Joint photon-electron Lorentz violation parameter plane from LHAASO data

2025-05-05 0 0 357.61KB 8 页 10玖币

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Joint photon-electron Lorentz violation parameter plane from LHAASO

data

Ping Hea, Bo-Qiang Maa,b,c

aSchool of Physics, Peking University, Beijing, 100871, China

bCenter for High Energy Physics, Peking University, Beijing, 100871, China

cCollaborative Innovation Center of Quantum Matter, Beijing, China

Abstract

The Large High Altitude Air Shower Observatory (LHAASO) is one of the most sensitive gamma-ray de-

tector arrays, whose ultrahigh-energy (UHE) work bands not only help to study the origin and acceleration

mechanism of UHE cosmic rays, but also provide the opportunity to test fundamental physics concepts such

as Lorentz symmetry. LHAASO directly observes the 1.42 PeV highest-energy photon. By adopting the

synchrotion self-Compton model, LHAASO also suggests that the 1.12 PeV high-energy photon from Crab

Nebula corresponds to a 2.3 PeV high-energy electron. We study the 1.42 PeV photon decay and the 2.3 PeV

electron decay to perform a joint analysis on photon and electron two-dimensional Lorentz violation (LV)

parameter plane. Our analysis is systematic and comprehensive, and we naturally get the strictest con-

straints from merely considering photon LV eﬀect in photon decay and electron LV eﬀect in electron decay.

Our result also permits the parameter space for new physics beyond relativity.

Keywords: ultrahigh-energy cosmic photon, Lorentz violation, photon decay, electron decay, photon and

electron Lorentz violation parameter plane

The Large High Altitude Air Shower Observatory (LHAASO) is a new-generation mountain observatory

with unprecedented ultrahigh-energy (UHE) photon detection capability [1,2]. Recently, LHAASO reported

more than 530 UHE photons with energies larger than 100 TeV from twelve astrophysical gamma-ray sources

within the Milky Way, including the highest-energy photon detected at about 1.42 PeV [1]. LHAASO also

reported the detection of gamma-ray spectrum from 5 ×10−4PeV to 1.12 PeV from Crab Nebula, and these

UHE photons exhibit the presence of a PeV electron accelerator [2]. These high-energy photons not only help

to study the origin and acceleration mechanism of UHE cosmic rays, but also provide the opportunity to test

fundamental physics concepts such as Lorentz symmetries of photons [3,4] and electrons [5]. By analysing

the LHAASO 1.42 PeV highest-energy photon [1], Ref. [3] got a photon superluminal linear Lorentz viola-

tion LV constraint — E(p,sup)

LV ≥2.74 ×1033 eV from photon decay research. By analysing two gamma-ray

sources LHAASO J2032+4102 and J0534+2202, LHAASO collaboration got a photon superluminal linear

LV constraint E(p,sup)

LV ≥1.42 ×1033 eV from photon decay research [4]. By analysing the Crab Nebula

1.12 PeV highest-energy photon, Ref. [5] obtained the most strict constraint on electron superluminal linear

modiﬁed parameter E(e,sup)

LV ≥9.4×1025 GeV from the electron decay research.

In conventional case of relativity, there are no photon decay and electron decay phenomena in vacuum,

but in LV case, things might be diﬀerent. If photon or electron does decay, it is a sign for photon or electron

LV eﬀect. On the other hand, the UHE photon and electron data set very strict constraints on photon and

electron LV eﬀects. In previous photon decay analyses [3,4], only initial photon LV eﬀect is considered,

with LV eﬀect for the out-going electron-positron pair neglected. But since the out-going particles obtain

Email address: mabq@pku.edu.cn (Bo-Qiang Ma)

Preprint submitted to Physics Letters B 835 (2022) 137536, doi:10.1016/j.physletb.2022.137536 November 8, 2022

arXiv:2210.14817v3 [astro-ph.HE] 7 Nov 2022

the whole energy-momentum of initial photon, it is necessary to consider the LV eﬀect of out-going electron-

positron pair. In previous electron decay analysis [5], there is a supposition that the emitted photon is soft

enough that its LV eﬀect can be neglected. But if we check the electron decay reaction we can ﬁnd that: in

some case, the out-going photon can obtain the half energy-momentum of the initial electron, so it is also

necessary to consider the out-going photon LV eﬀect in electron decay.

To get a systematic and comprehensive analysis on photon and electron LV parameter plane from

LHAASO results, we restudy photon decay and electron decay. As the LV eﬀects are very tiny, we in-

troduce tiny LV modiﬁcations on the photon and electron dispersion relations:

(ω2=k2[1 + ξn(k

EPl )n] photon;

E2=m2+p2[1 + ηn(p

EPl )n] electron/positron,(1)

where EPl is the Plank scale, and ξn,ηnare the nth-order LV parameters of photon and electron respectively.

For a threshold reaction, when the ﬁnal particle momenta are parallel and the initial momenta are antipar-

allel, the threshold occurs [6], so we only consider the modulus of the momentum k=|~

k|, and p=|~p|, to

obtain the threshold. If we only consider the linear modiﬁcation (n= 1), we simplify the notation: ξ1:≡ξ

and η1:≡η.

For photon decay γ→e−+e+, considering a high-energy photon with momentum kthat decays into

an electron with momentum xk (x∈[0,1]) and a positron with momentum (1 −x)k, using photon and

electron dispersion relations Eq. (1) and the energy-momentum conservation relation, only considering the

linear (n= 1) modiﬁcation, and expanding it to the leading-order of the LV parameters and the leading-order

of (m/k)2, we get [7]:

k[1 + ξ

EPl

] = xk[1 + m2

2(xk)2+η

EPl

] + {x↔1−x}.(2)

After simple algebraic operations, Eq. (2) becomes [7]:

m2EPl

k3=x(1 −x)[ξ−((1 −x)2+x2)η].(3)

Finding the threshold of the photon decay is equivalent to ﬁnding the minimum value of kon the left side

of the Eq. (3). When ξ→0 and η→0, k→+∞, and it is the classic case where photon cannot decay, and

that is to be expected, since any case must go back to classical case when the LV eﬀects do not at work.

Then we get the thresholds in diﬀerent LV parameter conﬁgurations [7,8,9]:

th =









+∞(a)ξ−η < 0 and 2ξ−η < 0;

(8m2EPl

2ξ−η)1/3(b)ξ > 0 and 2ξ−η > 0;

(−8ηm2EPl

(ξ−η)2)1/3(c)η < ξ < 0.

In case (a), kp

th = +∞means that there is no photon decay. In case (b), the momenta of the out-going

particles are equally distributed, that is to say, the out-going electron/positron gains half momentum from

photon, so it is necessary to consider the out-going electron/positron LV eﬀect. In case (c), the momentum

distribution is not equal, and it is also necessary to consider the out-going particle LV eﬀects since they get

the whole momentum from photon.

When the photon energy exceeds the threshold, the photon decay can occur and result a rapid drop in

photon energy. On the other hand, observing a photon, whose energy is Ep, means that Epdoes not reach

the decay threshold kp

th:kp

th > Ep. In diﬀerent LV parameter conﬁgurations, it is same as [7]:











no extra constraints (a)ξ−η < 0 and 2ξ−η < 0;

0<2ξ−η < 8m2EPl

p(b)ξ > 0 and 2ξ−η > 0;

0< ξ −η < q−8m2EPlη

p(c)η < ξ < 0.

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摘要：

Jointphoton-electronLorentzviolationparameterplanefromLHAASOdataPingHea,Bo-QiangMaa,b,caSchoolofPhysics,PekingUniversity,Beijing,100871,ChinabCenterforHighEnergyPhysics,PekingUniversity,Beijing,100871,ChinacCollaborativeInnovationCenterofQuantumMatter,Beijing,ChinaAbstractTheLargeHighAltitudeAirShow...

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Joint photon-electron Lorentz violation parameter plane from LHAASO data

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