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spin 1 - Indico
Non-SUSY, Exotic の今後 阿部智広 名古屋⼤学⾼等研究院 KMI ! ! 新学術領域研究 (研究領域提案型) ヒッグス粒子発見後の素粒子物理学の新展開 ∼LHCによる真空と時空構造の解明∼ キックオフ会合 ! 2016.8.31 世話人からの要望 • 今後5年くらいを俯瞰してnon-susy のレ ビューをしてほしい • diphoton についても触れてほしい(ICHEP の結果が出る前の依頼) 750 GeV • more than 400 papers!!!! • 飢えた理論屋と統計の罠 (local ~4σ , global ~2σ ) • global が重要ってヒッグスの発⾒の前に 強調されたいたのに… • ⾊々アイデアが出たのは良かった ICHEP2016でのrappoccio氏のスライドより ZV Limits : 2015 data • #650isthenew750? • Deja vu all over again? • ATLAS talk up next! • Remember LookElsewhere Effect accounts only for other masses in THIS plot • Does not account for the >1000 other LHC searches ;) • Stay tuned for 2016 data on the way 5 Aug 2016 3.9 sigma local, 3.5 sigma global (global = other masses in this plot) 21 Why BSM? SMで説明できないもの • 暗⿊物質 (?) • バリオン数⽣成 • ニュートリノの質量の起源 •… Why BSM @ TeV scale? 階層性問題 (electroweak scale << Planck scale) • TeV scale SUSY • Warped extra dimension • Little Higgs • Gauge Higgs unification • composite Higgs • technicolor •… 昨今、どれも厳しい雰囲気が漂う。微調整などが必要。 ! TeVスケールに新物理があるというロジックが他に何かあるとうれしい 歴史に学ぶ Fermi theory ⌫µ ⌫µ µ ⌫¯e e / GF E 2 Λ ~ 300GeV ? µ ⌫¯e W mW = 80 < 300GeV e WW scat W W Λ < 1TeV ? W W 2012年ヒッグス粒⼦発⾒ mh = 125 GeV < 1TeV amplitude. In the SM, the Higgs boson contr are proportional to E 4 E −2 = E 2 , where E −2 WL WL WL 4 terms which are proportional to E . hVV coupling がもしずれていたら = ig W W WL WL = + = WL W WL WL WL W 4E 2 M ' 2 (1 v WL 10 2V ) < 32⇡ L@TeVD = ig 2 WL WL WL 6 4L W WL WL WL 2 0.80 WL 0.85 WL WL 4 m4 f WL WL abe cde f ! " #s 2 (−4 − x)c=+ −iδ O(xab)δ cd, v WL WL # $ # 4 4 E E 15 2 ace bde ac bd c − −ig 2 4 f abe f cde (−4 + 4x)c = ig f f (1 − c)(3 + c) + = −iδ δ m + m4 +…2 4 2E ace bde −ig +L2x(c − 1)] WL WL m4 f f [(1 WL− c)(3 + c)W 4 WL WL 2E ade bce −ig f f [(1 + c)(3 − c) + 2x(c + 1)] , # WL m4 WL # (2.1.2) = −iδ ad $δ bc − 4 E 15 = ig 2 4 f ade f bce (1 + c)(3 − c) + − c m 2 W W L WL 8WL WL 2E WL WL L WL From eqn.(2.1.7) and eqn.(2.1.11)–(2.1.12), we " E abe cde ! 2 f f (−4 − x)c + O(x ) , m4 where 4 (2.1.3) m2h % ab cd i 2 δ δ + δ ac δ bd + v This is not a monotonically increasing function m2 ≡ high , c ≡&cosinθ,the SM. # can$be keptx % at 2 energy 4 E E 15 3 = ig 2 4 f ace f bde (1 − c)(3 + c) + c− x + O(x2 ) , m and where cos θ is the scattering 2 2 angle. As we can see from eqn.(2 9 dependence is canceled among the diagrams, and the leading term (2.1.4) # $ % & 4 E 15 3 2 = ig0.90 f ade f bce 0.95 (1 + c)(3 − c) + − c− x + O(x2 ) , 1.00 4 m 2 2 kV 8 (2.1.5) ヒッグス粒⼦の精密測定は今後重要!! where m2 x ≡ 2 , c ≡ cos θ, E (2.1.6) 歴史に学ぶ Fermi theory ⌫µ ⌫µ µ ⌫¯e e / GF E 2 Λ ~ 300GeV ? µ ⌫¯e W mW = 80 < 300GeV 教訓 • 現象をとにかく式で書き下す • カットオフ(Λ)が出てくる • Λ以下に新物理があるはず! • アノマリーがあったら同じことをやってみよう!! e e anomalous magnetic moment of the muon aµ ⌘ (g 2)/2, so-called muon g 2, やってみよう a very precisely measured observable. The latest measurement of aµ by the E821 laboration [1] gives アノマリー exp • ミュオン ag-2 µ = 11 659 208.0 (5.4)(3.3) ⇥ 10 10 . (1) • フレーバー (B → D(*)τν、Br(B → K μ μ)/Br(B → K e e)) it has been well known that there is a discrepancy between the experimental value •… d the prediction of the standard model (SM). According to the calculation evaluated Refs. [2, 3] ミューオン g-2: 3σ以上のずれ aexp µ aSM µ = (28.7 ± 8.0) ⇥ 10 10 aexp µ aSM µ = (26.1 ± 8.0) ⇥ 10 10 , Davier et.al. et. (2011) (Davier al.) , Hagiwara et.al. (2011) (Hagiwara et. al.) ! discrepancy more由来なら、そのスケールはどこ? than the 3 level, which can be considered as an indirect evidence これがisBSM the existence of a new physics model. This discrepancy will be further probed at rmilab [4] and J-PARC [5] in the near future. Since the size of the deviation is the me order as the electroweak contribution aEW = 15.4 ⇥ 10 µ 10 [6], we expect that new ysics exists at the electroweak scale if the strength of new interactions is as large as ミュオン g-2 SM 次元6演算⼦ c0 g 0 ¯ + `L 2 2 (4⇡) ⇤ aµ µ⌫ Amp ⇠ ūi q⌫ ✏ µ u 2mµ µ⌫ HeR Bµ⌫ c g ¯ `L 2 2 (4⇡) ⇤ v 1 aµ = 2mµ p 2 (4⇡)2 ✓ µ⌫ Wµ⌫ HeR + (h.c.) c c 2 02 + 2 ⇤ ⇤ ◆ 0.01 1.3 0.001 0.42 0 例)c = 0 のとき c Λ [TeV] 1 13 TeV スケールが強く期待できる! 0.1 4.2 実験スケジュール 2016 2017 2018 2019 2020 2021 LHC E989@FNAL 1512.07214 E34@JPARC 1512.07214 ? ? ? http://agenda.linearcollider.org/event/6772/contributions/33275/attachments/27394/41633/muon_g-2EDM_MS.pdf 今まさにやるべき。 ? 模型あれこれ spin 0 • charged Higgs • two-Higgs doublet •… ミュオンg-2 spin 1/2 • new vector-like leptons •… spin 1 • abelian • non-abelian … •… spin-0 の寄与 1-loop • δaμ > 0 for CP-even • δaμ < 0 for CP-odd, charged. 2-loop (1-loop と逆転) • δaμ < 0 for CP-even • δaμ > 0 for CP-odd, charged. 単純に荷電スカラーを⼊れるだけだと、より実験との乖離が⼤きくなる c ¯ `L `L + ++ c µR µR spin-0 でうまくいく例 [TA, Sato, Yagyu (2015)] lepton specific two-Higgs doublet model • SM + one more Higgs doublet • two Higgs : H1 and H2 ★ ★ SM-like Higgs (h) new scalars (H0, A0, H±) • important parameter: tanβ ( 1 < tanβ < 100) • the lepton Yukawa interactions are enhanced by tanβ u, d ℓ 0 0 ± H ,A ,H u, d ⇠ SM yu,d 1 ⇥ tan H0, A0, H± ℓ ⇠ y`SM ⇥ tan lepton physics • new particles affect to all the physics with leptons ℓ H0, A0, H± ℓ • good point : muon g-2 f f 0 0 ± A 0 , 0H ,±H A ,H ,H µµ ★ ★ 0 0 ± ± ,A ,H H 0 , A0 , H H , Z, W ± µ, ⌫µ µµ, ⌫µ µ µ, ⌫µ, µ ⌫µ tanβ • On the other are important ⇠ y`SM ⇥ tan tanβ ,Z tanβ Figure 1: 1: One-loop One-loop (left) andand two-loop Barr-Zee (right) (right) diagramsdiagrams which givewhich correc Figure (left) two-loop Barr-Zee to the muon g 2. to muon g 2. hand,theconstraints on the lepton couplings From the kinetic terms of the scalar fields, the ratios of the coupling constant am the scalars kineticand terms the scalar fields, asthe ratios of the coupling theFrom CP-even gaugeofbosons are extracted ⌧! µ⌫ ¯µbosons , ⌧ !aree⌫extracted ¯e lepton coupling universality! ⌧⌫ ⌧⌫ the CP-even scalars and gauge as ghV V gHV V = s ↵, = c ↵. (V = W, Z) LHC signature! ghV V,SM ghV V,SM ghV V gHV V = c ↵. (V = W, Z) ¯ ghV As it is seen in Eqs. (22), (23) and (24), in gthe limit of sin( a) ! 1, both hf f V,SM hV V,SM =s ↵, hV V couplings become the same as those in the SM, so that we can call this limit a As it is seen in Eqs. (22), (23) and (24), in the limit of sin( SM-like limit. a) ! hV V couplings become the same as those in the SM, so that we can call Result: g-2 with constraints mH0 = mH+ = 250 GeV 70 1σ d by exclude lietcy rbsy a ay e v i d n τ u d n lepto Exclude σ 2 Exc lud ed 50 parameters for the muon g-2 40 30 20 Excluded by Bs → µµ tanβ tanβ 60 →ττ lud by + e e → ττA Exc yZ ed b 10 20 30 40 50 60 ★ 10 GeV < mA < 30 GeV ★ 250 GeV < mH± < 350 GeV ★ mH0 = mH± ★ 30 < tanβ < 40 もっと広いパラメータでもできるという議論もある (aligned 2HDM) [Han, Kang, Sayre (2016)] mA [GeV] mA [GeV] mH0 = mH+ = 350 GeV • g-2 within 1σ region (dark blue) is completely excluded! • g-2 within 2σ region (light blue) is survive! • constraint from lepton universality is strong. by + e e → ττA 70 40 30 Exc tanβ 50 lud ed 60 y ded b Exclu τ Z →τ y y τ deca db Exclude mH+ [GeV] fb. take =other 20 GeV, mHonce m = 1 and sin( We ↵) !m 1. AIn words, sin( ↵)than 6 1 ↵) = is given, bothtan the = 35. H ± , sin( • hττ : =more 10% deviation couplings deviate from those of the SM values. In our scenario, the value 240 3% 302, the value 30(65), ssed in Sec.sections of sin( ↵) describes “SM-like ness” of h, namely, : Cross of the electroweak production processes expressed in Eq. 200 220 240 260 280 300 320 340 360 200 220 p se oftothe processes expressed Eqs. at s = 14 TeV in the ngs the multi-tau SM particles become the same as in those in (67)-(70) the SM prediction 0.0 h(125) couplings (1) 1.7 % 0.9 .04 13.0 −0 2.6−0.3% 1.1Higgs 16.2 o0determine2.1 the structure of the sector4 . 8.2 6% −0.25% 0 4.8the deviation 2.3 28.2 14.9 h couplings 23.2 2.3 tudying the3.9 pattern of in the various can be4.3 a 72.5 35 37.4 39.4 20.6 22.9 12.0 .0 −0 tant the property h from the 0 to study 9.7 in4.7 53.5 of 29.5 45.1SM prediction. 7.2 12.8 358.0the deviation 260 280 300 mH+ [GeV] 320 340 from the SM prediction edetermined importantfrom to study theThus, deviation the property of h from the SM prediction. Eq. (62). a smallinbut non-zero deviation from the -1 cular, given. studying the pattern of the deviation in the various h couplings can be a SM SM ghττκ/g l hττ 4 -1.1 sector describe thedetermine deviation inthe thestructure h couplings, the so-called scaling l tool to of we theintroduce Higgs . as discussed its deviation X = “SM-like X 1. From X = ghXX /g we inhXX Sec.and 2, the value offrom sin( unity; ↵) i.e, describes ness” 2σ bound from µττ at the LHCof h, namely, -1.2 and the approximate formulae given in Eqs. (28) and (29), we obtain h24)couplings to the SM particles become the same as those in the SM prediction -1.3 ◆ 2 1. In other words, once sin( imit of sin(V ' ↵) ! ↵) 6= (71) 1 is given, both the 1+ , 2 tan -1.4 ¯ ✓ nd hf f couplings deviate from 2 m2h those of the SM values. In our scenario, the value q ' (72) -1.5 2 tan2from2m ↵) is determined Eq. (62). Thus, a small but non-zero deviation from the H± m2h 2m2A -1.6 limit is given. ` ' 1 + 2 . (73) 2 mH ± mH ± ✓ m2h m2H ± 2m2A m2H ± ◆ m2A , m2H ± rder to describe the deviation in the h couplings, we introduce the so-called scaling -1.7 r panels of Fig. 8, we show the contour plots for SM V and q , where defined as X = ghXX /ghXX and its deviation -1.8 from unity; i.e, on the mH ± -tan = X 1. From X ± dependence plane. In the lower panel, we show the m H 200 220 240 260 280 300 320 3) and (24) and the approximate formulae given in Eqs. (28) and (29), we obtain he pattern of the deviation was investigated in various extended Higgs sectors; m e.g., [GeV] H+ ✓ ◆ n singlets, doublets and triplets at the tree level. For example, it was 2 shown that the 2 2 m 2m A the correlation h awa interactions in the 2HDM can be well discriminated by measuring ' 1 + , (71) V 2 2 2 [71] that even if tion in hdd¯ and h`` couplings [70]. Intan addition, it wasm clarified in Ref. m H± H± ✓ discrimination ◆ unt the one-loop corrections to the hf f¯ couplings, of the 2HDMs is still 2 m2h m2A q ' , (72) tan2 2m2H ± Vm2H ± 2 2 m 2m h ± 1 X 2 + 2A. (73) X ` ' 27 H mH ± mH ± ± 340 360 Contour plots for (upper left) and q (upper right) on here = 1. The m dependence of ` is shown in t = 35. We take m = M = m and m = 20 GeV in all th h(125) couplings (2) • hγγ : more than 10% deviation from the SM prediction γγ)SM 0.9 0.85 GeV 0 3 = mA 20 GeV γγ)/Br(h ↑ Br(h ↑ 10 GeV 0.8 2σ bound from µγγ at the LHC 0.75 0.7 200 220 240 260 280 300 mH+ [GeV] 320 340 360 Figure 10: Ratio of the branching fraction Br(h ! )/Br(h ! )SM in our scenario with tan = 35. The solid, dashed and dotted curves show the cases with mA =10, 20 and 30 GeV, respectively. The horizontal dashed line shows the bound from µ given in 0 H, 0 A, ± H at the LHC many tau leptons are produced at the LHC 14TeV q ⌧ ⌧ 0 W, Z A ⌧ H 0, H ± xsec [fb] mH ± [GeV] 200 250 300 350 q̄ H+H 18.6 8.0 3.9 2.1 H+H 22.0 9.7 4.8 2.6 A0 ⌧ W, Z H H 11.3 4.7 2.3 1.1 H+A 116 53.5 28.2 16.2 H A 67.0 29.5 14.9 8.2 AH 101 45.1 23.2 13.0 4⌧ 29.3 7.2 2.3 0.9 3⌧ 50.1 12.8 4.3 1.7 4⌧ W 4⌧ Z 143 72.5 39.4 22.9 70.7 37.4 20.6 12.0 Table 2: Cross sections of the electroweak production processes expressed in Eq. (65), p and those of the multi-tau processes expressed in Eqs. (67)-(70) at s = 14 TeV in the unit of fb. We take mA = 20 GeV, mH = mH ± , sin( ↵) = 1 and tan = 35. be quite important to study the deviation in the property of h Tsai from(2016)]) the SM prediction. (断⾯積以外にも議論している論⽂としては [Chun, Kang, Takeuchi, In particular, studying the pattern of the deviation in the various h couplings can be a spin-1/2 の例 extra heavy lepton [Kannike, Raidal, Straub, Strumia (2012)] Name U(1)Y SU(2)L SU(3)c Q = T3 + Y Lepton number couplings L0 L3/2 E0 Ea Na N0 1 2 3 2 1 1 0 0 2 2̄ 1 3 3 1 1 1 1 1 1 1 0, 1 1, 2 1 0, 1, 2 1, 0, +1 0 EL0 H ⇤ E(L3/2 ✏H) E 0 LH ⇤ E a (H ⇤ ⌧ a L) N a (H✏⌧ a L) N 0 LH +1 +1 1 1 1 1 Table 1. List of new leptons that can couple to the SM lepton doublet L = (⌫µ , µL ) or singlet 0 0 E = µR (with the same gauge quantum numbers as L and E ) and to the Higgs doublet H = p カイラリティー muon ではなく新しいパラメタでフリップできる SU(2) doubletYukawa with Y = 1/2). For each new complex field we also add the (0, v + h/ 2) (an を corresponding conjugate representation: e.g. L0 is accompanied by L̄0 in the 2̄ representation with なので one-loop で説明可能。計算が楽。 hypercharge +1/2. In this paper we assume that: a) The aµ anomaly [1, 2] exp aexp µ = aµ aSM µ ⇡ (2.8 ± 0.8) 10 9 (1.1) where the first term comes from the usual SM relation between fermion masses and their couplings to the Higgs boson, and the second term represents contributions from the ML;E terms. In the limit (6), the approximate analytic formulas for all the couplings of Z, W, and h can be easily obtained from diagonalization matrices (7) and (8). spin-1/2 の例 extra heavy lepton #aZ! m! X b 2 b 2 ¼" 2 2 ½ðjgZ!e j þ jgZ!e j Þm! FZ ðxZb Þ L R 8$ MZ b¼4;5 b Z!eb , gR Þmeb GZ ðxZb Þ*; þ ReðgZ!e L (32) where xZb ¼ ðmeb =MZ Þ2 , the couplings are given in Eqs. (12) and (13) with index ! + e2 , and the loop functions are as follows: [Dermisek, Raval (2013)] NATION OF THE MUON g ! 2 ANOMALY WITH . . . PHYSICAL R FIG. 1. Feynman diagrams contributing to the muon magnetic moment that involve loops of extra fermions and the Higgs, Z and W bosons. 0.5 < κμ <24 013017-5 mL < 200 GeV ALTAS bound: κμ <3.5 [ATLAS-CONF-2016-041] spin-1 の例 flavor blind flavor dependent U(1) hidden photon Lμ-Lτ non-diagonal … non-abelian … … • non-abelian はフレーバ物理など⽭盾する • hidden photon もダメ。 [Biggio, Bordone, Luzio, Ridolfi (1607.07621)] hidden photon 2015 Status%in%2015 遠藤基さんの益川塾でのトークスライドより http://www.cc.kyoto-su.ac.jp/project/MISC/slide/seminar-s/2015/150521-Endo.pdf electron g-2 KLOE electron g-2 BaBar WASA HADES PHENIX APEX test MAMI NA48 KLOE BaBar E774 Beam -dump Flavor factories Muon g-2 2015 update: NA48 → exclude g-2 E141 E137 [Endo,Hamaguchi,Mishima w/ updates] Fixed target 遠藤基さんの益川塾でのトークスライドより http://www.cc.kyoto-su.ac.jp/project/MISC/slide/seminar-s/2015/150521-Endo.pdf Lμ:Lτ%Gauge%Symmetry • (broken) U(1) symmetry: anomaly-free • interact only with 2nd & 3rd generation leptons g-2 = + SM Lμ-Lτ gauge boson 遠藤基さんの益川塾でのトークスライドより http://www.cc.kyoto-su.ac.jp/project/MISC/slide/seminar-s/2015/150521-Endo.pdf Viable%in%low:mass%region 8 und e.g. in [43]. muon-neutrino Therefore, the s is e↵ectively q µ Z µ severely constrainedµ by m ) . (33) q µ neutrino-trident production: s and coupling Z 0 Z0 sults from LEP ptons and neurelations. We gray in Fig. 3. arameter space tic mixing [45]. th ATLAS and measurement of ur charged lepnalysis [47] has C data set and o be compared 7 ± 0.03)10 6 . on to the prom the Feynman ediate on-shell Z (see also [19] in [47], genernterfaced with ts should have ding three with n is an electron cation efficienant mass of the CCFR Z→4l LHC FIG. 5. The main NP contribution to the Z ! 4` process at the LHC. ⌫ ⌫ Z0 µ µ+ g-2 [±2σ] N N FIG. 6. The leading order contribution of the Z 0 to neutrino trident production. This diagram interferes constructively (destructively) with the corresponding SM diagram involving a W -boson (Z-boson). [Altmannshofer,Gori,Pospelov,Yavin] II. A SIMPLIFIED MODEL kinetic Z thus removi Our simplified model Lagrangian for the Z 0 coupling straints, e.g non-diagonal model exclusively to the muon and tau sector of the SM is given beam dump [Altmannshofer, Chen, Dev, Soni (1607.06832)] by 0 LZ 0 = gL µ̄ ↵ PL ⌧ + ⌫¯µ 0 + gR µ̄ ↵ ↵ PL ⌫⌧ Z↵0 PR ⌧ Z↵0 + H.c. , where PL,R = (1 ⌥ 5 )/2 are the chirality projection operators. Due to SU (2)L invariance, the couplings of the left-handed neutrinos and charged leptons are identical, whereas we do not introduce right-handed neutrinos in order to⌧ keep the ⌧ model minimal. The left-handed and 0 0 right-handed 0couplings gL and gR could in principle conZ taindiagram CP violating phases. We will take into account the 1. Feynman for the Z contribution to the alous magnetic moment of the muon in our model. complex nature of these couplings in all the equations µ µ below; in our numerical analysis however, we will take 4 en by the general expression [70] 0 simplicity. We allow di↵erent LFV them to be real for Feynman diagram for the Z contribution to the " ⇢ ✓ ◆ 2 Z 1 0 2m⌧ in our model. mcouplings µ 2 2 the ous magnetic moment of muon of the Z to leftand right-handed charged lepdx C (x x ) x + 2 µ = V 4⇡ 2 0 mµ tons, which✓will be crucial for the (g 2)µ explanation. ◆ 2 x m⌧ 0 2 (m m ) x 1 We assume the Z can acquire mass from the spon⌧ µ 2m2Zgeneral expression mµ [70]4 n by the # ⇢ taneous breaking of some extra U (1)0 symmetry, under 0 0 3III. (2) M The flavo a new contr 2 This can b gauged U (1 the only an ments to SM light Z 0 wit Another po tau number der both SU 模型あれこれ spin 0 • charged Higgs • two-Higgs doublet •… ミュオンg-2 spin 1/2 • new vector-like leptons (~O(100)GeV) •… spin 1 • hidden photon • flavor dependent (100MeV, 100GeV, …) … • non-abelian •… Summary • テラスケールの物理を期待する根拠の1つ、ミュオンg-2 ! • spin-0, two-Higgs doublet model ★ hττ κγγ 10%以上ずれる ★ tau rich なシグナル ! • spin-1/2, O(100)GeV の新しいレプトン ! • spin-1, flavor dependent なやつ ★ Lμ - Lτ : O(100) MeV ★ non-diagonal (μ-τ-Zʼ coupling) : ~ O(100)GeV 29