Spontaneous SUSY breaking with anomalous U1 symmetry by
Spontaneous SUSY breaking with anomalous U(1) symmetry by metastable vacuum Hiroyuki Nishino collaborator : S. -G. Kim, N. Maekawa and K. Sakurai (Nagoya University) June 19, 2008 in Seoul
motivation Anomalous U(1)A gauge symmetry ・ The magnitude of VEV is decided by U(1)A charge. (Prog, Theor. Phys. 110, 93, (2003)) ・ This gauge symmetry can explain the origin of Yukawa hierarchy. SUSY can be spontaneously broken in a model with U(1)A symmetry. (Phys. Lett. B 51, 461 (1974)) ・ Problem in GUT (ex, 2 -3 splitting problem) can be solved by controlling potential using U(1)A charge. (Prog, Theor. Phys. 110, 93, (2003)) (where, vacuum to solve these problems is supersymmetric. ) infinite number of generic interaction terms、 no R symmetry. finite number of generic interaction terms、R symmetry.
motivation Anomalous U(1)A gauge symmetry ・ The magnitude of VEV is decided by U(1)A charge. (Prog, Theor. Phys. 110, 93, (2003)) ・ This gauge symmetry can explain the origin of Yukawa hierarchy. SUSY can be spontaneously broken in a model with U(1)A symmetry. (Phys. Lett. B 51, 461 (1974)) ・ Problem in GUT (ex, 2 -3 splitting problem) can be solved by controlling potential using U(1)A charge. (Prog, Theor. Phys. 110, 93, (2003)) (where, vacuum to solve these problems is supersymmetric. ) finite number of generic interaction terms、R symmetry. infinite number of generic interaction terms、 no R symmetry. If we can unify these two theories, anomalous U(1) theory not only solves some problems in the SM and GUT but also provides a SUSY breaking mechanism, simultaneously. It is economical. We will propose a spontaneous SUSY breaking model with anomalous U(1) gauge symmetry and no R symmetry.
Feature of anomalous U(1) gauge symmetry + no R symmetry (1): This theory has Fayet-Iliopoulos D term : , where V is gauge superfield. (2): The magnitude of each VEV is decided by corresponding U(1)A charge. (But, this vacuum is supersymmetric. ) , (cut off ) where we assumed that constant is much smaller than 1 ( through out in this talk each small letter represents U(1)A charge of corresponding field. ) This feature is important to explain the origin of Yukawa hierarchy and to solve GUT problem. (Prog, Theor. Phys. 110, 93, (2003)) Keeping the above attractive features, we would like to break supersymmetry spontaneously.
Review of SUSY breaking model with R symmetry Model: Then, there are following superpotential and U(1)A D term as follows. (cut off where ) is originated from Fayet-Iliopoulos term. We can obtain potential V: .
Review of SUSY breaking model with R symmetry (cut off We find that should be and ) in order to make potential minimized. Therefore can not be simultaneously zero. therefore SUSY is broken. This model has SUSY breaking vacuum at These values of VEVs , with the important VEV relation. , are satisfied magnification , . .
SUSY breaking model without R symmetry Next, we consider a SUSY breaking model without R symmetry. We will find that this model has meta-stable SUSY breaking vacuum!! Model: Then, there are following superpotential and anomalous U(1) D term as follows. (cut off ) Note that, here, since we do not impose R symmetry, we allow power of . We can obtain potential V , , where is derivative of respect to . ( . )
SUSY breaking model without R symmetry There are supersymmetric vacua where Potential approximately becomes the same as the previous model with R symmetry. because at. This model has meta-stable vacuum. The VEV of fields become , . These values of VEVs are satisfied with the important VEV relation. magnification We checked that this meta-stable vacuum is sufficiently stable. (compared with the universe age. )
General case Next, we consider a model that has many positively and negatively charged fields as follows, where index run from 1 to and run from 1 to . (1) In the case of , this model has supersymmetric vacuum in which VEV relation and. ‥‥ (2) In the case of , this model has a meta-stable vacuum. ‥‥ We can solve Yukawa hierarchy and doublet-triplet splitting problem in anomalous U(1) GUT in this case. SUSY can be easily broken by adding to only one positively charged field in the case of (1). In this case, one of all F terms can not have vanishing VEV. (Here, we assume. ) Then, potential becomes , where becomes the largest one to ensure the potential stability. SUSY breaking scale (weak scale) becomes very small naturally. Therefore, it is possible to explain that weak scale is smaller than cutoff.
summary and conclusion ・ We researched a SUSY breaking model with anomalous U(1)A gauge symmetry without R symmetry. As a result, we found out that this model has a meta-stable vacuum in which VEV relation , . ・ Till now, we could explain Yukawa hierarchy and solve GUT problem by using VEV relation , in supersymmetric U(1)A GUT. But, we found that SUSY can be easily broken by adding to only one positive field in supersymmetric U(1)A GUT and values of VEVs , are satisfied with the important VEV relation. . Potential of model with R symmetry Potential of model without R symmetry
Positively charged field VEV Positively charged field in the model without R symmetry has small VEV as follows: (cut off because VEV ) is decided by next relation, mass term Coefficient of tadpole mass This model has tadpole coming from therefore, the magnitude of VEV term: . (mass term come from is decided as , where superposition term ). If we assumed that takes weak scale and cut off is much larger than weak scale, VEVs would be much smaller than cut off and VEV. These values of VEVs VEV relation. . , are approximately satisfied with the important
notation Dilation stabilization We can stabilize the dilaton by using U(1)A potential: , ( , is dilston field ) where is kahler potential of and is kahler potential of dilaton. is reduction function of D if we assume and. We found that dilaton cannot be stabilized by using. We found that dilaton can be stabilized by using kahler potential. If contains dilaotn field and is much smaller than 1 at , dilaton can be stabilized as follows. constant , where is generic function of dilaton In fact, we checked that dilaton can be stabilized by using where , is parameter ( ). This kaher potential is generic, because we can ignore higher terms of at. ,
超対称性の破れをMSSMに伝えるメカニズムを考える。 gravity mediation sfermion soft mass ( O(1)係数、i: 世代の足) FCNCが気になる。 gaugino mass ( gaugino massは はgaugino) の大きなsuppressionを受ける。 gaugino massを生成、FCNCを抑えるために messenger fieldを導入し、gauge mediationを考える。
gauge mediation ‥‥gauge 相互作用でSUSYの破れを伝播。 standard model のgauge 群をもったmessenger field 導入する。 Superpotential はgauge singlet field SUSYは破れ、 の補助場 を とcoupleすると仮定する。 は真空期待値をもつとする。 gaugino massは下のdiagram から生成できる。 からgravity mediationより gaugino massを大きく出来る。
gauge mediation(続き) squrk, slepton massは下の 2 -loop のdiagramから出る。 : (hypercharge) ・ mass matrix は対角的 ・ 世代でchargeが等しいから 3世代全て同じmassをもつ term gauge mediationでは、 FCNCの心配はない。 一般に次のsuperpotential も許される。 ( 大 term Gauge mediationでは が大きい問題がある。 : Higgs ) Higgs massのfinetuning Higgsino mass term よりweak scaleにあ るべき。
以上の注意点から次のsuperpotentialを考える。 真空期待値を求めて、B-term , gaugino massを評価する。 ・B term ・ ・gaugino mass term ・D term ・sfermion mass ( : U(1)A charge) を抑えると、gaugino mass が大きく出ない!
SUGRA potential ; gravity mediation 宇宙項を小さくするために constant termを入れた。 Tadpole ;
potential: ( に関する部分) ・ , ・B term , , ・gaugino mass ・ term
真空期待値を求めて、B-term , gaugino massを評価する。 , ・B term ・gaugino mass ・gravitino mass ・D term ・ term を抑えると、gaugino mass が大きく出ない!
positive messenger Gaugino mass U(1)A不変なsuperpotential は以下の形である。
以上の注意点から次のsuperpotentialを考える。 真空期待値を求めて、B-term , gaugino massを評価する。 ・B term ・D term ・gaugino mass ・ term ・sfermion mass ( : U(1)A charge) を抑えると、gaugino mass が大きく出ない!
supersymmetry ・U(1)R 対称性‥‥SUSY代数を不変に保つ対称性 supersymmetric Lagrangian
motivation Anomalous U(1)A theory ・ VEVs are determinated by anomalous U(1) charge. ・ This theory can derive Yukawa hierarchy and solve doublet-triplet splitting problem. SUSY is spontaneously broken by anomalous U(1)A symmetry. (where, vacuum to solve those problems is supersymmetric. ) This theory has generic interaction and not R symmetry. This theory has generic interaction and R symmetry. Meanwhile, we can spontaneously breaking SUSY by anomalous U(1) symmetry imposed R symmetry.
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