BNV and LNV in MSSM. Mu-Chun Chen, University of California, Irvine

Transcription

1 BNV and LNV in MSSM Mu-Chun Chen, University of California, Irvine Based on Collaborations with Maximilian Fallbacher, Michael Ratz, Christian Staudt, Volodymyr Takhistov, Andreas Trautner, Patrick Vaudrevange INT Workshop on Neutron-Antineutron Oscillations: Appearance, Disappearance and Baryogenesis, Seattle, Oct 23-27, 2017

2 Baryon Number in the SM Standard Model Lagrangian: accidental symmetries B: no p-decay, no n-nbar oscillation L, Le, Lμ, Lτ: no nu-oscillation, no clfv Baryon Number violated at quantum level: non-perturbative effects associated with SU(2)L ΔB = ΔL = 3 Δ(B-L) = 0 at T=0: effects negligible V[N ] CS ) N CS L L L e µ Q 1 Q Q 3 2 2

3 Expectation for Baryon Number Violation B and L cannot be exact global symmetries all global symmetries violated by quantum gravity B or L symmetries are not exact gauge symmetries unless gauge coupling g < e Lee and Yang (1955) B and L conservation not sacred, violated by new particles and fields 3

4 Big Hint of Baryon Number Violation CMB anisotropy Big Bang Nucleosynthesis primordial deuterium abundance agree with WMAP 4 He & 7 Li discrepancies WMAP + Deuterium Abundance Cosmological matter-antimatter asymmetry n B n γ η B = (6.1 ± 0.3)

5 Three Sakharov Conditions Early Universe Universe Now [Picture credit: H. Murayama] Baryon number can be generated dynamically, if violation of baryon number violation of Charge-Conjugation (C) and Charge Parity (CP) departure from thermal equilibrium 5

6 Baryon Number beyond the SM SM as low energy effective theory: Weinberg (1979) L = L SM + O 5D M + O 6D M new physics effects EFT with quarks, leptons, and gauge fields QD > C On,, g QQQL Tf QQQEQE F B = L= 1 proton decay B = 2 neutronantineutron oscillation 6

7 Baryon Number beyond the SM SM as low energy effective theory: Weinberg (1979) L = L SM + O 5D M + O 6D M new physics effects EFT with quarks, leptons, gauge fields and the Higgs: 050 s Y LLMTHL L = 2 neutrino Majorana mass Unique window into high scale physics 7

8 MSSM Solution for gauge hierarchy problem BNV and LNV already at renormalizable level Gauge invariant superpotential terms up to order 4 W = µ H d H u + κ i L i H u + Y ij e L i H d E j + Y ij d Q ih d D j + Y ij u Q i H u U j + λ ijk L i L j E k + λ ijk L iq j D k + λ ijk U id j D k + κ (0) ij H u L i H u L j + κ (1) ijkl Q iq j Q k L l + κ (2) ijkl U iu j D k E l! 1/10 15 GeV in order to explain see saw suppressed ν masses Constraints from neutrino masses 8

9 MSSM Gauge invariant superpotential terms up to order 4 W = µ H d H u + κ i L i H u! TeV + Y ij e L ih d E j + Y ij d Q ih d D j + Y ij u Q ih u U j + λ ijk L i L j E k + λ ijk L iq j D k + λ ijk U id j D k + κ (0) ij H u L i H u L j + κ (1) ijkl Q iq j Q k L l + κ (2) ijkl U iu j D k E l Problematic terms µ/bµ problem(s) Why does µ know about the electroweak scale? 9

10 MSSM Gauge invariant superpotential terms up to order 4 W = µ H d H u + κ i L i H u Proton stability: + Y ij e L i H d E j + Y ij d Q ih d D j + Y ij u Q i H u U j + λ ijk L i L j E k + λ ijk L iq j D k + λ ijk U id j D k + κ (0) ij H u L i H u L j + κ (1) ijkl Q iq j Q k L l + κ (2) ijkl U iu j D k E l Problematic terms κ (1) 1121! 10 8 M P µ/bµ problem(s) dimension four and five proton decay operators 10

11 MSSM Traditional Cure of proton decay problem W = µ H d H u + κ i L i H u + Y ij e L i H d E j + Y ij d Q ih d D j + Y ij u Q i H u U j + λ ijk L i L j E k + λ ijk L iq j D k + λ ijk U id j D k + κ (0) ij H u L i H u L j + κ (1) ijkl Q iq j Q k L l + κ (2) ijkl U iu j D k E l need to be strongly suppressed 11

12 MSSM Traditional Cure of proton decay problem Farrar, Fayet (1978); Dimopoulos, Raby, Wilczek (1981) W = µ H d H u + κ i L i H u + Y ij e L i H d E j + Y ij d Q ih d D j + Y ij u Q i H u U j + λ ijk L i L j E k + λ ijk L iq j D k + λ ijk U id j D k + κ (0) ij H u L i H u L j + κ (1) ijkl Q iq j Q k L l + κ (2) ijkl U iu j D k E l forbidden by matter parity 12

13 MSSM Traditional Cure of proton decay problem Ibanez, Ross (1992) W = µ H d H u + κ i L i H u + Y ij e L i H d E j + Y ij d Q ih d D j + Y ij u Q i H u U j + λ ijk L i L j E k + λ ijk L iq j D k + λ ijk U id j D k + κ (0) ij H u L i H u L j + κ (1) ijkl Q iq j Q k L l + κ (2) ijkl U iu j D k E l forbidden by baryon triality 13

14 Traditional cure of proton decay problems MSSM Traditional Cure of proton decay problem W = µ H d H u + κ i L i H u W Gauge invariant superpotential terms up to order 4 include Babu, Gogoladze, Wang (2002); Dreiner, Luhn, Thormeier (2006) = µ H d H u + κ+ i YL i H e ij L ui H d E j + Y ij d Q ih d D j + Yu ij Q i H u U j + Ye ij L i H d + Eλ j + Y ij d Q ih d D j + Yu ij ijk L i L j E k + λ Q i H u U j ijk L iq j D k + λ ijk U id j D k + λ ijk L i L j + E k κ (0) + λ ijk iq j D k λ ijk U id j D k + κ (0) ij H u L i H u L j + κ (1) ij H u L i H u L j + κ (1) ijkl Q iq j Q k L l + κ (2) ijkl Q iq j Q k L l + κ (2) ijkl U iu j D k E l ijkl U iu j D k E l forbidden by proton hexality forbidden by proton hexality Babu et al. (2003b) ; Dreiner et al. (2006) Proton hexality = matter parity + baryon triality 14 Ibáñez and Ross (1992) Dreiner et al. (2006)

15 Proton Hexality Babu, Gogoladze, Wang (2002); Dreiner, Luhn, Thormeier (2006) Proton hexality P 6 = matter parity M 2 baryon triality B 3 Q Ū D L Ē Hu H d ν M B P Appealing features forbids dimension four and five proton decay operators allows Yukawa couplings & Weinberg operator κ (0) ij unique anomaly free symmetry with the above features H u L i H u L j However: not consistent with unification for matter (i.e. inconsistent with universal discrete charges for all matter fields) 15

16 Proton hexality Proton Hexality Disturbing aspects of proton hexality not consistent not consistent with (grand) with (grand) unification unification for matter for matter does does not address not address µ problem µ problem W = µ H d H u + κ i L i H u + Y ij e L i H d E j + Y ij d Q ih d D j + Y ij u Q i H u U j + λ ijk L i L j E k + λ ijk L iq j D k + λ ijk U id j D k + κ (0) ij H u L i H u L j + κ (1) ijkl Q iq j Q k L l + κ (2) ijkl U iu j D k E l +... needs to be suppressed as well... 16

17 Small mu term and SUSY Breaking before SUSY breaking: absence of mu term MSSM Hidden sector: dynamical SUSY SUSY W W Giudice-Masiero Mechanism for the mu problem after SUSY breaking: realistic effective mu term generated Giudice, Masiero (1988) we find a class of an µ W /M 2 P m 3/2 need a symmetry reason for the absence of these operators before SUSY breaking 17

18 Discrete We know R already Symmetries that { q = qθ 0 mod η R-parity ( ): q Hu = q Hd = 0 mod M Anomaly universality } only R symmetries anomaly freedom can forbid the µ term consistency with SU(5) A SU(3)2 = 3q R θ mod η =! q θ mod in the η = MSSM A SU(2)2 R M M Baryon triality nique 4 symmetry Lee et al. (2011) ; Chen et al. (2012) No continuous R symmetries available in MSSM Chamseddine, Dreiner (1996) η is even order M is a multiple of 4 Anomaly free Only remaining symmetries, option: Discrete µ R and symmetries unification Simplest possibility: M = 4 & q = q Higher order : θ = 1 R 4 symmetry Working assumptions: Anomaly freedom (i) anomaly freedom (allow for GS anomaly cancellation) Supersymmetric unification and R symmetries (iii) Yukawa couplings and Weinberg neutrino mass operator Lee et al. (2011) ; Chen et al. (2012) allowed (iv) SU(5) orr Consider M SO(10) symmetry GUT relations which commutes for quarkswith andso(10) leptons i.e. quarks and leptons have universal charge q Willbottom line: prove: 1. assuming (i) & SU(5) relations: only R symmetries can forbid the µ term uniqu commutes with R unique symmetry : 4 w/ q = q θ = 1 & q Hu = q Hd = 0 2. assuming (i) (iii) & SO(10) relations: unique R 4 symmetry R Unique R 4m symmetry4 with q = q symmetry θ = m & m Kurosawa, Maru, Yanagida (2001); Babu, Gogoladze, Wang (2002) Alternatives: (ii) µ term forbidden at perturbative level SO(10) implies unique symmetry However: these are only trivial extensions (as far as the MSSM is concerned) [Babu & Gogoladze & Lee, Raby, Ross, Rat 18 Kurosawa, Maru, Yan Lee, Raby, Ratz, Ross, Schieren, Schmiddt-Hoberg, Vaudrevaunge (2011)

19 Small mu term, Dirac Neutrinos and SUSY Breaking before SUSY breaking: absence of Dirac neutrino masses (as well as Weinberg operator) MSSM Hidden sector: dynamical SUSY SUSY W W Giudice-Masiero Mechanism for the mu problem we find a class of an µ W /M 2 P m 3/2 Giudice, Masiero (1988) after SUSY breaking: realistic effective Dirac neutrino masses generated Y ν m 3/2 M P µ M P Arkani-Hamed, Hall, Murayama, Tucker-Smith, Weiner (2001) need a symmetry reason for the absence of these operators before SUSY breaking 19

20 Dirac Neutrino Mass and the μ Term Anomaly-free, discrete R-symmetries in MSSM: M.-C. C., Ratz, Staudt, Vaudrevange (2012) absence of perturbative mu term constraints on R charges of Hu, Hd SUSY breaking mu term ~ TeV automatically arise we find a class of an µ W /MP 2 m 3/2 absence of perturbative Weinberg operator constraints on R charges of leptons SUSY breaking realistic Dirac neutrino mass automatically arise Y ν m 3/2 M P µ M P solutions automatically forbid dim-4 proton decay, automatically suppress dim-5 proton decay in superpotential 20

21 Dirac Neutrino Mass and the μ Term Search Abelian discrete R symmetries, anomaly freedom (a la Green-Schwarz) forbidding mu term perturbatively consistent with SU(5) allowing usual Yukawa couplings, that satisfy Weinberg operators forbidden perturbatively an example: R 8 symmetry M.-C. C., Ratz, Staudt, Vaudrevange (2012) classes of models found after SUSY breaking: W eff m 3/2 H u H d + m 3/2 LH u ν + m 3/2 QQQL M P MP 2 L = 2 operators forbidden no neutrinoless double beta decay L = 4 operators allowed new LNV processes M.-C. C., Ratz, Staudt, Vaudrevange (2012) A simultaneous solution possible with discrete generation dependent R symmetries (Abelian or non-abelian!) M.-C.C., M. Ratz, A. Trautner (2013) 21

22 MSSM with RPV Operators No sign of SUSY (yet!) at the LHC Rich phenomenology, though need to be careful about proton decay R Classifications of M symmetries compatible with MSSM models with RPV operators ks an (BNV, LNV) Dreiner, Hannusek, Luhn (2012) allowing BNV, LNV at dim-3, 4, 5; mu term allowing GS anomaly cancellation compatibility with GUT only for qθ = 1 with all R charges being integers 22

23 MSSM with RPV Operators Classifications of symmetries compatible with MSSM models with RPV operators ks an (BNV, LNV) Dreiner, Hannusek, Luhn (2012) allowing BNV, LNV at dim-3, 4, 5; mu term allowing GS anomaly cancellation R M compatibility with GUT only for qθ = 1 with all R charges being integers Complete Classifications with qθ > 1 with all R charges being integers M.-C. C, Ratz, Takhistov (2014) allowing for non-universal GS cancellation of discrete anomalies 23

24 Anomaly Cancellation For a U(1)R symmetry: A 3 = 1 [ ] 2q f Q 2 + qf + U qf 4q D θ +3q θ f = 3 ] [2q Q + q 2 U + q D 3q θ, A 2 = 1 [ q Hu + q Hd 2q θ + ( )] 3q f Q 2 + qf L 4q θ f +2q θ (2.20a) = 1 [ )] q Hu + q Hd +3 (3q Q + q L 5q θ, (2.20b) 2 A 1 = 1 [ q Hu + q Hd 2q θ + 1 ( )] q f Q qf U +2qf D +3qf L +6qf 20q E θ YL 2 i = 3 ] [q Hu + q Hd + q Q +8q 10 U +2q D +3q L +6q E 22q θ. (2.20c) Cancelled by GS axion with coupling to field strengths 24

25 Anomaly Cancellation For a discrete R N symmetry: A1, A2, A3 defined only up to modulo η = { N/2 if N is even, N if N is odd. Anomaly universality: universal axion couplings to field strengths Anomaly freedom + Grand unification + Green Schwarz anomaly cancellation Anomaly universality { M.-C. C, Fallbacher, Ratz (2012) A 3 A 2 A 1, where now means modulo η. Pati-Salam partial unification: non-universal anomaly cancellation allowed 25

26 R-parity Violating MSSM Renormalizable Superpotential W ren = µh u H d + Y u fg Q f U g H u + Y d fg Q f D g H d + Y e fg L f E g H d + κ f L f H u + λ fgh L f L g E h + λ fgh L f Q g D h + λ fgh U f D g D h Non-renormalizable BNV and LNV operators O 1 = [QQQL] F, O 2 = [ U U D E ] F, O 3 = [QQQH d ] F, O 4 = [ Q U EH d ]F, O 5 = [LH u LH u ] F, O 6 = [LH u H d H u ] F, [ ] O 7 = U D E, O 8 = [ H u H d E ], D D O 9 = [ Q UL ] [, O D 10 = QQD ], D 26

27 R-parity Violating MSSM To satisfy proton decay constrains (i) with renormalizable B violation: demand existence of U c D c D c, forbid LLE c (thus automatically LQD c ), forbid H d H u, forbid LH u (thus automatically O 4, O 7, O 8, O 9 ), forbid O 1 = QQQL; (ii) with renormalizable L violation: demand existence of LLE c (thus automatically LQD c ), forbid U c D c D c, forbid H d H u (thus automatically LH u, O 4, O 7, O 8, O 9 ), forbid O 1 = QQQL (thus automatically O 3 and O 10 ). Not compatible with SU(5): U c D c D c LLE c 27

28 R-parity Violating MSSM Pati-Salam Compatible q Q = q L,q U = q D = q E, and q Hu = q Hd, Allowing Yukawa couplings Allowing U c D c D c and forbidding LHu 3q Hu 3q L +4q θ = 0 mod N (U D D), q Hu + q L 2q θ 0 mod N (LH u ). PS compatibility allow U D D forbid LH u 2q Hu +2q L 2q θ 0 mod N Weinberg operator is forbidden. PS compatible RPV models with BNV prefer Dirac neutrinos 28

29 R-parity Violating MSSM Complete Classifications of discrete symmetries non-universal GS anomaly cancellation absence of mu term in renormalizable superpotential with R parity conserving renormalizable BNV renormalizable LNV no-perturbative BNV and LNV 29

30 P 2. the discrete symmetry forbids the µ term at the perturbative level. Further, we demonstrate additional features that were absent from DHL [16] including Solutions w/ Universal Anomaly Cancellation the compatibility of charges with (partial) unification, specifically whether the matter charges commute with the Pati Salam group G PS =SU(4) SU(2) L SU(2) R ; 2 a natural suppression of the neutrino masses either through the Weinberg operator or from supersymmetry breaking, λ & λ R parity thus 0 yielding light Dirac neutrinos. λ 0 no before no before This conserved paper is organized as follows. SUSY In Section 2, we present a SUSY novel method for classifying discrete symmetries. We comment on anomaly cancellation, provide a recipe for identifying and eliminating equivalent symmetries, and comment on the limitations of our analysis. In Section 3, we illustrate our methods by yespresenting models obtained no for anomaly universal as well as non universal scenarios while considering both R parity violationyes and conservation. Sectionyes 4 contains our conclusions. 2 Classification R 2.1 Goals of our classification small: 4 R 8 λ λ and λ λ In the MSSM, the renormalizable superpotential terms consistent with the SM gauge symmetry are W ren = µh u H d + Y u fg Q f U g H u + Y d fg Q f D g H d + Y e fg L f E g H d + κ f L f H u + λ fgh L f L g E h + λ fgh L f Q g D h + λ fgh U f D g D h, (2.1) 2 We do not consider compatibility of matter charges with SU(5) or SO(10) in the case of RPV. This 30

31 BNV at renormalizable superpotential universal anomaly cancellation up to order 12 symmetry residual symmetry N Q U D L E H u H d θ N Q U D L E H u H d W GS

32 Example: Z8 R Symmetry BNV at renormalizable super potential U c D c D c allowed at renormalizable superpotential Field Q U D L E H u H d θ R Compatible with Pati-Salam partial unification no neutron-antineutron oscillation 32

33 P 2. the discrete symmetry forbids the µ term at the perturbative level. Further, we demonstrate additional features that were absent from DHL [16] including Solutions the compatibility w/ Non-universal of charges with (partial) Anomaly unification, specifically Cancellation whether the matter charges commute with the Pati Salam group G PS =SU(4) SU(2) L SU(2) R ; 2 a natural suppression of the neutrino masses either through the Weinberg operator or from supersymmetry breaking, thus yielding light Dirac neutrinos. λ & λ R parity 0 λ 0 This paper is organized no as follows. beforein Section 2, no we present before a novel method for conserved classifying discrete symmetries. We comment SUSY on anomaly cancellation, SUSY provide a recipe for identifying and eliminating equivalent symmetries, and comment on the limitations of our analysis. In Section 3, we illustrate our methods by presenting models obtained for anomaly universal as well as non universal scenarios while yes considering both R parity no violation and conservation. Section 4 contains our conclusions. yes yes 2 Classification 2.1 Goals of our classification R λ λ 8 and λ λ R 4 R small: In the MSSM, the renormalizable superpotential terms consistent with the SM gauge 3 symmetry are Figure W ren 2: Summary = µh u H d of+ our Y results. We present the simplest discrete R symmetries with fg u Q f U g H u + Yfg d Q f D g H d + Yfg e L f E g H d non universal anomalies and the specified properties. The symbol indicates the + κ absence of a solution. f L f H u + λ fgh L f L g E h + λ fgh L f Q g D h + λ fgh U f D g D h, (2.1) 2 We do not consider compatibility of matter charges with SU(5) or SO(10) in the case of RPV. This 33

34 Example: Z3 R Symmetry BNV and LNV forbidden at renormalizable superpotential Non-universal anomaly cancellation BNV and LNV generated after SUSY breaking neutron-antineutron oscillations allowed, and can be enhanced if Mp M < Mp 34

35 Example: Z3 R Symmetry BNV and LNV forbidden at renormalizable superpotential Non-universal anomaly cancellation BNV and LNV generated after SUSY breaking is suppressed by, but the μ term is of order counter example: allowing LNV mu ~ kappa ~ m3/2 in SO(10) Acharya, Kane, Kumar, Lu, Zheng (2014) 35