What Shall We Learn from h^3 Measurement Maxim Perelstein, Cornell Higgs Couplings Workshop, SLAC November 12, 2016
The Shape of Things to Come LHC: spin-0, elementary-looking Higgs field This field is allowed to have a potential a new kind of object in real-world relativistic QFT What we know now: Measuring Higgs cubic coupling is the next step in extending our knowledge of the shape of V: 1
h^3 in the Standard Model SM postulates a simple Higgs potential: This leads to a tree-level prediction: Leading loop corrections can be taken into account with Coleman- Weinberg potential: Higgs-dependent masses : SM radiative corrections dominated by top and W/Z contributions, well known (direct measurement of top Yukawa would be helpful) 2
h^3 Beyond the SM Example: add a gauge-singlet real scalar Impose a symmetry: This fixes the potential: V = V SM (H)+ 1 2 M 0 2 S 2 + ζ H 2 S 2 No admixture of in the 125 GeV state no Br shifts If, shows up in exotic Higgs decays But if, direct signatures become much harder However, loops contribute to the CW potential: [e.g. S. Gori s talk] [e.g. Craig et. al., 1412.0258] Higgs cubic coupling measurement could be the first to discover such a scalar 3
Radiative EWSB An extreme example: what if (After all we know something s wrong with the The Higgs potential is term ) This has a minimum at Higgs boson mass constraint: In this model: breaks EW symmetry [Coleman, Weinberg, 73] +66% deviation from SM Perturbativity is questionable, but still this gives a useful illustration of how large the effects can be, without conflict with current data 4
d=6 EWSB Another extreme example: what if (After all we know something s wrong with the term ) EWSB can be achieved by balancing a negative quartic against a non-renormalizable operator: Reproducing the observed vev and Higgs mass requires Predict: +133% deviation from SM Applicability of EFT is questionable, but still this gives a useful illustration of how large the effects can be, without conflict with current data 5
ElectroWeak Phase Transition In our world, EW gauge symmetry is broken: Right after Big Bang, Universe is filled with high-t plasma Higgs moving through the plasma acquires a thermal mass (much like photon plasma mass ) Symmetry is restored at high T Electroweak phase transition at kt 100 1000 GeV, SU(2) U(1) Y U(1) em T 10 15 K How much can we learn about the dynamics of this transition? First-order ( boiling ) or second-order ( quasiadiabatic ) transition? 6
First- or Second-Order EWPT? First-order transition: bubbles of broken-symmetry phase nucleate inside restoredsymmetry phase, grow, collide, take over Non-equilibrium process, can enable baryogenesis (EWBG scenario) Second-order: field remains homogeneous at all times, vacuum gradually shifts from 0 to v Which one is it? Controlled by 7
EWPT and Collider Data Direct relics from the transition in the early universe unlikely to survive (possibly gravitational waves?) No possibility of producing plasma with restored EW symmetry (T-RHIC?) so no direct experimental probe However, finite-t physics is described by the same Lagrangian as the T=0 physics we will study at colliders Only particles with mass up to TeV scale are relevant for the EW phase transition ( decoupling ) Determine the TeV-scale Lagrangian at colliders order of the transition, critical temperature, etc. [see e.g. Grojean and Servant, 2006] What measurements will be necessary to address this? learn the 8
Finite-T Effective Potential Assume weakly coupled physics at the TeV scale (beware: perturbation theory at finite-t still tricky) Assume single physical higgs h participates in the transition (easy to generalize away from this assumption) One-loop effective potential has the form V T (h) = i V (h; T )=V t (h)+v T =0 (h)+v T (h) T=0 (Coleman-Weinberg) part: V T =0 (h) = g i ( 1) F i 64π 2 i Finite-T part: g i ( 1) F i T 2π 2 M 4 i ( log M i 2 ) µ 2 + C i Higgs-dependent Mass dkk 2 log[1 ( 1) F i exp( β k 2 + Mi 2)] In a renormalizable theory M 2 i = M 2 i,0 + a i h 2 9
Effective Potential: Ring Terms Beyond one-loop, include ring contributions ( Can be summed up to yield: V r (h, T )= T [Mb 3 (Mb 2 +Π b (0)) 3/2] 12π b [Carrington, PRD 1992] Only bosons contribute (due to IR divergence) Important for the first-order EWPT since at high T, which can produce the desired dip Higgs-dependent Mass V r T h 3 Ring terms controlled by the same parameters as the oneloop effective potential 10
First-Order Phase Transition V eff (h; T ) V eff (h; T ) V eff (h; T ) h h h T>T c T = T c T = T n T c critical temperature: nucleation temperature: V eff (h; T ) V eff (0) = V eff (v(t c )) Γ n H T 2 n M Pl Γ n e S T =0 h strong first-order transition (needed for EWBG): ξ = v(t c) 1 T c 11
Effective Potential from Colliders? To fully reconstruct finite-t potential, we need to know the following: Higgs zero-temperature tree-level potential: vev, mass Full spectrum of states (SM and BSM) with significant couplings to the Higgs and masses up to ~few 100 GeV Their fermion numbers and state multiplicities Their masses and couplings to the Higgs: M 2 i = M 2 i,0 + a i h 2 One possibility is to directly discover all new states, measure their masses and couplings This is difficult: e.g. V = V SM (H)+ 1 2 M 2 0 S 2 + ζ H 2 S 2 m S > m h with 2 12
EWPT and Higgs Cubic [Noble, MP, 071018] Idea: look for simple observables that are correlated with the order of the EWPT in a reasonably model-independent framework Proposal: use Higgs boson cubic self-coupling Heuristic explanation: λ 3 In the SM transition is cross over for a 125 GeV Higgs New physics must change the shape of V(h) at T c This changes the shape of V(h) at T=0 different λ 3 (v, m h ) Models with 1st order phase transition exhibit large (typically 20-100%) deviations of from its SM value λ 3 Evidence: analysis of a series of toy models designed to mimic the known mechanisms for getting a first-order PT 13
Toy Model 1: Quantum EWPT Single Higgs doublet, SM couplings to SM states, add a real scalar field S Scalar potential: V = V SM (H)+ 1 2 M 2 0 S 2 + ζ H 2 S 2 For simplicity, assume (for now) positive Compute effective Higgs potential as a function of temperature M 2 0,ζ S =0 Look for minima: V eff / h =0 If h =0and h 0minima coexist, 1st order transition Scan find points with first-order EWPT Physical Higgs boson cubic self-coupling: λ 3 = d3 V eff (v; T =0) dh 3 14
Blue points: bumpy T=0 3.0 potentials Quantum EWPT: Results Ξ vs Λ 3 2.4 Λ 3 vs m h for Ξ 1 Plots from 071018 2.5 2.2 2.0 2.0 Ξ 1.5 Λ 3 1.8 1.6 1.0 1.4 1.2 0.0 1.0 1.5 2.0 2.5 1.0 120 140 160 180 200 220 Λ 3 m h ~20% minimal deviation Exp. prospects: 27% for H-20 scenario at ILC [1506.05992] 5-10% at a 100 TeV pp collider Updates later in this session (talks by M. Klute, T. Tanabe) 15
Including Negative ( Two-Step ) ΛHS 8 6 4 2 Μ S 2 0 two step PT one step PT Μ S 2 0 1.2 1 0.6 ΛHS 8 6 4 2 [Curtin, Meade, Yu, 1409.0005] 2.2 3 2.5 4 2 1.8 1.6 1.4 1.2 1.1 0 0 1 2 4 200 400 600 800 1000 m S GeV 2 4 0.1 0.3 0.7 200 400 600 800 1000 m S GeV Two-step phase transitions are possible with, large shift in the cubic in most of the two-step region <10% deviations in a (funny) corner of parameter space 16
Cubic vs. Presicion Higgsstrahlung 8 6 4 3 2.5 2.2 2 1.8 1.6 1.4 8 6-3 -2-1 -0.8-0.6 - -0.4 4 1.2 1.1 4-0.3-0.2 ΛHS 2 HS 2-0.1 0 2 4 1 0.1 0.3 0.7 200 400 600 800 1000 m S GeV 0-2 -4-2 -0.1-3 -1-0.6-0.4-0.8 - -0.3-0.2 200 400 600 800 1000 m S [GeV] [in %] also makes a one-loop contribution to [Craig, Englert, McCullough, 1305.5251; Katz, MP, 1401.1827] Precision measurement at Higgs factories: e.g. CEPC claims % Comparable sensitivity to h^3, depends on details 17
A Word of Caution: Boson+Fermion 4 Ξ vs Λ 3 Extension of Toy Model: Add particles of opposite spin-statistics Ξ 3 2 V T =0 (h) = i g i ( 1) F i 64π 2 M 4 i ( log M i 2 ) µ 2 + C i 1 0 1.0 1.5 2.0 V T (h) = g i ( 1) F i T 2π 2 dkk 2 log[1 ( 1) F i exp( β k 2 + Mi 2)] i Cancellation between B and F contributions at T=0 can result in near-sm value of - counterexample to our claim λ 3 [But SUSY has to be broken by strong coupling to the SM via h M 100 GeV δλ 3 λ 3 7% Λ 3 accidental] 18
Charged/Colored Scalars Similar results if the scalars driving first-order EWPT are colored or electrically charged Couplings to are already measured at ~10-20% level, will improve to ~a few % with more LHC data This will completely cover the parameter space Plots withfrom viable EWPT Results: RH Stop 1401.1827 Plots from RH Stop If a signalresults: is seen, still want to measure Higgs cubic as it provides 1401.1827 h=1, f~h3, 1L2ê3, hgg h=1, f~h3, 1L2ê3, hgg direct information about the Higgs potential (admittedly at T=0) 0.17 350 350 0.05 h=1, f~h3, 1L2ê3, hgg h=1, f~h3, 1L2ê3, hgg 300 350 250 0.25 200 250 0.25 0.37 150 1.5 2.0 250 3.0 200 0.07 250 0.1 2.5 k 150 200 0.07 1.5 2.0 NOT ruled out if 3.0 2.5 k 0.1 0.37 m f HGeVL m f HGeVL 0.05 300 300 200 [Katz, MP, 1401.1827] 300 m f HGeVL m f HGeVL 350 0.17 in the Figure 1. The region a strongly first-order EWPT occurs of parameter space where 150 1.5 2.0 3.0 panel) 1.5 stop benchmark 2.0 2.5 3.0 RH model. Also shown are the fractional deviations of 2.5 the hgg (left k k and h (right panel) couplings from their SM values. Solid/black lines: contours of constant EWPT strength parameter (see Eq. (2.9)). Dashed/orange lines: contours of constant Figure 1. The region of parameter space where a strongly first-order EWPT occurs in the 150 MIN deviation ~17%, probed at 3-sigma at LHC-14 19
TM 2: Non-renormalizable EWPT An alternative way to get 1st-order EWPT: add a nonrenormalizable operator to the SM Higgs potential V = µ 2 H 2 + λ H 4 + 1 Λ 2 H 6 [Grojean, Servant, Wells 2004] Reasonable EFT if v Λ First-order transition can occur for 6 Ξ vs Λ 3 3.5 λ 1 µ 2 > 0,λ<0 Λ 3 vs m h for Ξ 1 Plots from 071018 5 3.0 Ξ 4 3 Λ 3 2.5 2 2.0 1 0 1.5 1.5 2.0 2.5 3.0 3.5 Λ 3 50-60% minimal deviation 120 140 160 180 200 m h 20
TM 3: Higgs-Singlet Mixing As in TM1, add 1 real scalar, but with a more general potential: V (H, S) =µ 2 H 2 + λ H 4 + a 1 2 H 2 S + a 2 2 H 2 S 2 + b 2 2 S2 + b 3 3 S3 + b 4 Generically, both H and S get vevs at zero temperature Strongly first-order EWPT possible, large deviations in Higgs cubic consistent with (current) constraints 4 S4 Tc 200 150 100 50-5% 13%- 30%- 50%- SM g 111 0 0 10 20 30 40 50 60 g 111 [Profume, Ramsey-Musolf, Wainwright, Winslow, 1407.5342] 21
Conclusions Measuring Higgs cubic coupling gives new information about the shape of the Higgs potential Large (up to ~factor-of-two) deviations from the SM are possible, consistent with current Higgs data Models with first-order electroweak phase transition (needed for viable electroweak baryogenesis) generically predict large deviations of Higgs cubic from the SM A ~10%-level measurement of the Higgs cubic would provide a stringer test of such models 22