Higgs Couplings and Naturalness

Transcription

1 Higgs Couplings and Naturalness Maxim Perelstein, Cornell PITT PACC Workshop, November 9, 3 Saturday, November 6, 3

2 Intro: Minimalist BSM Precision electroweak tests strongly suggest that physics remains weakly coupled until (at least) ~ TeV scale In this talk, I will take a modest attitude and only think about physics below TeV (do not insist on perturbative gauge coupling unification etc.) If only SM until TeV, the Higgs mass parameter needs to be fine tuned: Note: this assumes that the SM is an effective theory and new propagating d.o.f. s coupled to the Higgs appear at some scale, possibly >> TeV Avoiding this fine-tuning is the (only) motivation for new physics at the energy scale accessible to the LHC. Only O() mechanisms for doing so in a weakly-coupled theory are known. I will mostly focus on SUSY today. Saturday, November 6, 3

3 Minimalist SUSY Consider an effective SUSY theory with a TeV cutoff [e.g. Brust, Katz, Lawrence, Sundrum,.667] Only superpartners canceling the largest contributions to Stops and gluinos are especially important at the LHC. must appear. One-loop fine-tuning estimate in the effective theory is simply In SUSY literature, fine-tuning is typically quantified by measuring the dependence of the Higgs mass on input parameters, usually at a high (GUT) scale The above estimate, EFT FT. should be thought of as a rough modelindependent lower bound on FT Can physics at > TeV reduce tuning? Logically possible, but no concrete convincing example so far. Saturday, November 6, 3

4 Naturalness: Not Dead Yet LSP mass [GeV] CMS Preliminary s = 8 TeV SUSY 3 ~ ~ t-t production - ~ SUS-3-4 -lep+-lep (Razor) 9.3 fb ( t t χ ) - ~ SUS-3- -lep (leptonic stop)9.5 fb ( t t χ ) - ~ SUS-3- -lep (leptonic stop)9.5 fb ( t b m t ~-m χ =m W m t ~-m χ =m t m χ ± -m χ =m W Observed Expected + χ, x=.5) LSP mass [GeV] g- ~ g ~ production, CMS Preliminary s = 8 TeV Nov 3 Observed Observed - σ Expected SUSY theory m(gluino) - m(lsp) = m(w) + m(top) m(gluino) - m(lsp) = m(top) g ~ t t χ SUS--4 -lep ( E T +H T ) 9.4 fb SUS lep (razor) 9.3 fḇ SUS-3-7 -lep (n 6) 9.4 fb jets SUS-3-6 -lep (OS+b) 9.7 fb - SUS-3-3 -lep (SS+b) 9.5 fb - SUS lep (3l+b) 9.5 fb % natural, % alive stop mass [GeV] gluino mass [GeV] Direct stop searches currently do not exclude big regions of parameter space with, or even ~ in the stealthy region Gluino bounds OK too for now: is % natural if gluino is Dirac Saturday, November 6, 3

5 % is kept. mass discovery reach of approximately 5 GeV, up to 9 GeV (see Fig. ). This increase covers a significant part of the top squark range favored by naturalness arguments. In this study the same selection cuts were used for the two luminosity values. mχ [GeV] ATLAS Simulation s=4 TeV - 3 fb discovery reach 3 fb- exclusion 95% C.L. 3 fb- discovery reach 8 7 χ ± +m χ < mb m~t t P m χ m~t P t t m ~t m = χ mw -m ~t m = χ mt 3 + < mt 3 5 ~~ ~ pp t t *, t t χ -lepton channel Based on SUS-3- Estimated 5σ discovery reach 6 4 t ~ t t+ χ (m ± >> m~t ): s=7 TeV, 4.7 fb - 5 ~ t t+ χ (m ± >> m~t): -lepton (e,µ) + jets χ ~ ± t b+ χ ( m~t - mχ ± = GeV): -lepton (eµ) 6 9 mχ [GeV] CMS Preliminary m~t [GeV] ALTAS [5] and(a) CMS [53] projections of reaches for stop in (b) direct stop production, whe Even at 4 TeV, probing compressed spectra, as well as stealthy and RPV top quark and an LSP each (left), and the projected 5 discovery reache Figure -3. Figure : Discovery reach (solid lines) and exclusion limits (dashed lines) for top squarks in the t Figure 8: decay The modes. simplified model topology direct t + (red) andrun the t band + ±,HL-LHC. ± W + (green) scenarios, will remain non-trivial in direct searches based on current 6.3 Strong Production of Squarks and Gluinos strategies channels to charginos and neutralinos. Measuring them will paint a full picture of The results are summarized Fig. 8. discovery stop mass these channels willallow be subdominant, discovering require reach large for statistics. H A high-luminosity dataset would the discovery reach forand gluinos andinsquarks tothem beapushed masses of 3 45 GeV, is expected. totaylor-made the highest masses. Gluinosfor andlsp light-flavor squarks can be produced withsearch a largemore cross searches these regions (e.g. ISR-tags to for stringent selection requir in accomplishing this task. section at 4 TeV, and the most striking signature is still large missing transverse as the background further, leading to momentum an improvement of the signal-to-bac compressed spectra) may be developed part of large total effective An estimates optimized event for properties, a benchmark point withdetailed measurements To confirm themass. initial of selection the stop more covery potential. Also, when searching for stop signals at higher masses mq = mg = 3 GeV requires the missing transverse momentum significance, defined as / decays are boosted, butscalar the use of of thefor boosted top the taggers miss carried out. Indeed, there can behhighly other newtophysics scenarios, example Un EAn HT, be greater than 5 GeVstop. (The variable defined be the sum approach: indirect search by Higgs couplings T is measuring T /alternative extra sensitivity. the jet and lepton transverse and the missing transverse momentum the event.)therefore, Both (UED), which energies can gain have signals very similar to insusy. during the perio Saturday, November 6, 3 will be competing interpretations. To distinguish them, model independent measur 6 are necessary. Such measurements are difficult, since we can not fully reconstruct t Precise measurement of subtle features of kinematical distributions will be necessar level of HL-LHC will great enhance our capability of carrying out these measureme

6 . Higgs and Naturalness: General Argument X [Farina, MP, Rey Le- Lorier, ] One-loop quantum corrections to Higgs potential are given by the Coleman- Weinberg formula: V CW (h) = X g k ( The only input is Higgs-dependent masses of all particles; focus on tops The famous mass renormalization is just k ) F k Z d 4` ( ) 4 log ` + m k(h) µ! V CW h h=. X Top partner mass is m (T i )=m,i + c i h + X Cancellation of quadratic divergence gives a sum rule: 6y t = X i g i ( ) F i c i. Potential fine-tuning comes from the next (log-divergent) term: = µ µ.78 X i g i ( ) F m,i i c i log TeV m,i 6y t mt TeV log m t! Saturday, November 6, 3

7 Low-Energy Theorems give the top partner contributions to and in terms of the same object: Higgs-dependent top-partner mass L h = 9 v C hf µ F µ, L hgg = s v C ghg µ G µ C = C g = + Dirac fermions X f Dirac fermions X ln m N c,f Q f (v) f + ln v 3 C(r f ln m f ln v scalars X Very general, very robust result: inverse correlation between fine-tuning and non-sm contributions to and + 4 scalars X s s N c,s Q s C(r s ln m ln ln m ln v, Exceptions: non-colored, non-charged partners (see M. McCullough s talk tomorrow, maybe); or cancellations between different partner loops Cancellations may occur in SUSY, but no symmetry reason regarded as additional fine-tuning should be Benchmark example: a single top partner, spin, with quantum numbers of the SM top (e.g.: MSSM with degenerate stops) Saturday, November 6, 3

8 Spin- Top Partner Measurement Precision - - R g Farina, MP, Rey Le- Lorier, A % measurement of would probe the top partner mass of ~. TeV... LHC-8TeV LHC3 HL-LHC ILC5 ILC5-up ILC ILC-up TLEP CLIC4 CLIC3 Snowmass Higgs Report Saturday, November 6, 3

9 Saturday, November 6, 3... and imply fine-tuning of at least /5 if no deviation from the SM is seen

10 Spin- HBlueLêSpin-ê HRedL.6.4. Dots: 35, 5, 65, 8 GeV top partners Ellipses: LHC-8/LHC-4 Rg..8.6 LEP EWWG: within the MSM m h < 44 (8) GeV (95% CL) R g Precision Higgs coupling measurements give a robust test of naturalness, similar to strongly/weakly-coupled EWSB test via electroweak precision Complementary to direct stop searches: no compressed, stealthy, RPV holes Saturday, November 6, 3

11 . lambda-susy But, what if there are really no stops below TeV? Is fine-tuning needed? How robust is our FT estimate? Let s examine it more closely. In the MSSM, schematically Consider (Z3-invariant) NMSSM: In this theory, is an output determined by potential minimization In the limit, sensitivity of to is parametrically suppressed, and the stop mass can be raised with no fine-tuning price: [Barbieri, Hall, Nomura, Rychkov, 6] Saturday, November 6, 3

12 In traditional NMSSM literature, a constraint perturbativity up to the GUT scale However with a TeV cutoff, larger values of is imposed to retain are possible - up to For the FT scaling with the stop mass becomes This yields up to ~ gain in FT w.r.t. MSSM for the same stop mass, or equivalently the stop mass can be raised by ~3 with no increase in FT However, there is a price to pay: large F-term contribution to the Higgs boson mass Prediction: Higgs mass ~35 GeV. Proven wrong. This is not surprising: decrease in FT is simply due to a larger Higgs quartic, which automatically raises the Higgs mass Saturday, November 6, 3

13 A way out: reduce the Higgs mass by mixing with the singlet [Hall, Pinner, Ruderman ] Consider the CP-even Higgs sector in the basis where has SM couplings to W/Z and does not couple to W/Z M = v sin + m Z cos ( v m Z )sin4 v µ apples + A sin (m Z v )sin + Bµ sin v apples + A cos apples(4apples + A apple )+ v s A sin (.6) To get some intuition, let s study The light mass eigenstate is m h M : the non-sm doublet decoupled M 4 3 M 33 It can be 5, but this requires a ~% cancellation on the RHS This should be regarded as another contribution to fine-tuning (purely tree level!) In the overall FT defined as sensitivity to input parameters, this tree-level FT and the usual loop-level FT are multiplied, and advantage of lambda-susy over MSSM is erased [Agashe et.al.; Gherghetta et.al. ] C A Saturday, November 6, 3

14 A way out: reduce the Higgs mass by mixing with the singlet [Hall, Pinner, Ruderman ] Consider the CP-even Higgs sector in the basis where has SM couplings to W/Z and does not couple to W/Z M = v sin + m Z cos ( v m Z )sin4 v µ apples + A sin (m Z v )sin + Bµ sin v apples + A cos apples(4apples + A apple )+ v s A sin (.6) To get some intuition, let s study The light mass eigenstate is m h M : the non-sm doublet decoupled M 4 3 M 33 It can be 5, but this requires a ~% cancellation on the RHS This should be regarded as another contribution to fine-tuning (purely tree level!) In the overall FT defined as sensitivity to input parameters, this tree-level FT and the usual loop-level FT are multiplied, and advantage of lambda-susy over MSSM is erased [Agashe et.al.; Gherghetta et.al. ] C A Saturday, November 6, 3

15 However, this argument assumes that the 5 GeV Higgs is an almost-pure doublet M = v sin + m Z cos ( v m Z )sin4 v µ apples + A sin (m Z v )sin + Bµ sin v apples + A cos apples(4apples + A apple )+ v s A sin (.6) If the 5 GeV state is mostly singlet ( impostor ), with another, SM-like Higgs at ~35 GeV. No (obvious) tuning. C A Interestingly, a large singlet admixture in the 5 GeV state is currently allowed by the LHC Higgs data (and PEW) tanb = LHC fit results tanb = D HDoublet FractionL.. D HDoublet FractionL S HSinglet FractionL S HSinglet FractionL tanb =3 tanb =4 Saturday, November 6, 3 ctionl. ctionl.

16 s HGeVL s HGeVL qualitative conclusions do not change for reasonable values of stop m?), and follow the notation of Refs. [?? ]. The scalar potential for the Higgs consider corrections due to loops of the Higgs-sector fields themselv Hd and S is given byshould the sum of the usual F- and D-term contributions, and the 5 So, it be possible to reduce the tree-level fine-tuning by making significant due to large values of of interest, these loops depend USY breaking terms: GeV state more singlet-like masses of which the Higgs-sector superpartners, 4% Mixing are at present very 3 Constraints Fine Tuning fo This is confirmed by a detailed analysis [Farina, MP, Shakya, 3.459] the data. We leave a detailed analysis of the loop corrections = mu Hu + md H + mby S + A SH H + A S + h.c.. (.) u d d intuition S 3 To summarize, the Higgs sector of our model (at tree level) is co Scan over the NMSSM7 parameters relevant for the tree-level Higgs sector: Lagrangian Higgs sector contains free parameters: 5 5 by five parameters: pi = {,, mu, md, ms, A, A }. {,, tan (.), s, A }. ssume all parameters be real; there neither explicit nor -5 Imposetoconstraints: no tachyons (CP-even, orspontaneous charged); 5 CP GeV-5 is the The region ofisinterest in thisodd, space is determined by the following c lightest state; mass > vacuum GeV; Z->(i.e. invisible; etc. in the Higgs sector of CP-even this model [? chargino ]. In the realistic a stable xhibiting EWSB) the neutral components of Hu and Hd, as well as the singlet Unrealistic minima (with no EWSB or ) are required to be above or at k k et vacuum expectation values (vevs): hhu i = vu, hhd i = vd, hsi = s, where most slightly below the correct vacuum 4% Mixing 5% Mixing + vd 74 GeV. These vevsconstraints are obtained from the minimization equations Fine Tuning Constraints Fine Tuning ggs potential d k 4% mixing k 5% Mixing 5 <D<3 3 <D -5 (.3) -. k 5% mixing k 5% Mixing Constraints Fine Tuning Constraints Saturday, November 6, 3 D< <D< s HGeVL s HGeVL s HGeVL -. v 5 µ(a + s) =, vu vu vu ) µ(a + s) =, vd -5-5 A v- =, u vd - vu vd µ.5 vd ) s HGeVL g E mhu + µ + vd + (vu g E mhd + µ + vu + (vd -5 ms + A µ + - µ + (v + v u d) 5 7 Fine Tuning

17 Green = OK; pink = OK with everything but the LHC Higgs fits; yellow = vacuum stability requires a -loop analysis. Observe a clear anti-correlation between fine-tuning and singlet fraction in the 5 GeV Higgs: more singlet = less tuning Should see deviations in Higgs couplings soon... or pushed into more tuned regions... Overall, FT levels are higher than naively expected, due to constraints (esp. CP-odd tachyon) Saturday, November 6, 3

18 Green = OK; pink = OK with everything but the LHC Higgs fits; yellow = vacuum stability requires a -loop analysis. As a bonus, we also observe an anti-correlation between fine-tuning and the non-sm doublet fraction in the 5 GeV Higgs: more doublet = less tuning Should see deviations in Higgs couplings soon... or pushed into more tuned regions... Saturday, November 6, 3

19 Green = OK; pink = OK with everything but the LHC Higgs fits; yellow = vacuum stability requires a -loop analysis. Tree-level FT can also be reduced by reducing tree-level mass, since this reduces the Correlations we found break down for However no suppression of the loop-level tuning with respect to the MSSM occurs in this regime Saturday, November 6, 3

20 Conclusions Higgs boson provides a new window into the EW-scale physics Precise measurements of the Higgs couplings give new opportunities for SM tests and BSM discoveries In this talk, we discussed two examples of using Higgs coupling measurements as a probe of EW naturalness. General: and contributions from top partners (e.g. stops). Specific model: lambda-susy In both cases, we showed inverse correlation between fine-tuning and non- SM contributions to Higgs couplings Since Nature must be Natural, non-sm Higgs couplings will be discovered soon. Saturday, November 6, 3