Search for Sphalerons at LHC and IceCube Kazuki Sakurai IPPP, - - PowerPoint PPT Presentation
Search for Sphalerons at LHC and IceCube Kazuki Sakurai IPPP, Durham In collaboration with: John Ellis and Michael Spannowsky 3/8/2016 @ IPMU Plan Introduction Review of Sphalerons Sphalerons at the LHC Sphalerons at
IPPP, Durham
3/8/2016 @ IPMU
In collaboration with:
John Ellis and Michael Spannowsky
2
3
pp
80 µb−1
W
35 pb−1
Z
35 pb−1
t¯ t tt−chan WW H
total VBF VH t¯ tH
Wt
2.0 fb−1
WZ
13.0 fb−1
ZZ ts−chan t¯ tW t¯ tZ
σ [pb]
10−1 1 101 102 103 104 105 106 1011
Theory LHC pp √s = 7 TeV Data 4.5 − 4.9 fb−1 LHC pp √s = 8 TeV Data 20.3 fb−1 LHC pp √s = 13 TeV Data 85 pb−1
ATLAS Preliminary Run 1,2
√s = 7, 8, 13 TeV
and perturbative calculations.
4
Fµν = ∂µAν − ∂νAµ + [Aµ, Aν]
Aµ → U †AµU + U †∂µU SEW → SEW
U ∈ SU(2) U = a + i(b · σ) a2 + b2 = 1
Aµ = 0
↔
A = U †∂µU
The space of vacua is equivalent to the space of these maps.
At a given t, U(x) is a function that maps from x ∈ R3 to U ∈ SU(2).
action: a vacuum: gauge trans.:
SEW = 1 2g2
5
Fµν = ∂µAν − ∂νAµ + [Aµ, Aν]
Aµ → U †AµU + U †∂µU
action:
SEW → SEW
U ∈ SU(2) U = a + i(b · σ) a2 + b2 = 1
a vacuum:
Aµ = 0
↔
A = U †∂µU
π3(S3) = Z
R3 = S3 + (·), SU(2) = S3
The map has distinctive sectors classified by the winding number!
SU(2)
gauge trans.:
The space of vacua is equivalent to the space of these maps.
At a given t, U(x) is a function that maps from x ∈ R3 to U ∈ SU(2). SEW = 1 2g2
6
E
perturbative
n
· · ·
An,µ(x) = Un(x)†∂µUn(x) Un(x) = exp
x · σ
7
E
instanton sphaleron
n
· · ·
An,µ(x) = Un(x)†∂µUn(x) Un(x) = exp
x · σ
8
˜ F µν = µνρσFρσ
1 16π2 Fµν ˜ F µν = ∂µKµ Kµ = 1 8π2 µνρσtrAν(∂ρAσ + 2 3AρAσ)
16π2 Fµν ˜ F µνd4x =
= h Z K0(t, x)d3x it=∞
t=−∞
= n(t = ∞) − n(t = −∞) = ∆n
Define a current K as Then it follows
Fµν(x) → 0 for x → ∞
therefore
finite energy condition:
, , ,
There exist evolutions of field configuration that change the winding number.
9
The triangle anomaly gives J(i)
µ
= ¯ ψ(i)
L γµψ(i) L
ψ(i)
L = {ˆ
uα
L, ˆ
cα
L, ˆ
tα
L, ℓe, ℓµ, ℓτ}
ˆ uL = uL dL
νe eL
with
∂µJ(i)
µ
= 1 16π2 Fµν ˜ F µν
10
The triangle anomaly gives J(i)
µ
= ¯ ψ(i)
L γµψ(i) L
ψ(i)
L = {ˆ
uα
L, ˆ
cα
L, ˆ
tα
L, ℓe, ℓµ, ℓτ}
ˆ uL = uL dL
νe eL
with We have
∂µJ(i)
µ
= 1 16π2 Fµν ˜ F µν
= ∆N (i)
F
∆n =
16π2 Fµν ˜ F µνd4x
= J(i)
0 d3x
t=∞
t=−∞
∆n = ∆Nˆ
uL = ∆Nˆ uL = ∆Nˆ uL
We find 12 related equalities
= ∆Nˆ
cL = · · ·
= ∆Nˆ
tL = · · ·
= ∆Nℓe = ∆Nℓµ = ∆Nℓτ
11
ˆ uL
ˆ cL ˆ tL
ℓτ ℓe ℓµ ˆ uL ˆ cL ˆ tL ˆ tL ˆ cL
ˆ uL
∆n = 1
The triangle anomaly gives J(i)
µ
= ¯ ψ(i)
L γµψ(i) L
ψ(i)
L = {ˆ
uα
L, ˆ
cα
L, ˆ
tα
L, ℓe, ℓµ, ℓτ}
ˆ uL = uL dL
νe eL
with
∂µJ(i)
µ
= 1 16π2 Fµν ˜ F µν
= ∆N (i)
F
∆n =
16π2 Fµν ˜ F µνd4x
= J(i)
0 d3x
t=∞
t=−∞
∆n = ∆Nˆ
uL = ∆Nˆ uL = ∆Nˆ uL
= ∆Nˆ
cL = · · ·
= ∆Nˆ
tL = · · ·
The event looks like a fire ball!
= ∆Nℓe = ∆Nℓµ = ∆Nℓτ
We have We find 12 related equalities
12
⟨n|n + ∆n⟩ ∼ e− ˆ
SE
SE is the Euclidean action at the stationary point, which is given by
The tunnelling rate can be estimated using the WKB approximation as
ˆ SE = 1 2g2
13
⟨n|n + ∆n⟩ ∼ e− ˆ
SE
Fd4x
F)2d4x ≥ 0
= ⇒
Note that:
SE is the Euclidean action at the stationary point, which is given by
The tunnelling rate can be estimated using the WKB approximation as
ˆ SE = 1 2g2
14
E
n
n+1
⟨n|n + ∆n⟩ ∼ e− ˆ
SE
Fd4x
F)2d4x ≥ 0
= ⇒
e− 4π
αW ∼ 10−170
The tunnelling rate is unobservably small Note that:
SE is the Euclidean action at the stationary point, which is given by
The tunnelling rate can be estimated using the WKB approximation as
ˆ SE = 1 2g2
= 1 2g2
Fd4x
g2
15
E
n
n+1
ESph
sphaleron
ESph = 2mW αW B mH mW
F.R.Klinkhamer and N.S.Manton (1984)
≃ 9 TeV
(for mH = 125GeV)
It plays an important role in baryo(lepto)genesis.
Γ ∝ exp
T
16
classical approach (perturbation in the instanton background).
10 20 30 40
0.0 0.5
(c ≃ 2)
instanton
E [TeV]
S(E)
instanton
σ(∆n = ±1) ∝ exp
αW S(E)
8 E E0 4
3 − 9
16 E E0 2 + · · ·
E0 = √ 6πmW /αW ≃ 18 TeV
+ · · ·
17
S.Khlebnikov, V.Rubakov, P.Tinyakov 1991, M.Porrati 1990, V.Zakharov 1992, …
(c ≃ 2)
E [TeV]
S(E)
instanton
10 20 30 40
0.0 0.5
classical approach (perturbation in the instanton background).
σ(∆n = ±1) ∝ exp
αW S(E)
8 E E0 4
3 − 9
16 E E0 2 + · · ·
E0 = √ 6πmW /αW ≃ 18 TeV
+ · · ·
18
S.Khlebnikov, V.Rubakov, P.Tinyakov 1991, M.Porrati 1990, V.Zakharov 1992, … P.Arnold, M.Mattis 1991, A.Mueller 1991, D.Diakonov, V.Petrov 1991, …
σ(∆n = ±1) ∝ exp
αW S(E)
8 E E0 4
3 − 9
16 E E0 2 + · · ·
E0 = √ 6πmW /αW ≃ 18 TeV
(c ≃ 2)
E [TeV]
S(E)
instanton
10 20 30 40
0.0 0.5
classical approach (perturbation in the instanton background).
19
Recently Tye and Wong (TW) have pointed out that the periodic nature of the EW potential is important and this effect was not taken into account in the previous calculations. They evaluated the sphaleron rate by constructing a 1D quantum mechanical system [1505.03690].
2m ∂2 ∂Q2 + V (Q)
Q = µ/mW nπ = µ − sin(2µ)/2
,
where Q is related to the winding number n as
˜ Φ = v (1 h(r)) U cos µ ! + h(r) v ! , Ai = i g(1 f(r))U∂iU†, U = cos µ + i sin µ cos θ sin µ sin θeiϕ sin µ sin θeiϕ cos µ i sin µ cos θ ! lim
r!0
f(r) r = h(0) = 0, f(1) = h(1) = 1,
By following a sphaleron trajectory in the original YM Lagrangian, they found:
V (Q) ' 4.75 TeV
◆
m = 17.1 TeV,
20
The wave functions in periodic potentials are given by Bloch waves.
k2 2m
E
The spectrum exhibits a band structure.
k
2 4 0.5 1.0 1.5 2.0 2.5
E
|Ψ(Q)|2 = |Ψ(Q +
π mW )|2
Ψ(Q) = eikQ uk(Q),
uk(Q) = uk(Q +
π mW )
21
2 4 0.5 1.0 1.5 2.0 2.5
π a 2π a 3π a 4π a −4π a −3π a −2π a −π a
k2 2m
E
(a = π/mW )
k
gaps bands
The spectrum exhibits a band structure. The wave functions in periodic potentials are given by Bloch waves.
|Ψ(Q)|2 = |Ψ(Q +
π mW )|2
Ψ(Q) = eikQ uk(Q),
uk(Q) = uk(Q +
π mW )
22
Manton AKY Band center energy(TeV) Width (TeV) Band center energy(TeV) Width (TeV) 9.113 0.01555 9.110 0.01134 9.081 7.192 × 10−3 9.084 4.957 × 10−3 9.047 2.621 × 10−3 9.056 1.718 × 10−3 9.010 8.255 × 10−4 9.026 5.186 × 10−4 8.971 2.382 × 10−4 8.994 1.438 × 10−4 8.931 6.460 × 10−5 8.961 3.747 × 10−5 8.890 1.666 × 10−5 8.927 9.279 × 10−6 8.847 4.114 × 10−6 8.892 2.198 × 10−6 8.804 9.779 × 10−7 8.857 5.008 × 10−7 8.759 2.245 × 10−7 8.802 1.101 × 10−7 8.714 4.993 × 10−8 8.783 2.341 × 10−8 8.668 1.078 × 10−8 8.745 4.828 × 10−9 8.621 2.262 × 10−9 8.707 9.673 × 10−10 8.574 4.622 × 10−10 8.668 1.886 × 10−10 8.526 9.210 × 10−11 8.628 3.580 × 10−11 8.477 1.792 × 10−11 8.588 6.622 × 10−12 8.428 3.411 × 10−12 8.548 1.211 × 10−12 8.379 6.395 × 10−13 8.506 2.167 × 10−13 8.328 1.208 × 10−13 8.465 3.553 × 10−14 . . . . . . . . . . . . 0.3084 ∼10−169 0.3146 ∼10−204 0.2398 ∼10−171 0.2454 ∼10−207 0.1712 ∼10−174 0.1759 ∼10−209 0.1027 ∼10−177 0.1061 ∼10−212 0.03421 ∼10−180 0.03574 ∼10−216
For E ≪ ESph, TW found the band width is exponentially small compared to the gap, corresponding to the small tunnelling rate found in the previous calculations. For E > ESph, the wave functions are approximately plane waves with their momentum larger than the potential barrier, implying the exponential suppression disappears!
10 20 30 40
0.0 0.5
TW
E [TeV]
S(E)
σ(∆n = ±1) ∝ exp
αW S(E)
23
24
S(E) = { (1 − a) ˆ E + a ˆ E2 − 1 for ˆ E < 1 for ˆ E ≥ 1 ˆ E = E/ESph
σ(∆n = ±1) =
We parametrise the sphaleron production rate as: The typical scale is given by 1/mW, and the unknown pre-factor is given by p(E), which we assume a constant p = p(ESph), because σ(E) very sharply peaks at E=ESph.
1 mW
σ0
(c ≃ 2)
We parametrise and use the TW’s exponent as
dLab dE = 2E E2
CM
Z − ln √τ
ln √τ
dyfa(pτey)fb(pτe−y)
(τ = E2/E2
Sph)
The parton luminosity function is given as usual as
a = −0.05
m2
W
dLab dE exp
αW S(E)
25
ˆ cL ˆ tL
ℓτ ℓe ℓµ
ˆ cL ˆ tL ˆ tL ˆ cL ˆ uL
∆n = 1
have to differ.
fa(x) → 1 2fa(x) fa(x)fb(x) → 1 3fa(x)fb(x)
(if a, b are the same generation)
26
p(E) = p = 1
ESph = 9 TeV
27
Sphaleron gg→H 13 TeV 7.3 fb 44 x 103 fb 14 TeV 41 fb 50 x 103 fb 33 TeV 0.3 x 106 fb 0.2 x 106 fb 100 TeV 141 x 106 fb 0.7 x 106 fb
ESph = 9 TeV
p = 1
[1601.03654]
28
(by M.Gibbs, B.Webber).
according to the phase space.
⟨I|(¯ ℓe¯ ℓµ¯ ℓτ)(¯ q¯ q¯ q)(¯ q¯ q¯ q)(¯ q¯ q¯ q)|F⟩
∆n = −1
qq → 3¯ ℓ + 7¯ q
⟨I|(ℓeℓµℓτ)(qqq)(qqq)(qqq) · (¯ qq) · (¯ qq)|F⟩
∆n = +1
qq → 3ℓ + 11q
EM charge is conserved.
I I
F F
lep
N 0.5 − 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Normalised Events 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
13TeV 3l7q 3l11q
top
N 0.5 − 0.5 1 1.5 2 2.5 3 3.5 Normalised Events 0.1 0.2 0.3 0.4 0.5 0.6 0.7
13TeV 3l7q 3l11q
[TeV]
T
H 2 4 6 8 10 12 Normalised Events 0.05 0.1 0.15 0.2 0.25
3l7q 13 TeV 14 TeV
[TeV]
miss T
E 0.5 1 1.5 2 2.5 Normalised Events 0.02 0.04 0.06 0.08 0.1
3l7q 13 TeV 14 TeV
[TeV]
miss T
E 2 2.5
[TeV]
T
H 10 12
lep
N 4 4.5
top
N 3.5
29
J.Ellis, KS [1601.03654]
(=e,μ)
HT =
pjet,i
T
30
[TeV]
T
H 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 Events / 0.1 TeV
1 −
10 1 10
2
10
3
10
= 9TeV, p = 0.2
Sph
3l7q: E = 9TeV, p = 0.2
Sph
3l11q: E
7, L = 3 fb ≥
jet
ATLAS13, n
njet ≥ HT > Hmin
T
(TeV) Expected limit (fb) Observed limit (fb) 3 5.8 1.63+0.70
−0.57
1.33 4 5.6 1.77+0.70
−0.57
1.77 5 5.5 1.56+0.73
−0.50
1.75 6 5.3 1.52+0.69
−0.50
2.15 7 5.4 1.02+0.36
−0.0
1.02 8 5.1 1.01+0.29
−0.0
1.01
We confront our sphaleron events with the ATLAS mini black hole search results @ 13TeV with 3.6/fb [1512.02586], where the signal regions are defined for different # of jets and HT.
HT =
pjet,i
T
J.Ellis, KS [1601.03654]
31
The best expected SR is SR8 for ESph < 9.3TeV, SR7 otherwise.
J.Ellis, KS [1601.03654]
32
33
34
ˆ uL ˆ cL ˆ tL ℓτ ℓe ℓµ ˆ uL ˆ cL ˆ tL ˆ tL ˆ cL ˆ uL ∆n = 1
What neutrino energy is required to create a sphaleron?
(mN, 0)
(Eν, Eν)
sNν = E2 − p2 = (mN + EN)2 − E2
N ≃ 2mNEν
sqν ≃ 2xmNEν
(x = Eq/EN)
Eν ≥ E2
Sph
2xmN ≃ (9 TeV)2 2x(0.94 GeV) ≃ 4 · 107 x GeV
To create a sphaleron, one needs
(for 10−3 x 10−1)
Eν 108−10 GeV
35
~106 GeV neutrinos have been
36
uot
~106 GeV neutrinos have been
Cosmic ray spectrum falling sharply above 1011 GeV has been observed.
p + γCMB → n + π+
p + γCMB → p + π0
Greisen–Zatsepin–Kuzmin (GZK) process:
(EγCMB ∼ 2.6 · 10−13 GeV)
Ep ≥ (mN + mπ)2 − m2
p
4EγCMB
∼ 3 · 1011 GeV
(pp + pγCMB)2 ≥ (mN + mπ)2
⇒
37
uot
~106 GeV neutrinos have been
p + γCMB → n + π+
p + γCMB → p + π0
Greisen–Zatsepin–Kuzmin (GZK) process:
(EγCMB ∼ 2.6 · 10−13 GeV)
Ep ≥ (mN + mπ)2 − m2
p
4EγCMB
∼ 3 · 1011 GeV
(pp + pγCMB)2 ≥ (mN + mπ)2
⇒
: π0 → γγ : π+ → µ+νµ → e+νe¯ νµνµ
These high energy neutrinos and photons should reach the earth. Cosmic ray spectrum falling sharply above 1011 GeV has been observed.
38 10−11 10−10 10−9 10−8 10−7 10−6 10−5 0.1 1 10 102 103 104 105 106 107 108 109 1010 1011 1012 E2J [GeV cm−2 s−1 sr−1] E [GeV]
maximal cascade
Emin = 1018.5 eV
HiRes I&II Fermi LAT p (best fit) ν, ¯ ν (99% C.L.) γ (99% C.L.)
M.Ahlers et.al [1005.2620]
ESph
ν
108−10 GeV
One could predict GZK neutrino and gamma ray fluxes by modelling the cosmic ray spectrum and fit it to the observed spectrum.
While neutrino energy is unchanged apart from redshift, the photons loose their energy by interacting with the intergalactic radiation fields.
γGZK + γ → e+e−
39
/GeV)
ν
(E
10
log
5 6 7 8 9 10 11
]
2
Neutrino Effective Area [m
10 1 10
2
10
3
10
4
10
5
10
e
ν
µ
ν
τ
ν
IC86
dEνAeff(Eν) d2Φ dEνdt dNCC/NC dt =
dEν σSph
νN (Eν)
σCC/NC
νN
(Eν) Aeff(Eν) d2Φ dEνdt
dNSph dt =
Event rate can be calculated using the energy dependent effective neutrino detection area.
J.Ellis, KS, M.Spannowsky [1603.06573]
ist
5 106 107 108 109 1010 1011 1012
10−11 10−10 10−9 10−8 10−7
E2Φ [GeV cm−2 s−1 sr−1]
E [GeV]
40
dEνAeff(Eν) d2Φ dEνdt dNCC/NC dt =
dEν σSph
νN (Eν)
σCC/NC
νN
(Eν) Aeff(Eν) d2Φ dEνdt
dNSph dt =
Event rate can be calculated using the energy dependent effective neutrino detection area.
41
J.Ellis, KS, M.Spannowsky [1603.06573]
(because the fall of PDF is faster than that of GZK neutrino spectrum)
42
p = 1
p = 0.05
the sphaleron events may be hidden in the GZK neutrino events via the ordinary EW interaction.
the event shape is important.
How do sphaleron events look different from the ordinary neutrino events at IceCube?
43
p = 1
p = 0.05
the sphaleron events may be hidden in the GZK neutrino events via the ordinary EW interaction.
the event shape is important.
How do sphaleron events look different from the ordinary neutrino events at IceCube?
44
“muon bundle” “shower” “double bang” νµN → µX
νeN → eX
νiN → νiX ντN → τX ντN → τX1 → X1ντX2
Eτ ∈ [106, 107] GeV
17 m
μ νμ νθ с
45
Eν 108−10 GeV mall ∼ ESph ∼ 9 TeV
ˆ uL
ˆ cL
ˆ tL ℓτ ℓe ℓµ ˆ uL
ˆ cL ˆ tL
ˆ tL ˆ cL ˆ uL
∆n = 1
“shower”
with θ > 10-2 rad ⇒ “double bundle”??
46
/GeV)
τ , µ
(E
10
Log
3 4 5 6 7 8 9 10 11
Events per Interaction
0.02 0.04 0.06 0.08 0.1 τ , µ Primary τ , µ Secondary
double bang
)
lep,lep
θ (
10
Log
7 − 6.5 − 6 − 5.5 − 5 − 4.5 − 4 − 3.5 − 3 − 2.5 − 2 −
Events per Interaction
0.005 0.01 0.015 0.02 0.025
1
τ ,
1
µ
2 i
, lep
1 i
lep
2 j
, lep
1 i
lep
2 i
, lep
2 i
lep
2 j
, lep
2 i
lep
Only 5% of the sphaleron-induced events have double bang taus.
double bundle
particles are highly collimated and double bundles cannot be expected.
47
not been observed experimentally.
the sensitivity of observing sphaleron-induced processes at the LHC and IceCube.
analysis already excludes some parameter region.
colliding with nucleus in the ice at IceCube. For ESph = 9TeV, the sensitivity is compatible with the 13TeV LHC with 3/fb.
100TeV hadron collider can explore up to p ~10-11.
48
e−SE
e−2SE ?
A B A B C
tAB = 1 ΓAB ∼ eSE
tAC = tAB + tBC ∼ eSE
tAC = 1 ΓAC ∼ e2SE ?
actual tunnelling rate is much larger!
49
For some energies, different paths interfere coherently.