Sbottoms as probes to MSSM with Nonholomorphic Soft Interactions Samadrita Mukherjee School of Physical Sciences Indian Association for the Cultivation of Science, Kolkata, India. (With Utpal Chattopadhyay, AseshKrishna Datta, Abhaya Kumar Swain) Based on JHEP10(2018)202 KEK-PH 2018 and the 3rd KIAS-NCTS-KEK workshop Phenomenology of ˜ Samadrita Mukherjee (IACS, Kolkata) b in NHSSM December 5, 2018 1 / 18
Outline 1 Minimal Supersymmetric Standard Model Generalized Soft Breaking Sector Non-Holomorphic soft terms 2 Results Sbottom Sector Phenomenology Corrections to bottom Yukawa coupling Effect of NH terms in parton level yields 3 Discussions Phenomenology of ˜ Samadrita Mukherjee (IACS, Kolkata) b in NHSSM December 5, 2018 2 / 18
MSSM : Different parts of Lagrangian The general form of Lagrangian density : L MSSM = L SUSY + L SOFT L SUSY = L gauge + L matter + L Higgs − Yukawa Superpotential : W MSSM = y u Q · H u ¯ U − y d Q · H d ¯ D − y e L · H d ¯ E + µ H u · H d = 1 −L MSSM g + M 2 ˜ W ˜ W + M 1 ˜ B ˜ 2( M 3 ˜ g ˜ B + c . c ) soft q iL · h d A d ij ˜ jR + ˜ u ∗ d ∗ e ∗ + (˜ q iL · h u A u ij ˜ jR + ˜ ℓ iL · h d A e ij ˜ jR + h . c . ) q † q jL + ˜ ℓ † l ij ˜ u † jR + ˜ d ij ˜ d † iL m 2 iL m 2 u iR m 2 d iR m 2 + ˜ q ij ˜ ℓ jL + ˜ u ij ˜ jR e † e iR m 2 jR + m 2 h u h ∗ u h u + m 2 h d h ∗ + ˜ e ij ˜ d h d + ( B µ h u . h d + c . c ) Phenomenology of ˜ Samadrita Mukherjee (IACS, Kolkata) b in NHSSM December 5, 2018 3 / 18
Possible origin & type of “soft”terms The MSSM Lagrangian is usually claimed to include all possible “soft supersymmetry breaking” terms, i.e. terms which split the masses of the particles and their superpartners, but which do not remove the supersymmetric protection against large radiative corrections to scalar masses. Nature Term order of magnitude origin F M [ XW α W α ] F 1 λλ M ∼ m w | F | 2 φ ∗ φ M 2 ∼ m 2 M 2 [ XX ∗ ΦΦ ∗ ] D 1 soft w φ 2 µ F µ M [ X Φ 2 ] F M ∼ m w φ 3 F M [ X Φ 3 ] F 1 M ∼ m w Phenomenology of ˜ Samadrita Mukherjee (IACS, Kolkata) b in NHSSM December 5, 2018 4 / 18
Possible origin & type of “soft”terms The MSSM Lagrangian is usually claimed to include all possible “soft supersymmetry breaking” terms, i.e. terms which split the masses of the particles and their superpartners, but which do not remove the supersymmetric protection against large radiative corrections to scalar masses. Nature Term order of magnitude origin F M [ XW α W α ] F 1 λλ M ∼ m w | F | 2 φ ∗ φ M 2 ∼ m 2 M 2 [ XX ∗ ΦΦ ∗ ] D 1 soft w φ 2 µ F µ M [ X Φ 2 ] F M ∼ m w φ 3 F M [ X Φ 3 ] F 1 M ∼ m w Are there any more possible soft terms? [Ref : S. Martin, Phys. Rev D., 2000; Possible non-holomorphic soft SUSY breaking terms] Phenomenology of ˜ Samadrita Mukherjee (IACS, Kolkata) b in NHSSM December 5, 2018 4 / 18
Possible origin & type of “soft”terms The MSSM Lagrangian is usually claimed to include all possible “soft supersymmetry breaking” terms, i.e. terms which split the masses of the particles and their superpartners, but which do not remove the supersymmetric protection against large radiative corrections to scalar masses. Nature Term order of magnitude origin F M [ XW α W α ] F 1 λλ M ∼ m w | F | 2 φ ∗ φ M 2 ∼ m 2 M 2 [ XX ∗ ΦΦ ∗ ] D 1 soft w φ 2 µ F M [ X Φ 2 ] F µ M ∼ m w φ 3 F M [ X Φ 3 ] F 1 M ∼ m w Are there any more possible soft terms? [Ref : S. Martin, Phys. Rev D., 2000; Possible non-holomorphic soft SUSY breaking terms] Nature Term order of magnitude origin M 3 ∼ m 2 | F | 2 1 φ 2 φ ∗ M 3 [ XX ∗ Φ 2 Φ ∗ ] D w M | F | 2 M 3 ∼ m 2 M 3 [ XX ∗ D α Φ D α Φ] D 1 “may be”soft ψψ w M | F | 2 M 3 ∼ m 2 M 3 [ XX ∗ D α Φ W α ] D 1 λψ w M Phenomenology of ˜ Samadrita Mukherjee (IACS, Kolkata) b in NHSSM December 5, 2018 4 / 18
NH trilinear terms and bilinear Higgsino term: Taking these terms in account, − L ′ φ 2 φ ∗ u ∗ + ˜ d ∗ + ˜ e ∗ + h . c q · h ∗ d A ′ q · h ∗ u A ′ d ˜ ℓ · h ∗ u A ′ ⊃ ˜ u ˜ e ˜ soft soft = µ ′ ˜ −L ′ ψψ h u · ˜ h d But these interactions are not considered generally.... Phenomenology of ˜ Samadrita Mukherjee (IACS, Kolkata) b in NHSSM December 5, 2018 5 / 18
NH trilinear terms and bilinear Higgsino term: Taking these terms in account, − L ′ φ 2 φ ∗ u ∗ + ˜ d ∗ + ˜ e ∗ + h . c q · h ∗ d A ′ q · h ∗ u A ′ d ˜ ℓ · h ∗ u A ′ ⊃ ˜ u ˜ e ˜ soft soft = µ ′ ˜ −L ′ ψψ h u · ˜ h d But these interactions are not considered generally.... Let us see why? High Scale Suppression: In a hidden sector based SUSY breaking, Non-Holomorphic trilinear terms and bare higgsino mass term go as ∼ m 2 M . M is a high scale, can be as large as Planck Scale. W Reappearance of divergences: If any of the chiral supermultiplets are singlets under the entire gauge group, these terms may lead to large radiative corrections. ∼ m 2 s ln ( m 2 X X s ) m 2 m 2 m s : mass of the singlet field, m X : mass of some heavy field. If m s << m X , then the correction becomes very large. However if m s ∼ m X , then there is no problem. Phenomenology of ˜ Samadrita Mukherjee (IACS, Kolkata) b in NHSSM December 5, 2018 5 / 18
NH trilinear terms and bilinear Higgsino term: Taking these terms in account, − L ′ φ 2 φ ∗ u ∗ + ˜ d ∗ + ˜ e ∗ + h . c q · h ∗ d A ′ q · h ∗ u A ′ d ˜ ℓ · h ∗ u A ′ ⊃ ˜ u ˜ e ˜ soft soft = µ ′ ˜ −L ′ ψψ h u · ˜ h d But these interactions are not considered generally.... Let us see why? High Scale Suppression: In a hidden sector based SUSY breaking, Non-Holomorphic trilinear terms and bare higgsino mass term go as ∼ m 2 M . M is a high scale, can be as large as Planck Scale. W Reappearance of divergences: If any of the chiral supermultiplets are singlets under the entire gauge group, these terms may lead to large radiative corrections. ∼ m 2 s ln ( m 2 X X s ) m 2 m 2 m s : mass of the singlet field, m X : mass of some heavy field. If m s << m X , then the correction becomes very large. However if m s ∼ m X , then there is no problem. MSSM contains no singlet under the entire gauge group, so we can always include L NH & L ψψ with the usual soft terms. Phenomenology of ˜ Samadrita Mukherjee (IACS, Kolkata) b in NHSSM December 5, 2018 5 / 18
Structures of Mass Matrices: Scalars & Electroweakinos 3 sin 2 θ W ) M 2 � m 2 Q L + ( 1 2 − 2 Z cos 2 β + m 2 − m u ( A u − ( µ + A ′ � u ) cot β ) ˜ u squarks = M 2 u = . ˜ 3 sin 2 θ W M 2 u + 2 − ( A u − ( µ + A ′ m 2 Z cos 2 β + m 2 u ) cot β ) m u ˜ u Similarly for down-type squark and sleptons we have in off-diagonal, − m d ( A d − ( µ + A ′ d ) tan β ) The Higgs mass up to one loop : � m ˜ ′ 2 ′ 2 � � �� Z cos 2 2 β + 3 g 2 m 4 2 ¯ t 1 m ˜ � X X t 2 m 2 h , top = m 2 t t t ln + 1 − . 8 π 2 M 2 m 2 ¯ m ˜ t 1 m ˜ 12 m ˜ t 1 m ˜ W t t 2 t 2 Here, X ′ t = A t − ( µ + A ′ t ) cot β . The Neutralino & Chargino mass matrices are, M 1 0 − M Z cos β sin θ W M Z sin β sin θ W 0 M 2 M Z cos β cos θ W − M Z sin β cos θ W M ˜ χ 0 = . − ( µ + µ ′ ) − M Z cos β sin θ W M Z cos β cos θ W 0 − ( µ + µ ′ ) M Z sin β sin θ W − M Z sin β cos θ W 0 √ � � M 2 2 M W sin β √ χ ± = . M ˜ ( µ + µ ′ ) 2 M W cos β Phenomenology of ˜ Samadrita Mukherjee (IACS, Kolkata) b in NHSSM December 5, 2018 6 / 18
Overview Minimal Supersymmetric Standard Model 1 Generalized Soft Breaking Sector Non-Holomorphic soft terms Results 2 Sbottom Sector Phenomenology Corrections to bottom Yukawa coupling Effect of NH terms in parton level yields Discussions 3 Phenomenology of ˜ Samadrita Mukherjee (IACS, Kolkata) b in NHSSM December 5, 2018 7 / 18
Non-trivial contributions through y b ✓ y b has the usual dependence on tan β as in the MSSM case. H ∗ H u u M 2 LR = µy b ˜ M 2 LR ≃ A t y t ˜ b R t L ˜ ˜ b L t R × × m ˜ µ b L g b R b L b R g s g s g � g � h ± ˜ h ± ˜ H ∗ H ∗ u u A ′ b y b ˜ ˜ b R ( µ + A ′ b ) y b b L ˜ ˜ b L b R × × m ˜ b L b R b L b R g s g g s µ g � g � χ 0 χ 0 1 1 2 α 3 v u 2 α 3 v u ∆ m (˜ g ) g A ′ I ( m 2 b 1 , m 2 b 2 , m 2 ∆ m (˜ g ) I ( m 2 b 1 , m 2 b 2 , m 2 NHSSM = g ) , m ˜ b y b √ MSSM = m ˜ g µ y b √ g ); ˜ ˜ ˜ ˜ ˜ b b ˜ 3 π 2 3 π 2 y 2 h + y t y b v u ˜ v u I ( m 2 t 1 , m 2 t 2 , µ 2 ); h 0 ˜ 16 π 2 µ ( µ + A ′ b I ( m 2 b 1 , m 2 b 2 , µ 2 ) . ∆ m MSSM = 16 π 2 µ A t y t √ ∆ m b NHSSM = b ) y b √ ˜ ˜ b ˜ ˜ 2 2 where, I ( a , b , c ) = − ab ln ( a / b )+ bc ln ( b / c )+ ca ln ( c / a ) . ( a − b )( b − c )( c − a ) In NHSSM, y b becomes a function of A ′ b quite similar to tan β reliance. Neutralino loop and gluino loop has A ′ b dependence. Phenomenology of ˜ Samadrita Mukherjee (IACS, Kolkata) b in NHSSM December 5, 2018 8 / 18
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