ARE THERE MOTIVATED DARK MATTER CANDIDATES?

.

ARE THERE MOTIVATED DARK MATTER CANDIDATES?

Gordy Kane, University of Michigan AMS Days, CERN, April 2015

 AXIONS

 LSPs … BUT strong constraints

 STRING/M-THEORY HIDDEN SECTOR CANDIDATES VERY WELL MOTIVATED! – IMPLICATIONS?

 Plus many ad hoc suggestions

 ALSO, NON-THERMAL COSMOLOGICAL HISTORIES IMPLIED BY STRING/M-THEORIES AND VERY WELL MOTIVATED! –

IMPLICATIONS?

Once the Standard Model was in place in 1970s, particle physicists could ask about its foundations, ask about an underlying theory covering all scales – a goal for many

Needed to develop many experimental facilities, search for signals beyond SM – LHC, DM detectors, etc

To make progress also needed to extend theories – string/M theory framework has emerged as an approach to an

underlying theory - incorporates SM, supersymmetry, etc

OUTLINE

• Introduction

o Compactified string/M theory as underlying theory o Progress, testable

o Gravitino o Moduli!

• Implications for DM

• More about compactified M Theory

• Moduli  non-thermal cosmology for relic density

• Scales, Planck to Electroweak – Hierarchy problem – LHC

• Axions

• Hidden sector DM, some results – DM candidate

• Signatures – Indirect – Direct – LHC

• Final remarks

[Some slides not for careful study]

String/M theory a powerful, very promising framework for

constructing an underlying theory that incorporates the Standard Models of particle physics and cosmology and provides a full

ultraviolet (high scale, unification scale) completion – solves the hierarchy problem, explains Electroweak Symmetry breaking, etc

-- we hope for such a theory!

-- significant progress in recent years

• String/M theory must be formulated in 10 (11) D to be a possible quantum theory of gravity, and must be projected to 4D

(“compactified”) for predictions, tests

• Compactified string/M theories are testable as normal physics – Don’t have to be somewhere to test physics there (e.g. big bang, dinosaurs)

Landscape of solutions? Maybe

– but no obstruction to finding and testing compactifications that might describe our world – lots in recent work

– examples show not premature to look for our vacuum

– in each vacuum perhaps most or all observables calculable (except CC?)

Curled up dimensions contain information on our world – particles and their masses, symmetries, forces, dark matter, more

Try out motivated examples for curled up dimensions, calculate predictions, test – lots of useful, relevant results – many

theoretical constraints, limited possibilities, few parameters – lots of examples now

Three new physics aspects:

o “Generic”

o Gravitino o moduli

Generic:

- Probably not a theorem (or at least not yet proved), might be avoided in special cases

- One has to work at constructing non-generic cases

GRAVITINO

-- In theories with supersymmetry the graviton has a superpartner, gravitino – if supersymmetry broken, gravitino mass (M

) splitting from the massless

graviton is determined by the form of supersymmetry breaking

– Gravitino mass sets the mass scale for the theory, for all

superpartners, for some dark matter

MODULI – new physics, from compactified string/M theories

-- To describe sizes and shapes and metrics of small manifolds the theory provides a number of fields, called “moduli” fields

-- In compactified M-theory supersymmetry breaking generates potential for all moduli

-- Moduli fields have definite values in the ground state (vacuum) – jargon is “stabilized” – then measurable quantities such as masses, coupling strengths, etc, are determined in that ground state – if not stabilized, laws of nature time and space dependent

-- Moduli fields (like all fields) have quanta (also called moduli), with masses fixed by fluctuations around minimum of moduli potential -- Moduli dominate after inflation, oscillate, stabilize – we begin there

PAPERS ABOUT M-THEORY COMPACTIFICATIONS ON G₂ MANIFOLDS (11-7=4)

Earlier work 1995-2004

; Witten 1995

• Papadopoulos, Townsend th/9506150, 7D manifold with G₂ holonomy preserves N=1 supersymmetry

• Acharya, hep-th/9812205, non-abelian gauge fields localized on singular 3 cycles

• Atiyah and Witten, hep-th/0107177

• Atiyah, Maldacena, Vafa, hep-th/0011256

• Acharya and Witten, hep-th/0109152, chiral fermions supported at points with conical singularities

• Witten, hep-ph/0201018 – shows embedding SU(5)-MSSM probably ok

• Beasley and Witten, hep-th/0203061, generic Kahler form

• Friedmann and Witten, th/0211269, SU(5) MSSM, scales – no susy breaking

• Lukas, Morris hep-th/0305078, generic gauge kinetic function

• Acharya and Gukov, hep-th/0409101 – review

Basic framework established – powerful, rather complete

Gravity mediated supersymmetry breaking because generically two 3-cycles won’t interact directly in 7D manifold

10

Particles!

We (Acharya, GK, Kumar and others) started in 2005 – since LHC coming, focused on moduli stabilization, supersymmetry breaking, etc

Already knew that gauge matter and chiral fermions were generic in G2 so would presumably would work all right

Indeed we showed that supersymmetry automaticaly was broken via gaugino and chiral fermion condensation and simultaneously all moduli were stabilized, in a de Sitter vacuum – calculate the supersymmetry soft-breaking

Lagrangian  precise M

, gluino and wino masses, CPV, etc

No free parameters

Some Discrete Assumptions

o Compactify M-Theory on G₂ manifold in fluxless sector - technically motivated and technically robust

o Compactify to gauge matter group SU(5)-MSSM – can try others o Use generic Kahler potential and gauge kinetic function

o Assume needed mathematical manifolds exist – considerable progress recently

o CC issues not relevant

o M-Theory Solution to Hierarchy Problem th/0606262, PhysRevLett 97(2006)

 Stabilized Moduli, TeV scale, squark masses = gravitino mass, heavy; gaugino masses suppressed 0701034

o Spectrum, scalars heavy, wino-like LSP, large trilinears (no R-symmetry) 0801.0478

o Study moduli, Nonthermal cosmological history– generically moduli  30 TeV so gravitino  30 TeV, squarks  gravitino so squarks  30 TeV 0804.0863

o CP Phases in M-theory (weak CPV OK) and EDMs 0905.2986

o Lightest moduli masses  gravitino mass 1006.3272 (Douglas Denef 2004; Gomez-Reino, Scrucca 2006; Acharya, GK, Kuflik 2010)

o Axions stabilized, strong CP OK, string axions OK 1004.5138 (Acharya, Bobkov, Kumar) o Gluino, Multi-top searches at LHC (also Suruliz, Wang) 0901.336

o Theory, phenomenology of µ in M-theory 1102.0566 via Witten o Baryogenesis, ratio of DM to baryons (also Watson, Yu) 1108.5178

o String-motivated approach to little hierarchy problem, (also Feldman) 1105.3765

 Higgs Mass and BR Predictions 1112.1059 (Kumar, Lu, Zheng) o Generic R-parity conservation (A, L, K, K, Z)

o EDMs

o Gluino, wino, bino LHC, future colliders

Take Higgs physics, superpartner masses more seriously since theory broadly applicable – now focusing on dark matter

Our M-theory papers --Review arXiv:1204.2795 , Acharya, Kane, Kumar

[Acharya, Kane, Vaman, Piyush Kumar, Bobkov, Kuflik, Shao, Lu, Watson, Zheng]

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Important connection between moduli and gravitino: Lightest eigenvalue of moduli mass matrix generically  gravitino mass

[Douglas, Denef 2004; Scrucca et al 2006; Acharya Kane Kuflik 2010]

– top down simple argument, scalar goldstino generically has gravitino mass, and mixes with moduli, so lightest eigenvalue of moduli mass matrix is about gravitino mass

• Moduli couple gravitationally to everything

• Moduli decay (when width  H) dilutes any previous population of DM by factor (T_freezeout/T_decay)³ if entropy conserved in process

[because T 1/a and volume  a³]

• So thermal freezeout occurs, typically at T  20 GeV ^,

but resulting DM diluted by  10

when moduli decay at T  20 MeV , shortly before nucleosynthesis

[first noticed by Moroi, Randall hep-ph/9906527 – generic in string/M theories]

• Moduli have BR to superpartners, axions  ¼ so regenerate DM 

“non-thermal cosmological history”

Possible bonus – Since moduli decay suppresses initial

baryon asymmetry (  1) to give actual baryon asymmetry (10

), and moduli decay also gives DM, perhaps can explain both and ratio [important – highest dimension of non-

renormalizable operators for Affleck-Dine known to be 9]

Solve hierarchy problem fully!

 Basic physics scales – supersymmetry broken (F terms

generated) at about 10¹⁴ GeV, and gravitino mass (M_3/2) is  50 TeV

 Three suppressions from gravitino mass to smaller scales:

* theory predicts gaugino masses (gluino, wino, bino, LSP) suppressed to  TeV because no contribution from F_chi

* “” incorporated into theory, not a parameter, suppressed order of magnitude from gravitino mass

* Radiative Electroweak Symmetry Breaking solutions

common, lightest higgs boson M_h<< M_3/2 ,

explains Higgs

mechanism, EW Symmetry Breaking

GAUGINO MASSES SUPRESSED

M

= K

F



f

f

doesn’t depend on hidden sector chiral

fermions, so term proportional to F

simply absent – F

/F

 V

/V

<<1

18

Visible sector gauge kinetic function

String, KK, etc

And maybe ok

Top-down, gravitino  factor 2

LHC

Squark masses  gravitino mass  tens of TeV GAUGINO MASSES  TeV

arXiv:1408.1961 [Sebastian Ellis, GK, Bob Zheng]

M

 1.5 TeV,

M

 450 GeV , all consistent with current data M

 620 GeV

_gluino 20 fb, wino pairs 20 fb [20fb x 100 fb^—1  2000 events]

Here is where supersymmetry is hiding at LHC

TURN TO DARK MATTER

AXIONS

• Every moduli has an associated axion

• Axions can be DM

• Well-motivated in string/M-theories – many axions, different masses

• Amount of DM depends on “misalignment angle” so can estimate generic amount but not precise amount

• Only change due to non-thermal cosmological history

Bounds on axion “decay constant” relaxed in non-thermal

cosmological histories – relic densities  1 allowed generically

• If axions, generically no observable signals in “indirect detection”

(AMS, Fermi, etc) or in “direct detection” (scattering on nuclei)

• Some good experiments to detect axions, but detected ones and DM ones need not be same

Gravitino mass  50 TeV so lightest moduli mass  50 TeV,

decays before nucleosynthesis – two possibilities for DM from moduli decay:

1. Wimp number density from moduli decay exceeds critical value – then wimp number density annihilates down to critical value H/<v> evaluated at temperature of moduli decay, “non-thermal wimp miracle”

2. Wimp number density from moduli decay below critical value – no further wimp annihilations – allows other DM candidates

So non-thermal history (DM from moduli decay) generic in compactified string theories, and can imply wino or bino or higgsino or other DM with masses  hundred(s) of GeV, TeVs

HIDDEN SECTOR DARK MATTER – work in progress

[Acharya, GK, Kumar, Nelson, Zheng]

o In M-theory, curled up 7D space has 3D submanifolds (“3- cycles”) that generically have orbifold singularities and therefore have particles in gauge groups – tens of them o We live on one, “visible sector”

o Supersymetry breaking due to ones with large gauge groups o Gravitational interactions, same gravitino and moduli for all o Others have their own matter, some stable and DM candidates

– can calculate spectra, relic densities

o Calculations underway: Bob Zheng, Piyush Kumar, Brent

Nelson, Bobby Acharya – already published “classification of dark matter production mechanisms with a non-thermal

cosmological history”, arXiv:1502.05406

o Now analyzing actual hidden sectors systematically for M- Theory

M-theory hidden sector model (analysis not complete):

• QCD-like, hidden sector SU(3) gauge group, 3 flavors of quark (superfields)

• ’_QCD < gravitino mass, so integrate out heavy dark squark fields

•  low energy gauge theory with 3 quark flavors, like QCD

• Expect “dark” baryons, M_baryon  ’_QCD and lightest dark baryon stable

• Expect lighter dark pions, dark proton will annihilate to them

• If dark proton gives full relic abundance then M

M

 1 TeV

• Large annihilation cross sections, probably cascade via dark sector matter, finally to visible sector particles

• (T_reheat is radiation temperature after moduli decay)

• The hidden sectors must have “strong dynamics”, like QCD, if the DM mass is of order few GeV or more – otherwise mass scales generated by radiative breaking will be  M_3/2 so

annihilation rates will be suppressed and universe overclosed

• Visible sector the one with heavy top quark so radiative breaking gives light higgs and gauge bosons – otherwise all have scale set by gravitino mass – one and only one fermion with yukawa coupling of order unity

Constrained here – decays must cascade via hidden sector matter to not be in

conflict – such cascades expected

Bob Zheng,

GK

o Expect many different hidden sectors with different gauge groups

o ’ scales exponentially sensitive to values of gauge couplings at compactification scale, which are determined by volumes of 3- cycles on which the hidden sector lives

o Expect gauge couplings to be uniformly distributed on linear scale

o Then ’ scales uniformly  distributed on log scale, so exponentially separated

o The hidden sector with  ’  TeV will provide dark

matter, while other hidden sectors decay to DM hidden

sector, or give small contributions to DM abundance –

typically several hidden sectors involved

For example,

<v>  4/M²_DM “SU(3) strong dynamics”

T_RH=10 MeV  full relic density for M_DM=800 GeV T_RH=100 MeV  “ 1500 GeV

DM is stable baryon-like particle of G₂ 3-cycle hidden sector annihilates to several visible and hidden sector particles

Don’t lose predictive power – relic abundance still depends

only on mass and v (non-thermal wimp miracle but at moduli reheat temperature), plus moduli mass  reheat temp

Some earlier work – hidden valleys, not really string/M theory sectors – Feng et al -- Major differences – always non-thermal history for M Theory – gravitino and scalars and trilinears  50 TeV for M Theory – will have gravitino mass suppressed

annihilation unless strong dynamics, Goldberger-Trieman size coupling

SIGNATURES

Indirect – yes

-- annihilation into hidden sector matter, cascade to some visible sector matter, gammas, positrons, antiprotons

Direct?

LHC

o gluino or winos produced – all decays in beam pipe o Decays prompt, perhaps signatures with SM particles

and dark light escaping stuff

o Decays slow, then look like escaping usual LSPs.

o No hidden sector production from vector boson fusion

FINAL REMARKS (1)

 String/M-theory too important to be left to string theorists

 String/M-theory may seem complicated – probably it is the simplest framework that could incorporate and explain all the phenomena we want to

understand

 Landscape? – if so, examples already show not an

obstacle to finding descriptions of our world

FINAL REMARKS (2)

 Moduli generically present – probably inevitable in M Theory – imply non-thermal cosmological history

 LHC: gluino  1.5 TeV , wino, bino  0.5 TeV good signatures

 Hidden sector dark matter candidates generic, probably inevitable – can be up to few TeV, or light – relic densities calculable – signatures calculable

o Indirect detection – yes

o Direct detection, maybe not

o LHC – yes, maybe subtle – gluino  LSP  hidden

sector matter