Feeble Interactions -A Theory Perspective- Martin Bauer March 18, - PowerPoint PPT Presentation

Feeble Interactions -A Theory Perspective- Martin Bauer March 18, 2019 � 1

The lifetime gap Example: Axion-like particle with perturbative coupling to photons α 2 γ 64 π 3 f 2 c 2 γγ m 3 α Γ a = 4 π f a F µ ν ˜ L = c γγ F µ ν a a γ Supernova ATLAS /CMS Red Giants Ions Beam dumps ` a = � a � a Γ a 10 − 9 m 10 − 6 m 10 − 3 m 10 3 m 10 6 m 10 9 m 1 m c γγ /f . 1 / 10 GeV − 1 � 2

The lifetime gap Example: Axion-like particle with perturbative coupling to photons Typically: Long lifetime = Weak couplings α 2 64 π 3 f 2 c 2 γγ m 3 Γ a = and small masses a Supernova ATLAS /CMS Red Giants Ions Beam dumps ` a = � a � a Γ a 10 − 9 m 10 − 6 m 10 − 3 m 10 3 m 10 6 m 10 9 m 1 m c γγ /f . 1 / 10 GeV − 1 � 3

The lifetime gap Example: Axion-like particle with perturbative coupling to photons Typically: Long lifetime = Weak couplings α 2 64 π 3 f 2 c 2 γγ m 3 Γ a = and small masses a �� � �� � �� � Why would a new particle be �� � light and weakly coupled? �� � �� - � 1nm �� - � 100m �� - � �� - � �� - � �� - � � �� � � 4

Feebly interacting particles New light states with sizeable couplings are largely ruled out. Many UV theories predict new heavy states with sizeable couplings to the SM. Light and weak interactions seem to be independent conditions, is this theoretically motivated ? Goldstone bosons New Gauge Bosons � 5

Goldstone bosons Every spontaneously broken continuous symmetry gives rise to massless spin-0 fields. V ( φ ) µ 2 < 0 V ( φ ) = µ 2 φφ † + λ ( φφ † ) 2 φ = ( f + s ) e ia/f m 2 s = 4 λ f 2 h = | µ 2 | 2 m 2 a = 0 Re φ Im φ 6

Goldstone bosons Since the GB corresponds to the phase of a complex field, it is protected by a shift symmetry φ = ( f + s ) e ia/f it is protected by a shift symmetry e ia ( x ) /f → e i ( a ( x )+ c ) /f = e ia ( x ) /f e ic/f This symmetry forbids a mass term, and all couplings are suppressed by the UV scale ∂ ν a L = 1 2 ∂ µ a ∂ µ a + c µ µ γ ν µ + . . . 4 π f ¯ 7

Goldstone bosons An exactly massless boson is very problematic. The global symmetry can be broken by explicit masses or anomalous effects ∂ ν a µ γ ν µ + . . . +1 L = 1 2 m 2 a a 2 2 ∂ µ a ∂ µ a + c µ 4 π f ¯ m a = µ 2 f Small masses Small couplings 8

Goldstone bosons ρ , P, N The most famous example is the pion q L i / q R i / D q L + ¯ D q R + m q ¯ q L q R L QCD = ¯ QCD ≈ GeV 3 q L q R i = Λ 3 h ¯ The pion mass is controlled by the explicit breaking through light quark masses π = m u + m d m 2 Λ 3 ≈ (140 MeV) 2 QCD f 2 π π 9

Goldstone bosons The most famous example is the pion Scales at f q L i / q R i / D q L + ¯ D q R + m q ¯ q L q R L QCD = ¯ QCD ≈ GeV 3 q L q R i = Λ 3 h ¯ The pion mass is controlled by the explicit breaking through light quark masses π = m u + m d m 2 Λ 3 ≈ (140 MeV) 2 QCD f 2 π ALP 10

Goldstone bosons Most general dimension five Lagrangian 2( ∂ µ a )( ∂ µ a ) − m 2 = 1 ν + ∂ µ a c i L D ≤ 5 α s G µ ν + a X ¯ 2 a 2 4 π f a G µ ν ˜ ψ i γ µ γ 5 ψ i , + c GG e ff f 2 i α α α α α ν + c γγ F µ ν + c γ Z Z µ ν + c ZZ 4 π f a F µ ν ˜ 4 π s w c w f a F µ ν ˜ w f a Z µ ν ˜ Z µ ν 4 π s 2 w c 2 Many possible signature. I will focus on photons here. Georgi, Kaplan, Randall, Phys. Lett. 169B, 73 (1986) � 11

How to close the gap? Different strategies: 1. High statistics �� � �� � 2. (Very) displaced vertices �� � �� � �� 3. Exotic decays � �� - � 1nm �� - � 100m �� - � Knapen et al. Phys. Rev. Lett. 118 (2017) �� - � �� - � �� - � � �� � ATLAS, Nature Phys 13 , no. 9, 852 (2017) � 12 CMS 1810.04602

How to close the gap? Ze High statistics: Pb Pb γ Photon fusion in Ion scattering a γ Pb Pb Ze �� � aF e F coupling log � � �� ! linear CMS , 36 pb � 1 �� � OPAL , 2 γ ATLAS , 2 γ 10 � 3 OPAL , 3 γ �� � ATLAS , 3 γ 1 / Λ (GeV � 1 ) �� � ATLAS , 2016 10 � 4 �� 1 nb � 1 Beam Dump b � 1 n 0 � 1 p - p p s = 7 TeV Pb - Pb p s NN = 5 . 5 TeV �� - � 10 � 5 0 − 2 0 − 1 0 0 1nm 5 20 40 60 80 100 1 1 1 �� - � m a (GeV) 100m �� - � Knapen et al. Phys. Rev. Lett. 118 (2017) �� - � �� - � �� - � � �� � ATLAS, Nature Phys 13 , no. 9, 852 (2017) � 13 CMS 1810.04602

How to close the gap? 200 m � (Really) displaced vertices: γ 20 m γ 100 m MATHUSLA, FASER, SHiP , CodexB,.. �� � Curtin et al 1806.07396 100 m MATHUSLA �� � Feng et. al. Phys. Rev. D 98 , 055021 a Gligorov et al. Phys. Rev. D 97 , no.1 015023, (2018) Alekhin et. al. Rept. Prog. Phys. 79 , 124201 (2016) ATLAS/CMS �� � �� � Z �� � �� � �� �� � �� � �� � m � �� � LHC γ m γ m �� � LHC & Z �� - � �� MATHUSLA m LA �� - � a � �� - � �� - � Z 1nm �� - � �� �� - � �� � �� � �� � 100m �� - � �� - � �� - � �� - � � �� � MB, Neubert, Thamm, Eur.Phys. J.C 79 � 14

How to close the gap? 200 m � (Really) displaced vertices: γ 20 m γ 100 m MATHUSLA, FASER, SHiP , CodexB �� � Curtin et al 1806.07396 100 m MATHUSLA �� � Feng et. al. Phys. Rev. D 98 , 055021 a Gligorov et al. Phys. Rev. D 97 , no.1 015023, (2018) Alekhin et. al. Rept. Prog. Phys. 79 , 124201 (2016) ATLAS/CMS �� � �� � Z �� � �� � �� �� � �� � �� � �� � MATHUSLA FASER �� � �� � �� �� � � SHiP �� - � �� - � 1nm �� - � � �� - � 100m �� - � � �� - � �� - � �� - � �� � MB, Neubert, Thamm, Eur.Phys. J.C 79 � 15

How to close the gap? Big Advantage of the LHC: The only place to make the Higgs! Z Z Z a h h h h h a a a �� � �� � L > 5 = c ah f 2 ( ∂ µ a ) ( ∂ µ a ) φ † φ + �� � �� � ln φ † φ + c 5 �� f ( ∂ µ a ) φ † iD µ φ + h.c. Zh � � µ 2 � φ + c Zh �� - � f 3 ( ∂ µ a ) � φ † iD µ φ + h.c. � φ † φ 1nm �� - � 100m �� - � � �� - � �� - � �� - � �� � MB, Neubert, Thamm, PRL 117, 181801 (2016) � 16 MB, Neubert, Thamm, JHEP 1712 044 (2017)

How to close the gap? Big Advantage of the LHC: Theoretically interesting: The only place to make the Higgs! Z Z Z Z Z h h h h h f a a �� � �� � L > 5 = c ah f 2 ( ∂ µ a ) ( ∂ µ a ) φ † φ + �� � �� � ln φ † φ + c 5 �� f ( ∂ µ a ) φ † iD µ φ + h.c. Zh � � µ 2 � φ + c Zh �� - � f 3 ( ∂ µ a ) � φ † iD µ φ + h.c. � φ † φ 1nm �� - � 100m c e ff �� - � Br( h → Za ) < 1 o / Zh = 0 . 015 oo �� - � �� - � �� - � � �� � MB, Neubert, Thamm, PRL 117, 181801 (2016) � 17 MB, Neubert, Thamm, JHEP 1712 044 (2017)

How to close the gap? Many experimental signatures: medium mass, Low mass, very small coupling small coupling small coupling 200 m � γ γ γγ 20 m γ 100 m �� � γ a a 100 m MATHUSLA �� � a h h ATLAS/CMS �� � Z Z Z �� � �� �� � �� � �� � Exotic signatures Very challenging Br( h → Z γ ) > Br SM ( h → Z γ ) exotic signatures Always enhanced! h → Z γγ h → Z + E T, miss a → γγ � 18

New Gauge Bosons New light gauge bosons have long history Holdom Phys.Lett 166B, (1986) L = − 1 2 F µ ν X µ ν − 1 4 F µ ν F µ ν − ✏ 4 X µ ν X µ ν Kinetic mixing as a renormalizable portal A 0 is a free parameter B µ ✏ µ 8 ⇡ 2 log Λ 2 ✏ ∝ g X e A 0 B µ m 2 µ Charged SM matter is milli- eA µ J µ EM − ✏ eA 0 µ J µ charged under U (1) X EM � 19

New Gauge Bosons New light gauge bosons have long history Holdom Phys.Lett 166B, (1986) L = − 1 2 F µ ν X µ ν − 1 − 1 4 F µ ν F µ ν − ✏ 4 X µ ν X µ ν 2 D µ SD µ S Hidden Photon mass term m A 0 = g X h S i 8 ⇡ 2 log Λ 2 ✏ ∝ g X e A 0 B µ m 2 µ Small masses Small couplings eA µ J µ EM − ✏ eA 0 µ J µ EM Universal � 20

� �� � �� � � �� New Gauge Bosons The new light gauge boson couples like a a massive photon � e + e − had µ + µ − �� - � τ + τ − �� - � � �� eA µ J µ EM − ✏ eA 0 µ J µ EM Universal � 21

New Gauge Bosons g - 2 e LHCb μμ �� - � �� - � KLOE APEX g - 2 μ A1 BaBar �� - � NA48 BaBar E774 �� - � �� - � 1 µ m E141 �� - � �� - � �� - � LHCb μμ �� - �� Orsay �� - � �� - �� NuCal �� - �� U70 Charm �� - � �� - �� 100m E137 �� - �� Universal LSND �� - � �� - �� �� - �� �� - � �� - � � �� - - - MB, Foldenauer Jaeckel, JHEP 1807 094 (2018) � 22