Baryogenesis and Dark Matter from B Mesons

Miguel Escudero Abenza [email protected]

Based on arXiv:1810.00880 Phys. Rev. D 99, 035031 (2019) with: Gilly Elor & Ann Nelson BLV19 24-10-2019

DARKHORIZONS The Universe Baryonic Matter

5 %

26 % Dark Matter

69 % Dark Energy

Planck 2018 1807.06209

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 2 SM Prediction:

Neutrinos

40 %

60 %

Photons

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 3 The Universe Baryonic Matter

5 %

26 % Dark Matter

69 % Dark Energy

Planck 2018 1807.06209

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 4 Baryogenesis and Dark Matter from B Mesons

arXiv:1810.00880 Elor, Escudero & Nelson

1) Baryogenesis and Dark Matter are linked

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 5 Baryogenesis and Dark Matter from B Mesons

arXiv:1810.00880 Elor, Escudero & Nelson

1) Baryogenesis and Dark Matter are linked

2) Baryon asymmetry directly related to B-Meson observables

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 5 Baryogenesis and Dark Matter from B Mesons

arXiv:1810.00880 Elor, Escudero & Nelson

1) Baryogenesis and Dark Matter are linked

2) Baryon asymmetry directly related to B-Meson observables

3) Leads to unique collider signatures

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 5 Baryogenesis and Dark Matter from B Mesons

arXiv:1810.00880 Elor, Escudero & Nelson

1) Baryogenesis and Dark Matter are linked

2) Baryon asymmetry directly related to B-Meson observables

3) Leads to unique collider signatures

4) Fully testable at current collider experiments

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 5 Outline 1) The Mechanism 1) C/CP violation 2) Out of equilibrium 3) Baryon number violation?

2) A Minimal Model

3) The Cosmology

4) Implications for Collider Experiments

5) Dark Matter Phenomenology

6) Summary and Outlook

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 6 Baryogenesis The three Sakharov Conditions (1967):

1) C and CP violation

2) Out of equilibrium

3) Baryon number violation

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 7 Baryogenesis from B Mesons 1) C and CP violation

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 8 Baryogenesis from B Mesons 1) C and CP violation The key quantity: the semileptonic asymmetry,

q B0 f B0 f¯ Aq =Im 12 = q ! q ! `` M q B0 f + B0 f¯ ✓ 12 ◆ q ! q !

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 8 Baryogenesis from B Mesons 1) C and CP violation The key quantity: the semileptonic asymmetry,

q B0 f B0 f¯ Aq =Im 12 = q ! q ! `` M q B0 f + B0 f¯ ✓ 12 ◆ q ! q ! s 5 A`` SM =(2.22 0.27) 10 small because | ± ⇥ 2 Standard Model d 4 (mb/mt) is small A =( 4.7 0.6) 10 ``|SM ± ⇥

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 8 Baryogenesis from B Mesons 1) C and CP violation The key quantity: the semileptonic asymmetry,

q B0 f B0 f¯ Aq =Im 12 = q ! q ! `` M q B0 f + B0 f¯ ✓ 12 ◆ q ! q ! s 5 A`` SM =(2.22 0.27) 10 small because | ± ⇥ 2 Standard Model d 4 (mb/mt) is small A =( 4.7 0.6) 10 ``|SM ± ⇥ s 3 A =( 0.6 2.8) 10 `` ± ⇥ (World averages, Measurements d 3 HFLAV) A =( 2.1 1.7) 10 `` ± ⇥

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 8 Baryogenesis from B Mesons 1) C and CP violation The key quantity: the semileptonic asymmetry,

q B0 f B0 f¯ Aq =Im 12 = q ! q ! `` M q B0 f + B0 f¯ ✓ 12 ◆ q ! q ! s 5 A`` SM =(2.22 0.27) 10 small because | ± ⇥ 2 Standard Model d 4 (mb/mt) is small A =( 4.7 0.6) 10 ``|SM ± ⇥ s 3 A =( 0.6 2.8) 10 `` ± ⇥ (World averages, Measurements d 3 HFLAV) A =( 2.1 1.7) 10 `` ± ⇥

• Plenty of BSM models can enlarge the asymmetries up to 10-3: SUSY, Extradim, LR, 2HDM, new generations, Leptoquarks, Z' models (see e.g. 1511.09466, 1402.1181).

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 8 Baryogenesis from B Mesons 2) Out of equilibrium and production of B Mesons

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 9 Baryogenesis from B Mesons 2) Out of equilibrium and production of B Mesons • Require the presence of an out of equilibrium particle that dominates the energy density of the Universe and reheats it to a temperature of T = (10 MeV) RH O

• This particle should be very weakly coupled, with lifetimes 3 ⌧ = (10 s) O

• The decays don't spoil BBN or the CMB provided TRH > 5 MeV de Salas et al. 1511.00672 Hasegawa et al. 1908.10189

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 9 Baryogenesis from B Mesons 2) Out of equilibrium and production of B Mesons ¯b • Scalar particle with m 11 100 GeV and 3 2 ⌧ = (10 s) generically decays into b-quarks O b

b-quarks Hadronize at T

e± e± • Coherent oscillations in the B0 system are maintained in the early Universe for Temperatures:

T . 20 MeV B0 B0

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 10 Baryogenesis and DM from B Mesons

3) Baryon number violation?

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 11 Baryogenesis and DM from B Mesons

3) Baryon number violation? •Baryon number is conserved in our scenario: B =0 In a similar spirit to Hylogenesis, Davoudiasl, Morrissey, Sigurdson, Tulin 1008.2399

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 11 Baryogenesis and DM from B Mesons

3) Baryon number violation? •Baryon number is conserved in our scenario: B =0 In a similar spirit to Hylogenesis, Davoudiasl, Morrissey, Sigurdson, Tulin 1008.2399

•We make Dark Matter an anti-Baryon and generate an asymmetry between the two sectors thanks to the CP violating oscillations and subsequents decays of B-mesons.

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 11 Baryogenesis and DM from B Mesons

3) Baryon number violation? •Baryon number is conserved in our scenario: B =0 In a similar spirit to Hylogenesis, Davoudiasl, Morrissey, Sigurdson, Tulin 1008.2399

•We make Dark Matter an anti-Baryon and generate an asymmetry between the two sectors thanks to the CP violating oscillations and subsequents decays of B-mesons.

Visible Sector Dark Sector (Baryons) (anti-Baryons)

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 11 Baryogenesis and DM from B Mesons

3) Baryon number violation? •Baryon number is conserved in our scenario: B =0 In a similar spirit to Hylogenesis, Davoudiasl, Morrissey, Sigurdson, Tulin 1008.2399

•We make Dark Matter an anti-Baryon and generate an asymmetry between the two sectors thanks to the CP violating oscillations and subsequents decays of B-mesons.

•Require a new decay mode of the B meson into DM and a visible Baryon!

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 11 A Summary of the Mechanism

Out of equilibrium B-mesons decay into CP violating Oscillations late time decay Dark Matter and hadrons

+ 0 0 ⇠ Dark Matter ¯b B Bd Bs anti-Baryon B

¯0 ¯0 b B Bd Bs ⇤ Baryon

d s TRH 20 MeV A A BR(B ⇠ + Baryon + ...) ⇠ `` `` ! Baryogenesis Dark Matter and 11 2 Y =8.7 10 ⌦ h =0.12 B ⇥ DM

q 0 With the Baryon asymmetry: YB A Br(B ⇠+ Baryon + X) / `` ⇥ q ! qX=s,d Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 12 New B-Meson decay

c c 1.2 GeV . m, ⇠ . 2.5 GeV y Y ⇤ ub¯ y Y ¯ s +h.c (McKeen et. al.) L ub s (anti Baryon)

mY > 1 TeV Dark Matter (4-jet/squark) ⇠ SM Singlets Y: Colored Triplet Scalar Y (3, 1, 1/3) Y ⇠ s

¯ u b Baryon 0 ⇤ Bd d d

4 4 3 mB m 1 TeV pyuby s Br(B ⇠ + Baryon) 10 ! ' 2 GeV m 0.53 ✓ ◆ ✓ Y ◆ Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 13 Any room for a new decay mode? Targeted decay modes are very constrained/well measured:

+ + 5 B-Factories Br(B K ⌫⌫¯ ) < 10 ! 0 + 9 LHC Br(B µ µ)=(2.7 0.6) 10 s ! ± ⇥

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 14 Any room for a new decay mode? Targeted decay modes are very constrained/well measured:

+ + 5 B-Factories Br(B K ⌫⌫¯ ) < 10 ! 0 + 9 LHC Br(B µ µ)=(2.7 0.6) 10 s ! ± ⇥

But our decay mode has not been targeted! B ⇠ + Baryon !

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 14 Any room for a new decay mode? Targeted decay modes are very constrained/well measured:

+ + 5 B-Factories Br(B K ⌫⌫¯ ) < 10 ! 0 + 9 LHC Br(B µ µ)=(2.7 0.6) 10 s ! ± ⇥

But our decay mode has not been targeted! B ⇠ + Baryon ! What about the total width of B-Mesons?

Measurement: Br(B+ c¯ + X) = (97 4)% ! ± Most stringent current constraint: Br(B ⇠ + Baryon + X) < 10% !

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 14 Any room for a new decay mode? Targeted decay modes are very constrained/well measured:

+ + 5 B-Factories Br(B K ⌫⌫¯ ) < 10 ! 0 + 9 LHC Br(B µ µ)=(2.7 0.6) 10 s ! ± ⇥

But our decay mode has not been targeted! B ⇠ + Baryon ! What about the total width of B-Mesons?

Measurement: Br(B+ c¯ + X) = (97 4)% ! ± Most stringent current constraint: Br(B ⇠ + Baryon + X) < 10% ! Ongoing searches with Belle-II data

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 14 The Boltzmann Equations

1 da 2 8⇡ Universe's Evolution H2 = (⇢ + m n ) ⌘ a dt 3m2 rad ✓ ◆ Pl

dn Late time Decay +3Hn = n and dt d⇢ Radiation rad +4H⇢ = m n dt rad

dn⇠ 2 2 B B +3Hn = v (n n )+2 n Br(B ⇠ + Baryon + X) dt ⇠ h i⇠ ⇠ eq,⇠ ⌘ ⇥ ! dn B q 0 q DM evolution +3Hn = v (n n ? n n ? )+ n [1 + A Br(¯b B ) f ] dt h i eq, eq, ⇥ `` ! q deco q X dn? B q 0 q +3Hn ? = v (n n ? n n ? )+ n [1 A Br(¯b B ) f ] dt h i eq, eq, ⇥ `` ! q deco q X

dn Baryon asymmetry: B +3Hn =2 n Br(¯b B0) f q Aq Br(B ⇠ + Baryon + X) dt B ! q deco `` ! n = n n ? q B X • Baryon asymmetry directly related to the CP violation in the B0 system and to the new decay of B mesons to a visible Baryon and missing energy. • We take into account the decoherence of the B0 system in the early Universe.

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 15 s Parameter Space A`` =0 All points correspond to the observed baryon asymmetry

4 Br(B ⇠ + Baryon + X)=5 10 0.1 Baryogenesis requires: d ! 5 3 ⇥ A = 10 10 `` Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 16 Dark Matter Phenomenology

? ? ⇠ ⇠ Since ⇠ ⇠ 1.2 GeV . m, ⇠ . 2.5 GeV ? ⇠ ⇠

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 17 Dark Matter Phenomenology

• Relic abundance obtained with: ⌦ h2 =0.12 v 25 v min[m ,m ]/GeV DM h idark ' h iWIMP ⇠

? ? ⇠ ⇠ Since ⇠ ⇠ 1.2 GeV . m, ⇠ . 2.5 GeV ? ⇠ ⇠

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 17 Dark Matter Phenomenology

• Relic abundance obtained with: ⌦ h2 =0.12 v 25 v min[m ,m ]/GeV DM h idark ' h iWIMP ⇠

• What kind of Dark Sector could allow for such cross sections but being compatible with the very strong constraints from the CMB observations?

Our scenario: Non-thermal DM See update in Planck 2018 1807.06209

Thermal relic Laene et al. 1805.10305

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 17 Possible Dark Sectors

1) Annihilation into Sterile Neutrinos 0711.4866 Pospelov, Ritz, Voloshin

The annihilation can be predominantly p-wave: 1607.02373, ME, Rius, Sanz

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 18 Possible Dark Sectors

1) Annihilation into Sterile Neutrinos 0711.4866 Pospelov, Ritz, Voloshin

The annihilation can be predominantly p-wave: 1607.02373, ME, Rius, Sanz

2) Annihilation into Active Neutrinos González-Macias, Illana and Wudka, 1506.03825,1601.05051, Blennow et. al. 1903.00006 Constraints on dark matter annihilating to neutrinos are very mild: Beacom, Bell, Mack astro-ph/0608090

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 18 Possible Dark Sectors

1) Annihilation into Sterile Neutrinos 0711.4866 Pospelov, Ritz, Voloshin

The annihilation can be predominantly p-wave: 1607.02373, ME, Rius, Sanz

2) Annihilation into Active Neutrinos González-Macias, Illana and Wudka, 1506.03825,1601.05051, Blennow et. al. 1903.00006 Constraints on dark matter annihilating to neutrinos are very mild: Beacom, Bell, Mack astro-ph/0608090

3) Additional particles carrying baryon number

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 18 Possible Dark Sectors

1) Annihilation into Sterile Neutrinos 0711.4866 Pospelov, Ritz, Voloshin

The annihilation can be predominantly p-wave: 1607.02373, ME, Rius, Sanz

2) Annihilation into Active Neutrinos González-Macias, Illana and Wudka, 1506.03825,1601.05051, Blennow et. al. 1903.00006 Constraints on dark matter annihilating to neutrinos are very mild: Beacom, Bell, Mack astro-ph/0608090

3) Additional particles carrying baryon number ? + + ? • New scalar Baryon with B = 1/3: ! A A A + ? + ? A ! A A 5 Which in order to get ⌦ DM / ⌦ b =5 . 36 will require m mp 1.6 GeV • A ⇠ 3 ⇠ • Gives an understanding for the observed Dark Matter to Baryon energy density ratio.

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 18 Summary

Baryogenesis and Dark Matter from B-mesons: • Which actually relates the CP violation in the B0 system to Baryogenesis • Baryon number is conserved and hence Dark Matter is anti-Baryonic

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 19 Summary

Baryogenesis and Dark Matter from B-mesons: • Which actually relates the CP violation in the B0 system to Baryogenesis • Baryon number is conserved and hence Dark Matter is anti-Baryonic

Distinct experimental signatures: ds 5 • Positive leptonic asymmetry in B meson decays A`` > 10 • Neutral and charged B mesons decay into baryons and missing energy 4 Br(B ⇠ + Baryon + X) > 2 10 ! ⇥

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 19 Summary

Baryogenesis and Dark Matter from B-mesons: • Which actually relates the CP violation in the B0 system to Baryogenesis • Baryon number is conserved and hence Dark Matter is anti-Baryonic

Distinct experimental signatures: ds 5 • Positive leptonic asymmetry in B meson decays A`` > 10 • Neutral and charged B mesons decay into baryons and missing energy 4 Br(B ⇠ + Baryon + X) > 2 10 ! ⇥ Ongoing search for this process at Belle-II! B-factories should test this scenario given the constraints on other missing energy channels: + + 5 Br(B K ⌫⌫¯ ) < 10 !

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 19 Summary

Baryogenesis and Dark Matter from B-mesons: • Which actually relates the CP violation in the B0 system to Baryogenesis • Baryon number is conserved and hence Dark Matter is anti-Baryonic

Distinct experimental signatures: ds 5 • Positive leptonic asymmetry in B meson decays A`` > 10 • Neutral and charged B mesons decay into baryons and missing energy 4 Br(B ⇠ + Baryon + X) > 2 10 ! ⇥ Ongoing search for this process at Belle-II! B-factories should test this scenario given the constraints on other missing energy channels: + + 5 Br(B K ⌫⌫¯ ) < 10 ! The mechanism is fully testable at current collider experiments!

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 19 Outlook Theory •Are the flavor anomalies in b → s transitions related to our required positive semileptonic asymmetry?

Given that Leptoquarks and Z' models induce mass mixing in the Bs system and hence alter the semileptonic asymmetry.

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 20 Outlook Theory •Are the flavor anomalies in b → s transitions related to our required positive semileptonic asymmetry?

Given that Leptoquarks and Z' models induce mass mixing in the Bs system and hence alter the semileptonic asymmetry.

•What kind of UV theory contains our required heavy colored triplet scalar plus our dark matter particles at the GeV scale?

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 20 Outlook Theory •Are the flavor anomalies in b → s transitions related to our required positive semileptonic asymmetry?

Given that Leptoquarks and Z' models induce mass mixing in the Bs system and hence alter the semileptonic asymmetry.

•What kind of UV theory contains our required heavy colored triplet scalar plus our dark matter particles at the GeV scale?

Field Spin QEM Baryon no. Z2 Mass

0 0 0 +1 11 100 GeV E.g.: SUSY, 1907.10612 Y 0 1/3 2/3 +1 (TeV) squark Alonso-Álvarez, Elor, Nelson, Xiao O 1/2 0 1 +1 (GeV) Dirac Bino SEE GONZALO'S POSTER! O ⇠ 1/2 0 0 1 (GeV) O SUSY chiral 0 0 1 1 (GeV) O multiplet

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 20 Thank You! ⇠ B

⇤

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 21 Back Up

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 22 4.3 Elastic scattering of e±B e±B . 0 ! 0 As the B0 is neutral pseudoscalar particle the only possible interaction that an electron can have with it is through the e↵ective charge distributed within the B0. This charge distribution is parametrized 2 2 in terms of a an elastic electromagnetic form factor FB0 (q ). The actual form of FB0 (q )requires either data (which is not possible to get in the laboratory for this reaction) or some modelling of the quarks4.3 Elastic distributed scattering within the of eB±Bmeson.0 e±B Actually0. the form factors are usually parametrized in terms 0 ! ofAs the the chargeB0 is neutral radius whichpseudoscalar is defined particle as the only possible interaction that an electron can have with it is through the e↵ective charge distributed within the2 B . This charge distribution is parametrized 2 dF (q ) 0 r =6 2 2 . 2 (4.1) in terms of a an elastic electromagnetic form factordq FB0 (q ). The actual form of FB0 (q )requires 1.5 q=0 excluded at CL > 0.95  either data (which is not possible to get⌦ in↵ the laboratory for this reaction) or some modelling of the 4.6 evolutionWhichexcluded area for has a CL neutral> 0.95 particle leads to 4.6 evolutionquarks distributed withinγ the2.2B0 meson. Flavor Actually in the form Standard factors are Model usually parametrized in terms 1.0of the charge radius which is defined as 2 1 2 2 ∆m &F ∆(qm)= r q + ... (4.2) At some high temperature aboveThem spontaneousd , wes assume symmetry6 breaking that of thewas SM allows in thermal the quarks to equilibrium acquire mass via with the plasma, dF (q2) At some highsin temperature 2β2 above Yukawam,interactions we2 assume with⌦ the that↵ Higgs field,was without in breaking thermal gauge2 equilibrium invariance: 2 with the plasma, fixing its numberSince r densityis not measured, for T wem use antor estimate be=6 provided2 by. [24], who quotes r 0.187(4.1) fm . B0 . dq B0 0.51.5 q=0 i i ⇠ fixing its number density for excludedT at CL > 0.95 m to be  ij j ij j It is worth comparing this. result, with∆ thosem ofYukawa other= pseudoscalarsY Q D + Y thatQ U do+( haveh.c.)(2.4) been measured excluded⌦ area has↵ CL > 0.95 ⌦ ↵ d L d L R u L R ⌦ ↵ 4.6 evolutionWhich2ε for a neutral2 α particle2 leads to2 2 2 i,j r +K =0.439 fm , r + =0.34 fm , r 0 = 0.054 fm . We can safely use the quadratic expansion ⇡ γ K With theK Higgs field denoted⇣ with(3),and3 Yd,u representing the coupling constants. The 4.6 evolution γ β 2.2 Flavor in the Standard Model v mass of the quarks mqnare1 related= to their2 T coupling. to the Higgs field: mq = Yq . To write (4.22)

η 0.01.0for the form factor 4.2 since it will be valid2 for q <⇣21(3)/ 2 2r 3 100 MeV and we are interestedp2 in ⌦ ↵ ⌦ ↵ ⌦F (q ↵)= r q + B...0 (4.2) At some highα temperature above m∆md ,& we∆ms n assume| =| that⇡Ti,j . ⇠was in thermal equilibrium with the(4.22) plasma, Theproper spontaneous mass terms symmetry for quarks,6 breaking the2 Yd,u ofmatrices the SM need allows to be the diagonalized, quarks to acquire that is mass possible via T 10 MeV. Thus, we are left to calculate the scatteringq cross section for the process e±B e±B . 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We,and canY safelyrepresenting use the quadratic the coupling expansion constants.(4.3) The number provided⇡ it isd⌦T 4>EK2 sin15 GeV2 so| that| all the SM particles3 d,u but the top, the Higgs and the EW decγ β 2quarks are chosenε to be rotated, going from the flavor (o interaction) basis tov the mass -1.0 mass of the quarks mqnare related= to their2 T coupling. to the Higgs field: mq = Yq . To write (4.22) η 0.0 K ⇣(3) bosons arefor still the in form thermal factor 4.2 equilibrium.since it2 will be valid for q < 1/ 2r 3 100 MeV and we are interestedp2 in 1 The⌦ ModelCKM↵ ⌦ ↵ basis: ⌦ ↵ Bi,j0 1 bosons are stillα inf i t t e thermalr 2 equilibrium.2mB0 E (1 cossol.✓ w/) cos 2β the 0.95) scattering⇡q cross section for the process e±B0 e±B0. V mB + Eusing(1 fourcos independent✓) ' matrices.u 2 Only⌦ three↵ of themd can be freely chosend (redefining the Contents ⇠ ub Contents0 α 1 0 ! 4.6 evolution -1.5-0.5Which in the lab frame and2 ignoringquark fields the withB20 arecoil di↵erent reads phase), therefore if the up-type quarks are diagonalized, the In4.7 practice Meson-1.0 we Mixing will -0.5 used 0.0Tdec 0.5↵= 100 1.02 GeV. 1.5q althoughYu = 2.0I c we; noteYd = I thats0 the= VCKM results if fairly independent on this Baryogenesis4.7 Meson Mixingfrom B Mesonsdown-type2 quarks are left· 0 non-diagonal.1 By convention,· 0 1 the interaction· 0 1 eigenstates and In practiceContents we will use T=dec 2=⇡ 2 100rB GeV.0 1+ althought we note that theb0 result ifb fairly(4.5) independent on this At some high temperature above m, we assume that was indqd thermal2 equilibrium↵18 with✓ the4E2 plasma, 1 The Modelnumber provided it is T=dec1>ρ The15the Modelcos GeV mass2 eigenstatesF so(q that2) 2 are all@ chosen theA to be SM equal particles for the@ up-typeA but quarks, the@ whereasA top,1 the down-type(4.3) the Higgs and the EW 1 4 ✓ with✓ I theB0 identity◆ matrix and VCKM the Cabibbo-Kobayashi-Maskawa (CKM) matrix, fixing its number density for T .numbermMixing toB be provided isMeson described it isd by⌦Tdec the14>E0 2 HamiltonianMixingsin15 The⌦ GeVquarks↵ Model2 so are| chosen that|. to all be rotated, the SM going particles from the flavor but (o interaction) the top, basis the to the Higgs mass and the EW 1 The Model -1.0 d2 2 2 2⇡ ε 2 2 2 2 2⇡ 2 2 2 Mixingbosons is are described still in thermal by the= Hamiltonian equilibrium.thatdq relates= ↵ the.H flavorrK eigenstatesE = ↵ (d0,sr0,b0)tothemasseigenstates(E d, s, b). (4.6) 1) CP violation in the MesonCKM System 22basis: B0 B0 1Figure The 2.1: ModelUnitarity Triangle: Constraints2m2BdqE (1 in thecos (sol.⇢✓, w/H9)⌘ cos) plane2β < 0 [22]. ✓ 9 1 bosons are still⇣(3) inf i 3t t e thermalr γ 2 equilibrium.4E 0 2 2 Summer 14 q = Z (excl. at CL > 0.95)4E sin Vud Vus Vub (4.4) n = 2 T . ⌦ (4.22)↵ ⌦ ↵ 2 mB0 + Ed(1 cosB✓q)(t') u 2 ¯0 q + d0 B5 q(t)2 0 d q ⇡ VCKMq =B Vcd l VcsX Vcb rB l X 4.6 evolution 1 The-1.5 Model¯0 + d 0Bq(t) q 13 qq T Bq(t) B0q 12 SM:Standard Box Diagrams Model4.7 example Meson diagrams: MixingB l Xv n2i B(E =3| Tl) nX2Y(uiT=) I =3 c 10M; q GeV+Y0id = I s0 | =1VCKMi s (4.7) (4.23) q -1.0 -0.5q d 0.0 0.5↵ie 2 1.0q|2 ¯ 1.5qie = 2.0A· 0SLM=1q +12i !Vtd · 0V|ts 1Vtb¯ i · 0! 1 =Im q (4.23) (1.1) In practice we will use Tdec = 1004.7 GeV. although MesonA we= Mixing note that! the⌘h= result2⇡i if fairly'rdt independent¯!1+Bq(t) on=Im⇠ this ⇥t ¯0 210+ MeVb¯ Bq(t0).1870 (1.1)b (4.5) At some high temperature above m , we assumeSLW that+ was0 in thermal2 + equilibriumdtB0 0B withq(t the) 2 plasma, q B2@q ✓ l XB0 q◆(+tA) ⌦ Bq↵! lX M12 B¯ dq l X +18 BThe | CKMl u,c,4X matrixEt i is unitary.✓ M The o↵-diagonal◆ element| show i a strong hierarchical order:✓ ◆ number provided it is Tdec > 15 GeV__ so that all the SM particlesq __ but theρ top, theq Higgs| ✓ and i the◆ EW✓@ A 12 !◆@| A i 2 @! A 0 __V withandI theV identityare about matrix 0.22,✓__ andV VCKMand◆ theV Cabibbo-Kobayashi-Maskawaof order 4 10 and V and (CKM)V of matrix, order fixing its number density for T . mMixingb toB be isMeson describedand thereforeq! by we notice the1 HamiltonianMixing that The⌦ theus↵ Modele!±B00cd e±.B+0 scatteringq cb rate0 willts be way higher thanub theq Hubbletd db 2⇡ 2 2⇡ 2 bosons are still1 in thermal The equilibrium. ModelMixing is described by__ the Hamiltonian2 that| 2| relates3 B¯|2 the!| . flavor2l eigenstatesX2 | 2__ (|d0,sB0,b2| 0)tothemasseigenstates(| 2l X · | d,| s, b). | | B where Mq is the mass matrix=17 Tq and5dq10q=.+is↵ Asq the the matrixHr decayB isE- unitary= matrix.↵ and globalrBq The phasesE diagonal are not observable, elements four free12 parameters(4.6)M11 = mB, M22 = m ¯ whereq Figureu,c,Mt is 2.1:rate theUnitarityHu,c, masst 4 Triangle: matrix10Bq Constraints andBq 2GeV.· inis theW the (⇢, ⌘) decay plane 0 W [22]. matrix.B The0 diagonal elements M = m , M = m ¯ B M12 q ⇣(3) ⇠ ⇥ 10A4 MeVE2 dq=remain.q ThreeH9! are the quark mixing9q angles! and one is a=Im complex phase.q This11 complex B 22 B(1.1) q 3 b Z SL 0 + 0 V V V 4.7 Meson Mixing / are then meson= T and. anti-mesonq masses. B¯ ⌦ Thel(4.22)↵ X diagonal+b B⌦ elements↵ud lus Xub of the122 decayM matrix, are the decay are the meson⇡2 and anti-meson masses.phased givesBqq rise( Thet) to CP diagonal violation in elementsthe¯0q Standardq +ASL Model, ofB=Im5 q the( i.e.t)2 the0 decay di↵erent12 matrix, behavior of areq the decay (1.2) 4.4- Parameters0 + for thedB0 decays0B12(t) VCKMq =B Vcd l TVcsXB V(cbt) rB ✓ l X ◆ 1 TheW Model¯ i particles|q andu,c, anti-particles!t i =q in theM13q weak+ interaction.0qiq ! Theq| CKM-matrix1 Bi0qM can be expressed in 12 (4.23) Standard Model exampleq diagrams: Bq lAXSLv =Imne B(Eq =3Tl ) nXe(T ) A3 10= 12GeV !V V V !(1.2)12 (4.7)=Im (1.1) Mixing is described by the Hamiltonianwidths;. inverse of the mesoni andtermsdt | of anti-mesonB¯= (Vit) ,upto= SLM lifetimes.(4q)terms+ i 40 2td CPT+|ts Btb¯ invariance(it)✓0 ◆ requires M11q = (4.23)M22 and In practice we will use Tdec = 100widths; GeV. althoughH inverseA We we+= note need of that to the fill! the meson⌘h resulti if fairly and' independent anti-mesonM¯!12 q us on=Im⇠ this lifetimes.⇥ q B¯ CPT10l MeVX¯ invariance+q0.B187 !(1.1) requiresl X M11M= M22 and SLW ¯0 + dt The0B CKMq(t)| matrix| is unitary.O✓ The o↵2@-diagonalq ✓ ◆ elementBq◆(tA) show⌦ aq strong↵ hierarchical order: 12 Figure 2.2: Dominant Feynman B diagramsq l responsibleX + forB✓ neutralq | lB◆u,cmesonX i mixing inM the12 SM. ! | i ! ✓ ◆ number provided it is Tdec > 15 GeV__ so that= all the. SM Meson particles__ mixing but the top, results__ the  Higgs| from andi the non-zero EW✓ i__ o2 ↵ diagonal◆i | elements.3 i 2 The o↵-diagonal elements d 11Bq=(t) 22. Mesonq mixingq!Bq(t) resultsVus fromand! Vicd non-zeroare aboutM11 0.22,✓1 oV11↵cb M/diagonaland2 12◆ Vts of12 order elements.A 4 (10⇢ i⌘and) Vub Theand V otd↵of-diagonal order elements 11b 22 and therefore we notice thatb the e±B00 e±B+0 scattering2q rate0 will2 be way higher than theq Hubble bosons are still in thermal equilibrium.i | i = Mq + i | __ i 2 | =|M3 B¯| !|V= l(4.23)= X i | __| B|1i|122l/2 X ·A2 |+ | (4) | (4.8)| dtB whereB¯q(t) Mq is the2 massB¯q matrix(t17) Tq andH5 10q .+is As2q the theCKM matrix decayM is⇤ - unitary matrix.⇤ andM global22 q The phases22n diagonalB are notn observable,B¯ elements four10 free12 parametersM11 = mB, M22 = m ¯ 12 whereq of theu,cM massisrate the matrixHu,c, masst 4 matrix account10Bq andB forq GeV. the· isW the dominant, decay AW120 matrix. dispersive2=Im3 12B The2 contributions diagonal2 elements1 ofO theM box= m diagrams, M = (internalm ¯(1.2)B of | thei mass q ✓ matrix⇠◆ account⇥| i 10A for MeV the=remain.q dominant, Three! are the dispersiveSL quarkA(1 mixing⇢q i angles⌘) contributions! andA one is a1=Im complex of10 phase. the boxq This11 complex diagramsB (internal22 B(1.1) (1.3) / q b nB SLnB¯ 100 + 0M 4.7 Meson Mixing are the meson and anti-mesonqphase masses. givesB¯ rise to Thel CPX@ violation diagonal+b inB the elements Standard12l X Model,s of i.e.⇠ the theA 12 di decay↵Merent behavior matrix, of are the decay where Mq is the mass matrixB andq Btop-quark).qqistransitions the decay matrix. involve The theThe exchange o diagonal↵-diagonal elements of two W elementsMbosons.114 10= mB Theyq, M of22 are= them the¯ so decay called box matrixq 0 A account=Im for(1.3) absorptive12 contributions, i. (1.2) top-quark).are the meson4.4- The and Parameters o↵ anti-meson-diagonal for the elements masses.B0 decaysFor12 the CP of Theviolating the diagonal measurement decayB matrix in the elements✓B sector account◆ presentedSL of the in this for thesis decay absorptive✓ it is su matrix,cient◆ to write contributions, are the decay i. ! W s particles⇠ andu,c anti-particles! in the weak3 interaction.! The CKM-matrix0 M12 can be expressed in are the meson and anti-mesondiagrams masses., shown The in diagonal Fig. 2.2. elements ofA theSL decay=Im matrix,the CKM-matrixmB areM the includingH decayM termsL =2 up toM12( ). For measurements¯ in the Bs sector,(1.2) it is helpful(4.9) to include Mixing is described by the Hamiltonianwidths;. inverse of the mesonmass and eigenstates: anti-meson5 BL/H lifetimes.4 =Op B4 q CPTBq invariance✓ ¯ ◆ requires M11 = M22 and widths;e. real inverse intermediateWe need of to the fill decays meson to andterms a anti-mesonstateM up of12 to =⌘(BV),us given,upto that lifetimes.f the( phase)terms| B of| the.Thus matrix CPT element invarianceBVts isand playing¯ aB role requires inare that case: notM eigenstates= M and for the Duee. to real GIMH intermediate suppression [26], in decays these diagrams to a the state leading BO q| contributionq| | f O isiB givenq.Thus|q by? i ±|Biq andq Bq areq not eigenstates11 for22 the widths; inverse of the mesonFigure and 2.2: anti-mesonDominant lifetimes. Feynman diagramsCPT invariance responsible¯ requires for✓ neutralM11 B◆=mesonM22 mixingand in2Ref( thei SM.ML/H1212 mass eigenstates: BL/H = p Bq Bq time evolve: B L/H!1 !(2t/)2=!=i!4/e8 H iBL/H(0) A3(⇢ i⌘) (4.10) CP violatingthe top dmixing quark.11 = Therequires22 amplitude. Meson a relative of the sum mixing phase of the diagrams results between including fromB i 12 H all non-zero andM theL up-typeM121 o2 quarkM/↵2 diagonal A elements.3(⇢ i⌘) The o↵-diagonal elements 11 = 22. Meson mixing resultsweakweak11 fromBq=(t interaction.) non-zero interaction.| 22.i Meson o↵ diagonal|q The The mixingiB±| elements.q box(t) boxi diagrams results diagrams The o↵-diagonal from include include⌘| non-zero elements2 elementsn511B elementsi2 on11↵B¯Mdiagonal from12122 from|2 2 the12 the elements.4 CKMi CKM2 matrix, matrix, The2 and o↵ and-diagonal so6 M so Mand elementsand may may i | i = Mq + ii L/H| i =VCKMM = = + A(4.23) [1 q2(⇢2+ i⌘)]/21 /2210q (1 + 4A2)/8 A 4 (4.8)+ ( ) time evolve: ¯B (t)¯ = e ¯B (0) 0 VCKM3 = 2 i | 12| 12i12 /42 A + 2(4 ) 1 O contributionsdt Bq(L/Ht) to the b q transition, 2H B isq(L/Ht proportional) measureH to: of CPV:2 A [1 1M(1⇤ /2)(⇢⇤+=i⌘M)] 222A10 sin+A22n[1B 2(⇢n+Bi¯⌘)]/21A10 /2 (1.3) of the mass matrix account for theof dominant, the mass dispersive! 1 matrixThis equationcontributions account is the non-relativistic of the for box the diagrams formula dominant, given (internalA for120SL an dispersivep electron2=Im3 12 interactingM 2 contributions2 with12 target with1 a chargeofO the density box⇢ diagrams (internal(1.2) ofbebe| the| complex. complex.i mass ✓i matrix2 ◆2 account|| i fori the. dominant,@  dispersiveAs(1 ⇢ ⇠i⌘12) contributionsA 1 of10 the boxA diagrams (internal (1.3) BSM? q 2 12 niq~Bq~r 3 nB¯ 10 M s top-quark). The o↵measure-diagonal elements of CPV: of 1 the decaywhere= matrixF (2q ) 2 accountsin⇢(r) e2 ford ~r absorptive. 2 contributions, i. 12 ⇠ p 2 2M ⌘ 2 212 4 10 2 2 @ 2 2 0 2 2A (1.3) where Mq is the mass matrixB andq top-quark).Btop-quark).qqistransitions theB¯ decayB¯BB matrix. involve(t The()t The)m theTheu oVuq↵ exchange o12 diagonalV-diagonalq/p↵ub⇤-diagonalq/p+ mc elementsand ofVcq¯and twoVcb⇤ elements+WB elementsmMbosons.tB11VtqBFor=¯VtbBm⇤ the¯(Bt TheyCP) of,(Mtviolating) of22 the are= them the measurement decayp/qB¯ so decayp/q called,so matrix(2.13) in,so thebox✓ matrixa B=1asector=1 account◆ presented accountq/pq/p in this foris thesis a foris absorptive measure a it absorptiveis measure su cient toof write contributions, CPV of contributions, CPV in B in BB¯ i. B¯ i. e. real intermediate decays to! a state Bq q qfq q Bq.ThusBR q and Bqs are not⇠q eigenstatesq q q for¯ the 3 11 0 q q q q are the meson and anti-mesondiagrams masses., shown The!mass in diagonal Fig.! eigenstates:2.2. elements of theB decay matrix,the= CKM-matrixpmBB areq M the includingH decayBM termsqL =2 up toM12( ). For measurements¯ in the Bs sector, it is helpful(4.9) to include |h|h | | i|i|//| | | | L/Hmass|h |h eigenstates:| | i5| i|/B/| L/H| | =|Op Bq BnqB||n|B¯ | ¯ 10 weak interaction. The box diagramse. include real intermediate elements from the decaysCKM matrix, toterms and a state upso toM⌘(andB), givenmay thatf the phase| B of| the.Thus matrix elementBVts isand playing¯ aB role inare that case: not eigenstates for the Z' modelsDuee.mixing.mixing. to real(even GIM intermediate suppression at tree level) [26], in, decays theseLeptoquarks diagrams| to ai the state leading etc| BO iq contribution...±|q | f i isiB givenq.Thus|q by? i ±|Biq andq Bq10areq not eigenstates for the (1.4) widths; inverse of the meson and anti-meson lifetimes. CPT invariance¯ requires iM11L/H= M22 and 2Ref(i ML/H1212 mass eigenstates: timeB evolve:= p B B B (t) = e H B !2 (0)!4 s ⇠ 3 be complex. the top quark. TheL/H amplitude of theq sumL/Hn ofqB14 thetime diagramsnB¯ evolve: includingB10 BHL/H! all1L/H the(Lt/)2= up-type!= /e8 quarkH BL/H(0) A (⇢ i⌘) (4.10) = . Meson mixing resultsweak from non-zero interaction. o↵ diagonal The elements. box diagrams The o↵-diagonal include elements2 n5 B elementsn ¯M 2 from2 the4 CKM2 matrix,2 and6 so M and may 11 22 2 2 weak interaction.2| i2 i | Thei| ±| box2 i diagramsi VCKM10 include= 2⌘| | +A elements [1 i2(⇢2+ii⌘B)]/21 from12 | the/210 (1 CKM +i 4A )/8 matrix,(1.4)A and+ ( so) M and may B¯q Bq(t) q/p and Bq B¯q(t) p/q¯ ,soa =1L/H q/p is a measureq 2 ofsee CPV 0 e.g. in B Nirq 9911321B¯qqqq q | 12| q 1 O time evolve:contributionsBL/H to the(t)b =qetransition,H B isL/H proportional(0)smeasure to:⇠ of12 CPV:A3[1 1(1–8–2/2)(⇢ +=i⌘)] A102sin+ A4[1 2(⇢ + i⌘)]/21A24/2 (1.3) of the|h mass| matrixi| / account| | for|h the| dominant,i| measure/ | dispersive!| 1This of equationcontributions CPV:| is the| 1 non-relativistic of the box= diagrams formula2 given (internalsin for12 an12p electron12 interactingMq2 q with12 target with a charge density ⇢ mixing. bebe| complex. complex.i 2 2 | ip . M@12 s ⇠12 A q 2 12 iq~q~r 3 a =a = q qsinsin12, , (4.24)(4.24) top-quark). The o↵measure-diagonal elements of CPV: of 1 the decaywhere= matrixF (2q ) 2 accountsin⇢(r) e2 ford ~r absorptive. 2 contributions, i. 12 p 2m2MV ⌘V ⇤ + m2 2V12 V ⇤ + m V V ⇤ 2 2 MM2 2(2.13) 2 2 2 B¯B¯BBq(t()t) u uq12q/pubq/pcandcq¯andcb BtBtqB¯tbB¯(t)(t) p/q12p/q12,so,so a =1a =1⌦q/pq/ph is ais0 measure.1 a measure of CPV of CPV in B in BB¯ B¯ (1.5) e. real intermediateMiguel Escudero decays to(KCL) a state Bq q qBaryogenesisfq12q Bq.Thusq and BRDMq andfromB Bq Mesonsare notq eigenstatesq q q forPlanck¯ the 04-06-19 1123 DM q q q q |h a !=mass| ! eigenstates:sini| /, | | BL/H|h =| p Bqi| /(4.24)B|q | n | n| ¯ ⇠ weak interaction. The box diagrams include|h elements| q i from|12 / the| CKM| matrix, |h and so| M and i| may/ | | B| B | 10 mixing.mixing. M12 | i2 i | i ±|nBi nB¯ 10 10 (1.4) wherewhere thetime the theoretical theoretical evolve: B quantities quantities⌦(tDM) 0=hMeM12¯012/H.1L/H/1212and¯B0and their(0) their relative relative10 phase phases 12,⇠12 can, (1.5) can be be related related to observables to observables(1.4) be complex. L/HnB14 BnqB¯=⇠bq and10 BqL/H= bq¯ where¯ the theoretical2 quantities2 M12¯/12 and2 their2 relative phase| 122 , cani be2 related| 10i to2 observables| ¯| q si i ⇠ (1.4) Bq Bq(t) q/p and BqMBMqq(t,) ,qp/q.. Here,so Herea =1 the the massq/p massis eigenstates a measure eigenstatesq of CPV12B inH/LBBq are–8–Bqqare relatedq related to to the the flavor/CP flavor/CP eigenstates eigenstates by: by:BL/HB = = M|h, | . Herei| / the| 0 mass| ¯ eigenstates|h | ¯Bqi0| measure/ are| q related| of to CPV: the| flavor/CP| 1 s eigenstates⇠= by:2 BsinH/L = q L/H mixing.q q B = bq and B H/L= bq¯ p M L/H 1212 12 q | | i i ¯ q p B q q B¯¯ . 12a| =a =i q qsinsin12, , (4.24)(4.24) p Bq q Bq . | i p Bq q q| Bqiq . 12 | i ± | i | i ± | q i MM12 2 | i ± | i 12 ⌦DM h 0.1 (1.5) 12 q a = q sin 12 , (4.24) 2 ⇠ References M12 2 nB⌦DMnBh¯ 0.110 (1.5) wherewhere the the theoretical theoretical quantities quantities⌦DM0hMM12¯0/.1/12 and¯0and their their relative relative phase phase12, can,(1.5) can be be related related to observables to observables References Bq = bq12and12Bq = bq¯ ⇠10 12 (1.4) where the theoretical quantities MReferences/ and their relative phase , can be related⇠| i to observables| si ⇠ [1] K. Aitken, D. McKeen, T. Neder12M andq12, A. E. Nelson,q. HereBaryogenesis the mass from12 Oscillations eigenstates of CharmedB or are related to the flavor/CP eigenstates by: B = 0 Mq0, 0 q. Here¯ the¯ mass0 eigenstates H/LBH/L are related to the flavor/CP eigenstates by: L/HBL/H = MqBeautiful, q. Here Baryons theB, massPhys.= ¯ eigenstatesbq Rev. andD96 (2017)B¯BH/L=B 075009qarebq¯= related[1708.01259bq toand the].B flavor/CPq = bq eigenstates¯ by: BL/H = | | i i ¯ q p[1]B K.q Aitken,q B¯¯ .| D.i McKeen, T.| Nederi and A.| E. Nelson,i Baryogenesis from Oscillations of Charmed or p Bq q Bq . | i p[1]Bq q K. Aitken,q| Bqiq . D. McKeen, T. Neder and A. E. Nelson, Baryogenesis from Oscillations of Charmed or |[2] iJ.± Bramante,| i K. Fukushima and| J.| Kumar,iBeautifuli±±Constraints| | i Baryonsi on bosonic, Phys. dark matter Rev. fromD96 observation(2017) of 075009 old [1708.01259]. neutron stars, Phys. Rev. D87 (2013) 055012Beautiful[1301.0036 Baryons]. , Phys. Rev. D96 (2017) 075009 [21708.01259]. References ⌦DM h 0.1 (1.5) [3] T. Venumadhav, F.-Y. Cyr-Racine,[2] K.J. N. Bramante, Abazajian and K. C. M. Fukushima Hirata, Sterile and neutrino J. Kumar, dark matter:Constraints on bosonic dark matter from observation of old ReferencesReferences[2] J. Bramante, K. Fukushima and J. Kumar, Constraints⇠ on bosonic dark matter from observation of old [1] K.Weak Aitken, interactions D. McKeen, in the T. strong Neder coupling andneutron A. epochE. Nelson,, Phys. starsBaryogenesis Rev., Phys.D94 (2016) from Rev. Oscillations 043515D87[1507.06655(2013) of Charmed 055012]. or [1301.0036]. neutronB0 = stars¯bq and, Phys.B¯0 Rev.= bqD87¯ (2013) 055012 [1301.0036]. [4] L.Beautiful Kawano, BaryonsLet’s go:, Phys. Early Rev. universe.D96[1] (2017)K. 2. Primordial Aitken, 075009q [1708.01259 nucleosynthesis: D. McKeen,]. q The T. Computer Neder way and,. A. E. Nelson, Baryogenesis from Oscillations of Charmed or [3][1]T.K. Venumadhav, Aitken,| D.i McKeen, F.-Y. Cyr-Racine, T.| i Neder and K. N. A. Abazajian E. Nelson, andBaryogenesis C. M. Hirata, fromSterile Oscillations neutrino of dark Charmed matter: or [5][2] R.J. Bramante, J. Scherrer K. and Fukushima M. S. Turner, and J.Primordial[3] Kumar,BeautifulT. Venumadhav,Constraints Nucleosynthesis Baryons on bosonic with, F.-Y.Phys. Decaying dark Cyr-Racine,matter Rev. Particles. fromD96 observation 1.(2017) Entropy K. N. of 075009 Abazajian old [1708.01259 and C.]. M. Hirata, Sterile neutrino dark matter: Producingneutron stars Decays., Phys. 2. Rev. InertD87 Decays(2013), Astrophys.Weak 055012Beautiful interactions[1301.0036 J. 331 Baryons(1988)]. 19 in. , Phys. the strong Rev. couplingD96 (2017) epoch 075009, Phys.[1708.01259 Rev. D94 (2016)]. 043515 [1507.06655]. Weak interactions in the strong coupling epoch, Phys. Rev. D94 (2016) 043515 [1507.06655]. [3] T. Venumadhav, F.-Y. Cyr-Racine,[2] K.J. N. Bramante, Abazajian and K. C. M. Fukushima Hirata, Sterile and neutrino J. Kumar, dark matter:Constraints on bosonic dark matter from observation of old [4][2]L.J. Kawano, Bramante,Let’s K. go: Fukushima Early universe. and J. 2.Kumar, PrimordialConstraints nucleosynthesis: on bosonic The dark Computer matter from way,. observation of old Weak interactions in the strong coupling[4]neutronL. epoch Kawano,, Phys. stars Rev.,Let’sPhys.D94 (2016) go: Rev. Early 043515D87[ universe.1507.06655(2013) 055012]. 2. Primordial[1301.0036 nucleosynthesis:]. The Computer way,. neutron stars, Phys. Rev. D87 (2013) 055012 [1301.0036]. [4] L. Kawano, Let’s go: Early universe.[5] R. 2. Primordial J. Scherrer nucleosynthesis: and M. The S. Turner, Computer wayPrimordial,. Nucleosynthesis with Decaying Particles. 1. Entropy [3][5]T.R. Venumadhav, J.– Scherrer 10 – and F.-Y. M. Cyr-Racine, S. Turner, Primordial K. N. Abazajian Nucleosynthesis and C. M. with Hirata, DecayingSterile Particles. neutrino dark 1. Entropy matter: [5] R. J. Scherrer and M. S. Turner, Primordial[3]ProducingT. Venumadhav, Nucleosynthesis Decays. with 2.F.-Y. Decaying Inert Cyr-Racine, Particles.Decays, 1.Astrophys. Entropy K. N. Abazajian J. 331 (1988) and C. 19 M.. Hirata, Sterile neutrino dark matter: Producing Decays. 2. Inert Decays, Astrophys.WeakProducing interactions J. 331 (1988) Decays. 19 in. 2. the Inert strong Decays coupling, Astrophys. epoch, Phys. J. 331 Rev.(1988)D94 19(2016). 043515 [1507.06655]. Weak interactions in the strong coupling epoch, Phys. Rev. D94 (2016) 043515 [1507.06655]. –1– [4] L. Kawano, Let’s go: Early universe. 2. Primordial nucleosynthesis: The Computer way,. [4] L. Kawano, Let’s go: Early universe. 2. Primordial nucleosynthesis: The Computer way,. [5] R. J. Scherrer and M. S. Turner, Primordial Nucleosynthesis with Decaying Particles. 1. Entropy [5] R. J.– Scherrer 10 – and M. S. Turner,–1– Primordial Nucleosynthesis with Decaying Particles. 1. Entropy Producing Decays. 2. Inert Decays, Astrophys.– J. 10331 – (1988) 19. Producing Decays. 2. Inert Decays, Astrophys.– J. 10331 – (1988) 19. –1–

–1– – 10 – – 10–1– –

–1– CP violation in the B system 20

0 0 where Cd and Cs depend on the relative production rates of B and Bs mesons, as well as their respective probabilities to have mixed (which may depend on the selection requirements). A possible additional term in Eq. (18) is discussed below. Another approach to determine these asymmetries inclusively is to tag B particles produced in top quark decays [102]. This method, recently implemented by ATLAS [103], however results in low yields so that the measurements do not currently have competitive precision.

0 d 0 s Table 4: Summary of the latest results for the B mixing (asl) and Bs mixing (asl) CP b asymmetries, as well as the inclusive dimuon asymmetry Asl measured at D0. In all cases the statistical uncertainty is quoted first and the systematic second. All values are percentages. d s b The world averages [12] are from a fit to all asl, asl and Asl results, except for the latest LHCb s asl result [104]; an earlier result [105] is included instead. The latest SM predictions [9,101] are given for comparison.

d s b asl (%) asl (%) Asl (%) +0.38 BaBar K-tag [84,106] 0.06 0.17 0.32 –– ± BaBar `` [107] 0.39 0.35 0.19 – – ± ± Belle `` [85] 0.11 0.79 0.70 – – ± ± LHCb [83,104] 0.02 0.19 0.30 0.39 0.26 0.20 – ± ± ± ± D0 [86,108,109] 0.68 0.45 0.14 1.12 0.74 0.17 0.496 0.153 0.072 ± ± ± ± ± ± World average [12] 0.15 0.17 0.75 0.41 ± ± SM 0.00047 0.00006 0.0000222 0.0000027 0.023 0.004 ContentsB Meson± Decays± ± Semileptonic Asymmetry measurements This is a measured1 The Modelin experiments: 1 Lenz et al 1511.09466 1 Standard Model [%] s sl 1 Thea 0 Model X

ν

µ

s 0 + 0 q B¯ l X B lX −1 D q q q 12 A = D0 ! ! =Im (1.1) SL B¯0 l+X + B0 l X M q q µ q 12 !µ ! ✓ ◆

LHCb

−2 X ν (*) µ LHCb D µνX 12 s (*) ASL =Im (1.2) D D0 D µνX M12 −3 BaBar D*lν ✓ ◆

D0 BaBar ll Belle ll nB nB¯ 10 −4 10 (1.3) −3 −2 −1 s0 ⇠ 1 d asl [%]

CurrentMiguel measurement: Escudero (KCL)s AddBaryogenesis=( 0and.0021 DM from B0 .Mesons0017) , As BLV19=( 24-10-190.006 0.0028)24 (1.4) Figure 6: Measurements of asl and aslSL, with simple± one-dimensionalSL averages ± (that di↵er from the values shown inmass Table eigenstates: 4) shown⇥ B as⇤ horizontal= p B andB¯ vertical⇥ bands,⇤ respectively [104]. The | RoomL/H i for| newqi ±| physicsqi i L/H yellow ellipse representstime evolve: the D0B inclusiveL/H (t) = e dimuon H BL/H measurement(0) [86] with d set to its SM expectation value. | i | i

0 ¯ ¯ d,s ⌘B ✏d,s Br(Bd,s +...)Br( ⇠)ASL (1.5) d s b / ⌘ ! ! Measurements of asl, asl and Asl have been2 performed by the BaBar, Belle, LHCb, q 2 12 q measure of CPV: 1 p = M 2 sin 12 and D0 collaborations. The latest results are12 collected in Table 4 together with the world nB nB¯ 10 10 (1.6) s ⇠

⌦ h2 0.1 (1.7) DM ⇠ B0 = ¯bq and B¯0 = bq¯ q | i q | i

–1– Back Up: Flavourful Variations

Operator Initial State Final state M (MeV) Bd + ⇤ (usd) 4163.95

0 Bs + ⌅ (uss) 4025.03 bus ⇠ B+ + ⌃+ (uus) 4089.95 ¯ 0 Y ⇤b + K 5121.9 s Bd + n (udd) 4340.07 ¯b u ⇤ Bs + ⇤ (uds) 4251.21 B0 bud d B+ + p (duu) 4341.05 d d 0 ⇤b ¯ + ⇡ 5484.5

0 Bd + ⌅c (csd) 2807.76

Bs + ⌦c (css) 2671.69 bcs + + u B + ⌅c (csu) 2810.36 + ¯ + K ⇤b + D + K 3256.2 s¯ Bd + ⇤c + ⇡ (cdd) 2853.60 u 0 ⇠ Bs + ⌅c (cds) 2895.02 ¯ bcd 0 ? + ⇤b b Y ? B + ⇤c (dcu) 2992.86 0 ⇤b ¯ + D 3754.7 d u¯ ⇡ Table 1: Here we itemize the lightest possible initial and final states for the d B decay process to visible and dark sector states resulting from the four pos- sible operators. The diagram in Figure ?? corresponds to the first line. The mass di↵erence between initial and final visible sector states corresponds to the kinematic upper bound on the mass of the dark sector baryon.

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 25 Back Up: Parameters

8

Parameter Description Range Benchmark Value Constraint

m mass 11 100 GeV 25 GeV - 23 21 22 Inflaton width 3 10 < /GeV < 5 10 10 GeV Decay between 3.5MeVm + m⇠

m⇠ Majorana DM 0.3GeV 1.2GeV | | yd Yukawa for = yd ¯⇠ 0.3 < p4⇡ L 4 3 Br(B ⇠ +..)BrofB ME + Baryon 2 10 0.110 < 0.1[5] !s ! 6⇥ d 4 4 d A`` Lepton Asymmetry Bd 5 10 Lepton Asymmetry Bs 10

TABLE II. Parameters in the model, their explored range, benchmark values and a summary of constraints. Note that the q benchmark value for A`` Br(Bq ⇠ + Baryon + X), for v and v ⇠ are fixed by the requirement of obtaining the ⇥ ! 11 h i h i 2 observed Baryon asymmetry (YB =8.7 10 ) and the correct DM abundance (⌦DMh =0.12) respectively. ⇥ e↵ects are small, this is e↵ectively equivalent to the lep- by Br(B ⇠ + Baryon + X)); the greater the value tonic charge asymmetry for which one integrates over all of this branching! fraction, the more DM is generated. times. Therefore, in the present work we will use the two From Equation (16), we see that the asymmetry also de- interchangeably. pends on this parameter but weighted by a small number; 0 q 3 Maintaining the coherence of B oscillation is crucial A`` < 4 10 . Therefore, generically a region of param- for generatingMiguel Escudero the asymmetry; (KCL) additionalBaryogenesis interactions and DMeter from space B⇥ Mesons that produces the observedBLV19 baryon 24-10-19 asymmetry26 with the B mesons can act to “measure” the state of the will overproduce DM, and we require additional interac- 0 ¯0 B meson and decohere the Bq Bq oscillation [32, 33], tions with the DM to deplete this symmetric component 2 thereby diminishing the CPV and so too the generated and reproduce ⌦DMh =0.120. baryon asymmetry. B mesons, despite being spin-less and charge-less particles, may have sizable interactions with electrons and positrons due to the B’s charge dis- B. Numerics and Parameters tribution. Electron/positron scattering e±Bq e±Bq,if faster than the B0 oscillation, can spoil the coherence! of q We use Mathematica [36] to numerically integrate the the system. We have explicitly found that this interaction set of Boltzmann Equations (9), (10), (11), (13), and (16) rate is two orders of magnitude lower than for a generic subject to the constraint Equation (8). To simplify the baryon [29], but for temperatures above T 20 MeV numerics it is useful to use the temperature T as the evo- the process (e B e B) occurs at a much higher' rate ± ± lution variable instead of time. Conservation of energy than the B meson oscillation! and therefore precludes the yields the following relation [37, 38]: CP violating oscillation. We refer the reader to Ap- pendix 1 for the explicit calculation of the e±B e±B ! dT 3H(⇢SM + pSM) nm scattering process in the early Universe. = , (19) Generically, decoherence will be insignificant if oscilla- dt d⇢SM/dT tions occur at a rate similar or faster then the B0 me- which above the neutrino decoupling temperatures T & son interaction. By comparing the e±B e±B rate q ! q 3 MeV simplifies to [39]: with the oscillation length mBq , we construct a step- like function (we have explicitly checked that a Heaviside 4 2 dT 4Hg ,sT (30/⇡ ) mn function yields similar results) to model the loss of coher- = ⇤ ⇥ . (20) 4 d log g ence of the oscillation system in the thermal plasma: dt T g (1 + ⇤ ) ⇤ d log T

0 0 q (e±Bq e±Bq )/mBq fdeco = e ! . (18) We can therefore use Equation (20) in place of Equa- tion (10). For the number of relativistic species con- 13 We take mBd =3.337 10 GeV and mBs = tributing to entropy and energy g ,s(T ) and g (T ), we use 11 ⇥ 0 0 ⇤ ⇤ 1.169 10 GeV [5], and e±B e±B = the values obtained in [40]. Finally, since the DM parti- ⇥ q ! q 10 11 GeV (T/20 MeV)5 (see Appendix 1 for details). cles generically have masses greater then a GeV we can Even without numerically solving the Boltzmann equa- safely neglect the inverse scatterings in the DM Boltz- 2 tions, we can understand the need for additional interac- mann equations i.e. the neq term. To make the inte- tions in the dark sector v ⇠,. From Equations (11) gration numerically straightforward we change variables and (13), we see that theh i DM abundance is sourced and solve the equations for log n and log T , such that Back Up: Decoherence

⌧B =1.52 ps

mBs /Bs = 26.9

mBd /Bd =0.77 e± e± 0 0 0 0 (e±B e±B ) < m 0 Bs Bs ! B ¯b b 5 r2 2 11 T B0 e B0 e B0 10 GeV h i ± ! ± ' 20 MeV 0.187 s s¯ B0 B0 ✓ ◆ ✓ ◆

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 27 Results: Ad < 0 and As > 0

m⇠ =1.8 GeV m =1.3 GeV

m > m⇠ 4 3 10 Y Br(B ⇠ +Baryon)=5.6 10 ! ⇥ 7 ⇥ s 3 10 A`` =10 d 4 A = 4.2 10 `` ⇥

s ? / 9 Y + Y 10 n

⌘ Y Y Y ? B ⌘ Y 11 10 Y⇠ 2 ⌦DMh =0.12 11 v ? XX =46 v WIMP YB =8.7 10 13 h i ! h i ⇥ 10 30 10 3 1 T (MeV)

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 28 An Explicit Model Minimal Particle Content B-mesons decay into DM (missing energy) and a Baryon Field Spin QEM Baryon no. Z2 Mass

0 0 0 +1 11 100 GeV ⇠ Y 0 1/3 2/3 +1 (TeV) O Y s 1/2 0 1 +1 (GeV) O ¯ u ⇠ 1/2 0 0 1 (GeV) b O 0 ⇤ Bd 0 0 1 1 (GeV) d d O Heavy Colored Triplet Scalar:

c c y Y ⇤ ub¯ y Y ¯ s +h.c mY > 1 TeV (4-jet/squark) L ub s yuby s eff = 2 usb also possible csb ,udb ,cdb H mY (CP and Baryon B =0 operator induces new b-quark decay ¯b us ! number conserving) 4 4 3 mB m 1 TeV pyuby s Br(B ⇠ + Baryon) 10 ! ' 2 GeV m 0.53 ✓ ◆ ✓ Y ◆ Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 29 An Explicit Model Minimal Particle Content B-mesons decay into DM (missing energy) and a Baryon Field Spin QEM Baryon no. Z2 Mass

0 0 0 +1 11 100 GeV ⇠ Y 0 1/3 2/3 +1 (TeV) O Y s 1/2 0 1 +1 (GeV) O ¯ u ⇠ 1/2 0 0 1 (GeV) b O 0 ⇤ Bd 0 0 1 1 (GeV) d d O The Dark Sector:

ψ : Dirac Dark Baryon

For the b-quark decay to happen: m

• ψ needs to have decays into other dark sector particles or will decay 4 back to visible baryons and undo the Baryogenesis ⌧( p + ⇡) 10 years ! ⇠

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 30 An Explicit Model Minimal Particle Content B-mesons decay into DM (missing energy) and a Baryon Field Spin QEM Baryon no. Z2 Mass

0 0 0 +1 11 100 GeV ⇠ Y 0 1/3 2/3 +1 (TeV) O Y s 1/2 0 1 +1 (GeV) O ¯ u ⇠ 1/2 0 0 1 (GeV) b O 0 ⇤ Bd 0 0 1 1 (GeV) d d O The Dark Sector:

φ : Charged Stable Scalar anti-Baryon ξ : Dark Stable Majorana Fermion

Minimal Dark sector interaction y ¯ ⇠ with Z2 symmetry • L d • Constraints: • ψ -> φξ Decay: m + m⇠ m > 1.2 GeV McKeen, Nelson, Reddy, Zhou 1802.08244

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 31 d Parameter Space A`` =0 11 All points correspond to Y =8.7 10 B ⇥

Baryogenesis can be achieved with just the CP violation in the SM! provided Br(B ⇠ + Baryon + X) > 0.05 ! d and A`` =0

4 Br(B ⇠ + Baryon + X)=2 10 0.1 Baryogenesis requires: ! ⇥ s 5 3 A = 10 10 `` Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 32 Parameter Space Ad = Ad `` ``|SM

SM value

• Baryogenesis can take place even if one asymmetry is negative provided the other is positive and large enough.

Miguel Escudero (KCL) Baryogenesis and DM from B Mesons BLV19 24-10-19 33