HIGGS-GRAVITATIONAL INTERATIONS! IN PARTICLE PHYSICS & COSMOLOGY

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1 HIGGS-GRAVITATIONAL INTERATIONS! IN PARTICLE PHYSICS & COSMOLOGY beyond standard model ZHONG-ZHI XIANYU Tsinghua University June 9, 015

2 Why Higgs? Why gravity? An argument from equivalence principle Higgs: unique fundamental scalar mass term sensitive to UV physics (gravity!) the unique non-minimal gravitational coupling term mechanism of electroweak symmetry breaking? Gravitation top-down approach spontaneous dimensional reduction bottom-up approach effective field theory

3 3 Outline LHC / future colliders low energy, very high luminosity cosmic inflation very high energy, poor luminosity two complementary colliders

4 4 Outline Spontaneous dimensional reduction 1) an effective theory ) new mechanism of unitarization / EWSB Non-minimal coupling 1) frame independence ) equivalence theorem 3) unitarity bound 4) collider signature SM Higgs inflation 1) unitarity problem ) quantum correction Beyond SM 1) Extending Higgs inflation with TeV new particles ) Higgs inflation with noscale SUSY GUT 3) Asymptotically safe Higgs inflation

5 5 Spontaneous dimensional reduction SDR - a novel effect in many quantum gravity models asymptotic safety CDT Hořava gravity loop QG... Ds n 1 HmL 4 3 = g=1.5 g= = σ from J. Ambjørn et al, PRL95 (005) L SDR = 5TeV = 5TeV m HTeVL µ n(µ) =4 SDR

6 6 Effective theory of EWSB with SDR Dimension as a scaling property ) Effective theory approach ) Spacetime integral measured ) d n x, n = n(µ) L = 1 4 W a µ W µ a 1 4 B µ B µ + M W W + µ W µ + 1 M Z Z µ Z µ ) [L ]=n(µ), [g] =(4 n)/ g ) g = g M (4 n/) W g : gauge coupling : dimensionless HJ He and ZZ Xianyu, Eur. Phys. J. Plus 18 (013) 40! HJ He and ZZ Xianyu, Phys. Lett. B 70 (013) 14

7 7 Effective theory of EWSB with SDR Partial wave unitarity WW! ZZ scattering in a Higgsless SM: T g E 4MW a 0 (E) = E n 4 (16 ) (n/) 1 ( n 1) Z 0 d sin n 3 T(E, ) a 0 < 1 a (b) γ=1.5 unitarity violation 4D 6TeV 5TeV σ exp (pb) (a) SM(600GeV) unitarity violation 5TeV 4d HLSM 6TeV TeV 10 SM(15GeV) 4TeV E (TeV) E (TeV) HJ He and ZZ Xianyu, Eur. Phys. J. Plus 18 (013) 40! HJ He and ZZ Xianyu, Phys. Lett. B 70 (013) 14

8 8 Effective theory of EWSB with SDR Non-standard Higgs + SDR anomalous couplings: L H =( applevh + 1 apple 0 h ) M W v W + M Z v (a) M h =15GeV Δκ=+0.3 unitarity violation SM+AC Z Δκ M h =15GeV 4TeV 5TeV 4d SM+AC (b) M h =15GeV Δκ=-0.3 E (TeV) 6TeV unitarity violation SM+AC σ exp (pb) 10 3 σ exp (pb) SM 4TeV 5TeV 6TeV SM 4TeV 5TeV 6TeV E (TeV) E (TeV) HJ He and ZZ Xianyu, Eur. Phys. J. Plus 18 (013) 40! HJ He and ZZ Xianyu, Phys. Lett. B 70 (013) 14

9 9 Non-minimal Higgs-gravitational coupling SM + GR as an effective theory p The unique non-minimal dim-4 operator Lagrangian in Jordan frame: L J p = M P g 1+ H H M P {z } (H) Weyl transformation R + D µ H g µ! g µ V (H) grh H to Einstein frame: L E p g = M P R + 3 M P 4 rµ (H H) + 1 D µh V (H) 4

10 10 Non-minimal Higgs-gravitational coupling Perturbative expansion Jordan frame: kinetic mixing between and Einstein frame: kinetic rescaling + higher dim. operators of Example:W + W! (t,u-channels not shown) h µ Jordan frame h W C L W L W C L W L W C L W L Einstein frame ZZ Xianyu, J Ren, HJ He, Phys. Rev. D 88 (013) ! J Ren, ZZ Xianyu, HJ He, JCAP 1406 (014) 03

11 11 Non-minimal Higgs-gravitational coupling Unitarity bound for Jordan-Einstein equivalence Goldstone boson ET Coupled-channel analysis: +, 0 0,, 0 s-wave amplitude: a 0 (E) 4 4 / E + O(E 0 ) unitarity condition: Re a 0 < 1 unitarity bound on E: E < ( )!1limit: E < p 8 v ξ Bound Higgs from measurement M P /v limit: E < p 8 MP E (GeV) ZZ Xianyu, J Ren, HJ He, Phys. Rev. D 88 (013) ! J Ren, ZZ Xianyu, HJ He, JCAP 1406 (014) 03

12 1 Non-minimal Higgs-gravitational coupling Weak boson scattering at LHC & future pp (100TeV) cross section (pb) (pb) (c) m h =15GeV E (TeV) ξ=10 15 W + W +! W + W + ξ= ξ=0 (SM) Universality: gravity is blind to internal gauge structure. Non-resonance: strong coupling at high energies Other probe of non-minimal coupling: h 3 coupling? cross section (pb) (pb) (c') W + W +! W + W + m h =15GeV E (TeV) ξ= ξ= ξ=0 (SM) ZZ Xianyu, J Ren, HJ He, Phys. Rev. D 88 (013) ! J Ren, ZZ Xianyu, HJ He, JCAP 1406 (014) 03

13 Higgs inflation 13 M P =1 The second rôle of the God Particle generating primordial density fluctuations during inflation! producing all particles in the universe during reheating Non-minimal coupling in action Higgs potential in Einstein frame:v ( )= / 4 Normalized inflaton: ' p 3/ log =1+ Inflaton potential: V ( ) ' 4 1 e p /3

14 14 Higgs inflation Fitting observables V ( ) ' 4 1 e Scalar amplitude (V / ) 1/4 ' 0.07 ' 0.13 Scalar tilt n s ' and tensor-to-scalar ratio r ' independent of parameter input (as long as 1 ) An apparent unitarity problem? p /3 Typical energy density during inflation V 1/4 O(10 16 GeV) on the other hand, O(10 4 ) ) M P / O(10 14 GeV) ) O(10 4 )

15 15 Higgs inflation Background-field-dependent unitary bound WW! ZZ channel with arbitrary background : a 0 = 1+ apple E 10 1/ 1/ p a 0 ' 3 8 E a 0 ' 1 16 E E. 1/ E. 1/ p E/M P Strong Gravity ξ=10 ξ=10 ξ=10 3 ξ=10 4 (a) ϕ /M P J Ren, ZZ Xianyu, HJ He, JCAP 1406 (014) 03

16 16 Higgs inflation Background-field-dependent unitary bound The most stringent bound can be found from coupled-channel analysis. ξ (b) Large-ϕ Unitarity Bound EW vacuum Unitarity Bound Inflation Scale E (GeV) Unitarity of Higgs inflation E/M P 10 Strong Gravity 1 ξ= ξ=10 ξ=10 3 ξ=10 4 (a) ϕ /M P J Ren, ZZ Xianyu, HJ He, JCAP 1406 (014) 03

17 17 Higgs inflation Quantum correction Running of Higgs self-coupling: = 1 16 (4 6y t + ) Importance of precise measurement of Higgs & top masses Metastable l 0.05 Unstable Central Values M t HGeVL s in M t 17 4s in M H s in a m HGeVL M H HGeVL from A. Spencer-Smith, arxiv:

18 18 Higgs inflation with new physics A successful Higgs inflation needs new physics. Three mechanisms for Higgs inflation: 1. Higgs inflation with TeV scale new particles. Higgs inflation in no-scale supersymmetric GUT 3. Asymptotically safe Higgs inflation

19 19 Extending Higgs inflation New TeV SU() L U(1) Y Z S (1, 0, ) T L (1, 3,+) T R (1, 3, ) Scalar potential & Yukawa terms: V (H, S) = µ 1H H 1 µ S + 1 (H H) S S H H + apples. L tt = y 1 Q e 3LHtR y Q e 3LHTR y p 3 ST L T R y p 4 ST L t R +h.c. HJ He, ZZ Xianyu, JCAP 1410 (014) 019

20 0 Extending Higgs inflation Improved UV behavior of Higgs self-coupling 1 = 1 1 (4 ) y 6y 4 1y 1 y Sample u m S m T A 7 TeV 3.08 TeV 3.08 TeV D 4 TeV 1.6 TeV 1.6 TeV Sample A λ Sample D λ i λ λ i λ 3 λ 0 λ (SM) λ 1 0 λ (SM) λ μ (GeV) μ (GeV) HJ He, ZZ Xianyu, JCAP 1410 (014) 019

21 1 Extending Higgs inflation (V(h)/M Pl 4 ) Sample A h/m Pl (V(h)/M Pl 4 ) Sample D h/m Pl Inflation potential HJ He, ZZ Xianyu, JCAP 1410 (014) 019

22 Extending Higgs inflation (V(h)/M Pl 4 ) Sample A (V(h)/M Pl 4 ) Sample D r h/m Pl Planck TT+Low P Planck TT,TE,EE+Low P D n s A B C sample h/m Pl A B C D 670 HJ He, ZZ Xianyu, JCAP 1410 (014) 019

23 3 Extending Higgs inflation Prediction of observables ( n s, r ) Large range of tensor-to-scalar ratio Heavy fine tuning in critical region (A,B,C) Standard Higgs inflation recovered in large region (D) r Planck TT+Low P Planck TT,TE,EE+Low P D n s A B C sample A B C D 670 HJ He, ZZ Xianyu, JCAP 1410 (014) 019

24 4 Higgs inflation in no-scale GUTs Supersymmetric Higgs inflation in general Non-minimal coupling in SUGRA tachyonic instability in NMSSM eta-problem in generic SUGRA models No-scale supergravity SUSY with zero vacuum energy gravitino mass undetermined classically simple string compactification rich flat directions Grand unification GUT scale ~ inflation scale: any underlying connection? J Ellis, HJ He, ZZ Xianyu, Phys. Rev. D 91 (015) 0130(R)

25 5 Higgs inflation in no-scale GUTs No-scale SU(5) model + h i = H = q Hc H u Z H = Hc eh d 15 hsi diag 1, 1, 1, 3, 3 (Slightly deformed) no-scale Kähler potential & superpotential K = 3 log T + T 1 3 tr ( ) 1 3 H + H + (HH +h.c.) W = 1 m tr ( )+µhh tr ( 4 ) 1H H (HH) J Ellis, HJ He, ZZ Xianyu, Phys. Rev. D 91 (015) 0130(R)

26 6 Higgs inflation in no-scale GUTs No-scale SU(5) model + Superpotential at low energies: 4 W = H c (µ 9 1S )H c + H u (µ 1S ) H e d + h i = H = q Hc H u Z H = Hc eh d 15 hsi diag 1, 1, 1, 3, 3 After GUT breakinghsi u ) µ = 1 u, M c = 5 9 1u J Ellis, HJ He, ZZ Xianyu, Phys. Rev. D 91 (015) 0130(R)

27 7 Higgs inflation in no-scale GUTs F-term scalar potential V = e G apple K IJ Inflation trajectory:h 1 = Hu 0 + @ J 3 Assuming modulus stabilized att = T =1/ G K+ log W V (H 1 )= Removing singularities: 1 u4 1 1 u H 1 H 1 1 (1 6 H1 ) = 1 3 1(1 )u J Ellis, HJ He, ZZ Xianyu, Phys. Rev. D 91 (015) 0130(R)

28 8 Higgs inflation in no-scale GUTs Simplified inflation potential:v (H 1 )= 1 Normalizing the inflaton field:h 1! h Two interesting limits: =0 ) V (h) =3 1u 4 tanh (h/ p 6) =1 ) V (h) = 1 1u 4 H 1 1u 4 h (a) Planck TT+Low P Planck TT,TE,EE+Low P (b) Planck TT+Low P Planck TT,TE,EE+Low P 0.15 = r r = n s n s J Ellis, HJ He, ZZ Xianyu, Phys. Rev. D 91 (015) 0130(R)

29 9 Higgs inflation in no-scale GUTs Simplified inflation potential:v (H 1 )= 1 Normalizing the inflaton field:h 1! h Two interesting limits: Generalization: Flipped SU(5) & Pati-Salam GUTs Phenomenologically viable (nucleon decay etc.) Colored Higgs mass disentangled from inflation scale No discrete symmetry needed 1u 4 H 1 =0 ) V (h) =3 1u 4 tanh (h/ p 6) =1 ) V (h) = 1 1u 4 h J Ellis, HJ He, ZZ Xianyu, Phys. Rev. D 91 (015) 0130(R)

30 30 Asymptotically safe Higgs inflation Asymptotic safety UV-complete GR with a non-gaussian fixed point Running Coupling asympotic safety in gravitational sector M P μ/μ tr Transition scale µ tr O(µ 0 ) ) µ tr = Cµ 0 M P λ asympotic freedom in matter sector μ (GeV) M h =15GeV 16GeV 17GeV ZZ Xianyu, HJ He, JCAP 1410 (014) 083

31 31 Asymptotically safe Higgs inflation AS Cosmology: FRW solution with running M P Friedmann s equation: M P(µ) =M P0 1+ µ µ tr How to choose renormalization scale µ? 3MP(µ)H = V = 1 4 (µ)h4 V = X j z j M 4 j 16 log M j µ M j = O( j )h + O(1)H SM: j 'O(1) ) µ ' h AS: j! 0 ) µ 'H ZZ Xianyu, HJ He, JCAP 1410 (014) 083

32 3 Asymptotically safe Higgs inflation 3M P(H)H = 1 4 (H)h 4 ) flat inflation potential: Agreements with collider measurements improved V 1/4 (GeV) h (GeV) m h =17GeV m h =16GeV m h =15GeV m t (GeV) σ 1σ r Planck TT+Low P Planck TT,TE,EE+Low P tiny tensor mode, r O(10 7 ) m h (GeV) n s ZZ Xianyu, HJ He, JCAP 1410 (014) 083

33 33 Summary & Outlook SDR & Non-minimal TeV An explicit construction of SDR? Other probe of non-minimal coupling? Higgs inflation and extensions Jordan frame formulation? Frame dependence? UV dynamics of Higgs inflation? Reheating in various Higgs inflation models General properties of Higgs inflation Non-Gaussianity

34 THANK YOU