Double Higgs Production S. Dawson CMS HH Workshop January 18, 2016 S. Dawson

Outline Why measure the Higgs-self couplings? What do we expect? Standard Model Issues with the top mass dependence Beyond the Standard Model Resonances Effective Field Theory S. Dawson

Higgs self-couplings a prediction hhh and hhhh couplings predictions of theory They are perturbative: In general: Corrections to relationship between l3 and l4 of O(1/L2) * This is NOT true in models with new light particles S. Dawson

Production of hh h h h Sensitive to heavy colored particles (eg stops or top partners) h h h h Sensitive to anomalous top-Higgs couplings h h Sensitive to anomalous VVhh couplings h h h S. Dawson

Small Rates for hh Only gluon fusion likely to be relevant sNLO(fb) sNLO(fb) dl3 √S (TeV) Only gluon fusion likely to be relevant Large increase in hh rate at high energy * Light bands, LO, Solid bands NLO [Frederix et al, 1408.5147] S. Dawson

Two Higgs Production at LHC Cross section has spin-0 and spin-2 contributions mt2>>s, pT2 (low energy theorem) (hhh coupling/hhhSM) For large s, dependence on dl3 suppressed More sensitivity to negative dl3 Exact cancellation in SM at threshold S. Dawson

Double Higgs Production Cancellation in large mt limit between box and triangle diagrams QCD corrections computed in mt infinity limit and weighted by exact LO Greatly restricted by single Higgs production h h h [Dawson, Dittmaier, Spira, hep-ph/9805244] S. Dawson

Progress in SM Calculations Dominant process is gg  hh Threshold resummation at NNLL matched to NNLO Scale uncertainty reduced at NNLL Good convergence These calculations are in mt ∞ limit Fixed Order Resummed *MSTW2008 PDFs [De Florian, Mazzitelli, 1505.07122] S. Dawson

Using newest NNLO PDFs NEW: PDF uncertainty significantly reduced from MSTW PDFs [De Florian, Mazzitelli, 1505.07122; Contribution to LHC Higgs Cross Section Working Group] S. Dawson

Choosing the Scale S. Dawson

Radiative corrections in large mt limit? Large mt limit known to poorly reproduce distributions at LO Exact LO ds/dMhh (fb/GeV) ds/dpTj (fb/GeV) mt∞ Mhh (GeV) pTj (GeV) Adding extra powers of 1/mt2 doesn’t help distributions [Dawson, Furlan, and Lewis, arXiv:1210.6603;Dolan, Englert, and Spannowsky, arXiv:1206.5001] S. Dawson

Towards including mt effects at NLO, NNLO HOW BIG ARE 1/mt2 CORRECTIONS? Compute NLO with virtual corrections in mt∞ limit and real corrections with exact mt dependence (improved HEFT) Compute 1/mt2n corrections to NNLO and normalize to exact LO Different results from 2 approaches Arbitrarily assign ±10% uncertainty from mt dependence [1/mt2 corrections: Grigo,Hoff, Melnikov, Steinhauser, arXiv:1305.7340; Grigo, Melnikov, Steinhauser, arXiv:1408.2422; Grigo, Hoff, Steinhauser, arXiv: 1508.00909; HEFT: Maltoni, Vryonidou, Zaro, arXiv: 1408.6542; Frederix et al, arXiv:1401.7340] S. Dawson

Compute NLO corrections to hh production O(s3) contributions Compute as expansion in small external momentum Can keep as many terms in expansion as desired Need 2 loop box integrals with mt, Mh Known Easy New [Borowka, Di VitaGreiner, Heinrich, Jones, Kerner, Luisoni, Mastrolia, Schlenk, Schubert, Zirke] S. Dawson

Gudrun’s plot S. Dawson

Andrea’s Plot S. Dawson

What is contributing to hh? Do we know it’s a top quark? Could it be a stop? Or other colored scalar? Parameters restricted by requirement that ggh has SM value S. Dawson

Colored scalar in loop? Could we replace the top with a scalar? Physical mass (m0=0 all mass from EWSB) Color octet: SM 1h rate predicts highly suppressed 2h rate s/sSM Color triplet: SM 1h rate obtained for k=±3.7 k S. Dawson [Dawson, Ismail, Low, arXIv:1504.05596]

What about adding a scalar? At high invariant mass, distributions different in presence of color triplet scalar 13 TeV 100 TeV ds/dMhh (fb/GeV) ds/dMhh (fb/GeV) Mhh (GeV) Mhh (GeV) [Dawson, Ismail, Low, arXiv:1504.05596] [See also, Batell, McCullough, Stolarski, Verhaaren, arXiv: 1508.01208] S. Dawson

Need a resonance to increase rate! Simplest example: Add a scalar singlet, S Before EWSB, singlet only couples to Higgs doublet After EWSB, singlet mixes with SM Higgs boson For simplicity, impose Z2 symmetry: S. Dawson

Singlet Model Very predictive: Physical fields: Physical parameters: S. Dawson

Z2 symmetric singlet model Very simple model: If kinematically allowed, H  hh SM h,H Coupling to light Higgs ~ cos q Coupling to heavy Higgs ~ sin q SM

Branching ratio can be significant Large tan b gives problems with perturbative unitarity of hhhh S. Dawson

Limits on singlet model Limits from MW, Higgs coupling measurements, direct searches for heavy Higgs bosons |sin q (mqx) | MH (GeV) [Bojarski, Chalons, Lopex-Val, Robens, arXiv:1511.08120] S. Dawson

Resonant production of hh Large resonant effects when MH~2Mh NWA approximation accurate for MH < 400 GeV Can get factor of 20 enhancements *Similar effects in MSSM, NMSSM models [Dawson, Lewis, arXiv:1508.05397] S. Dawson

Large resonance/interference effects [Dawson, Lewis, arXiv:1508.05397] S. Dawson

NLO corrections to singlet model Computed in mt∞limit K factor ~ 2 (as in SM) [Dawson, Lewis, arXiv:1508.05397] S. Dawson

Higgs singlet model without Z2 Models without Z2 symmetry motived by desire to explain electroweak baryogenesis (They typically prefer negative a1, b3 and heavier H) [Profumo, Ramsey-Musolf, Wainwright, Winslow, arXiv:1407.5342; Curtin, Meade, Yu, 1409.0005]

Enhanced hh in singlet model without Z2 MH(GeV) s(pphh)/sSM ssinglet/sSM * Allowed in singlet model BR(Hhh) MH(GeV) Enhancements of hh by factors 10-15 if MH < 400 GeV Easy to arrange in many models…. Major constraint is gg h needs to have observed rate Minimum of potential must give v=246 GeV [Chen, Dawson, Lewis, arXiv:1410.5488]

No resonance: Use EFT Very simple EFT: gg h rate within d of SM prediction *Neglecting some derivative operators 1+ct Would be excluded by 20% measurement of tth cg

hh production breaks EFT degeneracy Single Higgs: If Higgs arises from a doublet, only (F+F) combination: Double Higgs rate not proportional to ct+cg c2h cgg cg ct dl3 ct [Chen, Dawson, Lewis, arXiv:1410.5488] S. Dawson

Fits to EFT Coefficients Many fits in literature Use kinematics of signal to improve fits (Correlations!) c2h, dl3 only probed in hh production 300, 3000 fb-1, bbgg 14 TeV, 600 fb-1, bbtt dl3 p values cgg 1s contours ct c2h [Azatov, Contino, Panico, Son, Arxiv: 1502.00539; Goertz, Papaefstathiou, Yang, Zurita, arXiv:1410.3471] S. Dawson

How big do you expect EFT coefficients to be? Singlet model only generates dl3 Top partner model Colored scalar triplet *Z2 symmetry assumed These estimated coefficients are much smaller than projected sensitivities [Dawson, Lewis, Zeng, arXiv:1501.04103 ; Chen, Dawson, Lewis, arXiv:1410.5488] [See also, Brehmer, Freitas, Lopez-Val, Plehn, arXiv:1510.03443] S. Dawson

Conclusions Measuring hh production required to understand Higgs potential Difficult to make hh rate much different from SM rate without resonant enhancement because of constraints from single Higgs production and electroweak measurements S. Dawson