Higgs Doublet and Complex Singlet and U(1) Extensions to the MSSM - PowerPoint PPT Presentation

Higgs Doublet and Complex Singlet and U(1)’ Extensions to the MSSM Valerie Plaus University of Wisconsin-Madison

Outline Doublet Extensions to MSSM Nelson-Randall Model Examples Conclusions Valerie Plaus, UW-Madison 2

Beyond Singlets: 4 Higgs Doublets and Singlets work in progress with Barger, Everett, McCaskey Fields SU (3) C , SU (2) L , U (1) Y , U (1) ′ (1 , 2 , − 1 / 2 , Q 1 , 3 ) H 1 , H 3 1 2 (1 , 2 , 1 / 2 , Q 2 , 4 ) H 2 , H 4 1 2 (1 , 1 , 0 , Q S i ) S i 1 1 Singlets added as needed to solve problem(s) µ Valerie Plaus, UW-Madison 3

Motivation Top-down models String theory: often has many doublets and singlets “natural” large with mixed terms tan β H 2 · H 3 , H 4 · H 1 (A. Nelson and L. Randall; hep-ph/9308277) Valerie Plaus, UW-Madison 4

As yet unstudied... not necessary for EW breaking issue of gauge unification extra exotics (GUTs) gauge unification not fundamental (string models) Valerie Plaus, UW-Madison 5

As yet unstudied... u i Q i · H 2 − h di ¯ W = µH 2 · H 1 + h ui ¯ d i Q i · H 1 − h ei ¯ e i L i · H 1 A major concern: >1 Higgs couples to up-type or down-type quarks tree level FCNCs W ⊃ h d i ¯ d i ¯ d i Q i · H 1 + h ′ d i Q i · H 3 We’ll address this on a case-by-case basis... Misiak, Pokorski and Rosiek; hep-ph/9703442 S.L. Glashow and S. Weinberg; Natural Conservation Laws for Neutral Currents: Phys. Rev. D, 1977 (ID 10.1103/PhysRevD.15.1958) Valerie Plaus, UW-Madison 6

Goal: to categorize and explore phenomenology of various extra doublet models that address the problem µ Observed theme: relatively difficult to get viable scenarios Reason: accidental global symmetries Challenge: to minimally break symmetries without reintroducing problem(s) µ Valerie Plaus, UW-Madison 7

Nelson-Randall Model W = µ 41 H 4 · H 1 + µ 23 H 2 · H 3 doesn’ t solve the problem µ Naive extension: W = a 1 SH 4 · H 1 + a 2 SH 2 · H 3 problem: 1 extra accidental symmetry 1 Goldstone boson after SSB 1 unobserved axion or extra force Valerie Plaus, UW-Madison 8

Aside problem was already observed for models with many singlets and a U (1) ′ (P. Langacker, G. Paz, I. Yavin arXiv:0811.1196) i | S i | 2 + g ′ 2 � � m 2 Q i | S i | 2 ) 2 V ( S 1 ...S N ) = 2 ( i i N-1 accidental symmetries to be broken by superpotential singlet terms bilinear terms: easiest, but new problem µ trilinear: harder to obtain by gauge invariance Valerie Plaus, UW-Madison 9

Now we have doublets as well -> even more constrained in field combinations Goal: to explore this issue systematically Are there any viable scenarios? Naive Nelson-Randall extension is out... Valerie Plaus, UW-Madison 10

2 Singlet Superpotentials 2 singlet N-R model W = a 1 S 1 H 4 · H 1 + a 2 S 2 H 2 · H 3 2 Goldstone bosons What about adding 2 extended N-R models? W = a 1 S 1 H 2 · H 1 + a 2 S 1 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 2 H 2 · H 3 2 Goldstone bosons -> only 1 can be broken by trilinear , or bilinear S 2 1 S 2 S 1 S 2 S 1 S 2 2 Valerie Plaus, UW-Madison 11

2 Singlet Superpotentials 2 singlet N-R model W = a 1 S 1 H 4 · H 1 + a 2 S 2 H 2 · H 3 2 Goldstone bosons What about adding 2 extended N-R models? W = a 1 S 1 H 2 · H 1 + a 2 S 1 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 2 H 2 · H 3 2 Goldstone bosons -> only 1 can be broken by trilinear , or bilinear S 2 1 S 2 S 1 S 2 S 1 S 2 2 Valerie Plaus, UW-Madison 11

2 Singlet Superpotentials 2 singlet N-R model W = a 1 S 1 H 4 · H 1 + a 2 S 2 H 2 · H 3 2 Goldstone bosons What about adding 2 extended N-R models? W = a 1 S 1 H 2 · H 1 + a 2 S 1 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 2 H 2 · H 3 2 Goldstone bosons -> only 1 can be broken by trilinear , or bilinear S 2 1 S 2 S 1 S 2 S 1 S 2 2 Valerie Plaus, UW-Madison 11

2 Singlet Superpotentials 2 singlet N-R model W = a 1 S 1 H 4 · H 1 + a 2 S 2 H 2 · H 3 2 Goldstone bosons What about adding 2 extended N-R models? W = a 1 S 1 H 2 · H 1 + a 2 S 1 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 2 H 2 · H 3 2 Goldstone bosons -> only 1 can be broken by trilinear , or bilinear S 2 1 S 2 S 1 S 2 S 1 S 2 2 Valerie Plaus, UW-Madison 11

2 Singlet Superpotentials 2 singlet N-R model W = a 1 S 1 H 4 · H 1 + a 2 S 2 H 2 · H 3 2 Goldstone bosons What about adding 2 extended N-R models? W = a 1 S 1 H 2 · H 1 + a 2 S 1 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 2 H 2 · H 3 2 Goldstone bosons -> only 1 can be broken by trilinear , or bilinear S 2 1 S 2 S 1 S 2 S 1 S 2 2 Valerie Plaus, UW-Madison 11

What about W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 1 H 2 · H 3 only 1 Goldstone! So we try... W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 1 H 2 · H 3 + µS 1 S 2 Correct mass behaviour, what about FCNCs? Q 1 = Q 3 Gauge invariance -> Q S 1 = − Q S 2 Q 2 = Q 4 + 2 Q S 2 Can only prevent FCNC from up-type or down-type, not both Valerie Plaus, UW-Madison 12

What about W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 1 H 2 · H 3 only 1 Goldstone! So we try... W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 1 H 2 · H 3 + µS 1 S 2 Correct mass behaviour, what about FCNCs? Q 1 = Q 3 Gauge invariance -> Q S 1 = − Q S 2 Q 2 = Q 4 + 2 Q S 2 Can only prevent FCNC from up-type or down-type, not both Valerie Plaus, UW-Madison 12

What about W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 1 H 2 · H 3 only 1 Goldstone! So we try... W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 1 H 2 · H 3 + µS 1 S 2 Correct mass behaviour, what about FCNCs? Q 1 = Q 3 Gauge invariance -> Q S 1 = − Q S 2 Q 2 = Q 4 + 2 Q S 2 Can only prevent FCNC from up-type or down-type, not both Valerie Plaus, UW-Madison 12

What about W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 1 H 2 · H 3 only 1 Goldstone! So we try... W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 1 H 2 · H 3 + µS 1 S 2 Correct mass behaviour, what about FCNCs? Q 1 = Q 3 Gauge invariance -> Q S 1 = − Q S 2 Q 2 = Q 4 + 2 Q S 2 Can only prevent FCNC from up-type or down-type, not both Valerie Plaus, UW-Madison 12

What about W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 1 H 2 · H 3 only 1 Goldstone! So we try... W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 1 H 2 · H 3 + µS 1 S 2 Correct mass behaviour, what about FCNCs? Q 1 = Q 3 Gauge invariance -> Q S 1 = − Q S 2 Q 2 = Q 4 + 2 Q S 2 Can only prevent FCNC from up-type or down-type, not both Valerie Plaus, UW-Madison 12

What about W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 1 H 2 · H 3 only 1 Goldstone! So we try... W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 1 H 2 · H 3 + µS 1 S 2 Correct mass behaviour, what about FCNCs? Q 1 = Q 3 Gauge invariance -> Q S 1 = − Q S 2 Q 2 = Q 4 + 2 Q S 2 Can only prevent FCNC from up-type or down-type, not both Valerie Plaus, UW-Madison 12

What about W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 1 H 2 · H 3 only 1 Goldstone! So we try... W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 1 H 2 · H 3 + µS 1 S 2 Correct mass behaviour, what about FCNCs? Q 1 = Q 3 Gauge invariance -> Q S 1 = − Q S 2 Q 2 = Q 4 + 2 Q S 2 Can only prevent FCNC from up-type or down-type, not both Valerie Plaus, UW-Madison 12

What about W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 1 H 2 · H 3 only 1 Goldstone! So we try... W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 1 H 2 · H 3 + µS 1 S 2 Correct mass behaviour, what about FCNCs? Q 1 = Q 3 Gauge invariance -> Q S 1 = − Q S 2 Q 2 = Q 4 + 2 Q S 2 Can only prevent FCNC from up-type or down-type, not both Valerie Plaus, UW-Madison 12

What about W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 1 H 2 · H 3 only 1 Goldstone! So we try... W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 2 H 4 · H 1 + a 4 S 1 H 2 · H 3 + µS 1 S 2 Correct mass behaviour, what about FCNCs? Q 1 = Q 3 Gauge invariance -> Q S 1 = − Q S 2 Q 2 = Q 4 + 2 Q S 2 Can only prevent FCNC from up-type or down-type, not both Valerie Plaus, UW-Madison 12

Superpotential W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 3 H 4 · H 1 + a 4 S 4 H 2 · H 3 Cases: all different S 1 � = S 2 � = S 3 � = S 4 3 different S i = S j � = S k � = S l only 2 singlets S i = S j � = S k = S l only 1 singlet S 1 = S 2 = S 3 = S 4 Valerie Plaus, UW-Madison 13

Superpotential W = a 1 S 1 H 2 · H 1 + a 2 S 2 H 4 · H 3 + a 3 S 3 H 4 · H 1 + a 4 S 4 H 2 · H 3 all or 3 different: 4 or 3 Goldstone bosons only 2 singlets: S 1 =S 3 or S 1 =S 4 : extra Goldstone boson S 1 =S 2 : correct Goldstone bosons only 1 singlet: correct Goldstone bosons Consequences: possible FCNCs Valerie Plaus, UW-Madison 14

Observations so far... Global symmetries -> breaking in superpotential restricts charges U (1) ′ In progress: study viable scenarios and examine FCNC problem in more detail Future: RGEs: connect to top down models Anomalies and GUT embedding consequences Valerie Plaus, UW-Madison 15