Double Higgs Production S Dawson CMS HH Workshop

Double Higgs Production S. Dawson CMS HH Workshop January 18, 2016 S. Dawson 1

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 2

Higgs self-couplings a prediction • hhh and hhhh couplings predictions of theory • They are perturbative: • In general: Corrections to relationship between l 3 and l 4 of O(1/L 2) * This is NOT true in models with new light particles S. Dawson 3

Production of hh h h h Sensitive to heavy colored particles (eg stops or top partners) Sensitive to anomalous top-Higgs couplings h h h Sensitive to anomalous VVhh couplings h h S. Dawson 4

s. NLO(fb) Small Rates for hh dl 3 √S (Te. V) • 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 5

Two Higgs Production at LHC • Cross section has spin-0 and spin-2 contributions • mt 2>>s, p. T 2 (low energy theorem) (hhh coupling/hhh. SM) • For large s, dependence on dl 3 suppressed • More sensitivity to negative dl 3 • Exact cancellation in SM at threshold S. Dawson 6

Double Higgs Production • Cancellation in large mt limit between box and triangle diagrams Greatly restricted by single Higgs production • QCD corrections computed in mt infinity limit and weighted by exact LO h h h [Dawson, Dittmaier, Spira, hep-ph/9805244] S. Dawson 7

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 Resummed Fixed Order *MSTW 2008 PDFs [De Florian, Mazzitelli, 1505. 07122] S. Dawson 8

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 9

Choosing the Scale S. Dawson 10

Radiative corrections in large mt limit? Exact LO ds/dp. Tj (fb/Ge. V) ds/d. Mhh (fb/Ge. V) • Large mt limit known to poorly reproduce distributions at LO mt ∞ Mhh (Ge. V) p. Tj (Ge. V) Adding extra powers of 1/mt 2 doesn’t help distributions [Dawson, Furlan, and Lewis, ar. Xiv: 1210. 6603; Dolan, Englert, and Spannowsky, ar. Xiv: 1206. 5001] S. Dawson 11

Towards including mt effects at NLO, NNLO • HOW BIG ARE 1/mt 2 CORRECTIONS? • Compute NLO with virtual corrections in mt ∞ limit and real corrections with exact mt dependence (improved HEFT) • Compute 1/mt 2 n corrections to NNLO and normalize to exact LO • Different results from 2 approaches • Arbitrarily assign ± 10% uncertainty from mt dependence [1/mt 2 corrections: Grigo, Hoff, Melnikov, Steinhauser, ar. Xiv: 1305. 7340; Grigo, Melnikov, Steinhauser, ar. Xiv: 1408. 2422; Grigo, Hoff, Steinhauser, ar. Xiv: 1508. 00909; HEFT: Maltoni, Vryonidou, Zaro, ar. Xiv: 1408. 6542; Frederix et al, ar. Xiv: 1401. 7340] S. Dawson 12

Compute NLO corrections to hh production • O( s 3) 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 New Easy [Borowka, Di Vita. Greiner, Heinrich, Jones, Kerner, Luisoni, Mastrolia, Schlenk, Schubert, Zirke] S. Dawson 13

Gudrun’s plot S. Dawson 14

Andrea’s Plot S. Dawson 15

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 16

Colored scalar in loop? • Could we replace the top with a scalar? • Physical mass EWSB) (m 0=0 all mass from s/s. SM Color octet: SM 1 h rate predicts highly suppressed 2 h rate Color triplet: SM 1 h rate obtained for k=± 3. 7 k [Dawson, Ismail, Low, ar. XIv: 1504. 05596] S. Dawson 17

What about adding a scalar? ds/d. Mhh (fb/Ge. V) 13 Te. V ds/d. Mhh (fb/Ge. V) • At high invariant mass, distributions different in presence of color triplet scalar Mhh (Ge. V) 100 Te. V Mhh (Ge. V) [Dawson, Ismail, Low, ar. Xiv: 1504. 05596] [See also, Batell, Mc. Cullough, Stolarski, Verhaaren, ar. Xiv: 1508. 01208] S. Dawson 18

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 Z 2 symmetry: S. Dawson 19

Singlet Model • Very predictive: • Physical fields: • Physical parameters: S. Dawson 20

Z 2 symmetric singlet model • Very simple model: SM Coupling to light Higgs ~ cos q Coupling to heavy Higgs ~ sin q h, H SM • If kinematically allowed, H hh 21

Branching ratio significant can be Large tan b gives problems with perturbative unitarity of hh hh S. Dawson 22

Limits on singlet model |sin q (mqx) | • Limits from MW, Higgs coupling measurements, direct searches for heavy Higgs bosons MH (Ge. V) [Bojarski, Chalons, Lopex-Val, Robens, ar. Xiv: 1511. 08120] S. Dawson 23

Resonant production of hh • Large resonant effects when MH~2 Mh • NWA approximation accurate for MH < 400 Ge. V Can get factor of 20 enhancements *Similar effects in MSSM, NMSSM models [Dawson, Lewis, ar. Xiv: 1508. 05397] S. Dawson 24

Large resonance/interference effects [Dawson, Lewis, ar. Xiv: 1508. 05397] S. Dawson 25

NLO corrections to singlet model • Computed in mt ∞limit K factor ~ 2 (as in SM) [Dawson, Lewis, ar. Xiv: 1508. 05397] S. Dawson 26

Higgs singlet model without Z 2 • Models without Z 2 symmetry motived by desire to explain electroweak baryogenesis • (They typically prefer negative a 1, b 3 and heavier H) [Profumo, Ramsey-Musolf, Wainwright, Winslow, ar. Xiv: 1407. 5342; Curtin, Meade, Yu, 1409. 0005] 27

ssinglet/s. SM MH(Ge. V) BR(H hh) s(pp hh)/s. SM Enhanced hh in singlet model without Z 2 * Allowed in singlet model MH(Ge. V) • Enhancements of hh by factors 10 -15 if MH < 400 Ge. V • Easy to arrange in many models…. Major constraint is gg h needs to have observed rate • Minimum of potential must give v=246 Ge. V [Chen, Dawson, Lewis, ar. Xiv: 1410. 5488] 28

No resonance: Use EFT • Very simple EFT: *Neglecting some derivative operators 1+ct gg h rate within d of SM prediction cg Would be excluded by 20% measurement of tth 29

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 ct ct [Chen, Dawson, Lewis, ar. Xiv: 1410. 5488] c 2 h cgg cg dl 3 S. Dawson 30

Fits to EFT Coefficients • Many fits in literature c 2 h, dl 3 only probed in hh production • Use kinematics of signal to improve fits (Correlations!) 14 Te. V, 600 fb-1, bbtt 300, 3000 fb-1, bbgg cgg dl 3 p values 1 s contours ct c 2 h [Azatov, Contino, Panico, Son, Arxiv: 1502. 00539; Goertz, Papaefstathiou, Yang, Zurita, ar. Xiv: 1410. 3471] S. Dawson 31

How big do you expect EFT coefficients to be? • Singlet model only generates dl 3 *Z 2 symmetry assumed • Top partner model • Colored scalar triplet These estimated coefficients are much smaller than projected sensitivities [Dawson, Lewis, Zeng, ar. Xiv: 1501. 04103 ; Chen, Dawson, Lewis, ar. Xiv: 1410. 5488] [See also, Brehmer, Freitas, Lopez-Val, Plehn, ar. Xiv: 1510. 03443] S. Dawson 32

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 33