Technical University Munich FCNC Processes in Supersymmetry Diego Guadagnoli Technical University Munich Outline Introduction: impact of FCNC processes on generic SUSY corrections ⇒ New-Physics ‘flavour problem’ Approach 1: use exp. info to constrain the general MSSM (general = with completely free soft terms) Approach 2: implement a natural “near-flavour-conservation” mechanism within the MSSM ⇒ MFV-MSSM D.Guadagnoli, Kick-off Meeting EC, May 14, 2007

So, New Physics is already there Exp. Facts about New Physics ☞ No hints (yet) of particle d.o.f. beyond the SM ones from collider experiments, directly exploring high energy/short distance  Ironically, many hints from astrophysics/cosmology, i.e. from the other end in the range of distance scales studied in physics. On one of them there is now large agreement: – Dark Matter – Many, very different, pieces of evidence for non-barionic, non-relativistic matter, which cannot be accounted for within the SM E.g., from CMB:  𝐷𝑀 ℎ 2 ≡  𝑀 −  𝐵  ℎ 2 = 0.105 −0.009 +0.007 83 % 17 % most of the ‘matter cake’ is a mystery within the SM alone (and a perfect subject for the EC) So, New Physics is already there D.Guadagnoli, Kick-off Meeting EC, May 14, 2007

‘Experimental’ scorecard of SUSY SUSY (with R-parity conservation) has a clear DM candidate, the Lightest SUSY Particle  R-Parity is appealing in many respects, so it is not simply some ad hoc quantum number it emerges naturally in the context of SO(10) GUTs (and string theory) it is the same mechanism stabilizing proton decay If the three SM couplings at the MZ scale are run upwards using the MSSM -functions, they meet at ≈ 1016 GeV  SUSY running From: M. Peskin SLAC-PUB-7479 That three lines cross at one point after 14 decades running in energy may be a coincidence. Maybe not. D.Guadagnoli, Kick-off Meeting EC, May 14, 2007

SUSY breaking and FCNC ☑ ☑ ☑ ☑ We know very well how to construct an R-conserving, SUSY- conserving MSSM. ☑ We know very poorly how to (softly) break it. Hence, we have to parameterize this sector in the most general way. ☑ The understanding of this sector is as difficult as ambitious. It would shed light on the structure of the theory far beyond the EW scale. ☑ FCNC are, at the moment, the most powerful tool in this task. ☑ In fact, in the SM, FCNC are forbidden at tree level, so they come with a loop suppression factor (+ the hierarchical pattern required by the CKM/quark masses). D.Guadagnoli, Kick-off Meeting EC, May 14, 2007

NON-diag.: Mass Insertion General parameterization of FCNC in SUSY In the CKM basis for quarks the squark mass matrices are still off-diagonal in flavour (and ‘chirality’) The “rotation” that makes quark masses diagonal does not need to diagonalize squark masses as well Then for squarks one chooses between: MI IJ 𝑞 𝐼 𝑔  𝑞  𝐽  ZIJ mass eigenstates ➊ Propagators diagonal ⇒ exact calculations However, many parameters: MJ , ZIJ MIJ  IJ 𝑞 𝐼 𝑔  𝑞  𝐽 flavour eigenstates ➋ Propagators perturbatively diagonalized through “Mass Insertions” Mass Matrices Interactions 𝑀≡  𝑀 11  12 LL ⋯  21 LL 𝑀 22 ⋯ ⋮ ⋮ ⋱  ≃ 𝑀  𝟏  0  12 LL ⋯  21 LL 0 ⋯ ⋮ ⋮ ⋱  Mass Insertion Approx SUSY source of FCNC's squark propagator (flavor basis + MIA) ≃ diagonal + × NON-diag.: Mass Insertion  D.Guadagnoli, Kick-off Meeting EC, May 14, 2007

Naïve assessment of SUSY effects hm   𝑀 SUSY  2 SUSY corrections ~ × f (SUSY mass ratios) Example: ∆F = 2 case ☞ kl Since mixing measurements check (within errors) with the SM, one has roughly: | SUSY corrections | ≤  exp 2   th 2 th > 10 % (!) Sensitivity to O(%) deviations from SM demands steady improvement on the non-pert. error bounds on  (or rather, on /MSUSY) D.Guadagnoli, Kick-off Meeting EC, May 14, 2007

⇒ ⇒ Analysing FCNCs in SUSY The SUSY (and NP in general) flavour problem a) assuming MSUSY ~ O(300 GeV) [if we want it to stabilize the EW scale] || < 10-2 ÷ 10-3 ⇒ in absence of a symmetry principle (e.g. GIM-like mechanism) such small numbers are ugly Let us write the down quark mass matrix, in the basis with diagonal interaction terms (the equivalent of the MIA basis) [values in GeV] 𝑚  𝑑 MIA basis ≡  𝑚 𝑑 0 0 0 𝑚 𝑠 0 0 0 𝑚 𝑏  ⋅ 𝑉 CKM + =  6.8× 10 −3 −1.6× 10 −3 5.22.3𝑖 10 −5 2.3× 10 −2 9.7× 10 −2 −4.2× 10 −3 0.91.4𝑖× 10 −2 1.8× 10 −1 4.3  ( does this matrix “look better” ? ) b) assuming || ~ O(1) MSUSY ≫ O(TeV) ⇒ back to “Separation-of-Scales” Problems D.Guadagnoli, Kick-off Meeting EC, May 14, 2007

Theoretical approaches to SUSY flavour effects ➊ Constrain the ‘general’ MSSM (with completely free soft terms) Take the  bounds “as they come” (from measured FCNCs) and study allowed effects on still-to-measure quantities (e.g. ACP [Bs  ], ...) not easy without simplifying assumptions: bulkiness of the parameter space  Maybe FCNC effects in SUSY are small, because already those in the SM are. Naturalness of “near-flavour-conservation” in SUSY: MFV-MSSM Hall & Randall D’Ambrosio et al. i.e. low-energy flavour breaking “building blocks” are the same in the SM and in the MSSM D.Guadagnoli, Kick-off Meeting EC, May 14, 2007

Constrain the general MSSM  Constrain the general MSSM

Example: constraints from b  s FCNCs y-axis: Im[(23)XY] x-axis: Re[(23)XY] Constraints □ = ms □ = b  s  □ = b  s l+ l- □ = all LL only, tan =3 ⇩ [-0.15,+0.15] + i [-0.25,0.25] RR only, tan =3 ⇩ [-0.4,+0.4] + i [-0.9,0.9] LL=RR, tan =3 ⇩ [-0.05,+0.05] + i [-0.03,0.03] LL=RR, tan =10 ⇩ [-0.03,+0.03] + i [-0.02,0.02]

Implication on the Bs – mixing phase In the SM one has Arg 𝑀 12 𝑆𝑀 ≡Arg 𝐵 𝑠 ∣ 𝐻 𝑒𝑓𝑓,𝑆𝑀 𝐵,𝑆=2 ∣ 𝐵 𝑠  =−2  2 ≃−0.04  What is the allowed range for with the previous limits on the ’s ? Arg 𝑀 12 𝑀𝑆𝑆𝑀 LR only, tan =3 no sizable deviations from the SM LL only, tan =3 ~ 10 × SM value are allowed RR only, tan =3 ~ 100 × SM value are easy to get (but RR is still mildly constrained...) LL=RR, tan =3 ~ 100 × SM value are again easy (yet LL=RR is severely constrained!) The CP asymmetry in Bs   will provide a truly fantastic probe! D.Guadagnoli, Kick-off Meeting EC, May 14, 2007

Minimal Flavour Violation  Minimal Flavour Violation in the MSSM

Minimal Flavour Violation (MFV) In the SM, FCNC are small, because of the GIM mechanism. Can extensions of the SM incorporate a similar mechanism of near-flavour-(and CP)-conservation? Controversial issue on how to define MFV ‘pragmatic’ definition, Buras et al., ‘00: in terms of allowed effective operators + explicit occurrence of the CKM ➊ EFT definition, D’Ambrosio et al., ‘02: in terms of the SM Yukawa couplings ➋ Def.  does not produce a consistent low-energy limit for the MSSM, even at low tan  Altmannshofer, Buras, D.G., ‘07 MFV can then only be defined as a ‘symmetry requirement’ for such new sources . In fact, in extensions of the SM one has (by def.) new, a priori unrelated sources of flavour (and CP) violation. The set of allowed operators and FV structures is an outcome of such requirement . D.Guadagnoli, Kick-off Meeting EC, May 14, 2007

☞ the SM Yukawa couplings are MFV ‘principle’ ☞ the SM Yukawa couplings are the only structures responsible for low-energy flavour and CP violation every new source of flavour violation must be expressed as function of the SM Yukawa couplings Example: soft mass term for ‘left-handed’ squarks 𝐿 soft =−  𝑚 𝑄 𝐼𝐽  2   𝑢  𝐿 𝐼  ∗ 𝑢  𝐿 𝐽   𝑑  𝐿 𝐼  ∗ 𝑑  𝐿 𝐽  ... a priori new source of flavour violation FC effects are naturally small: intuitively  = O(1)f(CKM) 𝑚 𝑄 2 𝑇 = 𝑚 2  𝑎 1 𝟏 𝑏 1 𝐾 + 𝑌 𝑢 2 𝐾 𝑏 2 𝑌 𝑑 2 𝑂 𝑌 𝑢 2 𝑌 𝑑 2  MFV expansion squark mass scale expansion coefficients and free parameters after the MFV expansion Strategy  After expansions, mass scales are only a few. Then: Dramatic increase in the predictivity and testability of the model  Fix them to scenarios  Extract just the expansion coefficients (12 indep. parameters) D.Guadagnoli, Kick-off Meeting EC, May 14, 2007

aligned with the SM value ∆F=2 example for mass scales chosen as Mg = 500 GeV (gluino mass) M1,2 = (100, 500) GeV (U(1)SU(2) gaugino masses)  = 1000 GeV (-parameter) m = 200 GeV (squark scale) Bs – Bs amplitude Comments Distributions of values, due to the extraction of the expansion parameters, are quite narrow ⇨ Corrections are naturally small ⇨ Corrections are dominantly positive. Signature of the MFV-MSSM at low tan  ⇨ Due to MFV, the mixing phase is aligned with the SM value D.Guadagnoli, Kick-off Meeting EC, May 14, 2007

Test of ‘constrained’ MFV (CMFV) within the MSSM The case of Q1 -dominated MFV (so-called CMFV) can be tested by looking at the ratio RCMFV  contrib. to operators other than Q1 contrib. to Q1 One can ‘define’ CMFV to hold when, e.g. | RCMFV | < 0.05 D.Guadagnoli, Kick-off Meeting EC, May 14, 2007

  “Conclusions” In either case, to resolve such effects, In the general MSSM, SUSY effects are typically constrained to be small (exceptions: (Bs ), ...) after imposing existing exp. input  In the MFV-MSSM, SUSY effects are naturally small, due to a ‘built-in’ GIM-like mechanism.  In either case, to resolve such effects, one needs a better control, O(few %), of the effective operator matrix elements D.Guadagnoli, Kick-off Meeting EC, May 14, 2007

Analysis of the separate contributions Note When  is large, LR entries in the squark mass matrices become relevant, even for low tan . Example with (GeV): m = 300 Mg = 300 M1,2 = (100,500)  = 1000 ☞ They manifest dominantly in gluino contributions, which become competitive with chargino’s. D.Guadagnoli, Kick-off Meeting EC, May 14, 2007