New Physics at the Electroweak Scale

Transcription

1 New Physics at the Electroweak Scale G.F. Giudice Florence, 7-8 Sep 007 1

2 Is there a Higgs? A ( W + L W " L # Z L Z ) L = G F E % 8 $ 1" E ' E & " m H ( * ) Without Higgs With Higgs E < 1. TeV m H < 780 GeV Most economical solution for EW breaking LEP gives indications for a light Higgs Preferred value m H = "4 GeV Upper limit m H <144 GeV (95% CL) including direct limit of 114 GeV : m H <18GeV (95% CL) LEPEWWG 07

3 The decrease in m t has worsened the SM fit LEP/SLD/m W /" W : m t =178.9 #8.6 GeV CDF/D$ : m t =170.9 ±1.8GeV The two best measurements of sin! W do not agree 0,b A fb " m H = (30 # 800)GeV A l (SLD) " m H = (13# 65)GeV This makes the argument for a light Higgs less compelling LEPEWWG 07 3

4 Still open is the possibility of no Higgs, and new strong dynamics flavour? EW precision data? "S # 1 & 6$ n TFN TC + ln % TC ( ' m Z ) + * Negative contributions to S? TC Walking at small N TC? Higgsless? EW broken by boundary conditions with KK gauge bosons curing unitarity up to about 10 TeV (or less) 4

5 What is the Higgs mass? Important indirect information from Higgs mass measurement EW vacuum is metastable for 115 GeV < m H < 15 GeV Non perturbative EWPT LEP ( ) +... d# 16" dlnµ = 6 4# + #y 4 t $ y t Cut-off scale (GeV) 5

6 Higgs mass is a good discriminator for BSM theories m H = M Z cos " + 3G 4 Fm t # log m t m +K t M Z = 3h t # m t log $ +K m t Smaller m t reduces loop correction to m H no mixing ( m t = TeV) : m H <11GeV gauge med ( m t = TeV) : m H <115GeV max mixing ( m t = TeV) : m H <18GeV split susy ( m =10 7 GeV) : m H <145GeV " perturb. up to 10 7 GeV : m H <150GeV 6

7 Is the Higgs a SM-like weak doublet? The choice of a single SU doublet is dictated by simplicity More Higgs doublets (susy) or new Higgs singlets Recent activity in studying extensions Link to mirror worlds? Higgs mass is only allowed super-renormalizable term L = c H O Hidden-sector operator 7

8 Evading m H upper bound from EWPT? Requires new physics with "T=0."0.3 and "S small Inert Doublet Model: parity H! " H and <H >=0 Lightest parity-odd Higgs can be DM No significant improvement in naturalness Susy with large #NH 1 H "T from Higgs-higgsino system Heavy Higgs, but validity only up to about 10 TeV New EW fermions DM candidate 8

9 Evading m H lower bound from LEP? Controversial signal at 115 GeV.3# excess at 98 GeV Excess at 100 GeV requires " $ # g hzz (SM) g hzz % ' & B( h ( bb ) ) 0. New decay modes (new particles) Change Higgs nature (mixing with other states) Limits on unconventional decay modes h " ## m h >117GeV h " bb bb m h >110GeV h " $ + $ % $ + $ % m h > 87GeV h " anything m h > 8GeV OPAL 9

10 Possible explanations in supersymmetry Reduced hzz coupling for the lightest Higgs with m H =98 GeV (and SM coupling for a Higgs with m H =115 GeV) SM Higgs couplings, but new decay channel into a light pseudoscalar (m A < m b ) h " a a " # + # $ (cc )# + # $ (cc ) Reanalysis of LEP data? Light neutralino with R-parity breaking decay h " # # " 6q Displaced vertices at LHCb? 10

11 Is the Higgs elementary or composite? Determine the nature of the force that breaks EW Elementary SM (with m H < 190 GeV) SUSY (H,Q,L are all chiral superfields; no new quartic interaction) Composite: Higgs is a light remnant of a strong force pseudogoldstone Little Higgs Gauge-Higgs unification Holographic Higgs. 11

12 HIGGS AS PSEUDOGOLDSTONE BOSON " = # + f ei$ / f " = f " % e ia " : &# % # ' ( $ % $ + a Non - linearly realized symmetry h % h + a forbids m h Gauge, Yukawa and self-interaction are non-derivative couplings!violate global symmetry and introduce quadratic divergences Top sector!!!! No fine-tuning If the scale of New Physics is so low, why do LEP data work so well? 1

13 Explain only little hierarchy One loop H LITTLE HIGGS At $ SM new physics cancels one-loop power divergences Two loops % m % m H = G $ = F G $ m F 4 SM m! 4 SM SM! #! SM #! " < $ G m F $ G F SM " TeV " 10TeV "! Collective breaking : many (approximate) global symmetries preserve massless Goldstone boson LH! 1!! H # m H =! "!! 4" 4"! 13

14 It can be achieved with gauge-group replication Goldstone bosons in G " G 1! G G / gauged subgroups, each preserving a non-linear global symmetry SM " G! G which breaks all symmetries 1 Field replication Ex. SU gauge with % 1, doublets such that V(% 1+ % 1,% + % ) and % 1, spontaneously break SU Turning off gauge coupling to % 1! Local SU (% )! global SU (% 1 ) both spont. broken $ m H 4 g " # ( 4 ) 4! H two loops 14

15 Realistic models are rather elaborate Effectively, new particles at the scale f cancel (same-spin) SM one-loop divergences with couplings related by symmetry Typical spectrum: Vectorlike charge /3 quark Gauge bosons EW triplet + singlet Scalars (triplets?) 15

16 New states have naturally mass New states cut-off quadratically divergent contributions to m H Ex.: littlest Higgs model Log term: analogous to effect of stop loops in supersymmetry Severe bounds from LEP data 16

17 NEW INGREDIENTS FROM EXTRA DIMENSIONS HIGGS AS EXTRA-DIM COMPONENT OF GAUGE FIELD A M = (A µ,a 5 ), A 5 " A 5 +# 5 $ forbids m A 5 gauge Higgs Higgs/gauge unification as graviton/photon unification in KK Correct Higgs quantum numbers by projecting out unwanted states with orbifold The difficulty is to generate Yukawa and quartic couplings without reintroducing quadratic divergences 17

18 Light Higgs pseudogoldstone of a strong force Belong to higher-dim gauge multiplet m h = 0 h " h + a A 5 " A 5 + # 5 $ Same thing? (duality) Relation between models of strong dynamics and extra dimensions 18

19 New extra dimensions or new strong forces? Warped gravity with SM fermions and gauge bosons in bulk and Higgs on brane A d S/ C F T Technicolor-like theory with slowly-running couplings in 4 dim As particle & wave are different aspects of the same reality, familiar concepts of dimension & force may not be distinct TeV brane 5 th dim Planck brane Duality position & energy (typical of a gravitational field) $ IR RG flow $ UV 19

20 Signatures at LHC? New resonances, W,Z,t, KK excitations Common low-energy theory of Higgs interactions What are the distinctive features of compositeness at the LHC? Recent progress on effective-theory description of a composite Higgs Describe Higgs with a $-model deformed by gauge and Yukawa interactions Specific patterns of modified Higgs couplings v f = 1 4 Deviations from SM Higgs couplings can test v / f up to LHC 0"40 % SLHC 10 % ILC 1 % & 4%f = 30 TeV 0

21 Genuine signal of Higgs compositeness at high energies In spite of light Higgs, longitudinal gauge-boson scattering amplitude violates unitarity at high energies W L h W L "( pp # V L V L $ X) = v 4 W L ( ) H f " pp # V 4 L V L $ X Modified coupling W L Identify hadronically-decaying W V L V L scattering is an important channel, even for light Higgs Higgs is viewed as pseudogoldstone boson: its properties are related to those of the exact (eaten) Goldstones Strong gauge-boson scattering & strong Higgs production 1

22 Is the stability of M W / M P explained by a symmetry or dynamical principle? BSM constructions have focused on the hierarchy problem Good examples of naturalness at work Cancellation of electron self-energy ( + -( 0 mass difference K L -K S mass difference gauge anomaly Existence of positron ' charm top Observations & CC ) 10-3 ev LEP constraints on BSM Theory No good symmetry explanation for & CC Landscape of vacua in string theory Different views on naturalness & hierarchy Anthropic selection principle at work

23 Complexity life * biochemistry * atomic physics * SM * final theory Microscopic probes Breaking of naturalness would require new principles the final theory is a complex phenomenon with IR/UV interplay some of the particle-physics parameters are environmental 3

24 Can we get experimental indications from LHC? Are there observable predictions? Evidence for unnaturalness at work Split Supersymmetry Heavy squarks and sleptons Keep DM gauge unif. Discard flavor problem very light Higgs fast p-decay Long-lived gluino at LHC (time delay & anomalous ionization energy loss; measuring long lifetimes of stopped gluinos) Modified gaugino couplings at the ILC Measurable effects in EDM 4

25 Little hierarchy in Supersymmetry If distribution of vacua grows with M susy and we require the prior of EW breaking M Z M susy " loop factor Value of the Higgs (and top) mass If distribution of vacua grows at small # and we require metastability of Higgs vacuum m H = 115 ± 6 GeV (better discover the Higgs quickly, because the end of the world is near) If also # top scans: m t = 17.4 " GeV 5

26 SUPERSYMMETRY Best solution to the hierarchy problem with valid extrapolation up to very high scales Its main problem is why neither the Higgs nor sparticles have been observed at LEP Break susy, but keep UV behavior & soft breaking 6

27 Some properties are robust Gauge-coupling unification ' s exp =0.1176±0.000 success of susy does not strongly depend on details of soft terms remarkable that M GUT is predicted below M P and above p-decay limit 7

28 EW breaking induced by quantum corrections RG running: gauge effects Yukawa effects If # t large enough & SU()(U(1) spontaneously broken If ' s large enough & SU(3) unbroken 8 Mass spectrum separation m < weak susy < strong susy

29 m S IS THE SEED OF EW BREAKING EW breaking is related to susy breaking, m S & m Z top stop "m = # 3$ t k dk ' & 8% k + m t m S plays the role of $ cutoff + 3$ t k dk ' & 8% k + m t + m S = # 3$ t 4% m S ln & m S The quantum correction is negative and drives EW breaking m H = M Z cos " + 3G 4 Fm t # log m t m +K t M Z = 3h t # m t log $ +K m t 9

30 Natural supersymmetry has already been ruled out 30

31 Characterizing the tuning as a criticality condition SM ( ) = "m H H + # H 4 V H Broken EW Unbroken EW 0 m H Why is nature so close to the critical line? Exact susy (and µ=0) & critical line Dynamical susy breaking M S ~M P e "1/+ & small departure from critical line stabilization of flat direction H 1 = H & natural supersymmetry with M S ~M Z 31

32 natural supersymmetry: M S << Q C << M P Q C ~ e "1/+ M P unrelated to M S (depends on ratios of soft terms and + a ) much smaller than UV scale M S and Q C equal to few % tuned supersymmetry: M S ~ Q C << M P M S < Q C broken EW; M S > Q C unbroken EW Why supersymmetry should prefer to be near critical? 3

33 Collider signatures of supersymmetry crucially depend on the structure of the soft terms THEORY OF SOFT TERMS Explain origin of supersymmetry breaking Compute soft terms Derive phenomenological properties SUSY??? Squarks, sleptons, gauginos, higgsinos What force mediates susy-breaking effects? 33

34 GRAVITY AS MEDIATOR Gravity couples to all forms of energy Assume no force stronger than gravity couples the two sectors Susy breaking in hidden sector parametrized by X with <F X >,0 1 M P d " X W # W # $ % m S && gaugino mass 1 M P 1 M P 1 M P $ d 4 " X + X ' + e V ' % m S ( + ( scalar mass $ d 4 " X + ' + e V ' % m S ( F * ( = )m S ( *f *( A - term $ d " X f (') % m S f (() A - term 1 $ d 4 " X + H 1 H % m S $ d " H 1 H µ term M P 1 d 4 " X X + $ H 1 H % m S H 1 H B µ - term M P m S = F X / M P m S = TeV & F X 1/ = GeV 34

35 ATTRACTIVE SCENARIO Gravity a feature of local supersymmetry Gravity plays a role in EW physics No need to introduce ad hoc interactions Justification for µ ) m S BUT Lack of predictivity (10 parameters) Flavour problem 35

36 - 0 LSP: most studied case ~ G LSP: It can be DM with stau as NLSP Long-lived charged particle at the LHC (.!.G) ~ ~ Distinctive ToF and energy loss signatures Stoppers in ATLAS/CMS caverns: Measure position and time of stopped ~.; time and energy of. Reconstruct susy scale and gravitational coupling With large statistics, the gravitino spin can be measured from ~ ~ 36.!./G distributions

37 GAUGE MEDIATION Soft terms are generated by quantum effects at a scale M << M P m Z If M << & F, Yukawa is the only effective source of flavour breaking (MFV); flavour physics is decoupled (unlike sugra or technicolour) Soft terms are computable and theory is highly predictive & F M P Free from unknowns related to quantum gravity M SUSY Messengers SUSY SM gauge loop 37

38 Higgs mass is the strongest constraint: stop masses at several TeV Large squark/slepton mass ratio and small A do not help with tuning 38

39 m 3 / = Crucial difference between gauge and gravity mediation F 3M P " in gravity m 3 / # m S, in gauge m 3 / # $ F ' & ) % 100 TeV( In gauge mediation, the gravitino is always the LSP q q~ ~ G L = " 1 F J µ Q# µ G = " 1 F " m on mass shell F Goldberger-Treimanino relation ) + * m $ ev % L $ + M g 4 &, a ' µ( a F µ(. G + h.c. - NLSP decays travelling an average distance # 100 GeV& l " % ( $ ' m NLSP 5 # F & % ( $ 100 TeV' 4 E m NLSP )1 0.1 mm From microscopic to astronomical distances 39

40 - 0 or ~. R are the NLSP (NLSP can be charged) In gravity-mediation, missing energy is the signature Susy particles F "10 6 GeV NLSP - 0 ~. R F "10 6 GeV F "10 6 GeV F "10 6 GeV //E E..E Stable charged particle Intermediate region very interesting (vertex displacement; direct measurement of F) 40

41 ANOMALY MEDIATION Supergravity mediation effects depend on higherdimensional couplings of hidden-visible sector There is an unavoidable effect & anomaly mediation In many cases it is subleading. In some cases it can become the dominant effect Consider coupling to gravity in superconformal formalism with the conformal compensator chiral superfield " =1# m 3 / $ Its couplings are dictated by conformal invariance 41

42 % L = d 4 "# + #Q + e V Q + d " # 3 f (Q) + 1 g W ( + + ' $ W $ + h.c. * & ) One can construct allowed couplings by considering all visible fields with d = R = 0 and % with d * = 1, R * = /3 By rescaling Q! Q/*, we can eliminate %, if f(q)~q 3 has no dimensionful couplings (it is the case of interest because µ has to come from susy breaking) Classically, but not quantum mechanically! (Scale anomaly) 4

43 % L = # d 4 "Z' & µ $ ( * Q + e V Q + #, d " ) f (Q) + S % µ ( /. ' & $ * W + W ) h.c. - 0 Can depend on both % and % +, but R-symmetry implies dependence only on %% + Holography implies dependence only on % Gravitino is heavy, m 3/ ~ TeV Form of soft terms invariant under RG transformations 0 function and threshold effects of heavy states exactly compensate Negative slepton square masses 43

44 Predictive power: all soft terms determined by low-energy parameters (up to overall scale m 3/ ) UV insensitivity: solution to the flavour problem 44

45 Characteristic features of anomaly mediation With gaugino unification In anomaly mediation LSP nearly degenerate W-ino M M 1 " M 1 M " 3 M 3 M 1 " 7 M 3 M " 7 m " ± # m " 0 $ % M W ( ) 1+ cos& W $165 MeV (tree level is typically smaller) This allows the fast decay W ± " # ± W 0 The pions are soft, making their detection difficult 45

46 MIRAGE UNIFICATION It is possible to have a mixed modulus and anomaly mediation such that F T T = M m 0 " 3 / ln( M P m 3 / ) For m 3 / "10 TeV, this is comparable to anomaly contribution Although uplift potential not consistent with extra dim, one finds M g = A = m at M mir = M GUT ( ) " M P m 3 / " is the ratio of anomaly/modulus contributions No physical threshold at M mir 46

47 small log large A compressed spectrum is best to reduce tuning 47

48 EXTRA DIMENSIONS AND THE WEAK SCALE Usual approach: fundamental theory at M Pl, while & W is a derived quantity Alternative: & W is fundamental scale, while M Pl is a derived effect New approach requires extra spatial dimensions confinement of matter on subspaces Natural setting in string theory & Localization of gauge theories on defects (D-branes: end points of open strings) We are confined in a 4-dim world, which is embedded in a higher-dim space where gravity can propagate 48

49 Suppose fundamental mass scale M D ~ TeV M Pl = M D RM D"4 ( ) D very large if R is large (in units of M -1 D ) Radius of compactified space R = ( 5 "10 #4 ev) #1 $ 0.4 mm D # 4 = ( 0 kev) #1 $10 #5 µm D # 4 = 4 ( 7 MeV) #1 $ 30 fm D # 4 = 6 Smallness of G N /G F related to largeness of RM D Gravity is weak because it is diluted in a large space (small overlap with branes) Need dynamical explanation for RM D >>1 49

50 graviton Probe gravity at colliders gluon Probability of producing a KK graviton " E M Pl "( pp # G (n ) jet) = $ s % G N =10 &8 fb 1 event ' run LHC for t U Number of KK modes with mass less than E (use m=n/r) " n D#4 $ ER Inclusive cross section ( ) D#4 $ E D#4 M Pl ( n M D D# "( pp # G (n ) jet) $ % se D&4 D& ' M D It does not depend on V D (i.e. on the Planck mass) Missing energy and jet with characteristic spectrum 50

51 L = ± 4" # T 4 T T = 1 & ( T T µ$ µ$ % 1 D % T µ ' Contact interactions from graviton exchange µ T $ $ Sensitive to UV physics d-wave contribution to scattering processes predictions for related processes Limits from Bhabha/di-/ at LEP and Drell- Yan/ di-/ at Tevatron: $ T > TeV ) + * L = ± 4" # $ $ $ = 1 ' ) ( & f = q,l f % µ % 5 f *, + Loop effect, but dim-6 vs. dim-8 1 only dim-6 generated by pure gravity $ 1 > TeV from LEP 51

52 G-emission is based on linearized gravity, valid at s << M D TRANSPLANCKIAN REGIME Planck length ( P & = $ % G D 3 c h #! " 1 ' + quantum-gravity scale Schwarzschild radius R S = & #. +, &. + #). G -$! $ D s! 3 * ' / $ +. + % "( % c! " classical gravity classical limit ( h " 0) : R S >> # P transplanckian limit ( s >> M ) D : R S >> # P same regime The transplanckian regime is described by classical physics (general relativity)! independent test, crucial to verify gravitational nature of new physics 5

53 Gravitational scattering in extra dimensions: two-jet signal at the LHC Diffractive pattern characterized by # b c " G s & D % ( $ h ' 1 ) 53

54 b < R S At b<r S, no longer calculable Strong indications for black-hole formation BH with angular momentum, gauge quantum numbers, hairs (multiple moments of the asymmetric distribution of gauge charges and energy-momentum) Gravitational and gauge radiation during collapse & spinning Kerr BH $ ~ %R S 10 pb (for M BH =6 TeV and M D =1.5 TeV) Hawking radiation until Planck phase is reached T H ~ R S -1 ~ M D (M D / M BH ) 1/(++1) Evaporation with, ~ M BH (++3)/(++1) / M D (++)/(++1) (10-6 s for M D =1 TeV) Characteristic events with large multiplicity (<N> ~ M BH / <E> ~ (M BH / M D ) (++)/(++1) ) and typical energy <E> ~ T H Transplanckian condition M BH >> M D? 54

55 WARPED GRAVITY A classical mechanism to make quanta softer For time-indep. metrics with g 0µ =0 & E g 00 1/ conserved. (proper time d, = g 00 dt ) Schwarzschild metric g 00 =1" G N M r # E obs " E em E em = g 00 "1 = " G N M r em On non-trivial metrics, we see far-away objects as red-shifted 55

56 GRAVITATIONAL RED-SHIFT ds = e "K y # µ$ dx µ dx $ + dy Masses on two branes related by m "R m 0 = e #"RK y=0 g 00 =1 y=%r g 00 =e -%RK Same result can be obtained by integrating S E over y R "10 K #1 $ m %R m 0 " M Z M GUT 56

57 PHYSICAL INTERPRETATION Gravitational field configuration is non-trivial Gravity concentrated at y=0, while our world confined at y=%r Small overlap & weakness of gravity WARPED GRAVITY AT COLLIDERS KK masses m n = Kx n e -%RK [x n roots of J 1 (x)] not equally spaced Characteristic mass Ke -%RK ~ TeV KK couplings ( (0) G L = "T µ# µ# * + ) M Pl n=1 (n) G µ# KK gravitons have large mass gap and are strongly coupled & ' $ % + - $ %. e "%RK M Pl / TeV, 57

58 RS with gauge bosons & fermions in the bulk is emerging as one of the most interesting model with extra dimensions Discovery through KK-gluon production qq " g (1) " tt It can be identified up to M KK = 5 TeV 58

59 Test of gravitational nature from KK-graviton production Using tt and ZZ final states, LHC can test up to M KK = TeV Possible to identify the spin- structure 59