Luca Buonocore, Paolo Nason, Francesco Tramontano, Giulia Zanderighi
备注：
43 pages, 14 figures. In V2 we have included a class of subleading O(alpha^2) contributions to the lepton PDFs and motivated this choice. Data in the LHAPDF files have been updated accordingly (see info file). V2 is identical to the published version
As is the case for all light coloured Standard Model particles, also photons and charged leptons appear as constituents in ultrarelativistic hadron beams, and admit a parton density function (PDF). It has been shown recently that the photon PDF can be given in terms of the structure functions and form factors for electron-proton scattering. The same holds for lepton PDFs. In the present work we set up a calculation of the lepton PDFs at next-to-leading order, using the same data input needed in the photon case. A precise knowledge of the lepton densities allows us to study lepton-initiated processes even at a hadron collider, with all possible combinations of same-charge, opposite-charge, same-flavour, different-flavour leptons and leptons-quarks, most of which cannot be realized in any other foreseeable experiment. The lepton densities in the proton are extremely small, so that their contribution to Standard Model processes is generally shadowed by processes initiated by coloured partons. We will show, however, that there are cases where these processes can be relevant, giving rise to rare Standard Model signatures and to new production channels, that can enlarge the discovery potential of New Physics at the LHC and future high energy colliders with hadrons in the initial state.
Majorana neutrino mass models with a scale of lepton number violation (LNV) of order TeV potentially lead to signals at the LHC. Here, we consider an extension of the standard model with a coloured octet fermion and a scalar leptoquark. This model generates neutrino masses at 2-loop order. We make a detailed MonteCarlo study of the LNV signal at the LHC in this model, including a simulation of standard model backgrounds. Our forecast predicts that the LHC with 300/fb should be able to probe this model up to colour octet fermion masses in the range of (2.6-2.7) TeV, depending on the lepton flav…
We investigate nucleon decays to light invisible fermion mediated by the coloured scalar $\bar S_1= (\bar 3, 1, -2/3)$ and compare them with the results coming from the mediation of $S_1 = (\bar 3,1,1/3)$. In the case of $\bar S_1= (\bar 3, 1, -2/3)$ up-like quarks couple to the invisible fermion, while in the case of $S_1 = (\bar 3,1,1/3)$ the down-like quarks couple to the invisible fermion. For the mass of invisible fermion smaller than the mass $m_p - m_K$, proton (neutron) can decay to $K$ and invisible fermion and the masses of $\bar S_1$ and $S_1$ are in the region $\sim 10^{15}$ GeV. T…
It is usually assumed that the proton stability requires the coloured triplet partner of the electroweak Higgs doublet to be superheavy (with a mass $\sim M_{GUT}$). We show that this is a very model-dependent statement and the colour triplet can be as light as the weak doublet without leading to the proton decay problem: instead of using the mass difference the splitting can occur between the doublet and triplet Yukawa coupling constants. In this scenario the GUT symmetry breaking automatically induces an extremely strong suppression $\sim M_W/M_{GUT}$ of the coloured Higgs effective Yukawa c…
We discuss proton and neutron decays involving three leptons in the final state. Some of these modes could constitute the dominant decay channel because they conserve lepton-flavor symmetries that are broken in all usually considered channels. This includes the particularly interesting and rarely discussed $p\to e^+ e^+ μ^-$ and $p\to μ^+ μ^+ e^-$ modes. As the relevant effective operators arise at dimension 9 or 10, observation of a three-lepton mode would probe energy scales of order 100 TeV. This allows to connect proton decay to other probes such as rare meson decays or collider physics. U…
We consider the inclusive production of hadrons in lepton-nucleon scattering. For a transversely polarized nucleon this reaction shows a left-right azimuthal asymmetry, which we compute this asymmetry in both TMD and in twist-3 collinear factorization formalisms. All non-perturbative parton correlators of the calculation are fixed through information from other hard processes. Our results for the left-right asymmetry agree in sign with recent data for charged pion production from the HERMES Collaboration and from Jefferson Lab. We discuss similarities and differences of two formalisms.
Analytical formulas for the cross section of the reaction $pp \to p + \ell^+ \ell^- + X$ are presented. Fiducial cross sections are compared with those measured recently by the ATLAS collaboration.
We make a fresh evaluation of contributions to (g-2) of the muon in the framework of a preonic model with coloured vectorlike leptons and heavy coloured Z bosons and discuss their implications in the light of the recent Brookhaven measurement. It is shown that the observed deviation can be explained within this framework with masses and couplings consistent with all constraints.
In this study, main parameters of Super proton-proton Collider (SppC) based lepton-proton colliders are estimated. For electron beam parameters, highest energy International Linear Collider (ILC) and Plasma Wake Field Accelerator-Linear Collider (PWFA-LC) options are taken into account. For muon beams, 1.5 TeV and 3 TeV center of mass energy Muon Collider parameters are used. In addition, ultimate $μ$p collider which assumes construction of additional 50 TeV muon ring in the SppC tunnel is considered as well. It is shown that $L_{ep}$ $\sim$ $10^{32}$ $cm^{-2}s^{-1}$ can be achieved with moder…
It is shown that the longitudinal double spin asymmetry $A_{ll}$ in polarized diffractive $Q \bar Q$ production depends strongly on the spin structure of the quark-pomeron vertex. Relevant experiments will be possible at HERA with a polarized proton beam.
It is shown that the parity--violating deep--inelastic scatterings of unpolarized charged leptons on polarized protons, $\ell^{\mp} + \vec P\to \stackrel{\scriptscriptstyle(-)}{ν_{\ell}} + X$, could provide a sensitive test for the behavior and magnitude of the polarized strange--quark density in a proton. Below charm threshold these processes are also helpful to uniquely determine the magnitude of individual polarized parton distributions.
Lepton mass effects play a decisive role in description of elastic lepton-proton scattering when the beam's energy is comparable to the mass of the lepton. The future MUSE experiment, which is devised to solve the "Proton Radius Puzzle", is going to cover the corresponding kinematic region for a scattering of muons by a proton target. We anticipate that helicity-flip meson exchanges will make a difference in comparison of elastic electron-proton versus muon-proton scattering in MUSE. In this article, we estimate the $σ$ meson exchange contribution in the $t$-channel. This contribution, mediate…
Vectorlike leptons are an intriguing possibility for physics beyond the Standard Model. We study the reach for discovering (at 5$σ$ significance) or excluding (at 95 per cent confidence) models of charged vectorlike leptons that mix predominantly with the tau, using multi-lepton signatures at various future proton-proton collider options: a high-luminosity LHC with $\sqrt{s} =$ 14 TeV, a high-energy LHC with $\sqrt{s} =$ 27 TeV, and possible new longer-tunnel colliders with $\sqrt{s} =$ 70 or 100 TeV. For weak isodoublet vectorlike leptons, we estimate that a 27 TeV high-energy LHC with 15 ab$…
General expressions, including the lepton mass, for the spin averaged differential cross section for the annihilation reaction lepton antilepton to proton antiproton are given, as well as general formulae for the single and double spin asymmetries in the centre of mass frame. In particular we discuss the single spin asymmetry, normal to the scattering plane, which measures the relative phase difference between nucleon electromagnetic form factors $G_E$ and $G_M$. Recent experimental investigations of these form factors in the space and time like region are reviewed. It is thought that measurem…
We discuss polarized lepton-proton scattering with special emphasis on the difference between target polarization defined relative to the lepton beam or to the virtual photon direction. In particular, this difference influences azimuthal distributions in the final state. We provide a general framework of analysis and apply it to the specific cases of semi-inclusive deep inelastic scattering, of exclusive meson production, and of deeply virtual Compton scattering.
It was recently proposed that all flavor mixing has a single source, namely the mixing of the three quark and lepton families with "extra" vectorlike fermions in 5 + 5-bar multiplets of SU(5). This was shown to lead to several testable predictions including neutrino masses and CP-violating phases. Here it is shown that the mixing angles within grand unified fermion multiplets are also predicted. Proton decay branching ratios would thus give several independent tests of the model. Certain model parameters could be determined independently from the quark and lepton spectrum and from proton decay…
The influence of the hard photon emission on the charge asymmetry in the (anti)lepton-proton elastic scattering was evaluated for the first time beyond the ultrarelativistic limit, while retaining the lepton mass at all steps of the calculation. This contribution - responsible for the charge asymmetry - is induced by interference between real photon emission from the lepton and proton. During the calculation any excited states of the intermediated proton are not considered, allowing us to use the standard fermionic propagator for this particle. The infrared divergence extracted using Lorenz-in…
The interpretation of high-precision lepton-nucleon scattering experiments requires the knowledge of higher-order radiative corrections. We present a calculation of the cross section for unpolarized lepton-proton scattering including leptonic radiative corrections up to second order, including one- and two-loop corrections, radiation of one and two photons and one-loop corrections for one-photon radiation. Numerical results are given for the planned P2 experiment at the MESA facility in Mainz, and some results are also discussed for Qweak and the suggested MUSE experiment.
The well-known baryon and lepton numbers of the standard model of quarks and leptons are extended to include new fermions and bosons in a simple structure with several essential features. The usual heavy right-handed neutrino singlets (for neutrino mass and leptogenesis) are related to the axion which solves the strong CP problem. At the same time, baryon number is broken softly, allowing the proton to decay. Associated with this breaking, a long-lived dark-matter candidate (called the pseudo-sakharon) emerges. This new insight connects proton decay to a new component of dark matter.
Arkani-Hamed and Schmaltz (AS) have shown that proton stability need not originate from symmetries in a high energy theory. Instead the proton decay rate is suppressed if quarks and leptons are spatially separated in a compact extra dimension. This separation may be achieved by coupling five dimensional fermions to a bulk scalar field with a non-trivial vacuum profile and requires relationships between the associated quark and lepton Yukawa couplings. We hypothesise that these relationships are the manifestation of an underlying symmetry. We further show that the AS proposal may suggest that p…
We calculate the transverse momentum distribution for the production of massive lepton-pairs in longitudinally polarized proton-proton reactions at collider energies within the context of perturbative quantum chromodynamics. For values of the transverse momentum Q_T greater than roughly half the pair mass Q, Q_T > Q/2, we show that the differential cross section is dominated by subprocesses initiated by incident gluons, provided that the polarized gluon density is not too small. Massive lepton-pair differential cross sections should be a good source of independent constraints on the polarized …
I study hard collisions between unpolarized protons and antiprotons where a lepton-antilepton pair is detected in coincidence with a final proton-antiproton pair, and no more particles are produced, in the regime 10 GeV^2 << s << 1000 GeV^2, M > 4 GeV, q_T < 3 GeV/c. The present work is centered on azimuthal asymmetries. Because of momentum conservation, a Boer-Mulders term in the momentum distribution of a quark implies a balancing effect in the momentum distribution of some spectators. This produces azimuthal asymmetries of the final hadrons. To analyze this, I have organized a parton-level …
We study two-photon contribution to the elastic lepton-proton scattering, associated with sigma meson exchange, with special attention paid to the low-Q2 region. We show that the corresponding amplitude grows sharply but remains finite at Q2->0. The analytical formula for the amplitude at Q2=0 is obtained. We also estimate the shift of the muonic hydrogen energy levels, induced by sigma meson exchange. For the 2S level the shift is approximately 30 times smaller than needed to resolve the proton radius puzzle, but still exceeds the precision of the muonic hydrogen measurements.
We consider the three lepton decay modes of the proton within the proton decay interpretation of the atmospheric neutrino anomaly. We construct higher dimensional operators in the framework of the standard model. The operators which allow the particularly interesting decay mode are of dimension 10 involving $SU(2)_L$ non-singlet higgs. We show how these operators can be comparable to the dimension 9 operators. We then present a simple left-right symmetric model which can give rise to the desired proton decay modes of the right order of magnitude.
We consider the charge-odd correlations (COC) in cross sections of processes of production of charged particles. The cases of a muonic pair and pion systems $π^{+}π^{-},π^{+}π^{-}π^{0}$ are considered in detail for electron-proton or photon-proton collisions in the proton fragmentation region kinematics. COC arise from interference of amplitudes which describe the different mechanisms of charged leptons (pions) creation. One of them corresponds to production of particles in the charge-odd state (one virtual photon or vector meson annihilation to this system of particles) and the other correspo…
The annihilation of proton and antiproton to electron-positron pair, including radiative corrections due to the emission of virtual and real photons is considered. The results are generalized to leading and next-to leading approximations. The relevant distributions are derived and numerical applications are given in the kinematical range accessible to the PANDA experiment at the FAIR facility.
We calculate the O(α_s) corrections to the production of a hard and isolated photon accompanied by one or two jets in deep inelastic lepton nucleon scattering at HERA. Numerical results are presented and the potential of this process for studies of parton distribution functions is discussed.
The electromagnetic form factors of hadrons as measured both in the space like and time like domains provide fundamental information on the nucleon structure and internal dynamics. General expressions, including the lepton mass, for the spin averaged differential cross section for the annihilation reaction lepton antilepton to proton antiproton are given, as well as general formulae for the single and double spin asymmetries. The time reversed reaction would involve a kinematic factor. We also present general expressions for the helicity amplitudes for this reaction.
SU(5) $\otimes$ SU(5) provides a minimal grand unification scheme for fermions and gauge forces if there are vector-like quarks and leptons in nature. We explore the gauge coupling unification in a non-supersymmetric model of this type, and study its implications for proton decay. The properties of vector-like quarks and intermediate scales that emerge from coupling unification play a central role in suppressing proton decay. We find that in this model, the familiar decay mode $p \to e^+ π^0$ may have a partial lifetime within the reach of currently planned experiments.
Charge-odd correlation of the charged pair components produced at electron-proton scattering can measure three current correlation averaged by proton state. In general these type correlation can be described by 14 structure functions. We restrict here by consideration of inclusive distributions of a pair components, which is the light-cone projection of the relevant hadronic tensor. Besides we consider the point-like approximation for proton and pion. Numerical estimations show that charge-odd effects can be measured in exclusive ep -> 2 pi X experiments.
Electron proton (ep) colliders could provide particle collisions at TeV energies with large data rates while maintaining the clean and pile~up-free environment of lepton colliders, which makes them very attractive for heavy neutrino searches. Heavy (mainly sterile) neutrinos with masses around the electroweak scale are proposed in low scale seesaw models for neutrino mass generation. In this paper, we analyse two of the most promising signatures of heavy neutrinos at ep colliders, the lepton-flavour violating (LFV) lepton-trijet signature and the displaced vertex signature. In the considered b…
We use the TMD quark densities of the proton to investigate unpolarized Drell-Yan lepton pair production in proton-proton collisions at the LHC energies. We investigate the case where the gluon-to-quark splitting occurs at the last evolution step and calculate the TMD sea quark density as a convolution of the CCFM-evolved gluon distribution and the TMD gluon-to-quark splitting function which contains all single logarithmic small-x corrections to the sea quark evolution for any order of perturbation theory. Based on the O(alpha) production amplitude of quark-antiquark annihilation calculated ac…
We present a Monte Carlo generator for exclusive vector meson production in charged lepton-proton interactions, l+p --> l+p+V, based on a QCD leading logarithm model calculation according to which the cross section for this process is proportional to the square of the gluon momentum density in the proton. The generator can be used for both fixed target and collider kinematics. Each event is assigned a weight equal to its cross section, so that the independent variables can be generated according to convenient distributions, not necessarily identical to the physics ones.
The hadroproduction of lepton pairs with mass $Q$ and finite transverse momentum $Q_T$ is dominated by quark-gluon scattering in the region $Q_T > Q/2$. This feature provides a new independent method for constraining the gluon density with data at hadron collider energies. Predictions are provided at the energy of the LHC.
We discuss recent suggestions on the resolution of the proton radius puzzle put forward in [1,2] and discovery of a nonperturbative quantum-electrodynamic contribution of order $(α/π)^5$ to lepton anomalous magnetic moments announced in [3,4]. We demonstrate that the ideas of [1, 2] do not resolve the proton radius puzzle. We explain why the nonperturbative correction calculated in [3,4] does not exist.
The charge asymmetry due to higher-order QED corrections in elastic lepton-proton scattering is estimated without employing the ultrarelativistic approximation. Our calculation is performed by generalizing the soft-photon approximation approach suggested by Tsai. Corresponding loop integrals that take a form of Passarino-Veltman scalar three-point functions are calculated analytically without neglecting the mass of the lepton. Our results provide model-independent charge asymmetry predictions for scattering of unpolarized and massive leptons on proton targets. These predictions can be used in …
Massive lepton-pair production, the Drell-Yan process, should be a good source of independent constraints on the gluon density, free from the experimental and theoretical complications of photon isolation that beset studies of prompt photon production. We provide predictions for the spin-averaged and spin-dependent differential cross sections as a function of transverse momentum $Q_T$.
We estimate the beam-normal single-spin asymmetry in elastic lepton-proton scattering without employing the ultrarelativistic approximation. Our calculation is relevant for analyses of muon scattering at energies of few hundred MeV and below -- when effects of the muon mass become essential. At such energies, the transverse polarization of the muon beam is expected to contribute significantly to the systematic uncertainty of precision measurements of elastic muon-proton scattering. We evaluate such systematics using an example of the MUSE experiment at PSI. The muon asymmetry is estimated at a…
The photoproduction of Drell-Yan lepton pairs at HERA is studied. We show that in the backward rapidity region the cross section is strongly sensitive to the small-$x$ behaviour of the quark distributions in the proton, and that with sufficient luminosity it should be possible to distinguish singular $xq \sim x^{-1/2}$ behaviour from standard Regge $xq \sim x^0$ behaviour. The effect on the event rate of experimental acceptance cuts is studied with the help of a Monte Carlo event generator.
We calculate the next-to-leading order QCD corrections to the `direct' part of the spin-dependent cross section for single-inclusive charged-hadron photoproduction. This process could be studied experimentally in future polarized fixed-target lepton-nucleon experiments, but also at the HERA ep collider after an upgrade to both beams being polarized. We present a brief numerical evaluation of our results by studying the K-factors and the scale dependence of the NLO cross section.
It is commonly assumed that a charged particle does not accelerate linearly along a spatially uniform magnetic field. We show that this is no longer the case if the interaction of the particle with the quantum vacuum is chiral, in which case parity and time-reversal symmetries are simultaneously broken. In particular, this is the situation of an electroweak interacting particle in the presence of a uniform magnetic field. We demonstrate first that, in a spatially uniform and adiabatically time-varying magnetic field, a proton coupled to the leptonic vacuum acquires a kinetic momentum antiparal…
The lepton pair production via the quark-antiquark annihilation subprocess in collisions of beam antiproton with the proton target at E_beam = 14 GeV (which corresponds to the center-of-mass energy of the p pbar system E_cm = 5.3 GeV) is studied on the basis of the event sample simulated by PYTHIA6 generator and PandaRoot package. Different kinematical variables which may be useful for design of the muon system and the electromagnetic calorimeter of the detector of PANDA experiment at FAIR, as well as for the study of proton structure functions in the available x-Q2 kinematical region, are con…
Observation of charge asymmetry by comparing electron and positron, or muon and anti-muon, scattering on a hadronic target presently serves as an experimental tool to study two-photon exchange effects. In addition to two-photon exchange, real photon emission also contributes to the charge asymmetry. We present a theoretical formalism, explicit expressions, and a numerical analysis of hard photon emission for the charge asymmetry in lepton- and antilepton-proton scattering. Different kinematic conditions are considered, namely, either fixed transferred momentum squared or a fixed lepton scatter…
In view of the significantly different proton charge radius extracted from muonic hydrogen Lamb shift measurements as compared to electronic hydrogen spectroscopy or electron scattering experiments, we study in this work the photoproduction of a lepton pair on a proton target in the limit of very small momentum transfer as a way to provide a test of the lepton universality when extracting the proton charge form factor. By detecting the recoiling proton in the $γp \to l^- l^+ p$ reaction, we show that a measurement of a ratio of $e^-e^+ + μ^-μ^+$ over $e^-e^+$ cross sections with a relative pre…
We present the full next-to-next-to-leading order (NNLO) coefficient functions for the polarized cross section $dΔσ/dQ$ for the Drell-Yan process $p + p\to l^+l^- + 'X'$. Here $'X'$ denotes any inclusive hadronic state and $Q$ represents the invariant mass of the lepton pair. All QCD partonic subprocesses have been included provided the lepton pair is created by a virtual photon, which is a valid approximation for $Q<50$ GeV. Unlike the differential distribution w.r.t. transverse momentum the dominant subprocess for the integrated cross section is given by $q+\bar q \to γ^* + 'X'$ and its high…
An extension of the left--right symmetric model has been constructed which gives in a natural way the three lepton decay modes of the proton which have been suggested as an explanation for the atmospheric neutrino anomaly. We write down the potential which after minimization gives the proper choice of the Higgs spectrum. With this Higgs spectrum we then study the evolution of the gauge coupling constants and point out that for consistency one has to include effects of gravity.
A potential explanation [U.~D.~Jentschura, Phys.\ Rev.\ A {\bf 88}, 062514 (2013)] of the proton radius puzzle originating from the non-perturbative lepton-pair content of the proton is studied. Well-defined quantities that depend on this lepton-pair content are evaluated. Each is found to be of the order of $10({α\over π})^2$, so that we find such a lepton-pair content exists in the proton. However, we argue that this relatively large result and general features of loop diagrams rule out the possibility of lepton-pair content as an explanation of the proton radius puzzle. In addition, the con…
We study angular distributions of Drell-Yan leptons in the proton-proton collisions invoking the hypothesis of quark Reggeization in t-channel exchanges at high energy.
I summarize the theoretical and experimental status of multijet production in DIS. I present the state of the art theoretical predictions and compare those to the corresponding experimental results obtained by analysing the data collected by the H1 and ZEUS collaborations at HERA. I also show new predictions for three-jet event-shape distributions at the NLO accuracy.
We discuss QED radiative corrections at first and second order for the parity violating asymmetry $A_\text{PV}$ in elastic electron proton scattering. A measurement of $A_\text{PV}$ is planned at low energies and with high precision by the forthcoming P2 experiment at the new MESA facility in Mainz. Bremsstrahlung leads to a shift of the momentum transfer $Q^2$ which affects the determination of the weak charge of the proton.
We use heavy baryon chiral perturbation theory to evaluate the two-photon exchange corrections to the low-energy elastic lepton-proton scattering at next-to-leading order accuracy, i.e., ${\mathcal O}(α, M^{-1})$, including a non-zero lepton mass. We consider the elastic proton intermediate state in the two-photon exchange together in the soft photon approximation. The infrared singular contributions are projected out using dimensional regularization. The resulting infrared singularity-free two-photon exchange contribution is in good numerical agreement with existing predictions based on stand…
We present the full next-to-leading order (NLO) corrected inclusive cross section $d^3Δσ/dQ^2/dy/dp_T$ for massive lepton pair production in longitudinally polarized proton-proton collisions $p + p\to l^+l^- + 'X'$. Here $'X'$ denotes any inclusive hadronic state and Q represents the invariant mass of the lepton pair which has transverse momentum p_T and rapidity y. All QCD partonic subprocesses have been included provided the lepton pair is created by a virtual photon, which is a valid approximation for $Q<50{\rm GeV}$. Like in unpolarized proton-proton scattering the dominant subprocess is g…
It is shown that in realistic SUSY GUT models of quark and lepton masses both the proton decay rate and branching ratios differ in general from those predicted in the minimal $SU(5)$ supersymmetric model. The observation of proton decay, and in particular the branching ratio $B[(p \rightarrow π^+ \overlineν)/(p \rightarrow K^+ \overlineν)]$, would thus allow decisive tests of these fermion mass schemes. It is shown that the charged lepton decay modes $p \rightarrow K^0 μ^+, p \rightarrow K^0 e^+$ arising through gluino dressing diagrams are significant and comparable to the neutrino modes in l…
