥ 10+1= 5+245+2: MD10+1⇥ 53= 5 245 2: MU3 3 6 6*See talk by Borut Bajc.
  • 11. FERMION MASSESv = 246 GeVY 10ij 10i10j45Y 5ij10i5j45⇤Y 10ij 10i10j5Y 5ij10i5j5⇤MD = Y 5v⇤45⇤MD =12Y 5v⇤5ME = 3Y 5 Tv⇤451 5 T ⇤1|v5|2/2 + 12|v45|2= v2v = 246 GeVY 10ij 10i10j45Y 5ij10i5j45⇤Y 10ij 10i10j5Y 5ij10i5j5⇤MD = Y 5v⇤45⇤MD =12Y 5v⇤5Y 10ij 10i10j45Y 5ij10i5j45⇤Y 10ij 10i10j5Y 5ij10i5j5⇤MD = Y 5v⇤45⇤MD =12Y 5v⇤5ME = 3Y 5 Tv⇤45ME =12Y 5 Tv⇤5p 5 5 TY 5ij10i5j45⇤Y 10ij 10i10j5Y 5ij10i5j5⇤MD = Y 5v⇤45⇤MD =12Y 5v⇤5ME = 3Y 5 Tv⇤45ME =12Y 5 Tv⇤5MU = 2p2(Y 5Y 5 T)v45p 10 10 T45ME =12Y 5 Tv⇤5MU = 2p2(Y 5Y 5 T)v45MU =p2(Y 10+ Y 10 T)v510 ⇥ 10 = 5 45 : MU10 ⇥ 5 = 5 45 : ME, MD10+1⇥ 10+1= 5+245+2: MD10+1⇥ 53= 5 245 2: MU3 3 6 6
  • 12. FERMION MASSESv = 246 GeVY 10ij 10i10j45Y 5ij10i5j45⇤Y 10ij 10i10j5Y 5ij10i5j5⇤MD = Y 5v⇤45⇤MD =12Y 5v⇤5ME = 3Y 5 Tv⇤451 5 T ⇤1|v5|2/2 + 12|v45|2= v2v = 246 GeVY 10ij 10i10j45Y 5ij10i5j45⇤Y 10ij 10i10j5Y 5ij10i5j5⇤MD = Y 5v⇤45⇤MD =12Y 5v⇤5Y 10ij 10i10j45Y 5ij10i5j45⇤Y 10ij 10i10j5Y 5ij10i5j5⇤MD = Y 5v⇤45⇤MD =12Y 5v⇤5ME = 3Y 5 Tv⇤45ME =12Y 5 Tv⇤5p 5 5 TY 5ij10i5j45⇤Y 10ij 10i10j5Y 5ij10i5j5⇤MD = Y 5v⇤45⇤MD =12Y 5v⇤5ME = 3Y 5 Tv⇤45ME =12Y 5 Tv⇤5MU = 2p2(Y 5Y 5 T)v45p 10 10 T45ME =12Y 5 Tv⇤5MU = 2p2(Y 5Y 5 T)v45MU =p2(Y 10+ Y 10 T)v510 ⇥ 10 = 5 45 : MU10 ⇥ 5 = 5 45 : ME, MD10+1⇥ 10+1= 5+245+2: MD10+1⇥ 53= 5 245 2: MU3 3 6 6
  • 13. FERMION MASSESv = 246 GeVY 10ij 10i10j45Y 5ij10i5j45⇤Y 10ij 10i10j5Y 5ij10i5j5⇤MD = Y 5v⇤45⇤MD =12Y 5v⇤5ME = 3Y 5 Tv⇤451 5 T ⇤1|v5|2/2 + 12|v45|2= v2v = 246 GeVY 10ij 10i10j45Y 5ij10i5j45⇤Y 10ij 10i10j5Y 5ij10i5j5⇤MD = Y 5v⇤45⇤MD =12Y 5v⇤5Y 10ij 10i10j45Y 5ij10i5j45⇤Y 10ij 10i10j5Y 5ij10i5j5⇤MD = Y 5v⇤45⇤MD =12Y 5v⇤5ME = 3Y 5 Tv⇤45ME =12Y 5 Tv⇤5p 5 5 TY 5ij10i5j45⇤Y 10ij 10i10j5Y 5ij10i5j5⇤MD = Y 5v⇤45⇤MD =12Y 5v⇤5ME = 3Y 5 Tv⇤45ME =12Y 5 Tv⇤5MU = 2p2(Y 5Y 5 T)v45p 10 10 T45ME =12Y 5 Tv⇤5MU = 2p2(Y 5Y 5 T)v45MU =p2(Y 10+ Y 10 T)v510 ⇥ 10 = 5 45 : MU10 ⇥ 5 = 5 45 : ME, MD10+1⇥ 10+1= 5+245+2: MD10+1⇥ 53= 5 245 2: MU3 3 6 6
  • 14. NOTATION(MASS MATRICES AND UNITARY TRANSFORMATIONS)UP-TYPE QUARKS, DOWN-TYPE QUARKS AND CHARGED LEPTONS:UTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 115 =0@H1A(p ! e+⇡0) ⇠↵2v45m438(VUD)11(VUD)13m⌧ mb2
  • 15. *H. Georgi and S.L. Glashow (1974).IS UNIFICATION WRONG WITHIN SU(5)?*1↵ 11(p ! e+⇡0) ⇠↵2v45m438(VUD)11(VUD)13m⌧ mb2(p ! µ+⇡0) ⇠↵2v45m438(VUD)11(VUD)12m⌧ ms2(p ! e+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232mb(VUD)132(p ! µ+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232ms(VUD)122(p ! e+⇡0) ⇠↵2(VUD)11[mu +3md] +1(V †UDU⇤2 MdiagE U†2 )112p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiXi=1,2,3(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵1p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiX(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵
  • 16. *H. Georgi and S.L. Glashow (1974).50M 1012GeV24 = (⌃8, ⌃3, ⌃(3,2), ⌃(¯3,2), ⌃24)✏abcuTa iCub j33 c10i 5i , i = 1, 2, 324 5 1516i , i = 1, 2, 3210 10 126 126120⌃3 = (1, 3, 0)a = (1, 3, 1)b = (3, 2, 1/6)ADDRESSING NEUTRINO MASSES ALSO ADDRESSES UNIFICATIONIN A SATISFACTORY MANNER!NEUTRINO MASSES WITHIN SU(5)?*¶I. Doršner and P. Fileviez Pérez, Nucl. Phys. B 723:53-76, 2005, hep-ph/0504276.‡B. Bajc and G. Senjanović, JHEP 0708 014, 2007, hep-ph/0612029.‡¶
  • 17. *See talk by Andrea Romanino.UNIFICATION IN SU(5)*1↵ 11(p ! e+⇡0) ⇠↵2v45m438(VUD)11(VUD)13m⌧ mb2(p ! µ+⇡0) ⇠↵2v45m438(VUD)11(VUD)12m⌧ ms2(p ! e+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232mb(VUD)132(p ! µ+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232ms(VUD)122(p ! e+⇡0) ⇠↵2(VUD)11[mu +3md] +1(V †UDU⇤2 MdiagE U†2 )112p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiXi=1,2,3(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵1p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiX(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵
  • 18. 1↵ 11(p ! e+⇡0) ⇠↵2v45m438(VUD)11(VUD)13m⌧ mb2(p ! µ+⇡0) ⇠↵2v45m438(VUD)11(VUD)12m⌧ ms2(p ! e+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232mb(VUD)132(p ! µ+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232ms(VUD)122(p ! e+⇡0) ⇠↵2(VUD)11[mu +3md] +1(V †UDU⇤2 MdiagE U†2 )112UNIFICATION IN SU(5)*p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiXi=1,2,3(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵1p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiX(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵*See talk by Andrea Romanino.
  • 19. 1↵ 11(p ! e+⇡0) ⇠↵2v45m438(VUD)11(VUD)13m⌧ mb2(p ! µ+⇡0) ⇠↵2v45m438(VUD)11(VUD)12m⌧ ms2(p ! e+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232mb(VUD)132(p ! µ+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232ms(VUD)122(p ! e+⇡0) ⇠↵2(VUD)11[mu +3md] +1(V †UDU⇤2 MdiagE U†2 )112UNIFICATION IN SU(5)*p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiXi=1,2,3(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵1p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiX(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵*See talk by Andrea Romanino.
  • 20. 1↵ 11(p ! e+⇡0) ⇠↵2v45m438(VUD)11(VUD)13m⌧ mb2(p ! µ+⇡0) ⇠↵2v45m438(VUD)11(VUD)12m⌧ ms2(p ! e+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232mb(VUD)132(p ! µ+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232ms(VUD)122(p ! e+⇡0) ⇠↵2(VUD)11[mu +3md] +1(V †UDU⇤2 MdiagE U†2 )112UNIFICATION IN SU(5)*p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiXi=1,2,3(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵1p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiX(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵*See talk by Andrea Romanino.
  • 21. 1↵ 11(p ! e+⇡0) ⇠↵2v45m438(VUD)11(VUD)13m⌧ mb2(p ! µ+⇡0) ⇠↵2v45m438(VUD)11(VUD)12m⌧ ms2(p ! e+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232mb(VUD)132(p ! µ+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232ms(VUD)122(p ! e+⇡0) ⇠↵2(VUD)11[mu +3md] +1(V †UDU⇤2 MdiagE U†2 )112UNIFICATION IN SU(5)*p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiXi=1,2,3(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵1p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiX(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵*See talk by Andrea Romanino.
  • 22. 1↵ 11(p ! e+⇡0) ⇠↵2v45m438(VUD)11(VUD)13m⌧ mb2(p ! µ+⇡0) ⇠↵2v45m438(VUD)11(VUD)12m⌧ ms2(p ! e+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232mb(VUD)132(p ! µ+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232ms(VUD)122(p ! e+⇡0) ⇠↵2(VUD)11[mu +3md] +1(V †UDU⇤2 MdiagE U†2 )112UNIFICATION IN SU(5)*p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiXi=1,2,3(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵1p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiX(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵*See talk by Andrea Romanino.
  • 23. 1↵ 11(p ! e+⇡0) ⇠↵2v45m438(VUD)11(VUD)13m⌧ mb2(p ! µ+⇡0) ⇠↵2v45m438(VUD)11(VUD)12m⌧ ms2(p ! e+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232mb(VUD)132(p ! µ+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232ms(VUD)122(p ! e+⇡0) ⇠↵2(VUD)11[mu +3md] +1(V †UDU⇤2 MdiagE U†2 )112UNIFICATION IN SU(5)*p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiXi=1,2,3(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵1p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiX(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵*See talk by Andrea Romanino.
  • 24. 1↵ 11(p ! e+⇡0) ⇠↵2v45m438(VUD)11(VUD)13m⌧ mb2(p ! µ+⇡0) ⇠↵2v45m438(VUD)11(VUD)12m⌧ ms2(p ! e+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232mb(VUD)132(p ! µ+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232ms(VUD)122(p ! e+⇡0) ⇠↵2(VUD)11[mu +3md] +1(V †UDU⇤2 MdiagE U†2 )112UNIFICATION IN SU(5)*p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiXi=1,2,3(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵1p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiX(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵*See talk by Andrea Romanino.
  • 25. 1↵ 11(p ! e+⇡0) ⇠↵2v45m438(VUD)11(VUD)13m⌧ mb2(p ! µ+⇡0) ⇠↵2v45m438(VUD)11(VUD)12m⌧ ms2(p ! e+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232mb(VUD)132(p ! µ+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232ms(VUD)122(p ! e+⇡0) ⇠↵2(VUD)11[mu +3md] +1(V †UDU⇤2 MdiagE U†2 )112UNIFICATION IN SU(5)*p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiXi=1,2,3(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵1p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12↵ 13a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiX(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵*See talk by Andrea Romanino.
  • 26. NOTATION(MASS MATRICES AND UNITARY TRANSFORMATIONS)MAJORANA NEUTRINOS:QUALITATIVE ASPECTS OF NEUTRINO PHYSICS ARE NOTRELEVANT FOR DISCUSSION OF p-DECAY!
  • 27. HOW PREDICTIVE IS SU(5) FOR p-DECAY?**H. Georgi and S.L. Glashow (1974).
  • 28. ≡ Yukawa coupling(s) ≡ Leptoquark mass*S. Weinberg, Phys. Rev. D 22:1694, 1980.p-DECAY WIDTHS(SCALAR CONTRIBUTIONS*)
  • 29. ≡ Yukawa coupling(s) ≡ Leptoquark mass*S. Weinberg, Phys. Rev. D 22:1694, 1980.p-DECAY WIDTHS(SCALAR CONTRIBUTIONS*)
  • 30. ≡ Yukawa coupling(s) ≡ Leptoquark mass*S. Weinberg, Phys. Rev. D 22:1694, 1980.p-DECAY WIDTHS(SCALAR CONTRIBUTIONS*)a6 ⇠Y 2m2LQE = DCD = ECU = UCU†D = VCKMN = IE = ID = I
  • 31. EXPERIMENTAL INPUT(PROTON DECAY)5PROCESS ⌧p (1033years)p ! K+¯⌫ 4.0p ! ⇡+¯⌫ 0.025p ! ⇡0e+13.0j = 1, 2, 3 j = 1, 2La ⌘ (1, 2, 1/2)a = (⌫a ea)TeCa ⌘ (1, 1, 1)aQa ⌘ (3, 2, 1/6)a = (ua da)T
  • 32. ≡ Yukawa coupling(s) ≡ Leptoquark mass*S. Weinberg, Phys. Rev. D 22:1694, 1980.p-DECAY WIDTHS(SCALAR CONTRIBUTIONS*)
  • 33. IS AN ACCURATE LIMIT?KEY QUESTION…
  • 34. LEPTOQUARK IN SU(5)(p-DECAY MEDIATING SCALAR LEPTOQUARK)THERE IS ONLY ONE SET OF PROTON DECAY MEDIATINGSCALARS IN THE MINIMAL SU(5) SETUP!1↵ 115 =0@H1A(p ! e+⇡0) ⇠↵2v45m438(VUD)11(VUD)13m⌧ mb2(p ! µ+⇡0) ⇠↵2v45m438(VUD)11(VUD)12m⌧ ms2(p ! e+⇡0) ⇠↵2v45m4 (VUD)11[mu +34md +14m⌧ ]232mb(VUD)132(p ! µ+⇡0) ⇠↵2(V ) [m +3m +1m ]23m (V )2
  • 35. SU(5) Y 1ij10i1j10⇤Y 5ij5i5j10(3, 1, 2/3)⌘ Y 1ijuC Ta i C⌫Cj⇤a 2 1/2✏abcY 5ijdC Ta i CdCb j cY 5= Y 5 TOH(d↵, e ) = a(d↵, e ) uTL C 1d↵ uTL C 1eOH(d↵, eC) = a(d↵, eC) uTL C 1d↵ eC†L C 1uC⇤OH(dC↵ , e ) = a(dC↵ , e ) dC↵†L C 1uC⇤uTL C 1eOH(dC↵ , eC) = a(dC↵ , eC) dC↵†L C 1uC⇤eC†L C 1uC⇤OH(d↵, d , ⌫i) = a(d↵, d , ⌫i) uTL C 1d↵ dTL C 1⌫iOH(d↵, dC, ⌫i) = a(d↵, dC, ⌫i) dC†L C 1uC⇤dT↵ L C 1⌫iOH(d↵, dC, ⌫Ci ) = a(d↵, dC, ⌫Ci ) uTL C 1d↵ ⌫Ci†L C 1dC⇤OH(dC↵ , dC, ⌫Ci ) = a(dC↵ , dC, ⌫Ci ) dC†L C 1uC⇤⌫Ci†L C 1dC↵⇤i(= 1, 2, 3)d = 6 PROTON DECAY OPERATORS(SCALAR CONTRIBUTIONS)(3, 1, 1/3) 2 1/2✏abcY 5ijuC Ta i CdCb j⇤c⌘2✏abc[Y 10ij + Y 10ji ]dTa iCub j c2 1/2Y 5ijuTa iCej⇤a Y 1ijdC Ta i C⌫Cj a2[Y 10ij + Y 10ji ]eC Ti CuCa j a2 1/2Y 5ijdTa iC⌫j⇤aSU(5) ⇥ U(1) Y 10ij 10+1i 10+1j 50 2(3, 1, 1/3) 2⌘12 1/2✏abc[Y 10ij + Y 10ji ]uTa iCdb j c3 1/2[Y 10ij + Y 10ji ]⌫C Ti CdCa j a↵, (= 1, 2)↵ + < 4L(= (1 5)/2)MU,D,E ! MdiagU,D,E
  • 36. SU(5) Y 1ij10i1j10⇤Y 5ij5i5j10(3, 1, 2/3)⌘ Y 1ijuC Ta i C⌫Cj⇤a 2 1/2✏abcY 5ijdC Ta i CdCb j cY 5= Y 5 TOH(d↵, e ) = a(d↵, e ) uTL C 1d↵ uTL C 1eOH(d↵, eC) = a(d↵, eC) uTL C 1d↵ eC†L C 1uC⇤OH(dC↵ , e ) = a(dC↵ , e ) dC↵†L C 1uC⇤uTL C 1eOH(dC↵ , eC) = a(dC↵ , eC) dC↵†L C 1uC⇤eC†L C 1uC⇤OH(d↵, d , ⌫i) = a(d↵, d , ⌫i) uTL C 1d↵ dTL C 1⌫iOH(d↵, dC, ⌫i) = a(d↵, dC, ⌫i) dC†L C 1uC⇤dT↵ L C 1⌫iOH(d↵, dC, ⌫Ci ) = a(d↵, dC, ⌫Ci ) uTL C 1d↵ ⌫Ci†L C 1dC⇤OH(dC↵ , dC, ⌫Ci ) = a(dC↵ , dC, ⌫Ci ) dC†L C 1uC⇤⌫Ci†L C 1dC↵⇤i(= 1, 2, 3)d = 6 PROTON DECAY OPERATORS(SCALAR CONTRIBUTIONS*)*P. Nath and P.F. Pérez, Phys. Rept. 441 (2007) 191-317.WE WILL TAKE NEUTRINOS TO BE MAJORANAPARTICLES IN WHAT FOLLOWS.
  • 37. SU(5) Y 1ij10i1j10⇤Y 5ij5i5j10(3, 1, 2/3)⌘ Y 1ijuC Ta i C⌫Cj⇤a 2 1/2✏abcY 5ijdC Ta i CdCb j cY 5= Y 5 TOH(d↵, e ) = a(d↵, e ) uTL C 1d↵ uTL C 1eOH(d↵, eC) = a(d↵, eC) uTL C 1d↵ eC†L C 1uC⇤OH(dC↵ , e ) = a(dC↵ , e ) dC↵†L C 1uC⇤uTL C 1eOH(dC↵ , eC) = a(dC↵ , eC) dC↵†L C 1uC⇤eC†L C 1uC⇤OH(d↵, d , ⌫i) = a(d↵, d , ⌫i) uTL C 1d↵ dTL C 1⌫iOH(d↵, dC, ⌫i) = a(d↵, dC, ⌫i) dC†L C 1uC⇤dT↵ L C 1⌫iOH(d↵, dC, ⌫Ci ) = a(d↵, dC, ⌫Ci ) uTL C 1d↵ ⌫Ci†L C 1dC⇤OH(dC↵ , dC, ⌫Ci ) = a(dC↵ , dC, ⌫Ci ) dC†L C 1uC⇤⌫Ci†L C 1dC↵⇤i(= 1, 2, 3)d = 6 PROTON DECAY OPERATORS(SCALAR CONTRIBUTIONS)⌘ Y 1ijuC Ta i C⌫Cj⇤a 2 1/2✏abcY 5ijdC Ta i CdCb j cY 5= Y 5 TOH (d↵, e ) = a(d↵, e ) uTL C 1d↵ uTL C 1eOH (d↵, eC) = a(d↵, eC) uTL C 1d↵ eC†L C 1uC⇤OH (dC↵ , e ) = a(dC↵ , e ) dC↵†L C 1uC⇤uTL C 1eOH (dC↵ , eC) = a(dC↵ , eC) dC↵†L C 1uC⇤eC†L C 1uC⇤OH (d↵, d , ⌫i) = a(d↵, d , ⌫i) uTL C 1d↵ dTL C 1⌫iOH (d↵, dC, ⌫i) = a(d↵, dC, ⌫i) dC†L C 1uC⇤dT↵ L C 1⌫iOH (d↵, dC, ⌫Ci ) = a(d↵, dC, ⌫Ci ) uTL C 1d↵ ⌫Ci†L C 1dC⇤OH (dC↵ , dC, ⌫Ci ) = a(dC↵ , dC, ⌫Ci ) dC†L C 1uC⇤⌫Ci†L C 1dC↵⇤i(= 1, 2, 3)OH(d↵, e ) = a(d↵, e ) uTL C 1d↵ uTL C 1eOH(d↵, eC) = a(d↵, eC) uTL C 1d↵ eC†L C 1uC⇤OH(dC↵ , e ) = a(dC↵ , e ) dC↵†L C 1uC⇤uTL C 1eOH(dC↵ , eC) = a(dC↵ , eC) dC↵†L C 1uC⇤eC†L C 1uC⇤OH(d↵, d , ⌫i) = a(d↵, d , ⌫i) uTL C 1d↵ dTL C 1⌫iOH(d↵, dC, ⌫i) = a(d↵, dC, ⌫i) dC†L C 1uC⇤dT↵ L C 1⌫iOH(d↵, dC, ⌫Ci ) = a(d↵, dC, ⌫Ci ) uTL C 1d↵ ⌫Ci†L C 1dC⇤OH(dC↵ , dC, ⌫Ci ) = a(dC↵ , dC, ⌫Ci ) dC†L C 1uC⇤⌫Ci†L C 1dC↵⇤i(= 1, 2, 3)↵, (= 1, 2)↵ + < 4L(= (1 5)/2)
  • 38. p-DECAY WIDTHS(SCALAR CONTRIBUTIONS)(p ! ¯⌫i⇡+) =(m2p m2⇡+ )232⇡f2⇡m3p|↵ a(d1, dC1 , ⌫i) + a(d1, d1, ⌫i)|2(1 + D + F)2(3, 1, 1/3)(3, 3, 1/3)(3, 1, 4/3)(3, 1, 2/3)SU(5) Y 10ij 10i10j50(3, 1, 1/3) 12 1/2✏abc[Y 10ij + Y 10ji ]dTa iCub j c⌧ ⇠ 1m > 1.0 ⇥ 1012✓↵0.0112 GeV3◆1/2GeV(p ! ⇡+¯⌫)(p ! K+ ¯⌫)= 9.01⌧ ⌘⌧ ⇠ 1PARTIAL LIFETIME
  • 39. d = 6 PROTON DECAY COEFFICIENTS(SCALAR CONTRIBUTIONS)SU(5) ⇥ U(1) Y 1ij10+1i 1+5j 10⇤ 6Y 5ij5i 5j 10+6(3, 1, 2/3)+6⌘ Y 1ijdC Ta i CeCj⇤a 2 1/2✏abcY 5ijuC Ta i CuCb j cY 5= Y 5 Ta(d↵, e ) =p2m2 (UT(Y 10+ Y 10 T)D)1↵ (UTY 5E)1a(d↵, eC) =4m2 (UT(Y 10+ Y 10 T)D)1↵ (E†C(Y 10+ Y 10 T)†U⇤C) 1a(dC↵ , e ) =12m2 (D†CY 5 †U⇤C)↵1 (UTY 5E)1a(dC↵ , eC) =p2m2 (D†CY 5 †U⇤C)↵1 (E†C(Y 10+ Y 10 T)†U⇤C) 1a(d↵, d , ⌫i) =p2m2 (UT(Y 10+ Y 10 T)D)1↵ (DTY 5N) ia(d↵, dC, ⌫i) =12m2 (D†CY 5 †U⇤C) 1 (DTY 5N)↵ia(d↵, dC, ⌫Ci ) =2m2 (UT(Y 10+ Y 10 T)D)1↵ (N†CY 1 †D⇤C)ia(dC↵ , dC, ⌫Ci ) =1p2m2(D†CY 5 †U⇤C) 1 (N†CY 1 †D⇤C)i↵
  • 40. d = 6 PROTON DECAY COEFFICIENTS(SCALAR CONTRIBUTIONS*)SU(5) ⇥ U(1) Y 1ij10+1i 1+5j 10⇤ 6Y 5ij5i 5j 10+6(3, 1, 2/3)+6⌘ Y 1ijdC Ta i CeCj⇤a 2 1/2✏abcY 5ijuC Ta i CuCb j cY 5= Y 5 Ta(d↵, e ) =p2m2 (UT(Y 10+ Y 10 T)D)1↵ (UTY 5E)1a(d↵, eC) =4m2 (UT(Y 10+ Y 10 T)D)1↵ (E†C(Y 10+ Y 10 T)†U⇤C) 1a(dC↵ , e ) =12m2 (D†CY 5 †U⇤C)↵1 (UTY 5E)1a(dC↵ , eC) =p2m2 (D†CY 5 †U⇤C)↵1 (E†C(Y 10+ Y 10 T)†U⇤C) 1a(d↵, d , ⌫i) =p2m2 (UT(Y 10+ Y 10 T)D)1↵ (DTY 5N) ia(d↵, dC, ⌫i) =12m2 (D†CY 5 †U⇤C) 1 (DTY 5N)↵ia(d↵, dC, ⌫Ci ) =2m2 (UT(Y 10+ Y 10 T)D)1↵ (N†CY 1 †D⇤C)ia(dC↵ , dC, ⌫Ci ) =1p2m2(D†CY 5 †U⇤C) 1 (N†CY 1 †D⇤C)i↵*R.N. Mohapatra, Phys. Rev. Lett. 43, 893 (1979).
  • 41. d = 6 PROTON DECAY COEFFICIENTS(SCALAR CONTRIBUTIONS*)*R.N. Mohapatra, Phys. Rev. Lett. 43, 893 (1979).1E = DCD = ECU = UCN = I U†D = VCKMm > 2.2 ⇥ 1011✓|↵|0.0112 GeV3◆1/2GeVm > 2.2 ⇥ 1011GeVE = DCD = ECU = UCU†D = VCKMN = IE = ID = Im > 2.2 ⇥ 1011✓|↵|0.0112 GeV3◆1/2GeVm > 2.2 ⇥ 1011GeVp!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dE = DCD = ECU = UCU†D = VCKMN = IE = ID = Im > 2.2 ⇥ 1011✓|↵|0.0112 GeV3◆1/2GeVm > 2.2 ⇥ 1011GeV
  • 42. MINIMAL SU(5) IS VERY PREDICTIVE BECAUSE IT IS NOT VIABLE!d = 6 PROTON DECAY COEFFICIENTS(SCALAR CONTRIBUTIONS*)*R.N. Mohapatra, Phys. Rev. Lett. 43, 893 (1979).
  • 43. MINIMAL VIABLE SU(5)(CHARGED FERMION MASSES)1⇤ ⌘✏↵ ⌘Yij 10↵i 10j 5⌘1⇤ ⌘✏↵ ⌘Yij 10↵i 10j 5⌘Yij 10↵i 5j 5⇤↵Yij 10↵i24⇤5j 5⇤↵Xi(DTYDN)↵i(DTYDN)⇤i =1v25((MdiagD )2)↵Xi(DTYU N)↵i(DTYU N)⇤i =4v25(V TUD(MdiagU )2V ⇤UD)↵1⇤ ⌘✏↵ ⌘Yij 10↵i 10j 5⌘Yij 10↵i 5j 5⇤↵Yij 10↵i24⇤5j 5⇤↵Xi(DTYDN)↵i(DTYDN)⇤i =1v25((MdiagD )2)↵Xi(DTYU N)↵i(DTYU N)⇤i =4v25(V TUD(MdiagU )2V ⇤UD)↵1⇤ ⌘✏↵ ⌘Yij 10↵i 10j 5⌘Yij 10↵i 5j 5⇤↵Yij 10↵i24⇤5j 5⇤↵Xi(DTYDN)↵i(DTYDN)⇤i =1v25((MdiagD )2)↵Xi(DTYU N)↵i(DTYU N)⇤i =4v25(V TUD(MdiagU )2V ⇤UD)↵CUTOFFY 10ij 10i10j45Y 5ij10i5j45⇤Y 10ij 10i10j5Y 5ij10i5j5⇤MD = Y 5 Tv⇤45⇤MD =12Y 5 Tv⇤5ME = 3Y 5v⇤45ME =12Y 5v⇤5Yij 10i10j45Y 5ij10i5j45⇤Y 10ij 10i10j5Y 5ij10i5j5⇤MD = Y 5 Tv⇤45⇤MD =12Y 5 Tv⇤5ME = 3Y 5v⇤45ME =12Y 5v⇤5MU = 2p2(Y 5Y 5 T)vMU =p2(Y 10+ Y 10 T)v10 ⇥ 10 = 5 45 : MU10 ⇥ 5 = 5 45 : ME, M10+1⇥ 10+1= 5+245+2
  • 44. PREDICTIONS*(MINIMAL VIABLE SU(5))(3, 1, 2/3)⌘ Y 1ijuC Ta i C⌫Cj⇤a 2 1/2✏abcY 5ijdC Ta i CdCb j cY 5= Y 5 TOH(d↵, e ) = a(d↵, e ) uTL C 1d↵ uTL C 1eOH(d↵, eC) = a(d↵, eC) uTL C 1d↵ eC†L C 1uC⇤OH(dC↵ , e ) = a(dC↵ , e ) dC↵†L C 1uC⇤uTL C 1eOH(dC↵ , eC) = a(dC↵ , eC) dC↵†L C 1uC⇤eC†L C 1uC⇤OH(d↵, d , ⌫i) = a(d↵, d , ⌫i) uTL C 1d↵ dTL C 1⌫iOH(d↵, dC, ⌫i) = a(d↵, dC, ⌫i) dC†L C 1uC⇤dT↵ L C 1⌫iOH(d↵, dC, ⌫Ci ) = a(d↵, dC, ⌫Ci ) uTL C 1d↵ ⌫Ci†L C 1dC⇤OH(dC↵ , dC, ⌫Ci ) = a(dC↵ , dC, ⌫Ci ) dC†L C 1uC⇤⌫Ci†L C 1dC↵⇤*I. Doršner, S. Fajfer and N. Košnik, Phys. Rev. D 86:015013, 2012, 1204.0674.
  • 45. PREDICTIONS*(MINIMAL VIABLE SU(5))UTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiXi=1,2,3(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵U†D ⌘ VUDU = UCK0UTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiXi=1,2,3(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵U†D ⌘ VUDU = UCK0*I. Doršner, Phys. Rev. D 86:055009, 2012, 1206.5998.
  • 46. PREDICTIONS(MINIMAL VIABLE SU(5))UTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiXi=1,2,3(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵U†D ⌘ VUDU = UCK0a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiXi=1,2,3(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵MU = MTUU†D ⌘ VUDU = UCK0(K0)11 = ei5 =0@H1A2
  • 47. PREDICTIONS(MINIMAL VIABLE SU(5))a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiXi=1,2,3(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵U†D ⌘ VUDU = UCK0(K0)11 = ei5 =0@H1A(p ! e+⇡0) ⇠↵2v45m438(VUD)11(VUD)13m⌧ mb2↵ 11a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiXi=1,2,3(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵U†D ⌘ VUDU = UCK0(K0)11 = ei5 =0@H1A5a(dj, dCk , ⌫i) =2m2 v25(VUDMdiagD )1k(DTMDN)jiXi=1,2,3(DTMDN)↵i(DTMDN)⇤i = (Mdiag 2D )↵MU = MTUU†D ⌘ VUDU = UCK0(K0)11 = ei5 =0@H1A(p ! e+⇡0) ⇠↵2v45m438(VUD)11(VUD)13m⌧ mb2
  • 48. PREDICTIONS(MINIMAL VIABLE SU(5))p!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11a(dj, dk, ⌫i) =2m2 v25(MdiagU K0VUD)1j(DTMDN)kia(dj, dC, ⌫i) =2(VUDMdiag)1k(DTMDN)ji
  • 49. PREDICTIONS(MINIMAL VIABLE SU(5))3 2 1 0 1 2 31.21.41.61.82.02.2Φm1011GeVp K Ν
  • 50. PREDICTIONS(MINIMAL VIABLE SU(5))ut of the way we are ready toproton decay mediating scalaro in the next section.AY LEPTOQUARKscalar that contributes to pro-imensional scalar representa-number violating dimension-es are [8]L C−1dj dTk L C−1νi,Ck†L C−1uC∗dTj L C−1νi,1, 2) (j + k < 4) representγ5)/2. Our notation is suchfor the d (s) quark. The colortensor in the SU(3) space isi) operators contribute exclu-with anti-neutrinos in the fi-ents for the p → π+¯ν (p →i=1,2,3DClearly, the lepton mixing matrix does not affect proton decaysignatures through scalar exchange. It is also clear that thep → π+¯ν decay rate is significantly suppressed compared tothe p → K+¯ν one. The suppression factor, as inferred fromEq. (11), is proportional to (md/ms)2.For the decay widths for p → π+¯ν and p → K+¯ν channelswe findΓp→π+ ¯ν = Cπ+ A (m2u + m2d + 2mumd cos φ)m2d,Γp→K+ ¯ν ≈ CK+ A (m2u + m2d + 2mumd cos φ)m2s,where we neglect terms suppressed by either (md/ms)2or|(VUD)12|2in the expression for Γp→K+ ¯ν . Here, A =4|α|2|(VUD)11|2/v4, eiφ= (K0)11 and we introduceCK+ =(m2p − m2K+ )232πf2πm3p1 +mp3mΛ(D + 3F)2. (12)After we insert all low-energy parameters we findΓp→π+ ¯ν /Γp→K+ ¯ν = 10−2. (13)m > 2.2 ⇥ 1011✓|↵|0.0112 GeV3◆1/2GeVm > 2.2 ⇥ 1011GeVp!⇡+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2dp!K+ ¯⌫ ⇠ (m2u + m2d + 2mumd cos )m2sUTMU UC = MdiagU DTMDDC = MdiagD ETMEEC = MdiagE↵ 11↵ 12
  • 51. CONCLUSIONSPredictions of the minimal viable version ofSU(5) for the two-body p-decay modes inducedthrough scalar leptoquark exchange exhibitminimal (one-phase only) model dependence forp → K+ ν and p → π+ ν channels.There exists an accurate limit on the mass of thescalar leptoquark.The ratio of p-decay widths for channels with π+and K+ in the final state is phase independent andpredicts strong suppression of the former widthwith respect to the latter one.
  • 52. THANK YOU!CONTACT E-MAIL:ILJA.DORSNER@IJS.SI

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