arXiv subjects

Gouranga C. Nayak

Publications and source records attributed to Gouranga C. Nayak.

At least 19 recordsLinked to original sources

arXiv2017

Is Renormalization in QCD Necessary at High Energy Colliders ?

In this paper by using the path integral formulation of the background field method of QCD in the presence of SU(3) pure gauge background field we simultaneously prove the renormalization of ultra violet (UV) divergences and the factorization of infrared (IR) and collinear divergences in QCD at all orders in coupling constant. We prove that although perturbative QCD is renormalizable but due to confinement in QCD it is not necessary to renormalize QCD to study hadrons production at high energy colliders. This is consistent with the fact that the partons are not directly experimentally observed but the hadrons are directly experimentally observed.

hep-ph↗

arXiv2016

Proof of NRQCD Factorization at All Order in Coupling Constant in Heavy Quarkonium Production

Recently the proof of factorization in heavy quarkonium production in NRQCD color octet mechanism is given at next-to-next-to-leading order (NNLO) in coupling constant by using diagrammatic method of QCD. In this paper we prove factorization in heavy quarkonium production in NRQCD color octet mechanism at all order in coupling constant by using path integral method of QCD. Our proof is valid to all powers in the heavy quark relative velocity. We find that the gauge invariance and the factorization at all order in coupling constant require gauge-completed non-perturbative NRQCD matrix elements that were introduced previously to prove factorization at NNLO.

hep-ph↗

arXiv2016

Jet Quenching and Gluon to Hadron Fragmentation Function in Non-Equilibrium QCD at RHIC and LHC

Theoretical understanding of the observed jet quenching measurements at RHIC and LHC is challenging in QCD because it requires understanding of parton to hadron fragmentation function in non-equilibrium QCD. In this paper, by using closed-time path integral formalism, we derive the gauge invariant definition of the gluon to hadron fragmentation function in non-equilibrium QCD which is consistent with factorization theorem in non-equilibrium QCD from first principles.

hep-ph↗

arXiv2016

$χ_{cJ}$ Polarization in Polarized Proton-Proton Collisions at RHIC

We study inclusive $χ_{cJ}$ production with definite polarizations in polarized proton-proton collisions at $\sqrt{s}$ = 200 GeV and 500 GeV at RHIC by using non-relativistic QCD (NRQCD) color-octet mechanism. We present results of rapidity distribution of $χ_{c0}$, $χ_{c1}$ and $χ_{c2}$ production with specific polarizations in polarized p-p collisions at RHIC within the PHENIX detector acceptance range. We also present the corresponding results for the spin asymmetries.

hep-ph↗

arXiv2016

Light-Like Wilson Line in QCD Without Path Ordering

Unlike the Wilson line in QED the Wilson line in QCD contains path ordering. In this paper we get rid of the path ordering in the light-like Wilson line in QCD by simplifying all the infinite number of non-commuting terms in the SU(3) pure gauge. We prove that the light-like Wilson line in QCD naturally emerges when path integral formulation of QCD is used to prove factorization of soft and collinear divergences at all order in coupling constant in QCD processes at high energy colliders.

hep-ph↗

arXiv2015

Proof of Factorization of $J/Ψ$ Production in Non-Equilibrium QCD at RHIC and LHC

$J/ψ$ suppression/production is one of the main signature of quark-gluon plasma detection at RHIC and LHC. In order to study $j/ψ$ suppression/production in high energy heavy-ion collisions at RHIC and LHC, one needs to prove the factorization theorem of $j/ψ$ production in non-equilibrium QCD medium, otherwise one will predict infinite cross section of $j/ψ$. In this paper we prove factorization theorem of $j/ψ$ production in non-equilibrium QCD at RHIC and LHC at all order in coupling constant.

hep-ph↗

arXiv2015

String Theory at LHC Using Supersymmetry Production From String Balls

If extra dimensions are found in the second run of LHC in the $pp$ collisions at $\sqrt{s}$ = 14 TeV then the string scale can be $\sim$ TeV, and we should produce string balls at LHC. In this paper we study supersymmetry (squark and gluino) production from string balls at LHC in $pp$ collisions at $\sqrt{s}$ = 14 TeV and compare that with the parton fusion results using pQCD. We find significant squark and gluino production from string balls at LHC which is comparable to parton fusion pQCD results. Hence, in the absence of black hole production at LHC, an enhancement in supersymmetry production can be a signature of TeV scale string physics at LHC.

hep-ph↗

arXiv2015

String Theory at LHC Using Jet Production From String Regge Excitations vs String Balls

If we find extra dimensions in the second run of the LHC in the $pp$ collisions at $\sqrt{s}$ = 14 TeV, then the string mass scale $M_s$ can be $\sim$ TeV and we should produce QCD jets in $2 \rightarrow 2$ partonic collisions via string Regge excitations at the LHC. QCD jets can also be produced from string balls via thermal radiation at Hagedorn temperature. In this paper we study jet production from string Regge excitations vs string balls in $pp$ collisions at $\sqrt{s}$ = 14 TeV at LHC and make a comparison with the standard model QCD jets. We find that high $p_T$ jet production from string Regge excitations can be larger than that from string balls and from standard model QCD jets. We also find resonances in the jet production cross section in string Regge excitation scenario which is absent in the other two scenarios. Hence TeV scale high $p_T$ jets can be a good signature to study string Regge excitations in the $pp$ collisions at $\sqrt{s}$ = 14 TeV at the LHC.

hep-ph↗

arXiv2015

Correct Definition of the Gluon Fragmentation Function at High Energy Colliders

Since the definition of the gluon to hadrons fragmentation amplitude $ $ involves gluon field $Q^{μa}(x)$ corresponding to single gluon incoming state $|g>$, the present definition of the gluon fragmentation function at high energy colliders [which involves non-abelian field tensor $F^{μνa}(x)=\partial^μQ^{νa}(x) -\partial^νQ^{μa}(x)+gf^{abc}Q^{μb}(x)Q^{νc}(x)$ instead of $Q^{μa}(x)$ in the initial state] is not consistent with the single gluon incoming state $|g>$. In this paper we derive the correct definition of the gluon fragmentation function at high energy colliders from first principles which is obtained from the single gluon incoming state $|g>$ and is gauge invariant and is consistent with the factorization theorem in QCD.

hep-ph↗

arXiv2015

Violation of Factorization Theorem in QCD and QED For Non-Light-Like Wilson Line

By using path integral formulation of QCD and QED we prove that the factorization theorem is valid for light-like Wilson line but is not valid for non-light-like Wilson line. This conclusion is shown to be consistent with Ward identity and Grammer-Yennie approximation. Hence we find that the factorization theorem is violated in all the previous studies which used the non-light-like Wilson line in the definition of the (transverse momentum dependent) parton distribution function and fragmentation function at high energy colliders.

hep-ph↗

arXiv2015

Correct Definition of the Gluon Distribution Function at High Energy Colliders

Unlike QED, since F_{μν}^a(x)F^{μνa}(0) in QCD contains cubic and quartic powers of the gluon field the present definition of the gluon distribution function at high energy colliders is not consistent with the number operator interpretation of the gluon. In this paper we derive the correct definition of the gluon distribution function at high energy colliders from first principles which is consistent with the number operator interpretation of the gluon and is gauge invariant and is consistent with the factorization theorem in QCD.

hep-ph↗

arXiv2013

General Form of Color Charge of the Quark

In Maxwell theory the constant electric charge e of the electron is consistent with the continuity equation $\partial_μj^μ(x)=0$ where $j^μ(x)$ is the current density of the electron where the repeated indices $μ=0,1,2,3$ are summed. However, in Yang-Mills theory the Yang-Mills color current density $j^{μa}(x)$ of the quark satisfies the equation $D_μ[A]j^{μa}(x)=0$ which is not a continuity equation ($\partial_μj^{μa}(x)\neq 0$) which implies that the color charge of the quark is not constant where a=1,2,...,8 are the color indices. Since the charge of a point particle is obtained from the zero ($μ=0$) component of a corresponding current density by integrating over the entire (physically) allowed volume, the color charge $q^a(t)$ of the quark in Yang-Mills theory is time dependent. In this paper we derive the general form of eight time dependent fundamental color charges $q^a(t)$ of the quark in Yang-Mills theory in SU(3) where a=1,2,...,8.

hep-ph↗

arXiv2013

General Form of the Color Potential Produced by Color Charges of the Quark

Constant electric charge $e$ satisfies the continuity equation $\partial_μj^μ(x)= 0$ where $j^μ(x)$ is the current density of the electron. However, the Yang-Mills color current density $j^{μa}(x)$ of the quark satisfies the equation $D_μ[A] j^{μa}(x)= 0$ which is not a continuity equation ($\partial_μj^{μa}(x)\neq 0$) which implies that a color charge $q^a(t)$ of the quark is not constant but it is time dependent where $a=1,2,...8$ are color indices. In this paper we derive general form of color potential produced by color charges of the quark. We find that the general form of the color potential produced by the color charges of the quark at rest is given by $Φ^a(x) =A_0^a(t,{\bf x}) =\frac{q^b(t-\frac{r}{c})}{r}\[\frac{{\rm exp}[g\int dr \frac{Q(t-\frac{r}{c})}{r}] -1}{g \int dr \frac{Q(t-\frac{r}{c})}{r}}\]_{ab}$ where $dr$ integration is an indefinite integration, ~~ $Q_{ab}(τ_0)=f^{abd}q^d(τ_0)$, ~~$r=|{\vec x}-{\vec X}(τ_0)|$, ~~$τ_0=t-\frac{r}{c}$ is the retarded time, ~~$c$ is the speed of light, ~~${\vec X}(τ_0)$ is the position of the quark at the retarded time and the repeated color indices $b,d$(=1,2,...8) are summed. For constant color charge $q^a$ we reproduce the Coulomb-like potential $Φ^a(x)=\frac{q^a}{r}$ which is consistent with the Maxwell theory where constant electric charge $e$ produces the Coulomb potential $Φ(x)=\frac{e}{r}$.

hep-ph↗

arXiv2012

Altarelli-Parisi Equation in Non-Equilibrium QCD

The $Q^2$ evolution of fragmentation function in non-equilibrium QCD by using DGLAP evolution equation may be necessary to study hadron formation from quark-gluon plasma at RHIC and LHC. In this paper we study splitting functions in non-equilibrium QCD by using Schwinger-Keldysh closed-time path integral formalism. For quarks and gluons with arbitrary non-equilibrium distribution functions $f_q({\vec p})$ and $f_g({\vec p})$, we derive expressions for quark and gluon splitting functions in non-equilibrium QCD at leading order in $α_s$. We make a comparison of these splitting functions with that obtained by Altarelli and Parisi in vacuum.

hep-ph↗

arXiv2011

Schwinger Mechanism for Quark-Antiquark Production in the Presence of Arbitrary Time Dependent Chromo-Electric Field

We study the Schwinger mechanism in QCD in the presence of an arbitrary time-dependent chromo-electric background field $E^a(t)$ with arbitrary color index $a$=1,2,...8 in SU(3). We obtain an exact result for the non-perturbative quark (antiquark) production from an arbitrary $E^a(t)$ by directly evaluating the path integral. We find that the exact result is independent of all the time derivatives $\frac{d^nE^a(t)}{dt^n}$ where $n=1,2,...\infty$. This result has the same functional dependence on two Casimir invariants $[E^a(t)E^a(t)]$ and $[d_{abc}E^a(t)E^b(t)E^c(t)]^2$ as the constant chromo-electric field $E^a$ result with the replacement: $E^a \rightarrow E^a(t)$. This result relies crucially on the validity of the shift conjecture, which has not yet been established.

hep-ph↗

arXiv2009

Shift Theorem Involving the Exponential of a Sum of Non-Commuting Operators in Path Integrals

We consider expressions of the form of an exponential of the sum of two non-commuting operators of a single variable inside a path integration. We show that it is possible to shift one of the non-commuting operators from the exponential to other functions which are pre-factors and post-factors when the domain of integration of the argument of that function is from -\infty to +\infty. This shift theorem is useful to perform certain integrals and path integrals involving the exponential of sum of two non-commuting operators.

hep-th↗

arXiv2009

Higgs Production and Decay from TeV Scale Black Holes at the LHC

We perform detailed study of the Higgs production and decay, when Higgs is emitted from the black holes produced in proton-proton collisions at the Large Hadron Collider. We show that black hole production can significantly enhance the signal for the Higgs search at the LHC. We evaluate rapidity distribution of diphotons and transverse momentum distribution of bottom quarks, photons, tau leptons, top quarks and W bosons from Higgs decay, when Higgs is emitted from the black hole and also in case when these particles are produced directly from the black hole evaporation. We compare our results with the standard model backgrounds. We find that Higgs production from black holes is dominant over standard model production for $p_T^H > 100$ GeV, when $M_P=1$TeV. Diphotons from Higgs, when Higgs is produced from evaporation of black holes, are dominant over the standard model prediction, for diphoton rapidity $|y_{γγ}| \leq 1$, while bottom quarks are dominant over QCD background for large bottom quark transverse momentum, $p_T^b > 300$ GeV, when $M_P=1$ TeV. We show that measurements of the photon and bottom quark transverse momentum distribution can provide valuable information about the value of the fundamental Planck scale. We also propose a new signal for black hole production at the LHC, an onset of increasing transverse momentum distribution of bottom quarks with large transverse momentum.

hep-ph↗

arXiv2009

Path Integration in QCD with Arbitrary Space-Dependent Static Color Potential

We perform path integral for a quark (antiquark) in the presence of an arbitrary space-dependent static color potential A^a_0(x)(=-\int dx E^a(x)) with arbitrary color index a=1,2,...8 in SU(3) and obtain an exact non-perturbative expression for the generating functional. We show that such a path integration is possible even if one can not solve the Dirac equation in the presence of arbitrary space-dependent potential. It may be possible to further explore this path integral technique to study non-perturbative bound state formation.

hep-th↗