THE HIGGS, VACUUM STABILITY, and OTHER CONSTRAINTS Matthew Reece Harvard University at the PCTS, April 26, 2013 THIS TALK

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THE HIGGS, VACUUM STABILITY, and OTHER CONSTRAINTS Matthew Reece Harvard University at the PCTS, April 26, 2013 THIS TALK THE HIGGS, VACUUM STABILITY, AND OTHER CONSTRAINTS Matthew Reece Harvard University at the PCTS, April 26, 2013 THIS TALK First, I’m going to explain some constraints on new physics scenarios that try to significantly alter Higgs properties. The motivation for dwelling on this is diminished given recent CMS updates on diphoton. Then I’ll talk a bit about Higgs vacuum stability in the Standard Model. LHC: WHERE WE STAND I looked over my slides from my PCTS talk almost exactly one year ago and still agree with what I said then: •No hint of strong dynamics. Technicolor, composite Higgs, Randall-Sundrum all look even less plausible than they did pre-Higgs. •Higgs mass puts SUSY in an awkward spot •“Natural SUSY”: the MSSM must be very tuned to fit a 125 GeV Higgs (despite many contrary claims in the literature in the last year). Models beyond the MSSM are typically awkward and/or complicated. •Semi-split SUSY: solve most of the hierarchy problem, put scalars at ~10 to 1000 TeV. Increasingly plausible. •Important to keep looking for small deviations from SM Higgs •Keep looking for naturalness signatures (stops, etc.), but bounds are already becoming very strong... HIGGS PROPERTIES Looking increasingly Standard Model-like as more data comes in. Still room for 30 to 50% (large!) deviations! Let’s say, for instance, thatm ˜ D dominates, and is 1 TeV, with ⌅ =0.1, Mmess = 100 TeV (which is consistent with √F 100 TeV as well), m = 2 TeV, and m = 150 GeV. Then ⇥ Y S we have: Let’s say, for instance, thatm ˜ D dominates, and is 1 TeV, with ⌅ =0.1, Mmess = 100 TeV Let’s say, for instance, thatm ˜ dominates, and is 1 TeV, with ⌅ =0.1, M = 100 TeV (which is consistentD with √F 100 TeV as well), m = 2 TeV,mess and m = 150 GeV. Then 2 2 Y 2 S (which is consistent with √F 100m TeV˜ = as⇥ well),2970m GeVY = 2 TeV, andm mS == 150150 GeV. Then2970 GeV 140 GeV. (2.4) we have: ⇥ S scalar we have: − ⇧ − ⇤ Let’s say, for instance, thatm ˜ D dominates, and is 1 TeV, with ⌅ =0.1, Mmess = 100 TeV ⇥ So, this2 model is easily2 compatible with2 the sort of splittings we’re interested in. (which is consistent with √F 100 TeV as well), mY = 2 TeV,2 and mS =m˜ 150S = GeV.2 2970 Then GeV m2scalar = 150 2970 GeV 140 GeV. (2.4) Let’s say, for instance, thatm ˜ D dominates,⇥ and is 1 TeV, with ⌅ =0m˜.1,S M=mess2970= 100 GeV TeV− mscalar =⇧ 150 2970 GeV −140 GeV. ⇤ (2.4) we have: − ⇧ − ⇤ (which is consistent with √F 100 TeV as well), mY = 2 TeV, and mS = 150 GeV. Then ⇥ ⇥ Let’s say, for instance,So, that thism ˜ D modeldominates,2.2 is Couplings easily and is compatible 1 TeV, to with Gauge⇥⌅ with=0.1, the BosonsMmess sort= of 100 and splittings TeV Gauginos we’re interested in. we have: 2 2 So, this2 model is easily compatible with the sort of splittings we’re interested in. m˜ = 2970 GeV mscalar(which= is150 consistent2970 with GeV√F 140100 GeV TeV. as well), m(2.4)Y = 2 TeV, and mS = 150 GeV. Then S − ⇧ − ⇤⇥ ¯ 2 2 we have:2 Now we will integrate out Y and Y and study the induced couplings of S to gauge bosons. m˜ S = 2970 GeV mscalar = 150 ⇥2.22970 Couplings GeV 2.2140 Couplings toGeV Gauge. Bosons(2.4) to Gauge and Bosons Gauginos and Gauginos So, this model− is easily compatible⇧ with the sort− of splittings⇤ we’re interested in. 2 2 To keep things2 simple, we will assume that the mass of the Y s is dominantly supersymmetric. ⇥ m˜ S = 2970Now GeV we will integratemscalar = ¯ out150 Y 2970and GeVY¯ and140 study GeV. the induced(2.4) couplings of S to gauge bosons. So, this model is easily compatible with the sort of splittingsNow we’re we will− interested integrate in.⇧In out thatY and case,Y and we− expect study the to⇤ induced find an couplings e⇤ective of operatorS to gauge of bosons. the form: 2.2 Couplings to Gauge Bosons and Gauginos ⇥ So, thisTo model keep is easily thingsTo compatible keep simple, things we with will simple, the assume sort of we splittings that will the assume we’re mass interested that of the theY in.s mass is dominantly of the Y s supersymmetric. is dominantly supersymmetric. 2.2 Couplings to Gauge Bosons and Gauginos Now we will integrate out Y and Y¯ and study theIn induced that case, couplingsIn we that expect case, of S to weto find gauge expect an bosons. e⇤ toective find operator an e⇤ective of the operator form:c of the2 form: α Now we will integrate out Y and Y¯ and study the2.2 induced Couplings couplings to Gauge of S Bosonsto gauge and bosons. Gauginos d ⇤SWαW + h.c. (2.5) To keep things simple, we will assume that the mass of the Y s is dominantly supersymmetric.c mY To keep things simple, we will assume that the massNow of we the willY s integrate is dominantly out Y supersymmetric.and Y¯ and study the induced2 couplingsc α of S2 to gauge bosons.α In that case, we expect to find an e⇤ective operator of the form: d ⇤SWαW +dh.c.⇤SWαW + h.c. (2.5) (2.5) In that case, we expect to find an e⇤ective operatorTo keep of the things form: simple, we will assume that the massmY of the Y s ism dominantly supersymmetric. Let’s work out the coe⌃Ycient c and then compute the resulting decays. c 2In that case,α we expect to findHIGGS an e⇤ective LOOP-LEVEL operator of the form: c d ⇤SWαWLet’s+ workh.c. out the coe⌃cientToc computeand then(2.5) compute the coe⌃ thecient, resulting let me decays. try to flesh out JiJi’s statement that it’s related to a md2⇤SW W α + h.c. Let’s work out the(2.5) coe⌃cient c and then compute the resulting decays. Y α c 2 α mY To compute the coe⌃cient,d ⇤SW letW me+ tryh.c. to flesh out JiJi’s statement(2.5) that it’s related to a To computembetaCOUPLINGS function the coeα ⌃ coecient,⌃cient. let me Suppose try to flesh we out have JiJi’s a Lagrangian statement that it’s related to a Let’s work out the coe⌃cient c and then computebeta the resulting function decays. coe⌃cient.Y Suppose we have a Lagrangian Let’s work out the coe⌃cient c and then compute the resulting decays.beta function coe⌃cient. Suppose we have a Lagrangian To compute the coe⌃cient, let me tryLet’s to flesh work out out JiJi’s the coe statement⌃cient c and that then it’s compute related the to resulting a decays. 1 To compute the coe⌃cient, let me try to flesh out JiJi’s statementA lot of interest that it’s in related this when to a both ATLAS1 and CMS a aµ⇧ To compute the coe⌃cient, let me try to flesh out JiJi’s statementa aµ that⇧ it’s related= to a 2 Gµ⇧G . (2.6) beta function coe⌃cient. Suppose we have a Lagrangian = Gµ⇧G . 1 a L aµ⇧−4g (2.6) beta function coe⌃cient. Suppose we have a Lagrangianbeta function coeshowed⌃cient. a Suppose high diphoton we have a rate. Lagrangian Recall:L − Higgs4g2 couplings= to G G . (2.6) photons, gluons related to low-energy theorem.L −4g2 µ⇧ 1 1 a aµ⇧ = a aµG⇧ G . Then in1 facta (2.6)gaµ⇧is a running coupling. In particular, suppose that we have fields at a scale M, = Gµ⇧G2 µ.Then⇧ in fact g is a running= coupling.(2.6)G G In. particular, suppose that we(2.6) have fields at a scale M, L −L4g2 −4g 2 µ⇧ with µ<M<Run fromThen ⇥ in , down so factwith thatL gtois the − µ<M< a4 gwith running beta an function intermediate coupling.⇥, so coe that⌃cient In the particular, changes beta function from supposeb below coe that⌃M wecientto haveb + changes fields∆b at from a scaleb belowM, M to b + ∆b ThenThen in fact in factg is ag runningis a running coupling. coupling. In particular, In particular,Then suppose inabove fact suppose thatg isthresholdM a we. running that Thenwith have we fields coupling.µ<M< taking have at above fields a account In scale particular, ⇥ at M,Mat a so of,.which scale Then that supposeM the threshold, the, taking beta that beta wefunction account function have fields of coe at that a⌃ scalecient threshold,M, changes from b below M to b + ∆b withwithµ<M<µ<M<⇥, so⇥ that, so thethat beta the function beta function coewith⌃cient coeµ<M<⌃ changescientchanges⇥ changes, from soabove thatb frombelow from theM beta .b M Thenbelow toto function b + takingM ∆ coeto b . ⌃b accountcient+ ∆b changes of that from b threshold,below M to b + ∆b 1 1 b ⇥ ∆b ⇥ aboveaboveM. ThenM. Then taking taking account account of that of threshold, that threshold,above M. Then taking account of that threshold,= + log +1 log 1 . b ⇥ ∆(2.7)b ⇥ RG: g2(µ) g2(⇥) 1 8⌃2 1µ 8⌃2b= M⇥ +∆b log⇥ + log . (2.7) 1 1 b ⇥ ∆b ⇥ 1 1 b ⇥ ∆b = ⇥ g2(+µ) logg2(⇥)+ 8⌃2log µ. 8⌃2 M (2.7) 1 1 b ⇥ ∆b ⇥2 = 2 + 2 log +2 2 log 2.
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