The search for supersymmetric matter at the Large Hadron Collider
Howard Baer University of Oklahoma WSU seminar Nov. 28, 2018
twin pillars of guidance: naturalness & 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 physics
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
higgsino 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!