isolated sectors: production and thermalisation · supervisors: john march-russel & subir...

Isolated sectors: production and thermalisation

Hannah TillimSupervisors: J. March-Russell & S. West

Dalitz Seminar, University of Oxford, October 2018

Dark Matter fromPrimordial Black Holes

O. Lennon, J. March-Russell, R. Petrossian-Byrne, H. Tillim,Black Hole Genesis of Dark Matter, JCAP 1804 (2018), arXiv:1712.07664

Hannah Tillim Isolated sectors: production & thermalisation October 11, 2018 1 / 12

Isolated sector DM

• The WIMP paradigm - requires couplingsbetween sectors - much of the parameter spacenow explored

• Important to explore alternatives

“Isolated”

Interactions

with SM purely

gravitational

• Production mechanisms(freeze-out, freeze-in) notapplicable to isolated sectors

• Coupling to gravity →Hawking radiation


Hawking radiation

Hawking temperature:

TBH =M2

Pl

8πMBH

Hawking radiation rate:

d

(dNs,i

dt

)=∑`,h

(2`+ 1)

2π

Γi,s,`,h(ω)

exp(ω/T (t)) + (−1)(2s+1)dω

S. Hawking, Commun.Math.Phys. 43 (1975) 199-220D. Page, Phys. Rev. D13 (1976) 198206


Hawking radiation

→ Ns,i 'fs,igs,i

2eT

(M0

MPl

)2{1 (T0 > mi/ds)

d2sT

20 /m

2i (T0 < mi/ds)

eT =∑i,s

gi,sei,s


Setup

• Model:• Population of micro pBHs with near-uniform initial density n0• Any other initial energy density is SM radiation (no DM)• DM is single species, long-lived, sub-Planckian massive

particles, spin ≤ 2

• Simplifying assumptions:• All Schwarzschild• All masses = M0

• T0 > vW


Setup

dρBH

dt+ 3HρBH = −eT

M4Pl

M2n

dρrad

dt+ 4Hρrad = +eT

M4Pl

M2n

H(t)2 = 8π(ρBH + ρrad)/3M2Pl

dM

dt= −

M4Pl

M2

∑s,i

es,igs,i ≡ −eTM4

Pl

M2

• Fast vs. slow evaporation

• Light vs. heavy DM

• Yield Yi ≡ ni/stot


Light DM results

Y slowi ' 1

2

fs,igs,i

g14∗ e

12T

(MPl

M0

) 12

Y fasti ' 1

2

fs,igs,i

g14∗ eT

(n0

M3Pl

) 14(M0

MPl

) 54

• Y ×mDM = 0.43 eV


Thermalisation

Ongoing work with J. March-Russell, S. West


Thermalisation

• Emitted with non-thermal spectrum and very high energy tail

• Underpopulated compared to equilibrium density

• Require redistribution of energy (2→ 2) and particle creation(2→ 3 ...)

Kinetic f(p) = 1/(exp[−(E − µ)/T ]± 1)Thermal Ti = TChemical

∑µini =

∑µfinj

• Other studies in this direction: S. Davidson & S. Sarkar arXiv:0009.078v3; M.Garny et. al. arXiv:1810.01428, S. Heeba; F. Kahlhoefer & P. Stocker arXiv:1809.04849, ....


Thermalisation

• Kinetic, thermal and ‘partial chemical’ → evolution to fullchemical

• Boltzmann equation governs evolution - depends on a collisionterm we can parameterise in many classes of models as:

n+ 3Hn =g

π2An

(T

M

)αT 4(Z2 − Z3)

Z = eµ/T , Z0 << 1→ Zeq = 1


Thermalisation: interim results


What’s next

• Robust model-independent framework for estimatingthermalisation timescales

• Concrete pheno of permanently underpopulated sectors

• Application to pBH production model to reopen light DM case

Thank you!


1

Rudin Petrossian-Byrne

Supervisors: John March-Russel & Subir Sarkar

October 2018

Dark matter and Baryogenesis from primordial black holes

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SM + DM from PBHs continued…Constraints: Free streaming!

Baryogenesis from Hawking radiationHR as tunnelling!

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OVERVIEW

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Constraints

Reheat temperature for BBN physics

Theoretical consistency

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Constraints: Free Streaming

For successful structure formation impose< 10% of DM relativistic when the SM plasma

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T ≈ 1 keV

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For successful structure formation impose< 10% of DM relativistic when the SM plasma T ≈ 1 keV

time

Instantaneous emission

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For successful structure formation impose< 10% of DM relativistic when the SM plasma T \sim 1 keV

time


Integrated spectrum at

‘fast’

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For successful structure formation impose< 10% of DM relativistic when the SM plasma T \sim 1 keV

time


Integrated spectrum at

‘fast’

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time

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time

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time

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time

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time

s=2

s=0

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s = 0, 1/2 excluded

s = 3/2 marginal at best s = 2 naively survives

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So far

mass

‘Heavy’ DM

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‘Heavy’ DM

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‘Heavy’ DM

Free streaming provides no extra constraint!

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Baryogenesis from PBHs

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Baryogenesis from PBHs

BHs violate all global charges

It is sufficient to provide an energy incentive to the BH to preferentially emit + over – charge

Environment can provide a chemical potential, e.g.Cohen & Kaplan (1988)Hook (2015)

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Hawing radiation as tunnellingParikh & Wilczek (1999)

WKB

is the classical action. horizon

r

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WKB


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Relativistic Hamilton – Jacobi equation

Gullstrand–Painlevé time

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WKB


r


Gullstrand–Painlevé time

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--

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Parikh & Wilczek (1999)

WKB


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Hawing radiation as tunnelling

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Parikh & Wilczek (1999)

WKB


r


Hawing radiation as tunnelling

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only time derivative matters!

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Asymmetry generation

Currently & in future looking at lots of interesting phenomenology!

e.g. - asymmetric dark matter scenarios

- properties of

. . . . . . much more

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Thank you!

where’s Rudin?www.jackfm.co.uk/news

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Thank you!

www.jackfm.co.uk/newsthere’s Rudin

Precision measurements of PDFs at the LHCSHAUN BAILEY

SUPERVISOR: LUCIAN HARLAND-LANG

1

Outline▪Basics: ▪What are PDFs?

▪Why are they useful?

▪How are PDFs fitted?

▪HL-LHC

▪𝑡 ҧ𝑡 fits

▪NNLO DIS

2

Basics

3

What are PDFs?

▪QCD factorization theorem allows us to split DIS/hadron collisions into low and high energy parts

▪Low energy is universal

▪High energy is calculable

𝑓(𝑥, 𝑄2)

ො𝜎(𝑥, 𝑄2)

4

𝑙𝑙′

𝛾/𝑊/𝑍

𝑝

𝑞

Why are PDFs useful?

gt

Ht

g g

g

X

5

High energy ⇒ high 𝑥

Resonant state

Errors increase as mass increases

How do we fit PDFs?

NNPDF MMHT CT HERA …..

HessianMonte Carlo

Global fits More restricted data sets

Theory, 𝜎 𝑥, 𝑄2

Data

𝜒2Minimise

New parameter set

Applgrid / fastNLO grid

Parameter set

ෝ𝜎 𝑥, 𝑄2

𝑓 𝑥, 𝑄2

6

HL-LHC

7

HL-LHC

▪Operating between ~ 2026-2038

▪ℒ = 3 ab−1 for ATLAS and CMS, ℒ = 0.3 ab−1 for LHCb

▪Any theory prediction will require a prediction of the PDFs at HL-LHC

8

Shortened version will appear in the HL-LHC Yellow Report

Collaboration between NNPDF, MMHT and CT

arXiv: 1810.03639

HL-LHCWant to generate pseudo-data (fake data) to quantify the predicted affect of the HL-LHC on PDFs

9

Statistics

stat ~ 𝑁

𝑁~𝑎ℒ𝜕𝜎

𝜕𝑥Δ𝑥

𝑎 = 𝐵𝑟 ×𝑁𝑜𝑏𝑠

𝑁𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑

Systematics

𝐹 = 𝑓corr × 𝑓red

sys 14 TeV ~ 𝐹 × sys 8/13 TeV

𝑓𝑐𝑜𝑟𝑟 = 0.5, 𝑓𝑟𝑒𝑑 = 0.2 − 1 (8 TeV)

HL-LHC

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High 𝑥 gluon Strange quark

High 𝑥 gluon + valence quarks Mid 𝑥 gluon + antiquarks

Flavour separation

Mid 𝑥 gluon

Hessian Profiling

Expand theory around minimum:

𝜎𝑖 → 𝜎𝑖 +

𝛼

𝛽𝑖𝛼𝜆𝛼

Δ𝜒2 =

𝑖𝑗

𝐷𝑖 − 𝜎𝑖 −

𝛼

𝛽𝑖𝛼𝜆𝛼 cov 𝑖𝑗−1 𝐷𝑗 − 𝜎𝑗 −

𝛾

𝛽𝑗𝛾𝜆𝛾 + 𝑇2

𝛼

𝜆𝛼2

DataOther data

setsError from

data

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𝜒2 = 𝜒02 + 𝑧𝑖𝑧𝑖 𝑧𝑖 = 𝑇 → Error PDF

HL-LHC

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▪ Good overall reduction▪ Mostly independent of the value of 𝐹▪ Reduction dominated by increased statistics

*Phenomenology plots available

My work has been to:▪ Generate the pseudo-data▪ Perform the profiling

HL-LHC▪Do not know full extent of correlations

▪In reality, data sets may be inconsistent and may disagree with each other

▪We have only selected a subset of processes

▪New techniques could be developed before the HL-LHC data is released

▪New processes might be considered

▪May expand formalism to LHeC

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𝑡 ҧ𝑡

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𝑡 ҧ𝑡

gt

tg

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▪ 8TeV, lepton + jet channel at ATLAS▪ First time differential distributions

used in MMHT▪ Should constrain high 𝑥 gluon PDF

High energy

𝑡 ҧ𝑡

𝜒2/𝑁

Baseline Fit

𝑝𝑇 3.88 → 3.26

𝑦𝑡 3.41 → 2.76

𝑦𝑡 ҧ𝑡 4.77 → 3.10

𝑀𝑡 ҧ𝑡 3.41 → 2.69

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Impact at high 𝑥 Reduction of errors High 𝜒2 values

𝑡 ҧ𝑡

𝜒2/𝑁

Correlated Decorrelated

𝑝𝑇 3.26 → 0.90

𝑦𝑡 2.73 → 1.24

𝑦𝑡 ҧ𝑡 3.10 → 1.99

𝑀𝑡 ҧ𝑡 2.69 → 0.69

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𝜒2 values still highStable gluon Further reduction of errors

𝑡 ҧ𝑡▪The total rapidity data is also inconsistent with correlation model

▪Try to decorrelate along 𝑦𝑡𝑡, however unsuccessful

▪We need a more flexible description of two-point correlators

▪We can use di-lepton data which has reduced QCD related errors

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DIS

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DIS and the strange quark

μ

s,d

c

s,d

νμ μ

νμ

WW

▪ Neutrino induced DIS at CCFR/NuTeV

▪ Searching for dimuon signal▪ Tension with ATLAS W/Z data▪ New NNLO calculations could

resolve this?

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DIS: GM-VFS▪Two different schemes

▪FFS – No charm PDF, production of charm only through gluon

▪ZM-VFS – Charm PDF included

▪Need to combine both but NNLO calculation only for FFS

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μνμ

W

W

μ

νμ

s,d

s,dc

c

g𝑚𝑐 ∼ 𝑄

𝑚𝑐 ≪ 𝑄

Thanks for you attention

Any questions?

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Backup slides

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Pheno - Higgs

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Pheno – Dijets + Diphoton

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Pheno – supersymmetry

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Luminosities

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2d Quantum Gravity and Matter

Praveen Xavier

October 11, 2018

Introduction

I Lorentzian GR has a causal structure

(i.e it has no closedtime-like or null paths and any causal diamond between twopoints has no ”missing points”).

I Such space-times are said to be globally hyperbolic.

I For the theory of QG to have a semi-classical limit with thisbehaviour, it might be a good idea to build this feature intothe space-times in the path integral. So, we consider onlyglobally hyperbolic spacetimes in the path integral.

Introduction

I Lorentzian GR has a causal structure (i.e it has no closedtime-like or null paths and any causal diamond between twopoints has no ”missing points”).



Introduction



I For the theory of QG to have a semi-classical limit with thisbehaviour, it might be a good idea to build this feature intothe space-times in the path integral.

So, we consider onlyglobally hyperbolic spacetimes in the path integral.

Introduction




Time slices

If the space-time is globally hyperbolic, there must exist a causalcurve connecting any point to an initial-value space-likehypersurface.

Figure: A causal curve connecting the point P to a space-likehypersurface

I Vice versa, all points can be reached by evolving aninitial-value hypersurface in time.

I It’s then clear that such a space-time will possess a global,proper-time slicing.

Figure: Proper-time slices

2d

My work has been in 2d. So let’s specialize and consider thismodel in 2d.

The action in 2d is:

S = −λVolM + topological term

To discretize, we propose to construct the surface using

I flat equilateral Lorentzian triangles

with 1 space-like edge (of length-squared a2) and 2 time-likeedges (of length squared −a2).

I This model of QG (without matter) in 2d is called the CausalDynamical Triangulation (CDT) model.

2d

My work has been in 2d. So let’s specialize and consider thismodel in 2d. The action in 2d is:

S = −λVolM + topological term

To discretize, we propose to construct the surface using

I flat equilateral Lorentzian triangles

with 1 space-like edge (of length-squared a2) and 2 time-likeedges (of length squared −a2).

I This model of QG (without matter) in 2d is called the CausalDynamical Triangulation (CDT) model.

2d

We start with a discrete initial line:

2d

We start with a discrete initial line: Then we add our flatequilateral triangles to evolve the line to one at a later time:

The area of one of these fundamental triangles is A =√

5a2

4 .

Therefore, the discrete version of the action is:

Sdscrte = −λN(T )A

where N(T ) is the number of triangles of the triangulation T .

I The geodesic distance is the shortest graph distancebetween any two points. Hence, each triangulation uniquelyspecifies an equivalence class of metric configurations.

The area of one of these fundamental triangles is A =√

5a2

4 .Therefore, the discrete version of the action is:

Sdscrte = −λN(T )A

where N(T ) is the number of triangles of the triangulation T .

I The geodesic distance is the shortest graph distancebetween any two points. Hence, each triangulation uniquelyspecifies an equivalence class of metric configurations.

Matter and DimersClassically, matter couples to the geometry via the metric and itsdescendants.

We propose to imitate matter at the classical level,by placing ”dimers” across two triangles, with the rule that theycannot meet on the face of any triangle.

I The latter rule ensures that the new degrees of freedomcouple to the geometry of the triangulation. Such dimers arereferred to as hard.

I Let’s refer to this dimer model as CDT-D

Matter and DimersClassically, matter couples to the geometry via the metric and itsdescendants. We propose to imitate matter at the classical level,by placing ”dimers” across two triangles, with the rule that theycannot meet on the face of any triangle.

I The latter rule ensures that the new degrees of freedomcouple to the geometry of the triangulation. Such dimers arereferred to as hard.

I Let’s refer to this dimer model as CDT-D

Dimer action

In the presence of dimers, we add to the action a termproportional to the number of dimers:

S = −λN(T )A+αN(D)

where N(D) is the number of dimers of a dimer configuration D.Therefore, the weight of a CDT-D configuration is:

Exp(iS) = Exp [−iλN(T )A + iαN(D)] =: gN(T )ξN(D)

where, g := Exp(−iλA) and ξ := Exp (iα)

Dimer action



where N(D) is the number of dimers of a dimer configuration D.

Therefore, the weight of a CDT-D configuration is:



Dimer action




Exp(iS)

= Exp [−iλN(T )A + iαN(D)] =: gN(T )ξN(D)


Dimer action




Exp(iS) = Exp [−iλN(T )A + iαN(D)]

=: gN(T )ξN(D)


Dimer action






Partition Function

The partition function (PF) of this model is the sum of theweight over all possible CDT-D configurations:

Z (g , ξ) =∑{T ,D}

gN(T )ξN(D) =∑

k

gk

∑l

ξl∑{Tk ,Dl}

1

where {T ,D} is the set of all CDT-D configurations and {Tk ,Dl}

is the set of CDT-D configs. with k triangles and l dimers.

I The radius of convergence of the power sum in g is it’scritical value denoted gc(ξ).

I At gc(ξ), the PF, Z (gc , ξ) behaves non-analytically.

I A critical point can be characterized by it’s Hausdorffdimension dH:

〈Area(R)〉∝RdH

Partition Function


Z (g , ξ) =∑{T ,D}

gN(T )ξN(D) =

∑k

gk

∑l

ξl∑{Tk ,Dl}

1






〈Area(R)〉∝RdH

Partition Function


Z (g , ξ) =∑{T ,D}

gN(T )ξN(D) =∑

k

gk

∑l

ξl∑{Tk ,Dl}

1

where {T ,D} is the set of all CDT-D configurations and {Tk ,Dl}is the set of CDT-D configs. with k triangles and l dimers.




〈Area(R)〉∝RdH

Partition Function


Z (g , ξ) =∑{T ,D}

gN(T )ξN(D) =∑

k

gk

∑l

ξl∑{Tk ,Dl}

1






〈Area(R)〉∝RdH

Labelled Trees

It was observed that CDT-D configurations have a bijection withlabelled trees (tree graphs with vertices carrying labels).

Figure: The tree that corresponds to a CDT-D configuration

Restricted Dimer Model

It turns out that these trees are non-local (i.e branches which donot share a root are nonetheless correlated).

I A ban on CDT-D configurations which are mapped tonon-local trees

I A ban on dimers falling across two backward triangles

Figure: Banned dimer type

In this restricted CDT-D model one can use the generatingfunctions of labelled trees to calculate Z (g , ξ).

A Summary of my work

There are 2 main things that I worked on and completed:

I Solving the un-restricted CDT-D model

I Finding the continuum propagator in the restricted CDT-Dmodel

The un-restricted dimer modelOne of the restrictions lifted was the ban on:

Figure: The now integrated dimer type

I One does not find any new critical points.

I The previously known result holds: there are values of ξ forwhich the PF has a cube-root singularity as g→gc withdH = 3 and 3/2 and others where the PF has a square-rootsingularity with dH = 2. The dH = 2 points corresponds topure CDT.

I Recently solved the model with the non-local trees too.Maybe this will have new critical points?




I The previously known result holds: there are values of ξ forwhich the PF has a cube-root singularity as g→gc

withdH = 3 and 3/2 and others where the PF has a square-rootsingularity with dH = 2. The dH = 2 points corresponds topure CDT.





I The previously known result holds: there are values of ξ forwhich the PF has a cube-root singularity as g→gc withdH = 3 and 3/2

and others where the PF has a square-rootsingularity with dH = 2. The dH = 2 points corresponds topure CDT.





I The previously known result holds: there are values of ξ forwhich the PF has a cube-root singularity as g→gc withdH = 3 and 3/2 and others where the PF has a square-rootsingularity with dH = 2.

The dH = 2 points corresponds topure CDT.





I The previously known result holds: there are values of ξ forwhich the PF has a cube-root singularity as g→gc withdH = 3 and 3/2 and others where the PF has a square-rootsingularity with dH = 2. The dH = 2 points corresponds topure CDT.


The Propagator

I The propagator, Gg ,ξ(l1, l2; t) is the transition amplitudefrom a loop of length l1 to one of length l2 in t time-steps.

I This can be calculated using the same labelled treetechniques

The Continuum limit

I We send a→ 0, keeping the physical time and boundarylengths, T := at; L1 := al1; L2 := al2 constant.

I Which means {t, l1, l2} → ∞, simultaneously.

I Hence, the weight of large graphs can’t be suppressed.

I So we must tune g to the radius of convergence gc(ξ) ofthe sum.

I The scaling behaviour of the approach to the critical value istaken to be (dH > 0):

g − gc ∝ adH Λ

I Λ: bulk cosmological constant.

I Finally the continuum propagator is obtained by:

GΛ(L1, L2;T ) = lima→0

aG(gc+adH Λ),ξ

(L1

a,L2

a;T

a

)

I Laplace transform in (L1, L2)→ (X,Y)

I GΛ(L1, L2;T )→ GΛ(X ,Y ;T )

I X and Y: boundary cosmological constants.

ResultsAround the critical point where dH = 3, the asymptotics of thecontinuum propagator is:

GΛ(X ,Y ,T →∞) =12Λ2/3e−

√3 3√ΛT

(√3 sin

(3√

ΛT)− cos

(3√

ΛT))

5(

3√

Λ + X)2 (

3√

Λ + Y)

GΛ(X ,Y ,T → 0) =2T

5

Laplace====⇒ 2T

5δ(L1)δ(L2)

The result from 2000 for the asymptotics of the continuumpropagator for pure CDT (the point with dH = 2) is:

GΛ(X ,Y ;T →∞) =4Λe−2

√ΛT

(√

Λ + X )2(√

Λ + Y )

GΛ(X ,Y ;T → 0) =1

X + Y

Laplace====⇒ δ(L1 − L2)

isolated sectors: production and thermalisation · supervisors: john march-russel & subir...

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