Shinshu University Yoshiharu Kawamura 2012. 3. 13

Shinshu University Yoshiharu Kawamura 2012. 3. 13“Beyond the Standard model and the origin of Higgs” “Soft Supersymmetry Breaking Masses and μ Parameter from Dynamical Rearrangement of Exotic U(1) Symmetries” Y. K. and T. Miura, IJMP A Vol.26 (2011), 4405 (arXiv:1106.0374 [hep-ph] ) . “μ Parameter from Dynamical Rearrangement of U(1) and θ Parameter” Y. K. and T. Miura, to appear in IJMP A (arXiv:1108.1004 [hep-ph]).. 【Contents】 １．Introduction„Goal, Approach‟ ２．Scenario„Background, Scenario‟ ３．A Model (Orbifold, Exotic U(1), Dynamical rearrangement). ４．Conclusion„Summary, Problems‟. １．Introduction 〈What we want to know〉 ☆ Physics around TeV scale (Beyond the Standard Model) and ☆ Ultimate Theory of Nature (Fundamental Theory of Physics). １．Introduction 〈What we want to know〉 ☆ Physics around TeV scale (Beyond the Standard Model) and ☆ Ultimate Theory of Nature (Fundamental Theory of Phyics). 〈Approach〉 Attack the Problems in the Standard Model.  ☆ Naturalness Problem (Gauge Hierarchy Problem) ☆ Incorporation of Gravity. ☆ Naturalness Problem (Gauge Hierarchy Problem) Unnatural fine-tuning is required to obtain the Higgs mass of order weak scale or to stabilize the weak scale!? 2.  2 m  m   VHiggs     m         4 2    2. 4. 2. 2. 4. Unnatural fine-tuning is required to obtain the Higgs mass of order weak scale or to stabilize the weak scale!?. m  m 2. ( 0) 2.  m. 2. 2 2    ~ 2 2 2 ( 0) 2 m  C   C m ln (0) 2  C M hep ln 2 m M hep  ~ C , C , C  O 1 100. . .  : Cutoff scale, M hep : High energy scale. Unnatural fine-tuning is required to obtain the Higgs mass of order weak scale or to stabilize the weak scale!?. m  m 2. ( 0) 2.  m. 2. 2 2    ~ 2 2 2 ( 0) 2 m  C   C m ln (0) 2  C M hep ln 2 m M hep.  : Cutoff scale, M hep : High energy scale. m  O(v ), v  246GeV 2. 2. If nature does not require the fine-tuning for the Higgs mass, New physics might exist around TeV scale. and/or. High-energy physics might have little to do with the SM.  Symmetry, Extremely weak coupling or …. A Candidate is Supersymmetry. (SUSY). SUSY cancels quadratic divergences ! When SUSY is broken softly, logarithmic divergence appears but harmless if the mass difference is less than of 2  order TeV.  2 2 2 m  C m  m ln. 2. m. If nature take advantage of SUSY, SUSY might be broken softly around the TeV scale. and. Superpartners might appear around the TeV scale.  2  2 mSUSY : Soft SUSY scale 2 2 2 m  C m  m ln 2  C mSUSY ln 2 m mSUSY  Mass of superpartners 2. . . 【Ordinary scenario】 A high-energy physics is described by a quantum field theory respecting SUSY, the SUSY is spontaneously broken in some hidden sector, and soft SUSY breaking terms are induced in our visible sector by the mediation of some messengers.. 【Ordinary scenario】. Sp. SUSY. Soft SUSY. Messenger Hidden sector. Visible sector. 【Our exotic scenario】 SUSY is explicitly broken, at some high-energy scale, in the presence of extra gauge symmetries in the bulk, but BCs of fields respects N＝1 SUSY on our brane and soft SUSY breaking terms are induced from dynamical rearrangement of extra gauge symmetries.. Explicit SUSY interactions.  Naturalness Problem Revisited?! m  m 2. ( 0) 2.  m. 2. 2 2    ~ 2 2 ( 0) 2 2 m  C   C m ln (0) 2  C M hep ln 2 m M hep.  m2   m2  ~ If C  O , C  O , no problem! 2 2        M hep . Explicit SUSY  Extremely weak (our assumption). ２．Scenario 〈Background, Scenario〉 ☆ Relevant preceding study for the origin of soft SUSY from extra dimensions and ☆ Basic ingredients of our scenario. ☆ Relevant preceding study (1) Scherk-Schwarz mechanism. SUSY terms originate from the different boundary conditions (BCs) between fields and those superpartners. Mass. 0 ( x) :   ( x, y  2R)  e 2i  ( x, y ) R     0 ( x) : 0  ( x, y  2R)   ( x, y ).   O( R / TeV1 ) is necessary to obtain mSUSY of O(1) TeV.. ☆ Relevant preceding study (1) Scherk-Schwarz mechanism. SUSY terms originate from the different boundary conditions (BCs) between fields and those superpartners. Mass. 0 ( x) :   ( x, y  2R)  e 2i  ( x, y ) R     0 ( x) : 0  ( x, y  2R)   ( x, y ) If R  O(1 / 1016 )GeV1 ,   O(1013 ) to obtain mSUSY of O(1) TeV.. ☆ Relevant preceding study (2) Application on SS mechanism „Ex.) MSSM on 5D space-time M4×(S1/Z2) ｛N＝1 SUSY in 5D｝ ＝｛N＝2 SUSY in 4D｝ The gaugino is SU(2)R doublet.  1    1   2 ( x, y )   5  2 ( x, y ) N＝1 SUSY in 4D         1  1   2i 2    2 ( x, y  2 )  e  2 ( x, y )  Gaugino masses         (soft SUSY). ☆ Relevant preceding study (3) Dynamical Rearrangement (A part of Hosotani mechanism) The physical symmetry and spectra are obtained after the determination of vacuum state fixed by the Wilson line phases..  ( x, y  2 )   ( x, y),. .  ( x, y  2 )  e. 2  Veff  0 Ay  Ay R. Gauge equivalent!. 2i.  ( x, y),. Ay  0. Dynamical gauge symmetry breaking!. Q. Is it possible to break SUSY from the dynamical rearrangement? Or does the Scherk-Schwarz mechanism work dynamically?  ( x, y  2 )   ( x, y )   ( x, y  2R)   ( x, y ) Dynamical rearrangement.  ( x, y  2 )  e 2i  ( x, y ) ?   ( x, y  2R)   ( x, y ). Major barriers ・ SUSY  Veff ＝ 0 ・ Relevant broken charges of SM particles vanish, but those of superpartners are non-zero. SM particles and their superpartners do not have a common quantum number?! „Ex.) MSSM on 5D space-time M4×(S1/Z2) Relevant broken charge is SU(2)R.  Local SU(2)R ?. ☆ Relevant preceding study (4) 5D Supergravity Why SUGRA?. G. v. Gerdoeff and M. Quiros, Phys. Rev. D65 (2002) 064016,“Supersymmetry breaking on orbifolds from Wilson lines” G. v. Gerdoeff, M. Quiros and A. Riotto, Nucl. Phys. B634 (2002) 90, “Radiative ScherkSchwarz supersymmetry breaking”. Local SU(2)R, which is not orthogonal to SUSY  Local SUSY After the dynamical rearrangement,.  ( x, y  2 )  e. 2i.  ( x, y),. SU ( 2) R y. A. 0. . Veff. 1  C ' (2  NV  N H ) 5 cos2n  n 1 n. NV : No. of vectormultiplets, N H : No. of hypermultiplets. ☆ Relevant preceding study (4) 5D Supergravity Why SUGRA?. G. v. Gerdoeff and M. Quiros, Phys. Rev. D65 (2002) 064016,“Supersymmetry breaking on orbifolds from Wilson lines” G. v. Gerdoeff, M. Quiros and A. Riotto, Nucl. Phys. B634 (2002) 90, “Radiative ScherkSchwarz supersymmetry breaking”. Local SU(2)R, which is not orthogonal to SUSY  Local SUSY After the dynamical rearrangement,.  ( x, y  2 )  e. 2i.  ( x, y),. SU ( 2) R y. A. 0.   0 or 1 / 2 in the absence of other SUSY breaking sources  mSUSY  0 or O(1 / R)  Large extra dimension!. ☆ Relevant preceding study 【No go theorem】. Soft SUSY parameters of O(1) TeV cannot be obtained via the Hosotani mechanism from any SUSY QFT without SUSY breaking sources and with flat small extra dimensions.. 【Finding】. Y. K. and T. Miura, “Soft Supersymmetry Breaking Masses and μ Parameter from Dynamical Rearrangement of Exotic U(1) Symmetries”, Int. J. M. P. A26, (2011) 4405 (arXiv:1106.0374 [hep-ph] ) .. There is a chance, if SUSY were broken in the bulk in the presence of exotic U(1) . Why U(1) ? What does “exotic U(1) ” mean?. How do SUSY terms come from?. ☆ Basic ingredients (1) Space-time is M4 × O. Here M4 is 4D Minkowski space and O is an extra space. Our 4D world is a brane in the bulk. (2) Gauge group is GSM × G′ . Here GSM is the SM gauge group and G′ is an exotic gauge group. Gauge multiplets live in the bulk.. ☆ Basic ingredients (3) The same number of bosonic fields and fermionic ones exists. The corresponding partners have a same SM gauge quantum number, but a different quantum number of G′ . SUSY is manifestly broken in the bulk. SUSY must mediate on the brane.  extremely weak coupling  tiny gauge coupling and/or charge. ☆ Basic ingredients (4) The G′ is broken down to its subgroup H′ on our brane by BCs relating extra dimension, which respect SUSY. N＝1 SUSY can be realized in the low-energy spectra on our brane at the tree level. We assume that all fields are singlets under H′ .. ☆ Basic ingredients (5) The MSSM fields come from zero modes of bulk fields. Physics can be described as the MSSM without soft SUSY terms on our brane at the tree level.. ☆ Basic ingredients (6) The dynamical rearrangement of G′/H′ occurs and soft SUSY masses are induced.. ・ Masses ∝ Ay  0 and Broken charges   Generators of G' /H' g A  H'. y. Ay : Extra - dimensiona l components of G' /H' gauge fields. ☆ Basic ingredients (6) The dynamical rearrangement of G′/H′ occurs and soft SUSY masses are induced.. ・ Masses ∝ Ay  0 and Broken charges Generators of G' /H' ・ Broken charge of superpartners ＝O(R/TeV-1) ＝ 0  tiny charge ( ) A  U(1) (Exotic U(1) M ( x, y) ). 3． A Model <Orbifold, Exotic U(1), Dynamical rearrangement>. Goal：To illustrate our scenario in a more abstract form. Not to present a complete model.. Structure of space-time M4×(S1/Z2). . x (  x) x  y. AM( ) ( x, y)  ( x, y). ( x, y). S1.  P1. ( x, y). Z2. (  0,1,2,3). Bulk field ( x, y).  (x).  P0. 5. Brane field.  (x).  P0 : y   y   P1 : y  2R  y U : y  y  2R  U  P1P0. Exotic U(1) Gauge Field AM(  ) ( x, y  2R)  AM(  ) ( x, y ), ( M  0,1,2,3, y ) A ( x, y )   A ( x, y ), (   0,1,2,3) ( ). ( ) y. (). ( ) y. A ( x, y )  A ( x, y ),. ・ Exotic U(1) is broken down because the massless mode ( ) of A is absent. ( ) ・ The massless mode of Ay becomes a dynamical one.. How to make Z2 of () y. () y. A ( x, y )  A ( x, y ),     ( y ) y.   y  iqA   0   1     2 . () y. ( ) y. A. even. Ref. K. Kojima, K. Takenaga and T. Yamashita, arXiv:1103.1234.. 1 ( x, y )  2 ( x, y), 2 ( x, y )  1 ( x, y) 2.  1     is Z 2 invariant! (  )   y  iqAy  2  0. : Eigenstates of exotic U(1). How to make Z2 of A even Eigenstates of B. C.  ,  ( ) y. 1 1  2 ,   2  ( x, y )   ( x, y ).   y  iqA   0 . () y. Ay(  ) ( x, y )  Ay(  ) ( x, y ),     ( y ) y.  1     (  )   y  iqAy  2 .  y   ()  iqA  y. 0. iqA. () y. y.           . 2. 2. Derivation of Soft SUSY mass   y  iqA   0 . ( ) y.  y   iq Ay(  ) . 2.  1   y     (  ) (  )   iqA  y  iqAy  2   y 0. iqA. ( ) y. y.           . 2. iq Ay(  )       q 2 A(  ) 2  (0) 2   y       y   . ( ) q A  O(1)TeV ? Q. How to derive y. 2. Derivation of Soft SUSY mass  A. ( ) y. 1 ( x, y )  2 ( x, y), 2 ( x, y )  1 ( x, y). R. U(1) charge of sfermions qi , gauginos qa and Higgs bosons qh . MSSM eff. V. 1  4C  5 cos2nqi   i n 1 n . . 1 1  4C  5 cos2nqa    8C  5 cos2nqh   a n 1 n n 1 n.  0.  Unbroken SUSY. Derivation of Soft SUSY mass  A. ( ) y. 1 ( x, y )  2 ( x, y ), 2 ( x, y )  1 ( x, y ). R. U(1) charge of sfermions qi  q, gauginos qa and Higgs bosons qh.  1 1   4C  5 cos 2n  q   i n 1 n  2 . MSSM eff. V. . . 1 1  4C  5 cos2nqa    8C  5 cos2nqh   a n 1 n n 1 n. 1  q  2. ( ) y.  q A. 1   O(1)TeV 2R. Introduction of SUSY sector  A. SM singlet . ( ) y. R.  eff.  1 1   4C  5 cos 2n  q    n 1 n  2. V. U(1) charge of  : q  qi , qa , qh . qi 1 1 ( )  q    qi Ay  q 2 R  O(1)TeV 2 . qi ( a ,h ) q.  O( R / TeV-1 )  Tiny charge!. 5． Conclusion We have proposed a scenario with an illustrating model. 【Our exotic scenario】 SUSY is explicitly broken, at some highenergy scale, in the presence of extra gauge symmetries in the bulk, but BCs of fields respects N＝1 SUSY on our brane and soft SUSY breaking terms are induced from dynamical rearrangement of extra gauge symmetries.. 【Exotics of new U(1) 】 ・ The eigenstates of U(1)  A( )  0 y ＝ The eigenstates of BCs.  Seed of dyn. rearrangement ・ The U(1) charge of SM particles ＝ The U(1) charge of superpartners  Seed of SUSY ・ The ratio of U(1) charges 1 is extremely small of O( R / TeV ) .  Seed of TeV scale. Open questions ・Origin of exotic U(1) ・Origin of space-time structure ・Origin of BCs ・・・. Thank you for your attention !.