Antineutrino science in KamLAND

The primary goal of KamLAND is a search for the oscillation of \({\bar{\nu }}_\mathrm{e}\) ’s emitted from distant power reactors. The long baseline, typically 180 km, enables KamLAND to address the oscillation solution of the “solar neutrino problem” with \({\bar{\nu }}_{e} \) ’s under laboratory conditions. KamLAND found fewer reactor \({\bar{\nu }}_{e} \) events than expected from standard assumptions about \(\overline{\nu }_e\) propagation at more than 9 \(\sigma \) confidence level (C.L.). The observed energy spectrum disagrees with the expected spectral shape at more than 5 \(\sigma \) C.L., and prefers the distortion from neutrino oscillation effects. A three-flavor oscillation analysis of the data from KamLAND and KamLAND + solar neutrino experiments with CPT invariance, yields \(\Delta m_{21}^2 \) = [ \(7.54_{-0.18}^{+0.19} \times \) 10 \(^{-5}\) eV \(^{2}\) , \(7.53_{-0.18}^{+0.19} \times \) 10 \(^{-5}\) eV \(^{2}\) ], tan \(^{2}\theta _{12}\) = [ \(0.481_{-0.080}^{+0.092} \) , \(0.437_{-0.026}^{+0.029} \) ], and sin \(^{2}\theta _{13}\) = [ \(0.010_{-0.034}^{+0.033} \) , \(0.023_{-0.015}^{+0.015} \) ]. All solutions to the solar neutrino problem except for the large mixing angle region are excluded. KamLAND also demonstrated almost two cycles of the periodic feature expected from neutrino oscillation effects. KamLAND performed the first experimental study of antineutrinos from the Earth’s interior so-called geoneutrinos (geo \({\bar{\nu }}_{e} \) ’s), and succeeded in detecting geo \({\bar{\nu }}_{e} \) ’s produced by the decays of \(^{238}\) U and \(^{232}\) Th within the Earth. Assuming a chondritic Th/U mass ratio, we obtain \(116_{-27}^{+28} {\bar{\nu }}_{e}\) events from \(^{238}\) U and \(^{232}\) Th, corresponding a geo \({\bar{\nu }}_{e}\) flux of \(3.4_{-0.8}^{+0.8}\times \) 10 \(^{6}\) cm \(^{-2}\)  s \(^{-1}\) at the KamLAND location. We evaluate various bulk silicate Earth composition models using the observed geo \({\bar{\nu }}_{e} \) rate.     

Split supersymmetry under GUT and current dark matter constraints

There are four types of two-Higgs doublet models under a discrete \(Z_2\) symmetry imposed to avoid tree-level flavor-changing neutral current, i.e. type-I, type-II, type-X, and type-Y models. We investigate the possibility to discriminate the four models in the light of the flavor physics data, including \(B_s\) – \(\bar{B}_s\) mixing, \(B_{s,d} \rightarrow \mu ^+ \mu ^-\) , \(B\rightarrow \tau \nu \) and \(\bar{B} \rightarrow X_s \gamma \) decays, the recent LHC Higgs data, the direct search for charged Higgs at LEP, and the constraints from perturbative unitarity and vacuum stability. After deriving the combined constraints on the Yukawa interaction parameters, we have shown that the correlation between the mass eigenstate rate asymmetry \(A_{\Delta \Gamma }\) of \(B_{s} \rightarrow \mu ^+ \mu ^-\) and the ratio \(R=\mathcal{B}(B_{s} \rightarrow \mu ^+ \mu ^-)_\mathrm{exp}/ \mathcal{B}(B_{s} \rightarrow \mu ^+ \mu ^-)_\mathrm{SM}\) could be a sensitive probe to discriminate the four models with future precise measurements of the observables in the \(B_{s} \rightarrow \mu ^+ \mu ^-\) decay at LHCb.     

Is the CNMSSM more credible than the CMSSM?

“Post-sphaleron baryogenesis”, a fresh and profound mechanism of baryogenesis accounts for the matter–antimatter asymmetry of our present universe in a framework of Pati–Salam symmetry. We attempt here to embed this mechanism in a non-SUSY SO(10) grand unified theory by reviving a novel symmetry breaking chain with Pati–Salam symmetry as an intermediate symmetry breaking step and as well to address post-sphaleron baryogenesis and neutron–antineutron oscillation in a rational manner. The Pati–Salam symmetry based on the gauge group \(\mathrm{SU}(2)_L \times \mathrm{SU}(2)_{R} \times \mathrm{SU}(4)_C\) is realized in our model at \(10^{5}\) – \(10^{6}\)  GeV and the mixing time for the neutron–antineutron oscillation process having \(\Delta B=2\) is found to be \(\tau _{n-\bar{n}} \simeq 10^{8}\) – \(10^{10}\)  s with the model parameters, which is within the reach of forthcoming experiments. Other novel features of the model include low scale right-handed \(W^{\pm }_R\) , \(Z_R\) gauge bosons, explanation for neutrino oscillation data via the gauged inverse (or extended) seesaw mechanism and most importantly TeV scale color sextet scalar particles responsible for an observable \(n\) – \(\bar{n}\) oscillation which may be accessible to LHC. We also look after gauge coupling unification and an estimation of the proton lifetime with and without the addition of color sextet scalars.     

Optimal N-Point Configurations on the Sphere: “Magic” Numbers and Smale’s 7th Problem

This paper inquires into the concavity of the map \(N\mapsto v_s(N)\) from the integers \(N\ge 2\) into the minimal average standardized Riesz pair-energies \(v_s(N)\) of \(N\) -point configurations on the sphere \(\mathbb {S}^2\) for various \(s\in \mathbb {R}\) . The standardized Riesz pair-energy of a pair of points on \(\mathbb {S}^2\) a chordal distance \(r\) apart is \(V_s(r)= s^{-1}\left( r^{-s}-1 \right) \) , \(s \ne 0\) , which becomes \(V_0(r) = \ln \frac{1}{r}\) in the limit \(s\rightarrow 0\) . Averaging it over the \(\left( \begin{array}{c} N\\ 2\end{array}\right) \) distinct pairs in a configuration and minimizing over all possible \(N\) -point configurations defines \(v_s(N)\) . It is known that \(N\mapsto v_s(N)\) is strictly increasing for each \(s\in \mathbb {R}\) , and for \(s<2\) also bounded above, thus “overall concave.” It is (easily) proved that \(N\mapsto v_{-2}^{}(N)\) is even locally strictly concave, and that so is the map \(2n\mapsto v_s(2n)\) for \(s<-2\) . By analyzing computer-experimental data of putatively minimal average Riesz pair-energies \(v_s^x(N)\) for \(s\in \{-1,0,1,2,3\}\) and \(N\in \{2,\ldots ,200\}\) , it is found that the map \(N\mapsto {v}_{-1}^x(N)\) is locally strictly concave, while \(N\mapsto {v}_s^x(N)\) is not always locally strictly concave for \(s\in \{0,1,2,3\}\) : concavity defects occur whenever \(N\in {\mathcal {C}}^{x}_+(s)\) (an \(s\) -specific empirical set of integers). It is found that the empirical map \(s\mapsto {\mathcal {C}}^{x}_+(s),\ s\in \{-2,-1,0,1,2,3\}\) , is set-theoretically increasing; moreover, the percentage of odd numbers in \({\mathcal {C}}^{x}_+(s),\ s\in \{0,1,2,3\}\) is found to increase with \(s\) . The integers in \({\mathcal {C}}^{x}_+(0)\) are few and far between, forming a curious sequence of numbers, reminiscent of the “magic numbers” in nuclear physics. It is conjectured that these new “magic numbers” are associated with optimally symmetric optimal-log-energy \(N\) -point configurations on \(\mathbb {S}^2\) . A list of interesting open problems is extracted from the empirical findings, and some rigorous first steps toward their solutions are presented. It is emphasized how concavity can assist in the solution to Smale’s \(7\) th Problem, which asks for an efficient algorithm to find near-optimal \(N\) -point configurations on \(\mathbb {S}^2\) and higher-dimensional spheres.     

Phase Transitions in Layered Systems

We consider the Ising model on \(\mathbb Z\times \mathbb Z\) where on each horizontal line \(\{(x,i), x\in \mathbb Z\}\) , called “layer”, the interaction is given by a ferromagnetic Kac potential with coupling strength \(J_{ \gamma }(x,y)={ \gamma }J({ \gamma }(x-y))\) , where \(J(\cdot )\) is smooth and has compact support; we then add a nearest neighbor ferromagnetic vertical interaction of strength \({ \gamma }^{A}\) , where \(A\ge 2\) is fixed, and prove that for any \(\beta \) larger than the mean field critical value there is a phase transition for all \({ \gamma }\) small enough.     

The Colored Hofstadter Butterfly for the Honeycomb Lattice

We rely on a recent method for determining edge spectra and we use it to compute the Chern numbers for Hofstadter models on the honeycomb lattice having rational magnetic flux per unit cell. Based on the bulk-edge correspondence, the Chern number \(\sigma _\mathrm{H}\) is given as the winding number of an eigenvector of a \(2 \times 2\) transfer matrix, as a function of the quasi-momentum \(k\in (0,2\pi )\) . This method is computationally efficient (of order \(\mathcal {O}(n^4)\) in the resolution of the desired image). It also shows that for the honeycomb lattice the solution for \(\sigma _\mathrm{H}\) for flux \(p/q\) in the \(r\) -th gap conforms with the Diophantine equation \(r=\sigma _\mathrm{H}\cdot p+ s\cdot q\) , which determines \(\sigma _\mathrm{H}\mod q\) . A window such as \(\sigma _\mathrm{H}\in (-q/2,q/2)\) , or possibly shifted, provides a natural further condition for \(\sigma _\mathrm{H}\) , which however turns out not to be met. Based on extensive numerical calculations, we conjecture that the solution conforms with the relaxed condition \(\sigma _\mathrm{H}\in (-q,q)\) .     

Investigation of conductivity of adhesive layer including indium tin oxide particles for multi-junction solar cells

We report connection conductivity ( \(C_{\rm c}\) ) of adhesive which including \(\hbox {In}_2\hbox {O}_3\) – \(\hbox {SnO}_2\) (ITO) particles developed for fabrication of stacked-type-multi-junction solar cells. The commercial 20- \(\upmu \) m sized ITO particles were heated in vacuum at temperature ranging from 800 to 1,300  \(^{\circ }{\rm C}\) for 10 min to increase \(C_{\rm c}\) . 6.2 wt% ITO particles were dispersed in commercial Cemedine adhesive gel to form 100 samples structured with n-type Si/adhesive/n-type Si (n-Si sample) and p-type Si/adhesive/p-type Si (p-Si sample). Current density as a function of voltage (J–V) characteristics gave \(C_{\rm c}\) . It ranged from 4.3 to 1.0 S/cm \(^2\) for the n-Si sample with 800 \(^{\circ }{\rm C}\) heat-treated ITO particles. Its standard deviation was 0.59 S/cm \(^2\) . On the other hand, it ranged from 2.0 to 0.6 S/cm \(^2\) for the p-Si sample with 800  \(^{\circ }{\rm C}\) heat-treated ITO particles. Its standard deviation was 0.22 S/cm \(^2\) . The distribution of \(C_{\rm c}\) mainly resulted from contact efficiency of ITO particles to substrate. We theoretically estimated that present \(C_{\rm c}\) achieved a low loss of the power conversion efficiency ( \(E_{\rm ff}\) ) lower than 0.3 % in the application of fabrication of multi-junction solar cell with an intrinsic \(E_{\rm ff}\) of 30 % and an open circuit voltage above 1.9 V.     

Maximal Distance Travelled by N Vicious Walkers Till Their Survival

We consider N Brownian particles moving on a line starting from initial positions \(\mathbf{{u}}\equiv \{u_1,u_2,\ldots u_N\}\) such that \(0 . Their motion gets stopped at time \(t_s\) when either two of them collide or when the particle closest to the origin hits the origin for the first time. For \(N=2\) , we study the probability distribution function \(p_1(m|\mathbf{{u}})\) and \(p_2(m|\mathbf{{u}})\) of the maximal distance travelled by the \(1^{\text {st}}\) and \(2^{\text {nd}}\) walker till \(t_s\) . For general N particles with identical diffusion constants \(D\) , we show that the probability distribution \(p_N(m|\mathbf{u})\) of the global maximum \(m_N\) , has a power law tail \(p_i(m|\mathbf{{u}}) \sim {N^2B_N\mathcal {F}_{N}(\mathbf{u})}/{m^{\nu _N}}\) with exponent \(\nu _N =N^2+1\) . We obtain explicit expressions of the function \(\mathcal {F}_{N}(\mathbf{u})\) and of the N dependent amplitude \(B_N\) which we also analyze for large N using techniques from random matrix theory. We verify our analytical results through direct numerical simulations.     

Dilaton gravity, (quasi-) black holes,and scalar charge

Electrically charged dust is considered in the framework of Einstein–Maxwell–dilaton gravity with a Lagrangian containing the interaction term \(P(\chi )F_{\mu \nu }F^{\mu \nu }\) , where \(P(\chi )\) is an arbitrary function of the dilaton scalar field \(\chi \) , which can be normal or phantom. Without assumption of spatial symmetry, we show that static configurations exist for arbitrary functions \(g_{00} = \exp (2\gamma (x^{i}))\) ( \(i=1,2,3\) ) and \(\chi =\chi (\gamma )\) . If \(\chi = \mathrm{const}\) , the classical Majumdar–Papapetrou (MP) system is restored. We discuss solutions that represent black holes (BHs) and quasi-black holes (QBHs), deduce some general results and confirm them by examples. In particular, we analyze configurations with spherical and cylindrical symmetries. It turns out that cylindrical BHs and QBHs cannot exist without negative energy density somewhere in space. However, in general, BHs and QBHs can be phantom-free, that is, can exist with everywhere nonnegative energy densities of matter, scalar and electromagnetic fields.     

A new deterministic model of strange stars

Experiments using polarized \(^{3}\) He atom beams to search for short range spin dependent forces are proposed. High intensity, high polarization, small beam size \(^{3}\) He atom beams have been successfully produced and used in surface science researches. By incorporating background reduction designs as combination shielding by \(\upmu \) -metal and superconductor and double beam paths, the precision of spin rotation angle per unit length could be improved by a factor of \(\sim \!10^{4}\) . By this precision, in combination with a high density and low magnetic susceptibility sample source mass, and reversing one beam path if necessary, sensitivities on three different types of spin dependent interactions could be improved by as much as \(\sim \!\!10^{2}\) to \(\sim \!\!10^{8}\) over the current experiments at the millimeter range.     

Rejection of randomly coinciding events in ZnMoO_4 scintillating bolometers

Random coincidence of events (particularly from two neutrino double beta decay) could be one of the main sources of background in the search for neutrinoless double beta decay with cryogenic bolometers due to their poor time resolution. Pulse-shape discrimination by using front edge analysis, mean-time and \(\chi ^2\) methods were applied to discriminate randomly coinciding events in ZnMoO \(_4\) cryogenic scintillating bolometers. These events can be effectively rejected at the level of 99 % by the analysis of the heat signals with rise-time of about 14 ms and signal-to-noise ratio of 900, and at the level of 92 % by the analysis of the light signals with rise-time of about 3 ms and signal-to-noise ratio of 30, under the requirement to detect 95 % of single events. These rejection efficiencies are compatible with extremely low background levels in the region of interest of neutrinoless double beta decay of \(^{100}\) Mo for enriched ZnMoO \(_4\) detectors, of the order of \(10^{-4}\)  counts/(y keV kg). Pulse-shape parameters have been chosen on the basis of the performance of a real massive ZnMoO \(_4\) scintillating bolometer. Importance of the signal-to-noise ratio, correct finding of the signal start and choice of an appropriate sampling frequency are discussed.     

The CMSSM and NUHM1 after LHC Run 1

We analyze the impact of data from the full Run 1 of the LHC at 7 and 8 TeV on the CMSSM with \(\mu > 0\) and \(<0\) and the NUHM1 with \(\mu > 0\) , incorporating the constraints imposed by other experiments such as precision electroweak measurements, flavour measurements, the cosmological density of cold dark matter and the direct search for the scattering of dark matter particles in the LUX experiment. We use the following results from the LHC experiments: ATLAS searches for events with \({E\!\!/}_{T}\) accompanied by jets with the full 7 and 8 TeV data, the ATLAS and CMS measurements of the mass of the Higgs boson, the CMS searches for heavy neutral Higgs bosons and a combination of the LHCb and CMS measurements of \(\mathrm{BR}(B_s \rightarrow \mu ^+\mu ^-)\) and \(\mathrm{BR}(B_d \rightarrow \mu ^+\mu ^-)\) . Our results are based on samplings of the parameter spaces of the CMSSM for both \(\mu >0\) and \(\mu <0\) and of the NUHM1 for \(\mu > 0\) with 6.8 \(\times 10^6\) , 6.2 \(\times 10^6\) and 1.6 \(\times 10^7\) points, respectively, obtained using the MultiNest tool. The impact of the Higgs-mass constraint is assessed using FeynHiggs 2.10.0, which provides an improved prediction for the masses of the MSSM Higgs bosons in the region of heavy squark masses. It yields in general larger values of \(M_h\) than previous versions of FeynHiggs, reducing the pressure on the CMSSM and NUHM1. We find that the global \(\chi ^2\) functions for the supersymmetric models vary slowly over most of the parameter spaces allowed by the Higgs-mass and the \({E\!\!/}_{T}\) searches, with best-fit values that are comparable to the \(\chi ^2/\mathrm{dof}\) for the best Standard Model fit. We provide 95 % CL lower limits on the masses of various sparticles and assess the prospects for observing them during Run 2 of the LHC.     

Dispersion dependence of two-photon absorption transition on frequency in Si PIN photodetector

The variation of two-photon absorption (TPA) coefficient \(\beta _{\mathrm{TPA}} (\omega )\) of Si excited at difference photon energy was investigated. The TPA coefficient was measured by using a picosecond pulsed laser with the wavelength could be tuned in a wide photon-energy range. An equivalent RC circuit model was adapted to derive the TPA coefficient \(\beta _{\mathrm{TPA}} (\omega )\) . The results showed that \(\beta _{\mathrm{TPA}} (\omega )\) varied from \(4.2 \times 10^{-4}\) to \(1.17 \times 10^{-3 }\)  cm/GW in the transparent wavelength region \(1.80<\lambda <1.36\,\upmu \) m of Si. The increasing tendency of \(\beta _{\mathrm{TPA}} (\omega )\) with the incident photon energy can be qualitatively interpreted as the photon energy increases from \(E_{\mathrm{ig}}/2\) to nearly \(E_{\mathrm{ig}}\) , the electrons excited from the valance band find an increasing availability of conduction band states. Comparing with the high-energy side transitions, the TPA coefficient in low-energy side is about 10 times too small. This can be attributed that the TPA transition in low-energy side is the process of photon-assisted electron transitions from valence to conduction band occurring between different points in k-space, while is direct transition in high-energy side.     

Line intensity measurements of methane’s \nu _3-band using a cw-OPO

We report on absolute line strength measurements of P(1), R(0) and R(1) singlet lines in the \(3.3\,\upmu\hbox {m}\,\nu _{3}\) (C–H stretching) band of methane \(^{12}\hbox {CH}_4\) at reference temperature \(T=296\)  K. Line strength measurements are performed at low pressure \((P \le 1\hbox { Torr})\) using direct absorption spectroscopy technique based on a widely tunable continuous-wave singly resonant optical parametric oscillator. The \(1\sigma \) overall accuracy in line strength determinations ranges between 7 and 8 % mostly limited by pressure and frequency measurements. A comparison with previous reported values is made. Our results show good agreement with the HITRAN 2012 database.     

Reunion Probabilities of N One-Dimensional Random Walkers with Mixed Boundary Conditions

In this work we extend the results of the reunion probability of \(N\) one-dimensional random walkers to include mixed boundary conditions between their trajectories. The level of the mixture is controlled by a parameter \(c\) , which can be varied from \(c=0\) (independent walkers) to \(c\rightarrow \infty \) (vicious walkers). The expressions are derived by using Quantum Mechanics formalism (QMf) which allows us to map this problem into a Lieb-Liniger gas (LLg) of \(N\) one-dimensional particles. We use Bethe ansatz and Gaudin’s conjecture to obtain the normalized wave-functions and use this information to construct the propagator. As it is well-known, depending on the boundary conditions imposed at the endpoints of a line segment, the statistics of the maximum heights of the reunited trajectories have some connections with different ensembles in Random Matrix Theory. Here we seek to extend those results and consider four models: absorbing, periodic, reflecting, and mixed. In all four cases, the probability that the maximum height is less or equal than \(L\) takes the form \(F_N(L)=A_N\sum _{\varvec{k}\in \Omega _{\text {B}}} \mathrm{e}^{-\sum _{j=1}^Nk_j^2}\mathcal {V}_N(\varvec{k})\) , where \(A_N\) is a normalization constant, \(\mathcal {V}_N(\varvec{k})\) contains a deformed and weighted Vandermonde determinant, and \(\Omega _{\text {B}}\) is the solution set of quasi-momenta \(\varvec{k}\) obeying the Bethe equations for that particular boundary condition.     

Near-Extreme Eigenvalues and the First Gap of Hermitian Random Matrices

We study the phenomenon of “crowding” near the largest eigenvalue \(\lambda _\mathrm{max}\) of random \(N \times N\) matrices belonging to the Gaussian Unitary Ensemble of random matrix theory. We focus on two distinct quantities: (i) the density of states (DOS) near \(\lambda _\mathrm{max}\) , \(\rho _\mathrm{DOS}(r,N)\) , which is the average density of eigenvalues located at a distance \(r\) from \(\lambda _\mathrm{max}\) and (ii) the probability density function of the gap between the first two largest eigenvalues, \(p_\mathrm{GAP}(r,N)\) . In the edge scaling limit where \(r = \mathcal{O}(N^{-1/6})\) , which is described by a double scaling limit of a system of unconventional orthogonal polynomials, we show that \(\rho _\mathrm{DOS}(r,N)\) and \(p_\mathrm{GAP}(r,N)\) are characterized by scaling functions which can be expressed in terms of the solution of a Lax pair associated to the Painlevé XXXIV equation. This provides an alternative and simpler expression for the gap distribution, which was recently studied by Witte et al. in Nonlinearity 26:1799, 2013. Our expressions allow to obtain precise asymptotic behaviors of these scaling functions both for small and large arguments.     

Effect of vacancies on magnetic behaviors of Cu-doped 6H-SiC

Magnetism in Cu-doped, Cu \(\rm _{Si}\) –V \(\rm _{Si}\) codoped, or Cu \(\rm _{Si}\) –V \(\rm _{C}\) codoped 6H-SiC are investigated using the first principle. The total density of states for the ferromagnetic Cu \(\rm _{Si}\) at doping concentration of 0.926 at. \(\%\) shows half-metallic behavior, which leads to the total magnetic moment of 2.84  \(\rm \mu _{B}\) per supercell. The total magnetic moment increases with increasing Cu content. The long-range ferromagnetic interaction between Cu atoms can be attributed to the C-mediated double exchange through the strong \(3d\) ? \(2p\) interaction between Cu and neighboring C ones. It is important to note that both V \(\rm _{Si}\) and V \(\rm _{C}\) play a negative role in ferromagnetic coupling between Cu ions. So, to obtain a larger magnetic moment from Cu-doped 6H–SiC, we should try to avoid the appearance of V \(\rm _{Si}\) and V \(\rm _{C}\) during the process of sample preparation. Our theoretical calculations give a valuable insight on how to get a large magnetic moment from Cu-doped 6H–SiC.     

Comprehensive Bayesian analysis of rare (semi)leptonic and radiative \varvec{B} decays

The available data on \(|\Delta B| = |\Delta S| = 1\) decays are in good agreement with the Standard Model when permitting subleading power corrections of about \(15\,\%\) at large hadronic recoil. Constraining new-physics effects in \(\mathcal {C}_{7}^{\mathrm {}}\) , \(\mathcal {C}_{9}^{\mathrm {}}\) , \(\mathcal {C}_{10}^{\mathrm {}}\) , the data still demand the same size of power corrections as in the Standard Model. In the presence of chirality-flipped operators, all but one of the power corrections reduce substantially. The Bayes factors are in favor of the Standard Model. Using new lattice inputs for \(B\rightarrow K^*\) form factors and under our minimal prior assumption for the power corrections, the favor shifts toward models with chirality-flipped operators. We use the data to further constrain the hadronic form factors in \(B\rightarrow K\) and \(B\rightarrow K^*\) transitions.     

Standard Model Gauge Couplings from Gauge-Dilatation Symmetry Breaking

It is well known that the self-energy of the gauge bosons is quadratically divergent in the Standard Model when a simple cutoff is imposed. We demonstrate phenomenologically that the quadratic divergences in fact unify. The unification occurs at a surprisingly low scale, \(\Lambda _\mathrm {u}\approx 4\times 10^7\)  GeV. Suppose now that there is a spontaneously broken rotational symmetry between the space-time coordinates and gauge theoretical phases. The symmetry-breaking pattern is such that the gauge bosons arise as the massless Goldstone bosons, whereas the dilatonic mode acts as the massive (Higgs) boson, whose vacuum expectation value determines the gauge couplings. In this case, the quadratic divergences or the tadpoles of the gauge boson self-energy should indeed unify because these divergences need to be cancelled by a universal dilatonic contribution, assuming dynamical symmetry breaking. If there is dynamical symmetry breaking, we are in principle able to calculate the value of the gauge couplings as well as the scale hierarchy \(\Lambda _\mathrm {cut}/\Lambda _\mathrm {u}\) . We perform this calculation by adopting a naive quartic symmetry-breaking potential which unfortunately violates local gauge invariance. Using tadpole-cancellation and dilatonic self-energy conditions, the value of \(\Lambda _\mathrm {cut}\) is then found to be approximately \(4\times 10^{18}\)  GeV in the Feynman gauge and \(5\times 10^{15}\)  GeV in the Landau gauge. The cancellation of an anomaly in the dilaton self-energy requires that the number of fermionic generations equals three. The symmetry-breaking needs to be driven by some other mass-generating mechanism such as electroweak symmetry breaking. Our estimation for \(\Lambda _\mathrm {u}\) is of the correct order if \(\Lambda _\mathrm {cut}\approx 5\times 10^{15}\)  GeV.     

QCD analysis of forward neutron production in DIS

Observing light-by-light scattering at the large hadron collider (LHC) has received quite some attention and it is believed to be a clean and sensitive channel to possible new physics. In this paper, we study the diphoton production at the LHC via the process \({{pp}}\rightarrow {{p}}\gamma \gamma {{p}}\rightarrow {{p}}\gamma \gamma {{p}}\) through graviton exchange in the large extra dimension (LED) model. Typically, when we do the background analysis, we also study the double Pomeron exchange of \(\gamma \gamma \) production. We compare its production in the quark–quark collision mode to the gluon–gluon collision mode and find that contributions from the gluon–gluon collision mode are comparable to the quark–quark one. Our result shows, for extra dimension \(\delta =4\) , with an integrated luminosity \(\mathcal{L} = 200\,\mathrm{fb}^{-1}\) at the 14 TeV LHC, that diphoton production through graviton exchange can probe the LED effects up to the scale \({M}_{S}=5.06 (4.51, 5.11)\,\mathrm{TeV}\) for the forward detector acceptance \(\xi _1 (\xi _2, \xi _3)\) , respectively, where \(0.0015<\xi _1<0.5\) , \(0.1<\xi _2<0.5\) , and \(0.0015<\xi _3<0.15\) .