The search for supersymmetric matter at the

Howard Baer University of Oklahoma WSU seminar Nov. 28, 2018

twin pillars of guidance: & simplicity

``The appearance of fine-tuning ``Everything should be in a scientific theory is like a made as simple as cry of distress from nature, possible, but not complaining that something simpler’’ needs to be better explained’’ A. Einstein S. Weinberg

Last particle to be accounted for: the spin-0 Higgs boson!

Can produce at LHC via gluon fusion; mass reconstruction via decay to 2 photons or 4 leptons LHC Higgs discovery: July 4, 2012! m 125 GeV h ⇠

2013 Nobel Excess of events also reported from CDF/D0 Standard Model is regarded as an ``effective field theory’’ valid at energy scales <1 TeV • Higgs mass instability • strong CP problem • unification with gravity • origin of generations • dark matter • dark energy • baryogenesis The first two of these have to do with naturalness and fine-tuning

Introduce notion of practical naturalness:

An observable is natural if all contributions to are < O O ⇠ O

e.g if = a + b c, and if a , then some independent contribution • such asOb would have to be fine-tuned O to large opposite-sign value such as to maintain at its measured value. O Such a fine-tuning is regarded as unnatural and implausible, and indicative • of some missing element in the theory (see Weinberg, Title page).

A pit-fall occurs if = a + b b + c where b large, i.e. contributions • are dependent: combineO dependent terms! before evaluating fine- tuning! Pie baking analogy:

1 kg pie= .2 kg(sugar)+.3 kg(flour)+ .1 kg(water)+.5 kg (apples)+ -.1 kg(evaporation)

Voila! It is very natural! An unnatural recipe:

1kg(pie)=.2 kg(sugar)+.3 kg(flour)+.5 kg(apples)+ 10^4 kg(water)-10^4 kg(evaporation) mathematically, it is possible- but success seems highly implausible: it is fine-tuned and hence unnatural How the Higgs boson is like an apple pie Biggest conundrum of SM: why is Higgs mass so small? 1. There is a lowest order mass term 2. Quantum corrections diverge quadratically with energy scale of new

3.To avoid the pathology of fine-tuning, SM must be valid only to ~1 TeV 4. Need theory which is free of quadratic divergences to extend e.g. to GUT scale

Three MSSM success stories: Unification of gauge couplings

m(t)~150-200 GeV required for EWSB

m(h) just right

If any of these had turned out different, I wouldn’t be here today recent search results from Atlas run 2 @ 13 TeV:

evidently mg˜ > 1.9 TeV compare: BG naturalness (1987): mg˜ < 0.35 TeV

or is SUSY dead? how to disprove SUSY? when it becomes ``unnatural’’? this brings up naturalness issue Mark Twain, 1835-1910 (or SUSY)

1897

Next: simple electroweak fine-tuning in SUSY: dial value of mu so that Z mass comes out right: everybody does it but it is hidden inside spectra codes (Isajet, SuSpect, SoftSUSY, Spheno, SSARD)

e.g. in CMSSM/ mSUGRA: one then concludes nature gives this: If you didn’t fine-tuned, then expect m(Z) at TeV

Natural value of m(Z) from pMSSM is ~2-4 TeV

scan over parameters Measures of fine-tuning: #1: Simplest SUSY measure: EW Working only at the weak scale, minimize scalar potential: calculate m(Z) or m(h) No large uncorrelated cancellations in m(Z) or m(h)

m2 ⌃u µ2 ⇠ Hu u with etc. simple, direct, unambiguous interpretation:

PRL109 (2012) 161802 radiative corrections drive m2 from unnatural Hu GUT scale values to naturalness at weak scale: radiatively-driven naturalness

EWS not broken natural: EWS is barely broken

unnatural u ˜ Large value of At reduces ⇥u(t1,2) contributions to EW while uplifting m to 125 GeV h ⇠ How much is too much fine-tuning?

HB, Barger, Savoy

Visually, large fine-tuning has already developed by µ 350 or 30 ⇠ EW ⇠ bounds from naturalness BG/DG Delta_EW (3%)

mu 350 GeV 350 GeV

gluino 400-600 GeV 6 TeV

t1 450 GeV 3 TeV

sq/sl 550-700 GeV 10-30 TeV

h(125) and LHC limits are perfectly compatible with 3-10% naturalness: no crisis! There is a Little Hierarchy, but it is no problem µ m ⌧ 3/2 Landscape of string theory vacua provides solution to cosmological constant

n 10500? vac ⇠

Weinberg; Bousso Polchinski; Susskind; Denef Douglas;…

Can similar reasoning explain scale of soft SUSY breaking? Statistical analysis of SUSY breaking scale in IIB theory: M. Douglas, hep-th/0405279

start with 10^500 string vacua states

• string theory landscape contains vast ensemble of N=1, d=4 SUGRA EFTs at high scales • the EFTs contain the SM as weak scale EFT • the EFTs contain visible sector +potentially large hidden sector • visible sector contains MSSM plus extra gauge singlets (e.g. a PQ sector, RN neutrinos,…) • SUGRA is broken spontaneously via superHiggs mechanism via either F- or D- terms or in general a combination Why do soft terms take on values needed for natural (barely-broken) EWSB? string theory landscape?

assume model like MSY/CCK where µ 100 GeV • ⇠ then m(weak)2 m2 • ⇠ | Hu | If all values of SUSY breaking field • FX equally likely, then mild (linear) statisticalh i draw towards large soft terms This is balanced by anthropic requirement • of weak scale m 100 GEV weak ⇠

Anthropic selection of m 100 GeV: weak ⇠ If mW too large, then weak interactions 4 (1/mW ) too weak weak⇠ decays, fusion reactions suppressed elements not as we know them

m(weak) < 400 GeV (Agrawal et al.) ⇠ Denef&Douglas: statistics of SUSY breaking in landscape

DD observation: W0 distributed uniformly as complex variable allows dynamical neutralization of ⇤ while not influencing SUSY breaking

Then, number of flux vacua containing spontaneously broken SUGRA with 2 SUSY breaking scale mhidden is:

dN [m2 ,m , ⇤]=f (m2 ) f f dm2 vac hidden weak SUSY hidden · EWFT · cc hidden

f ⇤/m4 where DD maintain m m and not m • cc ⇠ ⇠ string hidden 2 2 2nF +nD 1 fSUSY (mhidden) (mhidden) for uniformly distributed values of • F and D breaking⇠ fields f m2 /m2 (?) where m m m2 /m • EWFT ⇠ weak soft soft ⇠ 3/2 ⇠ hidden P n =2n + n 1 F D f mn SUSY ⇠ soft landscape favors high scale SUSY breaking tempered by f(EWFT) anthropic penalty! What about DD/AD anthropic penalty f m2 /m2 ? EWFT ⇠ weak soft This fails in a variety of practical cases: A-terms get large: CCB minima • ) m2 too large: fail to break EW symmetry • Hu Must require proper EWSB! Even if EWS properly broken, then large A reduces EWFT in the ⌃u(t˜ ) • t u 1,2 large m2 (m ) needed to radiatively drive m2 to natural value at Hu GUT Hu • weak scale

Better proposal: fEWFT ⇥(30 EW ) keeps calculated weak scale) within factor 4 of measured weak scale m m 100 GeV ⇠ weak ⌘ W,Z,h ⇠

Assume µ 100 200 GeV via e.g. rad PW breaking: then mZ variable and may be large⇠ depending on soft terms m2 and ⌃u,d(i) Hu,d u,d mHu =1.3m0

statistical draw to large soft terms balanced by anthropic draw toward red (m(weak)~100 GeV): then m(Higgs)~125 GeV and natural SUSY spectrum! Denef, Douglas, JHEP0405 (2004) 072 Giudice, Rattazzi, NPB757 (2006) 19; Dutta, Mimura, PLB648 (2007) 357 HB, Barger, Savoy, Serce, PLB758 (2016) 113 m0 =5TeV

statistical/anthropic draw toward FP-like region Recent work: place on more quantitative footing: scan soft SUSY breaking parameters in NUHM3 model as m(soft)^n along with f(EWFT) penalty

(flat) mu=150 GeV (fixed)

HB, Barger, Serce, Sinha, JHEP1803 (2018) 002 Making the picture more quantitative: dN [m2 ,m , ⇤]=f (m2 ) f f dm2 vac hidden weak SUSY hidden · EWFT · cc hidden

m(h)~125 most favored for n=1,2

HB,Barger, Serce, Sinha What is corresponding distribution for gluino mass?

typically beyond LHC 14 reach (may need HE-LHC) and m(t1)? first/second generation sfermions pulled to 10-30 TeV thus softening any SUSY flavor/CP problems Prospects for discovering SUSY with radiatively-driven naturalness at LHC and ILC Sparticle prod’n along RNS model-line at LHC14:

gauginos

gluinos

pair production dominant-but only soft visible energy release from higgsino decays largest visible cross section: wino pairs gluino pairs sharply dropping gluino pair cascade decay signatures

will need HE-LHC (27 TeV) to probe unified SUSY models Top squark searches: HE-LHC can see entire natural p-space: discover or falsify natural SUSY! Distinctive new same-sign diboson (SSdB) signature from SUSY models with light higgsinos!

(soft)

(soft)

wino pair production

This channel offers added reach of LHC14 for nSUSY; it is also indicative of wino-pair prod’n followed by decay to higgsinos See direct higgsino pair production recoiling from ISR (monojet signal)?

typically 1% S/BG after cuts: very tough to do! + What about pp Z˜ Z˜ j with Z˜ Z˜ ` ` ? ! 1 2 2 ! 1

Han, Kribs, Martin, Menon, PRD89 (2014) 075007; HB, Mustafayev, Tata, PRD90 (2014) 115007; use MET to construct m^2(tau-tau) HL-LHC14 can see most of nSUSY p-space via soft OS dilepton+MET channel Smoking gun signature: light higgsinos at ILC: ILC is Higgs/higgsino factory!

(higgsino) (Zh)

+ ˜1 ˜1 0 0 ˜1˜2

3-15 GeV higgsino mass gaps no problem in clean ILC environment

HB, Barger, Mickelson, Mustafayev, Tata arXiv:1404:7510 + + 0 0 e e ˜ ˜ (`⌫ ˜ )+(qq¯0˜ ) ! 1 1 ! ` 1 1 0 measure m(jj)

• SUSY very much alive: natural for mu~100-300 GeV

• EW naturalness: higgsino-like WIMP

• QCD naturalness: axion

• SUSY mu problem/Little Hierarchy: SUSY DFSZ axion-PQ gravity-safe

• DM=higgsino-like WIMP+DFSZ axion admixture?

• n-ton SI noble liquid detectors should probe all p-space

• axions: must probe broader and deeper!

• (HL)-LHC: maybe see SUSY, maybe not

• HE-LHC33 TeV may be required

• ILC is ideal for light higgsinos More slides: DM, baryogenesis, aspects of naturalness Dark matter from SUSY with radiatively-driven naturalness Mainly higgsino-like WIMPs thermally underproduce DM

green: excluded; red/blue:allowed

HB, Barger, Mickelson

IsaReD Factor of 10-15 too low But so far we have addressed only Part 1 of fine-tuning problem:

In QCD sector, the term must occur

But neutron EDM says it is not there: strong CP problem

(frequently ignored by SUSY types) Best solution after 35 years: PQWW/KSVZ/DFSZ invisible axion In SUSY, axion accompanied by axino and saxion

Changes DM calculus: expect mixed WIMP/axion DM (2 particles) mixed axion-neutralino production in early universe

neutralinos: thermally produced (TP) or NTP viaa ˜, s or G˜ decays • s,a˜ – re-annihilation at TD axions: TP, NTP via s aa, bose coherent motion (BCM) • saxions: TP or via BCM • – s gg: entropy dilution – s SUSY : augment neutralinos – s aa: dark radiation (N < 1.6) eff axinos: TP • – a˜ SUSY augments neutralinos gravitinos: TP, decay to SUSY • DM production in SUSY DFSZ: solve eight coupled Boltzmann equations

wimp

Bae, HB, Chun; Bae, HB, Lessa, Serce

radiation

gravitino saxion axino a(CO) re-heat usual picture => mixed axion/WIMP

KJ Bae, HB, Lessa, Serce much of parameter space is axion-dominated with 10-15% WIMPs => higgsino abundance

axion abundance

mainly axion CDM for fa<~10^12 GeV; for higher fa, then get increasing wimp abundance

Bae, HB,Lessa,Serce Direct higgsino detection rescaled for minimal local abundance ⇠ ⌦TPh2/0.12 ⌘

Bae, HB, Barger,Savoy,Serce

Xe-1-ton now operating!

natural SUSY

Can test completely with ton scale detector or equivalent (subject to minor caveats) Prospects for SD WIMP searches: Prospects for IDD WIMP searches:

suppressed by square of diminished WIMP abundance As ⇠ increases due to non-thermal WIMP production from saxion/ axino decay, then axion parameter space becomes constrained by WIMP searches SUSY DFSZ axion: large range in m(a) but coupling reduced may need to probe broader and deeper!

#2: Higgs mass or large-log fine-tuning HS

It is tempting to pick out one-by-one quantum fluctuations but must combine log divergences before taking any limit

2 2 2 2 Xt = mQ3 + mU3 + mHu + At neglect gauge pieces, S, mHu and running; then we can integrate from m(SUSY) to Lambda 3f 2 m2 t m2 + m2 + A2 ln(⇤/m ) Hu ⇠8⇡2 Q3 U3 t SUSY 2 2 m˜ ˜ < 500 GeV m /(m /2) < 10 t1,2,b1 HS ⇠ h h mg˜ < 1.5 TeV

old natural SUSY then At can’t be too big What’s wrong with this argument? In zeal for simplicity, have made several simplifications: most egregious is that one sets m(Hu)^2=0 at beginning to simplify m2 (⇤) and m2 are not independent! Hu Hu violates prime directive!

The larger m2 (⇤) becomes, then the Hu larger becomes the cancelling correction!

HB, Barger, Savoy HS ' EW

To fix: combine dependent terms:

m2 µ2 + m2 (⇤)+m2 where now both h ' Hu Hu µ2 and m2 (⇤)+m2 are m2 Hu Hu ⇠ Z After re-grouping: HS EW '

Instead of: the radiative correction m2 m2 Hu Z we now have: the radiatively-corrected m2⇠ m2 Hu ⇠ Z

HS ' EW Recommendation: put this horse out to pasture

2 2 3ft 2 2 2 m 2 m + m + A ln(⇤/mSUSY ) Hu ⇠8⇡ Q3 U3 t R.I.P.

sub-TeV 3rd generation squarks not required for naturalness EW is highly selective: most constrained models are ruled out except NUHM2 and its generalizations:

scan over p-space with m(h)=125.5+-2.5 GeV:

0.1%

1%

10%

HB, Barger, Mickelson,Padeffke-Kirkland, PRD89 (2014) 115019 Applied properly, all three measures agree: naturalness is unambiguous and highly predictive!

Radiatively-driven natural SUSY, or RNS:

(typically need mHu~25-50% higher than m0)

Why might mu<

µ f 2/m KN: PQ symmetry forbids mu term, ⇠ µ a P but then it is generated via PQ breaking m(soft) m m2 /m ⇠ 3/2 ⇠ hidden P Little Hierarchy due to mismatch between fa

Higgs mass m(h)~mu 1012 GeV m 6.2µeV a ⇠ f tells us where to look for axion! ✓ a ◆ Gravity safe, electroweak natural axionic solution to strong CP and SUSY µ problems HB, Barger, Sengupta, arXiv:1810.03713 1. Global symmetries fundamentally incompatible with gravity completion 2. Expect global symmetry to emerge as accidental (approximate) symmetry from some more fundamental gravity-safe (e.g. gauge or R-) symmetry 3. Krauss-Wilczek: gauge symmetry with charge Ne object condensing leaves charge e fields with Z_N discrete gauge symmetry 4. Babu et al.: Z22 symmetry works but charge 22 object in swampland? 5. Better choice: discrete R-symmetries which arise from compactification of extra dimensions in string theory A model which works: Z(24) R symmetry (see also Lee et al.)

c c c c W fuQHuU + fdQHdD + f`LHdE + f⌫ LHuN + 3 c c 2 3 p q p+q 3 MN N N /2+µX HuHd/mP + fX Y/mP + 3X Y /mP

Lowest dimension PQ breaking operator contributing to scalar PQ poten- • tial 1/m8 : enough suppression so that PQ is gravity-safe ⇠ P Also forbids/suppresses RPV/p-decay operators • µ f 2/m • ⇠ µ a P #3. What about EENZ/BG measure?

2 2 @ log mZ pi @mZ BG = maxi @ log p = maxi m2 @p | i | | Z i | pi are the theory parameters applied to pMSSM, then BG ' EW apply to high (e.g. GUT) scale parameters

applied to most parameters,

BG large, looks fine-tuned for e.g. mt˜1 1 TeV 2 ⇠ (Q ) 0.73 1000 100 BG 3 ' 91.22 ⇠ #3. What about EENZ/BG measure?

2 2 @ log mZ pi @mZ BG = maxi @ log p = maxi m2 @p | i | | Z i | applied to pMSSM, then BG ' EW What if we apply to high (e.g. GUT) scale parameters ?

For correlated scalar masses m0, Feng, Matchev, Moroi scalar contribution collapses:⌘ what looks fine-tuned isn’t: focus point SUSY Even with FP, still multi-TeV scalars are natural fine-tuned on m(gluino) :( But wait! in more complete models, soft terms not independent violates prime directive! e.g. in SUGRA, for well-specified hidden sector, each soft term calculated as multiple of m(3/2); soft terms must be combined!

in general: since µ hardly runs, then

m2 2µ2 + a m2 Z ' · 3/2 2µ2 2m2 (weak) ' Hu

m2 (weak) (100 200)2 GeV2 a m2 /2 Hu ⇠ ⇠ · 3/2

2 2 using µ and m3/2 as fundamental, then even using high scale parameters! BG ' EW