A peculiar aspect of the MSSM, the simplest supersymmetric extension of the
Standard Model, is that it is usually defined including an ad hoc symmetry,
R-parity, whose sole purpose is to forbid rapid proton decay. This symmetry
deeply alters the phenomenology of the MSSM, and renders the experimental
search strategies quite involved. Besides, the MSSM suffers from a number of
flavor puzzles. Generically, the superparticle contributions to Flavor Changing
Neutral Currents (FCNC) are too large compared to experiment, both in the quark
and lepton sectors. The Minimal Flavor Violation (MFV) hypothesis aims at
suppressing these contributions, and when enforced as a symmetry principle,
achieves this in a very natural and systematic way. In this talk, it will be
shown that imposing MFV is not only able to suppress supersymmetric
contributions to FCNC, it also naturally explains the apparent stability of the
proton. As a result, R-parity can be avoided altogether, motivating the search
for supersymmetry through simpler channels, like for example single stop
resonant production, whose strength is predicted by MFV.Comment: Parallel talk given at the 34th International Conference on High
  Energy Physics (ICHEP08), 29 July - 5 August 2008, Philadelphia, USA. 5
  pages, 1 figur

Smith, Christopher

English

arXiv

Bern Open Repository and Information System (BORIS)

arXiv:0809.3152v2  [hep-ph]  16 Oct 200834th International Conference on High Energy Physics, Philadelphia, 2008Minimal Flavor Violation as an alternative to R-parityChristopher SmithInstitut fu¨r Theoretische Physik, Universita¨t Bern, Sidlerstrasse 5, CH-3012 Bern, SwitzerlandA peculiar aspect of the MSSM, the simplest supersymmetric extension of the Standard Model, is that it is usuallydefined including an ad hoc symmetry, R-parity, whose sole purpose is to forbid rapid proton decay. This symmetrydeeply alters the phenomenology of the MSSM, and renders the experimental search strategies quite involved. Besides,the MSSM suffers from a number of flavor puzzles. Generically, the superparticle contributions to Flavor ChangingNeutral Currents (FCNC) are too large compared to experiment, both in the quark and lepton sectors. The Mini-mal Flavor Violation (MFV) hypothesis aims at suppressing these contributions, and when enforced as a symmetryprinciple, achieves this in a very natural and systematic way. In this talk, it will be shown that imposing MFV is notonly able to suppress supersymmetric contributions to FCNC, it also naturally explains the apparent stability of theproton. As a result, R-parity can be avoided altogether, motivating the search for supersymmetry through simplerchannels, like for example single stop resonant production, whose strength is predicted by MFV.1. INTRODUCTIONThe Minimal Supersymmetric extension of the Standard Model (MSSM) introduces many additional flavoredparticles – one scalar squark (slepton) superpartner for each of the chiral quark (lepton) fields. If light, their presenceforces us to fine-tune the parameters of the MSSM in order to satisfy all experimental constraints. This is the so-called MSSM flavor puzzle. For instance, the extensive and precise data from B and K physics on Flavor-ChangingNeutral Currents (FCNC) requires limiting squark-induced flavor mixings, including the possible additional CP-violating phases occurring there. Similarly, the non-observation of Lepton Flavor Violating (LFV) transitions likeµ → eγ restricts the acceptable level of flavor-mixing in the slepton sector. In these contexts, the Minimal FlavorViolation (MFV) hypothesis [1, 2] aims at restoring naturalness, by automatically limiting the maximal amount offlavor mixings in both the squark and slepton sectors (for phenomenological applications in the MSSM, see e.g. [3, 4]).There is yet another, more puzzling consequence of the presence of the squarks and sleptons. These scalar particlescan be used to write down renormalizable Yukawa-type interactions violating baryon (B) and lepton (L) numbers,which then drive proton decay at tree-level. This is a severe problem given the current experimental bounds onthe proton lifetime, well-beyond 1030 years for most decay modes. These bounds are actually so tight that theMSSM is usually equipped with an ad-hoc symmetry, R-parity [5], which simply forbids all the ∆B = 1 and ∆L = 1interactions. In this talk, we will present a different approach, in which all these couplings are not discarded outright.Instead, since these ∆B = 1 and ∆L = 1 interactions are also necessarily flavor-changing, proton stability will beconsidered as a manifestation of the MSSM flavor puzzle. Then, MFV will be called in to constrain all the R-parityviolating couplings, by using exactly the same strategy as for FCNC. That MFV is a viable alternative to R-paritywill finally emerge naturally [6], and will force a reassessment of possible supersymmetric signals at colliders.2. MFV AND THE ORIGIN OF THE FLAVOR STRUCTURESThe formulation of MFV is detailed in Refs. [2, 4, 6], and is only sketched here. To start with, one observes thatthe three generations of (s)quarks and (s)leptons have identical gauge interactions. In other words, the gauge sectorof the MSSM exhibits a global U(3)5 flavor-symmetry, one U(3) for each of the quark and lepton superfields [7]GF ≡ U(3)5 = Gq ×Gℓ × U(1)5, with Gq ≡ SU(3)Q × SU(3)U × SU(3)D, Gℓ ≡ SU(3)L × SU(3)E . (1)Of course, this symmetry is broken in many sectors of the MSSM – specifically, by the R-parity conserving andviolating superpotential and soft SUSY breaking couplings. However, at present, the only observed breakings ofGF are the non-equality of quark and lepton masses, and their mixings. All these entirely derive from the usual1source: https://doi.org/10.7892/boris.30936 | downloaded: 8.5.201634th International Conference on High Energy Physics, Philadelphia, 2008Yukawa couplings Yu,d,e, introduced in the MSSM through the superpotentialW (up to neutrino masses and mixings,discussed later)W ⊃ UYuQHu −DYdQHd − EYeLHd . (2)Therefore, the starting point of MFV is to assume that these Yukawa interactions actually represent the maximalflavor-symmetry breakings allowed in the full MSSM.This does not mean that the other MSSM sectors where GF is broken are ruled out, but forces all the parametersoccurring there to be related to the Yukawa couplings. To systematically investigate these relationships, MFV isformulated as a symmetry principle: The Yukawa interactions in Eq.(2) are formally GF -invariant if the Yukawa cou-plings are promoted to spurion fields, i.e. are made to transform under GF just such as to balance the transformationsof the quark and lepton superfields:Yu ∼ (3¯, 3, 1)Gq , Yd ∼ (3¯, 1, 3)Gq , Ye ∼ (3¯, 3)Gℓ . (3)These Yukawa spurions are then used to parametrize all the flavor-breaking couplings of the MSSM as formallyGF -invariant. Once this step is complete, Yu, Yd and Ye are frozen back to their physical values, thereby obtainingpredictions for the strength of these couplings under MFV.Having reconstructed all the flavor-breaking couplings in terms of the Yukawa couplings, they all become non-generic. They exhibit highly hierarchical structures directly inherited from those of the quark and lepton masses, aswell as of the CKM matrix. In this way, the fine-tunings required to satisfy the experimental constraints on FCNCand LFV transitions are to a large extent automatically achieved, and are just as natural (or unnatural) as theYukawa couplings themselves. In this sense, MFV does not explain the origin of the flavor structures, but reducesthem to the minimal irreducible set of elementary flavor-breaking structures shown in Eq.(3).3. THE ∆B = 1 and ∆L = 1 COUPLINGS ARE INTRINSICALLY DIFFERENT!The gauge quantum numbers of the quark and lepton superfields are such that possible renormalizable ∆B = 1 and∆L = 1 couplings have intrinsically different properties under the flavor group GF . Indeed, while it is immediatelypossible to parametrize the former, λ′′IJKU IDJDK , in terms of Yukawa spurions, for example asλ′′IJK = εLJK(YuY†d)IL, εLMNYILu YJMd YKNd , ... (4)the latter are forbidden as long as mν = 0. In other words, the charged lepton Yukawa spurion Ye alone does notpermit to write the µ′ILIHd, λIJKLILJEK or λ′IJKLIQJDK couplings as Gℓ-invariants.To account for the tiny neutrino masses without introducing unnaturally small numbers, we supplement theMSSM with a seesaw mechanism of type I, by adding right-handed neutrino terms 12NTMRN + NYνLHu to thesuperpotential [8]. Though this formally extends the flavor symmetry group to GF ×U(3)N , the heavy N fields neveroccur at low-energy and only the spurion combinations which are singlets under U(3)N are relevant. Expanding inthe inverse right-handed neutrino mass matrix MR, these areY†νYν , YTν (M−1R )Yν , YTν (M−1R )(M−1R )∗Y∗ν , ... (5)The unsuppressed spurion, Y†νYν , which tunes LFV effects as in the usual supersymmetric seesaw [9], transformsas (8, 1) under Gℓ, and is thus of no help to write the µ′, λ or λ′ couplings as Gℓ-invariants. The only way to getflavor-symmetric operators is to use the neutrino mass spurion, Υν ≡ vuYTν (M−1R )Yν ∼ O(mν/vu), which transformsas (6¯, 1). For example, the µ′, λ or λ′ couplings can be written asµ′I = µεILM (Υ†ν)LM , ... (6)λIJK = εILM (Υ†ν)LMYKJe , ... (7)λ′IJK = εILM (Υ†ν)LMYKJd , ... (8)234th International Conference on High Energy Physics, Philadelphia, 2008In fact, since the 6¯ is symmetric, while ε-tensors are antisymmetric, additional Ye insertions are needed to get non-vanishing contributions, e.g. εILM (Υ†ν)LM → εILM (Y†eYeΥ†ν)LM . We thus arrive at the conclusion that all ∆L = 1couplings are suppressed by the tiny neutrino masses as well as by the small charged-lepton masses.4. MFV CAN EXPLAIN THE VERY LONG PROTON LIFETIMETo ensure that MFV is sufficient to prevent a too fast proton decay, we must construct all the possible Gq ×Gℓ-invariant operators, and check that all experimental bounds [10] are passed. We will not go through this analysishere (see Ref. [6]), but rather take a simple illustrative example: the s-channel decay process shown in Fig.1.a, whosecorresponding experimental bound is∣∣λ′JMIλ′′∗11I ∣∣ < 10−26(m[d˜IR]/300GeV )2 , (9)for I, J = 1, 2, 3, M = 1, 2. Further, only the following three representative MFV operators for the λ′ and λ′′couplings are kept (with ai ∼ O(1)):λ′IJK = a0εILM (Y†eYeΥ†ν)LM (YdY†uYu)KJ , (10)λ′′IJK = a1εLJK(YuY†d)IL + a2εLMNYILu YJMd YKNd . (11)Freezing the spurions to their physical values, the MFV prediction for the combination of couplings of Fig.1.a reads∣∣λ′JMIλ′′∗11I ∣∣ ≈√∆m2atmvum2τv2dλ3mbm2tmuvdv3u(a0a1msvd+ a0a2mdmbv2d)(12)≈ a0a110−28 tan4 β + a0a210−31 tan5 β (13)(assuming normal hierarchy, with mlightestν = 0). Several suppression factors are immediately apparent. Besides theproportionality to the neutrino mass (actually, to the mass-difference), there are several light-quark mass factors, aswell as CKM matrix elements, which together account for about half of the overall suppression. They all arise fromthe antisymmetry of the ε-tensors, which forces the amplitude to be sensitive to the three generations.These two mechanisms –neutrino mass factor & ε-tensor antisymmetry– are sufficient to suppress proton decaybelow the current experimental limits. All the bounds are easily satisfied for small to moderate tanβ. For larger tanβvalues, several weaker suppression mechanisms could be at play – heavier lightest neutrino, GIM-like interferences,restricting the broken flavor U(1)’s, reducing the MFV coefficients ai,..., see Ref. [6] for more details.5. MFV PREDICTIONS FOR R-PARITY VIOLATING PROCESSESMFV is a viable alternative to R-parity, and can give rise to very distinctive experimental signatures. Proton decayis an obvious target, since it can be quite close to the current experimental bound, but replacing R-parity by MFVcan have profound consequences also in other sectors, in particular for SUSY searches at the LHC.All possible signals are driven by the ∆B = 1 couplings, εabcλ′′IJKUIaDJbDKc , since those violating L are proportionalto neutrino masses, and thus tiny (µ′/µ, λ and λ′ < 10−13). MFV predicts a very strong hierarchy for λ′′:λ′′312 ∼ 10−1 ≫ λ′′331,323,212 ∼ 10−4 > λ′′IJK 6=312,331,323,212 ∼ 10−5 or smaller , (14)so that only the t˜RsRdR, tRs˜RdR and tRsRd˜R couplings are significant. This immediately implies that the impacts onFCNC are negligible, since at least two couplings with different flavor indices are needed. Specifically, the amplitudesfor the diagrams shown in Fig.1.b scale as [10, 11]:b→ s(d) : |λ′′∗312λ′′331(323)| . 10−4, s→ d : |λ′′∗323λ′′331| . 10−7 , (15)334th International Conference on High Energy Physics, Philadelphia, 2008Figure 1: a) Example of a tree-level, s-channel proton decay mechanism. b) Example of corrections to FCNC processes tunedby the ∆B = 1 couplings. c–h) Possible consequences of ∆B = 1 couplings with MFV strength: c) single stop resonantproduction [14] and d) its associated single gluino production [15], e) top production from d˜R and s˜R decays [16], and f–h)possible t˜L, χ0 and τ˜ LSP decay cascades [13].to be compared with |V ∗tbVts| ∼ 10−2, |V ∗tbVtd| ∼ 10−3 and |V ∗tsVtd| ∼ 10−4 for the Standard Model contributions. Atcolliders, the situation is much more favorable. The most obvious processes induced by λ′′312 are shown in Fig.1.c–h.Most of these signatures depend strongly on the precise mass spectrum of the MSSM, and have already been analyzedin details [10, 12, 13, 14, 15, 16], though not within the MFV context yet. For example, whether the LSP decays inthe detector or not depends on its nature [13], since it may need to go through a lengthy cascade before reaching theλ′′312 couplings to finally decay (see Fig.1.f–h).6. CONCLUSIONThe MFV hypothesis accounts simultaneously for the non-observation of New Physics effects in flavor transitions,and for the tremendously long proton lifetime. The latter is then understood as a direct consequence of the smallnessof the neutrino masses and of the large hierarchies among quark masses and within the CKM matrix. Even if theorigin of the flavor structures is left aside by MFV, naturalness is restored for all the flavor-dependent couplings ofthe MSSM. In particular, it now appears rather unnatural to allow for O(1) R-parity violating couplings, since suchvalues correspond to breakings of the flavor-symmetry group that are many orders of magnitude larger than thosedue to the Yukawa couplings.In view of these successes of MFV, whether R-parity should be imposed or not needs to be reassessed. Indeed,the proton decay puzzle is generally thought to be so serious that one is ready to accept the thorough alteration ofthe MSSM phenomenology induced by R-parity – think in particular of the typical, but not experimentally friendly,topologies of SUSY events at the LHC. Once proton decay is taken care of by MFV, the motivations for neverthelessimposing R-parity have to be found elsewhere. In this respect, a few of the relevant issues for or against R-parityare: (1) Some dimension-five operators can induce proton decay even if R-parity conserving [17]. On the other hand,they are again very suppressed by MFV. (2) In Grand Unified Theories, R-parity is often built in, or nevertheless434th International Conference on High Energy Physics, Philadelphia, 2008required because their smaller flavor-symmetry group [18] impeaches the MFV suppression to be as powerful. Still,it is fair to say that building a viable GUT with low-energy MFV has, up to now, not been fully investigated. (3)Without R-parity, the LSP of the MSSM is no longer a viable dark matter candidate. Remember though that theremust be physics beyond the MSSM, since it is lacking a dynamical SUSY-breaking mechanism. (4) Having at handseveral B-violating couplings, which may also violate CP, could open new paths towards baryogenesis.In conclusion, since the viability of the MSSM is no longer in the balance, whether R-parity is present in Natureor not is much less clear, and simple tree-level resonant productions of supersymmetric particles at the LHC may bejust around the corner.AcknowledgmentsWork supported by the Swiss National Funds and by the EU RTN-CT-2006-035482 (Flavianet).References[1] L. J. Hall and L. Randall, Phys. Rev. Lett. 65 (1990) 2939.[2] G. D’Ambrosio, G. F. Giudice, G. Isidori and A. Strumia, Nucl. Phys. B645 (2002) 155; V. Cirigliano, B. Grin-stein, G. Isidori and M. B. Wise, Nucl. Phys. B728 (2005) 121.[3] G. Isidori, F. Mescia, P. Paradisi, C. Smith and S. Trine, JHEP 0608 (2006) 064; W. Altmannshofer, A. J. Burasand D. Guadagnoli, JHEP 0711 (2007) 065; P. Paradisi, M. Ratz, R. Schieren and C. Simonetto, Phys. Lett.668 (2008) 202.[4] G. Colangelo, E. Nikolidakis and C. 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Minimal Flavor Violation as an alternative to R-parity

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Minimal Flavor Violation as an alternative to R-parity

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