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Lifetime Difference in D 0 – D 0 Mixing within R-parity Violating Supersymmetry

Lifetime Difference in D 0 – D 0 Mixing within R-parity Violating Supersymmetry. Gagik Yeghiyan Wayne State University, Detroit, MI, USA Based on A. A. Petrov, G. K. Yeghiyan, Phys. Rev. D 77, 034018 (2008). Outline.

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Lifetime Difference in D 0 – D 0 Mixing within R-parity Violating Supersymmetry

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  1. Lifetime Difference in D0 – D0Mixing within R-parity Violating Supersymmetry Gagik Yeghiyan Wayne State University, Detroit, MI, USA Based on A. A. Petrov, G. K. Yeghiyan, Phys. Rev. D 77, 034018 (2008)

  2. Outline • We show that the contribution from RPV SUSY models with the leptonic number violation to ∆ΓDis negative, i.e. opposite in sign to what is implied by the recent experimental evidence. • It is possibly quite large in absolute value (may exceed the experimentally allowed values of ∆ΓD). • We derive new constraints on the relevant RPV coupling pair products. Unlike those coming from the study of ΔmD, our bounds are insensitive or weakly sensitive to assumptions on R-parity conserving (pure MSSM) sector. • We emphasize the necessity of taking into account of the transformation of RPV couplings from the weak eigenbasis to the quark mass eigenbasis.

  3. It is known that ΔΓDisdrivenby the physics of ΔC=1 sector both in the SM and beyond.

  4. It is known that ΔΓDisdrivenby the physics of ΔC=1 sector both in the SM and beyond. Let A[D0 → n] = An(SM) + An(NP), |n> is a charmless state

  5. It is known that ΔΓDisdrivenby the physics of ΔC=1 sector both in the SM and beyond. Let A[D0 → n] = An(SM) + An(NP), |n> is a charmless state

  6. It is known that ΔΓDisdrivenby the physics of ΔC=1 sector both in the SM and beyond. Let A[D0 → n] = An(SM) + An(NP), |n> is a charmless state

  7. It is known that ΔΓDisdrivenby the physics of ΔC=1 sector both in the SM and beyond. Let A[D0 → n] = An(SM) + An(NP), |n> is a charmless state Then for yD=ΔΓD/(2ΓD)

  8. The SM contribution is rather uncertain (due to long-distance effects): ySM ~ 10-4 ÷ 10-2 yDexp = (6.6± 2.1 )• 10-3 – is this due to the SM or NP or both of them?

  9. The SM contribution is rather uncertain (due to long-distance effects): ySM ~ 10-4 ÷ 10-2 yDexp = (6.6± 2.1 )• 10-3 – is this due to the SM or NP or both of them? The second term (interference of theSMandNPΔC=1transitions) – - yields yD ≤ 10-4

  10. Consider the last term in this equation:

  11. Consider the last term in this equation: An(NP) ~ MW2/MNP2– the last term is suppressed as (MW2/MNP2)2 - shouldn’t we neglect it? On the other hand… The SM contribution vanishes in the limit of the exact flavor SU(3) symmetry. In the real world where flavor SU(3) is of broken, the SM contribution is suppressed in powers ms/mc In many popular SM extensions and in particular within the RPV SUSY, the second term (interference of the SM and NPΔC=1 transitions) also vanishes in the limit of the exact flavor SU(3) symmetry, again is suppressed in powers of ms/mc If the last term non-vanishing in the exactflavor SU(3)limit, can it give numerically significant contribution? Yes, ifMW2/MNP2 > ms2/mc2. Consider the diagrams with two NP generated ΔC=1transitions as well!

  12. The purpose of our work was to revisit the problem of the NPcontribution to yD and provide constraints on RPV SUSY models as a primary example. We considered a general low-energy SUSY scenario with the leptonic number violation. No assumptions was made on a SUSY breaking mechanism at unification scales. The important point of the analysis:one must take into account the transformation of theRPV couplingsfrom theweak eigenbasisto thequark mass eigenbasis, in order to use properly the existing constraints on the RPV couplings(see the paper for more details). If this transformation is neglected,S. L. Chen, X. G. He, A. Hovhannissyan, H.S. Tsai - RPV SUSY contribution to yD is rather small – but this is not true!

  13. The dominant diagrams with RPV interactions. Neglecting numerically subdominant terms, Important: no dependence on msor md – this contribution does not vanish in the exact flavor SU(3) limit!

  14. The dominant diagrams with RPV interactions. R-parity conserving sectors of theory: Higgs sector: contribution of diagrams with the charged Higgs(es) is negligible: the relevant Yukawa couplings are ~mc / MWor ms / MW. Pure MSSM: contributes to ∆ΓDonly by NLO2-loop dipenguin diagrams and naturally is expected to be small. Important: our results are insensitive or weakly sensitive to assumption on R-parity conserving sector of theory.

  15. Numerically Within RPV SUSY models with the leptonic number violation, NP contribution to yD is predominantly negative and may exceed in absolute value the experimentally allowed interval yDexp = (6.6 ± 2.1) ● 10-3 To avoid a contradiction with the experiment: demand a large positive contribution from the SM (to have a destructive interference of two contributions) or place severe constraints on the relevant RPV coupling products and/or on the scalar lepton mass. A. Falk et al., Phys. Rev. D 65, 054034 (2002): due do the long-distance effects, ySM may be up to ~1/%. Thus, RPV SUSY contribution to yD should be ~1% or less as well.

  16. Impose , then either or if , new constraints on the RPV coupling products are derived (see the paper for more details). Recall thatpure MSSM contributes to ∆ΓDonly by NLO2-loop dipenguin diagrams and naturally is expected to be small. Our bounds on the RPV couplings, coming from the study of ∆ΓD are insensitive or weakly sensitive to the assumptions on the pure MSSM sector. This is contrast to the constraints coming from study of ΔmD: they are derived in the limit when pure MSSM contribution to ΔmDis negligible. The destructive interference between the pure MSSM and RPV sectors may distort bounds coming fromΔmD

  17. Summary of the main results: Within R-parity violating SUSY models, lifetime difference in D0 - D0 mixing may be large: it may exceed in absolute value the experimentally allowed interval, yDexp = ΔΓDexp/ΓD = (6.6 ± 2.1)●10-3, by an order of magnitude. When being large it is negative in sign. The existing experimental data may be the result of the destructive interference of the SM and RPV SUSY contributions. To derive this result it is very important to take into account transformation of RPV couplings from the weak eigenbasis to the quark mass eigenbasis. Using the existing experimental data on yD = ΔΓD/(2 ΓD) , we derive new bounds on the RPV coupling pair products and/or supersymmetric particle masses. Unlike those coming from studying of xD=ΔmD/ΓD, our bounds are insensitive or weakly sensitive to assumptions on the pure MSSM sector of the theory.

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