Post on 13-Oct-2020
Dark photons physics/theory, phenomenology, experiment/
G. KozlovJINR, Dubna
25.09.2019 G Kozlov J-PARC 10thY 2019 1
Dark Matter (what do we know)
DM established - Through gravitational interactions
• No exact particle nature of DM we have yet
Known more: DM originated as thermal relic from early Universe
If correct, - abundance of DM, if DM has non-gravitational interactions with SM Mass range for candidates
25.09.2019 G Kozlov J-PARC 10thY 2019
↓
𝑹𝒂𝒕𝒆𝑺𝑴 > 𝑹𝒂𝒕𝒆𝑯𝒖𝒃𝒃𝒍𝒆 𝒆𝒙𝒑.(𝒙𝒆𝑼)
~ 𝑀𝑒𝑉 − 10 𝑇𝑒𝑉𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑝𝑟𝑜𝑏𝑒 𝑡𝑜 𝑟𝑢𝑙𝑒 𝑜𝑢𝑡 𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝐷𝑀
v DM stems from BGRD of Dark Photons
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25.09.2019 G Kozlov J-PARC 10thY 2019
DM
Gravitational WIMP MiracleSUSY wimp ? ~ 100 GeV
Why?DM relic density consistent with weak interactions
Need low mass vector state – MEDIATOR to be consistent with DM Relic density
ΩJK~𝑚L∗N
𝑚OP Heavy “PHOTON”?
Dark Photon state ?
Ø Hidden sector scenario;DM does not interact directly to SM!
ü LDM requires new forces to correct relic abundance
DM search with WIMP (no results): 𝑆𝑈𝑆𝑌𝒏𝒐 𝒆𝒗𝒊𝒅𝒆𝒏𝒄𝒆 𝑨𝑻𝑳𝑨𝑺/𝑪𝑴𝑺
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o Hidden sector scenario
- DM charged under new U’(1) gauge field mediator by U’(1) gauge boson.
- DP mixes with
o If DP is the mediator, the issues do arise:
- What is the symmetry to be responsible to its propagation
- Experimental search for the mediator – DP (observables, etc.)
25.09.2019 G Kozlov J-PARC 10thY 2019
𝑼(𝟏)𝒀 𝒃𝒚 𝝐 (free parameter, mixing angle)
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vApproximate conformal breaking scenario
DM – SM mediator Dark Photon 𝑩𝝁 𝒙𝑖𝑛 𝑫𝒊𝒍𝒂𝒕𝒐𝒏 𝑐𝑜𝑛𝑑𝑒𝑛𝑠𝑎𝑡𝑒
𝑃j,𝑀jl 𝐷 𝐾j/Poincare/ /Scale/ /Conformal/
Generators of conformal group transformations
For any element g of Conformal group:
g 𝑒nopqp 𝑒n𝑩𝝁rp= 𝑒notpqp 𝑒n𝑩t𝝁rp 𝑒nuJ 𝑒nvpwKpw for 𝑥j , 𝑩𝝁 𝒙
Dark Photon field 𝑩𝝁 𝒙 ~𝑓yz𝜕j𝜎 𝑥
𝜎 𝑥 → 𝜎t 𝑥 = 𝜎 𝑥 + 𝜔𝑓, 𝑥j→ 𝑥jt = 𝑒�𝑥jNon-primary operator
GK, 2018
Ø Particle Physics / Cosmology:Ø All scales are subject of scale/conformal symmetry breaking
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25.09.2019 G Kozlov J-PARC 10thY 2019
v Experiment. Fixed target idea
𝐷𝑃 → 𝑙 ̅𝑙, 𝐸Jq ≈ 𝐸����
𝜃Jq ≈𝑚Jq
𝐸����
�P≈ 0 𝑛𝑎𝑟𝑟𝑜𝑤
𝐷𝑃 → 𝑙 ̅𝑙, Θ����� ~𝑚Jq
𝐸����
ü Vertexing DP decays requires detector close to target
Signature: - Invariant mass - Momentum/mass resolution
requiredEM calorimeter ID 𝑙 𝑎𝑛𝑑 ̅𝑙
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o Kinetic term: - mixing importance
• to estimate indirect/direct detection of DM - Indirect Annihilation to lepton-anti-leptons
- Direct DM scattering against nuclei
25.09.2019 G Kozlov J-PARC 10thY 2019
𝜎𝑣 ~𝛼JKP /𝑚�P . annihilation rate
𝑙�𝑙y : 𝜎𝑣 � ~𝝐𝟐𝛼 𝛼JK𝑚�P 𝑃 Δ
, Δ =𝑚Jq −𝑚�
𝑚�
𝜎𝑣 � ~𝝐𝟐𝛼 𝛼JK 𝜇��P
𝑚JqN
𝑍P
𝐴P, 𝜇�q =
𝑚� 𝑚�
𝑚� +𝑚�
𝝐𝟐
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25.09.2019 G Kozlov J-PARC 10thY 2019
vHeavy photon searches v Fixed target
NA 64 @ SPS, PRD 97 (2018) 072002 PRL 123 (2019) 121801
HPS @ Jlab, PRD 98 (2018) 091101
- J-PARC, T2K ?- DUNE @ FNAL ?
Ø Low , 𝒍𝒐𝒘𝒎𝑫𝑷 → 𝒍𝒐𝒏𝒈𝒆𝒓 lifetime
o EM Telescope SHUKET
𝛼JK
Detect weak DM-induced electric field 𝐸JK~𝜖 𝑚 𝜓JK
𝑒y𝑍 → 𝑒y𝑍𝛾∗ → 𝑒y𝑍𝜒�̅� invisible10y¤ ≤ 𝜖LyL∗ ≤ 10yP
𝑚L∗ ≤ 1 𝐺𝑒𝑉
19 < 𝑚L∗ < 81 𝑀𝑒𝑉, 𝜀PLyL∗~ 6 ¬ 10y
(𝜇𝑒𝑉 𝑚𝑎𝑠𝑠 @𝑚𝑖𝑥𝑖𝑛𝑔 ~10yzP )
v Colliders- LHC, FASER 480 m downstream of ATLAS int. point 2020-21?
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25.09.2019
LHC: DP experimental signature Overall signal strength in
Ø Origin: - SI breaking sector of CFT - Contribution from DP to BR
Salient feature: DP energy with cont. spectrum vs in SM Ø By measuring spectrum in one can discriminate the
presence of DP or not. Ø Strategy of the analysis: identify candidates by precise
reconstruction of the initial Higgs state. Ø The measured rate of such events has to be compared to that expected
from known sources ü DP signal (exp. signature): detected in missing and distribution
Once DP produced: spectrum is NO more -function peaked at but rather continuous with
gg → H σ( )→ γγ γγ∗( )
BR H → γγ∗( ) ≈ 1+aε2Ω( )BR SM H → γγ( ) , Ω~ 1−m 2 / mH2( )
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γ∗ H → γγ
Eγ
H → γγ
E p
Eγ
δ 0.5mHE
γ= 0 , 0.5mH"# $%
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25.09.2019
High Energies: SM coupled to Scale Invariant (SI) sector
ü SI d.o.f. – scalar dilaton (D) appearance
Breaking of SI at triggers EW symmetry breaking at Ø Collider physics case (importance)
Why LHC14 and HL LHC instead lower energy machines?
Ø Higgs case D triggers the breaking of gauge invariance through D mass operator
ΛCFT = 4πfΛEW = 4πv , f ≥v = 246 GeV
f =vSU L 2( )×UY 1( )
G Kozlov J-PARC 10thY 2019
𝑚°~𝑓~𝑠±/P
At √𝑠 below Λ´µ¶, → 𝛽 𝑔n ≠ 0 𝐶𝑜𝑛𝑓𝑜𝑟𝑚𝑎𝑙 𝑏𝑟𝑒𝑎𝑘𝑖𝑛𝑔
𝐿¼½���= °¾ 𝜃jj(𝑆𝑀)
𝜃jj = 𝜃j
j 𝑆𝑀 ¼½�� + 𝜃jj 𝑆𝑀 �¿À�, 𝜃j
j 𝑆𝑀 �¿À�
= −𝛼Á8𝜋 𝑏ÃÄ𝐺jl� 𝐺jl� −
𝛼8𝜋 𝑏ÅKÄ𝐹jl𝐹jl −
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Effect of DM sector on observable(s) Ø Mixing strength is bounded by
GK Nucl. Phys. B273 (2016)
ε ε <sd
v2Md−2( )2
25.09.2019 G Kozlov J-PARC 10thY 2019
s = 8−14 TeV, M = 800−1000 TeV, d = 4
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Upper limit on mixing angle e NP signals with DP increase with For : Relevant energy scale Result: DP visible @ LHC for the UV scale up to TeV, d=4 If , the only decay is appropriate within SM ü LHC is a very good facility where the DM Physics can be tested well
s, d
H→ γγ ∗ L ~ OSM OIR ~ εψ γµψ H B µM −1
Q ~ mq, q : top,...
ε < 3⋅10−2 , q : top , d = 4; M >v
M <103
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𝜀 → 0 𝐻 → 𝛾𝛾
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Upper limit on DP mass
No final state interactions: (partial decay width)
For
Am γ∗ → νν( ) = 12 f νν gVν γβ + g Aν γβγ5( )νγβ∗
fν2 = 4 2Gm 2 , G ~ 10−5GeV −2
Γ γ∗ → νν( ) = 23α⋅ε2m
↓
2Ggν2m 2
4πα, gVν
2 = g Aν2 = g
ν2 =14
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𝜀 < 3 ¬ 10yP → 𝑚 < 3.3 𝐺𝑒𝑉 GK (2016)
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To predict , the more detailed calculations need E.g., EMNFF
DP mass: Combined calculations give
mν
γ∗ ν
Γ γ∗ → νν( )~ α2m 5G 2 ln Λν2
ml2−16
)
*++
,
-..
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m≈ 𝑚j� PɱÊË
∑Í:Î,p Ï¿ÐwÑ
ÒÍÑy
ËÓ
→ 𝑚 = 0.83 𝐺𝑒𝑉
Λl~𝑂 𝑚Õ , 𝜺 = 𝟕. 𝟔 ¬ 𝟏𝟎y𝟑 𝐺𝐾 (2016)
e, 𝜇 𝑙𝑜𝑜𝑝𝑠
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v Field theory. SM𝐿ÜK= −
14𝐹jlP + Þ𝜓 𝑖𝐷j𝛾j − 𝑚� 𝜓 + 𝐷jΦ
P− 𝜆P Φ N
+ 𝜇ÃP Φ P
+ 2𝜂 yz𝑏 − 𝑏 𝜕 ¬ 𝐴 , 𝐷j= 𝜕j + 𝑖𝑒𝐴j
Ø Invariance under transformations:
𝐴j → 𝐴j + 𝜕jΛ, 𝑏 → 𝑏,
Φ → 𝑒nâãΦ, 𝜓 → 𝜓𝑒nâã, ∆PΛ 𝑥 = 0
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𝐿ÜK = −zN𝐹jlP + Þ𝜓 𝑖𝐷j𝛾j − 𝑚� 𝜓 + 𝐷jΦ
P − 𝜆P Φ N + 𝜇ÃP Φ P +2𝜂 yz𝑏 − 𝑏 𝜕 ¬ 𝐴 , 𝐷j= 𝜕j + 𝑖𝑒𝐴j
𝐴j → 𝐴j + 𝛼𝜖 𝐵j trick
−zN𝐹jlP → −z
N𝐹jlP - z
P𝛼𝜖 𝐹jl𝐵jl −
zN𝛼𝜖 P𝐵jlP
𝐿ÜK�Jq�JK= −
14𝐹jlP −
12𝛼𝜖 𝐹jl𝐵jl −
14𝛼𝜖 P𝐵jlP + Þ𝜓 𝑖𝜕j𝛾j − 𝑚� 𝜓 − 𝑒𝐴j𝐽j
− 𝑔𝐵j𝐽j + 𝐷jΦP− 𝜆P Φ N + 𝜇ÃP Φ P + �̅� 𝑖𝜕j𝛾j − 𝑚O 𝜒
− 𝑔J 𝐵 ¬ 𝐽J − 𝑏 𝜕 ¬ 𝐴 − 𝑏 𝛼𝜖 𝜕 ¬ 𝐵 +12𝜂 𝑏
P
𝑔 = 𝑒𝛼𝜖, 𝐽j = Þ𝜓𝛾j𝜓, 𝐽jJ = �̅�𝛾j 𝜒
v Weak Dipole Dark Photon Model (WDDPM)
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v WDDPM, symmetry breaking
Real fields 𝜙 + 𝑓 =12Φ +Φ∗ , 𝜑 =
−𝑖2Φ −Φ∗
Ω, 𝜑Ω = 0, 𝑓 = Ω, 𝜙 + 𝑓 Ω , Ω, Ω = 1
After symmetry breaking𝐿é= −
14𝐹jlP −
12𝛼𝜖 𝐹jl𝐵jl −
14𝛼𝜖 P 𝐵jlP − 𝑏 𝛼𝜖 𝜕𝐵 − 𝑏 𝜕𝐴 +
12𝜂𝑏P
+ �̅� 𝑖𝜕𝛾 − 𝑚O 𝜒 + Þ𝜓 𝑖𝜕𝛾 −𝑚� 𝜓 − 𝑒 𝐴𝐽 − 𝑔 𝐵𝐽 − 𝑔J 𝐵𝐽J
+𝒎𝟐
𝟐𝑩𝝁𝟐 +𝒎𝐵j𝜕j𝜑 −
12𝜇P𝜙P +
12
𝜕j𝜙P + 𝜕j𝜑
P
𝑚 = 𝑔𝑓 DP mas𝜇 = 2𝜆𝑓 𝑠𝑐𝑎𝑙𝑎𝑟 𝑑𝑖𝑙𝑎𝑡𝑜𝑛 𝑚𝑎𝑠𝑠 18
25.09.2019 G Kozlov J-PARC 10thY 2019
q Dark photon field itselfØBasic Eq.
𝑚P𝐵j +𝑚𝜕j𝜑 − 𝑔𝐽j − 𝑔J𝐽jJ + 𝛼𝜖 𝜕l𝐹lj+ 𝛼𝜖 P𝜕l𝐵lj + 𝛼𝜖 𝜕j𝑏 = 0
Ø Solution. DP field 𝑩𝝁 𝒙 = 𝒈𝑫𝒎𝟐 𝑱𝝁𝑫−
𝝏𝝁𝝋 𝒙𝒎
∆P∆P𝜑 𝑥 = �±�
∆P 𝜕 ¬ 𝐴 𝑥
𝑫𝑴 ← gôJôö → 𝑫𝑷 ← 𝜕ôφ → 𝑺𝑴↪ mediator
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GK (2019)
25.09.2019 G Kozlov J-PARC 10thY 2019
q DM couplingsAnnihilation cross-section 𝑺𝑴𝝍 → 𝑫𝑴 𝝌
𝜎𝑣 ~𝑔P𝑔JP
4𝜋𝑇 P , 𝑔 = 𝑒𝛼𝜖, Relic abundance: ΥO~10yNâÑâ#
Ñ K$Ͷ
If 𝑚O ~ 𝑂 𝑀𝑒𝑉𝑇%�½�À¿n� ��¼¼�½ ~ 𝑂 100 𝑀𝑒𝑉 < 𝑇� ~ 𝑂 170 𝑀𝑒𝑉
𝑔J~ 0.1 − 10if kinetic mixing for DP 𝜖 ~ 10y� − 10y¤
𝐿'( ⊃ 𝑒𝐽j𝐴j + 𝑔J 𝑄𝐽j + 𝐽jJ 𝐵j
𝑄~10y − 10yPØ DM – DP Mixing-coupling parameter
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vLight DM Phenomenology
𝐿𝑖𝑔ℎ𝑡 𝐷𝑀 𝑚 > 2𝑚O
Invisible decays of DP: Γ 𝐵 → �̅�𝜒 = â#Ñ
zPÉ𝑚 1 +P�,
Ñ
�Ñ 1 −N�,
Ñ
�Ñ
Observable abundance density
𝑔JP ≈ 0.3𝜗 zÃÊ.
�
P �Ã.z /�0
N Ã.Ãz /�0�,
P, ϑ ≤ 1, 𝐷𝑀 𝑓𝑒𝑟𝑚𝑖𝑜𝑛𝑠
E. Izaguirre et al., PRD91 (2015)
𝑔J > 𝑔 = 𝑒 𝛼𝜖
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§ DM search in missing energy events with NA 64 experiment
PRL 123 (2019) 121801D. Banerjee et al (NA64 Coll.)
Invisible decay of DP, to DM particles 𝑚JK ≤ 𝑚2L/2
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Physical observables.
Both DM and DP are observables under stochastic forces ℎj 𝑥 ONLY
DP 𝐵j 𝑥 𝑓luctuations in medium: probability 𝑃 𝐵j ~𝑒𝑥𝑝 −𝐺 ℎj 𝛽
𝐺 ℎj = 𝑙𝑛:𝑑𝐵j𝑒y ∫ �o < o �=p o %p o
𝐹= = :𝑑ℎj𝐺 ℎj 𝑒y ∫ �o=p> o , 𝑛 = 1,2,… 𝜕jℎj 𝑥 = 𝛿 𝑥
Both DM and DP are not observables. 𝑏 𝑥 , 𝐵j 𝑦 ≠ 0, 𝑏 𝑥 , 𝜒 𝑦 ≠ 0
vDM & DP in medium.
• 𝑫𝑴 𝜒 𝑥 → B𝝌 𝒙; 𝒉𝝁 = 𝑒𝑥𝑝 𝑖𝑔 ∫𝑑N𝑦ℎj 𝑥 − 𝑦 𝐵j 𝑦 𝜒 𝑥
o 𝑫𝑷 𝐵j 𝑥 → E𝑩𝝁 𝒙; 𝒉𝝁 = ∫𝑑N𝑦 𝛿lj𝛿 𝑥 − 𝑦 − 𝜕jℎl 𝑥 − 𝑦 𝐵l 𝑦
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v Dark photon explore: collider or fixed target?
𝑅µ¶/´ÀÏÏ =𝑁µ¶𝑁´ÀÏÏ
=𝐿µ¶𝐿´ÀÏÏ
𝐸µ¶𝐸´ÀÏÏ
P¿yP
𝑅µ¶/´ÀÏÏ =
10zzy¿ zÃà /�0 (�y����)<H´
10zNyI¿ zÃà /�0 (�y����) ÜqÜ ´Åé(<H´
,
10zyzz¿ z /�0 (�y����) J<��<H´
𝑛 = 0 𝑅µ¶/´ÀÏÏ ~10zzy 10z
𝑛 = 1 𝑅µ¶/´ÀÏÏ ~ 10¤
𝑛 = 2 𝑅µ¶/´ÀÏÏ ~10y − 10yz
𝑳𝒊𝒏𝒕/𝒎𝒆𝒅 = Ä𝒌,𝒍,𝒎,𝒏
𝒌�𝒍�𝒎L𝒏�𝟒𝑶𝑫𝑴
𝒌 𝑶𝑫𝑷𝒍 𝑶𝑺𝑴
𝒎
𝜦𝒏
𝜎~𝜖P𝜁P
𝐸P𝐸Λ
P¿Ø Production cross-section collider or fixed target?
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Conclusion
1. Abelian conformal-gauge model for DP and interactions.
2. DP solution. DP massive.
3. DM - SM interactions through DP (the portal) as non-trivial combination of the derivatives of dilaton field.
4. Influence of Conformal Sector to SM sector.
5. DP production rate for collider and fixed target modes.
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𝜺 = 7.6¬ 𝟏𝟎y𝟑, m = 0.83 GeV,
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Спасибо за внимание!Thank you!
DM
DP is the conformal portal to DM
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