Wino contribution to R K ( ) anomalies with R -parity violation - PowerPoint PPT Presentation

Wino contribution to R K ( ∗ ) anomalies with R -parity violation Kevin Earl , Thomas Gr´ egoire arXiv: 1805.xxxxx Carleton University May 7, 2018 Pheno 2018 1

Outline 1. Motivation 2. Calculations 3. Most important constraints 4. Results 2

Motivation R K ( ∗ ) anomalies � consider ratio of branching ratios R K ( ∗ ) R K ( ∗ ) = Br( B → K ( ∗ ) µµ ) Br( B → K ( ∗ ) ee ) � Standard Model predictions R SM R SM K [1 , 6] = 1 . 00 ± 0 . 01 and K ∗ [1 . 1 , 6] = 1 . 00 ± 0 . 01 � current experimental values R exp K [1 , 6] = 0 . 745 +0 . 097 R exp K ∗ [1 . 1 , 6] = 0 . 685 +0 . 122 and − 0 . 082 − 0 . 083 � each represent ∼ 2 . 6 σ deviations from the Standard Model � numbers from Capdevila, Crivellin, Descotes-Genon, Matias, Virto ‘17 3

Motivation Multiple b → s µµ anomalies � other observables related to b → s µµ exhibiting anomalous behaviour � includes things like angular variables P 1 , P ′ 4 , 5 , 6 , 8 , ... � one way to explain anomalies is to generate negative contributions to C µ LL defined by H eff = − 4 G F α 4 π C µ µγ α P L µ ) √ V tb V ∗ LL (¯ s γ α P L b )(¯ ts 2 � Capdevila, Crivellin, Descotes-Genon, Matias, Virto ‘17 give preferred 2 σ region − 1 . 76 < C µ LL < − 0 . 74 � see also Altmannshofer, Niehoff, Stangl, Straub ‘17 4

Calculations R -parity violating superpotential R p = 1 2 λ LLE c + λ ′ LQD c + 1 2 λ ′′ U c D c D c + ǫ H u L W ✚ � focus on λ ′ interactions � work in the super-CKM basis ν i d Lj ¯ d Lk + ˜ d Lj ν i ¯ d Lk + ˜ L ⊃ − λ ′ d ∗ ijk (˜ Rk ν i d Lj ) + ˜ e Li u Lj ¯ u Lj e Li ¯ d Lk + ˜ λ ′ d ∗ ijk (˜ d Lk + ˜ Rk e Li u Lj ) + h.c. � with ˜ λ ′ ijk = λ ′ ilk V ∗ jl 5

Calculations b → s µµ at tree level s µ u L ˜ b µ ˜ 2 j 2 ˜ λ ′ λ ′∗ 2 j 3 s γ α P R b )(¯ � L eff = − (¯ µγ α P L µ ) 2 m 2 u Lj ˜ � notice right-handed quark current � need to forbid → consider only single value for k � same approach taken in Das, Hati, Kumar, Mahajan ‘17 6

Calculations b → s µµ at loop level: box diagrams ˜ W W − b µ b µ u L ˜ u ν ν ˜ µ s µ s d ˜ d R (a) (b) ν ν ˜ b s b s ˜ ˜ d R d R d d µ µ µ µ u ˜ u L (c) (d) � diagrams (a) and (c) studied in Bauer, Neubert ‘15 � diagrams (a), (c), and (d) studied in Das, Hati, Kumar, Mahajan ‘17 7

Calculations W loop diagrams W b µ u ν µ s ˜ d R � m 2 23 k | 2 = | λ ′ � � C µ ( W ) t LL m 2 8 πα ˜ d Rk 8

Calculations Wino loop diagrams ˜ W − µ b u L ˜ ν ˜ µ s d √ 2 g 2 λ ′ 23 k λ ′∗ � 1 1 C µ ( ˜ W ) 22 k = ν µ − 1 + LL ts m 2 64 π G F α V tb V ∗ x ˜ x ˜ u L − 1 ˜ W ν µ − 2 x 2 u L − 2 x 2 ( x ˜ ν µ + x ˜ u L ) log( x ˜ ν µ ) ( x ˜ u L + x ˜ ν µ ) log( x ˜ u L ) � ˜ ˜ + + ν µ − 1) 2 ( x ˜ u L − 1) 2 ( x ˜ ( x ˜ ν µ − x ˜ u L ) ( x ˜ u L − x ˜ ν µ ) ν µ = m 2 ν µ / m 2 u L = m 2 u L / m 2 � where x ˜ W , x ˜ ˜ ˜ ˜ ˜ W 9

Calculations Four λ ′ loop diagrams ˜ W W − b µ b µ u L ˜ u ν ˜ ν µ s µ s d ˜ d R √ log( m 2 ν i / m 2 2 λ ′ i 3 k λ ′∗ i 2 k λ ′ 2 jk λ ′∗ u L ) � � 1 C µ (4 λ ′ ) 2 jk ˜ ˜ = − + LL m 2 m 2 ν i − m 2 64 π G F α V tb V ∗ ts ˜ ˜ ˜ u L d Rk 10

Calculations b → s µµ at loop level: penguin diagrams √ � m 2 �� 1 2 λ ′ i 33 λ ′∗ � � 4 � − 1 1 C µ ( γ ) = C µ ( γ ) i 23 b = − 3 + log + LL LR m 2 m 2 18 m 2 12 G F V tb V ∗ 3 ts ν i ˜ ν i ˜ ˜ b R � give equal contributions to C e ( γ ) and C e ( γ ) so should not affect R K ( ∗ ) LL LR � but should still affect various angular variables used to make fits � small in our setup 11

Calculations Setup � wino and left-handed up squarks with masses ∼ O (1 TeV) � to enhance wino loop contribution: λ ′ 22 k λ ′ 23 k positive and large � B s − ¯ B s mixing then requires right-handed down squarks and sneutrinos with masses ∼ O (10 TeV) � to make some four λ ′ loop diagrams negative: λ ′ 32 k λ ′ 33 k negative � τ → µ meson then requires us to take k = 3 � only right-handed down squark now relevant is the sbottom 12

Most important constraints τ → µ meson µ µ ˜ u L ˜ d R d u τ τ d u � 2 � 2 � � � 1TeV � 1TeV � ˜ 3 j 1 ˜ − ˜ 31 k ˜ � τ → µρ 0 : � � λ ′ λ ′∗ λ ′ λ ′∗ � < 0 . 019 � 2 j 1 21 k � m ˜ m ˜ u Lj d Rk � 2 � � � 1TeV � ˜ 3 j 2 ˜ � � � τ → µφ : λ ′ λ ′∗ � < 0 . 036 � 2 j 2 � m ˜ u Lj � these two bounds rule out k = 1 or 2 13

Most important constraints τ → µµµ µ µ µ µ γ Z ˜ ˜ ˜ ˜ b R b R b R b R τ µ τ µ u u b u µ µ τ τ ˜ ˜ u L ˜ u L ˜ b R b R µ µ µ µ b u � Current experimental upper limits Br( τ → µµµ ) < 2 . 1 × 10 − 8 (PDG) 14

Most important constraints B s − ¯ B s mixing ν b b s b s ˜ ˜ b R b R ν ν ˜ ˜ s b s b ν b � we follow the UT fit collaboration and define eff | ¯ C B s e 2 i φ Bs = � B 0 s | H full B 0 s � eff | ¯ � B 0 s | H SM B 0 s � with 2 σ bounds 0 . 899 < C B s < 1 . 252 and − 1 . 849 ◦ < φ B s < 1 . 959 ◦ 15

Most important constraints B → K ( ∗ ) ν ¯ ν s ˜ b R ν b ν � define ν = Γ SM+NP ( B → K ( ∗ ) ν ¯ ν ) R B → K ( ∗ ) ν ¯ Γ SM ( B → K ( ∗ ) ν ¯ ν ) � latest Belle search 1702.03224 provides upper limit R B → K ∗ ν ¯ ν < 2 . 7 16

Most important constraints LHC collider constraints p u L ˜ u ∗ ˜ p L q b b u L ˜ ˜ u L u L ˜ µ ˜ τ W � apply constraints from ATLAS search 1710.05544 � search looks for ˜ t pair production with ˜ t → ℓ b ( ℓ = e or µ ) 17

Results Plots 1 and 2 � left figure: λ ′ 323 = − λ ′ 333 = 1 . 4, m ˜ W = 300 GeV, m ˜ u L = m ˜ c L = m ˜ t L = 1 . 3 TeV, m ˜ b R = m ˜ ν µ = m ˜ ν τ = 13 TeV � right figure: masses the same as left figure 18

Results Plots 3 and 4 � parameters not being varied same as in plots 1 and 2 19

Results Neutrino masses � λ ′ couplings generate neutrino masses ˜ ˜ b R b L ν ν b log( m 2 b R / m 2 d Ll ) 3 ˜ ˜ M ν m d 2 16 π 2 λ ′ i 33 λ ′ ij = jl 3 m b ( ˜ LR ) l 3 + ( i ↔ j ) m 2 b R − m 2 ˜ ˜ d Ll � typical RPVMSSM values → M ν 22 ∼ 10 keV, too large m d 2 � impose U (1) R lepton number → ˜ LR forbidden by R -symmetry � m 3 / 2 � � R -symmetry broken by anomaly mediation → M ν 22 ∼ 1eV 1GeV 20