Phase Transi+ons in Twin Higgs Models

Transcription

1 Phase Transi+ons in Twin Higgs Models Kohei Fujikura (TITECH) Collaborators: Kohei Kamada (IBS), Yuichiro Nakai (Rutgers.U), Masahide Yamaguchi (TITECH). 1

2 Contents p Naturalness of the Higgs mass p Twin Higgs Models p Phase Transitions in Twin Higgs Models (Cosmological impact)

3 Contents p Naturalness of the Higgs mass p Twin Higgs Models p Phase Transi8ons in Twin Higgs Models (Cosmological impact) 3

4 Standard Model is incomplete SM describes phenomenology around the electroweak scale However, there are problems V (H) Dynamics of Electroweak Symmetry Breaking SM Higgs Potential:V ( )=m H + SM H 4 v SM p H m R = m bare + m O(M pl) O(M pl) Why??? 4

5 Naturalness of the Higgs mass Top quark SU() W Higgs self-coupling m h = + + 3y t 4 + 9g 3 : cut + 4 o scale 10 GeV M SM The measure of Fine-Tuning: (mr h ) m h For example, < 10 (m R h ) =(m bare h? Large Hierarchy Problem ) + m h 1565 = GeV M pl Unnatural Cancella5on! (1% tuning is needed) 5

6 <latexit sha1_base64="zon48/hki0lsjyqkjes6iuzmb8q=">aaacihichve9txtbeh0ccra7giemeo0v4wia01zwcy7cqqshicdybira1t1ldsffl+7wludkp8afsjeqkske0qrnwpr8grt8higspdqpmds7ilkqzgp3z97om37y4wue0ui6xfl9nhjsfgjj7n808mp6clm7g4cdcnbno3adaj9y4yf6/iikr3piv0weqznuwlp6rxkz/d6ioqdwg/i01aceeax77qd5qmtqolr1tjhlrlv1o99ex5yptustvf1jaykpkshtjttwolukk3dikpoqkgcupyxirfv0vaiplvslqtopcbq7xbgfsdofbwidk34wjmmcbnbbcxo6qmbax5tnan3kmnvllmezjqmdxo85ohiipsdpzthj3ylyznizhfl+k6xdevf6bp9of8p1kqygqmwu96taveerenzz/wf/v5veuc/gh9u7neg6uzvoe1hxmsvsie8htnb/razvl5av9obvw/56u6ypf4pfu7i81sfmoow7a718upuw0x6qgsrvkax1jikjzom5fvm7v7cotwyjydee4zo+4kusvzrlrtegqcrikdohv0zzuaccipf4</latexit> SUPERSYMMETRY SUSY provides an excellent solu9on to Hierarchy Problem m = H Top + H ' 3y t 8 m stop log m stop Stop Quadra9c divergence is cancelled by Top partner (Stop). (SUSY protects quadra9c divergence mass correc9ons.) SoF SUSY-breaking mass is important for fine-tuning. Scalartop is a colored state Strong Bounds Soft Mass must be Heavy M soft >> O(1)TeV LiNle Hierarchy Problem! <latexit sha1_base64="zon48/hki0lsjyqkjes6iuzmb8q=">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</latexit> <

7 Hierarchy Problem Large Hierarchy Problem 10 GeV TeV GeV Little Hierarchy Problem How to solve? SUSY and Composite Higgs provide solu<on m h = + + 3y t 4 + 9g Problem is quadra<c-divergence sensi<ve 3 : cut + 4 o scale 7

8 Contents p Naturalness of the Higgs mass p Twin Higgs Models p Phase Transitions in Twin Higgs Models (Cosmological impact) 8

9 Charge U(1) V U(1) A e L Electron mass is natural L QED = 1 4 F µ F µ + ē L µd µ e L +ē µ R D µ e R m e (ē L e R +ē R e L ), U(1) D µ iea V U(1) A invariant U(1) V invariant µ e A µ e R +1 1 e When we take m e! 0 limit, U(1) A symmetry is restored. m e! 0, (m e! 0) Naive dimensional analysis However, m e 10 19, ( M pl ) m e = m e 3 log Natural!! Why log sensi4vity? m e is the only parameter which breaks the U(1) A symmetry. m e / m e m e m e 9

10 U(1) Toy Model (Symmetry Protection) V ( ) = f a(x) 1 i f (x) = p (f + (x))e p (x) :Massive Mode m = f a(x) : Massless Goldstone Mode 1 L(, a) a(x)@ µ a(x) + L ( ) NG Boson has shi=-symmetry: a(x)! a(x) + const Add explicit breaking source:!0 LU (1)breaking = f 3 ( + p NG Boson acquires mass: ma = f U(1) symmetry is restored ma / ma ) 10

11 <latexit sha1_base64="izx+ghh3pvjiqsj+rvt3jjwqqla=">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</latexit> <latexit sha1_base64="izx+ghh3pvjiqsj+rvt3jjwqqla=">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</latexit> <latexit sha1_base64="izx+ghh3pvjiqsj+rvt3jjwqqla=">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</latexit> <latexit sha1_base64="izx+ghh3pvjiqsj+rvt3jjwqqla=">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</latexit> <latexit sha1_base64="5bkjwtydxk+sopa4yee8qqb5iac=">aaacl3ichvfnsxtrfdobbwx1truit0eg8vvufghrvaicixlfdqqoggygv+sh/pfzevqbv9a/4cik4uipt/chrv7a7rityhdptbnf96zdasvtney znvpchwzkalbhdb54ogjqenhmzkns0/nss/mtyk/g9qiyfuoh+5yziqc6ymgksoro0eotndyxla1vxnnt3sijktvfvchgwi6ztutlwmbiikju1onnlvdeu0pdcpxfof8uaoo1c60ljv9rfyy+jcxtnjwyecpre7j4opicpncp+9gi69uddrhcubdwoxg5mrpztoghcwfwtfezcrjljcxwhw9ouvwmumjnd57hnq9u9xgd94wstc7opyhrmxhib7tfxrsnxlh/tnr736sy/yyyhp1kgrampu04v67/+qxj4vompvpz0rtpam8srze5aw8snskb738xhyx68t9v/rof1k/c0ocs+gdf7zx+uitop4gco3r3u+6cxunhboopavrsrvsq0xmiry3zdr1fcgru0enstxoia37qfras918qjum0i1tzhrdcqn0ijnkw=</latexit> Twin Higgs [ Z. Chacko, H.-S. Goh, and R. Harnik,Phys. Rev. Lett.96, 3180 (006)] Twin Higgs provides an elegant solulon to the LiMle Hierarchy Problem SM Higgs is considered as pseudo-nambu-goldstone Boson H = C A Spontaneous symmetry breaking V = H f SM-like Higgs: H A 1 U(4) Fundamental RepresentaLon U(4)! U(3) h 4 i = f/ p <latexit sha1_base64="qsaqoqyjjfaf7z+fgkhfggek7jk=">aaacihichvhlsurafd1gx0c7aqsbytbbxsfveyocdxbeny5bnvbbsjpe6rawooljdymfod+gatxciliyryzazfza7pwewaxcm5cedsdkbkzvsfv556659apkjdumtzed1ge8enzq7unkzv577+gezg0hoc1cjpfl1abdgm68rcsv8utdrkbiarckquehvu3ljzfamuolgg/jd9eirtqlpxzvl6jmaqlm3zyversphyvewpkw7aqxzznncjvcj3zg84irkuxlmwcliic0ckhcjzembddvui+ncmfrze/g3baifkbhsn5ijgmlkxoekgttwuelzhmlvhy4wzrzt1ow/jbo1x7so/inwmhij33rnd/slbugppf+3vypp0frywlpb0oqwnhaysvb0oarks8buq+pdzxplzcrejxspe6z5cq+lrx+epqznry41vtif3bp/c7qjwz6bx3/0llfe6hky/adwv9f9fqxp5i3kwyttuyxf9cm68qwjgof7nsycllfakfc9xnf8we8jy5axbcysovdomv8jyfahiczzc</latexit> <latexit sha1_base64="qsaqoqyjjfaf7z+fgkhfggek7jk=">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</latexit> <latexit sha1_base64="qsaqoqyjjfaf7z+fgkhfggek7jk=">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</latexit> <latexit sha1_base64="qsaqoqyjjfaf7z+fgkhfggek7jk=">aaacihichvhlsurafd1gx0c7aqsbytbbxsfveyocdxbeny5bnvbbsjpe6rawooljdymfod+gatxciliyryzazfza7pwewaxcm5cedsdkbkzvsfv556659apkjdumtzed1ge8enzq7unkzv577+gezg0hoc1cjpfl1abdgm68rcsv8utdrkbiarckquehvu3ljzfamuolgg/jd9eirtqlpxzvl6jmaqlm3zyversphyvewpkw7aqxzznncjvcj3zg84irkuxlmwcliic0ckhcjzembddvui+ncmfrze/g3baifkbhsn5ijgmlkxoekgttwuelzhmlvhy4wzrzt1ow/jbo1x7so/inwmhij33rnd/slbugppf+3vypp0frywlpb0oqwnhaysvb0oarks8buq+pdzxplzcrejxspe6z5cq+lrx+epqznry41vtif3bp/c7qjwz6bx3/0llfe6hky/adwv9f9fqxp5i3kwyttuyxf9cm68qwjgof7nsycllfakfc9xnf8we8jy5axbcysovdomv8jyfahiczzc</latexit> 7 Goldstone Modes + one massive mode 4 of them are idenlfied with Standard Model Higgs Another Higgs : H B =

12 Mass correc)ons In general, ma0er sector breaks the U(4) symmetry explicitly y t QL HA u R + h.c. û : Twin top quark H A : SU() W U(1) Y SM Higgs cannot be considered as pngb Introduce copy of SM ŷ t ˆQL HB û R + h.c. H B : SU()Ŵ U(1)Ŷ 3 V e 8 (yt H A +ŷt H B ) (g H A +ĝ H B ) V e 3y t 8 + 9g 64 y t =ŷ t, g =ĝ ( H A + H B ) Large mass corrections respect the U(4) symmetry 1

13 Standard Model H A SU(3) C SU() W U(1) Y Quarks and Leptons Twin Higgs Let us introduce copy of SM Twin Z Symmetry Twin Partner H B SU(3)Ĉ SU()Ŵ U(1)Ŷ Twin Quarks and Leptons Higgs Mixing Every quadraec divergent mass correceons are cancelled by its Twin partner Most important point is that the Twin partners do not have SM charge! (Neutral Naturalness) 13

14 <latexit sha1_base64="opumfi4hrfb+urqsa3pczew9bq0=">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</latexit> <latexit sha1_base64="opumfi4hrfb+urqsa3pczew9bq0=">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</latexit> <latexit sha1_base64="opumfi4hrfb+urqsa3pczew9bq0=">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</latexit> <latexit sha1_base64="opumfi4hrfb+urqsa3pczew9bq0=">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</latexit> Higgs poten+al Sub-leadingcorrec+on does not respect the U(4) symmetry apple V (') CW = n m4 (H A, H B ) m (H A, H B ) 64 log V e = H A + H B f + f H A + apple( H A 4 + H B 4 ) Spontaneously symmetry breaking U(4)! U(3) This term must be dominant compared to U(4) breaking term >>, apple Twin Z breaking term f>v A Radia+ve Correc+ons V CW from top quark Twin top quark U(4) explicit breaking term controls pngb mass!, apple : Technically Natural 14

15 V low energy Low-Energy Effective Theory Integra5ng Out Massive Mode H B = f H A e = f applef H A +apple H A 4 It should match with SM Higgs potential! apple = ( apple)f = SM vsm SM, V low energy e is valid up to 4 f 5TeV $ f 400GeV > 1 10 How is the tuning? = v SM f 1 v SM f v SM f v SM f >

16 Contents p Naturalness of the Higgs mass p Twin Higgs Models p Phase Transi8ons in Twin Higgs Models (Cosmological impact) 16

17 Cosmology! Twin Higgs Collider searches Gravita<onal wave Large Hadron Collider LISA, DECIGO and BBO 17

18 Thermal History of the early Universe Spontaneous symmetry breaking in the early Universe Phase transition 18

19 First-order phase transi/on and GW First order phase transi/on h i6=0 First order phase transi/on proceeds through bubble nuclea/on Tunneling Order parameter is Higgs VEV. There are three sources of the Gravitational Wave Bubble collisions h i6=0 h i6=0 Sound Wave of the cosmic plasma T = T C T Turbulence of the plasma 19

20 Electroweak Phase Transition in SM T c /GeV M. LAINE (000) symmetric confinement phase 1st order transition nd order endpoint broken Higgs phase m H /GeV First-order phase transi5on Electroweak phase transi5on is not first order in SM. BSM can change the situa5on! Is it possible to realize first-order phase transi5ons in Twin Higgs Models? and If thephasetransi5on is first order, can we detect the GW? 0

21 v B V e = H B Phase Transition(s) in Twin Higgs Models There are two spontaneous symmetry breakings (Global U(4) symmetry and EW symmetry) H A + H B f + f H A + apple( H A 4 + H B 4 ) (1) (0, 0)! (0, v B )! (v A, v B ) v A (3) H A U(4) Breaking Phase TransiCon Electroweak Phase TransiCon () (0, 0)! (v A, v B ) U(4) Breaking Phase TransiCon and Electroweak Phase TransiCon occur simultaneously (3) (0, 0)! (v A, 0)! (v A, v B ) E Electroweak Phase TransiCon U(4) Breaking P phase TransiCon We consider the case (1) 1

22 Electroweak Phase Transition Background field H A = 0A p!, H B = 0B p! Take account of d.o.f Field dependent mass SU() W n W =6, : m W = g A 4, V ( A, SU()Ŵ U(1) Y Top quark Twin Top quark nŵ =9, : m Ŵ = ĝ B 4 n Z =3, : m Z =(g 1 + g ) n t = 1, : m t = y t nˆt = 1, : mˆt = y t B T )=V 0 + V CW + V Thermal + V ring Integra>ng out massive mode B = f A A B A 4 V ( A, T)

23 Validity of the perturbation in finite temperature f B = 1 e E 1, E k + m W ( ) m W ( ) g f B >> 1 when m W ( ) << 1 IR divergence comes from large occupa:on number Perturba:on theory breakdown when Linde.(1980) = g ( ) Expansion parameter T m W ( ) g T > 1 1 l l +1 three-gluon vertices and 3 propagators. T Numerical Simula:on g l T 4 for l =1, g 6 T 4 ln(t/m) for l =3 g 6 T 4 (g T/m) l 3 for l>3 If (T C ) > 1, we cannot believe perturbation! Peter Arnold(1994) Order of the phase transition should be analyzed by the non-perturbative method 3

24 Result of the electroweak phase transition V ( A, T) Red line represent the only SM contribu6on Allowed region cannot sa6sfy v SM f < 0.5 (T C ) T C >g 0.65 A(T C ) T C Perturba6ve descrip6on breakdown!! Sphaleron decoupling condi6on cannot be sa6sfied A(T C ) T C > 1 v SM f Large breaking scale f thermal decoupling (Boltzmann suppression) Twin sector correc6ons do not give a contribu6on 4

25 U(4) Breaking Phase Transition without UV completion Thanks to the Twin Z symmetry, the situa4on is similar to the electroweak phase transi4on in SM. U(4) breaking Phase Transi4on Twin Z Symmetry y t ' by t, g ' bg Electroweak phase transi4on in SM V = 1 M (T ) B M (T )= T ĝ 4 3/ B T 4 ĝ 4 f + ŷ t 4 T + 3ĝ 16 T apple(t )=apple B However 3 + (i) W ĝ v A 6= f, SM 6= + apple 4 Well known 3! + + apple 1(T ) 4 3ŷt 4 16 log af T µ + 9ĝ4 56 log ab T µ 5 4 B

26 Situation is similar to electroweak phase transition in SM SU() cw : bg $ SU() W : g ĝ ( ) g ( ) g ( ) Breaking Scale : f $ v SM (Cri6cal Temperature is different) Twin Top Quark : by t $ Top Quark : y t Higg self coupling : + apple $ SM In SM, order of electroweak phase transi6on depends on SM/g [K. Rummukainena, M. Tsypinb, K. Kajan6ec, M. Laine, and M. Shaposhnikov] (1998) U(4) breaking phase transition depends on ( + apple)/ĝ We can use the result of electroweak phase transi6on in SM! 6

27 Result of the U(4) Phase Transition 130 M. LAINE (000) SM Rusult + apple < 0.04 T c /GeV symmetric confinement phase 1st order transition broken Higgs phase m H /GeV SM < 0.04 nd order endpoint First order phase transion!! Matching condition with SM apple = SM 0.06 U(4) breaking phase transion cannot be first order without any UV compleon 7

28 Summary utwin Higgs provides excellent solu8on to the Li;le Hierarchy problem uelectroweak phase transi8on cannot be analyzed perturba8vely in Twin Higgs Models uit is difficult to realize the first-order U(4) breaking phase transi8on without any UV comple8on uwe also analyze the U(4) breaking phase transi8on with light twin stops in SUSY comple8on and calculate a typical GW amplitude 8