Testing Electroweak Phase Transition at Future Colliders

Transcription

1 Testing Electroweak Phase Transition at Future Colliders Maxim Perelstein, Cornell Hong Kong IAS Conference, January 19, 2016 Based on: Andrew Noble, MP, , PRD Andrey Katz, MP, , JHEP Katz, MP, Ramsey-Musolf, Winslow, , PRD

2 ElectroWeak Phase Transition In our world, EW gauge symmetry is broken: SU(2) U(1) Y U(1) em At high temperature, symmetry is restored (in most models) Early universe: electroweak phase transition at How much can we learn about the dynamics of this transition? First-order ( boiling ) or second-order ( quasiadiabatic ) transition? Cross-over? T 100 GeV Has implications for electroweak baryogenesis (1st order required to satisfy Sakharov s out-of-eq. condition) 1

3 EWPT and Collider Data Direct relics from the transition in the early universe unlikely to survive (possibly gravitational waves?) [see e.g. Grojean and Servant, 2006] 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 weak-scale states are relevant for the EW phase transition ( decoupling ) Determine the TeV Lagrangian at the colliders order of the transition, critical temperature, etc. learn the What measurements will be necessary to address this? 2

4 Finite-T Effective Potential Assume weakly coupled physics at the TeV scale (beware: finite-t may still require lattice simulations) Assume single physical higgs h participates in the transition (easy to generalize away from this assumption) One-loop effective potential has the form V (h; T )=V t (h)+v T =0 (h)+v T (h) Higgs-dependent Mass T=0 (Coleman-Weinberg) part: V T =0 (h) = g i ( 1) F i 64π 2 i Finite-T part: V T (h) = g i ( 1) F i T 2π 2 i In a renormalizable theory M 4 i ( log M i 2 ) µ 2 + C i dkk 2 log[1 ( 1) F i exp( β k 2 + Mi 2)] M 2 i = M 2 i,0 + a i h 2 3

5 Effective Potential: Ring Terms Beyond one-loop, include ring contributions Can be summed up to yield: [Carrington, PRD 1992] V r (h, T )= T [Mb 3 (Mb 2 +Π b (0)) 3/2] 12π b 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 4

6 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 n 2 M Pl Γ n e S T =0 h strong first-order transition: ξ = v(t c) 1 T c 5

7 Effective Potential from Colliders? So, to 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 6

8 EWPT and Higgs Cubic 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 This changes the shape of V(h) at T=0 T c different λ3(v, mh) Models with 1st order phase transition exhibit large (typically %) 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 7

9 Toy Model 1: Quantum EWPT Single Higgs doublet, SM couplings to SM states, add a real scalar field S Scalar potential: Assume positive Compute effective Higgs potential At high T, Look for minima: V eff / h =0 V = V SM (H)+ 1 2 M 2 0 S 2 + ζ H 2 S 2 M 2 0,ζ S =0 V eff (h; T )=(µ 2 + DT 2 )h 2 + ET h 3 + λh If h =0and h 0minima coexist, 1st order transition Scan m h,m 0,ζ find points with first-order EWPT Physical Higgs boson cubic self-coupling: λ 3 = d3 V eff (v; T =0) dh 3 8

10 Blue points: bumpy T=0 3.0 potentials Quantum EWPT: Results Ξ vs Λ Λ 3 vs m h for Ξ 1 Plots from Ξ Λ Λ ~20% minimal deviation m h Exp. prospects: 27% for H-20 scenario at ILC 5-10% at a 100 TeV pp collider [ ] 9

11 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 Λ 2 H 6 Reasonable EFT if v Λ λ 1 First-order transition can occur for µ 2 > 0,λ<0 6 Ξ vs Λ Λ 3 vs m h for Ξ 1 [Grojean, Servant, Wells 2004] Plots from Ξ 3 Λ Λ % minimal deviation m h 10

12 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 EWPT involves both H and S changing, order parameter is a linear combination of H and S Effective potential for order parameter contains tree-level cubic terms from possible strongly first-order EWPT 4 S4 Zero-T spectrum: two higgses (mixed H and S) Only H enters Yukawa couplings non-sm Yukawas Cubic self-coupling of the H-like higgs typically O(100%) away from the SM value 11

13 EWPT and Higgs-VB Couplings Measuring Higgs cubic provides direct information about the Higgs potential (admittedly at T=0)...but experimentally it s a difficult measurement In contrast, couplings to vector bosons ( ) are already measured at ~10-20% level, will improve to ~a few % with more LHC data, and <1% if e+e- Higgs factory is built Are these correlated with the order of EWPT? 12

14 HC and EWPT: Setup Focus on the quantum PT scenario: The cubic term at high-t is induced by loops of scalars Add a single complex scalar, with V = m apple 2 H Effective potential controlled by the H-dependent mass of : But the same H-dependent mass controls V 1 (') = g i( 1) F i 64 2 V T ('; T )= g it 4 ( 1) F i 2 2 C = C g = 1+ apple m 4 i (') log m2 i (') m 2 i (v) 3 Z 1 0 Dirac fermions X f dx x 2 log " 1 ( 1) F i ln m 2 N c,f Q 2 f (v) f + ln v 32 2 m4 i (')+2m 2 i (')m 2 i (v) ; r x 2 + m2 i (') T 2 L h = 2 9 v C hf µ F µ, L hgg = s 12 v C ghg µ G µ Dirac fermions X f C(r f ln m2 f ln v # loop contributions to HVV: scalars X s scalars X s N c,s Q ln m 2 s(v) ln v C(r s ln m2 ln v,, Expect direct correlation between the size of the cubic coupling induced at finite-t and non-sm contributions to and (unless is color and EM-neutral) 13

15 t ble when the e ective coupling is close to 1; specifically, < 0.3 is required, as can be seen in Fig. 1. This Xt /mt 2 region does not overlap with the region Xt /mt 2 1 allowed by the Higgs fits, regardless of the value of mt 2. Incidentally, this argument provides a clear understanding of the results of Ref. [19] regarding the MSSM, where mt TeV is required by the 125 GeV Higgs mass. Another useful representation of the same results is shown in Figs. 2 and 3, where the Xt parameter has been traded for the stop mixing angle t. These plots make it clear for a 100 GeV light stop, the Higgs fits imply a tight relationship between t and mt 2, which unfortunately is incompatible with the small-mixing regime required by the stop-catalyzed EWB. 6 Example: SUSY FIG. 1: Regions of stop parameter space allowed by the LHC Higgs measurements (blue - 67% CL and green - 95% CL) vs. the domain where the stop-catalyzed EWB can potentially be viable ( > 0) in pink. Mass of the light stop is fixed at 100 GeV. The unphysical region (no solution for t ) is shaded in purple. Stop-catalyzed 1st order EWPT (e.g. Xt 1 2 mté1 =100 GeV, tan b = 10 allowed 1.0 by Higgs measurements is a band around the line Xt mt 2 : this follows directly from Eq. (4) in the limit mt 1 mt 2. The crucial observation is that along the contours of constant EWPT strength, Xt also scales 0.8 linearly with mt 2. This is related to the fact that the effective coupling between the lightest stop and the Higgs is given by X t Lef f = yt2 1 H 2 t 1. (9) m2t m2t Plots from sin q procedure of Ref. [59], and the expressions for the coupling shifts from Ref. [50]. We also evaluated the constraints from EW precision measurements; however, we m = 100 GeV, tan b = 10 find1400 these to be consistently weaker that the Higgs fit constraints. Furthermore, for each point in the scan, we determined whether or not the EWPT is strongly 1st1200 order, using the procedure outlined in the previous section. We 1000 find that the 1st-order phase transition requires a < 110 GeV, independent of the other very light stop, mt 1 parameters. On the other hand, LEP-2 constraints imply > mt GeV, confining this parameter to a narrow band. Within this band, the Higgs fit constraints on the remaining parameters vary only slightly with mt 1. In the 600 plots below, we choose mt 1 = 100 GeV as a representative value, but the picture that emerges from these plots is valid400throughout the allowed range of mt 1. Likewise, we fix tan = 10 in the plots as a representative value. For larger values our results stay almost independent of 200 tan tan, while for lower tan the EWPT becomes weaker while the Higgs constraints are largely 1200 una ected Again, the picture that emergesmremains valid independent of t tan. main of results of our analysis are summarized FIG. The 1: Regions stop parameter space allowed by the LHC in Higgs measurements (bluethe - 67% CL and green - 95% CL) vs. is Figs. 1, 2 and 3. conclusion is clear: there thenodomain where the stop-catalyzed potentially overlap between the parameterewb spacecan regions allowed be by viable > 0) fit, in pink. Mass of the light with stop is at the ( Higgs and those consistent a fixed 1st-order 100EWPT GeV. The unphysical region (no solution for ) is shaded t within a perturbative calculation. Thus, the stopin catalyzed purple. EWB scenario is no longer viable. Perhaps the clearest way to understand this result is provided by Fig. 1. Not surprisingly, the region of parameter space procedure of Ref. [59], and the expressions for the coupling shifts from Ref. [50]. We also evaluated the constraints from EW precision measurements; however, we find these to be consistently weaker that the Higgs fit ) The thermal potential is determined almost exclusively by this e ective coupling, so that constant- contours in the regime mt 1 mt 2 correspond to a fixed ratio 0.2 Xt /mt 2. Crucially, a 1st-order transition is only possible when the e ective coupling is close to 1; specifically, < 0.3 is required, as can be seen in Fig. 1. This Xt /mt region does not overlap with 1 al the region 800 Xt /mt lowed by the Higgs fits, regardless of the value of mt. 2 Incidentally, this argument provides a clear understandingfig. of the of Ref. regarding MSSM,EWPT wherein 2: results Constraints and[19] regions with athe 1st-order mthe 100 TeV is required by the 125 GeV Higgs mass. (m, ) plane, for the light stop mass m = 100 GeV. t t 2 t 1 t 2 The regionuseful allowedrepresentation by Higgs fits at of 95% CLsame is shaded in blue. Another the results is The blue line 2shows contour = 0 and the line shown in Figs. and 3,the where the of Xt parameter hasred been showsfor thethe contour =. The region between the black traded stop of mixing angle t. These plots make it contours is allowed at the 95% CL if a non-zero Higgsainvisible clear for a 100 GeV light stop, the Higgs fits imply tight width is included ( inv = 0.1 using the definitions of [59]). relationship between t and mt 2, which unfortunately is incompatible with the small-mixing regime required by the stop-catalyzed EWB. 2 is already ruled out by the LHC Higgs data* (even allowing for non-mssm contributions to Higgs mass) * assuming no cancellations between stop loop and other SUSY loops in hgg mté1 =100 GeV, tan b =

16 Numerical Studies In general, no analytic solution for critical T and order parameter - solve numerically Numerical code includes one-loop T=0 (CW), daisy terms and SM contributions at finite-t and Analyzed a few toy models, representative of the range of possibilities for Model (SU(3),SU(2)) U(1) g C 3 C 2 W g 2 T 2 B g 02 T 2 RH stop ( 3, 1) 2/3 6 4/3 0 11/6 107/54 1/4 Exotic triplet (3, 1) 4/3 6 4/3 0 11/6 131/54 1/4 Exotic sextet ( 6, 1) 8/ /3 0 11/6 227/54 1/2 LH stau (1, 2) 1/ /4 2 23/12 1/6 RH stau (1, 1) /6 13/6 1/12 Singlet (1, 1) /6 11/6 1/12 Table 1. Benchmark models studied in this paper. h applet 2 [* we treat as a free parameter, unlike SUSY] 15

17 k k m f HGeVL m f HGeVL 300 Results: Sextet Figure 2. Same as Fig. 1,250for the Exotic Triplet model (see Table 1).Plots from h=1,f~h6,1l1ê3, hgg h=1, f~h6, 1L1ê3, hgg k k 400 m f HGeVL m f HGeVL Figure 1. The350region of parameter space where a strongly first-order EWPT occurs in the 350 RH stop benchmark model. Also shown are the fractional deviations of the hgg (left panel) and h (right panel) couplings from their SM values. Solid/black300lines: contours of constant EWPT strength parameter (see Eq. (2.9)). Dashed/orange lines: contours0.025 of constant 1 hgg/h corrections. (For the case of h the correction is always negative, and the plots show its absolute value.) In the shaded region, phase transition into a color-breaking vacuum 200 EWPT. occurs before the k reported by the ATLAS collaboration [? ] are k Figure 3. Same as Fig. 1, for the Sextet model (see Table 1). Rg = 1.08 ± 0.14, ATLAS: R = ruled out* (4.2) These results already have interesting implications for the possibility of a strongly first[* usual caveat: SM totalwill width in precision expected in future experiments allowassumed] these models to be probed. In order EWPT. In particular, the Sextet model, where the deviations in the hgg coupling 16 both models, the minimal deviation in the hgg coupling compatible with a strongly in the region with first-order EWPT are predicted to be 70% or above, is completely

18 Results: RH Stop Plots from h=1, f~h3, 1L 2ê3, hgg h=1, f~h3, 1L 2ê3, hgg mf HGeVL mf HGeVL k k NOT ruled out if Figure 1. The region of parameter space where a strongly first-order EWPT occurs in the RH stop benchmark model. Also shown are the fractional deviations of the hgg (left panel) 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 hgg/h corrections. (For the case of h the correction is always negative, and the plots show its NOTE: absolutethe value.) RH In the stop shaded can region, decay phase to transition 2 jets or into be a stealthy/ color-breaking vacuum occurs before the EWPT. MIN deviation ~17%, probed at 3-sigma at LHC-14 compressed avoid direct searches 17

19 Higgs and a Singlet does not need to have SM gauge interactions to drive a first-order EWPT Obviously this scenario would not produce any deviation in or However, it does predict a (small) deviation in McCullough, ] coupling [Craig, Englert, Consider, integrate it out a dim-6 operator: After Higgs gets a vev: Canonically normalized Higgs shift in coupling Effect is small, but coupling can be determined very precisely from Higgsstrahlung cross section: ~0.25% ILC, ~0.05% TLEP [Snowmass Higgs report] 18

20 Results: Singlet Plots from h=2, Singlet, hzz h=2, Singlet, h^ mf HGeVL mf HGeVL k k Figure 6. The region of parameter space where a strongly first-order EWPT occurs in th Singlet benchmark model. Also shown are the fractional deviations of the e + e hz cross section (left panel) and Higgs cubic self-coupling (right panel) from their SM va ues. Solid/black lines: contours of constant EWPT strength parameter (see Eq. (2.9)) 10-sigma at TLEP Dashed/orange lines: contours of constant hz/ 3 corrections. In the shaded region, phas transition into a color-breaking vacuum occurs before the EWPT. hzz: MIN deviation %, probed at ~2-sigma at hzz: MIN deviation %, probed at ~2-sigma at ILC, 10-sigma at TLEP 19

21 Results: LH Stau Plots from h=1, f~h1,2l -1ê2, hgg h=1, f~h1,2l -1ê2, hzz mf HGeVL mf HGeVL k k Figure 5. Same as Fig. 1, for the LH stau model (see Table 1). hzz: MIN deviation 0.8%, probed at 3-sigma at ILC electrically charged, and modifies the h coupling. The minimal shift in this coupling compatible with a strongly first-order EWPT is about 4 5% in both models. This is clearly too small to be constrained by the present data, but may be probed by future experiments. The Snowmass study [? ] projects a precision of about 2% at an upgraded ILC running at p s = 1 TeV, and about 1.5% at TLEP, enabling the entire 20

22 Conclusions Dynamics of EW phase transition is a fascinating question about the Early Universe It may be related to the origin of baryon asymmetry (EWBG scenario) Precise measurements of Higgs couplings may allow to infer the order of the phase transition For example, stop-catalyzed 1-sf order transition in SUSY is ruled out by LHC Higgs measurements e+e- Higgs factory and 100 TeV pp collider are needed to answer this question 21

23 Backup Slides

24 Quantum EWPT: Extensions Same calculations apply in a model with identical N real (or N/2 complex) scalars - simple scaling argument: ξ ξn 1/4 One-loop analysis is independent of the scalar s gauge charges - could be e.g. stops of the MSSM (in the decoupling limit - one Higgs), weak triplets, etc. Same picture in a model with 2 independent (non-identical) scalars (N ind. scalars is a reasonable conjecture) If scalar replaced with a fermion, no points with first-order EWPT found, due to the different structure of the fermion contribution to V eff (no ring terms no h 3 ) A more interesting case: add a scalar-fermion pair ( supermultiplet ) with same coupling to the Higgs, different masses

25 Quantum EWPT with BF Pair 4 Ξ vs Λ 3 Λ 3 vs m h for Ξ Ξ 2 Λ Λ Accidental Cancellation between B and F contributions at T=0 can result in near-sm value of λ 3 - counterexample to our claim [But SUSY is broken by strong coupling to the SM via h] M 100 GeV δλ 3 λ 3 7% m h

26 Conclusions: 2007 paper Higgs boson cubic self-coupling is correlated with the order of EWPT Stronger 1-st order phase transition larger deviation in Typical deviations large enough to be seen at the ILC or the SLHC/VLHC (or the currently discussed 100 TeV collider) λ 3 Correlation seen in 3 toy models, illustrating different mechanisms for getting a first-order EWPT All examples (known to us) violating this conclusion involve accidental cancellations of two large corrections to Observing SM value would strongly disfavor first-order phase transition (and hence EW baryogenesis) Caution: Models with 2nd order EWPT can still produce large deviations, though λ 3

27 Analytic Example A special case can be studied analytically*: High-temperature expansion of the thermal potential: V e ('; T )=V 0 (')+V T ('; T ) 1 2 µ 2 + g applet 2 ' 2 24 g apple 3/2 T 24 p 2 '3 + 4 ' 4. Location of the broken-symmetry minimum at finite T: Critical temperature: Solve together: T 2 c = g apple 1 24µ 2, ' + (T c )= g apple 2 g apple 3/2 T c 12 p 2. Strongly 1-st order if Gluon-Higgs coupling (assume fundamental ): R g = 1 8 applev 2 m applev2 2